C.S.E. Connection Study Envirorment: Report Explanation

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Introduction This document is intended as an explanation of some of the key concepts used in the CSE report. The results got in the report refer to all instances of the connection, no matter where they are placed in the original structure. Each instance of the connection may be got by a rigid body motion of another instance of the same connection. In order to check all the instances of this connection, the first instance of the connection is considered, and then loaded with all the forces arising by all the combinations for all the instances of the connection itself. In this way all the instances of the connections are actually checked. The software used to check the connections, CSE, is a very general tool which is able to treat complex structures with many different connections, having many possible different instances. The problem of checking connection is faced in the most general possible way: for this reason, some of the tool and of the checking rules adopted follow computational mechanics general rules, more than ad hoc, specific rules, valid only for some peculiar connection kind.

Background to the software program A detailed explanation of CSE is needed in order to make the reader able to understand the information and the results given in this report. Since the program is based on general rules, those of computational mechanics, and not on fixed structural schemes, the reader should need to understand the terminology used and the main hypotheses assumed, first of all. Then a description of connections computation is provided, starting from the forces applied to the extremities of the members and arriving to the stress levels in the components .

Introduction C.S.E. (Connection Study Environment) is an important and ambitious software project which is under continual development by Castalia s.r.l. The program aims to provide a suitable working environment for designing, verifying and drawing the connections in steel structures. The study of such connections involves some formidably complex issues, and can currently be considered one of the main challenges to be overcome in the field of design automation. There are two sides to this problem of the connections: drawing and calculation. If drawing the connections is a complex problem, calculating them is even more so, for various reasons: 1.There are no universal rules for calculating a simple joint, as various models are acceptable as long as they are balanced; 2.There are no universal rules for calculating the proportion of the stress transferred to a simple joint in the presence of other simple structural joints; 3.The addition or removal or a component can make a considerable difference to the stresses involved; 4.A given component can function in a completely different way depending on the context in which it is used. Analysing and calculating the connections is one factor which makes steel structures more computationally complex than those made of reinforced concrete. The current state of play is that although extensive approaches (creating a certain number of typical connections with limited validity) have been advanced, no sufficiently general intensive approach yet exists. The major problem with the extensive approach to automatic computation is its inflexibility, which does not allow software users either to add new connections or to vary or add to existing ones. An intensive-type connection calculation program should provide:  a general facility for defining connections between n members (generality)  the ability to create connections by freely adding or removing elementary components (flexibility)

 the ability to define the checking rules for individual components quickly and easily, so that the calculation code “learns” how to execute the computation (extendibility and customisability)  the ability to run consistency checks which prevent inefficient connections from being created or which detect inefficiency at the calculation stage (safety and consistency). CSE has been developed in order to provide a tool which meets these requirements as fully as is possible, thus considerably simplifying design practice. CSE successfully relieves the designer of a mountain of calculations which are highly subject to error, as it automatically carries out all computations needed to transfer the actions correctly from the extremities of the members to all the components of the joints (distributing the forces suitably among the various components), whilst of course adding all the moments of transport required without “throwing away” any stress component. It is an extremely laborious, difficult and error-prone job, as anyone who has had to do it at least once can testify, which CSE takes care of completely automatically. This is a highly significant development. CSE is a major step towards an acceptable engineering solution to all the problems associated with the computation of the connections in steel structures. It is a strategically important project which will certainly continue to be extended and enriched over the years to come. For more information see www.steelchecks.com/CSE.

Terminology Bearing surface: a bolt layout with bearing surface is a bolt layout in which part of the surfaces of the bolted components help in bearing the compressive forces developed by bending or compression. The most critical component material (e.g. the concrete in a concrete-steel interface) is described by a no tension constitutive law. The region where crushing due to compressive forces can occur is that enclosed by one or more bearing surface polygons specified by the user. The use of compression bolts provides further help in bearing the compressive part of the stresses.

Block tearing: is a failure mode in which part of a component is torn away. Generally it is caused by the simultaneous action of normal and shear stresses along the failure surface. The failure paths can be different and ideally all must be analysed; the failure happens along the most critical, depending on the forces applied.

Bolt layout: A bolt layout is a set of bolts which all have the same features (diameter, material grade, threaded area) and all connect the same components, in the same order. Chain: is the path that you must ideally take to go from a slave member to the master (member or cleat) or to a member to the constraint. Generally there can be n possible paths, depending on the complexity of the connection. For example: slave member m2 > weld layout W1 > plate P1 > bolt layout B1 > master member m1.

