FIBER CONCRETE : in construction. 9783658344801, 3658344806

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Bernhard Wietek

Fiber Concrete In Construction

Fiber Concrete

Bernhard Wietek

Fiber Concrete In Construction

Bernhard Wietek Sistrans, Austria

Editorial: Frieder Kumm

The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content. ISBN 978-3-658-34480-1 ISBN 978-3-658-34481-8 (eBook) https://doi.org/10.1007/978-3-658-34481-8 © Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2021 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Fachmedien Wiesbaden GmbH part of Springer Nature. The registered company address is: Abraham-Lincoln-Str. 46, 65189 Wiesbaden, Germany

Preface In construction area, a wide variety of materials are used. Each of these building materials has its own properties, which have different advantages and disadvantages. It is up to the engineers to choose the right materials for the application to achieve optimal solution of its structure. This requirement is not easy, as there are countless boundary conditions for such a decision to be take into account. This book should draw attention to a building material, which was pushed in the background in the last decades without its actual benefits properly appreciated. Fiber reinforced concrete as an extension of the concrete offers for the construction practice considerable advantages. The basis of the material properties reaches for a very long service life and thus are just for permanent constructions of great interest. Fiber reinforced concrete acts with its material properties over the entire cross-section and provides external attacks and protection against internal destruction. It is a building material that its full static effect is given in the uncracked state similar to most other building materials such as timber, steel, glass, and others. If cracks occur, so this building material is overloaded and thus overtaxed, but it shall occur no sudden break. In this case there is still further reduced carrying capacity in the material. Each client has the claim to non-destroyed building materials as a supporting element in its structure. Help should be given to the client with this book for applying fiber-reinforced concrete as a building material according to its properties in a building. So the client gets a building with fair costs and for long lifespan. I want to thank all the builders and construction companies for their good cooperation. We had a variety of problems on building sites via all the years and we almost solved most of these problems in a good understanding.

Sistrans near Innsbruck, January 2021

Bernhard Wietek

V

Acknowledgements I do not want to forget to thank those who gave so much confidence in me and asked me to work on this field in order to develop an engineering solution. In recent years I have interested many civil engineers with the books Stahlfaserbeton [9] and Faserbeton [60]to deal with this matter, but from the beginning on again and again the desire to not only steel fibers in concrete but also all common available fibers should be edited. Executing companies like Swietelsky and HTB and Felbermayr (FST) and Keller required on their various sites the use of fiber reinforced concrete not only with steel fiber, but also they have shown great interest for fiber reinforced concrete in all types and its use in number of cases. The company Rindler GmbH always supported my knowledge of all fibers used in practice and over again demonstrated new applications. Especially Alexander Rindler explained me the description of the different types of fibers and their properties, for which I am very grateful to him. It is shown here that a comprehensive description of the material and from different points of view is necessary, so that a possible independent preparation of products is achieved. Now we try to publish this book in english, because there is no comparable literature in english. The publishing company Springer/Vieweg opened up the possibility of automatic translation of the book Faserbeton [60] in its latest edition. So I have got a real help by the lectorers Ralf Harms and Frieder Kumm as well as Snehal Surwade who managed the translation and printing of the book. Now that the book, at least for a first printing is finished, I would like to thank all the mentioned People to thank for the support and trust. Translated now into english, I hope to interest also engineers in other countries outside the german area. It should be a help to use this old and new material from the view of construction engineering. A particular concern is me also to thank my dear wife Jutta, who always shows a lot of understanding for the activities of my free time and also suggest respects that I do not overwork me.

Bernhard WIETEK

VI

Contents 1 Introduction 1.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.1 Preface from Vitruv – De Architectura 27 B.C. . . . . . . . . . . 1.1.2 How long is concrete been used? . . . . . . . . . . . . . . . . . . 1.1.3 How long has fiber-reinforced concrete been used? . . . . . . . . 1.2 Basic Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.1 Classification of the building material . . . . . . . . . . . . . . . 1.2.2 Fire behavior of the building material . . . . . . . . . . . . . . . 1.2.3 dimensioning of the building material . . . . . . . . . . . . . . . 1.2.4 Requirements for standardization and for the construction industry 1.3 Standards and guidlines . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.1 Standarts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.2 Regulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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1 2 2 4 6 7 7 9 10 11 12 12 12

2 Definitions 15 2.1 Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.2 Characters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.3 Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3 Concrete 3.1 Concrete types . . . . . . . . 3.2 Concrete classes . . . . . . . . 3.3 Extended characteristic values 3.4 Cement . . . . . . . . . . . . 3.5 Aggregates (surcharge) . . . . 3.6 Water . . . . . . . . . . . . . 3.7 Additional concrete . . . . . . 3.7.1 Additives . . . . . . . 3.7.2 Concrete admixtures . 3.8 Concrete properties . . . . . . 3.8.1 Types of Concrete . .

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21 21 22 25 28 30 33 33 33 34 35 35 VII

VIII

3.9

Contents 3.8.2 Actions on the concrete . 3.8.3 Consistency . . . . . . . 3.8.4 Abbreviations . . . . . . 3.8.5 Shrinkage . . . . . . . . 3.8.6 Cement stone . . . . . . Environmental compatibility . .

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4 Fibers 4.1 General information . . . . . . . . . . . . . . . 4.2 Plastic fibers . . . . . . . . . . . . . . . . . . . 4.2.1 Mikrofibers . . . . . . . . . . . . . . . 4.2.2 Makrofibers . . . . . . . . . . . . . . . 4.3 Steel fibers . . . . . . . . . . . . . . . . . . . 4.3.1 Hook shape . . . . . . . . . . . . . . . 4.3.2 Waveform . . . . . . . . . . . . . . . . 4.3.3 Compressed form . . . . . . . . . . . . 4.4 Glass fibers . . . . . . . . . . . . . . . . . . . 4.4.1 Alkali-resistant fibers . . . . . . . . . . 4.4.1.1 Integral glass fibers . . . . . 4.4.1.2 Water dispersible glass fibers 4.4.2 Non-alkali-resistant fibers . . . . . . . 4.5 Natural fibers . . . . . . . . . . . . . . . . . . 4.5.1 Plant fibers . . . . . . . . . . . . . . . 4.5.2 Animal fibers . . . . . . . . . . . . . .

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36 38 38 39 40 45

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47 47 48 48 49 50 52 53 53 54 54 55 56 57 57 57 57

5 FC processing 5.1 Types of concrete to be used . . . . . . . . . . . . . 5.2 Additives for pumped concrete . . . . . . . . . . . . 5.3 Common dosages . . . . . . . . . . . . . . . . . . . 5.4 Addition of fibers . . . . . . . . . . . . . . . . . . . 5.5 Hedgehog formation . . . . . . . . . . . . . . . . . 5.6 Installation of fiber-reinforced concrete . . . . . . . 5.6.1 In building construction and civil engineering 5.6.2 For fiber-reinforced shotcrete . . . . . . . . . 5.7 Different fiber materials . . . . . . . . . . . . . . . . 5.7.1 Plastic fiber concrete . . . . . . . . . . . . . 5.7.1.1 Constructive applications . . . . . 5.7.1.2 Statically effective applications . .

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59 59 59 60 60 62 64 64 68 71 72 72 72

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Contents

IX

5.7.2

5.7.3

5.7.4

5.7.1.3 Thermally effective applications . . . . . . . . . . . . 5.7.1.4 Effects of interest from a building biology point of view Steel fiber concrete . . . . . . . . . . . . . . . . . . . . . . . . . 5.7.2.1 Constructive applications . . . . . . . . . . . . . . . . 5.7.2.2 Statically effective applications . . . . . . . . . . . . . Glass fiber concrete . . . . . . . . . . . . . . . . . . . . . . . . . 5.7.3.1 Constructive applications . . . . . . . . . . . . . . . . 5.7.3.2 Statically effective applications . . . . . . . . . . . . . Carbon fiber concrete . . . . . . . . . . . . . . . . . . . . . . . . 5.7.4.1 Constructive applications . . . . . . . . . . . . . . . . 5.7.4.2 Statically effective applications . . . . . . . . . . . . .

6 Properties 6.1 Concrete properties . . . . . . . . . . . . . . . . . . . 6.2 Fiber properties . . . . . . . . . . . . . . . . . . . . . 6.2.1 Plastic fibers . . . . . . . . . . . . . . . . . . 6.2.1.1 Microfibers . . . . . . . . . . . . . 6.2.1.2 Macrofibers . . . . . . . . . . . . . 6.2.2 Steel fibers . . . . . . . . . . . . . . . . . . . 6.2.3 Glass fibers . . . . . . . . . . . . . . . . . . . 6.3 Setting process . . . . . . . . . . . . . . . . . . . . . 6.4 Fibers to prevent shrinkage cracks . . . . . . . . . . . 6.4.1 Mix calculation for concrete . . . . . . . . . . 6.4.2 Determination of the grain surface . . . . . . . 6.4.3 Determination of the fiber surface . . . . . . . 6.4.4 Avoidance of shrinkage cracks . . . . . . . . . 6.5 Composite effect of fibers . . . . . . . . . . . . . . . . 6.5.1 Material characteristics of the fibers . . . . . . 6.5.2 Geometry of the fibers . . . . . . . . . . . . . 6.5.3 Geometry factor . . . . . . . . . . . . . . . . 6.5.4 Dosage . . . . . . . . . . . . . . . . . . . . . 6.5.5 Spatial distribution of the fibers in the concrete 6.5.6 Shape angle for power transmission . . . . . . 6.5.7 Friction factors of the fibers . . . . . . . . . . 6.5.8 Determining the fiber tension . . . . . . . . . . 6.5.8.1 From the concrete strain . . . . . . . 6.5.8.2 From the fiber characteristics . . . .

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73 73 74 74 75 75 75 75 76 76 76

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X

Contents 6.6

Material testing experiments . . . . . . . . . . . . 6.6.1 Experimental arrangement . . . . . . . . . 6.6.1.1 Simple bending beam . . . . . . 6.6.1.2 Simple bending beam with notch 6.6.1.3 Standard bending beam . . . . . 6.6.2 Experimental procedure . . . . . . . . . . 6.6.3 Evaluation of the measured data . . . . . .

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7 FC dimensioning 7.1 Dimensioning procedure . . . . . . . . . . . . . . . . . . . . . 7.1.1 Service load method . . . . . . . . . . . . . . . . . . . 7.1.2 Load method . . . . . . . . . . . . . . . . . . . . . . . 7.1.3 Design with partial safety factors . . . . . . . . . . . . 7.2 Reliability concepts . . . . . . . . . . . . . . . . . . . . . . . . 7.2.1 Deterministic reliability principle . . . . . . . . . . . . 7.2.2 Probabilistic reliability principle . . . . . . . . . . . . . 7.2.3 Semiprobabilistic reliability principle . . . . . . . . . . 7.2.4 Verification of structural safety . . . . . . . . . . . . . . 7.2.5 Verification of suitability for use . . . . . . . . . . . . . 7.3 Dimensioning theorie . . . . . . . . . . . . . . . . . . . . . . . 7.3.1 Dimensioning for material selection - dosage . . . . . . 7.3.1.1 Bending . . . . . . . . . . . . . . . . . . . . 7.3.1.2 Bending with longitudinal force . . . . . . . . 7.3.1.3 Compression struts . . . . . . . . . . . . . . 7.3.1.4 shear check . . . . . . . . . . . . . . . . . . 7.3.1.5 Breakout of a support . . . . . . . . . . . . . 7.3.2 Dimensioning for cross-section selection - Dimensioning 7.3.2.1 Bending . . . . . . . . . . . . . . . . . . . . 7.3.2.2 Bending with longitudinal force . . . . . . . . 7.3.2.3 Compression struts . . . . . . . . . . . . . . 7.3.2.4 shear check . . . . . . . . . . . . . . . . . . 7.3.2.5 Breakout of a support . . . . . . . . . . . . . 7.4 Dimensioning samples . . . . . . . . . . . . . . . . . . . . . . 7.4.1 Cross-section in bending . . . . . . . . . . . . . . . . . 7.4.1.1 Plastic fiber . . . . . . . . . . . . . . . . . . 7.4.1.2 Steel fiber . . . . . . . . . . . . . . . . . . . 7.4.1.3 Glass fiber . . . . . . . . . . . . . . . . . . .

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112 112 112 113 116 118 119

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121 121 122 123 124 125 125 126 126 126 128 129 129 129 135 140 142 145 147 148 149 152 154 157 158 159 159 166 174

Contents

XI 7.4.2

7.4.3

7.4.4

7.4.5

Cross-section in bending with normal force . . . . . . . . . . . . . . . . 177 7.4.2.1

Plastic fiber . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

7.4.2.2

Steel fiber . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182

Cross-section in compression (buckling) . . . . . . . . . . . . . . . . . . 185 7.4.3.1

Plastic fiber . . . . . . . . . . . . . . . . . . . . . . . . . . . 185

7.4.3.2

Steel fiber . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187

Cross section on shear force . . . . . . . . . . . . . . . . . . . . . . . . 189 7.4.4.1

Plastic fiber . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

7.4.4.2

Steel fiber . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191

Application with shotcrete . . . . . . . . . . . . . . . . . . . . . . . . . 193 7.4.5.1

Plastic fiber . . . . . . . . . . . . . . . . . . . . . . . . . . . 193

7.4.5.2

Steel fiber . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201

7.4.6

Application with inverted T-beam . . . . . . . . . . . . . . . . . . . . . 205

7.4.7

Design for a bridge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206

7.4.8

Design for a harbor wall without anchor . . . . . . . . . . . . . . . . . . 210

7.4.9

Comparison of design with different fibers . . . . . . . . . . . . . . . . 216 7.4.9.1

Comparison with different fibers . . . . . . . . . . . . . . . . 216

7.4.9.2

Comparison with shrink fiber and different fibers . . . . . . . . 217

8 Applications 8.1

8.2

8.3

8.4

8.5

221

Base plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 8.1.1

Residential buildings . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221

8.1.2

Industrial floors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222

Walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 8.2.1

Basement walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223

8.2.2

Wall scopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224

Ceilings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 8.3.1

Residential buildings . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226

8.3.2

Industrial buildings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227

Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 8.4.1

Undercoats and overcoats . . . . . . . . . . . . . . . . . . . . . . . . . 228

8.4.2

Single beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228

8.4.3

Roadways . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229

Galleries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 8.5.1

Footpaths and cycle paths . . . . . . . . . . . . . . . . . . . . . . . . . 229

8.5.2

Roads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230

XII

Contents 8.6

Tunnel lining . . . . . . . . . . . . . 8.6.1 support measures . . . . . . . 8.6.2 Inner lining . . . . . . . . . . 8.7 Tubbings . . . . . . . . . . . . . . . 8.7.1 Tunnel construction . . . . . . 8.7.2 Shaft sinking . . . . . . . . . 8.8 Prefabricated parts . . . . . . . . . . 8.8.1 Pipes . . . . . . . . . . . . . 8.8.2 Slabs and ceilings . . . . . . . 8.8.3 Stairs . . . . . . . . . . . . . 8.8.4 Retaining walls . . . . . . . . 8.9 Construction pit and slope stabilisation 8.9.1 Construction pits . . . . . . . 8.9.2 Slope protection . . . . . . . 8.9.3 Wall protection . . . . . . . . 8.10 Videos of construction sites . . . . . .

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231 232 233 234 234 235 235 236 236 237 238 239 239 242 243 245

Appendix

247

List of Tables

249

List of Figures

251

Bibliography

259

Index

263

1 Introduction

If one deals with a building material and uses it in practice in a building, it is interesting and also necessary to know how the building material was created, how it behaves in the environment and also how it is evaluated by experts. Also the general recognition of a building material in the given time is always worth a discussion.

In principle, it is worth recalling at this point a preliminary remark from the book Vorlesungen ueber Massivbau (Lectures on solid construction) (1979) by F. Leonhardt on the Deutsches Institut fuer Normung (DIN; German Institute for Standardization) regulations:

DIN regulations and standards are not laws, but guidelines that must be observed as a rule. In special cases - particularly in the case of large bridges and new types of construction or construction methods - deviations from DIN regulations can be made with the approval of the authority responsible for building law if the conditions of stability and serviceability are demonstrably met. In special cases, it is even necessary to deviate from the standard if new findings are available, which have not yet been taken into account in the DIN. It should be noted that the incorporation of new findings into DIN sheets in the Federal Republic of Germany often takes several years. On the other hand, no one escapes responsibility for their own actions by applying DIN standards. Any liability of DIN and those involved in the preparation of DIN standards is excluded.

Starting from a historical view of a different kind than the usual one, some basic ideas are also listed here, which appear to the author as an important information, so that one can better understand the procedure and the kind of explanations. The aim is to create as neutral a mechanical view as possible for the building material fiber-reinforced concrete, which, without economic constraints, results in as good a description as possible.

The following passages will address these generally useful pieces of knowledge.

© Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2021 B. Wietek, Fiber Concrete, https://doi.org/10.1007/978-3-658-34481-8_1

1

1 Introduction

2

1.1 History Mostly in this area the reader is spoiled with years and inventors the first desire to read on, here this chapter is to be dealt with in a different way, which possibly also makes some think. The building material concrete and thus also fiber concrete is very old, but we will not go into the history of the building material in detail here, but rather refer back to an over 2,000 years old foreword to a specialist book on the art of building, which has lost nothing of its topicality, but is even more valid in the present day:

1.1.1 Preface from Vitruv – De Architectura 27 B.C. VITRUV1 (Marcus Vitruvius Pollio)

Roman architectural theorist of the first century B.C., author of the ten-volume work of Marcus Vitruvius Pollio, based on his own experience as a builder (temple at Fanum - Fano) and on intensive study of Greek sources [43] . Famous sportsmen who had won victories at Olympia, at the Pythia, Istmia, and Nemeen, the ancestors of the Greeks bestowed such high, honorable distinctions upon them that they not only reaped glory standing in the festive assembly with palm of victory and wreath of victory, but also, when they returned victorious to their city, were driven in a triumphal procession on a four-horse carriage to their native city and to their father’s house, and enjoyed a life-long honorarium voted by the citizenry. Considering this, then, I must wonder why the same honorable distinctions, and even greater ones, have not been bestowed upon writers, who have rendered infinite good service to all the world for all eternity. For it would have been more worthy of this institution, since athletes steel their own bodies by training, but writers enrich not only their own minds, but the general spiritual life, since they provide teachings through their books, so that through them one may acquire knowledge and create the spirit. For what use are Milon of Creton, because he remained invincible, or the rest, who were victors in the same field, to the people? Only during their lifetime did they enjoy esteem among their own fellow citizens. The teachings of Pythagoras, but also of Democritus, Plato, Aristotles, and the rest of the philosophers, which relate to daily life and are cultivated with untiring diligence, bring forth fresh and sweet-smelling fruit 1 Vitruv.

Darmstadt

Ten Books on Architectura. translated and annotated by Dr. Curt Fensterbusch. Primus Publishing House,

1.1 History

3

not only to their fellow citizens but also to all mankind. Those who, from their earliest youth, fill themselves with an abundance of learned knowledge from these writings, have the best, wisest thoughts, and become in their communities the creators of human-moral conduct, of equality of rights, of laws, without which no state can safely exist. Since, therefore, such significant gifts are bestowed upon men by the wise writers, both in private and in public life, I think that not only should palms and wreaths be bestowed upon them, but even triumphs should be decreed for them, and they should be found worthy of a place among the gods. How times do not change! Let us take any super athlete today, such as Michael Schumacher (car racer) or Hermann Maier (skier) or Tiger Woods (golfer) and compare them with Peter Mitterhofer or Josef Madersperger - what, you do not know these gentlemen? Peter Mitterhofer (1822 - 1893): carpenter - inventor of the typewriter; died impoverished what would we do today without a typewriter as the predecessor of today’s computers? Josef Madersperger (1786 - 1850): master tailor - inventor of the sewing machine; died impoverished - what would our clothes be without a sewing machine?

Fig. 1.1: typewriter from Mitterhofer 1864 (Techn. Museum Vienna)

Fig. 1.2: sewing hand from Madersperger 1830 (Techn. Museum Vienna)

This digression is intended to give us something to think about and to put things in perspective in our fast-moving times. In public, the essential is not always recognized. We are called upon

1 Introduction

4 to contribute a little for a balance. But now back to our topic:

Construction has been a discipline in human activity since the first building, where omniscient bunglers have always been at work, producing damage and thus creating their own monuments. However, those who accumulated knowledge and put it to good use joined together to form communities and passed on the knowledge within them. This expertise was largely kept secret, it was only with the Enlightenment and the introduction of technical universities that technical knowledge became public. It is only from this point that we can access knowledge in public libraries. Before that, only a few and also uncertain literatures are known.

1.1.2 How long is concrete been used? Concrete is understood to be natural pieces of rock held together by means of a binder (nowadays cement). With this definition, one must give credit to Mother Nature that the first concrete was made by nature without human influence. Conglomerate and breccia are naturally occurring sedimentary rocks that were formed from older rock fragments and a binder. It only took observation of nature to produce a building material similar to these rock formations. A new building material was thus obtained from two components , which slowly hardened with water in a mould and thus became a rock-like structure such as conglomerate or breccia. The advantage was the freedom of shaping, which is still used very much today. In antiquity, there were more or less successful attempts to produce concrete buildings, which, however, did not show any lasting progress and thus almost fell into oblivion. Thus, in countries such as India, Mesopotamia, as well as China, some structures with concrete-like building materials had been tried without much imitation. The successes were not exhilarating, so these systems were not adopted by subsequent cultures such as Egyptians and Greeks. It was not until the Romans [42] again that they tried concrete, already using a cement-like substance as a binder. The Romans used burnt, ground limestone and later also volcanic ash in a mixture as cementum. In addition, depending on the application, natural fibers (sisal) were

5

1.1 History

added to improve the properties in bending and tensile stress. This made it possible to build the Pantheon (dome with Diameter = 43m; 1,700 years largest dome in the world), which would no longer be possible with today’s concrete and the normal static knowledge. With the production of cement , concrete acquired a reproducible strength, which was refined more and more in the following years and decades. In particular, the clearly defined grain mixtures and the types of cement with their grinding fineness allow today a precise production of concrete with very predictable properties.

Fig. 1.3: The dome of the Panthenon in Rome 128 AD Around 1861, flower pots were to be made of concrete, but they always broke when filled. So Mr. Josef Monier remembered that the Greeks and Romans held their wine vessels together with ropes and likewise the wooden barrels with iron rings. He did this with an iron mesh that he poured into the concrete, and it worked. Thus the Monierbeton was found as the first reinforced concrete. Soon it was also used in construction, especially for ceilings and bridges. The calculation was also put on a theoretical basis and so the dimensioning for reinforced concrete was found. In the course of this, the addition of fibers was no longer required, as the steel absorbed the tensile forces in their entirety. The addition of fibers was even completely dispensed with in the production of concrete and later also prohibited. This naturally increased the sales of steel in

1 Introduction

6 reinforced concrete.

Fig. 1.4: modern skyscrapers in New York 2019 One of the main problems with concrete has always been that water escapes during the setting process or is also used in the chemical process and thus a reduction in volume takes place. This leads to so-called shrinkage cracks in the setting process, which can run through the entire building material. This is the reason why concrete can hardly be subjected to tensile stress, as it already has many cracks in it.

1.1.3 How long has fiber-reinforced concrete been used? People have always wanted to avoid shrinkage cracks during the setting process, so fibers were mixed into the fresh concrete to prevent cracking during the setting process. Fibers to improve the properties of concrete and mortar have therefore been used from the earliest times.

1.2 Basic Aspects

7

Most often it was plant fibers or animal hair, but they have the disadvantage that they can decompose or rot and therefore are not sufficiently durable. The use of fibers has always prevailed in the craft, so remember the various plasters, which, mixed with animal hair, had a better loadbearing capacity. This form of plaster was used successfully until the middle of the twentieth century. In years 1950–1960, there were first experiments with short steel wires, which were later gradually shaped and thus came onto the market as steel fibers from 1970 onwards. As there was no comparable design method as for reinforced concrete, steel fiber concrete was only approved for subordinate applications. An application for flexural beams or slabs and ceilings was explicitly rejected in the various guidelines. With the design for fiber-reinforced concrete now available, nothing more stands in the way of using this building material for load-bearing components such as columns, slabs and ceilings. This opens up a wide range of possible applications that can still be used in practice.

1.2 Basic Aspects The reader will ask why yet another book that does not conform to the general literature, but goes its own way in looking at the subject matter. The answer to this is that, in the author’s opinion, an erroneous development has currently set in in the area of the approach to fiber-reinforced concrete, which is not sustainable in the long term, since the traceability of the individual steps is not given and thus the door is opened to wild manipulation by various interests. The aim of this book is to show ways to prevent such possibilities and to ensure that the building material fiber-reinforced concrete receives the technically comprehensible treatment to which it is entitled.

1.2.1 Classification of the building material The Austrian guideline for fiber-reinforced concrete requires fiber-reinforced concrete classes with indication of the respective tensile strength. This may give the impression that little atten-

1 Introduction

8

tion is paid to the composition (concrete strength class and fiber dosage) to achieve this strength. In practice, this can lead to uncertainties for the user. Example 1: (tensile strength) The structural engineer usually requires a fiber concrete of a certain class (bending tensile strength) and specifies a certain strength class. In many cases, neither the fiber type nor the fiber dosage is specified. It is therefore left to the producing companies to provide the required proof of the fiber concrete class. In practice, this looks as follows: Test report of a laboratory: Sample 1: FRSpC 25/30/III/J2/XC4/EV700/BZ4,5/F59/GK8 with 3,0 [kg/m3 ] macro fibers Sample 2: FRSpC 25/30/III/J2/XC4/EV700/BZ6/F59/GK8 with 4,5 [kg/m3 ] macro fibers Both specimens meet the requirements of the Fiber Concrete Guideline. The same concrete is specified for both specimens , only the dosage of the fiber results in the difference in the flexural strength. This theoretically results in the following static values: Sample 1: Minimum bending tensile strength 3.20 [N/mm2]. Sample 2: Minimum bending tensile strength 4.25 [N/mm2]. The difference is 1.05 [N/mm2] with the addition of 1.5 [kg/m3] macrofibers. This appears very high as a pure result from the increase in fiber dosage and thus other frame components to achieve a higher concrete quality need to be examined more closely. In any case, reliable results can be obtained by comparing the results with a tested unreinforced initial concrete of the same composition (preferably of the same application batch). How is that possible? The finished (concreted and fibered) samples are taken to the laboratory for testing. The concrete and fiber specifications are given to the laboratory by the fiber concrete manufacturer. As the initial concrete is not tested, more cement is added to sample 2 to increase the tensile strength. Thus, both samples meet their requirements according to the guideline for fiber-reinforced concrete. This gives the impression that the fiber can achieve a great increase in tensile strength, but in practice this is not the case. The structural engineer and also the builder are thus not properly informed, since the test materials do not have the same composition with respect to the concrete.

1.2 Basic Aspects

9

Consequence: The main focus should not be on the flexural strength of the fiber-reinforced concrete, but at the same time the same initial concrete without fibers should be tested for each sample. In this way, the influence of the respective fiber can be clearly identified and misleading interpretations can be prevented. The mere verification of the flexural strength of the fiber-reinforced concrete appears to be insufficient here, as this can only be done by taking samples on the construction site during installation and testing them after 7 or 28 days, that is, only after installation. For this reason, every planner or engineer is already required to ensure that the component to be calculated meets the requirements of the respective standard at least in terms of cement addition and mixing ratios of the required concrete strength class during the design phase. This was certainly the reason why such precise regulations for the verification of material quality were drawn up in concrete and reinforced concrete construction. In the case of fiber-reinforced concrete, the concrete and the fibers must also be subject to separate and then combined quality control so that the technical requirements for fiber-reinforced concrete are actually met.

1.2.2 Fire behavior of the building material Fiber-reinforced concrete with plastic fibers is increasingly being used for building components that have to be fire resistant. Especially in traffic tunnels, where relevant fire accidents have already occurred, a fire-resistant building material is required. Example 2: (Fire resistance) In tunnel construction, great importance is attached to the fire behaviour of plastic fibers. In the course of the tendering process, well-defined requirements are placed on the fibers, which must be verifiably fulfilled. It is necessary that the test certificates submitted by the respective suppliers are comparable in the essential points to be documented. These points are: • Number of fire tests passed in direct succession. • Indication of the size of the test series • Experimental equipment and applied laboratory standards.

1 Introduction

10

• Precise record of the test specimen condition, the type of firing, the heat development, the exposure time. • Indication of the type and dosage of fibers used and the type of concrete used. • Test report with indication of laboratory and tester. Especially in this sensitive area - and bearing in mind the consequences of the terrible tunnel fires of the past - it seems important to achieve transparency of properties and test methodology with guaranteed reproducibility.

1.2.3 dimensioning of the building material Especially in the design of building materials, it is important that the correct technical approach is taken. Therefore, a widespread uncertainty is pointed out here and how to deal with it correctly from a materials science point of view Example 3: (bending calculations) When calculating the bending moments that can be absorbed, quite a few technicians simply add the bending tensile strength of the concrete and the fiber content and thus obtain the total bending tensile strength. This is physically incorrect and cannot be carried out in this way. Calculate tensile stress from combination of concrete proportion and fiber pullout: The strain can be calculated from the maximum tensile stress of the concrete in the bending case via the E-modulus of the concrete. The load-bearing capacity of the fiber is determined by the pull-out, which creates a joint in the concrete, so that for the fiber pull-out, the concrete is the decisive factor in determining the force. It is therefore the skin friction of the fiber that enables stress transfer. It is now necessary to combine the concrete tensile strength with the directional skin friction of the fibers in order to obtain a common tensile strength of the fiber-reinforced concrete. Larger expansions cause a bending tension in the concrete, which it can no longer absorb, and you no longer have an uncracked building material, as the concrete with the integrated fibers cracks. As a result, the building material fiber-reinforced concrete is no longer fully load-bearing and loses its flexural capacity. In the cracked state, only the fiber portion is responsible for dissipating the tensile forces in tension and thus it is no longer a homogeneous building material that can absorb load to an

1.2 Basic Aspects

11

elastic and thus recurring extent. The absorption of tensile stresses by the fiber portion alone considerably reduces the flexural load-bearing capacity of the fiber-reinforced concrete. Only in the non-cracked state can the fiber-reinforced concrete make full use of its properties and must therefore be calculated like a homogeneous building material with a specified permissible compressive and tensile stress in accordance with the laws of statics. The permissible compressive and tensile stress must be determined from the concrete properties and the fiber properties with consideration of the dosage. A different determination of these permissible stresses is technically not reasonable, since the stresses that can be absorbed in the building material must already be known before construction and it is not only clear 1 month after the construction of the building whether the component is load-bearing or not.

1.2.4 Requirements for standardization and for the construction industry From a technical point of view, it is absolutely necessary that, in contrast to the Fiber Concrete Guideline, the building material fiber concrete is regarded as a composite building material consisting of a mixture of two basic building materials, concrete and fibers, which are joined together according to a precisely comprehensible mixing ratio. For this purpose, each basic building material itself should provide the necessary evidence and the composition should be made possible in a technically comprehensible analytical manner by calculating the mixing ratios. Thus, both the concrete in its properties, in particular the resulting shrinkage cracks and the resulting bending tensile strength, and the added fibers with the corresponding properties are to be taken into account. This requirement is taken for granted in other composite structures such as reinforced concrete or even in composite bridge construction, so why not in fiber-reinforced concrete. In the present book, the required path is consistently followed, and this leads to the measurements shown, which have also been positively confirmed in practice by numerous examples.

12

1 Introduction

1.3 Standards and guidlines

1.3.1 Standarts Germany: DIN EN 206-1 DIN 1045-2 DIN 1045-3 DIN EN 197-1 DIN EN 12350 DIN EN 12350 DIN EN DIN EN 14651 DIN EN 14721 DIN EN 14845 DIN EN 14889

Beton; Festlegung, Eigenschaften, Herstellung und Konformitaet Beton; Festlegung, Eigenschaften, Herstellung und Konformitaet Tragwerke aus Beton; Bauausfuehrung Zement; Zusammensetzung, Anforderungen und Konformitaetskriterien Pruefverfahren fuer Frischbeton Pruefverfahren fuer Festbeton Nachweis der Betondruckfestigkeit im Bauwerken Pruefverfahren fuer Beton mit metallischen Fasern Pruefverfahren fuer Beton mit metallischen Fasern Pruefverfahren fuer Fasern in Beton Fasern fuer Beton (2 Teile)

Austria: OENORM B 4701 OENORM B 4708

Betontragwerke; EUROCODE-nahe Berechnung, Bemessung und konstruktive Durchbildung Faserbeton; Bemessung und konstruktive Durchbildung

1.3.2 Regulations Germany: DAfStb DBV VDS

(Deutscher Ausschuss fuer Stahlbeton) Richtlinie Stahlfaserbeton, Berlin 2005 Deutscher Betonverein e.V. Merkblatt Stahlfaserbeton, 2001 Verband deutscher Stahlfaserhersteller - diverse Bauregeln

Austria: OEVBB

oesterr. Vereinigung fuer Beton und Bautechnik - Richtlinie Faserbeton, Wien 2008

1.3 Standards and guidlines

13

International: BS EN 14889-1:2006 formity BS EN 14845-1:2007 ASTM A820-06

¯ for Concrete. Steel Fibres. Definitions, specifications and conFibres

¯ Test methods for fibres in concrete

¯ Specification for Fiber-Reinforced Concrete Standard

¯ Test Method for Flexural Toughness and First-Crack, Strength ASTM C1018-97 Standard of Fiber-Reinforced Concrete (Using Beam With Third-Point Loading) ¯ and Design for Steel Fibre Reinforced Concrete, MateRILEM (RILEM TC 162 TDF) Test rials and Structures (2003) Vol. 36 ¯ RILEM (RILEM TC 162 TDF) Design of Steel Fibre Reinforced Concrete - Method, Recommondations, , Materials and Structures (2001)

2 Definitions 2.1 Terms The terms listed here are described in order to obtain a unique Definition, which is used in this book.

РConcrete cured mixture consisting of aggregate, cement and water with additives. РFresh concrete ready-mixed, still fluid concrete before its processing and curing. РHardened concrete concrete that has been placed and cured to its specified strength. РStandard concrete concrete according to composition according to the standard. РConcrete by properties concrete whose properties and requirements are specified by the manufacturer. РConcrete by composition concrete whose composition is specified by the manufacturer. РFiber concrete concrete to which fibers are added in a definied quality and quantity. РCement hydraulic binder which hardens with the addition of water and thus forms a hardened cement paste. РAggregate natural or artificial mineral substances which, with a derfinished grain size distribution, are the basis for concrete. РFibers short, thin additives in concrete, which consist of different materials and forms. РDosage weight proportion of fibers in 1 m3 concrete (e.g., 40 kg/m3 ). РCompressive strength maximum compressive stress before breakage. РTensile strength maximum tensile stress before breakage. РInitial testing testing of the fresh concrete to monitor all requirements. РAdditive small amount of chemical agent added during mixing.

© Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2021 B. Wietek, Fiber Concrete, https://doi.org/10.1007/978-3-658-34481-8_2

15

16

2 Definitions

2.2 Characters The following Definitions are far as possible based on international customs, but additional letters and characters are used here to make the calculations clear.

Forces and moments and fiber directions with capital letters Compressiv force [N]. D... F1 ...F4 . . . Direction of the fibers in half-space. Single-fiber tensile force [N]. Fz . . . Load during the bending test [N] . F ... g... Load from own weight [kN/m2 ]. M ... Momentum [Nmm]. Nk . . . Vertical buckling load [N]. Nzul . . . Allowed buckling load [N]. N∗ . . . Vertical load capacity [N]. Load from payload [kN/m2 ]. p... Absorbed shear force in a cross section [N]. Qk . . . q... Load from the sum of all loads [kN/m2 ]. Rated value of the resistance (building materials) [N]. Rd . . . Characteristic value of resistance [N]. Rk . . . S... Service load[N]. Rated value of the load (loads) [N]. Sd . . . Sk . . . Characteristic value of load [N]. ∗ S ... Payload [N]. Z ... Tractive force [N]. Zc . . . Tensile force from concrete [N]. Zf ... Tensile force from fiber [N]. Modulus of elasticity of concrete [N/mm2 ]. Ec . . . Es . . . Modulus of elasticity of steel [N/mm2 ]. Modulus of elasticity of fiber material [N/mm2 ]. Ef ... Tensions with greek lowercase letters σd . . . compressive stress [N/mm2 ]. σz . . . Tensile stress [N/mm2 ]. Fiber tensile stress in concrete [N/mm2 ]. σf ... Normal stress in the break joint [N/mm2 ]. σ ...

2.2 Characters σn . . . σm . . . σmd . . . σmz . . . τ ... τo . . . τc . . .

Stress from normal force [N/mm2 ]. Stress from moment [N/mm2 ]. Compressive stress at medium center [N/mm2 ]. Tensile stress at medium eccentricity [N/mm2 ]. Shear stress in the fracture joint [N/mm2 ]. Shear stress at normal stress = 0 [N/mm2 ]. Cohesion [N/mm2 ].

Lengths with lowercase a... Height of the remaining sphere section [mm]. d ... Diameter of the individual fiber [mm]. h... Height of the cross section [mm] . h... Height of the spherical cap [mm]. i... Radius of interia of a cross section [mm]. Length of the individual fiber [mm]. l ... lk . . . Buckling length [m]. r... Crack depth in the cross section [mm]. R... Radius of the hemisphere [mm]. Height of the pressure section [mm]. x... Height of the tension section [mm]. y... Distance between tensile and compressive force [mm]. z... zd . . . Distance for the compression force [mm]. Distance for the tractive force [mm]. zz . . . Areas in uppercase or lowercase Cross-sectional area of a fiber [mm2 ]. AF . . . Cap surface in half-space [mm2 ]. a... b... A verage ring surface in half-space [mm2 ]. c... Lower ring area in half-space [mm2 ]. Fb . . . Area in the fracture plane of the test specimen [cm2 ]. Fe . . . Contact area of the test body [mm2 ]. Weight of a fiber [g]. GF . . . I ... Moment of inertia of cross section [mm4 ]. Surface of the spherical cap with angular α [mm2 ]. Oα . . . Surface of the hemisphere [mm2 ]. OH . . . Surface of the spherical cap [mm2 ]. Ok . . . VF . . . Volume of a fiber [mm3 ].

17

18

Material stresses indexed lowercase Design value of the concrete compressive strength [N/mm2 ]. fcd . . . fc f k . . . Characteristic compressive strength of the fiber concrete [N/mm2 ]. fc f tk . . . Characteristic tensile strength of the fiber concrete [N/mm2 ]. fck . . . Characteristic concrete compressive strength [N/mm2 ]. fck,cube . . . Cube compressive strength [N/mm2 ]. fcm . . . Characteristic cylinder compressive strength of concrete [N/mm2 ]. Characteristic concrete tensile strength [N/mm2 ]. fctk . . . fctm . . . Average concrete tensile strength [N/mm2 ]. fctm, f l . . . Bendimg tensile strength of concrete [N/mm2 ]. ff ... Fiber tensile stress in the bending test [N/mm2 ]. ffk ... Specific fiber tensial stress [N/mm2 ]. f pk . . . Characteristic prestressing steel yield strenght [N/mm2 ]. fyd . . . Design value of steel yield strength [N/mm2 ]. characteristic steel yield strength (tensile strength) [N/mm2 ]. fyk . . . Angle with lowercase greek letters Breakage angle of the concrete. α ... α ... Solid angle of the active fibers. Solid angle of the active fibers only in state 1. α1 . . . Solid angle of the active fibers only in state 2. α2 . . . δ ... Breakage angle of the concrete. Shearing angle according to Coulomb. ϕ ... Factors indexed lowercase Df ... Dosage of fibers in the concrete [kg/m3 ]. df ... Factor of the fiber density [fibers/mm3 ]. ε ... Elongation. Concrete expansion. εb . . . steel expansion. εs . . . Slenderness in compression rods. λ ... Factor of the total influence of the fibers. mf ... m f ,o . . . Factor of the influence of the fiber surface. m f , f . . . Factor of the influence of the fiber form Buckling values for concrete ω ...

2 Definitions

19

2.3 Units Conditions or collateral with lowercase greek letters γc . . . Partial safety factor for concrete. γy . . . Partial safety factor for steel. γf ... Partial safety factor for fiber. Safety for loads when verifying the load-bearing safety. γS . . . Safety for building materials in the verification of structural safety. γR . . . ηf ... Degree of utilization of the fiber tension. η ... Safety with the working load method. Overall safety in the playload method. ν ... νL . . . Safety for loads during playload procedure. νR . . . Safety for building materials in the load-bearing method.

2.3 Units The common units for the processing and calculation of fiber concrete are given here. lengths

mm

cm

m

areas

mm2

cm2

m2

forces

N

kN

MN

stresses

N/mm2

kN/cm2

MN/m2

In addition, a conversion table is provided to facilitate the changeover between different units of stresses. stresses 1

N/mm2

N/cm2

kN/cm2

MN/m2

bar

MPa

1

100

0,1

1

10

1

1 N/cm2 =

0,01

1

0,001

0,01

0,1

0,01

1 kN/cm2 =

10

1.000

1

10

100

10

MN/m2

1

100

0,1

1

10

1

1 bar =

0,1

10

0,01

0,1

1

0,1

1 MPa =

1

100

0,1

1

10

1

1

=

N/mm2

=

3 Concrete The concrete used in construction today consists of cement, aggregate (sand and gravel) and water and often additives. Immediately during production, concrete has a plastic to liquid property after the mixing process as fresh concrete, which slowly changes into a solid substance, the concrete, after the curing time. After the curing time, the concrete is referred to as hardened concrete.

3.1 Concrete types According to the composition, the degree of hardening, special properties, etc., concrete is divided into different types: • Bulk density – Lightweight concrete up to 2,0 [to/m3 ]. – Normal concrete 2,0 to2,6 [to/m3 ]. – Heavy concrete over 2,6 [to/m3 ]. • Curing condition: fresh concrete; young concrete; hardened concrete. • Consistency: stiff concrete; plastic concrete; soft concrete; flowable concrete; self-compacting concrete. • Properties: high strength concrete; water impermeable concrete; frost resistance; frost deicing salt resistance; chemical attack; wear resistance; radiation protection concrete; exposed concrete; mass concrete; drainage concrete. • Composition: sand concrete; gravel-sand concrete; grit concrete • Place of production: site mixed concrete; transport-mixed concrete; ready-mixed concrete; in-situ concrete; precast concrete; underwater concrete. • Microstructure: closed microstructure; concrete with a porous structure; single-grain concrete; aerated concrete; air-entrained concrete. © Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2021 B. Wietek, Fiber Concrete, https://doi.org/10.1007/978-3-658-34481-8_3

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3 Concrete

22

• Reinforcement: unreinforced concrete; reinforced concrete; prestressed concrete; fiber concrete. • Conveying: tamped concrete; vibrated concrete; pumped concrete; roller concrete; shotcrete; spun concrete; vacuum concrete.

3.2 Concrete classes In the standards, it is common to divide concrete into classes according to its compressive strength (after 28 days). These strength classes also form a basis for the structural design of a cross-section. When testing concrete in the past, a concrete cube was subjected to a compression test. The pressure values obtained were used for classification. It was not until about 10 years ago that a prism was used in the comparison of the compression test and it was found that lower compressive stresses occurred at fracture. The reason for this lies in the general fracture mechanics of solids.

Fig. 3.1: Differences at Prism Cube compression test A prismure line develops when loaded at an angle of: α = 45 + ϕ/2

(3.1)

where ϕ is the shear angle in degrees according to Coulomb’s shear law for solids such as all soils and solids (rock, concrete, steel, etc.) and can be read directly from the σ − τ diagram.

23

3.2 Concrete classes

Fig. 3.2: Fracture criterion according to Coulomb The fracture angle at a load is clearly seen in the plot with Mohr’s stress circle and Coulomb’s shear limit and has the relationship (3.1).

Fig. 3.3: Mohr’s stress circle with Coulomb’s shear line For shear angles ϕ of 10-45°measured in nature, formula (3.1) gives values for a fracture angle α of 50-67.5°. Assuming the highest value of 67.5°, the height of the specimen is: h = a ∗ tanα = 15 ∗ tan(67, 5) = 36, 2cm

(3.2)

24

3 Concrete

Since 36.2 < 40 cm (see Fig. 3.1), the angle of rupture can be set as required for the concrete test prism. Therefore, this book will continue to work only with the values of the concrete test with prism. In contrast, the fracture surface of the cube cannot be freely adjusted, but the fracture angle is forced to 45°. This results in constraining forces at the two end faces where the force is applied. These constraining forces, together with the forced fracture angle, result in fracture loads on the cube that do not correspond to natural body mechanics. For this reason, the test specimen for the concrete compression test was changed from the cube to the prism. In the following, only the results of the prism sample will be used for calculations, because with them, the usual material laws of mechanics, such as the Moh-Coulomb material behaviour, can be used. Higher material laws such as those of Tresca, Rankine, von Mises, Huber, etc. can also be applied. In the abbreviated designation, the letter C means the English designation concrete, the number is the cylinder compressive strength at a specimen height of 300 mm and a specimen diameter of 150 mm. The second number, the cube compressive strength, which is still sometimes used, is omitted here, as this value does not satisfy the material properties according to the valid material laws. concrete class

fck

fctm

Ec

[kN/cm2 ]

[kN/cm2 ]

[kN/cm2 ]

C8

0,8

0,12

2.530

C 12

1,2

0,16

2.700

C 16

1,6

0,19

2.860

C 20

2,0

0,22

2.990

C 25

2,5

0,26

3.140

C 30

3,0

0,29

3.200

C 35

3,5

0,32

3.400

C 40

4,0

0,35

3.520

C 45

4,5

0,38

3.620

C 50

5,0

0,41

3.720

Table 3.1: concrete strength classes

In bold letters in the table above classes are the usual in practice for fiber concrete strength classes.

25

3.3 Extended characteristic values

The strength classes reach even higher, but for the application with fiber concrete and also with the concretes commonly used in practice, these are only very rarely used, so that they have been omitted here. Likewise, the strength classes for lightweight concrete are not given here, as it is not yet possible to produce fiber-reinforced concrete with them. fck [kN/cm2 ] ... compressive strength the cylinder compressive strength is used fctm [kN/cm2 ] ... tensile strength is calculated Ec [kN/cm2 ] ... modulus of elasticity is calculated 2/3

fctm = 0, 30 ∗ fck

(3.3)

Ec = 2200 ∗ ( fck + 0, 8)0,3

(3.4)

This relationship is valid up to a concrete grade of C50, above which is a different relationship that will not be discussed further here, as these concrete grades are rarely used.

3.3 Extended characteristic values The bending tensile strength fct, f l is given quite differently depending on the tensile strength. fct, f l = 2, 0 ∗ ( fctm

(3.5)

This is the maximum specified bending tensile stress in the literature Valentin [10] . In the reinforced concrete standard EN 1992-1-1, the bending tensile stress is given as a function of the component thickness fct, f l = max((1, 6 − H/1000) ∗ fctm ; fctm )

Thereby is: H the total height of the component in mm fctm Mean value of the centric tensile strength

(3.6)

3 Concrete

26

This is because the curing of the concrete only has an intensive effect on the surface. The stronger a component, the less influence curing has on cracking due to shrinkage.

Fig. 3.4: Flexural strength according to EN 1992-1-1 If we now assume that the different factors for the flexural tensile strength arise as a result of the shrinkage cracks, the concrete can also be regarded as partially cracked. In this case, the maximum value of the flexural tensile stress is reached when the concrete has no shrinkage cracks (3.5). Since this bending tensile strength is twice as high as the tensile strength (3.3), the shrinkage cracks must assume a proportion of 50%. In the reinforced concrete standard, it is therefore assumed that the concrete has a crack content of 20% at the surface, which increases to 50% up to a depth of 60 cm and then remains the same. This is independent of any different curing. It must therefore be stated that a very pessimistic view is taken here, and as a result the flexural strength is on the extremely safe side. This is always from the point of view that the tensile stresses are absorbed by the steel reinforcement anyway. If we now consider this crack proportion (50%) as the maximum crack proportion in concrete, the factor for a calculation of the bending tensile strength can be defined as follows: r = 2 ∗ (1 − p)

(3.7)

27

3.3 Extended characteristic values

r... crack factor p... percentage of cracks in the concrete This crack factor can now be determined for the possible crack components:

Crack fraction p

0%

10 %

20 %

30 %

40%

50 %

Crack faktor r

2,0

1,80

1,60

1,40

1,20

1,00

Table 3.2: Crack factor for different crack proportions

Thus, the formula for the bending tensile strength can now take the following form:

fct, f l = r ∗ fctm

(3.8)

A calculation of the common bending tensile strengths can be taken from the following diagram.

Fig. 3.5: Flexural tensile strengths with possible crack components The question now is: How can these crack components be reduced to a minimum in order to

3 Concrete

28 achieve the highest possible bending tensile strength for a structure?

Until today, the answer has been to add sufficient moisture to the concrete with proper curing so that the shrinkage cracks do not become too large and only occur in the minimum range. This also led to the differentiation of the component thicknesses for which the curing is effective. This is also how the relationship in formula (3.6) came about.

3.4 Cement The strength of concrete is produced by cement. This is a hydraulic binder which, when mixed with water, produces a cement paste. Through hydration, the cement paste slowly solidifies both in the air and under water to form a solid cement stone. This encases the aggregate and also the installed steel parts, so that a composite building material is created. There are five main groups for the cements: CEM

I

Portland cement

CEM

II

Portland (composite) cement

CEM

III

Blastfurnace cement

CEM

IV

Pozzolanic cement

CEM

V

Composite cement

The names of the cement are somewhat long, but unambiguous. The following is an example of a common cement designation, then the individual parts are explained in more detail. Portland-slag cement EN 197–1 – CEM II/A-S 32,5 R Mention of the standard, hyphen Designation of the main group, slash Indication of the quantity of additive (A, B, C), hyphen Indication of additive type (S, V,...) Indication of the minimum compressive strength after 28 days Indication of the early strength (N: normal; R: rapid)

29

3.4 Cement The indication of the quantity of additives is defined as follows::

CEM I

only griding ≤ 5%

CEM II/A

Grinding from 6 to 20 % mass

CEM II/B

Additive grinding from 21 to 35 % mass

CEM III/A

Pulverization from 36 to 65 % mass (only S)

CEM III/B

Pulverization from 66 to 80 % mass (only S)

CEM III/C

Grinding of 81–95 % mass (only S)

CEM IV/A

Additive grinding from 11 to 35 % mass

CEM IV/B

Additive grinding from 36 to 55 % mass

CEM V/A

Additive grinding of 18–30 % mass (P,Q,V) u.(S)

CEM V/B

like A but 31–50 % mass

Furthermore, there are types of additives that are added to the cement, thus changing the properties considerably in some cases. The exact dosage must be clarified in advance with the cement works. The specification of the additive types is defined as follows:

S

Slag (blast furnace slag)

V

Siliceous fly ash

W

High lime fly ash

D

Microsilika

L

Limestone (TOC ≤ 0,5 % mass)

LL

Limestone (TOC ≤ 0,2 % mass)

P

Natural puzzolan

Q

Artificial pozzolan

T

Burnt shale

M

Mixture with specification of the components, for example, M(S–V–L)

For the strength classes of the cements, the following strengths are required after defined periods of time following the manufacture of the test specimens:

3 Concrete

30 strengthclass

compressiv strength [N/mm2] initial strength 2 days

≥ 16

32,5 N 32,5 R

7 days

≥ 10

Start of solidication

Elongation

standard strength

begin

amount

28 days

[min]

[mm] ≤ 10

≥ 32,5

≤ 52,5

≥ 75

≥ 42,5

≤ 62,5

≥ 60

≥ 52,5

-

≥ 45

-

42,5 N

≥ 10

-

42,5 R

≥ 20

-

52,5 N

≥ 20

-

52,5 R

≥ 30

-

Table 3.3: requirements for cements according to EN 197–1

The cement must be protected from all contamination and moisture. It may only be filled and transported in clean transport containers and then stored, which do not contain residues of previous cement deliveries or other substances. Even small quantities of substances that are incompatible with the cement may have a detrimental effect on the concrete. When storing cement on the construction site, special care must also be taken to ensure that moisture such as rain and snow cannot get to the cement. The cement should therefore be covered with tight tarpaulins at all times and these should be additionally secured. Cements of different types and classes should not be mixed. This should only be done, if necessary, under the guidance of cement experts from the manufacturer’s works.

3.5 Aggregates (surcharge) Natural aggregate or crushed concrete may be used as aggregate. In any case, this aggregate may only have mineral components. Organic inclusions are not permitted. As soon as the concrete contains steel reinforcement or steel fibers, no harmful quantities of salts may be contained in the aggregate. This could accelerate the corrosion of the steel and cancel out the general corrosion protection of the concrete. In this book, no further treatment of recycled materials as aggregates is given, as these have not yet been used in fiber-reinforced concrete.

31

3.5 Aggregates (surcharge)

GK [mm]

Application

4

Screed, fine grained components

8

Sprayed Concrete

Fiber-reinforced concrete

11 16 22

Normal concrete Mass concrete

32 Table 3.4: Concrete applications with specification of the maximum aggregate size

Aggregates from naturally occurring rocks are subject to wide variations, especially when considering the grading curve. For this reason, all concrete standards specify a grading curve range that is dependent on the maximum aggregate size of the concrete. When selecting the grading curve, the largest grain size should be chosen rather large if possible, but it is usually the boundary conditions that lead to the choice of the largest grain size. The maximum grain size should be smaller than 0.3 times the smallest cross-section dimension or smaller than 0.5 times the smallest reinforcement spacing. The following table provides help for the selection of the maximum grain size.

32

3 Concrete

Fig. 3.6: Grading curves for concrete depending on the maximum aggregate size GK

With the aid of these specified grain size ranges, most types of concrete can now be produced. In the case of special conditions such as single-grain concrete or drainage concrete, tests are necessary to clarify the strength properties, the results of which are then incorporated into the structural engineering application and design.

33

3.6 Water

3.6 Water Any naturally occurring water is suitable as an addition water, provided that there are no constituents that impair the concrete properties. Thus, any groundwater, rainwater, stream and river water is suitable in principle, but not moor water. Drinking water (tap water) and also residual water from concrete production is always suitable. Contaminants such as high salt content (e.g. drainage along roads) or industrial waste water should be avoided as far as possible. Mineral-enriched water must be tested for its usability by means of a chemical analysis. All water that attacks concrete must be excluded as water for addition.

3.7 Additional concrete A distinction is made between admixtures and admixing agents due to the different modes of action in concrete.

3.7.1 Additives

These are usually added in fine granular structure in larger quantities during the mixing process of the fresh concrete and must therefore also be taken into account in terms of quantity in the respective mixing ratios. Two different types are used as additives: Type I:

Inactive additives such as rock flour, pigments, etc.

Type II: Pozzolanic or latent hydraulic additives such as fly ash, silica, dust, etc. By adding the concrete additives, the concrete property is brought into a desired property through the chemical or physical effect. This concerns consistency, workability, strength, impermeability and colour. Additives must generally be harmless and thus not change the important properties such as hardening, durability and corrosion protection of the reinforcement. In the case of application, a quality control must be submitted.

3 Concrete

34

3.7.2 Concrete admixtures Admixtures are usually chemically or physically effective agents that favourably influence defined concrete properties. These are only added to the concrete in small quantities during mixing. These addition quantities are limited depending on the application and must be precisely recorded by the concrete manufacturer. A combination of the admixtures is possible in principle, but should be clarified with the manufacturer before use.

BV

Concrete cizer

plasti-

Reduce the water demand of fresh concrete by lowering the surface tension of the water; thus, a low W/B value can be maintained.

FM

Superplasticiser

for the production of flowing concrete

LP

Air entraining agent

Create microscopic air voids in the fresh concrete, which improves the frost/de-icing salt resistance Air entraining condenser combination of LP agent and condenser

LPV DM

Sealant

Are intended to improve the water permeability of the concrete, but their mode of action is limited

VZ

Retarders

Postpone the onset of setting of the concrete, application, for example, in hot weather or for long concreting works (mass concrete)

BE

Accelerator (solidification accelerator)

Reduce the onset of solidification to a few seconds, for example, for shotcrete or as a sealant in case of water ingress in tunnel and gallery construction

FS

Antifreeze

FS Antifreeze Are intended to accelerate the strength development of the young concrete; caution: do not use FS containing chloride for reinforced concrete and steel fiber concrete as well as prestressed concrete Table 3.5 Admixtures for concret Table 3.5: Admixtures for concrete

35

3.8 Concrete properties

3.8 Concrete properties In addition to the strength class (see point 3.1.2), other points must be taken into account in the production of concrete. All these properties have their own designations, which should be listed when naming the concrete. In the following, these properties are dealt with relatively briefly so that the reader understands the context. However, for a more in-depth study of concrete, the relevant technical literature is strongly recommended in order to correctly experience the respective valid standard situation.

3.8.1 Types of Concrete The types of concrete generally differ in their application. It is important to deal with the different types of concrete, as this already plays a decisive role in the composition of the concrete. It is precisely the composition, the degree of hardening and the special properties required on the construction site that lead to the individual types of concrete.

Designation

Property

UB1, UB2

Underwater concrete

PB

Pumping concrete

SB

Exposed concrete

SCC

Self-compacting concrete

BL

Low blood concrete

W

Heat generation (W40 –> up to 40°C)

VV

extended processing time

ES, EM, EL, E0

Hardening fast, medium, slow, very slow

RS

Reduced shrinkage

A

Specified tear strength Table 3.6: Types of concrete

The type of concrete must be specified during planning; this is important not only for the concrete manufacturer, but especially for the construction company. This specifies boundary conditions that must be taken into account for the mixing ratio and the formwork, as well as the type of placement and compaction.

3 Concrete

36

3.8.2 Actions on the concrete The influences acting on the component from the environment are summarised in exposure classes. The exposure is designated by an uppercase letter X (exposure classes) and another uppercase letter, which originates from the type of exposure. C ... of carbonation D ... from deicing S ... of seawater F ... of frost A ... of agressiv environment (Aggressive area) M ... from mechanical attack (eng. Mechanical treatment) The class X0 shows that there is no risk of damage. Designation

Risk

Environment

Application examples

No

Unreinforced concrete, no frost, no chem. or mechan. attack, reinforced concrete inside

unreinforced foundation slab, fillingand leveling concrete

XC 1

Carbonation

Dry or constantly wet

Buildings, residential and commercial including wet rooms; foundations in groundwater

XC 2

Carbonation

Wet, rarely dry, no water pressure (h < 2 m)

Indoor rooms with high humidity, livestock stables, structures in groundwater

XC 3

Waterpressure

Waterpressure h = 2-10 m

Hydraulic structures and impervious hydraulic structures

Waterpressure > 10 m

Hydraulic structures and impervious hydraulic structures

moderate humid

Concrete surface attack in chloride attack

XD 2

Wet, rarely dry

Chloride-attack, swimming pools, industrial buildings

XD 3

Alternating wet

Chloride-containing spray water, standing chloride-h. Water, road surfaces, parking decks

X0

XC 4 XD 1

Corrosion by chlorides

37

3.8 Concrete properties Table continued for Exposure classes

Designation

Risk

Environment

Application examples

Frost and de-icing agents

Moderate water saturation, without de-icing agents

Surfaces exposed to rain and frost, without waterlogging

XF 2

Moderate water saturation with de-icing agent

Surfaces exposed to rain, frost and deicing materials, without waterlogging

XF 3

High water saturation, without de-icing agent

Concrete surfaces with waterlogging, frost-resistant hydraulic structures

XF 4

High water saturation with de-icing agent

Road surface, bridges, defence barriers, spray water

Chemically aggressive environment

Driving = XA 1T releasing = XA 1L

XA 2

Chemically moderately aggressive environment

Driving = XA 2T releasing = XA 2L

XA 3

Chemically aggressive environment

Driving = XA 3T releasing = XA 3L

Moderate wear

Road surfaces of residential streets

XM 2

Hevy wear

Road surfaces of main roads, heavy forklift traffic

XM 3

Extreme wear

Tracked vehicle traffic, hydraulic engineering Tos basin

XF 1

XA 1

XM 1

Chemical attack

Wear

Table 3.7: Exposure classes in concrete

The exposure class describes the environmental impact on the component. Normally, several exposure classes occur simultaneously. Based on this information, the concrete admixtures are selected in the concrete plant.

Particular attention must be paid to mutual compatibility. Therefore, these concrete additives (additives and admixtures) should be discussed with the respective manufacturer in order to obtain the guarantee of the respective property.

3 Concrete

38

3.8.3 Consistency The consistency of a concrete is measured either with the compaction in a cylinder or with the spread on a special folding table. This is used to control the workability of the concrete.

designation

description

demand fo

OENORM

DIN

C0

C0

C1

C1

Stiff

1,45–1,26

C2

C2

Stiff plastic

1,26–1,11

F38

F2

Plastic

F45

F3

Soft

42–48 cm

F52

F4

Very soft

49–55 cm

F59

F5

Flowable

56–62 cm

F66

F6

Very flowable

63–69 cm

F73

SVB

Extremely flowable

70–76 cm

Very stiff

Densification measure

Spread

< 1,45

35–41 cm

Table 3.8: Consistencies of concrete

3.8.4 Abbreviations In order to simplify the concrete designations, additional abbreviated designations were introduced, with which many environmental influences are already dealt with and thus the concrete designation is again somewhat simpler. The subdivision of the abbreviated designations is based on purely practical aspects and is intended for both the planner and the user. The selection criteria are as follows: - Concretes for underlays and fillings. - Concretes for purely static purposes. - Concrete with reinforcement and static purposes. - Waterproof concretes with reinforcement and static purposes.

39

3.8 Concrete properties - Environmentally contaminated concretes with reinforcement and static purposes.

A practice-oriented compilation led to the seven concrete classes, which will certainly be supplemented by one or the other short designation in the future. Overall, however, this is a desirable summary of detailed properties for practical use.

Abbreviation

Covered environmental class

W/B-value

air content [%]

B1

XC3(A)

0,60

-

B2

XC3/XD2/XF1/XA1L/SB(A)

0,55

-

B3

XC3/XD2/XF3/XA1L/SB(A)

0,55

2,5

B4

XC4/XD2/XF1/XA1L/SB(A)

0,50

-

B5

XC4/XD2/XF2/XA1L/SB(A)

0,50

2,5

XC4/XD2/XF3/XA2L/XA2T/SB(A)

0,45

2,5

XC4/XD3/XF4/XA1L/SB(A)

0,45

4,0

B6 C3A-free B7

Table 3.9: Abbreviations for concrete

3.8.5 Shrinkage Shrinkage in concrete is the process that occurs when fresh concrete releases water, since not all water is chemically bound. This water release occurs more and faster at the edge than in the middle of a component. Therefore, a curing of the concrete surface is necessary to avoid a too fast water withdrawal.

Fig. 3.7: Early shrinkage in young concrete (from Cement + Concrete 2008)

40

3 Concrete

The shrinkage process starts immediately after the concrete has set. The first part of the shrinkage process, which is still in the setting time of the first hour up to 1e day, is called early shrinkage. As can be seen from Fig. 3.2, an expansion in the order of magnitude of approximately 0.4 occurs here. Subsequently, the concrete shrinks more and more slowly and is also always measured. A typical series of measurements is shown in Fig. 3.8.

Fig. 3.8: Shrinkage in concrete in the first year (from Bauingenieur 3/2008)

It can be seen in the graph that in the first 28 days from day 1 the deformation during shrinkage is approximately 0.2-0.3% and only after 1 year it takes on the magnitude of approximately 0.50.6%.

3.8.6 Cement stone During the setting and hardening of concrete, an additional important effect must be taken into account. A chemical reaction takes place which is called hydration. In this process, minerals are formed starting from the cement particles, which create a bond with the cement and the aggregates and thus give the concrete its strength properties. It is a very complex process, which will not be discussed in detail here, as it is dominated by chemical processes and only the mechanical effects are of interest here. As these minerals als grow, the solid content increases in the form of hardened cement paste. At first, this results in the liquid concrete becoming somewhat tougher, which is then called stiffening. The liquid state thus changes into a plastic state, which hardens more and more

41

3.8 Concrete properties

until it finally becomes a solid. This stiffening and hardening are decisive for the absorption of compressive and tensile forces in the concrete. If one looks at the development of the minerals in detail, it can be seen that after an initial mineral formation, delicate mutual contacts already develop, which are also essential for the subsequent force transmission. If these first contacts are disturbed by shrinkage cracks, only a reduced force transmission in the concrete can result. It is therefore particularly important that the concrete is not moved during the phase of initial crystal formation until the growing crystals are well connected. This is the only way to ensure that the concrete retains its load-bearing capacity.

Fig. 3.9: first crystals

Fig. 3.10: Crystals growth

Fig. 3.11: finished crystals

If one looks at the material composition of the concrete in the first days during curing, one can see on the one hand the shrinkage due to a reduction in the water content and also the somewhat delayed increase in the cement in the form of hardened cement paste.

Fig. 3.12: Schematic material distribution for concrete Over the initial period, there is a decrease in volume resulting from the evaporation of water near the surface and the chemical reaction of the water with the cement.

3 Concrete

42

Fig. 3.13: Volume behavior during shrinkage of concrete However, from the formation of crystals during the chemical reaction of the water with the cement particles, a cement stone is formed, which actually consists of crystals that constantly increase in size with increasing reaction. This leads to an increase in the volume of the solid.

Fig. 3.14: Volume increase due to crystal formation during the setting process

3.8 Concrete properties

43

These two effects are decisive for the strength development of the concrete. In the process, the solid bridges are formed between the individual parts of the aggregate, which enable the transmission of forces, especially for the tensile forces. If one plots these two effects of the volume change over time (logarithmically), one can see the following relationship.

Fig. 3.15: Volume changes during the setting process The loss of water due to evaporation produces the lower curve. This already begins when the concrete is placed in the formwork. Only after about 1–2 h (the period can be controlled by admixtures) the crystallization occurs (in the graph at 1 h). The volume loss up to this point takes place in the liquid state of the fresh concrete, and no cracks can form in the process. Therefore, the volume loss curve can be shifted to 0 at the onset of crystal formation. The volume loss that occurred before this time has no effect on the strength development of the concrete. From the time of the first crystal formation, there is an increase in volume of the solid, which slowly closes the pores. This curve goes upwards in the diagram. If the curve for shrinkage (lower curve) is now mirrored upwards, two areas (surfaces) arise as the difference between the two effects, which are to be examined more closely. In the first (blue) area, the volume decreases due to shrinkage, as this increases more than due to crystal growth. This leads to the shrinkage cracks, since the plastic concrete can still absorb too little tensile stress. Only with increasing mineral growth can the tensile stresses be absorbed,

3 Concrete

44

although in this case the defects caused by existing shrinkage cracks are no longer closed or are closed only inadequately. Although these cracks are very small at first, they become larger and also visible as a result of the further volume changes during the setting phase. Thus, after the first stiffening of the concrete, a tensile stress is present due to the volume reduction, which the first growing minerals in their bond cannot absorb. This is clearly visible in the blue part of the first area. As a further consequence of the setting process due to mineral growth, a cement paste is formed whose volume increases more than the decrease due to shrinkage. This creates a pressure condition in the concrete, which only further opens the cracks created by shrinkage. Therefore, the shrinkage cracks in the concrete increase especially in the first days. With this volumetric consideration, the purpose of the curing of fresh concrete is clearly recognizable. If sufficient water is added to the concrete during curing up to the hardened state, there is only a slight reduction in volume and the minerals can develop almost undisturbed. After the hardening phase, the mineral bond is so strong that the tensile stresses due to drying can be easily absorbed without cracks forming in the concrete. It is therefore crucial that during the initial stiffening and hardening phase of the concrete, the tensile stresses resulting from the volume reduction either do not occur or are absorbed by the building material system. By adding water, an area can be supported on the surface in such a way that hardly any cracks occur. However, the deeper one looks into the component, this effect becomes less, as the water from the surface cannot penetrate so deeply. In the area below the surface, the addition of water is hardly noticeable from 25 to 30 cm. Thus, this effect is only effective close to the surface.

Fig. 3.16: Concrete in the setting phase

3.9 Environmental compatibility

45

This has also led to the fact that the tensile bending stresses that can be absorbed depend on the thickness of the component when considering concrete for reinforced concrete (see Fig. 3.4). If fibers are used, this initial tensile stress can be absorbed by the fibers so that no cracks form in the concrete. This is explained in more detail in Chapter 6 FB properties.

3.9 Environmental compatibility Concrete is a natural, environmentally friendly building material created from naturally occurring materials. It consists of sands and gravels with a defined mixing ratio and a binder made of fired clay. The setting and hardening of the binder is based on the formation of water-containing compounds, which are formed during the reaction between the cement constituents and the mixing water. In general, the cement reacts in a relatively low-water, plastic mixture with water-cement ratios between about 0.3 and 0.6. The setting process is a very complex chemical process in the course of which the pH value of the pore solution assumes comparatively high values. This high pH value in concrete (about 13–14) is primarily due to the Ca(OH)2 formed during the setting process. At the fresh concrete surface, flowing groundwater is affected by this. It is therefore required in many cases to return the groundwater to an approximately neutral pH value.

Fig. 3.17: Neutralization of alkaline water as a result of concrete setting process

3 Concrete

46

This is usually carried out with a neutralizing system, wherein the blown into the basic water CO2 , until an approximately neutral condition. Since concrete is a porous material that diffuses CO2 gas under normal environmental conditions in its interior, where it with existing Ca(OH)2 reacts, forming CaCO3 (and H2 O). This process of carbonation represents no acute threat to the hardened cement, but lowers the pH in the concrete.

Fig. 3.18: Carbonation of concrete The now formed on the surface of carbonated concrete has a pH of about 7 and is therefore completely neutral to the environment. The disadvantage here is that in this area of the protection of steel reinforcement (steel fibers) no longer exists. It can corrode the steel fibers in this area. Other fibers do not have this problem. When set, and thus hardened state of concrete is completely environmentally friendly and is not subject to more changes. Only the stress can be detrimental when exceeding given limits. Therefore, all components must be sized to prevent overloading. After use of the concrete member, it is possible to crush concrete and then reused. By recycling this measure is a diverse set of new inputs possible, and there is thus also with old discarded concrete parts does the environmentally supply.

4 Fibers Only fibers that are used with concrete processing are shown here. Starting with artificial fibers such as synthetic, steel and glass fibers, the natural fibers that are used less frequently today, such as plant and animal fibers, are also shown.

4.1 General information In general, it must be mentioned here that the fiber concrete should only be used in non-cracked condition for a practical building application. As soon as a crack occurs in the fiber concrete, the fiber concrete loses its load-bearing effect for the dissipation of bending moments or shear forces. Furthermore, in the cracked state, the fiber concrete loses its waterproofness, which is very important in practice (basement wall). It thus reduces its strength and density properties from the moment a crack occurs. Therefore, the fiber concrete is only able to take over the forces acting on it in an uncracked state. In the Fiber Concrete Guidelines, cracked concrete cross-sections (similar to reinforced concrete) are mainly assumed. Therefore, the statements of the Guideline for Fiber Concrete are not applicable to non-cracked fiber concrete. The fiber-reinforced concrete shown and treated here in the book is always in the non-cracked state when used, just like most other building materials (wood, steel, glass, concrete, etc.). With all fibers a problem occurs that is very difficult to get a grip on. The fibers are provided with a surface protection (usually a thin coating) by the producer at the factory, which in combination with the fresh concrete can have a great effect on the properties. It has been repeatedly observed that fibers from the same basic material have different properties in combination with fresh concrete. Thus, a fiber coating can affect the following properties: • Water binding on the fiber (different spreading dimensions) • Air void binding on the fiber (different pore content) © Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2021 B. Wietek, Fiber Concrete, https://doi.org/10.1007/978-3-658-34481-8_4

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This has a decisive influence on the compressive strength and also the water permeability of the fiber concrete. These properties cannot be judged by the appearance of the fiber alone, but the water and air void binding to the respective fiber must be proven by means of traceable tests. Only with the results of these tests can the fibers be used and approved for practical application. A corresponding certification is still pending in order to obtain clarity about these properties of the respective surface-coated fibers. The fibers used here in the book have only a very small influence on the fresh concrete, so that this change in properties will not be discussed further, but special care must be taken when using other fibers.

4.2 Plastic fibers These consist mainly of polypropylene (PP). PP is a semi-crystalline thermoplastic and produced industrially on a large scale since 1954. PP is odorless and hypoallergenic, for applications in the food industry and the pharmaceutical industry, it is appropriate, it is physiologically harmless. From a technical perspective, this fiber has the following properties: • density of PP is 0.895 to 0.920 g/cm3 • E-Modulus of PP is between 5.000 N/mm2 and 7.000 N/mm2 • PP has a glass transition temperature of 0 to -10 °C and is therefore brittle in cold weather • the upper service temperature of PP is 100 to 110 °C. • the melting range is from 160 to 165 °C. With this material, two different fiber types are produced:

4.2.1 Mikrofibers Straight fibers with a length of 5–20 mm and a diameter of 0.02–0.20 mm. Their use is mainly in hall floors, on and under concretes, in screeds and walls.