Check sections of a bolt layout: are the sections of the bolt layout at the interface (tangent planes) between the connected plates. It is here that the internal forces are computed. Cleat: is a component which is neither a member nor a joiner. Usually a through is used to transfer forces from one point to another or to stiffen a component (a member or another cleat), such as angle brackets, plates or stiffeners. Component: is any three dimensional solid which forms part of the connection: the components can therefore be members, cleats or joiners. Compressed bolts: bolts are not checked for compression by default in CSE (because usually this compression is carried by surfaces in contact), but the user can specify that the bolt checks should take into account this internal force carried by the bolts, working with any bearing surface present. Connector: is a components chain made up with cleats and joiners. The first and the last components must be joiners. A connector has the following scheme: joiner-cleat-...-joiner. Constraint: there is a "constraint" wherever there is a constrained or restrained node in the FEM model. If the constraint is due to fixed degrees of freedom in the FEM node, the constraint is rigid; on the other hand, if the restraint is only due to other elements not modelled in CSE (plates, membranes or solids) then the constraint is elastic. Flexibility index: this parameter has been introduced in CSE in association with bolt layouts or weld layouts, in order to modify their translational stiffness, which is inversely proportional to the cube of the flexibility index. Instance of a connection: is the repetition of the same identical connection in different parts of the structure, possibly with different orientations. Joiner: is a set of elementary components (bolts or welds) which implement the connection between several joined components. Joiner extremities (bolt layout): are at the mid-plane of the thicknesses of the bolted objects, at the points corresponding to the bolt layout centroids. Joiner extremities (weld layout): one extremity of the weld layout lies in the plane of the face containing the welds; the other is along a segment normal to this face, at a distance from the first extremity equal to a proportion of the throat section of the welds. Master: is a component of a node to which all members connect. Usually the master is the only non interrupted member, but it can be also a cleat (or a set of cleats). Member: is a straight or curved solid element consisting of a single piece, along with the work processes that has been done on it. Member net cross-section: is a reduction of member gross cross-section due to bolt holes, bevels, cuts, or other work processes. Member types: a member can be interrupted or un-interrupted in the node. If it is not interrupted, it can be "cuspidal" (if it ends in the node) or "passing". No tension: a no tension computation is based on a constitutive law which has compressive but no tensile stresses. To compute the material which acts as the bearing support for the bolt layouts, CSE has four different no tension constitutive laws: indefinitely elastic, elastic-perfectly plastic, parabola-rectangle and trilinear. Offsets: it may be that the extremities of a finite element do not coincide with the nodes: in this case there will therefore be eccentricities and thus rigid offsets.

Pin: is a special kind of bolt layout with specific features. The bolt layout has necessarily one pin only. Due to computational reasons the bolt layout is not "shear only", is not an anchor, and does not use a bearing surface, is not slip resistant, etc. Principal axes of a joiner: CSE automatically computes the principal axes of a weld or bolt layout, depending on the position of the elements in the layout and, for weld layouts, also depending on the thickness of the individual welds (throat section); the bolts in one of these layouts, however, always have the same diameter. Renode: the term is derived from the words REal and NODE. It is a complete connection, with all information needed to build it up and to compute it. A renode therefore incorporates all the components needed to define it, together with all their work processes and all the rules and choices devised in connection with the checks. Shear key: is an object embedded into the constraint block so as to carry mainly shear forces and torque, leaving more or less unchanged axial force and bending moments.

Shear-only bolt layout: are bolt layouts with negligible bending and axial stiffness, so that bolts will be loaded by shear forces only (not by axial forces). If more than one bolt layout is capable of bearing a set of actions, and some of the available bolt layouts do not have a relevant stiffness, then the relevant bending and axial forces will be carried only by those joiners which have a relevant stiffness. So if there is more than one bolt layout in the connection, the loads will migrate to those joiners which have suitable stiffness. Shear-only bolt layouts are usually organized so that one or more subset takes some actions while other sets take the others. It is therefore a computational hypothesis set by the user which deals with how the actions are distributed among the joiners of the various components. Slave: is a member which is interrupted in the node so as to connect to the master. Throat section/thickness of a fillet weld: is the height of the largest triangle (with equal or unequal sides) that can be inscribed within the fusion faces and the weld surface, measured perpendicular to the outer side of this triangle (EN 1993-1-8, paragraph 4.5.2). In CSE, fillet welds have triangular cross-section: the effective throat section is therefore the height of this triangle.

Through: see cleat User checks: besides the automatic checks already provided by CSE according to different standards, the user can "teach" the program how to perform further checks. With the system’s genuine internal compiler, the user can actually add variables and conditions, which can be additional checks or pre-requisites that the joint must satisfy in order to be applied. Weld layout: is a set of welds (fillet or penetration) that join the same couple of components, which may be cleats or members. Work processes: 3D modifications done on a member or cleat; available work processes include cuts, bevels, face rotation and translation, etc.

Main rules adopted by the program for the different checks CSE deals with steel connections in a general way. No fixed structural scheme is assumed: the simplest and the most typical connections are just general connections, as well the most complex ones. The program is able to compute applied forces distribution between the components according to equilibrium of forces. Once forces distribution is known, it is possible to compute components utilisation factors. The following steps are followed by the program to check a connection: 1. Internal input forces in the members are distributed between the joiners (weld layouts and bolt layouts) according to their properties (type, stiffness, options settings, etc.) and position. Internal forces depend on user's choice about the combinations to be used (coming from FEM analysis of the structure, imported via table, depending on members elastic or plastic limit forces, etc.). 2. Once forces in joiners have been computed, forces in single welds and in single bolts are computed. 3. Bolts and welds resistance is checked. 4. By the action and reaction principle, forces in the joiners are applied, with sign reversed, to members and cleats. 5. Members and cleats resistance is checked. 6. If defined, user's additional conditions are checked. All the previous steps are explained in following topics.