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They are mainly used in fresh concrete to influence the setting properties. On the one hand, the consistency (flow properties of fresh concrete) and/or the shrinkage properties during the setting process can be influenced. The waterproofness of concrete can also be positively influenced. They also improve the properties of the concrete by increasing fire resistance, improving impact and shock resistance and reducing abrasion. The concrete gets a much better frost and thaw behavior and generally shows a better resistance. The dosage is usually 1–2 bags (0.9 kg) per cubic meter of concrete.

Fig. 4.1: Microfibers in different application forms

4.2.2 Makrofibers These are manufactured with a length of 30–65 mm and normally have a diameter of 0.4–1.2 mm. Their use should have a positive influence on the mechanical properties of concrete. In addition, these fibers are offered with straight or corrugated and also specially shaped surfaces. The surface shape is intended to improve the transmission of forces between concrete and fibers and thus enable shorter fibers.

Fig. 4.2: Makrofibers in different application form

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With the improved mechanical properties, fiber concrete with these fibers can also be used for load-bearing components. It replaces the steel reinforced concrete completely in some components. Especially for waterproof constructions and in aggressive environments, this fiber concrete is better than steel reinforced concrete, because the waterproofness acts on the full cross-section and corrosion does not occur because the plastic does not corrode.

4.3 Steel fibers Steel fibers are added to the concrete during the mixing process. They are placed in the formwork with the concrete and compacted. A wide variety of steel fibers are used. There is currently no restriction on the shape and dimensions of the steel fibers, so each steel fiber producer has its own steel fibers, which are difficult to compare with each other.

Fig. 4.3: Steel fibers in frequent application form The composite building material steel fiber concrete looks in cross section after manufacture relatively evenly from this shown in the following image. It can thus be assumed that the spatial distribution of the steel fibers randomly set when the direction of the individual fibers in the concrete is not affected by any means, such as rakes or magnets.

Fig. 4.4: Steel fiber concrete, in cross-section; image ArcelorMittal

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In the case of components made of steel fiber concrete that are exposed to the weather, the formation of rust stains on the surface is to be expected if these have not been impregnated or coated or if stainless steel fibers have not been used. On the other hand, weakening of the steel fibers through corrosion and thus impairment of their beneficial effect is to be feared at most in the carbonated zone, in areas with an impermissibly high chloride content or in the area of wide cracks, if the moisture required for corrosion is also present at the same time. There is no evidence in the literature of serious damage caused by corrosion of the steel fibers. If load is applied, the steel fiber concrete will crack under a certain load. However, this is not the state of failure, but the steel fibers continue to bear the load. Thus, this building material can absorb forces beyond its crack load. The extent of the deformation now depends on the load and also on the density of the steel fibers.

Fig. 4.5: Steel fiber concrete cracked, but a force-transmitting; image ArcelorMittal The tensile strength is specified by the respective producer of the steel fibers. In practice, values of 800‚Äì2,000 N/mm2 are common here. In most fillings, the tensile strength of the steel fibers is specified as 1,000 N/mm2 . The maximum force that can be transmitted by each steel fiber depends on the cross-section of the steel fiber and the force transmission to the concrete. Instead of reinforcing steel, a more or less precisely defined quantity of steel fibers is added to the steel fiber concrete. The dosage of the fibers is usually given in kg/m3 concrete. These steel fibers have the following different properties in contrast to iron reinforcement in steel concrete: • Fiber diameter is very small (usually 1 mm or less). • Fiber length mostly small against component size (3-6 cm). • Fibers are distributed over the entire component.

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4 Fibers • Fibers are not directional, but be anywhere in device. • Not all fibers contribute to force dissipation. • In torn condition, the steel fibers still carry.

It is precisely these differences that make the design of a component difficult. It is therefore necessary to take a closer look at the fibers. The steel fibers are not all the same. It is not only the length and diameter (cross-sectional shape) that are very different, there are also different shapes. This generally distinguishes the steel fibers from reinforcing bars, which are normally straightened. It is worth considering the different forms that currently exist, as this may play a role in the calculation, or one must certainly recognise these differences in order to be able to estimate their effect on the calculations.

4.3.1 Hook shape This form is probably the best known steel fiber form, which is used in all conditions.

Fig. 4.6: steel fiber in hook form The diameter of these steel fibers is between 0.3 and 1.5 mm, the length is 3–6 cm. The tensile strength of these fibers varies according to the steel grade of the starting material. However, the manufacturers do not clearly indicate the consequences of this. The difference is not explained much in the company brochures, but it seems to depend on the production process on the one hand and on the processability on the other.

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4.3.2 Waveform An equally common form is the corrugated form, which is commercially available as round wire or corrugated sheet metal.

Fig. 4.7: steel fiber in waveform The dimensions are also small here. Their diameter is 0.5–1.3 mm, the length is about 4–6 cm. There are several differences in shape, especially since some manufacturers have added additional geometric dents to create a better bond with the concrete.

4.3.3 Compressed form

In order to achieve better compatibility when processing the fiber concrete, a straight piece of wire was compressed at both ends. This allows easier pumping of the fresh concrete mass with embedded steel fibers, reducing wear on the pump and hoses. The bond to the concrete is created by the widened ends of the wire. This is equivalent to wedging in the concrete.

Fig. 4.8: Steel fiber in compressed form In the future, there will be even more geometric variations of the design on the market. There will probably always have to be a trial effort to achieve further optimizations in the shape of the steel fibers.

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4.4 Glass fibers Glass shows characteristics of both a solid and a liquid, it is an amorphous substance. It obeys Hook’s law up to brittle fracture, that is a spontaneous, unannounced break, and shows completely elastic behaviour without a flow area. Thus its mechanical behaviour is similar to that of a solid. If you look at the arrangement of the atoms, glass is a liquid. However, it reaches such a high viscosity during cooling that its physical behaviour can be described as a solid. The strength varies greatly, depending on how the fiber is pre-damaged during processing. It starts at 3,500 N/mm2 , , for the individual fiber, and can in extreme cases be below 500 N/mm2 ,for example for woven products. Glass fibers have a completely elastic elongation behaviour, there is no permanent deformation. The brittle fracture occurs between 2 and 5 % elongation. Glass and glass fibers have a modulus of elasticity of 72,000 N/mm2 and a shear modulus of 15 to 36 kN/mm2 , with a transverse contraction from 0.13 to 0.32. The values are independent of the temperature. With glass fibers, there is a problem with cementitious binders. It is the compatibility with the cement stone, which is strongly alkaline. The conventional silicate glasses, soda-lime glass (A-glass) or borosilicate glass (E-glass), are not resistant to alkaline solutions as they may be present in moist hardened cement paste or concrete. This leads to corrosion similar to pitting corrosion on the surface of the glass, which, due to the notch effect, results in a severe loss of strength and embrittlement. E-glass or C-glass can therefore only be used for a few purposes with concrete fibers. For this reason, there are generally two types of glass fiber, which differ from alkaline concrete due to their chemical resistance [27].

4.4.1 Alkali-resistant fibers The glass fibers are produced from the molten glass by means of jet drawing or jet blowing and the foils are then provided with a so-called coating. This after-treatment, the so-called finish, is intended to enable or facilitate further processing of the fibers. At the same time, this surface coating provides the necessary protection against the attack of the hardened cement paste.

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Fig. 4.9: glass fibers in the bundle wound (acc to Zorn) The fibers thus prepared are as fiber bundle beach s) then wound on coils (drums), before they are then cut to the so-called short fiber. There are two types that differ in their properties and fields of application:

4.4.1.1 Integral glass fibers

Fig. 4.10: integral glass fibers (acc to Zorn) The fiber bundles are cut to lengths of 6-24 mm and packed loose.

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4.4.1.2 Water dispersible glass fibers

Fig. 4.11: water-dispersible glass fibers (acc to Zorn) The fiber bundles, which dissolve in contact with water and are thus effective as individual fibers in the concrete, are cut to lengths of 6–24 mm and packed. This means that, in contrast to the integral fibers, there are no longer fiber bundles, but the individual fibers are located in the concrete matrix. This ensures a much finer distribution of the individual fibers, which are also considerably thinner than the integral needles. Alkali-resistant glass fibers in small dosage quantities change and improve the processing properties of the fresh concrete and the service properties of the solidifying and cured concrete. In order to differentiate it from the usual fiber concretes, it is referred to as fiber-modified concrete (FMB) at such low dosage quantities. In fresh concrete, the glass fibers cause a greater cohesion of the matrix, and in hardening concrete, glass fibers prevent micro-crack formation in the structure. The avoidance of cracks in young concrete as a result of various constraining stresses is thus achieved. These properties give the concrete structure, which is decisive for the later stressing, its decisive and decisive quality. The minimum thickness of a component with glass fiber concrete can thus be reduced to a few millimetres. This allows the production of extremely filigree forms.

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4.4.2 Non-alkali-resistant fibers Although these fibers are still occasionally available, they dissolve on contact with the fresh concrete and lose their strength. As a result, these fibers are not or only very briefly effective as reinforcement in concrete. Mechanically positive influences of these products on the component are questionable, as they do not show sufficient resistance in fresh concrete. These fibers will therefore not be discussed further in this book.

4.5 Natural fibers These are rarely used today in combination with concrete. Their technical properties vary greatly and a uniformity in the distribution of the fibers and thus fiber effect is rather difficult to achieve.

4.5.1 Plant fibers Of the large number of vegetable fibers used in the building industry for mixing into concrete, mortar and plaster, only the so-called hard fibers are suitable. These are: • Leaf fibers such as flax and sisal • coconut fiber The mechanical properties of plant fibers are not uniform and difficult to classify technically in terms of strength properties, so the technical application is no longer given today, but rather of historical interest. This is especially true for the renovation of older buildings.

4.5.2 Animal fibers These fibers were previously used in concrete and more often in mortar, as they are cheap and readily available. Mainly coarse animal hair is used here, which is available locally.

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58 • Horse hair, was used especially in mortar and wall plaster until 1950 • Cattle hair, especially the hair of yaks (in Asia) • Goat hair, for plaster (also fine plaster)

Since the mechanical properties of animal hair are subject to great variation, the technical application is no longer given today, but rather of historical interest. This is especially true for the renovation of older buildings.

5 FC processing As with any composite building material, there are some basic rules to be followed with fiberreinforced concrete in order to achieve good workmanship. The end result should be a uniform building material that meets the expectations of the planning engineer in all its components.

5.1 Types of concrete to be used In principle, all types of concrete can be used for fiber-reinforced concrete. However, the properties of the fibers are not optimally utilised for all types. It has been proven in practice that the best utilisation of the respective fiber used is given from a concrete quality of C16 up to a concrete strength class of C50. It appears to be important for the concrete compositions that the aggregates lie favourably in the grading curve range, that is, between the grading curves A and B. In addition, the proportion of fines should be somewhat generous, because this is where the embedding of the fibers in the concrete is decided.

5.2 Additives for pumped concrete Additives in the form of rock flour should be added to the usual good grading curves. This can be added up to max. 400 [kg/m3 ] (above this see approval for aggregate). This improves the coating of the fibers in the concrete. The aggregate to be used is composed of: Cement Rock flour 0/0,0125 mm and concrete admixture. With the W/B factor prescribed for the concrete strength class, the consistency of the fresh concrete should be at a spreading dimension of 35‚Äì48 cm, that is, plastic to soft. However, there is the possibility that the spreading dimension changes when fibers are added. Changes of © Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2021 B. Wietek, Fiber Concrete, https://doi.org/10.1007/978-3-658-34481-8_5

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5–12 cm were measured depending on the dosage. This should be checked in each case when using fibers and appropriate additives should be used to regulate the spread.

5.3 Common dosages Different dosages are used depending on the fiber materials and the static requirements. The minimum fiber content also depends on the material.

Fig. 5.1: Dosage for fiber concrete With the dimensioning of the fiber-reinforced concrete in the following chapters, this necessary dosage of the fibers used for a stressed component is determined as the respective result.

5.4 Addition of fibers Fibers can now be added by various methods:

• Manual addition: In this case, the fibers are added to the mixer manually by one person, whereby care must be taken that they are not thrown in all at once in a concentrated manner, but rather that they are evenly distributed. We advise against this type of fiber addition, as it does not ensure uniform distribution of the fibers in the fresh concrete.

• Addition with dosing device: The fibers stored in the device are evenly added to the mix via a dosing mechanism.

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Fig. 5.2: Dosing device for fibers of the company Incite The container is filled with fibers from cartons, sacks or big bags. The admixture quantity or batch is set in kg. The batching is normally done directly into the mixer onto the aggregates or into the gravel scale or onto a conveyor belt where it is fed into the mixer.

• Blow-in unit: The fibers are blown into the dry mix from a storage container by means of compressed air. With this technology, the fibers are blown in from the ground and thus mixed in. This process produces a very good mixing of the mix.

Fig. 5.3: Blow-in device for fibers from the company La Matassina These machines can be loaded with any type of fibers. The fibers are filled from the pack-

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aging and separated in such a way that they no longer have any mutual cohesion. They are then blown into the mixer by means of compressed air. The dosage can be adjusted by the time (kg/min).

• Conveyor belt: Especially in concrete plants, the fiber often has to be transported over a longer distance. This can be done with the help of a conveyor belt, whereby a weighing station can also be integrated here in order to precisely maintain the desired dosage.

5.5 Hedgehog formation Especially when processing fiber-reinforced concrete, in particular with end-bent steel fibers, the so-called hedgehog formation occurs time and again. These are balls about the size of a fist that are formed during the mixing process. Especially at higher dosages, the material in the truck mixer tends to form lumps (hedgehogs). It seems that this hedgehog formation depends on the mutual interlocking of the fibers, as this condition has not been observed with straight fibers. Recently, research has also been conducted into three-dimensionally bent or curved fibers, which enable a significantly better load-bearing effect. These fibers are currently being tested as steel fibers and plastic fibers. Particular attention must be paid to mutual interlocking, because these fibers already interlock when loose, so strong hedgehog formation is to be expected.

Fig. 5.4: Typical hedgehog formation during removal from the truck mixer

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It is obvious that this formation of hedgehogs must not occur when installing fibers, as otherwise the uniformity of the fiber distribution in the concrete is no longer given. This would decisively weaken the static load-bearing capacity of the fiber-reinforced concrete. It is therefore essential to avoid the occurrence of hedgehogs in the fresh fiber-reinforced concrete.

In many places, the processing crew helps themselves by crushing these hedgehogs with a manual tool after the truck mixer before feeding them to the concrete pump. This is the right method, but it is not sensible to do this work by hand in this day and age.

Fig. 5.5: Destruction of the hedgehogs with hammer in front of the inlet to the pump

In the above illustration, this crushing is shown with a hammer. In the future, however, this work should be done by a machine which presses or beats the material from the truck mixer through a sieve in order to crush the hedgehogs. This would solve the problem of hedgehog formation.

The loose mix can now be transported by a concrete pump to the place of placement, where it can be placed in exactly the same way as fresh concrete.

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5.6 Installation of fiber-reinforced concrete When installing fiber-reinforced concrete, a distinction is made between normal fiber-reinforced concrete, which is to be treated like any normal concrete, and fiber-reinforced shotcrete, which is used in special civil engineering, which must have special installation properties and must therefore also be considered separately.

5.6.1 In building construction and civil engineering The fiber-reinforced concrete must be placed evenly and quickly. Particular attention must be paid to this during delivery and also during transport to the construction site, whether by pump or bucket. The paving personnel must be specially instructed in this respect. As transport to the paving site is usually carried out with truck mixers, care must be taken to ensure that no hedgehogs occurs during transport and that the correct consistency is then achieved by adding water or admixtures when the concrete is discharged to the concrete pump.

Fig. 5.6: Inlet from truck mixer to concrete pump (picture by Rindler GmbH The picture above shows a fresh fiber concrete as it comes out of the truck mixer, which can be pumped on with a uniform consistency without forming hedgehogs.

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The compaction of the freshly placed fiber concrete is the same as for normal fresh concrete, it depends on the vibrator used. When using self-compacted concrete as fiber concrete, this work step is unnecessary.

Fig. 5.7: Concreting with fiber-reinforced concrete (image from Krampe Harex Fibrin GmbH The placement can be done not only by hand, as shown in the picture, but also, especially with large slabs, by means of suitable machines that vibrate the fiber concrete and additionally smooth the surface so that an even surface is created. Care must be taken to ensure uniform curing of the installed fiber-reinforced concrete so that the surface of the fresh fiber-reinforced concrete is not damaged by drying out too quickly and the colouring of the surface also remains uniform. In the case of structural elements such as columns, beams and walls, the production process of the component concerned is simplified, as the formwork can be erected in a single operation and then work can begin immediately on placing the fresh fiber-reinforced concrete. This results in considerable cost and time savings. Basement walls are worth a separate consideration here. For the tightness of basement walls is usually provided 30 cm reinforced concrete. This dimension results from the fact that the reinforced concrete in the cracked state (only in this way reinforced concrete works) can be cracked max. 80% of the cross-section. This is 24 cm crack depth for a 30 cm thick wall. This leaves only 6 cm for water tightness. The water permeability of concrete is only guaranteed from 5 cm. In the test, the water must not penetrate more than 5 cm into the concrete so that it can be classified as impermeable to water. Thus, a reinforced concrete basement wall must be at least 30 cm thick to be considered watertight.

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In contrast, when using fiber-reinforced concrete, the design of the basement wall is carried out in the non-cracked state. This means that the crack criterion of reinforced concrete is not applicable here and the basement wall can be freely selected thinner than 30 cm. In a practical application, the basement wall was used with 20 cm fiber concrete (C25 with fiber HE 55/35 and dosage 30 kg/m3 ).

Fig. 5.8: Basement wall d = 20 cm made of fiber-reinforced concrete on fiber-reinforced concrete floor slab

Through the use of fiber concrete, the wall thickness could be reduced by 1/3, although this was of course noticeable in the corresponding construction costs. This shows that considerable savings can be made in the construction of residential buildings using fiber technology. Another example of the use of fiber-reinforced concrete is the production of precast slabs for terrain support with additional anchoring. The precast slabs are placed directly into the free space during excavation and immediately installed and mortared in the subsoil using self-drilling small anchors ( soil nails). With this system it is possible to save a further temporary excavation support. Thus, also with this application of this system with prefabricated parts made of fiberreinforced concrete, a considerable reduction of construction time and costs can be achieved.

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Fig. 5.9: Precast wall as retaining wall made of fiber-reinforced concrete After a positive initial test, this precast wall is now already in use on high mountain roads and also on railway lines, where a construction thickness of 15 cm is sufficient. Work is also underway to use this wall for greater heights and also to anchor it several times. Prefabricated constructions with berms are also being developed. This will probably open up a wide range of possible applications. A special case of the application of fiber concrete was the foundation of a cable car support to be fixed into a vertical rock-wall during the construction of the Karlesjochbahn in the Kaunertal glacier area at an altitude of approximately 3,300 m. Here, for geological reasons, the rock surface could not be straightened. Rock anchors protruded from the rock face and the bar anchors for the column embedment protruded from the formwork. It was therefore not possible to additionally integrate a steel reinforcement cage here in such a way that it force-fitted the entire concrete volume. It was therefore decided to use fiber-reinforced concrete for the first time for this component for the column foundation suspended from the wall. The Austrian cableway authority (Federal Ministry of Innovation and Technology) gave its positive approval to this step, even though there was no standard basis for this construction method.

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Fig. 5.10: Foundation mountain station Karlesjochbahn 3.300 m (a) Rock face with anchors (b) Concreting process with fiber concrete All the concrete was transported by helicopter and placed in the foundation from there. The steel fiber FE 65/35 with a dosage of 60 [kg/m3 ] was installed in this foundation. The concrete used was strength class C30, with appropriate admixtures being used in accordance with the need for the elevation and the degree of stress.

5.6.2 For fiber-reinforced shotcrete Fiber concrete is particularly suitable for shotcrete, as it offers considerable advantages over normal shotcrete: • can be produced from the basket in inaccessible terrain, no working scaffold necessary; • applicable directly after excavation; • no measuring of reinforcement fields; • the entire sprayed concrete thickness can be applied immediately; • after spraying, anchoring can be carried out immediately.

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A related application in impassable terrain is shown in the next picture, where a very brittle rock face was secured from the basket with fiber concrete and ground nails.

Fig. 5.11: Application of fiber sprayed concrete (Gerlosberg Zillertal-Tyrol)

Since it is no longer necessary to cut the reinforcement to size and mount it individually on the ground surface, a working scaffold is also no longer required and the securing work can be carried out entirely from the cage. This is a great step forward, especially in insecure terrain and also in excavations, whereby safety is considerably increased, especially for the work crew. Due to the usually long transport times in the truck mixer (approx. 70 min. at the construction site shown), the risk of hedgehog formation is very high. Measures must be taken here to prevent the formation of these hedgehogs and to ensure that they can be processed properly afterwards. The surface of fiber shotcrete always shows protruding fibers. This is due to the irregular spatial distribution of the fibers. Although an alignment of the fibers transverse to the spraying direction would be advantageous, this could not be detected in any application. Thus, one can also assume a spatial distribution of the fibers here.

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Fig. 5.12: Surface of the fiber sprayed concrete

If the protruding fibers (steel fibers) interfere, the surface should be reworked immediately after the spraying process or an additional layer of shotcrete without fibers should be applied. This only applies to steel fiber shotcrete, for all other fibers this is not necessary.

Fig. 5.13: Slope stabilisation on the A-13 Brenner motorway next to the Luegg bridge

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In the case of excavation shoring, a direct connection to existing shotcrete walls is possible; only the contact point should be freed from cement dust with water (high-pressure cleaner) beforehand. The fibers protruding from the shotcrete and the roughness of the shotcrete surface result in a good bond, so that in most cases no transitional construction such as butt reinforcement is necessary.

Fig. 5.14: Excavation support for a ski depot in Fiss-Tirol When securing for an excavation in Fiss (Tyrol), relatively small working areas had to be exposed and immediately closed again due to the changeable subsoil. The advantage of fiberreinforced concrete became apparent, as no time had to be spent on installing steel reinforcement. The individual opened fields were exposed and closed again within a period of 3–5 min. This prevented the soil from caving in and saved a considerable amount of time in the construction of the excavation support.

5.7 Different fiber materials In the following chapters, the reader will be introduced to the application of the various different fibers, whereby on the one hand the most diverse fibers and on the other hand the numerous

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possible applications will be dealt with, without showing the static calculations here, but rather highlighting the economic and processing solutions. Fiber concrete has not only static tasks as well as building biological properties, but additionally fulfills its tasks in the thermally broad spectrum, which must be taken into account in the individual applications. From all these angles of view, quite different application strengths of the respective different fibers result. This also testifies to the very large variation of fibers in material and form that are currently offered on the market.

5.7.1 Plastic fiber concrete The use of fiber-reinforced concrete with plastic fibers has shown a strong upward trend in recent years. More and more areas of application are being exploited with fiber-reinforced concrete, as the production is very simple and the required material quality can also be well maintained through constant technical testing monitoring.

5.7.1.1 Constructive applications Due to the different fiber types such as microfiber and macrofiber, there are also generally two different applications: Microfiber: These are used on the one hand mainly against the shrinkage of concrete (e.g. screeds, floor slabs, etc.), and on the other hand for structures subject to high thermal loads (tubbings and tunnel walls) in tunnel construction. Macrofiber: These are used as reinforcement mainly in structural components such as basement walls and concrete slabs and in drivable external surfaces, and increasingly also with shotcrete for terrain stabilisation. Structural components such as slabs, walls, columns and beams can also be designed in uncracked material.

5.7.1.2 Statically effective applications With the possibility to carry out a static design of the building material fiber-reinforced concrete, the application in structural components has increased considerably.

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In this book, numerous areas of application are shown on the one hand calculated and on the other hand shown as examples in practice.

5.7.1.3 Thermally effective applications Building materials are normally only delivered to temperatures between ‚Äì30 and +50 °C. A major exception is the case of fire. Here, temperatures of up to 1,000 °C are nothing unusual and this has also led to the introduction of additional requirements for the building structures and building materials used in many components and also rooms. A typical building code gives the following requirements regarding fire safety: The building materials used in escape routes, such as floor coverings, wall coverings, ceiling coverings and the like, must be designed in such a way that in the event of fire the rapid and safe exit from the building is not impaired by fire, smoke or burning droplets. If this is necessary, in particular due to the size or intended use of the building, additional actions such as technical fire protection equipment, escape route orientation lighting, safety lighting and the like must be provided. In the following, components are listed which are relevant in terms of fire protection and for which a new assessment should be made on the basis of the material properties of plastic fiber concrete: Escape routes, stairwells, guest rooms, tunnels, stadiums, schools, assembly rooms, public spaces. In the case of a fire protection re-evaluation of a structure, the question arises as to whether, for example, a staircase with stair flights made of plastic fiber concrete is not safer than the currently common stair flights, since the load-bearing strength of the staircase is hardly or only slightly reduced by the slight spalling that occurs in the event of a fire. Thus, these staircases are fully statically functional at all times, even after a fire.

5.7.1.4 Effects of interest from a building biology point of view

For years, especially in residential and accommodation buildings, attention has been paid to natural building materials and a group has formed that prefers natural construction methods. Thus, the building materials stone, wood, brick and clay are mainly used for the carcass and

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this is supposed to give a better feeling of living than the technical building materials such as reinforced concrete and steel and also composite building materials. Particularly in the case of reinforced concrete components, it is repeatedly claimed by groups such as radiesthesians and also Feng Shui followers that changes in the natural radiation range emanate from the metal mesh, which are not conducive to health. However, this may be, till now physics cannot make any reliable statements about this, but this possibility may well exist. This attitude can be supported by the findings of physics regarding the dark mass in space, which up to now is not measurable, but is only used mathematically as a regulator to the existing physics, in order to be able to explain the effects of space. According to this, there are still physical effects that cannot be proven to this day, but which do exist. The effects of the radiesthesians and Feng Shui proponents are also based on this level of thought. If one does not want to have the influence of radiation in one’s building, a fiber concrete with plastic fibers or glass fibers fulfills the requirements of the building material, since the fiber concrete can be equated with a natural rock (conglomerate). With the now possible static dimensioning of the fiber-reinforced concrete, it is also possible to calculate ceilings that can span spans of over 6.0 m in residential building construction. Thus, a possible radiation impairment in residential building construction can be counteracted by the use of fiber-reinforced concrete with corresponding fibers.

5.7.2 Steel fiber concrete This is used today as a substitute for reinforced concrete or also, but increasingly rarely, as a supplement to reinforced concrete. These are mostly load-bearing components that must have a better material quality than pure concrete due to the stresses they are subjected to.

5.7.2.1 Constructive applications

Here, the main use is made of two properties that arise in fiber-reinforced concrete due to the use of fibers: Frost resistance: During frost, tensile stresses occur in the concrete due to the formation of ice in the pore water. These stresses are taken over by the fibers and thus material spalling no longer occurs.

5.7 Different fiber materials

75

Avoidance of shrinkage cracks: Shrinkage causes internal tensile stresses in the fresh concrete, which are taken over by the fibers and thus no shrinkage cracks can occur.

5.7.2.2 Statically effective applications With the possibility to carry out a static design of the building material fiber-reinforced concrete, the application in structural components has increased considerably. In this book numerous areas of application are shown and on the one hand calculated and on the other hand shown as examples in practice.

5.7.3 Glass fiber concrete

Components made of glass fiber reinforced concrete are usually thin-walled components that can be assembled. They are normally manufactured by casting or spraying. In both cases, the components are produced in moulds (formwork). After the curing time, these parts are removed from the formwork and released for assembly. The type of installation and fasteners are selected according to the possibilities of the installation location. Steel mouldings are usually used as fasteners. Fiber glass-reinforced concrete components are not normally wearing parts but are designed for a long service life. The service life then also determines the type and design of the fasteners that are used.

5.7.3.1 Constructive applications As thin-walled components, a wide range of applications is possible within very broad limits.

5.7.3.2 Statically effective applications The possibility of static dimensioning of components also increases the range of application to many component shapes.

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5 FC processing

5.7.4 Carbon fiber concrete The carbon fiber is not only used as a textile, but also as a single fiber. Here, the geometric sizes are comparable with microfibers. A special feature is the high modulus of elasticity, which results in a very high tensile strength fiber concrete. At present, the economic efficiency is not yet given everywhere due to the fiber price, however, with continuing larger application quantities, this problem will also solve itself.

5.7.4.1 Constructive applications Highly stressed and thin components can be manufactured very safely with carbon fibers and have the additional advantage of being corrosion-free.

5.7.4.2 Statically effective applications Particularly rounded thin components are economically advantageous, whereby the determination of the internal forces is dependent on high-quality calculation programs.

6 Properties The building material fiber-reinforced concrete consists of two different materials, the concrete and the fiber. Together, they are a composite building material whose properties are composed of the two basic materials. Based on the designs for composite construction materials, as they are common in reinforced concrete construction [36], [48], a division of the influences of the concrete and the fibers is made here. Thus, it is deviated from other authors who determine a closed material law of steel fiber concrete [18], [17]. As already mentioned, the usual material parameters are used. Their determination can be taken from the already known investigations and also from existing tables.

6.1 Concrete properties Concrete is very precisely defined by the relevant standards in Europe. Even the production of the individual concrete types is precisely prescribed. These specified values are continuously checked by factory inspections and also on the construction site. The designation of the strength class of concrete, for example, C25 consists of C ..... Concrete 25 ... characteristic compressive strength fck [N/mm2 ] (prism test) The cube compressive strength is deliberately omitted here, as this type of concrete test is no longer carried out. The average concrete tensile strength is calculated, whereby this applies to the load case of general tension: © Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2021 B. Wietek, Fiber Concrete, https://doi.org/10.1007/978-3-658-34481-8_6

77

78

6 Properties

2/3

fctm = 0, 3 ∗ fck

[N/mm2 ]

(6.1)

The bending tensile strength required for the design of cross-sections can be determined according to the formulas (3.7) and (3.8). This gives the bending tensile strength as a function of the proportion of cracks due to shrinkage.

Fig. 6.1: Flexural tensile strengths with possible crack components

The question now is: How can these crack components be reduced to a minimum in order to achieve the highest possible bending tensile strength for a structure? Until today, the answer has been to add sufficient moisture to the concrete with proper curing so that the shrinkage cracks do not become too large and only occur in the minimum range. This also led to the differentiation of the component thicknesses for which the curing is effective. This is also how the relationship in formula (3.6) came about. However, there is also a second way of preventing cracking in concrete. This is possible with the addition of fibers. This was already carried out very successfully in ancient times. Recently, numerous fibers have been offered on the market that are supposed to prevent cracks when the concrete sets.

79

6.1 Concrete properties

With a minimum dosage of the most varied fibers, the formation of shrinkage cracks is achievable with almost all fibers. In any case, apart from minor cracks, the concrete is maintained in a very good condition, so that the flexural tensile strength can now normally be regarded as adequate with a crack content of 10 %. This now results in the following relationship in the case of fiber-reinforced concrete:

2/3

fctm = 0, 54 ∗ fck

[N/mm2 ]

(6.2)

The bending tensile strength thus depends on the use of the concrete.

Compression

Tension

Bending

fck

fctm

fctm, f l

[kN/cm2 ]

[kN/cm2 ]

[kN|cm2 ]

C8

0,8

0,12

0,22

C 12

1,2

0,16

0,28

C 16

1,6

0,19

0,34

C 20

2,0

0,22

0,40

C 25

2,5

0,26

0,46

C 30

3,0

0,29

0,52

C 35

3,5

0,32

0,58

C 40

4,0

0,35

0,63

C 45

4,5

0,38

0,68

C 50

5,0

0,41

0,73

Concrete

Table 6.1: Concrete properties at 10 % crack content

These values are now also used in the calculations of the individual cross-sections to be designed. The material values give no indication of the shear capacity of the concrete. For this reason, reference is made here to Mohr’s material correlations, the fundamentals of which are repeated here. For this specimen, the load σ2 is increased until the fracture of the specimen occurs. A fracture joint occurs at the angle δ . The limit stresses σ and τ occur in the fracture joint. Mohr proved the

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6 Properties

connection between the quantities σ1 , σ2 , σ and τ with his stress circle and the Mohr envelope curve (shear line) at the angle ϕ to be determined with it.

Fig. 6.2: Specimen in fracture state

Fig. 6.3: Mohr’s stress circle It is proved that the fracture angle δ is directly related to the shear angle ϕ:

81

6.1 Concrete properties

δ = 45 + ϕ/2

(6.3)

As can be seen in the figure of the Mohr stress circle, the Mohr envelope (shear line) intersects the axis in tension at angle ϕ . The point of puncture is the condition in the concrete at which the maximum tensile stress σz can be absorbed. This maximum absorbable tensile stress has already been determined as fctm, f l and calculated for each concrete strength class. If we now look at these correlations again in the τ − σ diagram, we obtain the following figure.

Fig. 6.4: Mohr’s stress circle, relationships at rupture

The shear line is a tangent to two Mohr stress circles. First the tensile case, where the circle is given by the tensile stress σz and the zero stress 0. Then the compression case, where the second circuit is bounded by the zero stress 0 and the compressive stress σd . With the stresses σd and ¬σz , the angle of the shear line ϕ and the shear stress τ0 (shear strength) can be calculated from Mohr’s relationship. The relationship for the shear angle ϕ can be taken from the following figure.

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6 Properties

Fig. 6.5: Graphic for determining the shear angle ϕ The following relationship can be identified: sinϕ = ((σd − σz )/2)/(σd + σz )/2))

(6.4)

From this, you can now write the equation simplified as: sinϕ = (σd − σz )/(σd + σz )

(6.5)

Additionally interesting is the shear stress, where there is no normal stress. This shear stress is called shear strength œÑo or also cohesion or also bond stress (in reinforced concrete construction). It is simply calculated as: τ0 = σd /2 ∗ tan(45 − ϕ/2)

(6.6)

Thus, all parameters of the material concrete are known in Mohr’s representation. The characteristic values ϕ and œÑo calculated in this way are important for determining the question of which stresses can actually be absorbed by the concrete building material. With the two Mohr circles for the tensile case and the compressive case and additionally the area below

6.1 Concrete properties

83

the Coulomb shear line, the stable stress states can now be defined. With this definition, the range that limits the possible stable stress states can be specified.

Fig. 6.6: Active stress surface in Mohr’s representation This marked stress area is therefore the area in which stresses are possible. Stresses outside this area cannot be absorbed by the material - fracture occurs. Cohesion can also be calculated from Coulomb’s relationship. Here, the normal stress applied to the sliding surface is used as the stress.

Fig. 6.7: Fracture criterion according to Coulomb

84

6 Properties The relationship can be written with the following context. τ = c + σz ∗ tanϕ

(6.7)

Where c is called cohesion and corresponds to τ0 in Mohr’s representation. In the following table, all these values have been calculated for the individual concrete strength classes with a crack content of 10 % due to shrinkage.

Concrete type

fck = σd

σz = fctm, f l

ϕ

τo

σd /σz

Ecm

C

[kN/cm2 ]

[kN/cm2 ]

[Grad]

[kN/cm2 ]

[−]

[kN/mm2 ]

8

0,8

0,22

34,7

0,21

3,64

2.530

12

1,2

0,28

38,4

0,29

4,29

2.700

16

1,6

0,34

40,5

0,37

4,71

2.860

20

2,0

0,40

41,8

0,45

5,00

2.990

25

2,5

0,46

43,6

0,54

5,43

3.140

30

3,0

0,52

44,8

0,62

5,77

3.280

35

3,5

0,58

45,7

0,71

6,03

3.400

40

4,0

0,63

46,7

0,79

6,35

3.520

45

4,5

0,68

47,5

0,87

6,62

3.620

50

5,0

0,73

48,2

0,96

6,85

3.720

Table 6.2: Concrete properties according to Mohr’s derivation

6.2 Fiber properties The fibers currently on the market are assessed according to their mechanical properties on the one hand and their thermal properties on the other. Since the difference in these properties is very large, the individual types of fibers must be treated separately.

6.2 Fiber properties

85

6.2.1 Plastic fibers These fibers have a much lower modulus of elasticity than concrete, so they are softer than the hardened concrete. Even as relatively soft fibers, they have an essential role to play during the setting period of the concrete. Both compressive forces and tensile forces can be assumed. These adjust themselves according to the deformation of the young concrete. In solid concrete, the plastic fibers have a relatively small share in the load transfer, since they are much softer than concrete. Therefore, they only transfer a small proportion of the load, which is, however, easy to calculate. Polypropylene fibers show a positive effect when exposed to fire. An effective reduction of explosive spalling in concrete can be achieved by a pore system that leads to a sufficient reduction of the vapor pressure that forms when water evaporates in the event of fire. This is achieved by adding fibers made of plastic, which on the one hand melt during fire from approximately 160 °C and create continuous micropores, and on the other hand form a porous transition zone through which the vapor pressure created during fire can be dissipated. In fresh concrete, plastic fibers have the property of strongly influencing the spread of the fresh concrete. For example, a change in the dosage of 1 [kg/m3 ] PP fiber results in a reduction in the slump of 5‚Äì7 cm. This means that the concrete consistency (slump) must be adjusted to the fiber dosage. 6.2.1.1 Microfibers Microfibers have a specific surface area of 5-200 mm2 /cm3 calculated on the unit cube of 1 cm3 , depending on the dimension and dosage of the fiber. This specific surface area alone shows that a considerable influence is to be expected at the contact surface of the fiber with the concrete. This is to be expected especially in the setting phase of the fresh concrete, since here the bonding crystals grow and establish the bond between aggregates, hardened cement paste and the fibers. This surface effect is particularly noticeable when the fresh concrete is setting, which is why the microfiber is also particularly popular for preventing shrinkage cracks in fresh concrete. Fire behavior when using microfibers What can happen to the tunnel shell in the event of a tunnel fire is made clear by past accidents. In the case of the fire catastrophe in the Gotthard tunnel in October 2001, or the Tauern tunnel

86

6 Properties

fire in May 1999, explosive spalling occurred due to the sudden impact of extreme heat on the concrete components. This endangered life and limb and also made subsequent refurbishment of the tunnel section difficult and very expensive. The cause of this explosive spalling at the time was that the residual liquid contained in the concrete (capillary water) began to boil due to the sudden heat and the resulting steam could not escape from the concrete. This vapor pressure led to the bursting of the component with the known, serious consequences. Gotthard tunnel disaster in 2001: 11 deaths and subsequent 2-month tunnel closure for renovation. Tauern tunnel disaster 1999: 12 dead, followed by second tunnel tube and renovation of the first tube.

Fig. 6.8: Tunnel fire - explosive heat development (Image: Propex)

Plastic microfibers added to concrete usually lead to a considerable improvement in fire behavior from a minimum dosage of 1 kg/m3 of concrete. This occurs, on the one hand, due to the homogeneous distribution of the individual fibers in millions and, on the other hand, due to their property that plastic microfibers melt when exposed to heat. The immediate melting of the fibers when exposed to explosive heat creates cross-linked microcracks in the concrete, which allow the water vapour to escape from the concrete. The resulting damage caused by spalling poses a minor risk to life and limb, the supporting structure of the tunnel is better appreciated and the affected tunnel section can therefore be easily rehabilitated at a later date.

6.2 Fiber properties

87

Fig. 6.9: Tunnel section Vomp-Terfens of the Brenner Railway (Fibermesh 150)

The relatively large number of fibers in the unit cube results in improved properties in the event of fire, as the porosity of the concrete increases as a result of the melting of the fibers, and the water vapor produced in the concrete by the heat can be easily dissipated, thus preventing spalling.

6.2.1.2 Macrofibers The specific surface of the macro fibers is 5–30 mm2 /cm3 , depending on the dimension and dosage of the fiber. This shows already in comparison to the microfiber that in the setting phase the influence on a consistency is not so great. However, the contribution to the force is all the better, since the shaping enables a better transfer of force from the hardened cement paste to the fiber. Even in the case of a large temperature load as a result of fire, large pore spaces are created by the melting of the fibers and thus the vapor pressure created in the concrete can be dissipated without any problems, so that hardly any spalling is the result.

88

6 Properties

6.2.2 Steel fibers The stiffness of the steel fibers is about ten times that of concrete. Therefore, the effect of the steel fibers is very effective for load transfer. This means that the individual steel fibers can be used very well for load transfer. With regard to the influence of fire, the steel fiber is not optimal, since the steel has a better thermal conductivity than concrete, the temperature is transferred faster from the surface to the depth. Thus, in the event of a fire, a greater depth heats up with steel fiber concrete than with concrete alone. Since no additional pores are created, spalling to greater depths than with normal concrete is also a given. However, the advantage of steel fiber concrete over normal concrete is that the fibers usually still retain the spalled part and thus the spalled ends are still attached to the concrete and do not fall down uncontrollably. In fresh concrete, steel fibers have hardly any influence on the workability, in particular the consistency is only insignificantly changed. An unpleasant side-effect is the formation of hedgehogs in ready-mix concrete, whereby fibers clump together and thus do not mix evenly in the concrete. Corrosion of steel fibers In general, the basic state of the concrete protects the reinforcement from corrosion. Only in the area of carbonation is the pH value below 9, and corrosion of the installed steel parts can occur. There are three conditions that must coincide for steel to corrode in concrete: • the pH value of the concrete must be lower than 9; • oxygen must be available; • water must be available; If one of the three conditions is not present, steel cannot corrode. This is the basis of corrosion prevention. Thus, the following methods of corrosion prevention: • Seal the surface so that no water can get to the steel (paint, etc.) • Place concrete under water to prevent oxygen from reaching the steel (e.g. groundwater is low in oxygen, etc.). • Electrical polarisation (cathodic corrosion protection) - not possible with fiber-reinforced concrete, as the fibers are not connected and therefore current cannot flow.

6.3 Setting process

89

If these methods are not possible, corrosion of the steel parts in the carbonated area can occur. Schadde [44] has dealt in detail with this corrosion, especially in the case of steel fibers, and comes to the following conclusions: In non-cracked steel fiber concrete, lightly corroded fibers have so far only been detected to a maximum depth of about 4 mm. The great advantage is that the corrosion only exerts such low forces that no spalling of the concrete surface can be caused. In practice, damaging corrosion of steel fibers in non-cracked concrete is not to be expected. This is true even at high chloride levels in concrete with appropriate exposure. In order to avoid corrosion within a component, in addition to exact compliance with the standard-compliant production, great importance must be attached to good curing of the fresh concrete so that an increase in carbonation resistance and a reduction in chloride diffusion is achieved.

6.2.3 Glass fibers Glass shows characteristics of both a solid and a liquid, it is an amorphous substance. It obeys Hook’s law up to brittle fracture, that is, a spontaneous, unacceptable fracture, and exhibits perfectly elastic behavior without a flow region. Thus, its mechanical behavior resembles that of a solid. Looking at the arrangement of atoms, glass is a liquid. However, it reaches such a high viscosity during cooling that its physical behavior can be described as a solid. The strength varies greatly depending on how the fiber is pre-damaged during processing. It starts at 3,500 N/mm2 , for the single fiber, and in extreme cases can be below 500 N/mm2 , for example, for woven products. Glass fibers have a perfectly elastic elongation behavior, no permanent deformation occurs. Brittle fracture occurs between 2 and 5 % elongation. Glass and glass fibers have a modulus of elasticity of 72,000 N/mm2 and a shear modulus of 15‚Äì36 kN/mm2 , with a transverse contraction between 0.13 and 0.32. The values are independent of temperature.

6.3 Setting process Concrete - a mixture of rock, cement and water with the addition of other agents - only starts to react after water has been added. After the processing time, the concrete hardens and can slowly

90

6 Properties

absorb compressive and tensile stresses. During this time, changes occur in the concrete that are very decisive for the load-bearing capacity.

Fig. 6.10: Concrete strength development

From the usual way of showing the strength development here, it can only be seen that the compressive and tensile strength develops in the first few hours, and here it may be crucial to know how the whole thing proceeds in order to gain an understanding of the partial development as well. If you look in particular at the first phase of the setting process, you can get an idea of the microscopic processes with the following pictures. The cement present in the concrete reacts with the water and forms new crystals, which over time mutually grow together and thus create a bond. To do this, chemically the cement (the cement grain) and the water are used as starting materials, and a new mineral is formed in which both components are incorporated. This process slightly changes the volume of the material (crystals have a different density than cement and water together). At the same time, water evaporates from the surface, creating additional pores.

91

6.3 Setting process

Fig. 6.11: Development of the cement structure during the setting process (illustrations taken from VDZ teaching aid: 4. Hydration of the cement and structure of the hardened cement paste) This leads to a reduction in volume during the setting process, which is called shrinkage. When the individual solid parts contract, tensile stresses are created which are referred to as shrinkage stresses. In the setting phase, the various stresses increase, with the result that the instantaneous tensile strength in the fresh concrete is exceeded, which then leads to the appearance of cracks called shrinkage cracks.

Fig. 6.12: Concrete in the setting phase

92

6 Properties

Concrete is generally characterized by the fact that it can absorb very high compressive stresses, but only allows low tensile stresses. In general, the maximum tensile stresses are only approximately 1/5 of the maximum compressive stresses. However, this varies with the different types of concrete. The development of the stresses in the setting phase shows that the absorbable tensile stress develops only very slowly, whereas the visual wind stress develops much faster at the beginning of the setting phase. This leads to the dreaded shrinkage cracks in hardening concrete. As can be seen from the following diagram, the critical time range in which the shrinkage stress is greater than the tensile stress that can be absorbed is limited in time. After that, no new shrinkage cracks occur. There are now several methods to counteract this shrinkage: • Concrete curing by constant moistening of the surface. • Chemically increase the tensile strength during the setting process ‚Äì stiffening. • Addition of fibers which can already take over tensile stresses at the beginning of the crystallisation phase. If we now consider the setting process with fibers in concrete, the following relationship results, which can be derived from the presentation of the setting process in Chapter 3:

Fig. 6.13: Fiber concrete in the setting phase

6.3 Setting process

93

In the initial setting phase of concrete, the liquid state changes as crystallization begins. A plastic mass is formed, which increasingly gains strength. In this phase, the decrease in volume due to water extraction is greater than the increase due to mineral formation, resulting in tension in the fresh concrete, which causes the concrete to crack and thus shrinkage cracks to form. If fibers are embedded in the concrete, these fibers prevent the concrete from cracking because they temporarily compensate for the tension occurring in the concrete with pressure in the fiber. The fibers are like a support system to which the fresh concrete can attach itself locally, thus preventing cracking. The tensile and compressive stresses that occur are so low that they can be absorbed by the individual fibers and thus the plastic concrete does not crack. Under these conditions, mineral formation can proceed unhindered and the concrete can develop its full tensile strength through the coalescence of the individual minerals without cracking. After this first phase, the increase in volume due to mineral formation exceeds the decrease in volume due to water loss. This results in an internal pressure in the fresh concrete which, without fibers, leads to a further opening of the shrinkage cracks that have already formed. However, if fibers are now embedded in the concrete, these fibers take over the internal mineral pressure as a fiber tensile force and thus prevent the fresh concrete from cracking. Thus, the fibers also have a decisive task in this second setting phase to prevent cracking in the fresh concrete. Due to their relatively large surface area (long body with small diameter), the fibers in fresh concrete have, on the one hand, a large water-binding capacity and, on the other hand, they have direct contact with many cement grains. When new minerals are formed on the surface of the cement grains, the fibers are immediately in contact and forces can be transferred. This means that tensile or compressive forces can be transmitted at any time during the setting process. This transfer of forces during the entire setting process of the concrete ensures that almost no internal cracks prevent the tensile transfer inside the concrete. The concrete can develop its strength properties undisturbed, which means that the approach using the Mohrs stress circle together with the fracture criteria is fully effective. The exact effect of the fibers in the fresh concrete during the setting phase is now dependent on the type of fiber, the dosage and the tensile strength of the fibers. It seems logical that many small fibers should certainly provide an advantage in the setting process. A detailed investigation will be made in the next chapter.

94

6 Properties

Fig. 6.14: Shrinkage cracks in concrete

Fig. 6.15: Avoidance by fibers

With regard to fiber-reinforced concrete, it is always asked which fiber is better suited for the prevention of shrinkage cracks. Since only very small tensile forces are involved in the prevention of shrinkage cracks, the individual fiber does not necessarily have to be able to take on large tensile forces. It is more important that the fiber has a very small distance between each other and can immediately transmit a small shear stress along its surface. However, this is a question of the geometry of the fiber and not the material. The difference between steel fiber and plastic fiber is as follows: Steel fibers still have an oil or grease film on the surface from production, which prevents shear transmission and only allows shear forces to be transmitted after a movement. The associated deformation path with force transmission has not yet been researched in detail, but the phenomenon is very well known. In the case of a plastic fiber, the surface is not covered with a lubricating layer, which means that shear forces can be transmitted immediately. Therefore, the plastic fiber is much more suitable for the application in this practical case than a steel fiber. The shrinkage of the fresh concrete cannot be prevented, but due to the existing fibers no or only insignificantly small cracks occur, so that the concrete can fully assume its tensile properties.

6.4 Fibers to prevent shrinkage cracks As already indicated in the previous chapter, it is not the material of the fibers used that is decisive for the prevention of shrinkage cracks in fresh concrete, but their surface and mutual spacing. It is therefore a question of the surface area and dosage of the fibers used to prevent cracking. A reaction of the surface of the grain mixture of the fresh concrete with the surface of the fibers takes place. In practice, it has been shown that shrinkage cracks disappear completely when the proportion of the fiber surface to the grain surface is 5–6%. Assuming this ratio, the

6.4 Fibers to prevent shrinkage cracks

95

proportion of fibers required to prevent shrinkage cracks can be determined from the composition of the concrete. The basis for such a consideration is the relationship in a mix calculation for normal concrete. This allows the individual proportions of the parts contained in the concrete to be calculated.

6.4.1 Mix calculation for concrete This is carried out according to the information given in the cement leaflet Bautechnik B20 2.2017; Composition of normal concrete - mix calculation.

Fig. 6.16: Mix calculation for normal concrete

6.4.2 Determination of the grain surface The mean curve B of the surface of the grains is determined here using the example of the grain distribution with the largest grain size of 32 mm used in the mixture calculation.

96

6 Properties

Fig. 6.17: Grain distributions for GK32 mm The grain curves are displayed on a logarithmic scale, so that this also has an influence on further calculations. The following values are given for the grain curve:

Fig. 6.18: Geometry of the grains The mean grain size is calculated from the logarithmic mean of the lower and upper limit of a grain group: dm = 10(log(d−min)+log(dmax ))/2 For example, in the above table dmin = 0, 25mm dmax = 0,50 mm dm = 10(log(0,25)+log(0,5))/2 = 0, 35mm

(6.8)

6.4 Fibers to prevent shrinkage cracks

97

With this average grain size as an imaginary sphere, the further values of the respective corngroup are determined, assuming a total weight of the grains of 1,842 kg/m3 as shown in Fig. 6.16.

Fig. 6.19: Grain surface of the grain distribution

6.4.3 Determination of the fiber surface Microfibers made of plastic are mainly used as fibers for the prevention of shrinkage cracks. These have a large surface area at a relatively low dosage, which results in a dense distribution in the cement paste. Thus, the mutual distances of the individual fibers are small and the small tensile stresses can be easily absorbed during the setting phase. In this example, the plastic fiber Fibumesh 150 is used to prevent shrinkage cracks. The following figure shows the individual data of the fiber.

Fig. 6.20: Surface area of the fibers at a given dosage At a dosage of 0.8 kg/m3 fresh concrete, this fiber creates a surface area of around 110 m2 .

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6 Properties

6.4.4 Avoidance of shrinkage cracks If the selected dosage of fibers is now added to the fresh concrete, the surface area of the materials held together by the cement paste increases. As already mentioned, the added fibers are only a protection against shrinkage cracks when the proportion of fibers exceeds a factor of 5–6%.

Fig. 6.21: Use of microfibers to prevent shrinkage cracks In the example shown, the surface area for the cement paste increases by 6.4%, which means that the cement paste must also be increased by this amount. This can then ensure the stability of the fresh concrete in its quality. In the present example, 14.3 l of water and 31.9 kg of cement must be added to the fresh concrete in addition to the fibers. These fiber additions are not only there to prevent shrinkage cracks, but they also help to dissipate tensile stresses in hardened concrete. Therefore, these fibers can also be taken into account in the design of individual cross-sections with fiber-reinforced concrete in addition to the fibers used for force dissipation.

6.5 Composite effect of fibers Now we come to the interesting points. How should the composite effect between concrete and the fibers be classified? Does one go the way that is outlined in reinforced concrete construction and deals with the effect of each steel part, or should one rather try to reach the goal by a completely new approach? So there are two possibilities here in the further processing: • actual composite calculation as for Pfyl [56]; • statistical evaluation of the bonding effect based on the spatial distribution of the fibers in the matrix of the concrete. Several authors have already tried to determine the mode of action of the individual fiber and then to convert this to the spatial distribution of the fibers, as Pfyl did. This may have been

99

6.5 Composite effect of fibers

successful for a straight fiber, but the majority of fibers is not straight and also do not have a constant shape of the cross section. The essential result of all these investigations is that the shear connection at the fiber surface contributes significantly to the stress transfer.

Fig. 6.22: Fiber extraction tests according to Pfyl All these tests showed that the shear failure occurred when the respective fiber was pulled out in the concrete. As a result, the transmission of the fiber force is dominated by the concrete. In all cases, the fiber can be pulled out of the concrete and thus the concrete fails first before a barrel breaks.

Fig. 6.23: Fiber extract smooth fiber

Fig. 6.24: Extract of final compressed fiber

In the case of a fiber that is smooth on one side or compressed on the other, the force distribution of the shear forces along the fiber surface is different when the fiber is pulled out, as shown in the above figures. Thus, the shape of the fiber as well as the ratio of the material stiffnesses

100

6 Properties

has a decisive influence on the shear stress distribution along the fiber surface. This has been measured and thus also proven in numerous investigations by several testing institutes. Assuming mechanical prerequisites, the bonding effect of the fiber with the concrete is a very complex matter. It is assumed that the concrete as a homogeneous body has the same properties in all spatial directions, which is usually the case in most applications. The possible special properties of the concrete should not and will not be discussed here.

Fig. 6.25: Concrete fracture with spatially distributed fibers For the bond of the fiber in the concrete, the individual possible influences can be divided, which affect the force or stress progression within the component: • Material characteristics of the fiber. • Geometric sizes of the fiber. • Geometric shape of the fiber. • Dosage of the fibers in the concrete. • Spatial distribution of the fibers in the concrete. • Influence of the fiber shape on the force transmission. All these points are then processed individually and then put together again for the effect of the composite.

6.5.1 Material characteristics of the fibers The fibers offered and used on the market consist of a wide variety of materials. When selecting the materials, the chemical compatibility of the fiber material with the concrete or mortar is primarily required.

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6.5 Composite effect of fibers

The stiffness of the material, which is expressed in its E-modulus, has a very large influence. In the case of fibers whose modulus of elasticity is higher than that of concrete (steel and glass), the transmission of shear forces will always take place in the concrete and therefore, for these fibers, it is sufficient to consider the shear values of the concrete. In the case of softer fibers such as plastic or natural fibers, the E-modulus (Young’s moduli) of the fiber is of decisive importance in force transmission. If one assumes in a simplified way that the shear stress that can be applied changes according to the ratio of the elastic moduli, the respective composite stress for the fiber can be calculated and transferred to the dimensioning of the fiber stress. Shotcrete plays a special role here. In this case, the load is absorbed after a very short time and the full load-bearing capacity is usually achieved after only 3‚Äì5 days. This means that the modulus of elasticity of the corresponding strength class has not yet developed and only reaches about half the standard value. This means that the fiber takes on a higher tensile value, as it is also stretched correspondingly more. This is particularly noticeable with soft fiber material.

Fig. 6.26: Young’s moduli of different fiber materials

6.5.2 Geometry of the fibers

The wide variety of materials is the reason why there are so many variations of fibers.

Fig. 6.27: Geometry of the Fibers

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6 Properties

Each fiber is specified by the manufacturer in its length and diameter or equivalent diameter. This makes it possible to calculate the sheath area and also the volume of a fiber. Mf = df ∗ π ∗ l

(6.9)

V f = d 2 ∗ /pi/4 ∗ l

(6.10)

With the additional specification of the density of the fiber material, the weight of the individual fiber can be calculated. G f = Vf ∗ γ f

(6.11)

The fiber weight is needed when calculating the dosage of the fibers.

6.5.3 Geometry factor Since the fiber receives its force via the shear stress, the surface area is a crucial value for determining the fiber force. If the fiber is straight, the surface of a straight bar can be used and the above formula of the surface is correct. However, if the fiber is corrugated or deformed at the ends, the sheath area that the corrugated or deformed fiber has in the concrete at the face of the shear transfer must be determined.

Fig. 6.28: Influence of the fiber type on the geometry factor The geometry factor results from the ratio of the respective shell surface on which the shear stress acts to the shell surface of a straight round fiber.

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6.5 Composite effect of fibers

6.5.4 Dosage The dosage of a fiber is usually given in [kg/m3 ] of concrete. With the help of the geometric data such as diameter and length of a fiber, the volume can be determined. With the help of the weight of the fiber material, the dead weight of a fiber can be calculated. It is now possible to determine the number of fibers in a cubic meter of concrete using the dosage value. Based on this value, the number of fibers per cm3 and also the fiber density per cm2 must now be specified for the calculation of a design. If you divide this number of fibers of one m3 of concrete by 1 million, you get the number of fibers per cm3 . However, since the fiber is longer than 1 cm, it extends beyond this. Thus, as shown in the graph, depending on the length, there may be several fibers in the cm3 unit of space. The number is then the number of fibers times the length in cm.

Fig. 6.29: Explanation of fiber density

d f = (D f /G f )/1.000.000 ∗ l[ f ibers/cm2 ]

(6.12)

If all fibers were now aligned in one direction, the fiber density df would be calculated on the unit area cm2 . Using the surface area of the fibers in the unit cube of the concrete, the theoretical fiber stress can be calculated:

f f = τ0 /2 ∗ M f ∗ d f

(6.13)

In accordance with the experiments of Pfyl [55], half the shear stress τ0 (bond stress) of the concrete was used. Based on this fiber stress, the other influences must now also be duly taken into account.

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6 Properties

6.5.5 Spatial distribution of the fibers in the concrete Each fiber obviously has a different direction in the concrete. It must first be clarified how the fibers are spatially distributed and positionally oriented in the concrete. The single fibers are obviously arranged arbitrarily spatially so that it does not seem to make sense to read in the single fibers, but one should solve the problem from a theoretical point of view and then think about a possible maldistribution. In the following, this path is followed, whereby numerous examples applied in practice certainly support this type of distribution consideration.

Fig. 6.30: Concrete fracture with spatially distributed fibers If one assumes a uniform distribution of the fibers in the entire space, the spatial influence relative to the direction of the force can be easily understood. Assuming that each fiber has a different solid angle with respect to the force direction, the effect of each individual fiber in the force direction can be specified.

Fig. 6.31: Force corner for any fiber distributed in space If the longitudinal force in the fiber is taken as force 1, the force component acting in the force axis is 1 * cos α. The fibers lying in the concrete must be seen in relation to the respective direction of force.

6.5 Composite effect of fibers

105

If you look at the position of the fibers in relation to the direction of force, they are distributed in space. With this consideration, one does not get any further at first, unless one deals with the effect of the fibers during the force transmission. The fibers only have an effect along their axis.

Fig. 6.32: Fiber distribution shifted with respect to the direction of force If one looks at an arbitrary configuration of the fibers with respect to the force direction, one can also move the individual fibers here to the origin of the relative coordinate system without changing the spatial influence in the process. One then obtains an image in which all fibers pass through the origin and thus the angle α between the force direction and the respective fiber can be measured.

Fig. 6.33: Fiber distribution in relation to the direction of force

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6 Properties

With a spatially regular distribution of the fibers, each fiber must now have the same spatial angular distance from the next. This can be well represented with a hemisphere, which lies in the same origin as the fibers. The uniform angular spacing of the fibers results in an associated surface area on the surface of the hemisphere for each fiber that is always the same size. If this condition is met, the fibers are regularly distributed in space.

Fig. 6.34: Fiber distribution on a hemisphere In the illustration, the surface associated with a fiber is drawn in gray. The fiber penetrates this surface at the center of gravity. Thus, the regular distribution of the fibers in the concrete can be simulated via the surface distribution in the case of a hemisphere. For each of these partial surfaces, the angle α must now be calculated as a deviation from the direction of force. If we now look at a hemisphere and divide it into layers, each with a center angle of 10°, we obtain disks whose surfaces always have the same arc lengths on the hemisphere.

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6.5 Composite effect of fibers

Fig. 6.35: Section through hemisphere with layer separation Viewed in section, the same arc lengths can now be determined. In the example opposite, the semicircle has been divided into 10°slices, each of which has an arc length of: b = π ∗ r ∗ β /180

(6.14)

β ... Centre-angel (here 10°) With this arc length in the section, you can now form a square. In each layer, the number of squares of the same size can now be calculated.

Fig. 6.36: Hemisphere with uniform area division

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6 Properties

The center of gravity of these squares mapped on the hemisphere is then the piercing point of a fiber. Thus the angle α of the fiber is known and also the number of fibers in this layer.

Fig. 6.37: Calculation of the average fiber angle If one now forms the sum of the cosines obtained by the fibers and divides this value by the number of squares (fibers), one obtains the mean value of the cosine of the angle Œ±andthusalsotheangle± itsel f .A f terthiscalculation, onecanassumeamean f iberangleo f α = 60°. This average fiber angle ofα = 60°now represents the position of the fiber in relation to the direction of force. This can be used to determine the influence of the fiber on the fiber concrete. However, it should additionally be noted that the natural fiber distribution is an imperfect system, and thus the fibers are distributed somewhat disorderly in space. This uneven fiber distribution has a positive or negative influence depending on the direction of the force. For the design of a cross-section, the negative influence of an uneven spatial distribution of the fibers is decisive. The spatial effect of such an uneven fiber distribution is described by the increase of the fiber angle. It is now possible to either specify the misalignment angle directly or to assume it as a percentage depending on the mean fiber angle.

Fig. 6.38: Influence of loss of fiber strength due to faulty fibers The effect of the uneven fiber distribution of 4% results in a mean fiber direction of 62.5°inclination against the force direction and thus a force loss of 7.3% compared to a perfect spatial fiber distribution. In the absence of measured data, this assumption is used for further calculations. It is left to future measurements to determine the value of the missing fibers more precisely and then also to introduce it into a design.

6.5 Composite effect of fibers

109

6.5.6 Shape angle for power transmission As already described, the fibers differ not only in size but also in shape. This shape of the respective fiber affects on the one hand the fiber force, since the surface does not always correspond to the geometric producer specifications, but has a much larger surface due to, for example, wave shape, and on the other hand as a result of the bending up or volume changes the force effect can expand spatially significantly, This must be taken into account here. For the individual fiber shapes, the forces can be transmitted at a fiber angle dependent on the shape, deviating from the fiber axis. With the straight form, only an axis-parallel force transmission is possible, thus only shear forces along the fiber. In the case of the fiber with end hook (steel fiber), a force transmission of up to 10°deviating from the fiber axis is possible. Although the fiber is only bent in one plane, the angle is considered spatially as a mean. In the case of the end-squeezed fiber (steel fiber for shotcrete), a force transmission of up to 12°deviating from the fiber axis is also possible. This fiber is also only squeezed in the plane, but the effect can also be considered spatial. This compressed fiber (steel fiber) has a better spatial effect than the crushed one, therefore 15°can be used here as the angle between force transmission and fiber axis. The corrugated fiber (steel and plastic fiber) can achieve an angle of 25°between the force transmission and the longitudinal axis of the fiber due to the corrugation in one plane. The spatial situation is already taken into account here.

Fig. 6.39: Fibers with forming angle This allows the fiber angles for the different fiber shapes to be specified in summary, which must be taken into account in a design. This shape angle of the respective fiber used is taken into account together with the mean solid angle in the force transmission.

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6 Properties

6.5.7 Friction factors of the fibers The individual fibers each have a bond with the adjacent concrete. Depending on the roughness of the surface of the fiber, the bond can be adopted differently according to the concrete shear capacity. In the case of the fibers, however, the shear force transfer depends on the surface condition. Thus, the shear force can be transferred only partially. This must be taken into account with the corresponding friction factors ρ.

Fig. 6.40: Friction factors depending on surface condition With these friction factors, the forces that can be transmitted to the fiber can now be determined.

6.5.8 Determining the fiber tension The calculation of the fiber tension must now be considered from two sides: 6.5.8.1 From the concrete strain The concrete has a maximum specified tensile stress that it may absorb. With the E-modulus corresponding to the concrete quality, the corresponding concrete strain can be calculated: εc = maxσct ∗ Ec

(6.15)

This concrete strain also produces the same fiber strain ε f . From this fiber strain, one can now calculate the maximum fiber stress œÉf with the E-modulus of the fiber. maxσ f = ε f ∗ E f

(6.16)

This fiber tension of a single fiber can be reached at maximum. However, this is only possible if the fiber is aligned exactly in the direction of the applied concrete stress.

6.5 Composite effect of fibers

111

6.5.8.2 From the fiber characteristics The fiber tension in the total cross section can now be calculated with the following relationship: σ f t = τo /2 ∗ M f ∗ d f ∗ c f ∗ cos(α − δ ) ∗ ρ ∗ ce

(6.17)

...are there: σ f t ... Fiber tensile stress in concrete cross section [kN/cm2 ] τo ..... Concrete shear stress (bond stress) [kN/cm2 ] Fig. 6.6 M f .... Outer surface of a single fiber [cm2 ] Formula 6.9 √ d f .... Ares related dosage [St ck/cm2 ] Fig. 6.29 c f .... Geometry factor of the fiber [−] Fig. 6.28 α ..... Solid angle for the spatial distribution of the fibers [◦ ] Fig. 6.34 δ ..... Shape angle of the fiber [◦ ] Fig. 6.39 ρ ..... Friction factor of the fiber surface Fig. 6.40 ce ..... Stiffness factor E f /Ec This fiber tensile stress can now be added to the concrete tensile stress and the tensile stress for the fiber concrete is obtained. σ f ct = σ f t + σ f c

(6.18)

Now that the tensile stress of the fiber-reinforced concrete has been determined, it is also necessary to determine the compressive stress of the fiber-reinforced concrete. Since the tensile stress of the entire body increases as a result of the fiber addition, this also affects the compressive stress. This can be recognized from Mohr’s stress circle.

Fig. 6.41: Mohr’s stress circuit

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6 Properties

If the tensile stress increases, the shear line shifts parallel and a new compressive stress is created. This is calculated as: σ f ct = (σ f t ∗ σc )/σct

(6.19)

Now, the maximum permissible tensile and compressive stress can be used to design a homogeneous building material, as is the case with fiber-reinforced concrete.

6.6 Material testing experiments As with all building materials, a constant check of the mechanical characteristic values is necessary. Particularly in the case of composite building materials, as is the case with concrete as a starting material, the effect of adding fibers must be checked in the case of fiber-reinforced concrete. It is now up to the standardization in individual countries to specify the regularity of the examinations in order to ensure consistent quality.

6.6.1 Experimental arrangement There are several possibilities for investigating the material properties of fiber-reinforced concrete. In this book, three test engineering possibilities are shown, which differ in the geometry of the test specimens and the different loading equipment. First, the simplest test arrangement is described, which is geometrically and also experimentally possible. This is followed by the improved solution chosen by ArcelorMittal. Then the possibility, as it is also specified in the various German and also Austrian guidelines for fiber-reinforced concrete, is shown. The simpler geometric test arrangements offer the advantage over the standard arrangement that the crack that develops during the test always occurs at the same point as far as possible and can therefore be better documented. 6.6.1.1 Simple bending beam The first possibility to determine the material characteristics by testing is the simple bending beam. Here, for the beam with the dimensions 150/150/600 mm, the load is applied via a loading point. The dimensions are based on the proposal of the tests for fiber-reinforced concrete of the guidelines for fiber-reinforced concrete of Germany and Austria. The general size of the test

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6.6 Material testing experiments

specimens depends on the one hand on the aggregates of the concrete and on the other hand on the length of the steel fibers. The dimensions chosen here are to be regarded as sufficient for a maximum grain size of 22 mm and a fiber length of 60 mm.

Fig. 6.42: Simple bending beam for the test procedure In this configuration, the loading arrangement is simple and therefore less prone to error. The resulting crack is in the area of the beam centre and thus no longer free, but reasonably fixed by the loading arrangement. With this simple configuration, the crack is now roughly fixed and there is thus the possibility of precisely following and also documenting the crack in its formation during the test. Future documented tests will be able to provide detailed information about the crack initiation and its propagation, as well as the situation of the failure of the bending beam.

Fig. 6.43: Moment line due to simple load The moment line shows the maximum moment in the middle of the bar. This is calculated for this bar as follows: maxM = 300F/2[Nmm]

(6.20)

The resulting crack should actually occur at smaller loads as with the standard beam, since the moment is influenced by the larger edge distance. 6.6.1.2 Simple bending beam with notch At the suggestion of ArcelorMittal, the simple bending beam was slightly varied by cutting a notch in the beam so that the crack must start exactly at this notch. The geometric size was also

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6 Properties

changed somewhat, the beam was made 300 mm wide. The reason for this change was that when the test specimens were made, the steel fibers had mostly aligned themselves with the floor and as a result the spatial distribution of the steel fibers no longer appeared to be given. It was the wish to be able to exclude these edge influences at all costs when determining material characteristics. The depth of the notch of 30 mm was chosen in such a way that the spatial distribution of the fibers was absolutely given. The width of the test specimens was also increased to 300 mm in order to prevent lateral influences of the edge formwork.

Fig. 6.44: Simple bending beam with notch for test execution Thus, the edge influences are even smaller with the steel fiber arrangement, and the beam already shows a transition to the plate. With this improved configuration, the crack is now precisely fixed, and there is thus the possibility of very precisely following, measuring and also documenting the crack in its formation during the test. Future documented tests will be able to provide detailed information about the crack initiation and its propagation, as well as the situation of the failure of the flexural beam.

Fig. 6.45: Moment line due to simple load The moment line is similar to that of the simple beam, only the beam height reduced by the notch at the bottom must be taken into account when calculating the edge stresses. In the two pictures shown below, the crack development during a bending test can be seen very clearly. The crack goes from the notch at the bottom to the load beam above and can now also be examined more closely. The crack development in the course of the load can be traced very well with a suitable measuring device.

6.6 Material testing experiments

115

Fig. 6.46: Bending beam crack development (Image: FH Aachen) This proves that this is not a case of brittle fracture in steel fiber concrete, but that the influence of the steel fibers decisively changes the behavior of the composite construction material steel fiber concrete.

Fig. 6.47: Bending beam crack measurement (Image: FH Aachen) This shows a decisive difference to concrete as well as reinforced concrete in the material behavior, which proves to be particularly advantageous in practical application. This difference comes to bear in the case of failure of the building material fiber-reinforced concrete. Here, there is not the feared brittle fracture, but first a crack develops, which then continues according to the further load. The continuation of the crack then depends essentially on the fiber properties and the dosage of the fibers in the concrete. Basically, one can speak here of a post-crushing load-bearing capacity in which the component slowly loses its load-bearing capacity after the occurrence of the crack, whereby this can also still be controlled via the dosage.

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This type of test thus also allows the deformation along the crack to be monitored more precisely. With the arrangement of the transducers shown, the deformations at the individual beam heights can be observed and evaluated separately over the entire course of the test. This provides additional information about the condition 1–2 and its crack progression. Thus, the crack development can be precisely traced with the force action and thus the moment progression. Shown below are the two unfolded crack surfaces of the steel fiber reinforced concrete beam after the bending test.

Fig. 6.48: Bending beam crack surface (Image: FH Aachen)

6.6.1.3 Standard bending beam The tests are carried out on the basis of a standard bending beam as specified in the Fiber Concrete Guideline, which is shown in the following figure. This test setup is recommended by most German and Austrian guidelines, but is not mandatory from the point of view of determining the material properties.

Fig. 6.49: Bending beam for the test (Image: Krampe-Harex Fibrin GmbH)

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6.6 Material testing experiments

In the case of the bending beam in the picture, you can see the cracking on one side of the double load. This is the decisive point, which occurs freely. In this test, the crack can therefore develop completely freely between the two load points, since the local stress between the two load points is the same. The dimensioned drawing of the experiment is shown in the next figure.

Fig. 6.50: Standard bending beam for the test procedure By loading the beam at two points, it is achieved that the largest moment arising in the beam acts over a third of the length of the beam and thus the spatial distribution of the fibers must certainly come into play. Accordingly, the crack will occur freely between the two loads at the weakest point from the point of view of the material properties. The following figure shows the moment line that is generated with the load. The maximum moment extends across the middle area of the bending beam and reaches the following value:

Fig. 6.51: Moment line due to load

maxM = 200F/2[Nmm]

(6.21)

The individual tests should be displacement-controlled so that an accurate record of the load and the deformation of the bending beam is possible. The average deformation of the load points relative to the supports should be measured as the deformation displacement. This is usually the path of the load piston relative to the supports. Especially in the last load stages, it is necessary to observe the crack depth in the fiberreinforced concrete. This should also be recorded. It would be desirable to know at which load the crack depth of 50-90% of the beam height is reached, whereby the data should be given

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in steps of 10%. For this purpose, it is suggested that these beam heights be marked with pencil lines before the test.