Determination of the forces flowing in the joiners

Example: forces from member (left) to bolt layout (right)

A detailed description would be very long and complex, as well as being out of the scope of this report. Here we will confine ourselves to a few helpful pointers for using the program and understanding its general behaviour. 1. Once the checks have been launched, the program firstly reconstructs all the chains (see Terminology) and examines all the connections, in search of unconnected or poorly connected components. If this check is successful, the program moves on to the next step. 2. This step entails the preparation of the calculation model. This is a suitable finite element model, in which each component is conveniently modelled using rules which take the basic hypotheses into account (see below). The stiffness of a bolt layout depends on all the parameters which help to define it: the number of bolts, their length, diameter and their exact layout with all the respective distances. The stiffness of a weld depends, similarly, on all its component seams, their throat sections, lengths and exact spatial positions. Solving the model ensures a response which is balanced with the applied forces. Nothing is lost, all the components and moments of transport are correctly taken into account. The model does not discard or neglect any part of the response. The respective allocation of the components of the forces among the various components, as calculated from the model, is the product of the specific simplifying hypotheses established in order to get the model working. In the vast majority of cases, these simplifying hypotheses, which in any case lead to a response which is balanced with the applied loads, do not result in the distribution of internal forces being much different from what it would have been with simplifying hypotheses in a manual calculation. For this to be the case, however, it is critical that any “shear only” bolts are actually specified as “shear only”, in order that the forces flow correctly. The model has as many load cases as there are combinations for analysis. The model is computed internally by the program, giving the notional displacements of the parts that make up the renode, along with the internal actions at the various sections for checking and the various extremities of the joiners. The output of this calculation is the sextuple of internal forces which, in a given combination, stresses a bolt or weld layout. Basic hypotheses CSE is a very large and complex piece of software which can carry out a major proportion of the checks associated with the computation of the joints automatically. The problem that CSE solves is essentially the following: given a collection of members connected up together via cleats and joiners, subject to a certain known state of stress according to beam theory, to calculate the forces which apply to each joiner and to check each joiner, cleats and member. The “known state of stress” consists of the internal forces at the ideal extremities of the members. This state of stress can be evaluated in CSE in different ways (imported results from FEM analysis, imported combinations, elastic or plastic limits for members, etc.; see the description of combinations for more information). In order to compute forces distribution in joiners, CSE adopts some fundamental hypotheses which must always apply. These are set out in the numbered list below, which is followed by a brief discussion. 1. The internal forces at the ideal extremities of the connected members are known. 2. Each joiner connects n components. All the sub-components of the joiner must connect the same components. Joiners which are used partly to connect certain connectors and partly to connect others are not acceptable. 3. The minimum number of connected components is 2. 4. Each component must be connected to something. 5. Each joiner must be connected to something. 6. A joiner cannot be connected to another joiner. 7. There must be an unbroken chain of joiners/cleats from each member to the master ("hierarchical" connections) or from each member to the constraint block (attachments) or from each member to the central body ("central" connections). 8. The joined components can be considered to be much more rigid than the joiners. 9. The behaviour of the joiners under deformation is to be describable with simple linear laws.

Point 1 is part of the preliminaries and has already been discussed. Points 2-7 are typically satisfied during creation of the renode, via the addition of appropriate numbers of suitably located components and joiners in order to achieve the desired aim. Point 8 is largely satisfied in most cases (given that the components must withstand the forces applied without significant local deformations). Hypothesis 8 is not strictly necessary: it may be removed in later versions of CSE which use a more sophisticated computation model (where this is deemed necessary: all the tests carried out up to now do not appear to require this). The FEM modelling after the initial calculation (i.e. the computation which determines the internal actions in the joiners), however, discards this hypothesis and enables the deformation of the joined units modelled to be understood in detail. There is a consequence of considering highly rigid cleats and members, and largely restricting the deformability in the first analysis cycle to the joiners only: i.e. that all the components which connect two parts of a given component (cleat or member) will not be subject to any state of stress at the end of the first calculation sweep (stiffeners). Only parts which connect different objects will be subject to a state of stress. This means that it is not possible to calculate the members’ internal stiffening ribs immediately during the first analysis cycle, but only with the second, once the forces transferred to the member by the joiners “external” to the member itself are known. The FEM modelling of the members and cleats removes this constraint. It may be noted that all the stiffening ribs connecting different objects are subject to a state of stress (e.g. the stiffening plates that join a column to its base plate). Hypothesis 9 is not strictly essential either for CSE, and it may be replaced in future releases with more complex models, provided that there is a genuine need for this. The results obtained for typical joints confirm, however, that this hypothesis does not entail significant losses in the overall calculation of the renode, but only minor readjustments.

Determination of the stresses into joiners sub-components

Example: forces from bolt layout (left) to single bolts (right) Once the internal forces in each joiner are known, the program computes the stresses at each of the joiner’s sub-components (its individual bolts and welds) in all its check sections. The program then will run the joiners resistance checks.

Bolts The shear stresses due to Vu, Vv are distributed equally across the bolts (u and v are bolt layout principal axes, n is the number of bolts, i is the generic bolt):

Vu N Vv Vv ,i  N Vu ,i 

The torque Mt generates a shear in the bolts, which is distributed using the polar moment of inertia of the bolt layout about its center of gravity and the distance of each bolt from it (JP is the polar moment of inertia):