6.6.2 Experimental procedure It would be desirable for a series of tests to be carried out on one day and by one test team. This is in order to achieve reproducibility. When selecting concrete, the same type of concrete with the specified maximum grain size should always be used for a series. Ready-mixes are recommended, because then the individual mixing ratios of the grain sizes are always constant. This results in no or only minor measurement differences. Water should be added to the dry mix until a W/B value of 0.5 is reached. If possible, a slump of 450 mm should be achieved in order to achieve good workability. The following volumes are to be achieved for the production of the test specimens: • One test body = 15.75 dm3 or 16 l corresponds to approximately 38 kg. • One test series = 3 test bodies = 47.25 dm3 or 48 l corresponding to approximately 114 kg. • Total test series = 3 test series = 142 dm3 or 142 l corresponds to approximately 342 kg. The distribution of the fibers should be specified for each series of tests. The concrete with the admixed fibers is to be placed in the respective formwork in one go and vibrated at the vibrating table until no more compaction takes place. Then cover the freshly concreted beam with a damp cloth and protect it from sunlight. After 24 h, the formwork is stripped and the beam is placed in a water bath, where it remains for 48 h before it has the remaining 25 days to harden in fresh air without sunlight, at temperatures of 5‚Äì25 °C. Only then are the load tests carried out. Only then are the load tests carried out. During the production of the beams, the following data is collected in each case: • Geometric data (length, width, height) • Concrete details (grading curve, origin of aggregate, cement content, cement type) • Concrete dry weight

6.6 Material testing experiments

119

• Water addition • Fiber addition (dosage) • Weight of fresh concrete with formwork • Weight after 7 days with formwork • Weight of the beam after 7 days without formwork • Weight of the beam after 28 days without formwork After the curing time of 28 days, the individual test specimens are loaded in the bending test. The deformation is increased in small steps and the respective associated load is measured. This is carried out throughout the test until the respective specimen has cracked at least 90% of its height. The deformation, the load and the crack depth are recorded in the corresponding log. In the first series of tests (without fiber), the test is terminated after the fracture, because the fracture goes through the entire cross-section and the load-bearing capacity is abruptly terminated. In the further series of tests, after the first crack, a change in load occurs with increasing deformation, with the crack depth increasing as a function of deformation. Here, the test is continued until the crack(s) have reached approximately 90% of the beam height. An essential part of the logging is the recording of the crack depth. The deepest crack is to be followed in each case. Even if several cracks occur, the deepest crack should be recorded, because this is where the stresses that are decisive for the total cross-section are present.

6.6.3 Evaluation of the measured data The individual test series must be produced and also carried out simultaneously with the same concrete mix in order to achieve absolute comparability. This is the only way to ensure that the influence of the fibers can be determined reproducibly from the tests. It is therefore recommended to mix the concrete for the entire series of tests and to place it in the prepared formwork. Although this requires a large number of moulds, it ensures that the same concrete can really be assumed. This means that the differences in the various test series can then really only be attributed to the dosage and the type of fiber.

7 FC dimensioning Static calculation is used to determine the forces and moments in a system (structure or component) that is to be implemented in nature. So the requirement of the load is known from the statics, now only the right material and its dimension must be found, which corresponds to these requirements. This conversion of forces and moments into materials and their dimensions is called dimensioning. Of course, the design of a building component is decisive for its load-bearing capacity and service life. Starting from the purely empirical values of earlier master builders, the detailed consideration of individual building materials became established at some point and their properties, such as strength and deformation behaviour, were studied in tests. This provided the basis for the calculation of the cross-section or the design, which was later also laid down in the standards of the individual countries.

7.1 Dimensioning procedure The design of a component is not only dependent on the forces acting on this component, but also on the materials to be used. The material properties, as determined for fiber-reinforced concrete in the last chapter, are of great importance. When designing a cross-section of a structural component, the following different systems are related to each other: - the static forces and moments; - the material properties; - the necessary security. Apart from the determination of the forces and moments in a cross-section, which are determined with more or less effort in structural analysis, the material properties have to be determined by laboratory tests. These determined values are naturally subject to scatter, and one must take this scatter into account when determining the material values to be used. This is prescribed in the various regulations for determining the characteristic values in the relevant standards.

© Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2021 B. Wietek, Fiber Concrete, https://doi.org/10.1007/978-3-658-34481-8_7

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7 FC dimensioning

122

In addition, the safety must be defined. This is to be understood as a factor that indicates by how much the considered value should actually be greater than the theoretical one in order to cover all contingencies and coincidences. This factor depends on the imaginable risk and the willingness to evaluate this risk in engineering terms. Design procedures that have evolved historically are addressed here to provide an understanding of how fiber-reinforced concrete is designed today.

7.1.1 Service load method The oldest and longest used method is the comparison of stresses. The loads are added together (service load) and the resulting stresses are determined in the respective component. These are then compared with the permissible stresses of the respective building materials. res σ

≤ per σ

(7.1)

The allowable stress of the individual materials were each provided with a safety factor over the break state hedged. σ f rac (7.2) η The safety is assigned as a value only to the building material. Thus, all risks are compensated with the one safety factor. per σ

=

This safety factor η was defined specifically for each building material.

Building material

Safety η

concrete

2,50

steel

1,70

timber

2,00

Table 7.1: Safety factors for the service load method

Thus, a dimensioning is or was relatively easy to perform. However, this had the disadvantage that no satisfactory statement could actually be made about detailed safety.

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7.1 Dimensioning procedure

In some areas of construction, this service load method is still used, but only where only a single building material is used. This design method has been abandoned for composite building materials.

7.1.2 Load method Since concrete exhibits a non-linear deformation behavior in compression, a new design procedure was introduced in 1953 that takes into account this special stress curve in concrete. In this process, the individual building materials are assigned limit deformations that must not be exceeded. When these limit deformations are reached in concrete and steel, the so-called ultimate load is reached in the cross-section. The limit deformations of the individual building materials were defined as follows: concrete upsetting

εc = 0, 002 or 2 per mill

steel expansion

εs = 0, 004 or 4 per mill

The stres-strain curve in the compression area of the concrete has been defined as a parabola, and thus a bearing load S* can be calculated for a cross-section. If one now compares this ultimate load with the loads determined from the static calculation, the service load S, the design equation looks as follows: ν ∗ S ≤ S∗

(7.3)

Here ν tis he safety of the ultimate load and is assigned to the load. This safety factor ν is specifically defined for reinforced concrete. Building material

safety ν

Reinforced concrete

1,75

Table 7.2: safety factor for the ultimate load method

This rigid assignment of safety values either to the building material or to the load can be accepted, but it always leads to uncertainties in the assessment of a condition. Therefore, in recent years, there has been an increasing shift to the next method, which is somewhat more in line with the engineering understanding of the assignment of safety.

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124

7.1.3 Design with partial safety factors From the discussion of safety in the ultimate load method, the safeties have now been directly assigned to the individual areas and the situation can thus be better assessed in each case. Both the loads and the building materials are assigned the corresponding safety values. This results in the following design equation: νL ∗ S ≤ S∗ /νR

(7.4)

The corresponding safety factors for the forces acting on the static system have been introduced as follows: forces

safety νL

Permanent load

1,35

=ne variable load

1,50

Multible variable loads

1,35

Table 7.3: Safety of the forces in the ultimate load method

Therefore, the different safeties must already be taken into account in the load combination of the static calculation in order to calculate the load of the cross-section as a total value. Since the safeties must already be taken into account in the various load combinations, the use of the safety of the forces is already taken into account in the static calculation, so that these are already dealt with in the actual design of a cross-section. In any case, it must be explicitly stated in the structural analysis whether or not the safety factors have already been taken into account. Thus, only the safeties for the different building materials need to be taken into account. Materials

safety νR

Concrete

1,50

Steell

1,15

Proposal for fiber

1,35

Table 7.4: Safety of the building materials in the ultimate load method

These safeties are to be applied when using the corresponding building material. In the absence of a standard specification for the fiber, a rather conservative value is suggested here, which should be used until another value is shown to be appropriate in practice.

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7.2 Reliability concepts

If the total safety is calculated, this results in the value used in the ultimate limit state method. ν = νL ∗ νR

(7.5)

Thus, the overall security is given, but a much greater transparency is achieved for the individual states.

7.2 Reliability concepts So how do you arrive at the safety factors? They are certainly not adopted by chance. Here, too, a comprehensible system is expected. This system is the reliability concepts. This is where the values for the required individual safeties are determined. There are different methods of obtaining these values. These are described in a little more detail in the next points.

7.2.1 Deterministic reliability principle The collateral values are determined on the basis of experience. The amount is freely determined and provides the corresponding collateral for the respective situation. This principle is therefore based exclusively on empirical values, which are of course always adjusted by special events. Especially in the case of new building materials, this safety determination is made on the basis of comparable building materials in order to have at least an initial safety. Later, these values are improved on the basis of experience and measurements. For fibers in the building material fiber reinforced concrete, a safety of νR = 1.35 is initially proposed here. This is somewhat higher than the comparable steel safety of 1.15. After an introduction period of 3‚Äì5 years, this deterministic value should be reviewed again or replaced by a probabilistic value. This system of deterministic safety values is difficult to understand and is therefore used less and less or replaced by the following principles.

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7.2.2 Probabilistic reliability principle Here, the values of the safety are determined with the aid of probability methods. This applies in particular to the safety of the building materials, since the quality is subject to a greater or lesser degree of scatter. The scatter of the measured values and their frequency distribution are measured and the required safety is derived from this. For a structure, the largest load case to be expected must always be smaller than the smallest resistance on the part of the building materials. moreover, it should still be possible to achieve a distance between these two values. The problem is that all values are derived from statistical calculations (material values) and the reliability to be calculated is determined by probability considerations (loads).

7.2.3 Semiprobabilistic reliability principle In this principle, the values determined in the probability method are replaced by characteristic values specified in regulations. The partial safety factors are also set as fixed values. This provides the designer with a quite clear method of calculation, since all safety factors are of comprehensible origin and also reach a comparable level. A distinction is made between two concepts, each of which must be demonstrated.

7.2.4 Verification of structural safety This is considered to be fulfilled if the following equation is met: Sd ≤ Rd means: Sd ... the design value of the stress (loads) and Rd ... the rated value of the resistance (materials).

(7.6)

127

7.2 Reliability concepts

The design value of the stress is the product of all load effects multiplied by the respective partial safety factors γs . Sd = γs ∗ Sk

(7.7)

The partial safety factors γ for the stress can be taken from the following table. load effect

unfavorable

constantly

1,35

variable just a load

1,50

variable more loads

1,35

prestressing

1,00

favorable

1,00

Table 7.5: Partial safety factors for load stresses

Also, the design value of the resistance emanating from the building materials is the limit value of the resistance of the material load divided by the corresponding partial safety factors.

Rd =

Rk γR

(7.8)

The partial safety factors γ for this are also given below: partial safety

concrete γc

steel γy

fiber γ f

basic combination

1,50

1,15

1,35

exceptional combination

1,30

1,00

1,15

Table 7.6: Partial safety factors for material resistance

In the above table, the safeties for the fiber are given as deterministic values. After an application period of 3–5 years, these values should be replaced by a measured value so that an equivalent safety assessment is available. With these partial safety factors for the loads and also for the materials, the design of the individual cross-sections can now be carried out.

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7 FC dimensioning

7.2.5 Verification of suitability for use The serviceability check verifies whether the components (materials) can actually absorb the load effects without damage. This is called the serviceability. In most cases, the deformation in the form of deflection or crack widths is recalculated. In the different standards, there are the maximum permissible values of the deformations, which are specified differently depending on the component and also the building material.

7.3 Dimensioning theorie

129

7.3 Dimensioning theorie The characteristic values for the fiber-reinforced concrete determined in Section 6 are now used for the design. For the actual dimensioning of a component, there are generally two possibilities. Firstly, the dosage, that is, the material composition of the component is searched for, secondly, the required cross-section of a component is searched for given material composition. Both methods are known in structural design engineering. Thus, the material composition is used in reinforced concrete construction and the cross-section search is used also in timber and steel construction.

7.3.1 Dimensioning for material selection - dosage 7.3.1.1 Bending 7.3.1.1.1 Condition 1 (not cracked): The bending measurement, which is provided for beams and slabs, can be carried out according to the following calculation procedure. Following [25] and [24] , the individual calculation steps are now carried out with the support of graphical representations. Fiber-reinforced concrete is a composite building material consisting of concrete and fibers. In state 1, that is, uncracked, this building material is to be regarded as a continuum that reacts according to the material properties of a solid. In state 1, all stress curves in the cross-section are linear. The compressive and tensile stresses at the edge of the cross-section are equal, but with the opposite effect. Since the compressive stress fc1 is far below the maximum permissible compressive strength fc f k , a linear stress curve is given in any case.

Fig. 7.1: Condition 1, Concrete is uncracked

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130

The following stress analysis is carried out with the possible limit stresses. This means that the cross-section is considered under the maximum possible stresses. In state 1, this is the limit state that prevails shortly before the cross-section tears. With the tensile stress component from the fiber concrete, the tensile force in the cross-section can now be determined: Z = fc f tk ∗ h/2

(7.9)

For reasons of equilibrium, the compressive force must now be equal to the tensile force and act in the opposite direction (actio = reactio). Now, using the relationship shown in the previous figure, you can calculate the maximum moment that can occur in state 1, or this moment can be absorbed by the given cross-section at most in state 1. M = 2/3 ∗ Z ∗ h

(7.10)

In most cases, the beam cross-section and the moment are given from the static calculation and one will now change the fiber quantity until one has reached an overview of the moments that can be absorbed in state 1.

Fig. 7.2: Rectangular beam with specified values It is therefore proposed to perform these calculations with a variation in the dosage of the fibers. In the present case, both a steel fiber and a plastic fiber were included in the calculation in order to show the difference in the load-bearing capacity of the two types of fiber.

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131

A hooked end fiber from Arcelor was calculated as the steel fiber, since this fiber is one of the most widely used steel fibers. In comparison, a plastic fiber from Propex, the permanently corrugated Enduro 600, was used, as this is also one of the most common plastic fibers in structural engineering.

Fig. 7.3: Load-bearing moments for condition 1 as a function of dosage for two types of fibers The above figure gives an impression of the load-bearing moments that can be absorbed in state 1. The moment in state 1 was determined for the specified girder made of fiber-reinforced concrete C25 with a steel fiber or with a plastic fiber. The data for the fibers used were obtained from back calculation of examples from practice. The calculation in detail is shown in the next chapter.

7.3.1.1.2 Condition 1-2 (partly cracked) If the determined bearing moment of state 1 is exceeded, the composite material fiber-reinforced concrete cracks. However, this crack does not occur suddenly, but because of the fibers present everywhere, the concrete slowly cracks from its tensile side to beyond the centre of the component. In contrast to reinforced concrete, where the cracked state 2 is assumed to be the maximum cracked state in the calculation, with fiber-reinforced concrete the individual partial steps of the advancing concrete crack must be considered separately. This leads to the fact that first a small crack is assumed, which then becomes larger and larger until the possible final state is reached. Since the force system of the internal forces changes during this process, it makes sense to pay special attention to these individual partial steps. In states 1 and 2, the stresses are assumed to be linearly distributed, just as in state 1. The

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concrete stress fc2 can assume a value up to fc f k . In a first observation, the crack is still small, so that the concrete still has a triangular stress distribution and can also still absorb tensile stresses. The stress pattern is similar to that of state 1, except that in the area of the crack only the fibers are still bearing. Here, the fibers take on the full specific fiber stress f f k,2 [N/mm2 ], although this is only half of the fiber stress in the uncracked state due to the cracked situation.

Fig. 7.4: Condition 1-2, concrete is partially cracked In order to arrive at the tensile or compressive force here, x,y and fc2 must first be calculated. The following relationships can be derived from the geometric relationships as shown in the drawing: a = y−r

h = x+y

(7.11)

fc f tk fc f tk ∗ (h − y) fc2 = fc2 = (7.12) x y−r y−r Now the compressive force and the two tensile forces can be written down as a formula: D = fc2 Zc = fc f tk

fc f tk ∗ x ∗ (h − y) x = 2 2 ∗ (y − r)

(7.13)

y−r 2

(7.14)

Z f = f f k,2 r

D = Zc + Z f

(7.15)

From these equations, the height of the tension zone can be calculated using the following equation y = (r2 − h2 −

2 ∗ f f k,2 ∗ r2 2 ∗ f f k,2 ∗ r ) / (2r − 2h − ) fc f tk fc f tk

(7.16)

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7.3 Dimensioning theorie

When inserted into the previous equations, D and Z can be calculated. The lever arm of the moment is calculated as: z=

2x Zc + 3

2(y−r) 3

+ Z f ( 2r + y − r) Zc + Z f

(7.17)

and thus the support moment that can be absorbed: M = D∗z

(7.18)

It is now possible to calculate the change in moment with increasing crack. In the following figure, the same beam was used as for the non-cracked state and thus one can see the development of the moment absorption starting from the non-cracked state up to a crack width of 90% of the beam height.

Fig. 7.5: Load-bearing moments with increasing crack If the crack becomes so large that the concrete edge stress fc2 is greater than fc f k , this calculation must be aborted and the perfect crack state in state 2 determined.

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7 FC dimensioning

7.3.1.1.3 Condition 2 (maximum cracked) In this state, the cross-section is cracked in the entire tensile area, only in the compressive area the concrete still takes over forces. In the tensile area, only the fibers are still involved in the force transfer. The graphical representation of this is shown in Fig. 7.6. This relationship is taken from SIA [30].

Fig. 7.6: Condition 2, concrete is maximaly cracked The calculation of the compression and tension range is calculated to: D = 0, 8 ∗ fc f k ∗ x

(7.19)

Z = f f k,2 ∗ y

(7.20)

and the ruptured zone: y=

h f

1 + 0,8f k,2 f

(7.21)

cfk

And now the bearing moment for the maximum torn cross-section to: M = D∗z

(7.22)

In order to see the properties of the cross-section with varying dosage, the moments for the different dosages are now calculated. It is normally the case that the cross-section with a crack bears less than in state 1; however, this also depends to a large extent on the dosage. Thus, the dosage of the fibers can be adjusted until the required load-bearing moment is reached.

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135

Fig. 7.7: Load-bearing moments for condition 2 as a function of the dosage Figure 7.7 gives an impression of the load-bearing moments that can be absorbed in state 2. The same beam was used as for the example with non-cracked state and the ultimate moment in state 2 was determined. The data for the fibers used were obtained from back calculation of examples from practice. The calculation in detail will be shown in more detail in the next chapter.

7.3.1.2 Bending with longitudinal force

Only the compressive force is considered here as the longitudinal force. The design for the tensile force is currently not recommended, as the calculation method has not yet been developed and the building material fiber-reinforced concrete does not appear to be very suitable for tensile forces. In this case, other building materials such as steel or reinforced concrete are recommended. The bending with longitudinal force is separated into three different parts according to the different calculations. According to the center of the compressive force, it is distinguished, as is already common in reinforced concrete, into: • Small eccentricity: cross section is uncracked; linear stress state • Mean eccentricity: cross section is cracked, nonlinear stress state • Large eccentricity: cross section is cracked, nonlinear stress state

The individual calculations are looked at in more detail in the following subsections.

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136

7.3.1.2.1 Small eccentricity The uncracked cross-section in state 1 shows only linear stress states due to its low eccentricity of the compressive load. The limit state is calculated here, whereby smaller moments can always be allowed.

Fig. 7.8: Stress state at small eccentricity According to the stress distribution shown in the figure, the following relationships can be identified: fc1 = σn + σm

(7.23)

fc f tk = −(σn − σm )

(7.24)

From the normal force, the stress œÉn can be calculated by dividing the load by the crosssectional area. Now the stress œÉm can be determined from one of the two stresses of the fiber concrete: σm1 = fc f k − σn

(7.25)

σm2 = fc f tk + σn

(7.26)

When comparing the calculated stresses σm1 and σm2 there are 3 possibilities: • σm1 > σm2 permissible; Normal force could be increased • σm1 = σm2 permissible; Normal force is utilized • σm1 < σm2 mean eccentricity must be expected.

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137

In the first two cases, the calculation can be continued with a small eccentricity. The moment that can be absorbed is now calculated from the boundary stresses: M = σm2 ∗

b ∗ h2 6

(7.27)

The corresponding moment can now be calculated from the variation of the fiber dosage. Since the fc f k and fc f tk increase slowly with increasing dosage, each dosage must be calculated separately. The comparison with the moment required from the static calculation then results in the dosage of the fiber concrete. 7.3.1.2.2 Mean eccentricity If in state 1 the uncracked cross-section on the compression side has a non-linear stress distribution, similar to the stress distribution of concrete in state 2, average eccentricity is to be expected.

Fig. 7.9: Stress state at mean eccentricity If one looks at the limit state, the boundary stresses are: σmd = fc f k − σn

(7.28)

σmz = fc f tk + σn

(7.29)

In order to calculate the absorbable moment in this stress state as well, several intermediate steps are necessary, which can be derived from Fig. 7.9. h = a+b+c

(7.30)

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138

b D = σmd ∗ (a + ) = Z = σmz ∗ c 2 σmd σmz = b c From the last Eq. (7.32), one can determine b: b=

(7.31)

(7.32)

c ∗ σmd σmz

(7.33)

If we now substitute b into the first Eq. (7.30), we can resolve it to a: a = h − c ∗ (1 +

σmd ) σmz

(7.34)

This result, now finally substituted into the second Eq. (7.31), gives: h ∗ σmd

c=

σ2

(7.35)

σmd + 2∗σmdmz + σ2mz With these three lengths a, b and c, the compressive force and also the tensile force of the same magnitude can now be calculated: b c D = σmd ∗ (a + ) Z = σmz ∗ (7.36) 2 2 Attention, the beam width must also be taken into account here. This is not shown in the formula above, as the width is normally calculated as 1 m for slabs. For other beam widths, this must be used accordingly. The lever arm between the tensile and compressive force z is calculated proportionally towards the neutral line for the compressive force zd and separately for the tensile force zz and then added to the total lever arm. First the lever arm for the compression force: zd =

σmd ∗ a ∗ (b + 2a ) + σmd ∗ b2 ∗ 2∗b 3 σmd ∗ (a + b2 )

(7.37)

And now the lever arm for the traction: 2 ∗c 3 Thus, the total lever arm for the moment is calculated to: zz =

(7.38)

z = zd + zz

(7.39)

These sizes can now be absorbed by the cross-sectional moment load capacity calculated:

139

7.3 Dimensioning theorie

M = D∗z = Z ∗z

(7.40)

The corresponding moment can now be calculated from the variation of the dosage of the fibers. Since the values fc f k and fc f tk increase slowly with increasing dosage, each dosage must be calculated separately. The comparison with the moment required from the static calculation then results in the dosage of the fiber concrete. 7.3.1.2.3 Large eccentricity As soon as the stress fc f tk is exceeded on the tensile side, the fiber-reinforced concrete cracks. Thus, a new type of stress distribution occurs in the crosssection. In order to achieve a differentiation from the systems in the non-cracked state, the cracked state for bending with longitudinal force (compression) is referred to as the load case of the large eccentricity.

Fig. 7.10: Stress state at large eccentricity We will refrain from calculating this load case for the time being, because there are several reasons why such cross-sections should not be permitted. • Pressure components such as columns should not have any cracks. • Basement walls should not have cracks because of moisture sealing. • Cracked walls and columns create insecurity for users. It is left to a future treatment of this chapter to complete the detailed mathematical and static calculations for this load case.

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140 7.3.1.3 Compression struts

Pure compression bars are a special feature of the load. The load that can be absorbed depends not only on the base material, but the buckling of the compressed cross-section must also be investigated. The buckling of the straight compression member is explained in detail by Fritsche [21] and Lohmeyer [24]. It is recommended to read this static literature when working on compression members in more detail. The definition of the stable, indifferent and unstable equilibrium is the basis for the introduction of the different loading cases. The four Euler buckling cases are introduced here, which must be considered for all compression members.

Fig. 7.11: Buckling according to Euler The mathematical static solution leads via differential equations to relatively complex solutions, which additionally depend on the different materials. Therefore, the different material properties must be taken into account in the calculations of the buckling cases For concrete, the plastic stress range must be considered in addition to the elastic stress range. The solution for this was worked out by Engesser and can be found in Valentin [10]. The result leads to the well known ω-method, in which the vertical buckling load is related to the vertical ultimate load based on the material properties. Nk ω The relationship of ω is shown in the following formula. N∗ =

(7.41)

λ 2 λ 2 ) ]∗( ) (7.42) 100 100 The occurring number λ is the slenderness of the compression member. This depends on the buckling length lk according to Euler and the radius of gyration i of the cross section. ω = 1 + 0, 1 ∗ [6 + (

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7.3 Dimensioning theorie

λ=

lk i

r i=

(7.43)

I A

(7.44)

Here, I is the moment of inertia of the cross-section and A is the associated cross-sectional area. ω–values λ = lk /i

0

2

4

6

8

0

1,00

1,00

1,00

1,00

1,00

10

1,01

1,01

1,01

1,02

1,02

20

1,02

1,03

1,03

1,04

1,05

30

1,05

1,06

1,07

1,08

1,09

40

1,10

1,11

1,12

1,13

1,14

50

1,16

1,17

1,18

1,20

1,21

60

1,23

1,25

1,26

1,28

1,30

70

1,32

1,34

1,36

1,38

1,40

80

1,42

1,45

1,47

1,50

1,52

90

1,55

1,58

1,61

1,64

1,67

100

1,70

1,73

1,77

1,80

1,84

110

1,87

1,91

1,95

1,99

2,03

120

2,07

2,11

2,16

2,20

2,25

Table 7.7: Buckling values ω for concrete

For a compression member, the buckling load can now be determined using the following formula: N∗ =

A ∗ fc f k ω

(7.45)

Since the value fc f k increases slowly with increasing dosage, each dosage must be calculated separately. If the corresponding partial safety factors are then taken into account, the dosage for the pressure component can be determined.

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142 7.3.1.4 shear check

If we look at the course of the internal forces in a single-span beam, we first determine the shear force, which indicates how the vertical forces run in a beam, and then the moments. If both are considered together, as is possible in the following figure, it can be seen that the two curves are quite different. Where the shear force is at a maximum, the moment line shows a minimum and vice versa. This means that the smallest shear force is at the maximum moment. If you move from the maximum moment in the direction of the support, the moment decreases with a simultaneous increase in the shear force.

Fig. 7.12: Single span beam shear force and moment line

If we now look at the effect of the moment on the cross-section, the already familiar picture of the stress distribution in the cross-section emerges. Each moment generates stresses in the cross-section, which in turn can be combined into forces and, with the lever arm, result in the respective moment. Thus, at the maximum moment, the stresses σd and σz arise. If the moment becomes smaller, one moves more towards the support, smaller stresses σo and σu arise.

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7.3 Dimensioning theorie

Fig. 7.13: Stress distribution in the beam

For all these stresses, an associated shear stress τ can be recorded in each case. According to Coulomb’s law of matter, these are calculated as follows: τ = τc + σ ∗ tan(ϕ)

(7.46)

The shear stress τc is the shear strength of a material and can be calculated from the compressive strength fc f k using the following formula: fc f k ϕ ∗ tan(45 − ) (7.47) 2 2 These connections become clear in the presentation of Mohr’s circle and can be traced there. τc =

Fig. 7.14: Mohr’s stress circle with shear stress Thus, if for each stress σ one obtains an associated shear stress τ, this is confusing at first, but

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144

when considering a linear stress profile in the cross-section, a simple picture emerges.

Fig. 7.15: Shear stress in the cross-section according to Coulomb In state 1 (uncracked cross-section), the two external stresses œÉo and œÉu are equal in magnitude, only they have different signs. They oscillate around the 0-point and thus generate shear stresses which, on average, also oscillate around the shear strength τc . Thus, for a cross-section in state 1, one can certainly use the average value τc over the entire cross-section. Thus, the shear force that can be absorbed in a cross-section is given by: Qk = A ∗ τc

(7.48)

where A is the cross-sectional area of the component under consideration. The result is the shear force that can be absorbed by a cross-section as a function of the compressive strength: fc f k ϕ ∗ tan(45 − ) (7.49) 2 2 Since the two values fc f k and ϕ change with increasing dosage of fibers and thus the shear forces that can be absorbed increase, the respective shear strength must be determined. Qk = A ∗

145

7.3 Dimensioning theorie 7.3.1.5 Breakout of a support

In the case of a support of a beam or also a slab, all forces are diverted. In the process, situations arise in the vicinity of the support that can lead to the support breaking away. This can generally occur through two different types of failure: • Punching through - failure due to exceeding of the shear force at the bearing section. • Breakout - failure due to exceeding the tensile force in an inclined fracture joint. The case of punching is carried out in the shear force check, so it does not need to be considered further here. An inclined fracture line or fracture surface is considered during breakout. In this case, a fracture line or fracture surface is to be found that has the lowest safety for the forces to be absorbed. If one looks at the situation now, the position of the fracture surface is an important assumption in the calculation.

Fig. 7.16: Possible fracture situation for a support The length of the fracture surface changes with the choice of the fracture angle α. This must be taken into account when checking the forces and stresses that occur. d (7.50) cosα With this oblique length, the fracture surface Ab can now be determined for both a beam and a slab. If we now consider the possible forces in the fracture surface, the bearing force is divided into a shear force acting parallel to the fracture surface and a tensile force acting perpendicular to the fracture surface. l=

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146

Fig. 7.17: Force corner in the oblique fracture joint at angle α These forces occurring in the fracture surface can be converted into the corresponding stresses: τ = A ∗ sin(α)

σ = A ∗ cos(α)

(7.51)

These two stresses must be taken at arbitrary angles. The shear stress τ is certainly not the problem, since this has already been verified on a smaller area for punching with the shear force. Thus, the possible tensile stress in the fracture joint must now be verified.

Fig. 7.18: Distribution of tensile stresses as a function of the fracture angle for an example In a practical example, the tensile stress occurring at the fracture joint under a changing fracture angle was recalculated for a beam, and a maximum was found at an angle α = 45°. Therefore, the tensile stress must be verified for this fracture angle.

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7.3 Dimensioning theorie

The tensile stresses that occur are now compared with the tensile stresses that can be absorbed. The tensile stress that occurs must now be multiplied by the partial safety factor for the loads as the design value of the stress: σd = σ ∗ νL

σr = ( fctk + f f k1 ) ∗ νB

(7.52)

The design value of the resistance that can be calculated from the material is calculated with the sum of the material strengths. The rated stress of the load must now be lower than the rated stresses of the resistor. σd < σr

(7.53)

Since the values fc f k change with increasing dosage of fibers and thus the tensile forces that can be absorbed increase, the respective tensile strength must be determined.

7.3.2 Dimensioning for cross-section selection - Dimensioning The design for the material selection has shown that the calculated cross-section has the best load-bearing capacity in the non-cracked state. An increase in the load-bearing capacity into the cracked state can only be achieved with a fairly large dosage of fibers. Then, however, because of the consideration of the safety factors, the state of the cross-section is still in the uncracked state, since the maximum increase in the possible load is smaller than the safety factor then takes away again. The question therefore arises as to whether it is economical to calculate at all in the cracked state for fiber-reinforced concrete or not. In the following calculations for the design, the building material fiber-reinforced concrete has the decisive advantage over reinforced concrete that the entire non-cracked cross-section is available for watertightness, for example, for external basement walls. This means that the thickness of the outer basement wall can be reduced to the statically necessary dimension and no longer necessarily requires the usual 30 cm.

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148 7.3.2.1 Bending

The design of a cross-section for the stress case bending is based on the limit case at which the tensile stress reaches the maximum possible stress. With this assumption, the necessary height of the cross-section is determined. The composite material fiber-reinforced concrete can be considered as a continuum in the uncracked state. Since the maximum permissible stresses are different for tension and compression, the lower stress must be considered decisive for the stress case of bending. In the present case, this is the tensile stress.

Fig. 7.19: Condition 1 concrete is uncracked The material is specified in its composition. Thus, the concrete strength class and the choice of fiber together with the necessary dosage are assumed to be given. The tensile strength of the composite material fc f tk [kN/cm2 ] can be calculated using the material values. Since the two edge stresses must be equal in the non-cracked state, this results in the following relationships: fc1 = fc f tk bh 2h bh2 ∗ = fc f tk ∗ 4 3 6 With this you can now calculate the required height of the cross section to: M = Z ∗ z = fc f tk ∗

s hmin =

6M b fc f tk

(7.54) (7.55)

(7.56)

If the required partial safety factors for the loads γs = 1.35 and the partial safety factor for fiber-reinforced concrete γc f = 1.50 are now also taken into account, the following formula relationship results:

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7.3 Dimensioning theorie

s her f =

6 M γs γc f b fc f tk

(7.57)

This height must be maintained as a minimum in order to be able to absorb the required moment.

7.3.2.2 Bending with longitudinal force Only the compressive force is considered here as the longitudinal force. The design for the tensile force is currently not recommended, as the calculation method has not yet been developed and the building material fiber-reinforced concrete does not appear to be very suitable for tensile forces. In this case, other building materials, such as steel, are recommended. The bending with longitudinal force is separated into three different parts according to the different calculations. According to the eccentricity of the compressive force, it can be divided, as is already common in reinforced concrete, into: • Small eccentricity: cross section is uncracked; linear stress state. • Mean eccentricity: cross section is uncracked, nonlinear stress state. • Large eccentricity: cross section is cracked, non-linear stress state. The individual calculations are examined in more detail in the following subsections, whereby the condition with a large eccentricity is omitted here, since in this condition the cross-section is partially cracked and thus no longer fully effective.

7.3.2.2.1 Small eccentricity Due to its small eccentricity of the compressive load, the uncracked cross-section shows only linear stress states, whereby the occurring tensile stress can be absorbed by the building material fiber-reinforced concrete. The limit state of the possible boundary stresses is calculated here, at which the tensile stress is maximally utilized. Smaller moments can always be allowed if the maximum tensile and compressive stresses are not exceeded.

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150

Fig. 7.20: Stress state at small eccentricity According to the stress distribution shown in the figure above, the following relationships can be identified: fc1 = σn + σm

(7.58)

fc f tk = −(σn − σm )

(7.59)

The stresses σn and σm are to be calculated from the specified stresses. The stresses can be determined with the cross-section height h, which is still unknown: N bh

(7.60)

M M 6M = 2 = 2 bh W bh

(7.61)

σn =

σm =

6

Substituting these two equations into Eq. (7.59) for fc f tk , we obtain the following expression: fc f tk =

6M N − bh2 bh

(7.62)

After transforming this equation by multiplying by bh2 , we get: h2 b fc f tk + hN − 6M = 0 This quadratic equation can be solved, and it gives the height h to:

(7.63)

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h=

−N +

p N 2 + 24Mb fc f tk 2b fc f tk

(7.64)

With this height, the stresses σn and σm must now be calculated and thus the boundary stress fc1 . If the value of fc1 is smaller than fc f k , the height h is sufficient and the design is completed. However, if the value of the boundary stress fc1 is greater than fc f k , the boundary stress is exceeded and the height must be calculated with the mean eccentricity.

7.3.2.2.2 Mean eccentricity With relatively high compressive forces, it can happen that the maximum possible stress of fc f k is reached or even exceeded at the compression edge. This compressive stress in excess of fc f k cannot be absorbed and the concrete enters a creep movement. This is maintained until the moment equilibrium assumes a stress state in which the edge stress does not exceed the value fc f k . The cross-section should be dimensioned in such a way that only the compressive stress fc f k occurs on one edge and the tensile stress fc f tk on the other edge. The distribution of the stresses in the cross-section is shown in the following graph.

Fig. 7.21: Stress state at mean eccentricity This condition is a limit case that has not yet been worked through in its full consequence. It should be borne in mind that the compressive force has reached its maximum and, as in the limit case in reinforced concrete, no longer exhibits linear stress-deformation behavior at the edge. A linear relationship is given in the plot shown, but this is an approximation. Furthermore, it is not

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clear how far this reduced stress range (dimension a in the illustration) extends. Even with these currently still very uncertain boundary conditions, relatively complicated systems of equations result for the determination of the height hat a given dosage, which have not yet been solved. It is therefore proposed to exclude this design case for dimensioning and to calculate for the small eccentricity using the relationships shown. This results in only slightly larger component dimensions, which are, however, on the safe side.

7.3.2.3 Compression struts Pure compression bars are another type of load. The load that can be absorbed depends not only on the base material used, but the buckling of the compressed cross-section must also be investigated. The buckling of the straight compression member is explained in great detail by Fritsche [21] and also Lohmeyer cite Lohmeyer. It is recommended to consult this structural analysis literature when working on compression members in more detail. The definition of stable, indifferent and unstable equilibrium is the basis for the introduction of the different loading cases. The four Euler buckling cases are introduced here, which must be considered for all compression members.

Fig. 7.22: Buckling cases according to Euler The mathematical static solution leads via differential equations to relatively complex solutions, which additionally depend on the different materials. Therefore, the different material properties must be taken into account in the calculations of the buckling cases. For concrete, the plastic stress range must be considered in addition to the elastic stress range. The solution for

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this was worked out by Engesser 1 and can be found in Valentin [25]. The result leads to the well-known ω-method, in which the vertical buckling load is related to the vertical ultimate load based on the material properties. Nk ω The relationship for ω is shown in the following formula. N∗ =

(7.65)

λ 2 λ 2 ) ]∗( ) (7.66) 100 100 The occurring number λ is the slenderness of the compression member. This depends on the buckling length lk according to Euler and the radius of gyration i of the cross section. ω = 1 + 0, 1 ∗ [6 + (

r

I (7.67) A With this slenderness, the slenderness of the compression member can now be determined, taking into account the buckling length that results according to the respective Euler case. i=

lk (7.68) i Here I is the moment of inertia of the cross section A is the corresponding cross-sectional area. With this value of slenderness either the necessary buckling value ω can be calculated with formula (7.66), or the buckling coefficient ω can be taken from Table 7.7, whereby intermediate values can also be interpolated. For a compression member, the buckling load can now be determined using the following formula: λ=

A ∗ fc f k (7.69) ω For the design, the cross-section must now be varied until the result meets the requirements. This means that for each assumption, the radius of inertia and the slenderness must be determined separately before the buckling load of this cross-section is calculated. N∗ =

1 F.

Engesser 1848-1931; TH-Karlsruhe

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154 7.3.2.4 shear check

If we look at the course of the internal forces in a single-span beam, we first determine the shear force, which indicates how the vertical forces run in a beam, and then the moments. If both are considered together, as is possible in the following figure, it can be seen that the two curves are quite different. Where there is a maximum for the shear force, there is a minimum for the moment line and vice versa. This means that the smallest shear force is at the largest moment. If you move from the maximum moment towards the support, the moment decreases while the shear force increases. The maximum shear force occurs at the support. The shear force must be verified here. Since in fiber-reinforced concrete the stresses that can be absorbed depend on the selected dosage in both the compressive and tensile ranges, the moment coverage, which contains the dosage, must first be verified. The maximum possible tensile stresses fc f tk are then known, which must be greater than the occurring tensile stress σz . If we now look at the effect of the moment on the cross-section, the already familiar picture of the stress distribution in the cross-section emerges. Each moment generates stresses in the cross-section, which in turn can be combined to form forces and, together with the lever arm, produce the respective moment.

Fig. 7.23: Single span beam shear force and moment line

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7.3 Dimensioning theorie

At the maximum moment occurring in a beam due to the load, the compressive stress σd and the tensile stress σz thus arise. If the moment becomes smaller, one moves more towards the support, smaller stresses σo and σu arise.

Fig. 7.24: Stress distribution in the beam For all these stresses, an associated shear stress τ can be recorded in each case. According to Coulomb’s law of matter, these are calculated as: τ = τc + σ ∗ tan(ϕ)

(7.70)

The shear stress τc is the shear strength of a material and can be calculated from the compressive strength fc f k using the following formula: τc =

fc f k ϕ ∗ tan(45 − ) 2 2

(7.71)

These connections become clear in the presentation of Mohr’s circle and can be traced there.

Fig. 7.25: Mohr’s stress circle with shear stress

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Thus, if for each stress σ one obtains an associated shear stress τ, this is confusing at first, but when considering a linear stress profile in the cross-section, a simple picture emerges.

Fig. 7.26: Shearing stress in cross-section according to Coulomb

In state 1 (uncracked cross-section), the two external stresses are equal in magnitude, but they have different signs. They oscillate around the 0-point and thus generate shear stresses that also oscillate around the shear strength τc on average. Thus, for a cross-section in state 1, one can certainly use the average value τc over the entire cross-section. Thus, the shear force that can be absorbed in a cross-section results in: Qk = A ∗ τc

(7.72)

where A is the cross-sectional area of the component under consideration. Now the absorbable shear force of a cross-section results as a function of the compressive strength: Qk = A ∗

fc f k ϕ ∗ tan(45 − ) 2 2

(7.73)

Since the two values fc f k and ϕ do not change based on the concrete parameters with a given dosage of steel fibers, the necessary cross-sectional area can be calculated for a given shear force. A=

2Qk fc f k ∗ tan(45 − ϕ2 )

(7.74)

Based on this cross-sectional area, the height of a beam with width b can now be determined: h=

A b

(7.75)

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7.3 Dimensioning theorie

The shear force can also occur as a punching force for slab supports. In this case, the crosssectional area is to be seen as the area of the circular section around the support, and this is calculated from the circumferential length of the support U and the slab height h. Here again, the necessary height of the ceiling can be determined as follows:

h=

A U

(7.76)

Thus, the proof of punching through ceilings is also verifiable.

7.3.2.5 Breakout of a support

This verification should be performed in addition to the verification of punching. It is performed in the manner described in Chapter 7.3.1.5.

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7.4 Dimensioning samples The desire to use the building material fiber-reinforced concrete in general is increasing more and more. It is shown here that fiber-reinforced concrete is not easy to design, but that some steps have to be taken in the calculation. This is due to the material properties of the composite building material fiber-reinforced concrete. In practice, the following applications exist for fiber-reinforced concrete: - Screeds - Base plates and troughs - Stripes and point foundations - Ceilings, circumferential and point supported - Walls - Piles and supports - Support general and independent of form As can already be seen in the determination of the material characteristics, the fiber-reinforced concrete can be considered in three states.

Condition

description

1

The entire cross-section is uncracked and there is linear stress distribution

1-2

The cross section is partially cracked and there is linear stress distribution

2

The cross section is maximally cracked and there is non-linear stress distribution

Table 7.8: Possible states in the design of fiber-reinforced concrete

For all design types, the individual cross-sections must now be checked for the three possible states. The respective load type indicates which design calculation method is to be used. The individual relationships were described in detail in the last chapter. The design of the fiber-reinforced concrete cross-section is shown here using examples that follow the structure of the design theory in the sequence. The examples are taken from practice

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159

and have therefore already been carried out in part. Since the building material fiber-reinforced concrete is mixed as a whole for a component, the maximum stress on the entire component must be investigated in each case when designing a component. The same cross-section shape is assumed. As soon as the cross-section changes, the design must be carried out again with the new cross-section. This has the consequence that an adjustment to the static forces can be carried out with the help of cross-section changes..

7.4.1 Cross-section in bending For building materials to be used in structural engineering, the load case of bending is particularly important. Since the cross-section of fiber-reinforced concrete is uniformly mixed with fibers, the direction of the moment is also irrelevant, since the building material can also absorb the same moments in any direction with the same cross-section. The material properties indicate whether a building material can be subjected to static and dynamic stresses. In the field of civil engineering, these are primarily building materials that do not exhibit any time-dependent deformations. This is the case with fiber-reinforced concrete. In the following, examples are calculated which have been taken from practice and are also intended to be representative of the application.

7.4.1.1 Plastic fiber

Two examples are given here to illustrate the different use of plastic fibers in pure bending design. Hall floor In the case of industrial halls, the floor is usually designed to be trafficable and also has the additional requirement of transferring relatively high concentrated loads such as the support loads of racks or high racks or also of machine supports. In the following case, paper machines are installed in a factory hall, which introduce relatively high concentrated loads into the floor slab and must be distributed or absorbed by it. The following figure shows a section through the workshop, with the floor structure indicated in more detail. The size of the individual slab elements is indicated as 6.0/6.0 m in each case.

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Fig. 7.27: cross section of the hall The loads to be included in the dimensioning of the base plate are determined by the intended use and also by the machine weights.

Fig. 7.28: Load data for the floor With a static calculation, the moments for this slab were now determined, whereby the corresponding safeties are already included here.

Fig. 7.29: Moments to be absorbed in the floor slab With the values entered, the fiber density and the fiber tensile stress of the fiber concrete can now be determined. Here is the calculation for the dosage 5 kg/m3 :

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161

Fig. 7.30: Input data for calculating with enduro HPP 45

With the entered values the fiber density and fiber tension of the fiber concrete can now be determined. Here the calculation of the dosage 5 kg/m3 : d f = D ∗ 1000/g f /(100 ∗ 100 ∗ 100) ∗ l f /10 = 5 ∗ 1.000/0, 032/(1.000.000) ∗ 45/10 = 0, 70 f f k1 = τo /2 ∗ O f ∗ d f ∗ cα ∗ cg ∗ ce = 0, 400/2 ∗ 141, 4/100 ∗ 0, 70 ∗ cos(57, 22 − 25) ∗ 2, 5 ∗ 0, 22 = 0, 093 Now the tensile strength and the compressive strength can be determined according to the Mohr‚ÄìCoulomb approach as described in Section 6 for the individual dosages. A crack fraction of 10% is taken into account. fc f tk = fctk + f f k1 = 0, 256 + 0, 093 = 0, 350 [kN/cm2 ] fctk = fc f tk / fctk ∗ fck = 0, 350/0, 256 ∗ 2, 50 = 3, 41 [kN/cm2 ] The width of the cross-section to be designed is now entered as well as the moment to be covered with the required safety factors, then the actual calculation can be carried out.

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Fig. 7.31: Geometry and moments and safeties The safety of the loads has already been taken into account when determining the moments, hence the value 1.0 here. Following the input, the calculation of the strength loaded with the respective safety is carried out. Now the tensile force for state 1 can be calculated and thus also the load-bearing moment for the specified dosage.

Fig. 7.32: Result of the calculation fc f ts = fc f tk /η f b = 0, 350/1, 25 = 0, 280 [kN/cm2 ] fc f s = fc f k /η f b = 3, 41/1, 25 = 2, 73 [kN/cm2 ] Ms = Md /ηl = 26, 90/1, 0 = 26, 90 [kNm] This allows the required section modulus to be determined for rectangular cross-sections with a given boundary stress. With this required section modulus, the required height of the crosssection can be calculated: er fW = Ms ∗ 100/ fc f ts = 26, 90 ∗ 100/0, 280 = 9.611 [cm3 ] er f h =

p p 6 ∗ er fW /b = 6 ∗ 9.611/100 = 24, 0 [cm]

The result shows that a floor slab with fiber concrete made of plastic fiber is very possible. In practice, several floor slabs have already been produced with plastic fiber.

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7.4 Dimensioning samples

staircase Precast stairs are being used more and more in residential buildings. The following example shows how a precast staircase consisting of straight flights of stairs can be designed with fiberreinforced concrete. An exposed concrete quality is required here. This is the reason why a synthetic fiber was chosen here. There is no change to the surfaces and therefore the staircase can also be used as exposed concrete in its raw state.

Fig. 7.33: straight stair flight The following dimensions and also force effects are taken from the static calculation of the stair flight: Staircase width = 1.20 m Staircase construction height = 20 cm maximum bending moment in the plate M = 17 kNm (without safety) With these basic values, a dimensioning of the stair flight can already be carried out. As materials the fiber type and dosage as well as the concrete quality are to be indicated. In the present case, a concrete for precast elements of grade C30 is used. A synthetic fiber, Enduro 600, is selected as the fiber and a dosage of 5 kg/m3 is used.

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Fig. 7.34: Input data for calculation

With the values entered, the fiber density and the fiber tensile stress of the fiber concrete can now be determined. Here is the calculation for the dosage 5 kg/m3 : d f = D ∗ 1000/g f /(100 ∗ 100 ∗ 100) ∗ l f /10 = 5 ∗ 1.000/0, 020/(1.000.000) ∗ 50/10 = 1, 24 f f k1 = τo /2 ∗ O f ∗ d f ∗ cα ∗ cg ∗ ce = 0, 466/2 ∗ 117, 8/100 ∗ 1, 24 ∗ cos(57, 22 − 25) ∗ 2, 5 ∗ 0, 21 = 0, 154 Now the tensile strength and the compressive strength can be determined according to the Mohr‚ÄìCoulomb approach as described in section 6 for the individual dosages. A crack fraction of 10 % is taken into account. fc f tk = fctk + f f k1 = 0, 290 + 0, 154 = 0, 444 [kN/cm2 ] fctk = fc f tk / fctk ∗ fck = 0, 444/0, 290 ∗ 3, 00 = 4, 50 [kN/cm2 ] The width of the cross-section to be designed is now entered as well as the moment to be covered with the required safety factors, then the actual calculation can be carried out.

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Fig. 7.35: Geometry and moment and safeties Following the input, the calculation of the strength loaded with the respective safety is carried out. Now the tensile force for state 1 can be calculated and thus also the load-bearing moment for the specified dosage.

Fig. 7.36: Result of the calculation fc f ts = fc f tk /η f b = 0, 444/1, 35 = 0, 329 [kN/cm2 ] fc f s = fc f k /η f b = 4, 60/1, 35 = 3, 40 [kN/cm2 ] Ms = Md /ηl = 15, 6/1, 35 = 21, 06 [kNm] This allows the required section modulus to be determined for rectangular cross-sections with a given boundary stress. With this required section modulus, the required height of the crosssection can be calculated: er fW = Ms ∗ 100/ fc f ts = 21, 06 ∗ 100/0, 329 = 6.407 [cm3 ] er f h =

p

6 ∗ er fW /b =

p

6 ∗ 6407/100 = 19, 6 [cm]

The result shows that a staircase slab with fiber-reinforced concrete made of synthetic fiber is very possible. In practice, several staircase slabs have already been produced with synthetic fiber, including spiralled stair flights, as shown in the next chapter.

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7.4.1.2 Steel fiber

Test plate in Bissen (Luxembourg) In 2004, ARCELOR manufactured a point-supported steel fiber concrete slab and subjected it to a load test. The slab consisted of a total of 9 square panels of 6/6 m each. The panels were arranged in a 3/3 square so that three panels were continuous in each direction. The slab was supported by steel columns at each corner point, so that one must speak of a punctiform support. The slab thickness was designed with a uniform 20 cm throughout. Only steel fiber concrete was used, and no additional measures were taken in the support areas either. It is shown here with the design that this slab meets all safety requirements with the boundary conditions specified there. The load was applied in the midspan by slowly filling water tanks while recording the deformations of the slab very accurately. With an applied load from the water tanks of 8 kN/m2 of the midspan, the largest vertical deformations of the slab were measured at 12 mm, with no cracks yet appearing. The static recalculation of the test slab resulted in the following values, which are used in the design of steel fiber concrete: System length 6.0 m Total load q = 11kN/m2 maximum bending moment M = 16.9 kNm Slab thickness 20 cm Concrete type C20 Steel fiber TABIX

The cross-section of the experimental panel is shown in Fig. 7.37. A top view of the plate is shown in the following figure, from which the field division can be seen.

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Fig. 7.37: Test plate cross-section

Fig. 7.38: Top view of test plate

Figure 7.39 shows the detailed input for the calculation performed using an EXCEL spreadsheet. After entering the site data, a fiber is selected. The steel fiber TABIX 1/30 is used and the corresponding fiber properties are given. Afterwards the concrete type C20 is entered and the corresponding concrete characteristic values are given.

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Fig. 7.39: Input field of the design for fiber-reinforced concrete With these values, the fiber density and the fiber tensile stress of the respective fiber concrete can now be determined. Here the calculation for the dosage 40 kg/m3 with a missing fiber value of 10%: d f = D ∗ 1000/g f /(100 ∗ 100 ∗ 100) ∗ l f /10 = 40 ∗ 1000/0, 186/(1.000.000) ∗ 30/10 = 0, 65 f f k1 = τo /2 ∗ O f ∗ d f ∗ cα ∗ cg ∗ ce = 0, 332/2 ∗ 94, 2/100 ∗ 0, 65 ∗ cos(57, 22 − 25) ∗ 2, 5 ∗ 1, 0 = 0, 171 Now the tensile strength and the compressive strength can be determined according to the Mohr‚ÄìCoulomb approach as described in Section 6 for the individual dosages. A crack fraction of 10% is taken into account. fc f tk = fctk + f f k1 = 0, 221 + 0, 171 = 0, 392 [kN/cm2 ] fctk = fc f tk / fctk ∗ fck = 0, 392/0, 221 ∗ 2, 00 = 3, 55 [kN/cm2 ] Then the height and width of the cross-section to be designed are entered. Finally, the moment to be covered is specified with the required safety, then the actual calculation can be performed.

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169

Fig. 7.40: Enter the dimensions of the moment and the safety Following the input, the calculation of the strength specified with the respective safety is carried out. Now the tensile force for state 1 can be calculated and thus the load-bearing moment for the respective dosage.

Fig. 7.41: Determination of the load-bearing moments that can be absorbed for the fiberreinforced concrete The individual calculation steps are now given here for the dosage of 40 kg/m3 : fc f ts = fc f tk /η f b = 0, 541/1, 35 = 0, 401 [kN/cm2 ] fc f s = fc f k /η f b = 2, 72/1, 35 = 2, 02 [kN/cm2 ] Ms = Md /ηl = 16, 9 ∗ 1, 5 = 25, 35 [kNm] This allows the required section modulus to be determined for rectangular cross-sections with a given boundary stress. With this required section modulus, the required height of the crosssection can be calculated: = Ms ∗ 100/ fc f ts = 25, 35 ∗ 100/0, 401 = 6.321 [cm3 ] p p 6 ∗ er fW /b = 6 ∗ 6.321/100 = 19, 47 [cm] req h = reqW

The calculation shows that with a dosage of 40 kg/m3 and a safety factor for the load of 1.5, the required load-bearing moment of 16.9 [kNm] is achieved.

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The steel fiber slab calculated here was manufactured by Arcelor in 2004 as a test slab and subjected to a detailed load test. The recalculation confirms that slabs with fiber-reinforced concrete are feasible in principle and also economical. If one thinks in particular of the usually complicated laying of reinforcement bars, one recognizes here one of the main advantages of fiber concrete. The span width of 6.0 m selected for this test slab is certainly a limit value of the span width for economic applications, but it has been proven that in residential construction, where span widths are usually less than 5.0 m, an economic application of this building material is given.

Fig. 7.42: Test plate 1 and load 2 of the Bissen 2004 test; Image: ArcelorMittal

The two pictures show the steel fiber concrete slab first unloaded and in the right picture with the applied load by the water canisters. The results of the present calculation now also show the proof of load-bearing capacity mathematically in a very well reproducible form, which can be used in practice for most applications.

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Hall floor In the following, the slab for the hall floor already designed with a plastic fiber (Fig. 7.27) is designed with the load data (Fig. 7.28) and the moments (Fig. 7.29) for a steel fiber and the required slab thickness is calculated. With the values given in Section 7.4.1.1, a design for steel fibers can now be carried out. In the present case, a concrete grade C 25 is assumed, to which steel fibers of the type TABIX 1/30 are added at a dosage of 40 kg/m3 .

Fig. 7.43: Input data for calculation with TABIX 1/30l

With the values entered, the fiber density and the fiber tensile stress of the fiber concrete can now be determined. Here is the calculation for the dosage 50 kg/m3 : d f = D∗1000/g f/(100∗100∗100)∗l f /10 = 40∗1.000/0,186/(1.000.000)∗30/10 = 0,65[Stk/cm2 ] f f k1 = τo /2 ∗ O f ∗ d f ∗ cα ∗ cg ∗ ρ ∗ ce = 0, 537/2 ∗ 94, 2/100 ∗ 0, 65 ∗ cos(66 − 25) ∗ 2, 0 ∗ 0, 7 ∗ 1 = 0, 173[kN/cm2 ] Now the tensile strength and the compressive strength can be determined according to the Mohr‚ÄìCoulomb approach as described in Section 6 for the individual dosages.

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fc f tk = fctk ∗ 1, 8 + f f k1 = 0, 256 ∗ 1, 8 + 0, 173 = 0, 635 [kN/cm2 ] fctk = fc f tk /( fctk ∗ 1, 8) ∗ fck = 0, 537/(0, 256 ∗ 1, 8) ∗ 2, 50 = 3, 44 [kN/cm2 ] The width of the cross-section to be designed is now entered as well as the moment to be covered with the required safety factors, then the actual calculation can be carried out.

Fig. 7.44: Geometry and moment and safeties

The safety of the loads has already been taken into account when determining the moments, hence the value 1.0 here. Following the input, the calculation of the strength loaded with the respective safety is carried out. Now the tensile force for state 1 can be calculated and thus also the load-bearing moment for the specified dosage.

Fig. 7.45: Result of the calculation

173

7.4 Dimensioning samples fc f ts = fc f tk /η f b = 0, 635/1, 35 = 0, 470 [kN/cm2 ] fc f s = fc f k /η f b = 3, 44/1, 35 = 2, 55 [kN/cm2 ] Ms = Md /ηl = 26, 90/1, 0 = 26, 90 [kNm]

This allows the required section modulus to be determined for rectangular cross-sections with a given boundary stress. With this required section modulus, the required height of the crosssection can be calculated: reqW

req h

= Ms ∗ 100/ fc f ts = 26, 90 ∗ 100/0, 470 = 5.723 [cm3 ]

=

p

6 ∗ er fW /b =

p

6 ∗ 5.723/100 = 18, 53 [cm]

The result shows that a floor slab with fiber concrete made of steel fiber is very possible. In practice, numerous floor slabs have already been produced with steel fibers.

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174 7.4.1.3 Glass fiber

In the booklet Glasfaserbeton - Konstruieren und Bemessen (Glass fiber reinforced concrete design and dimensioning) published by Beton-Verlag, examples are given, whereby an example is to be recalculated here in order to obtain a comparison of the calculation methods. In contrast to the usual structural components in the building industry, glass fiber concrete is used to produce quite thin-walled structural components such as slabs, angles and tubes in various geometric designs. A GFB facade panel fixed to a substructure is loaded by wind with a surface load of 1.40 [kN/m2 ]. A span width of 70 [cm] results in a moment to be transferred of: M = q x l 2 / 8 = 1,4 x 0,72 / 8 = 0,086 [kNm] This moment is to be absorbed by the 10 mm thick glass fiber concrete. For the comparative calculation, a concrete grade of C25 is used and the F 18 A fiber is calculated with a usual dosage of 4 [kg/m3 ].

Fig. 7.46: Static system of a facade slab

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175

The calculation of the glass fiber concrete is carried out in the same way as for the steel and plastic fiber concrete.

Fig. 7.47: Input field of the design for fiber-reinforced concrete With the values entered, the fiber density and the fiber tensile stress of the fiber concrete can now be determined. Here is the calculation for the dosage 4 kg/m3 : d f = D∗1000/gf/(100∗100∗100)∗l f /10 = 4∗1000/0,000015/(1.000.000)∗18/10 = 472[Stk/cm2 ] f f k1 = τo /2 ∗ O f ∗ d f ∗ cα ∗ cg ∗ ρ ∗ ce = 0, 537/2 ∗ 1, 13/100 ∗ 472 ∗ cos(60 − 0) ∗ 1, 0 ∗ 0, 8 ∗ 1 = 0, 573[kN/cm2 ] Now the tensile strength and the compressive strength can be determined according to the Mohr‚ÄìCoulomb approach as described in Section 6 for the individual dosages. fc f tk = fctk ∗ 1, 8 + f f k1 = 0, 256 ∗ 1, 8 + 0, 573 = 1, 035 [kN/cm2 ] fctk = fc f tk /( fctk ∗ 1, 8) ∗ fck = 1, 035/(0, 256 ∗ 1, 8) ∗ 2, 50 = 5, 60 [kN/cm2 ] The width of the cross-section to be designed is now entered as well as the moment to be covered with the required safety factors, then the actual calculation can be carried out.

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176

Following the input, the design of the strength loaded with the respective safety is carried out. Now, the required cross-section height is determined if the allowable tensile stress or the allowable compressive stress is used. This results in the required section heights in both cases. These must now be examined to determine whether the other stress is also permissible. This then results in the decision which of the two sides (compression side or tension side) is decisive for the cross-section height.

Fig. 7.48: Geometry and forces and safeties for the GFB plate

Fig. 7.49: Result of the calculation for the GFB plate In the present case, a slab thickness of 0.94 cm is sufficient in this design cross-section. In the calculation from the booklet for glass fiber concrete, a calculation thickness of 0.9 cm is assumed, at which the required safeties for the glass fiber concrete are verified. Thus, there is a good agreement between the dimensioning of the two documents and thus the calculation shown can also be regarded as quite applicable, as it is also on the safe side. GFB components are usually thin-walled components due to the relatively high fiber price, which are usually used in the assembly process. The production of these components is usually carried out by casting or injection moulding, whereby the components are usually produced in prefabricated moulds as formwork.

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177

7.4.2 Cross-section in bending with normal force The load case bending with longitudinal force occurs very often, especially with wall-like components and beams. Particularly in the case of walls, water tightness often plays a decisive role. Here, fiber-reinforced concrete has a considerable advantage as a building material in the non-cracked state, since the entire cross-section serves to repel water and thus the cross-section does not become permeable to water due to any cracks. This is a particularly frequent requirement for walls in the subsoil, also for bank constructions and structures located on or in the water.

7.4.2.1 Plastic fiber

The use of a macro fiber is shown here, with which the concrete is reinforced in order to also be able to transfer bending moments. The use of synthetic fibers is particularly recommended for the construction of underground walls, as further advantages can be exploited in addition to the load-bearing properties. The use of a plastic fiber for components in contact with groundwater has two advantages over other solutions, namely: –No corrosion can occur, as there are no steel parts in the component. –The watertightness is guaranteed by the entire uncracked cross-section. For underground walls, diaphragm walls have become established as excavation pit walls or also as bank shoring walls. The particular advantage lies in the low deformation of these constructions, even though they are subject to very high loads. In the following, a diaphragm wall is recalculated which was constructed as a reinforced concrete wall and it is to be shown by this calculation that this diaphragm wall can also be produced equivalently by a fiber-reinforced concrete wall with synthetic fibers. The excavation pit has a total depth of 11.0 m and is excavated in both intermediate sections at 3.0 and 8.0 m and anchored in each case before the final state is excavated. With the calculation of the moment distribution, one can recognize the two maximum acting cross sections with their moments. For the design, however, not only the moment but also the longitudinal force present in the respective cross-section is important. This is caused by the dead weight of the wall up to the calculation cross-section.

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Fig. 7.50: Diaphragm wall with indication of moment distribution

In the following, the two most highly stressed cross-sections are shown with their respective loads:

Section

Depth

Moment

Normal force

[m]

[kNm]

[kN]

First

5,0

150

-100

End

12,5

180

-210

Table 7.9: Stress on the diaphragm wall

With these loads, a design is now carried out for the diaphragm wall with fiber concrete of concrete strength class C25 using the Enduro 600 fiber with a dosage of 5 kg/m3 .

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Fig. 7.51: Input field of the design for fiber-reinforced concrete

With the values entered, the fiber density and the fiber tensile stress of the fiber concrete can now be determined. Here is the calculation for the dosage 5 kg/m3 : d f = D ∗ 1000/g f /(100 ∗ 100 ∗ 100) ∗ l f /10 = 5 ∗ 1000/0, 020/(1.000.000) ∗ 50/10 = 1, 24 f f k1 = τo /2 ∗ O f ∗ d f ∗ cα ∗ cg ∗ ρ ∗ ce = 0, 537/2 ∗ 117, 8/100 ∗ 1, 24 ∗ cos(66 − 25) ∗ 2, 5 ∗ 1, 0 ∗ 0, 22 = 0, 142[kN/cm2 ] Now the tensile strength and the compressive strength can be determined according to the Mohr‚ÄìCoulomb approach as described in Section 6 for the individual dosages. fc f tk = fctk ∗ 1, 8 + f f k1 = 0, 256 ∗ 1, 8 + 0, 142 = 0, 604 [kN/cm2 ] fctk = fc f tk /( fctk ∗ 1, 8) ∗ fck = 0, 604/(0, 256 ∗ 1, 8) ∗ 2, 50 = 3, 27 [kN/cm2 ] The width of the cross-section to be designed is now entered, as well as the moment to be covered and the acting longitudinal force with the required safety factors, then the actual calculation can be carried out.

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Fig. 7.52: Geometry and forces and safeties at 5 m depth

The input is followed by the calculation of the strength to which the respective safety is applied. Now it is examined which cross-sectional height is necessary if the permissible tensile stress or the permissible compressive stress is utilized in each case. This results in the required crosssection heights in both cases. These must now be examined to determine whether the other stress is also permissible. This then results in the decision as to which of the two sides (compression side or tension side) is decisive for the cross-section height.

Fig. 7.53: Result of the calculation at 5 m depth

In the present case, a diaphragm wall thickness of approximately 53.3 cm is sufficient in this design cross-section. As there are no diaphragm wall grabs in this width, the next grab width must be used. This is 60 cm. It will now be seen in the second design cross-section in 12.5 m whether the diaphragm wall thickness of 60 cm can be found to be sufficient. Now, however, the second design cross-section at a depth of 12.5 m must be recalculated.

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Fig. 7.54: Geometry and forces and safeties at 12.5 m depth

Following the input, the strength loaded with the respective safety is calculated again. Now it is examined which cross-section height is necessary if the permissible tensile stress or the permissible compressive stress is utilized in each case. This results in the required cross-section heights in both cases. These must now be examined to see whether the other stress is also permissible. This then results in the decision as to which of the two sides (compression side or tension side) is decisive for the cross-section height.

Fig. 7.55: Result of the calculation at 12.5 m depth

In the present case, a diaphragm wall thickness of approximately 57 cm is sufficient in this design cross-section. This now shows that the diaphragm wall with a thickness of 60 cm can also be safely produced with a fiber concrete and is capable of absorbing the static forces that occur. If we now think of underground situations where the soil or groundwater is saline, corrosion cannot occur in the diaphragm wall, which is made with plastic fiber. This is an important aspect especially near the coast for all seas. If corrosion is no longer an issue in harbor constructions, the maintenance costs of these walls are many times lower than if steel parts are built into the wall, for example, as reinforcement.

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182 7.4.2.2 Steel fiber

Another application of fiber-reinforced concrete in practice is a basement wall in an apartment building.

Fig. 7.56: Section of a multi-family house in Winklarn A basement wall is to be constructed in fiber concrete with steel fibers. The section shown reveals an excavation pit with a depth of 3.4m. The resulting working space will be backfilled after construction, creating an earth pressure on the basement wall. This earth pressure must be transferred together with the wall load from the ground floor and the wall loads above. When determining the earth pressure, an increased earth pressure is to be applied, whereby the entire earth pressure of the backfill space is to be calculated on the basement wall in order to be additionally on the safe side.

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The building material used is a normal concrete of strength class C25. For the fiber, the choice fell on a steel fiber HE 55/35 with a desired dosage of max. 40 kg/m3 .

Fig. 7.57: Input field of the design for fiber-reinforced concrete With the values entered, the fiber density and the fiber tensile stress of the fiber concrete can now be determined. Here is the calculation for the dosage 40 kg/m3 : d f = D ∗ 1000/g f /(100 ∗ 100 ∗ 100) ∗ l f /10 = 40 ∗ 1.000/0, 0656/(1.000.000) ∗ 35/10 = 2, 14 f f k1 = τo /2 ∗ O f ∗ d f ∗ cα ∗ cg ∗ ρ ∗ ce = 0, 537/2 ∗ 60, 47/100 ∗ 2, 14 ∗ cos(66 − 10) ∗ 1, 0 ∗ 0, 7 ∗ 1 = 0, 136[kN/cm2 ] Now the tensile strength and the compressive strength can be determined according to the Mohr‚ÄìCoulomb approach as described in section 6 for the individual dosages. fc f tk = fctk ∗ 1, 8 + f f k1 = 0, 256 ∗ 1, 8 + 0, 136 = 0, 598 [kN/cm2 ] fctk = fc f tk /( fctk ∗ 1, 8) ∗ fck = 0, 598/(0, 256 ∗ 1, 8) ∗ 2, 50 = 3, 24 [kN/cm2 ] The width of the cross-section to be designed as well as the moment to be covered and the acting longitudinal force are now entered. The moment is generated by the determined earth pressure acting on the wall, which can be calculated with a span of 2.70 m. The moment can be calculated by entering the required safety factors. After entering the required safety factors, the

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Fig. 7.58: Geometry and forces and safeties for basement wall Following the input, the strength loaded with the respective safety is calculated. Now it is examined which cross-section height is necessary if the permissible tensile stress or the permissible compressive stress is utilized in each case. This results in the required cross-section heights in both cases. These must now be examined to see whether the other stress is also permissible. This then results in the decision as to which of the two sides (compression side or tension side) is decisive for the cross-section height.

Fig. 7.59: Result of the calculation for basement wall In the present case, a basement wall thickness of 25 cm is sufficient. This now shows that the basement wall with a thickness of 25 cm can be constructed with a fiber concrete and is capable of absorbing the static forces that occur. In addition, it should be noted that the 25 cm thick wall is in any case impermeable to water, since it is not cracked on the full wall thickness, and thus fully complies with the requirement of a basement wall with respect to damp proofing.

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7.4.3 Cross-section in compression (buckling) Here, mainly columns and wall-like supports are considered, which are mainly loaded by vertical loads. The respective bearing of the column at the bottom and top must be determined and calculated according to the Euler fillings for buckling.

7.4.3.1 Plastic fiber In an underground car park, the wall elements are to be made of fiber concrete. Because of the possible salt fogging in the driving area, a plastic fiber is to be used in order to avoid problems with corrosion of the components.

Fig. 7.60: Input field of the design for fiber-reinforced concrete The specification for the concrete quality came from the C30 floor concrete and Enduro 600 was selected as the synthetic fiber, whereby a dosage of max. 5 [kg/m3 ] was desired. The fiber density and the associated fiber tensile stress are calculated according to the previous examples and do not need to be repeated here. As a result of the building material values, a tensile strength of 0.617 [kN/cm2 ] and a compressive strength of 3.55 [kN/cm2 ] were calculated.

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Fig. 7.61: Geometry and forces and buckling case After entering the geometric sizes and the type of support (Euler case), the buckling length, the cross-section values and the buckling value ω can be calculated as explained in Section 7.3.2.3. After the necessary specification of the vertical load and the safeties for the building material fiber concrete and the load, the normal force can now be determined with certainty.

Fig. 7.62: Result of the calculation for the columns with buckling load After calculating the buckling load and the permissible buckling load calculated with consideration of the corresponding safety, a comparison of the loads can now be made: Ns ≤ Nzul

Ns = 12.150kN ≤ Nzul = 12.192kN

The buckling load capacity for this wall column has thus been verified.

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7.4.3.2 Steel fiber A rectangular column in a shopping arcade is designed here, which is only loaded with compressive forces. The design is carried out with the buckling check according to Euler’s load cases.

Fig. 7.63: Input field of the design for fiber-reinforced concrete The specification of the concrete quality came from the slab concrete C25 and HE 55/35 was chosen as the steel fiber, with a dosage of max. 30 [kg/m3 ] being used. The fiber density and the corresponding fiber tensile stress are calculated according to the previous examples and the calculation procedure does not need to be repeated here. The fiber density is 1.60 [pcs/cm3 ] and the fiber tensile stress is 0.102 [kN/cm2 ]. As a result of the building material values, a tensile strength of 0.557 [kN/cm2 ] and a compressive strength of 3.02 [kN/cm2 ] were calculated.

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Fig. 7.64: Geometry and forces and buckling case After entering the geometric quantities and the type of support (Euler case), the buckling length, the cross-section values and the buckling value ω can be calculated as explained in Section 7.3.2.3. After the necessary specification of the vertical load and the safeties for the building material fiber concrete and the load, the normal force can now be determined with certainty.

Fig. 7.65: Result of the calculation for the columns with buckling load After the necessary specification of the vertical load and the safeties for the building material fiber concrete and the load, the normal force can now be determined with certainty. Ns ≤ Nzul

Ns = 2.889kN ≤ Nzul = 2.916kN

This provides evidence of the buckling load capacity for these columns.

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7.4.4 Cross section on shear force These verifications are usually carried out in the support area of beams and slabs. As in the case of a usual beam static analysis, a beam loaded with a uniform load is to be statically analyzed according to the moment line and shear force line. The largest values of the moments and also of the shear forces must be verified.

Fig. 7.66: Single span beam with shear force and moment line As shown in Fig. 7.66, the highest shear forces are at the supports. Thus, in most cases, the shear forces must be verified in these areas. 7.4.4.1 Plastic fiber The shear check for the precast staircase in the area of the stair support is shown here.

Fig. 7.67: Detail of stair support for shear check

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The specification of the concrete quality for the prefabricated staircase was C30 and the plastic fiber Enduro 600 was selected as the fiber, whereby a dosage of 5 [kg/m3 ] was specified.

Fig. 7.68: Input field of the design for fiber-reinforced concrete The fiber density and the corresponding fiber tensile stress are calculated according to the previous examples and the calculation procedure does not need to be repeated here. The fiber density is 1.24 [pcs/cm3] and the fiber tensile stress is 0.158 [kN/cm2 ]. As a result of the building material values, a tensile strength of 0.617 [kN/cm2 ] and a compressive strength of 3.55 [kN/cm2 ] were calculated. The staircase uniform load was 12.4 [kN/cm2 ], with this the bearing force at the support can be calculated to be 20.5 [kN/m], and with a stair width of 1.20 m, this gives the total bearing force of 24.6 [kN].