Vu ,i   Vv ,i 

Mt vi Jp

Mt ui Jp

Bolts can be shear-only: in this case, the axial and flexural stiffness of the bolt layout is very small but not zero. If the connection also has other, more rigid joiners which can “take” those force components then these other joiners will be suitably loaded and the shear-only bolt layout will be almost unloaded. This is the normal condition. If, on the other hand, there are no other joiners which can take those force components, then the tensile and bending forces will act on the “shear-only” bolt layout, thus generating highly significant displacements (translations and rotations). Indeed this condition, which is characterised by very high displacements, highlights a contradiction in the definition of the joint, precisely in that the bolt layout cannot be “shear only”. The right way to solve this problem is to remove the “shear only” limitation or to add other joiners which can take the offending forces. Otherwise, if bolts are not shear-only, the normal force and the two bending moments generate normal forces (tension or compression) in the bolts, which are computed using very different methods depending on whether or not the bolt layout has a bearing surface. If the bolt layout does not have a bearing surface then its neutral axis of bending is through the centre of gravity of the bolt set, and the tensile and compressive forces in the individual bolts are determined simply by the formula

Ni 

M N Mu  vi  v u i n Ju Jv

In particular:

n

Ju  v i 1

2 i

n

Jv  u i 1

2 i

n



J p   u i2  vi2



i 1

This kind of operation is on the safety side, of course, but it also neglects the significant contribution to the absorption of the compression forces provided by the contact between the bolted surfaces (i.e. the bearing surface). In effect, the combined bending and compressive/tensile action is thus uniquely absorbed by the bolt layout. In order partially to mitigate the undue conservatism of this nonetheless useful and very common approach, it can sometimes be a good idea not to consider the compression in the bolts, i.e. to calculate it but then neglect it during checking.

If the bolt layout has a bearing surface, a surface therefore will take the unilateral compression forces. The surface reacts to compression but cannot react to tension. The bolt layout calculation becomes non-linear and follows the general approach taken, for example, for computing sections in reinforced concrete, where the concrete does not react to tension. The use of the bearing surface enables more realistic results to be achieved, in particular for smaller tensile forces within the bolt shafts, although it does involve a non-linear calculation for the section and also requires a certain amount of care. The non-linear calculation is carried out by CSE on the basis of the no tension constitutive law which is specified for the bearing surface. This may be a parabola-rectangle, elastic-perfectly plastic, trilinear or unlimited elastic law. The constitutive law for the bolts is elastic perfectly plastic. Having established the constitutive law for the bearing surface, there are several key points to bear in mind. The bearing surface must resist the pressures applied and must readily satisfy the constitutive law applied. There are two typical cases: a) a reinforced concrete foundation for which a parabola-rectangle or unlimited linear law will be adopted; b) a flanged joint where the bearing surface is the flange, which will need to be suitably stiffened to withstand the pressures applied. The bearing surface must be specified so as to be strong and so as not to give rise to situations which are physically impossible (e.g. a bearing surface acting in an area where there is only one surface, as opposed to two in contact). Suffice it to say that for bolt layouts with a bearing surface, the computations are non-linear and the surface must be of suitable dimensions to be able to bear the loads applied (also see inherent topic). Note well: CSE always computes the parasitic moments in the bolt shafts (then user can decide to neglect them for bolts checks).

Welds Fillet welds or individual weld layouts are checked using the throat sections projected onto the face of contact between the two joined components. This is the face which the two welded objects must, for constructional reasons, have in common. Thus projected, the throat sections constitute a collection of rectangles in various orientations. These give rise to an overall shape whose centre of gravity and principal axes can be calculated. The weld’s internal actions are also computed by CSE in relation to the principal axes of the weld itself. As already mentioned, for each weld there is a rectangle of length L and throat section t. The weld’s moment of inertia, Lt3/12, about its minor axis of inertia is set to zero by CSE, since the flexure about the weak axis of the individual weld would give rise to a perpendicular variation of n in the thickness, which is not permitted by the checking models currently available for welds. The upshot of this is that a weld layout comprising a single weld has no stiffness for that flexure and thus is a potential point of static indeterminacy. This is flagged up by the program at the analysis and checking stage, although it is not necessarily a problem: if there are other stiffnesses which can limit those rotations, the model will still be computable. To circumvent hypostaticity, CSE will nevertheless add a small stiffness for numeric purposes only. Given the polar and bending moments of inertia, the areas and the six actions applied in the principal reference (N, Vu, Vv, Mt, Mu, Mv), the software calculates the values of tper, tpar and nper for each weld seam at each of its extremities.  tpar is the tangential stress acting parallel to the direction of the weld (i.e. the line joining its extremities P 1 and P2).  tper is the tangential stress acting at right angles to the weld.  nper is the stress normal to the weld (i.e. along the z-axis).

 The weld’s extremities P1 and P2 lie on the mid-point of the segment of length equal to the throat section, respectively at the two extremities of the weld length L. The components tu and tv are first calculated then reprojected to give tper and tpar. The formulae are as follows:

tu ,i , j 

Vu M t  vi , j A Jp

tv ,i , j 

Vv M t  ui , j A Jp

n per ,i , j 

N Mu M  vi , j  v ui , j A Ju Jv

where i is the ith weld, j is extremity 1 or 2, A is the area of the layout, Jp is its polar moment of inertia, and Ju and Jv are its moments of inertia about the principal axes (u, v). If  is the angle between the principal axes (u,) and the reference axes (x,y) of the weld, and i is the angle of the ith weld in relation to the axes (x,y), then:

t par  tu cos(i   )  tv sin(i   ) t per  tu sin(i   )  tv cos(i   ) Bolts checks EN1993-1-8 IS 800:2007-WS (Working Stress) IS 800:2007-LS (Limit States) AISC-ASD (Allowable Stress Design) AISC-LRFD (Load and Resistance Factor Design) CNR 10011 AS (Allowable Stresses) CNR 10011 SL (Limit States)