Fig. 7.69: 69 Geometry and forces for supports After entering the geometric quantities and the shear force as support force as well as the safety factors, the shear force check can be carried out.

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Fig. 7.70: Result of the calculation for the stair support For this check, a minimum height of the support cross-section of 0.6 cm is required. It can therefore be seen that in the present case the shear check is on the very safe side and the fiberreinforced concrete is not exploited to its load-bearing capacity. 7.4.4.2 Steel fiber The maximum support for the test slab in bites (Fig. 7.38) is recalculated here. This slab was already calculated as an example in the bending analysis. The default concrete grade for the test slab in bites was C25 and Tabix 1/30 steel fiber was selected as the fiber, with a dosage of 50 [kg/m3 ].

Fig. 7.71: Input field of the design for fiber-reinforced concrete

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The fiber density and the corresponding fiber tensile stress are calculated according to the previous examples and the calculation procedure does not need to be repeated here. The fiber density is found to be 0.81 [pcs/cm3 ] and the fiber tensile stress is found to be 0.216 [kN/cm2 ]. As a result of the building material values, a tensile strength of 0.557 [kN/cm2] and a compressive strength of 3.02 [kN/cm2 ] were calculated. The support force for the centre support is 196 [kN] and with a support area of 20/20 cm, the support circumference is 4/20 = 80 cm.

Fig. 7.72: Geometry and forces for supports After entering the geometric quantities and the shear force as support force as well as the safety factors, the shear force check can be carried out.

Fig. 7.73: Result of the calculation for the slab support For this verification, a minimum height of the support cross-section of approximately 8 cm is required. It can therefore be seen that in the present case the shear design is on the safe side and the fiber-reinforced concrete is not used to its load-bearing capacity, but has an increased safety for the load case of the support punching.

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7.4.5 Application with shotcrete In combination with shotcrete, fibers are mainly used for slope and excavation stabilization. The technology of applying shotcrete to the subsoil has undergone great development in recent years. The equipment such as pumps and also the spraying nozzles have developed further, so that fiber concrete can also be used well. The spraying nozzles in particular have undergone development, and the rebound has been greatly reduced as a result, which has also increased the efficiency. The lateral deflection of fibers in the air flow is well controllable with the new generation of nozzles, so this problem has also been solved to a certain extent. All in all, the use of fiber-reinforced shotcrete can be regarded as very economical, and it has already been used positively on large terrain slopes, as the following two examples show. 7.4.5.1 Plastic fiber For a construction project in Aldrans-Tyrol, a temporary excavation pit protection with a depth of approximately 9.5 m had to be carried out diagonally below an existing neighbouring house.

Fig. 7.74: Excavation pit in Aldrans-Tirol

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The shotcrete walls are calculated in individual layers, in each of which the earth pressure is determined for one anchor layer. This earth pressure can then be used to select the soil nail to be used, with a general distinction being made here between temporary and permanent nailing. In the case of temporary nailing, the soil nails are also introduced into the calculation as they are supplied, with corrosion only being taken into account in extreme cases. In the case of permanent use of the soil nails, either permanently corrosion-protected soil nails or, for some years now, soil nails taking into account an rust off rate must be used. In the present case, the securing was temporary and its useful life was less than 3 years, so that corrosion of anchors and soil nails need not be taken into account.

Fig. 7.75: Section showing the shoring of the excavation pit The geotechnical calculation provided the standard section shown with the corresponding static design bases.

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Fig. 7.76: Concrete quality for BV Aldrans When selecting the shotcrete grade SpC 25, the smaller modulus of elasticity is taken into account in contrast to normal concrete C 25. The fiber and its dosage must then be selected. It was decided to use a plastic fiber of the Enduro HPP 45 with a dosage of 5 [kg/m3 ].

Fig. 7.77: Fiber quality and dosage for BV Aldrans

The fiber density and the corresponding fiber tensile stress are calculated according to the previous examples and the calculation procedure does not need to be repeated here. The fiber density is found to be 0.80 [pcs/cm2 ], and the fiber tensile stress is found to be 0.276 [kN/cm2 ].

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Fig. 7.78: Fiber-reinforced concrete parameters for given materials As a result of the building material values, a tensile strength of 0.738 [kN/cm2] and a compressive strength of 3.99 [kN/cm2 ] were calculated.

Fig. 7.79: Fiber-reinforced concrete characteristic values with safety Including a safety factor for the fiber concrete of 1.5, the permissible tensile strength is 0.492 [kN/cm2 ] and the permissible compressive strength is 2.66 [kN/cm2 ]. With these material values, the layer-by-layer calculation of the excavation shoring can now be started. The geotechnical calculation resulted in maximum moments in each calculation layer, which must now be covered with the building material fiber concrete. As with the design for bending already shown, the necessary section modulus of the cross-section is calculated and the required minimum height (thickness) of the calculated layer can now be determined using the permissible maximum stresses.

Fig. 7.80: Layer-by-layer design of the fiber-reinforced concrete wall at the excavation pit in Aldrans The calculated minimum heights are now compared with the selected height (shotcrete thickness) and the overall safety is determined. It can be seen that with 16 cm fiber shotcrete the moments can be absorbed sufficiently well. A frequently asked question with shotcrete is the formation of the transitions between the individual spraying processes.

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Fig. 7.81: Fugenanordnung beim Spritzbeton In this case, a sliding transition is generally necessary so that a corresponding transmission of force is also possible. It has proven to be advantageous if the transition is made at an angle over a length of 25-35 cm.

Fig. 7.82: Joint arrangement for shotcrete underpinning in Fiss-Tirol However, the transitions should be made with a maximum time interval of 2–4 days, because during this time the two shotcrete layers still bond well. This results from mineral growth during the setting phase of the shotcrete. This growth results in an interlocking and thus a possible force transmission in the joint. However, a time interval of 4 days should not be exceeded, otherwise this effect of the bond will be too weak. Tests were carried out specifically on this subject, with fiber sprayed concrete being sprayed onto the substrate and a second layer of sprayed concrete being sprayed on 2 days later.

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Fig. 7.83: Spray test for the spray joint The spray sample was then exposed to the natural weather for 7 days and deliberately not post-treated, so that this also mimicked the natural site conditions.

Fig. 7.84: Core drilling during spray test for joint formation Subsequently, two core samples were drilled out and marked. With the respective samples the joints are recognizable, whereby here also in the detail of the transition it is to be seen very clearly that the transition does not possess any faults but is characterized only by the absence of larger rock grains.

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Fig. 7.85: Joint formation in the two core samples

In addition to the two core drillings shown, a third core drilling was carried out. Subsequently, these core samples were taken to the laboratory and tested for resistance to demolition.

Fig. 7.86: Drill cores for testing in the laboratory

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For each drill core, a tear-off test was carried out in the undisturbed fiber concrete and in the area of the sprayed joint. The results of the tests show no significant differences in the measured values within the scatter. This shows that the shotcrete can still produce a good bond for up to 3-5 days if the bond area is cleaned and pre-moistened beforehand. This is a common procedure for shotcrete work and is also observed by the professional work teams.

Fig. 7.87: Results of the tear-off strength test in the laboratory In comparison, the theoretically calculated tensile strength of the fiber-reinforced concrete with the plastic fiber Enduro HPP45 is shown.

Fig. 7.88: Strength of fiber shotcrete at a given dosage The fiber tensile values of 3.21 [N/mm2 ] calculated for a given mix are achieved by both the sprayed concrete itself (2.91) and the sprayed joint (2.80). The measured values show the strength after 7 days, there will probably be an increase in the strength values of up to 15% until the 28-day strength is reached. Thus, the required values for the tensile strength of the fiber sprayed concrete are achieved in the joint as well. fct f k = 2,91 / 0,85 = 3,42 kN/cm2

bzw.

= 2,80 / 0,85 = 3,29 kN/cm2

It can be seen here in practice that the process of cement stone formation, as described in Section 3.7.6, lasts for several days and thus the connection of two sprayed concretes that are separated in time can ultimately also be regarded as a single unit, not only visually but also statically. The static effect via a sprayed joint is therefore also fully given.

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7.4.5.2 Steel fiber On the occasion of the Federal Garden Show in Koblenz (Germany) in 2012, an inclined elevator was built to Ehrenbreitenstein Castle. The bottom station had a cut in the terrain with a height of almost 13 m, which had to be secured. A large part of this protection was still to be visible later, as the cut was only to be partially filled.

Fig. 7.89: Construction pit in Koblenz-Pfalz with steel fiber shotcrete on the occasion of BUGA 2012 A nailed shotcrete protection with fiber concrete was chosen, using steel fibers. To avoid contact with the steel fibers on the surface, the entire surface was then covered with a thin skin of shotcrete. This solved the problem of the risk of injury from protruding steel fibers. A slope inclination of 80°was specified for the site cut, which is almost 13 m high in total. The entire height of the cut was planned in one go without a berm (intermediate step). This was dispensed with because there were no objects above the shotcrete protection that were at risk of falling.

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Fig. 7.90: Section showing the shoring of the excavation pit The geotechnical calculation provided the standard section shown with the corresponding static design bases.

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The quality of the shotcrete was now determined with SpC 25 and the corresponding material parameters of the tensile and compressive strength of the shotcrete were determined.

Fig. 7.91: Concrete quality for BV bottom station Ehrenbreitenstein castle lift After the choice of the shotcrete type, the fiber and its dosage also had to be selected. It was decided to use a steel fiber, namely FE 65/34 from Arcelor with a dosage of 40 [kg/m3 ].

Fig. 7.92: Fiber quality and dosage for BV valley station Ehrenbreitenstein castle lift The fiber density and the corresponding fiber tensile stress are calculated according to the previous examples and the calculation procedure does not need to be repeated here. The fiber density is 1.53 [pcs/cm3 ] and the fiber tensile stress is 0.22 [kN/cm2 ].

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Fig. 7.93: Fiber-reinforced concrete characteristic values for given materials As a result of the building material values, a tensile strength of 0.68 [kN/cm2 ] and a compressive strength of 3,68 [kN/cm2 ] were calculated.

Fig. 7.94: Fiber-reinforced concrete characteristic values with safety Including a safety factor of 1.35, the permissible tensile strength is 0.504 [kN/cm2 ] and the permissible compressive strength is 2,73 [kN/cm2 ]. With these material values, the layer-by-layer calculation of the excavation shoring can now be started. The geotechnical calculation resulted in maximum moments in each calculation layer, which must now be covered with the building material fiber-reinforced concrete. As with the design for bending already shown, the necessary section modulus of the cross-section is calculated and the required minimum height (thickness) of the calculated layer can now be determined using the permissible maximum stresses.

Fig. 7.95: Layer-by-layer design of the fiber-reinforced concrete wall in the excavation pit at the Ehrenbreitenstein castle lift valley station The calculated minimum heights are now compared with the selected height (shotcrete thickness) and the overall safety is determined. It can be seen that with the selected thickness of the fiber shotcrete, the moments can be absorbed sufficiently well.

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7.4.6 Application with inverted T-beam An inverted T-beam consists of a plate onto which beams or webs are placed in a shear-resistant manner. Thus, in contrast to the T-beam, where the webs are arranged under the plate, these are above. Inverted T-beams are used for high wall constructions where earth and/or water pressure must be absorbed. The inverted T-beam is intended to transfer the load to the supports for larger spans. The bending in the cross-section caused by the load generates tensile and compressive forces. Since the permissible tensile and compressive stresses are very different in fiber-reinforced concrete, the bending moment resulting from the bending, consisting of compressive and tensile force, is assigned the area in each case that the tensile or compressive cross-section is utilised. Therefore, the compression cross-section is much smaller (T-area) than the tension cross-section (plate). The thickness of the plate depends on the thickness of the tensile area, which is normally half the cross-sectional height of the total cross-section.

Fig. 7.96: Stresses with inverted T-beam The design is carried out with an uncracked cross-section (state 1). Therefore, in pure bending, the web width is in the same ratio to the contributing slab width as the permissible compressive stress to the permissible bending tensile stress. These two values depend on the concrete strength and the type of fiber and dosage (fiber concrete). Once the fiber concrete strength has been determined, the effective slab width can be easily determined and thus the design can be carried out in state 1.

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7.4.7 Design for a bridge It should be shown at this point that even small to medium-sized bridges for normal traffic can certainly be made of fiber-reinforced concrete. This is particularly the case with plastic fiber concrete in order not to have to take into account the troublesome corrosion of our traffic routes. This would make it possible to achieve considerably longer life cycles for these bridges and thus ensure their profitability in any case. As an example, an 35 m wide bridge is calculated here, which can be designed for small to medium-sized roads.

Fig. 7.97: Cross-section of a bridge As a load for this cross-section, a volume weight of the construction of 24 [kN/m3 ] was assumed for the dead load. In addition, a surface load of 5 [kN/m2 ] was assumed for the construction of the carriageway (decking). The live load of the bridge was assumed to be a uniform live load (full load) of 10 [kN/m2 ], which corresponds to a generous equivalent load for bridges. With these load data at the given geometry, the cantilever moment with a size of 31.43 kNm and the maximum field moment can be determined to be 59.30 kNm. These two moments must now be absorbed by the fiber-reinforced concrete alone. If the concrete grade C25 and a plastic fiber Enduro HPP45 with a dosage of 5 [kg/m3 ] are selected for the bridge, the following strengths result for the fiber-reinforced concrete:

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Fig. 7.98: Fiber concrete tensile, compressive strength With these stresses, the necessary cross-sections can now be calculated, taking into account the partial safety factors for the load and the material. The following results for the cantilever arm:

Fig. 7.99: Cantilever arm

Fig. 7.100: Field plate

This means that 26.4 cm are required for the cantilever arm, which is also complied with by the selected 30 cm slab thickness at the edge of the beam. The field plate must be at least 36.2 cm, with the selected 40 cm these are also complied with. Thus, this cross-section shape can be used for the selected bridge with its specified loads and partial safety factors.

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If we now look at the longitudinal section of the bridge, we see an arch bridge consisting of the two bridge girders with the supporting structure slab on top.

Fig. 7.101: Longitudinal section of a bridge With the stated 35.0 m span, the bridge can certainly be considered to have a medium span.

Fig. 7.102: from diagonally below

Fig. 7.103: from diagonal above

The load is now determined individually for each arch girder, whereby this results in a load of 126.57 [kN/m] in the present case. With a total weight of 4,430 [kN] per bridge girder, this load must now be transferred to the two abutments. The arch girder is calculated as a three-hinged arch, resulting in the following edge forces: • max. peak force = 6.460 kN • max. bearing force = 6.830 kN These forces are now to be taken over by the arch girder on the one hand at the apex directly under the carriageway slab in the middle of the bridge and on the other hand by the foundations

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as bearing forces. The compressive forces are verified as buckling bars, whereby the necessary storey height is set at 15 m, which is already on the very generous side. The following values result from the fiber-reinforced concrete design:

Fig. 7.104: Design of the arch girder for buckling This shows that a bridge chosen in this way can also meet today’s traffic standards and that no steel is used, only fiber-reinforced concrete. It may give some bridge builders food for thought that there are also solutions for traffic bridges that do not corrode and thus have a much longer service life than the bridges currently made of reinforced and prestressed concrete.

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7.4.8 Design for a harbor wall without anchor In most port facilities, especially the quay walls at seaports, the corrosion of the metal parts is a very big problem, as it is only possible to get a grip on it in a time-consuming and costintensive way. Therefore a possibility is shown here, which constructs a component, which does not consist of metal but only on fiber concrete and thus no corrosion problems concerning metal corrosion can have. This has an effect on the durability of the construction and thus increases the profitability of the overall construction.

Fig. 7.105: Basic section for a harbor wall Basically, a harbor wall must absorb the earth pressure and excess water pressure acting on the harbor basin. Normal harbor basins are subject to very high forces in this respect, which is why very stable retaining walls are often chosen. In recent decades, steel sheet piling with steel anchors has become increasingly popular. However, the consequence of this is that corrosion protection is becoming more and more important and also dominates the costs. If one wants to move away from these boundary conditions, a new construction must be chosen, which is somewhat more cost-intensive during construction, but hardly causes any maintenance costs. This is quite possible with a construction made of fiber-reinforced concrete and will also be demonstrated here.

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7.4 Dimensioning samples

Fig. 7.106: Ground plan of a harbor wall First of all, a dissolved construction is chosen in the ground plan in such a way that two walls are connected by means of diaphragm walls with spacer walls, so that a kind of hollow wall is created, which is, however, very well connected to each other by overlaps and thus also has a full connection in terms of forces. The result is a composite wall with extremely high load-bearing capacity, whose geometric cross-sectional values per meter of wall are as follows: • Cross section = 2,34 [m2 ] • Moment of interior = 5,13 [m4 ] • Section modulus = 2,44 [m3 ] With these cross-section values, a harbor wall is now calculated, which comes to rest in a subsoil with the following soil properties:

Fig. 7.107: Soil properties for the harbor wall On average, the harbor basin should have a total depth of 15 m and the groundwater level is 2.0 m below ground level. The harbor water level fluctuates and takes the value of 4.0 m as the greatest depth.

7 FC dimensioning

212 At following sectional view situation is shown once more.

Fig. 7.108: Section of a harbor wall The cover plate indicated in the section connects the individual elements and also enables a roadway to be installed on the harbor wall on which vehicles and/or harbor cranes can move. A surface load of 15 [kN/m2 ] was taken into account in the calculation. These acting vertical loads can easily be taken over by the harbor wall, they are even to be evaluated as a positive phenomenon in the wall loading, since moments are thus overpressed and the tensile stresses in the cross-section are reduced. The calculation of the harbor wall was carried out according to Blum’s method with a layer thickness of approximately 50 cm up to a total depth of 27.0 m. This corresponds to an embedment depth of the harbor wall of 12 m in the subsoil below the harbor basin. In addition, a resting pressure of 30% was taken into account in the calculation in order to be on the safe side in the design.

7.4 Dimensioning samples

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Fig. 7.109: Bending moments and normal forces in the wall The bending moments determined at a depth of approximately 21 m are very high at 8,138 [kNm], but are strongly pressed by the normal force of 1,211 [kN] occurring in the process, whereby the tensile stresses resulting from the bending moment are reduced. The entire wall is restrained in the deeper subsoil, so the forces can be absorbed well, with no additional anchoring required. The large bending moment is reduced relatively quickly, so that a clamping depth of 12.0 m is sufficient. The total height (depth) of the wall can thus be maintained at 27 m, whereby this includes a pool depth of 15 m. As a result of the resolved wall construction with the relatively high section modulus, only low tensile stresses arise in the wall, which assume a value of 0.28 [kN/cm2 ] at the depth of the maximum bending moment, which the fiber-reinforced concrete is also able to absorb well.

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214

Fig. 7.110: Edge stresses in the wall In the case of the harbor basin, a better type of concrete should be used, since the stress is additionally stressed by the impact effects of the mooring ships and the continuous waves. For this reason, a concrete strength class of C30 is selected. The plastic fiber Enduro HPP45 is mixed into this concrete with a dosage of 5 [kg/m3 ] and thus fiber concrete is produced. This is installed using the usual placement method for the diaphragm wall. It must be taken into account that the individual adjacent elements must be produced within 3 days. Only within this period of time can the individual wall panels join together flush with the force. This is due to the mineral growth in the fresh concrete during the setting phase. This results in the following characteristic values for the fiber-reinforced concrete for the design of the wall.

7.4 Dimensioning samples

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Fig. 7.111: Characteristic values of fiber-reinforced concrete

Fig. 7.112: Design of the fiber concrete of the wall The tensile and compressive stresses acting in the structure are smaller than the permissible stresses. Thus, this type of harbor wall is sufficiently dimensioned. It is thus shown that fiber-reinforced concrete can be used quite cost-effectively in the long term, even for large structures, while complying with all the safety requirements currently stipulated by the codes in force.

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7.4.9 Comparison of design with different fibers In order to have an overview of the use of different fibers in a structural component, the following calculation example for the test slab in bites (see Section 7.4.1.2) shows the design for the fiber-reinforced concrete with the most varied fibers. For this purpose, the following basic static values and materials are given for the respective design: Concrete quality C 20 Panel thickness d = 20 cm max. bending moment M = 16.9 kNm The cross-section and the overall situation are shown under Section 7.4.2.1.

7.4.9.1 Comparison with different fibers Only one design is shown here, as this type of calculation has already been shown several times. A calculation is shown with a fiber that has not yet been used in a design in this book, so that the detailed data of the fiber can also be recognized.

Fig. 7.113: Design of the slab with glass fiber concrete

Now follows a compilation of the result of different fibers for the ceiling in bites.

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Fig. 7.114: Comparison of different fibers in fiber-reinforced concrete It can be seen that the steel fiber and the plastic fiber are roughly equivalent, since the purchase price of 40 kg of steel fiber is also roughly equivalent to the price of 5 kg of plastic fiber. Thus, the choice depends on conditions other than price. Often decisive criteria between these two fiber materials are the processability and the possible corrosion. The glass fiber is slightly better in its load bearing capacity, but this is usually offset by the price of the fiber, so that this fiber also competes with plastic and steel. The carbon fiber shows considerable static advantages. This is noticeable in the low height required. Since this also requires a low dosage, the relatively high price for this fiber can also definitely lead to a favorable component. It is therefore up to the planner and builder to choose the optimum fiber for his application from the large number of fibers on offer and then to use it.

7.4.9.2 Comparison with shrink fiber and different fibers

In this comparison, a microfiber is applied first to prevent the shrinkage cracks. This means that two different fibers are in use, which complement each other in the transmission of force. This is used in particular for larger components. This ensures that no or only minor shrinkage cracks occur. In the calculation, 10% shrinkage cracks are assumed, so that in contrast to reinforced concrete, the concrete and thus the fiber-reinforced concrete can transmit considerable tensile stresses. In the following design, a carbon fiber is used which is applied to the plate in bites. The detailed data of this fiber can be taken from the following dimensioning.

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Fig. 7.115: Design of the slab with carbon fiber concrete

In the following compilation of the designs for the different fibers, it can be seen in comparison with the previous chapter that slightly lower design heights are required here. This is the effect of the fiber to prevent the shrinkage cracks. The share of tensile strength is relatively low, which is why these microfibers are actually used almost exclusively to prevent shrinkage cracks.

Fig. 7.116: Comparison of different fibers in fiber-reinforced concrete

Overall, when comparing the different fibers, it can again be seen that the choice of fiber mainly depends on workability and possible corrosion. In the case of the glass fiber, the chemical compatibility must also be checked because of the alkaline concrete. In addition, when using carbon fibers, it must be taken into account that the small dimensions of the respective individual fibers result in a relatively large surface area of the installed fiber,

7.4 Dimensioning samples

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even with small dosages. In the present case, the carbon fiber forms a surface area of 635 [m2 ] at a dosage of 2 [kg/m3 ]. This means that, as described in Chapter 6.4 (Fibers to prevent shrinkage cracks), a supplement is necessary when mixing the fresh concrete. In the given case with a fiber surface of 635 [m2 ] , for a concrete quality of C 20 with the largest grain size of GK 32 mm and a grain distribution line B as well as a plastic consistency, the following proportions result, which must be added additionally to the fresh concrete: Water 67,4 Liter Cement 119 kg With these additional quantities, the strength class of the desired concrete is then also given again.

8 Applications Fiber-reinforced concrete is a building material that, due to its now comprehensible properties, is gaining an ever wider range of applications. The fact that the building material is so variable in its form and also simple to produce, provides the basis for using this building material wherever possible and thus also exploiting the economic efficiency.

8.1 Base plates Often the exact position of the walls and columns that transfer the building loads to the floor slab are not yet known or must be variable (e.g. in the case of shelf storage), so a homogeneous building material is advantageous as a floor slab. In addition to the load distribution, the design variant fiber concrete offers the advantage that it is watertight and can be divided into relatively large individual fields, the mutual sealing of which is no longer a problem today.

8.1.1 Residential buildings Especially in the construction of residential buildings, a floor slab with fiber concrete is very good to use.

Fig. 8.1: Floor slab for residential house © Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2021 B. Wietek, Fiber Concrete, https://doi.org/10.1007/978-3-658-34481-8_8

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The static calculation and dimensioning is carried out as usual for slab foundations, whereby coves can also be formed below large concentrated loads, which then also distribute the load in an ephemeral manner.

8.1.2 Industrial floors The fiber reinforced concrete slab has been very well established in large hall constructions such as wholesale markets. The usual point loads of the racks are comparable with the wheel loads of the forklifts used in the halls. These loads can be well distributed with the building material fiber-reinforced concrete.

Fig. 8.2: Production of a hall floor with fiber concrete (Photo: Rindler) Steel fibers have been the reinforcement standard for industrial floors since the 1990s.

Fig. 8.3: Finished hall floor with fiber concrete (Photo: Rindler) A finished hall floor for a factory hall in which the furnishings can still be set up individually.

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8.2 Walls

8.2 Walls The strength of a wall depends on its load and also on the dimensions. Large walls in particular need to be optimized, as the cubature of the building material is a decisive factor in the price of the wall. Here, fiber-reinforced concrete offers significant advantages over existing wall constructions, which will be discussed in more detail below.

8.2.1 Basement walls These usually have a height of the basement floor and are thus at 2.5–3.5 m. This means that the load on the wall is relatively low and the material properties of the fiber concrete can be fully utilised.

Fig. 8.4: Fiber-reinforced concrete basement wall in Jerzens (Tyrol) If the usual earth pressure on a basement wall is taken into account, plus water pressure up to half the height of the wall, a wall thickness of 20 cm with fiber-reinforced concrete is sufficient. The watertightness of the wall is in any case given with an uncracked fiber-reinforced concrete

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of 20 cm. Watertight floor connections can also be achieved with joint tapes..

Fig. 8.5: Fiber-reinforced concrete basement wall in Imst-Tyrol Thus, compared to the currently common wall thicknesses of 30 cm for basement walls made of concrete brick or reinforced concrete, there is a considerable savings potential in construction costs. A steel reinforced concrete wall must be at least 30 cm thick, since in the cracked state the pressure range is only approximately 5–6 cm and water tightness with concrete can only be guaranteed from 5 cm uncracked material. Thus, the non-cracked fiber reinforced concrete has a material-technical advantage with regard to watertightness.

8.2.2 Wall scopes In the case of higher wall slabs that are also backfilled, the absorption of the large earth pressure forces can also be achieved with an inverted T-plate. In this case, the wall slab is introduced into the analysis as a tension zone and the associated beams as a compression zone. Thus, a T-plate is only calculated with reversed stresses. Although the arrangement is unusual, it is very effective, as considerable material can be saved compared to the usual wall plates. There is therefore no superfluous material that does not contribute to load transfer.

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Fig. 8.6: Stress during reversed T-beam

The design is carried out with a non-cracked cross-section, that is, in state 1. Therefore, in the case of pure bending, the web width must be calculated in the same ratio to the contributing slab width as the permissible compressive stress to the permissible bending tensile stress. These two values depend on the concrete strength and the type of fiber and dosage. Once the fiber concrete strength has been determined, the contributing slab width can be easily determined and thus the design can be carried out in the non-cracked cross-section.

Fig. 8.7: Exterior wall as T-beam of the Muldenbahn garage in the Pitztal valley

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In the example shown, the construction was applied to a poured-in-place wall with a wall height of almost 6.0 m. The wall was then build with a fiber-reinforced concrete. No steelreinforcement, such as lintel reinforcement, was incorporated into the fiber-reinforced concrete, even for the wide window opening immediately adjacent to it. This design has now proven itself in practice.

8.3 Ceilings Normally, ceilings have a relatively slim construction, which are subjected to considerable bending moments. When using fiber-reinforced concrete, the construction heights are usually somewhat higher than with comparable prefabricated ceilings or also reinforced concrete ceilings, but the somewhat stronger construction height also offers advantages. Especially for the vibration behavior and the deflection of ceilings, a somewhat more solid construction is definitely advantageous.

8.3.1 Residential buildings Here, spans of 4.5 m with a slab thickness of 20 cm are possible. This then also has the advantage that the slab shows only slight deformations under the load usual in residential construction. Especially in the construction of single-family houses and apartment buildings, the fiberreinforced concrete floor is a cost-effective variant, since here there is also the additional advantage that no reinforcement bars have to be checked for their correctly installed position, but the building material fiber-reinforced concrete alone carries the loads on walls.

Fig. 8.8: Test ceiling with 3/3 fields in Bissen Luxembourg The above example is a test slab from Arcelor in Luxembourg, which was designed and loaded with a thickness of 20 cm and three times three spans of 6.0 m each. Proof of the load-bearing capacity was provided.

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8.3 Ceilings

If the ceiling is supported by columns, beams must be used to distribute the loads. Fiberreinforced concrete can also be used for this purpose if this is statically verified. In such cases, the load transfer of the structural components must generally be carried out or monitored by a structural engineer.

8.3.2 Industrial buildings The use in slabs in industrial is rather limited because of the limited range in fiber concrete applications. It is therefore to be expected rather few applications in this area. In case indicated below a garage ceiling has been performed with wingspan of 6.0 m with a 30 cm thick fiber concrete ceiling at a valley station of the cable car. This is the valley station at the high wall construction with the run-beam was performed. The ceiling itself has little payload, as on the ceiling, the chair of the cable car be moved into a sort of station and not be stacked to the ceiling. When the load of the ceiling is only to the staff of the cable car to operate the chair slings.

Fig. 8.9: Ceiling of a garage building at a cablecar station

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8.4 Beams Fiber-reinforced concrete can also be used to a limited extent for beams, especially where for geometric reasons there is a large construction height where bending moments only allow limited tensile stresses to develop.

8.4.1 Undercoats and overcoats In building construction, the dimensions of superstructures and beams are usually determined by the architecture. It is often possible to dissipate bending moments with fiber-reinforced concrete.

Fig. 8.10: Beam at cable car station structure In the case of the garage building of the cablecar station, the superstructures and beams were also made of fiber-reinforced concrete.

8.4.2 Single beam The variation of beams is very large. When using fiber-reinforced concrete, it is essential to ensure that the tensile stresses in the cross-section do not exceed the permissible values at any

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8.5 Galleries point. These are specified by the concrete type, the fiber in its dosage.

8.4.3 Roadways Fiber-reinforced concrete can be used as a load distribution slab for carriageways (tram and car roads), and this is usually cost-effective.

Fig. 8.11: Fiber-reinforced concrete carriageway Similar to industrial floors, the fiber-reinforced concrete slab enables a good load distribution on the subfloor and thus small irregularities in the subfloor can be easily bridged.

8.5 Galleries Galleries are built to protect traffic routes in the mountains from avalanches or rockfall. The rounded ceilings cause difficulties, especially when they are made of reinforced concrete, as it is not easy to bend the reinforcement exactly to the planned radius and then to place the concrete completely in this shape. For this reason, the desire arose to build the gallery with the building material fiber concrete.

8.5.1 Footpaths and cycle paths In the case of a footpath and cycle path in the high mountains, a gallery is to be placed in front in the area of a rock face, as the rock face behind it is very susceptible to fracture and is also very

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stellar over 50 m. An alternative network of the slope would generate too high costs.

Fig. 8.12: Rockfall gallery for pedestrians and cyclists A gallery in prefabricated construction was planned and calculated, whereby the prefabricated parts can be moved by the excavator and thus no one has to stay in the unappreciated areas even during construction. The client has accepted this planning and the execution is currently being planned in terms of costs.

8.5.2 Roads Within the framework of a diploma thesis at the University of Innsbruck, a street gallery was also investigated to determine whether such a gallery could also be constructed with fiber-reinforced

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8.6 Tunnel lining

concrete. In principle, this would be a great advantage for the design and also for the maintenance, which can, however, only be exploited if a static proof of feasibility is provided and also the economic investigation brings a positive result.

Fig. 8.13: Road gallery for avalanche protection In the diploma thesis of Alexander Klotz at University in Innsbruck, a gallery already constructed in reinforced concrete was calculated with steel fiber concrete, whereby a comparison was also made here between the design as proposed in this book and the design according to the guideline for fiber concrete. It was shown that this selected gallery for a two-lane road is certainly statically feasible with fiber-reinforced concrete and can also be produced in an economically interesting way.

8.6 Tunnel lining Currently, a great deal of shotcrete is used in tunnel construction, which is always supported by steel-reinforcement mats and, if necessary, also by tunnel arches. When using fiber shotcrete, the question arises as to whether the mesh reinforcement can be dispensed with and to what

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extent the use of tunnel arches can be reduced. There are not yet sufficient comparisons here, but individual construction sites already indicate a trend towards fiber-reinforced concrete.

8.6.1 support measures Fiber shotcrete is excellent for immediate support of the rock mass after excavation. It can be placed directly after excavation, either manually with a man or via a controlled spray nozzle attached to the gun carriage..

Fig. 8.14: Tunnel in Oberlech Backup The support shown here was provided in a tunnel under a hotel, which was excavated in boulder-interspersed solid clay. With excavation depths of 0.5 to 0.8 m, the support could be installed immediately. Due to the small cross-section, no further support was required. The tunnel was broken through from below into the existing basement of the hotel and then also developed as a passageway. The entire measure was carried out without any deformations or cracks in the hotel, which can be attributed to the very short free standing time of the subgrade. The subgrade had no time to deform, the securing was installed very quickly and thus the client’s requirements were met.

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8.6 Tunnel lining

8.6.2 Inner lining The fiber shotcrete can also be used as an inner shell. Since this usually only has to absorb compressive forces, fiber-reinforced shotcrete is very well suited for this purpose.

Fig. 8.15: Tunnel in Oberlech upgraded

In the above example, a synthetic fiber was used for the inner shell and there was no need to rework the spray-finished surface; both the architect and the client agreed with this resulting surface.

Fig. 8.16: Tunnel upgraded in Norway (Photo Rindler)

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The above picture shows an inner shell of a tunnel in Norway, which was produced with fiber concrete. The use of synthetic fibers is particularly noteworthy here, as these have a very positive property in the event of a fire in the tunnel and the inner shell has much better load-bearing properties than normal concrete.

8.7 Tubbings Segments are prefabricated parts which, when assembled, form a load-bearing ring. They are often used in tunnel construction and also in shaft construction. Since these individual parts are mainly loaded in compression, fiber-reinforced concrete is ideally suited for use. In addition, when using a synthetic fiber, the material properties in case of fire are recommendable.

8.7.1 Tunnel construction More and more tunnels are being produced using full face cutting machines. Since the excavated or milled cross-section has an exact circular shape, the use of segments as support and lining means is of decisive economic advantage.

Fig. 8.17: Segments before installation

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8.8 Prefabricated parts

The segments are prefabricated in sufficient numbers and used depending on the advance rate of the tunnel boring machine.

Fig. 8.18: Tubbings installed

8.7.2 Shaft sinking Since manholes have always been produced with prefabricated parts and these are also mainly loaded in compression, it was obvious to also produce these manhole rings from fiber-reinforced concrete. This made it possible to achieve a significant economic advantage, while also simplifying production.

8.8 Prefabricated parts Fiber-reinforced concrete is particularly suitable for use with precast elements. Since complicated shapes are often involved here, a homogeneous building material such as fiber-reinforced concrete has an advantage over concrete reinforced with structural steel, since the latter can only be adjusted poorly in the case of curves and general curves.

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8.8.1 Pipes This is probably the form in which fiber concrete was first used. If one thinks in particular of spun concrete, fiber concrete is possible with the same installation method and can apply its material properties well here.

Fig. 8.19: Fiber-reinforced concrete pipes The sizes of fiber-reinforced concrete pipes have now reached every diameter and also every shape (oval and also egg shaped). Thus, every pipe can also be manufactured in fiberreinforced concrete and most dimensions are also available in the prefabricated parts trade with fiber-reinforced concrete as a building material.

8.8.2 Slabs and ceilings

Fig. 8.20: Precast wall element made of fiber-reinforced concrete (Photo Rindler) In house construction, more and more prefabricated parts made of fiber-reinforced concrete are being used, for example, as walls.

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8.8.3 Stairs Staircases in residential construction, whether straight or spiral, have been in use as precast elements for a long time. They are manufactured with almost all building materials such as wood, steel, reinforced concrete. Fiber-reinforced concrete can also take on the emerging stresses of staircases. Some tests have been started with fiber-reinforced concrete and numerous prefabricated staircases have already been produced and installed for use in residential buildings.

Fig. 8.21: Precast fiber-reinforced concrete staircase formed and erected in the factory Plastic fibers were used in the calculation of these prefabricated stairs. The dimensioning showed that the load-bearing cross-section is only slightly stronger than it would have to be if reinforced concrete had been used. A dosage of 5 [kg/m3 ] was calculated and found to be sufficient. Thus, the fiber-reinforced concrete staircase was sufficiently dimensioned with a relatively low dosage. For the application in the factory, the production with fiber concrete is much easier and so this form will also prevail in After the curing time, during which the fiber concrete reaches its strength and thus loadbearing capacity, the prefabricated staircase is lifted out of the formwork and processed further. The prefabricated stairs are transported to the construction site by truck and installed there by means of the lifting device of the truck or also by crane. Thereby own hanging devices are integrated in the stair flights, which can be closed or poured out after use.

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The staircase shown here was installed in a residential building in Upper Austria.

Fig. 8.22: Precast stairs made of fiber-reinforced concrete installed

8.8.4 Retaining walls Here, prefabricated elements were produced with steel fiber concrete, which were then anchored into the subsoil with two soil nails. The front elevation was made with a special formwork that suggests natural stone masonry. This makes the precast wall look more like a masonry retaining wall, which is what the client wanted.

Fig. 8.23: Retaining wall of precast concrete with fiber

8.9 Construction pit and slope stabilisation

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8.9 Construction pit and slope stabilisation Fiber concrete used as shotcrete is particularly suitable for securing natural slopes such as construction pits, natural slopes and also for securing high brick walls.

8.9.1 Construction pits Here, especially the quick force closure after the excavation is possible with the application of fiber shotcrete. The exposed soil is held in place within a very short time and cannot slip any further. Especially with sandy and gravelly soils, the rapid force bond is necessary and also advantageous. In the excavation pit shown (depth approx. 10 m), loose sand layers were problematic during excavation, as the sand threatened to slide off, thus allowing a fracture behind the shotcrete shell. With excavation depths of 60–80 cm (see small picture), the fiber concrete was sprayed on immediately after excavation and the soil was thus retained. The theoretical quantities could be maintained with very little overprofile.

Fig. 8.24: Slope stabilization in Patsch near Innsbruck

The transitions between the individual spraying processes only had to be bevelled, so they were produced in a running manner. After the adjacent injection, the wall was able to bear the

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loads that occurred and no cracks appeared in the shotcrete. Thus, the transition between the individual spraying processes is completely unproblematic, it only has to be ensured that the newly applied shotcrete is applied to a clean surface. A particularly challenging excavation support was behind an existing hotel in Ischgl. The space between the existing hotel and the ground was used underground as an extension. For this purpose, a shotcrete protection of the excavation pit with fiber shotcrete was chosen.

Fig. 8.25: Excavation support in Ischgl - plans The plan shows that the total height to be secured was approximately 16 m, whereby a 4-storey hotel had to be considered as a superimposed load above the securing. Fiber shotcrete in concrete grade SpC 25 and plastic fiber Enduro 45 with a dosage of 6 kg/m3 was used. The thickness of the fiber shotcrete was staggered from 15 to 20 cm, whereby the adjustment to the natural subsoil also had to be taken into account. It can be seen in the pictures that stones and metre-sized boulders were encountered in the subsoil, some of which protruded into the excavation pit or also created corresponding cavities during excavation, which had to be closed. Not only the depth of the excavation pit, but also the confined space conditions in particular were only possible through the appropriate use of equipment and very good work preparation, together with the construction sequence that was organised down to the last detail. The two pictures below show the excavation pit at a depth of approximately 12 m. The removal of the excavated material became increasingly difficult as a former excavation support had to be removed

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in this area at the same time as the excavation progressed, as it was located in the middle of the excavation area.

Fig. 8.26: Securing the excavation pit in Ischgl - pictures Special measuring marks were set to observe the wall movements, which were visually checked daily by the construction company. In addition, wall deformation was measured at five points by an independent surveying office. At the time of the recorded images, there were movements in the entire wall shell in the horizontal direction of approximately 10 mm and vertically of approximately 12 mm. These relatively low deformations could only be achieved because some of the soil nails were additionally prestressed after installation in order to achieve the anchor force as early as possible without major soil deformation.

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8.9.2 Slope protection In the case of natural slopes, protection is usually not limited to flat surfaces. Fiber-reinforced sprayed concrete is particularly suitable here, as any terrain shape can be sprayed in without any major additional consumption of sprayed concrete. In the case of high and unstable slopes, the fiber-reinforced shotcrete can also be applied from the crane, the terrain does not have to be climbed through by the work crew, which makes the work much easier from a safety point of view. The slopes, which are often interspersed with large rock ribs, cannot always be secured with level protection. The following example shows slope stabilization on rock-interspersed terrain which still has a very coarse structure even after anchoring with rock bolts. This shape can only be achieved with fiber shotcrete. The economic efficiency has given the application preference over the reinforced method of slope stabilization.

Fig. 8.27: Spraying a slope protection on the Gerlosberg - Tyrol It is not only the economic efficiency but also the optical appearance that is an additional cri-

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terion in the high mountains. Thus, the structures of the rock base can still be recognized behind the shotcrete shell and this makes a very harmonious impression to the neighboring nature. It appears to blend into the landscape much better than hard geometric structures.

Fig. 8.28: Slope stabilization near the Brenner motorway The anchorage for this securing could be completely integrated into the shotcrete for the observer, so that it is not visible..

8.9.3 Wall protection During the demolition of an inner-city house, a gap was created where the old walls of the neighbouring houses adjoined. After examining the wall thickness, it was found that the brick wall was only 15 cm thick and rather poorly mortared. It was feared that the wall, which was so open, would not withstand the stresses of wind and weather. It was therefore necessary to secure or reinforce the brick wall.

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A 5 cm fiber shotcrete shell was provided, as it was not possible to dowel reinforcement mats to the existing brick wall. This would have possibly caused loosening of the masonry, which was guarded against. With the fiber-reinforced concrete layer then in place, the wall was deemed safe against wind and weather and was able to protect the old brick wall for the construction period of approximately 1 year.

Fig. 8.29: Securing a house wall in Innsbruck

8.10 Videos of construction sites

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8.10 Videos of construction sites Pictures of several construction sites are shown in this book. In addition, videos were recorded at selected construction sites, which were combined into short films. The simple processing of fiber-reinforced concrete should also be shown here. Videos can be viewed on the youtube website at the following addresses:

Fig. 8.30: Production of a floor slab in residential construction with fiber-reinforced concrete

Fig. 8.31: Tests with fiber shotcrete

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Fig. 8.32: Construction of a tunnel with fiber-reinforced concrete

Fig. 8.33: Construction of a deep excavation pit shoring with fiber-reinforced shotcrete

Appendix

List of Tables 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9

concrete strength classes . . . . . . . . . . . . . . . . . . . . . . . . . Crack factor for different crack proportions . . . . . . . . . . . . . . . requirements for cements according to EN 197–1 . . . . . . . . . . . . Concrete applications with specification of the maximum aggregate size Admixtures for concrete . . . . . . . . . . . . . . . . . . . . . . . . . Types of concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Exposure classes in concrete . . . . . . . . . . . . . . . . . . . . . . . Consistencies of concrete . . . . . . . . . . . . . . . . . . . . . . . . . Abbreviations for concrete . . . . . . . . . . . . . . . . . . . . . . . .

6.1 6.2

Concrete properties at 10 % crack content . . . . . . . . . . . . . . . . . . . . . 79 Concrete properties according to Mohr’s derivation . . . . . . . . . . . . . . . . 84

7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9

Safety factors for the service load method . . . . . . . . . safety factor for the ultimate load method . . . . . . . . . Safety of the forces in the ultimate load method . . . . . . Safety of the building materials in the ultimate load method Partial safety factors for load stresses . . . . . . . . . . . . Partial safety factors for material resistance . . . . . . . . Buckling values ω for concrete . . . . . . . . . . . . . . . Possible states in the design of fiber-reinforced concrete . . Stress on the diaphragm wall . . . . . . . . . . . . . . . .

© Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2021 B. Wietek, Fiber Concrete, https://doi.org/10.1007/978-3-658-34481-8

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24 27 30 31 34 35 37 38 39

122 123 124 124 127 127 141 158 178

249

List of Figures 1.1 1.2 1.3 1.4

typewriter from Mitterhofer 1864 (Techn. Museum Vienna) . . . sewing hand from Madersperger 1830 (Techn. Museum Vienna) The dome of the Panthenon in Rome 128 AD . . . . . . . . . . modern skyscrapers in New York 2019 . . . . . . . . . . . . . .

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3 3 5 6

3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.11 3.12 3.13 3.14 3.15 3.16 3.17 3.18

Differences at Prism Cube compression test . . . . . . . . . . . . . . . . . Fracture criterion according to Coulomb . . . . . . . . . . . . . . . . . . . Mohr’s stress circle with Coulomb’s shear line . . . . . . . . . . . . . . . . Flexural strength according to EN 1992-1-1 . . . . . . . . . . . . . . . . . Flexural tensile strengths with possible crack components . . . . . . . . . . Grading curves for concrete depending on the maximum aggregate size GK Early shrinkage in young concrete (from Cement + Concrete 2008) . . . . . Shrinkage in concrete in the first year (from Bauingenieur 3/2008) . . . . . first crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Crystals growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . finished crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Schematic material distribution for concrete . . . . . . . . . . . . . . . . . Volume behavior during shrinkage of concrete . . . . . . . . . . . . . . . . Volume increase due to crystal formation during the setting process . . . . Volume changes during the setting process . . . . . . . . . . . . . . . . . . Concrete in the setting phase . . . . . . . . . . . . . . . . . . . . . . . . . Neutralization of alkaline water as a result of concrete setting process . . . Carbonation of concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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22 23 23 26 27 32 39 40 41 41 41 41 42 42 43 44 45 46

4.1 4.2 4.3 4.4 4.5 4.6 4.7

Microfibers in different application forms . . . . . . . . . . . . . . . . . Makrofibers in different application form . . . . . . . . . . . . . . . . . Steel fibers in frequent application form . . . . . . . . . . . . . . . . . . Steel fiber concrete, in cross-section; image ArcelorMittal . . . . . . . . . Steel fiber concrete cracked, but a force-transmitting; image ArcelorMittal steel fiber in hook form . . . . . . . . . . . . . . . . . . . . . . . . . . . steel fiber in waveform . . . . . . . . . . . . . . . . . . . . . . . . . . .

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49 49 50 50 51 52 53

© Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2021 B. Wietek, Fiber Concrete, https://doi.org/10.1007/978-3-658-34481-8

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251

List of Figures

252 . . . .

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53 55 55 56

5.1 5.2 5.3 5.4 5.5 5.6 5.7

Dosage for fiber concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dosing device for fibers of the company Incite . . . . . . . . . . . . . . . . . . Blow-in device for fibers from the company La Matassina . . . . . . . . . . . . Typical hedgehog formation during removal from the truck mixer . . . . . . . . Destruction of the hedgehogs with hammer in front of the inlet to the pump . . Inlet from truck mixer to concrete pump (picture by Rindler GmbH . . . . . . . Concreting with fiber-reinforced concrete (image from Krampe Harex Fibrin GmbH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Basement wall d = 20 cm made of fiber-reinforced concrete on fiber-reinforced concrete floor slab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Precast wall as retaining wall made of fiber-reinforced concrete . . . . . . . . . Foundation mountain station Karlesjochbahn 3.300 m (a) Rock face with anchors (b) Concreting process with fiber concrete . . . . . . . . . . . . . . . . . . . . Application of fiber sprayed concrete (Gerlosberg Zillertal-Tyrol) . . . . . . . . Surface of the fiber sprayed concrete . . . . . . . . . . . . . . . . . . . . . . . Slope stabilisation on the A-13 Brenner motorway next to the Luegg bridge . . Excavation support for a ski depot in Fiss-Tirol . . . . . . . . . . . . . . . . .

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60 61 61 62 63 64

5.8 5.9 5.10 5.11 5.12 5.13 5.14

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Steel fiber in compressed form . . . . . . . . glass fibers in the bundle wound (acc to Zorn) integral glass fibers (acc to Zorn) . . . . . . . water-dispersible glass fibers (acc to Zorn) . .

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4.8 4.9 4.10 4.11

Flexural tensile strengths with possible crack components . . . . . . . . . . . . Specimen in fracture state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mohr’s stress circle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mohr’s stress circle, relationships at rupture . . . . . . . . . . . . . . . . . . . Graphic for determining the shear angle ϕ . . . . . . . . . . . . . . . . . . . . Active stress surface in Mohr’s representation . . . . . . . . . . . . . . . . . . Fracture criterion according to Coulomb . . . . . . . . . . . . . . . . . . . . . Tunnel fire - explosive heat development (Image: Propex) . . . . . . . . . . . . Tunnel section Vomp-Terfens of the Brenner Railway (Fibermesh 150) . . . . . Concrete strength development . . . . . . . . . . . . . . . . . . . . . . . . . . Development of the cement structure during the setting process (illustrations taken from VDZ teaching aid: 4. Hydration of the cement and structure of the hardened cement paste) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.12 Concrete in the setting phase . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.13 Fiber concrete in the setting phase . . . . . . . . . . . . . . . . . . . . . . . . 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 6.10 6.11

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68 69 70 70 71

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78 80 80 81 82 83 83 86 87 90

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253

List of Figures 6.14 6.15 6.16 6.17 6.18 6.19 6.20 6.21 6.22 6.23 6.24 6.25 6.26 6.27 6.28 6.29 6.30 6.31 6.32 6.33 6.34 6.35 6.36 6.37 6.38 6.39 6.40 6.41 6.42 6.43 6.44 6.45 6.46 6.47 6.48 6.49 6.50

Shrinkage cracks in concrete . . . . . . . . . . . . . . . . . . . Avoidance by fibers . . . . . . . . . . . . . . . . . . . . . . . . Mix calculation for normal concrete . . . . . . . . . . . . . . . Grain distributions for GK32 mm . . . . . . . . . . . . . . . . . Geometry of the grains . . . . . . . . . . . . . . . . . . . . . . Grain surface of the grain distribution . . . . . . . . . . . . . . Surface area of the fibers at a given dosage . . . . . . . . . . . . Use of microfibers to prevent shrinkage cracks . . . . . . . . . . Fiber extraction tests according to Pfyl . . . . . . . . . . . . . . Fiber extract smooth fiber . . . . . . . . . . . . . . . . . . . . . Extract of final compressed fiber . . . . . . . . . . . . . . . . . Concrete fracture with spatially distributed fibers . . . . . . . . Young’s moduli of different fiber materials . . . . . . . . . . . . Geometry of the Fibers . . . . . . . . . . . . . . . . . . . . . . Influence of the fiber type on the geometry factor . . . . . . . . Explanation of fiber density . . . . . . . . . . . . . . . . . . . . Concrete fracture with spatially distributed fibers . . . . . . . . Force corner for any fiber distributed in space . . . . . . . . . . Fiber distribution shifted with respect to the direction of force . Fiber distribution in relation to the direction of force . . . . . . Fiber distribution on a hemisphere . . . . . . . . . . . . . . . . Section through hemisphere with layer separation . . . . . . . . Hemisphere with uniform area division . . . . . . . . . . . . . . Calculation of the average fiber angle . . . . . . . . . . . . . . Influence of loss of fiber strength due to faulty fibers . . . . . . Fibers with forming angle . . . . . . . . . . . . . . . . . . . . . Friction factors depending on surface condition . . . . . . . . . Mohr’s stress circuit . . . . . . . . . . . . . . . . . . . . . . . . Simple bending beam for the test procedure . . . . . . . . . . . Moment line due to simple load . . . . . . . . . . . . . . . . . Simple bending beam with notch for test execution . . . . . . . Moment line due to simple load . . . . . . . . . . . . . . . . . Bending beam crack development (Image: FH Aachen) . . . . . Bending beam crack measurement (Image: FH Aachen) . . . . . Bending beam crack surface (Image: FH Aachen) . . . . . . . . Bending beam for the test (Image: Krampe-Harex Fibrin GmbH) Standard bending beam for the test procedure . . . . . . . . . .

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94 94 95 96 96 97 97 98 99 99 99 100 101 101 102 103 104 104 105 105 106 107 107 108 108 109 110 111 113 113 114 114 115 115 116 116 117

List of Figures

254

6.51 Moment line due to load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 7.10 7.11 7.12 7.13 7.14 7.15 7.16 7.17 7.18 7.19 7.20 7.21 7.22 7.23 7.24 7.25 7.26 7.27 7.28 7.29 7.30 7.31 7.32 7.33 7.34

Condition 1, Concrete is uncracked . . . . . . . . . . . . . . . . . . . . . . . . Rectangular beam with specified values . . . . . . . . . . . . . . . . . . . . . Load-bearing moments for condition 1 as a function of dosage for two types of fibers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Condition 1-2, concrete is partially cracked . . . . . . . . . . . . . . . . . . . Load-bearing moments with increasing crack . . . . . . . . . . . . . . . . . . Condition 2, concrete is maximaly cracked . . . . . . . . . . . . . . . . . . . . Load-bearing moments for condition 2 as a function of the dosage . . . . . . . Stress state at small eccentricity . . . . . . . . . . . . . . . . . . . . . . . . . Stress state at mean eccentricity . . . . . . . . . . . . . . . . . . . . . . . . . Stress state at large eccentricity . . . . . . . . . . . . . . . . . . . . . . . . . . Buckling according to Euler . . . . . . . . . . . . . . . . . . . . . . . . . . . Single span beam shear force and moment line . . . . . . . . . . . . . . . . . . Stress distribution in the beam . . . . . . . . . . . . . . . . . . . . . . . . . . Mohr’s stress circle with shear stress . . . . . . . . . . . . . . . . . . . . . . . Shear stress in the cross-section according to Coulomb . . . . . . . . . . . . . Possible fracture situation for a support . . . . . . . . . . . . . . . . . . . . . Force corner in the oblique fracture joint at angle α . . . . . . . . . . . . . . . Distribution of tensile stresses as a function of the fracture angle for an example Condition 1 concrete is uncracked . . . . . . . . . . . . . . . . . . . . . . . . Stress state at small eccentricity . . . . . . . . . . . . . . . . . . . . . . . . . Stress state at mean eccentricity . . . . . . . . . . . . . . . . . . . . . . . . . Buckling cases according to Euler . . . . . . . . . . . . . . . . . . . . . . . . Single span beam shear force and moment line . . . . . . . . . . . . . . . . . Stress distribution in the beam . . . . . . . . . . . . . . . . . . . . . . . . . . Mohr’s stress circle with shear stress . . . . . . . . . . . . . . . . . . . . . . . Shearing stress in cross-section according to Coulomb . . . . . . . . . . . . . cross section of the hall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Load data for the floor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Moments to be absorbed in the floor slab . . . . . . . . . . . . . . . . . . . . . Input data for calculating with enduro HPP 45 . . . . . . . . . . . . . . . . . . Geometry and moments and safeties . . . . . . . . . . . . . . . . . . . . . . . Result of the calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . straight stair flight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Input data for calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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131 132 133 134 135 136 137 139 140 142 143 143 144 145 146 146 148 150 151 152 154 155 155 156 160 160 160 161 162 162 163 164

255

List of Figures 7.35 7.36 7.37 7.38 7.39 7.40 7.41 7.42 7.43 7.44 7.45 7.46 7.47 7.48 7.49 7.50 7.51 7.52 7.53 7.54 7.55 7.56 7.57 7.58 7.59 7.60 7.61 7.62 7.63 7.64 7.65 7.66 7.67 7.68 7.69 7.70

Geometry and moment and safeties . . . . . . . . . . . . . . . . . . . . . . . . Result of the calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Test plate cross-section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Top view of test plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Input field of the design for fiber-reinforced concrete . . . . . . . . . . . . . . Enter the dimensions of the moment and the safety . . . . . . . . . . . . . . . Determination of the load-bearing moments that can be absorbed for the fiberreinforced concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Test plate 1 and load 2 of the Bissen 2004 test; Image: ArcelorMittal . . . . . . Input data for calculation with TABIX 1/30l . . . . . . . . . . . . . . . . . . . Geometry and moment and safeties . . . . . . . . . . . . . . . . . . . . . . . . Result of the calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Static system of a facade slab . . . . . . . . . . . . . . . . . . . . . . . . . . . Input field of the design for fiber-reinforced concrete . . . . . . . . . . . . . . Geometry and forces and safeties for the GFB plate . . . . . . . . . . . . . . . Result of the calculation for the GFB plate . . . . . . . . . . . . . . . . . . . . Diaphragm wall with indication of moment distribution . . . . . . . . . . . . . Input field of the design for fiber-reinforced concrete . . . . . . . . . . . . . . Geometry and forces and safeties at 5 m depth . . . . . . . . . . . . . . . . . . Result of the calculation at 5 m depth . . . . . . . . . . . . . . . . . . . . . . Geometry and forces and safeties at 12.5 m depth . . . . . . . . . . . . . . . . Result of the calculation at 12.5 m depth . . . . . . . . . . . . . . . . . . . . . Section of a multi-family house in Winklarn . . . . . . . . . . . . . . . . . . . Input field of the design for fiber-reinforced concrete . . . . . . . . . . . . . . Geometry and forces and safeties for basement wall . . . . . . . . . . . . . . . Result of the calculation for basement wall . . . . . . . . . . . . . . . . . . . . Input field of the design for fiber-reinforced concrete . . . . . . . . . . . . . . Geometry and forces and buckling case . . . . . . . . . . . . . . . . . . . . . Result of the calculation for the columns with buckling load . . . . . . . . . . Input field of the design for fiber-reinforced concrete . . . . . . . . . . . . . . Geometry and forces and buckling case . . . . . . . . . . . . . . . . . . . . . Result of the calculation for the columns with buckling load . . . . . . . . . . Single span beam with shear force and moment line . . . . . . . . . . . . . . . Detail of stair support for shear check . . . . . . . . . . . . . . . . . . . . . . Input field of the design for fiber-reinforced concrete . . . . . . . . . . . . . . 69 Geometry and forces for supports . . . . . . . . . . . . . . . . . . . . . . . Result of the calculation for the stair support . . . . . . . . . . . . . . . . . . .

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165 165 167 167 168 169

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169 170 171 172 172 174 175 176 176 178 179 180 180 181 181 182 183 184 184 185 186 186 187 188 188 189 189 190 190 191

List of Figures

256

Input field of the design for fiber-reinforced concrete . . . . . . . . . . . . . . Geometry and forces for supports . . . . . . . . . . . . . . . . . . . . . . . . . Result of the calculation for the slab support . . . . . . . . . . . . . . . . . . . Excavation pit in Aldrans-Tirol . . . . . . . . . . . . . . . . . . . . . . . . . . Section showing the shoring of the excavation pit . . . . . . . . . . . . . . . . Concrete quality for BV Aldrans . . . . . . . . . . . . . . . . . . . . . . . . . Fiber quality and dosage for BV Aldrans . . . . . . . . . . . . . . . . . . . . . Fiber-reinforced concrete parameters for given materials . . . . . . . . . . . . Fiber-reinforced concrete characteristic values with safety . . . . . . . . . . . . Layer-by-layer design of the fiber-reinforced concrete wall at the excavation pit in Aldrans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.81 Fugenanordnung beim Spritzbeton . . . . . . . . . . . . . . . . . . . . . . . . 7.82 Joint arrangement for shotcrete underpinning in Fiss-Tirol . . . . . . . . . . . 7.83 Spray test for the spray joint . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.84 Core drilling during spray test for joint formation . . . . . . . . . . . . . . . . 7.85 Joint formation in the two core samples . . . . . . . . . . . . . . . . . . . . . 7.86 Drill cores for testing in the laboratory . . . . . . . . . . . . . . . . . . . . . . 7.87 Results of the tear-off strength test in the laboratory . . . . . . . . . . . . . . . 7.88 Strength of fiber shotcrete at a given dosage . . . . . . . . . . . . . . . . . . . 7.89 Construction pit in Koblenz-Pfalz with steel fiber shotcrete on the occasion of BUGA 2012 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.90 Section showing the shoring of the excavation pit . . . . . . . . . . . . . . . . 7.91 Concrete quality for BV bottom station Ehrenbreitenstein castle lift . . . . . . . 7.92 Fiber quality and dosage for BV valley station Ehrenbreitenstein castle lift . . . 7.93 Fiber-reinforced concrete characteristic values for given materials . . . . . . . 7.94 Fiber-reinforced concrete characteristic values with safety . . . . . . . . . . . . 7.95 Layer-by-layer design of the fiber-reinforced concrete wall in the excavation pit at the Ehrenbreitenstein castle lift valley station . . . . . . . . . . . . . . . . . 7.96 Stresses with inverted T-beam . . . . . . . . . . . . . . . . . . . . . . . . . . 7.97 Cross-section of a bridge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.98 Fiber concrete tensile, compressive strength . . . . . . . . . . . . . . . . . . . 7.99 Cantilever arm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.100Field plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.101Longitudinal section of a bridge . . . . . . . . . . . . . . . . . . . . . . . . . 7.102from diagonally below . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.103from diagonal above . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.104Design of the arch girder for buckling . . . . . . . . . . . . . . . . . . . . . . 7.71 7.72 7.73 7.74 7.75 7.76 7.77 7.78 7.79 7.80

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191 192 192 193 194 195 195 196 196

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196 197 197 198 198 199 199 200 200

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201 202 203 203 204 204

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204 205 206 207 207 207 208 208 208 209

257

List of Figures

8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 8.10 8.11 8.12 8.13 8.14 8.15 8.16 8.17 8.18 8.19 8.20 8.21 8.22 8.23 8.24

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210 211 211 212 213 214 215 215 216 217 218 218

Floor slab for residential house . . . . . . . . . . . . . . . . . . . . . . . . Production of a hall floor with fiber concrete (Photo: Rindler) . . . . . . . . Finished hall floor with fiber concrete (Photo: Rindler) . . . . . . . . . . . Fiber-reinforced concrete basement wall in Jerzens (Tyrol) . . . . . . . . . Fiber-reinforced concrete basement wall in Imst-Tyrol . . . . . . . . . . . . Stress during reversed T-beam . . . . . . . . . . . . . . . . . . . . . . . . Exterior wall as T-beam of the Muldenbahn garage in the Pitztal valley . . . Test ceiling with 3/3 fields in Bissen Luxembourg . . . . . . . . . . . . . . Ceiling of a garage building at a cablecar station . . . . . . . . . . . . . . . Beam at cable car station structure . . . . . . . . . . . . . . . . . . . . . . Fiber-reinforced concrete carriageway . . . . . . . . . . . . . . . . . . . . Rockfall gallery for pedestrians and cyclists . . . . . . . . . . . . . . . . . Road gallery for avalanche protection . . . . . . . . . . . . . . . . . . . . Tunnel in Oberlech Backup . . . . . . . . . . . . . . . . . . . . . . . . . . Tunnel in Oberlech upgraded . . . . . . . . . . . . . . . . . . . . . . . . . Tunnel upgraded in Norway (Photo Rindler) . . . . . . . . . . . . . . . . . Segments before installation . . . . . . . . . . . . . . . . . . . . . . . . . Tubbings installed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fiber-reinforced concrete pipes . . . . . . . . . . . . . . . . . . . . . . . . Precast wall element made of fiber-reinforced concrete (Photo Rindler) . . . Precast fiber-reinforced concrete staircase formed and erected in the factory Precast stairs made of fiber-reinforced concrete installed . . . . . . . . . . Retaining wall of precast concrete with fiber . . . . . . . . . . . . . . . . . Slope stabilization in Patsch near Innsbruck . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . .

221 222 222 223 224 225 225 226 227 228 229 230 231 232 233 233 234 235 236 236 237 238 238 239

. . . . . . . . . . . .

. . . . . . . . . . . .

. . . . . . . . . . . .

. . . . . . . . . . . .

7.105Basic section for a harbor wall . . . . . . . . . . . . . . . 7.106Ground plan of a harbor wall . . . . . . . . . . . . . . . . 7.107Soil properties for the harbor wall . . . . . . . . . . . . . 7.108Section of a harbor wall . . . . . . . . . . . . . . . . . . . 7.109Bending moments and normal forces in the wall . . . . . . 7.110Edge stresses in the wall . . . . . . . . . . . . . . . . . . 7.111Characteristic values of fiber-reinforced concrete . . . . . 7.112Design of the fiber concrete of the wall . . . . . . . . . . . 7.113Design of the slab with glass fiber concrete . . . . . . . . 7.114Comparison of different fibers in fiber-reinforced concrete 7.115Design of the slab with carbon fiber concrete . . . . . . . 7.116Comparison of different fibers in fiber-reinforced concrete

List of Figures

258 8.25 8.26 8.27 8.28 8.29 8.30 8.31 8.32 8.33

Excavation support in Ischgl - plans . . . . . . . . . . . . . . . . . . . . . . . . 240 Securing the excavation pit in Ischgl - pictures . . . . . . . . . . . . . . . . . . . 241 Spraying a slope protection on the Gerlosberg - Tyrol . . . . . . . . . . . . . . . 242 Slope stabilization near the Brenner motorway . . . . . . . . . . . . . . . . . . . 243 Securing a house wall in Innsbruck . . . . . . . . . . . . . . . . . . . . . . . . . 244 Production of a floor slab in residential construction with fiber-reinforced concrete 245 Tests with fiber shotcrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245 Construction of a tunnel with fiber-reinforced concrete . . . . . . . . . . . . . . 246 Construction of a deep excavation pit shoring with fiber-reinforced shotcrete . . . 246

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Index ω-method, 140 additives, 21, 33 admixtures, 34 aggregate, 21, 30 aggressive environments, 50 Alkali-resistant fibers, 54 anchor, 67 anchors, 194, 210 Animal fibers, 57 applications, 221 artificial fibers, 47 ASTM, 13 bar anchor, 67 Base plates, 221 basement wall, 65, 182, 223 basic material, 77 beach, 55 beam, 65, 142, 177, 228 bearing force, 145 bending, 148 bending beam, 112 bending tensile strength, 79 Bending with longitudinal force, 135 bond stress, 82 breakout, 145 Breakout of a support, 145, 157 breccia, 4 BS, 13 buckling, 140 building material, 51, 221

building materials, 112 Bulk density, 21 calculation, 121 calculation method, 158 capillary water, 86 carbon fiber, 76 carbonated area, 89 carbonated zone, 51 carbonation, 46 ceilings, 226 cement, 21, 28, 90 cement stone, 42 cementum, 4 civil engineering, 64 classification, 22 coating, 47 cohesion, 82 coils, 55 colum, 65 column, 185 Compressed form, 53 Compression struts, 152 compressive force, 149 compressive strength, 143 compressive stress, 81 Concrete, 4 concrete, 21 Concrete classes, 22 concrete compositions, 59 concrete strength class, 59

© Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2021 B. Wietek, Fiber Concrete, https://doi.org/10.1007/978-3-658-34481-8

263

Index

264 conglomerate, 4 Consistency, 21 consistency, 38, 85, 88 construction pit, 239 corrode, 46 corrosion, 30, 50, 88, 177 corrosion prevention, 88 corrosion protection, 30, 210 Coulomb, 22, 83, 143 Coulomb’, 155 crack components, 78 crack proportion, 26 cracked state, 47 cross-section, 78, 79, 159 crystal, 90 crystallization, 93 crystals grow, 85 cube, 24, 77 deformation, 51, 85, 119, 123 degree of hardening, 21 density, 51 design theory, 158 dimension, 121 Dimensioning, 129 DIN, 12 direction of force, 106 distribution, 69 dosage, 51, 79, 94, 103, 147 dosing device, 60 E-Modulus, 48 E-modulus, 101 earth pressure, 210 economic efficiency, 221 EN, 13 Engesser, 140 environment, 45

environmental impact, 37 Euler, 140, 152 excavation, 69, 193 excavation pit, 177 excavation support, 66 exposure classes, 36 fiber, 4 fiber bundle, 55 fiber force, 99 fiber shape, 109 fiber tension, 110 fiber-reinforced concrete, 7, 64 fiber-reinforced shotcrete, 64 Fire behavior, 85 fire protection, 73 fire resistance, 49 fire resistant, 9 flexural strength, 26 floor slab, 221 For fiber-reinforced shotcrete, 68 formwork, 118 foundation, 67 fracture, 23, 119, 145 fracture surface, 145 friction factors, 110 frost, 74 Galleries, 229 geometry factor, 102 glass fiber, 75 Glass fibers, 54, 89 Gotthard tunnel, 85 grading curve, 31 grading curves, 59 grain curve, 96 grain size, 31, 95

265

Index hall constructions, 222 Hall floor, 159 harbor wall, 210 hardened concrete, 98 hardening of concrete, 40 Heavy concrete, 21 hedgehog, 62, 69, 88 hemisphere, 106 History, 2 Hook shape, 52 hydration, 28 hydraulic binder, 28 imperfect system, 108 impermeable, 65 increasing crack, 133 Industrial buildings, 227 Industrial floors, 222 Integral glass fibers, 55 inverted T-plate, 224 Karlesjochbahn, 67 laboratory, 8 laboratory tests, 121 Large eccentricity, 135, 149 Leaf fibers, 57 Lightweight concrete, 21 limestone, 4 limit state, 149 liquid state, 40, 93 Load method, 123 load-bearing capacity, 121, 147 load-bearing moments, 131 longitudinal force, 135 macro fiber, 177 macrofiber, 72 Madersperger, 3

Makrofibers, 49 manhole rings, 235 manufacture, 50 material properties, 121 material selection, 129 maximum cracked, 134 Mean eccentricity, 135, 149 microcracks, 86 microfiber, 72 Microfibers, 85 micropores, 85 microscopic processes, 90 Mikrofibers, 48 mineral, 90 mineral components, 30 minerals, 40 Mitterhofer, 3 mixer, 60 modulus of elasticity, 85 Moh-Coulomb, 24 Mohr, 23, 79, 111, 143, 155 Mohr envelope, 81 Mohr–Coulomb, 161 moisture, 30, 78 moment, 113, 142 moment of inertia, 141, 153 Monier, 5 Monierbeton, 5 mortar, 6 Natural fibers, 57 natural radiation, 74 natural slope, 239 neutralizing system, 46 Non-alkali-resistant fibers, 57 non-cracked, 224 non-cracked state, 66, 147, 177

Index

266 Normal concrete, 21 normal stress, 82 notch in the beam, 113

Residential buildings, 226 resistance, 147 Retaining wall, 238 RILEM, 13

OENORM, 12 Pantheon, 5 partial safety, 124 partly cracked, 131 permeability, 48, 65 pH value, 45, 88 Pipes, 236 Plant fibers, 57 plastic fiber, 72, 94, 159 Plastic fibers, 48, 85 plastic microfibers, 86 plastic state, 40 polypropylene, 48 Polypropylene fibers, 85 pores, 88 Portland, 28 Pozzolan, 28 precast slab, 66 precast wall, 67 prefabricated, 235 prefabricated ceilings, 226 preventing cracking, 78 prism, 22 prism sample, 24 properties, 77 punching, 145 punctiform support, 166 radiesthesian, 74 Rankine, 24 ready-mix concrete, 88 Ready-mixes, 118 reinforced concrete, 5, 65

safety factor, 122, 124, 147 setting process, 90 shear capacity, 79 shear check, 142, 154 shear force, 99, 142, 189 shear strength, 144 shear stress, 82 shotcrete, 68, 72, 193, 231 shotcrete shell, 244 shrinkage, 26, 40, 49, 72, 75, 78, 91 shrinkage cracks, 6, 94 slab, 160 slenderness, 153 slope, 193 slump, 85 Small eccentricity, 135, 149 soil nails, 66, 194 solid concrete, 85 spraying direction, 69 spraying process, 70 staircase, 163 Stairs, 237 standards, 77 Standarts, 12 state 1, 131 static calculation, 160 steel fiber, 68, 94 Steel fiber concrete, 74 steel fibers, 7, 50, 88 stiffening, 40 strength classes, 24 stres-strain curve, 123

267

Index stress analysis, 130 stress area, 83 structural components, 72 structural engineering, 159 surface area, 94, 97 synthetic fiber, 163 T-plate, 224 Tauern tunnel, 85 temperature, 88 tensile force, 135, 149 tensile forces, 94 tensile strength, 8, 51 tensile stress, 25, 81, 97 Test plate in Bissen, 166 test specimen, 24 thermal conductivity, 88 thermal loads, 72 Tresca, 24 truck mixer, 62 Tubbings, 234 tunnel, 231 tunnel arches, 231 tunnel boring machine, 235 Tunnel lining, 231 types of concrete, 35, 59 ultimate load, 123

uncracked, 129 uncracked material, 72, 224 uniform distribution, 104 vapor pressure, 85 videos, 245 Vitruv, 2 volcanic ash, 4 von Mises, 24 wall, 65, 177 wall constructions, 223 Wall protection, 243 water, 33 water bath, 118 Water dispersible glass fibers, 56 water pressure, 210 water tightness, 177 water-binding, 93 waterproof, 47, 49 watertight, 221 watertightness, 177, 224 wave shape, 109 working scaffold, 69 young concrete, 85 Young’s moduli, 101