Eurocode 3 - EN1993-1-8 Bolts

Resistance check formulae for bolts not being slip-resistant are given below. The presence of a pre-load does not affect the computation.

eN   M , 2

N M  kM   M ,2 0.9 f u Ares 0.9 f uWcomp

V eV   M , 2 ( bolt class 4.6,5.6,8.8); 0.6 f u Acomp eV   M , 2

V ( bolt class 4.8,5.8,6.8,10.9); 0.5 f u Acomp

if ( eV  1.e  3) AND ( eN  1.e  3)e  eN elseif ( eV  1.e  3) AND ( eN  1.e  3)e  max{ eV ,eN } elseif ( eN  1.e  3) AND ( eV  1.e  3)e  eV

elseif ( eN  1.0)OR ( eV  1.0)e  max eV , eN  else e  eV  if (total )

eN 1.4 Acomp  A

elseif (threaded ) Acomp  Ares if (total )

Wcomp  W

elseif (threaded ) Wcomp  Wres In previous formulae, if parasitic bending has been neglected, we have kM=0, otherwise kM=1.

Slip-resistant bolts

A slip-resistant joint can be associated with a bolt layout. In this case, resistance checks on the bolt layout take account of tension only, which is necessarily going to be present, and not shear. Instead, the latter is divided by a suitable limit shear value, which depends on the effective tension in the bolt, and also of course on the active standard and the settings specified for the bolt layout: pre-load, coefficient of friction, etc. If the joint is slip-resistant then bearing stress checks do not apply. The bolt layout is subject to two checks: the tension check in the shaft, and the shear check. If parasitic moments in the shaft have not been neglected, the stress associated with them is then added to the stress due to the tension. The part of component total utilisation associated to axial force ( eN ) is the same one already explained in bolts resistance checks. If a bolt layout is just-shear and slip-resistant, bendings on the layout cause axial forces in bolts, not bending. Check formulae are the following:

Fp ,C  K n  f ub  Ares

eV   M 3

F

p ,C

V  0.8 N   

eV  99.

F F

p ,C

 0.8 N , N with sign

p ,C

 0.8 N 





e  max eV , e N  Fp,C is the preload force, expressed as the fraction Kn of the bolt’s ultimate load; fu,b is the bolt ultimate stress; Ares is the net area of the threading; V is the maximum computed shear;  is the coefficient of friction;  is hole coefficient; eV > 1 means the limit value is exceeded, resulting in a slip of connection.

Anchor bolts If a bolt layout is classed as an anchor, the pull-out checks are used to supplement the normal strength checks made on the layout. In practice, the pull-out force N on each bolt is compared with a limit value Fd, thus generating a utilisation index. This utilisation index is associated with the bolt layout, not the constraint block on which the bolt layout is presumably anchored. As in the other cases, this index is compared with that obtained for the bolt layout after the other checks and, if larger, is stored along with the cause which gave rise to it. In detail the rule is the following:

E

N Fd

Fd 

FL



where the safety factor  is equal to 1 for Eurocode 3. This check is omitted if a compression is present, as it is assumed that there will be a bearing surface to react it.

The calculation of limit pull-out force FL depends on the kind of the anchor defined by the user and on some parameters. It is possible to define 5 different kinds of anchor, that are checked in 5 different ways.

Kind 1 The bond stress between the bar and concrete is responsible for the resistance. The rule is:

    f bd  FL    l      2  n 1       a   fbd

is the design tangential bond stress between the bar and concrete;  it is the bar diameter a it is the minimum distance between the bar and the free surface of the constraint block (end of concrete) ln it is the straight length of anchor Kind 2 Similar to kind 1 but also a hook is resisting, which increases the pull-out force. The rule is:

    f bd   ln  7.4  r  3.5  l2      FL   2     1      a  fbd

is the design tangential bond stress between the bar and concrete; it is the bar diameter a it is the minimum distance between the bar and the free surface of the constraint block (end of concrete) ln it is the straight length of anchor



r l2

is the hook radius is the length of the straight part of the bar, after the hook

Kind 3 Similar to kind 1, but also a washer circular plate is present. The rule is:

      f bd   2 FL    l      f    r  n cd 2   1           a      fbd fcd

is the design tangential bond stress between the bar and concrete; is the design compressive stress of concrete  it is the bar diameter a it is the minimum distance between the bar and the free surface of the constraint block (end of concrete) ln it is the straight length of anchor r is the washer radius Kind 4 Similar to kind 3, but the resisting mechanism use concrete cone detachment from constraint block. Basically the formula provided in Eurocode 2, §6.2 is assumed, considering the maximum force guaranteed by such mechanism and checking that specific limit between dimensions are met. The rule is:

FL  3  f cd    r 2

ln  2  r a  3 r fcd is the design compressive stress of concrete a it is the minimum distance between the bar and the free surface of the constraint block (end of concrete) ln it is the straight length of anchor r is the washer radius The program checks also that the dimensions meet the necessary inequalities, and thus also a, r and ln are used. Kind 5 If the user wishes to directly input the limit pull-out force (unfactored) he/she may wish to input directly the value of FL (that will be later divided by  to get Fd).

Pins The resistance checks of a pin are generally different from those of a bolt. The pin shaft is always computed keeping into account the computed bending, no matter the choice to neglect "parasitic bending" in bolt layouts. The checks of the pin shaft are different from those of a bolt for three main reasons: 1. the limit allowable stress due to axial force is set equal to 1N/mm 2 (1MPa). If the axial force is higher than the value 1MPa x r2, the pin does not pass the check. If it is lower, the force is discarded. 2. The limit tangential stress allowable for torsion Mt is equal to 1N/mm 2. If the torque applied is higher than this limit (equal to 1MPa x r3/2), the shear V in the shaft of the pin is notionally set equal to 1x1012N and consequently the pin will not pass the check. 3. The combination rule of the effects due to shear V and bending M for some standard is different from that of the bolts.

Therefore the expected forces carried by a pin are shear V and bending M, while axial force N and torque Mt, should be negligible.

eM   M 0

M 1.5W gp  f yp

eV   M 2

V 0.6 f up Agp

if (eV  1.e  3) AND (eM  1.e  3) e  eM

else if (eV  1.e  3) AND (e M  1.e  3) e  max eV , e M  else if (eM  1.e  3) AND (eV  1.e  3) e  eV



else e  eV2  eM2



Note well: pin's torsional inertia moment is theoretically null; in order to prevent large displacements in case of very small offsets multiplied by high forces, a fictitious torsional inertia moment is assigned to the pin (Jt,pin). Conventionally, it is equal to 1/1000 of shaft circle's torsional inertia moment.

J t , pin 

J t ,circle 1000



 r4 2

1  1000

Indian Standard IS 800:2007-WS (Working Stress) Bolts Resistance check formulae for bolts not being slip-resistant are given below. The presence of a pre-load does not affect the computation.

e N 1  max{  m ,b

N N ;1.1 } 0.6  0.9 f u Ares 0.6  0.9 f y A

e N 2  k M   m ,b

M 0.6  0.9 f uWcomp

eN  eN1  eN 2 eV   m ,b

3V 0.6 f u Acomp

if (eV  1.e  3) AND (e N  1.e  3)e  e N elseif (eV  1.e  3) AND (e N  1.e  3)e  max{ eV , e N } elseif (e N  1.e  3) AND (eV  1.e  3)e  eV else e  e N2  eV2 if (total )

Acomp  A

elseif (threaded ) Acomp  Ares if (total )

Wcomp  W

elseif (threaded ) Wcomp  Wres In previous formulae, if parasitic bending has been neglected, we have kM=0, otherwise kM=1.

Slip-resistant bolts

A slip-resistant joint can be associated with a bolt layout. In this case, resistance checks on the bolt layout take account of tension only, which is necessarily going to be present, and not shear. Instead, the latter is

divided by a suitable limit shear value, which depends on the effective tension in the bolt, and also of course on the active standard and the settings specified for the bolt layout: pre-load, coefficient of friction, etc. If the joint is slip-resistant then bearing stress checks do not apply. The bolt layout is subject to two checks: the tension check in the shaft, and the shear check. If parasitic moments in the shaft have not been neglected, the stress associated with them is then added to the stress due to the tension. The part of component total utilisation associated to axial force ( eN ) is the same one already explained in bolts resistance checks. If a bolt layout is just-shear and slip-resistant, bendings on the layout cause axial forces in bolts, not bending. Check formulae are the following:

F p ,C  K n  f ub  Ares eV   m , f

V 0.6  F p ,C    

e  eV2  e N2 Fp,C is the preload force, expressed as the fraction Kn of the bolt’s ultimate load; fu,b is the bolt ultimate stress; Ares is the net area of the threading; V is the maximum computed shear;  is the coefficient of friction;  is hole coefficient; eV > 1 means the limit value is exceeded, resulting in a slip of connection. In the code, no prescription was found in order to take into account the possible decreasing of limit shear as a function of applied loads.

Anchor bolts If a bolt layout is classed as an anchor, the pull-out checks are used to supplement the normal strength checks made on the layout. In practice, the pull-out force N on each bolt is compared with a limit value Fd, thus generating a utilisation index. This utilisation index is associated with the bolt layout, not the constraint block on which the bolt layout is presumably anchored. As in the other cases, this index is compared with that obtained for the bolt layout after the other checks and, if larger, is stored along with the cause which gave rise to it. In detail the rule is the following:

E

N Fd

Fd 

FL



where the safety factor  is equal to 1.666 for IS800WS. This check is omitted if a compression is present, as it is assumed that there will be a bearing surface to react it. The calculation of limit pull-out force FL depends on the kind of the anchor defined by the user and on some parameters. It is possible to define 5 different kinds of anchor, that are checked in 5 different ways.

Kind 1 The bond stress between the bar and concrete is responsible for the resistance. The rule is:

    f bd   l   FL   2     n 1       a   fbd

is the design tangential bond stress between the bar and concrete;  it is the bar diameter a it is the minimum distance between the bar and the free surface of the constraint block (end of concrete) ln it is the straight length of anchor Kind 2 Similar to kind 1 but also a hook is resisting, which increases the pull-out force. The rule is:

    f bd   ln  7.4  r  3.5  l2      FL   2     1      a  fbd

is the design tangential bond stress between the bar and concrete;  it is the bar diameter a it is the minimum distance between the bar and the free surface of the constraint block (end of concrete) ln it is the straight length of anchor r l2

is the hook radius is the length of the straight part of the bar, after the hook

Kind 3 Similar to kind 1, but also a washer circular plate is present. The rule is:

      f bd   2 FL    l      f    r  n cd 2   1           a      fbd fcd

is the design tangential bond stress between the bar and concrete; is the design compressive stress of concrete  it is the bar diameter a it is the minimum distance between the bar and the free surface of the constraint block (end of concrete) ln it is the straight length of anchor r is the washer radius Kind 4 Similar to kind 3, but the resisting mechanism use concrete cone detachment from constraint block. Basically the formula provided in Eurocode 2, §6.2 is assumed, considering the maximum force guaranteed by such mechanism and checking that specific limit between dimensions are met. The rule is:

FL  3  f cd    r 2

ln  2  r a  3 r fcd is the design compressive stress of concrete a it is the minimum distance between the bar and the free surface of the constraint block (end of concrete) ln it is the straight length of anchor r is the washer radius The program checks also that the dimensions meet the necessary inequalities, and thus also a, r and ln are used. Kind 5 If the user wishes to directly input the limit pull-out force (unfactored) he/she may wish to input directly the value of FL (that will be later divided by  to get Fd).

Pins The resistance checks of a pin are generally different from those of a bolt. The pin shaft is always computed keeping into account the computed bending, no matter the choice to neglect "parasitic bending" in bolt layouts. The checks of the pin shaft are different from those of a bolt for three main reasons: 1. the limit allowable stress due to axial force is set equal to 1N/mm 2 (1MPa). If the axial force is higher than the value 1MPa x r2, the pin does not pass the check. If it is lower, the force is discarded. 2. The limit tangential stress allowable for torsion Mt is equal to 1N/mm 2. If the torque applied is higher than this limit (equal to 1MPa x r3/2), the shear V in the shaft of the pin is notionally set equal to 1x1012N and consequently the pin will not pass the check. 3. The combination rule of the effects due to shear V and bending M for some standard is different from that of the bolts.

Therefore the expected forces carried by a pin are shear V and bending M, while axial force N and torque Mt, should be negligible.

e M   m ,b

M 0.6  0.9 f uW gp

eV   m ,b

3V 0.6 f u Agp

if (eV  1.e  3) AND (e M  1.e  3)e  eM elseif (eV  1.e  3) AND (eM  1.e  3)e  max{ eV , e M } elseif (eM  1.e  3) AND (eV  1.e  3)e  eV else e  e M2  eV2 Note well: pin's torsional inertia moment is theoretically null; in order to prevent large displacements in case of very small offsets multiplied by high forces, a fictitious torsional inertia moment is assigned to the pin (Jt,pin). Conventionally, it is equal to 1/1000 of shaft circle's torsional inertia moment.

J t , pin 

J t ,circle 1000



 r4 2



1 1000

Indian Standard IS 800:2007-LS (Limit States) Bolts Resistance check formulae for bolts not being slip-resistant are given below. The presence of a pre-load does not affect the computation.

e N 1  max{  m ,b

N N ;1.1 } 0.9 f u Ares 0. 9 f y A

e N 2  k M   m ,b

M 0.9 f uWcomp

eN  eN1  eN 2 eV   m ,b

3V f u Acomp

if (eV  1.e  3) AND (e N  1.e  3)e  e N elseif (eV  1.e  3) AND (e N  1.e  3)e  max{ eV , e N } elseif (e N  1.e  3) AND (eV  1.e  3)e  eV else e  e N2  eV2 if (total )

Acomp  A

elseif (threaded ) Acomp  Ares if (total )

Wcomp  W

elseif (threaded ) Wcomp  Wres In previous formulae, if parasitic bending has been neglected, we have kM=0, otherwise kM=1.

Slip-resistant bolts

A slip-resistant joint can be associated with a bolt layout. In this case, resistance checks on the bolt layout take account of tension only, which is necessarily going to be present, and not shear. Instead, the latter is

divided by a suitable limit shear value, which depends on the effective tension in the bolt, and also of course on the active standard and the settings specified for the bolt layout: pre-load, coefficient of friction, etc. If the joint is slip-resistant then bearing stress checks do not apply. The bolt layout is subject to two checks: the tension check in the shaft, and the shear check. If parasitic moments in the shaft have not been neglected, the stress associated with them is then added to the stress due to the tension. The part of component total utilisation associated to axial force ( e N ) is the same one already explained in bolts resistance checks. If a bolt layout is just-shear and slip-resistant, bendings on the layout cause axial forces in bolts, not bending. Check formulae are the following:

F p ,C  K n  f ub  Ares eV   m , f

V F p ,C    

e  eV2  e N2 Fp,C is the preload force, expressed as the fraction Kn of the bolt’s ultimate load; fu,b is the bolt ultimate stress; Ares is the net area of the threading; V is the maximum computed shear;  is the coefficient of friction;  is hole coefficient; eV > 1 means the limit value is exceeded, resulting in a slip of connection. In the code, no prescription was found in order to take into account the possible decreasing of limit shear as a function of applied loads.

Anchor bolts If a bolt layout is classed as an anchor, the pull-out checks are used to supplement the normal strength checks made on the layout. In practice, the pull-out force N on each bolt is compared with a limit value Fd, thus generating a utilisation index. This utilisation index is associated with the bolt layout, not the constraint block on which the bolt layout is presumably anchored. As in the other cases, this index is compared with that obtained for the bolt layout after the other checks and, if larger, is stored along with the cause which gave rise to it. In detail the rule is the following:

E

N Fd

Fd 

FL



where the safety factor  is equal to 1 for IS800LS. This check is omitted if a compression is present, as it is assumed that there will be a bearing surface to react it. The calculation of limit pull-out force FL depends on the kind of the anchor defined by the user and on some parameters. It is possible to define 5 different kinds of anchor, that are checked in 5 different ways.

Kind 1 The bond stress between the bar and concrete is responsible for the resistance. The rule is:

    f bd   l   FL   2     n 1       a   fbd

is the design tangential bond stress between the bar and concrete;  it is the bar diameter a it is the minimum distance between the bar and the free surface of the constraint block (end of concrete) ln it is the straight length of anchor Kind 2 Similar to kind 1 but also a hook is resisting, which increases the pull-out force. The rule is:

    f bd   ln  7.4  r  3.5  l2      FL   2     1      a  fbd

is the design tangential bond stress between the bar and concrete;  it is the bar diameter a it is the minimum distance between the bar and the free surface of the constraint block (end of concrete) ln it is the straight length of anchor r l2

is the hook radius is the length of the straight part of the bar, after the hook

Kind 3 Similar to kind 1, but also a washer circular plate is present. The rule is:

      f bd   2 FL    l      f    r  n cd 2   1           a      fbd fcd

is the design tangential bond stress between the bar and concrete; is the design compressive stress of concrete  it is the bar diameter a it is the minimum distance between the bar and the free surface of the constraint block (end of concrete) ln it is the straight length of anchor r is the washer radius Kind 4 Similar to kind 3, but the resisting mechanism use concrete cone detachment from constraint block. Basically the formula provided in Eurocode 2, §6.2 is assumed, considering the maximum force guaranteed by such mechanism and checking that specific limit between dimensions are met. The rule is:

FL  3  f cd    r 2

ln  2  r a  3 r fcd is the design compressive stress of concrete a it is the minimum distance between the bar and the free surface of the constraint block (end of concrete) ln it is the straight length of anchor r is the washer radius The program checks also that the dimensions meet the necessary inequalities, and thus also a, r and ln are used. Kind 5 If the user wishes to directly input the limit pull-out force (unfactored) he/she may wish to input directly the value of FL (that will be later divided by  to get Fd). Pins The resistance checks of a pin are generally different from those of a bolt. The pin shaft is always computed keeping into account the computed bending, no matter the choice to neglect "parasitic bending" in bolt layouts. The checks of the pin shaft are different from those of a bolt for three main reasons: 1. the limit allowable stress due to axial force is set equal to 1N/mm 2 (1MPa). If the axial force is higher than the value 1MPa x r2, the pin does not pass the check. If it is lower, the force is discarded. 2. The limit tangential stress allowable for torsion Mt is equal to 1N/mm 2. If the torque applied is higher than this limit (equal to 1MPa x r3/2), the shear V in the shaft of the pin is notionally set equal to 1x1012N and consequently the pin will not pass the check. 3. The combination rule of the effects due to shear V and bending M for some standard is different from that of the bolts.

Therefore the expected forces carried by a pin are shear V and bending M, while axial force N and torque Mt, should be negligible.

eM   m ,b

M 0.9 f uWgp

eV   m ,b

3V f u Agp

if ( eV  1.e  3) AND ( eM  1.e  3)e  eM elseif ( eV  1.e  3) AND ( eM  1.e  3)e  max{ eV ,eM } elseif ( eM  1.e  3) AND ( eV  1.e  3)e  eV else e  eM2  eV2 Note well: pin's torsional inertia moment is theoretically null; in order to prevent large displacements in case of very small offsets multiplied by high forces, a fictitious torsional inertia moment is assigned to the pin (Jt,pin). Conventionally, it is equal to 1/1000 of shaft circle's torsional inertia moment.

J t , pin 

J t ,circle 1000



 r4 2



1 1000

American Standard AISC-ASD (Allowable Stress Design) Bolts Resistance check formulae for bolts not being slip-resistant are given below. The presence of a pre-load does not affect the computation.

eN 

N M  kM  0.75  0.5 f u Ares 0.75  0.5 f u  Wcomp

eV 

V (total ); 0.5  0.5 f u A

eV 

V (threaded ); 0.5  0.4 f u Ares

if (eV  1.e  3) AND (e N  1.e  3)e  e N elseif (eV  1.e  3) AND (e N  1.e  3)e  max{ eV , e N } elseif (e N  1.e  3) AND (eV  1.e  3)e  eV else e  e N2  eV2 if (total )

Wcomp  W

elseif (threaded ) Wcomp  Wres In previous formulae, if parasitic bending has been neglected, we have kM=0, otherwise kM=1.

Slip-resistant bolts

A slip-resistant joint can be associated with a bolt layout. In this case, resistance checks on the bolt layout take account of tension only, which is necessarily going to be present, and not shear. Instead, the latter is divided by a suitable limit shear value, which depends on the effective tension in the bolt, and also of course on the active standard and the settings specified for the bolt layout: pre-load, coefficient of friction, etc. If the joint is slip-resistant then bearing stress checks do not apply. The bolt layout is subject to two checks: the tension check in the shaft, and the shear check. If parasitic moments in the shaft have not been neglected, the stress associated with them is then added to the stress due to the tension. The part of component total utilisation associated to axial force ( e N ) is the same one already explained in bolts resistance checks. If a bolt layout is just-shear and slip-resistant, bendings on the layout cause axial forces in bolts, not bending. Check formulae are the following:

F p ,C  K n  f ub  Ares eV  1.76

  F p ,C 

V [( F p ,C  1.5 N/1.13), N with sign] 1.5 N      1.13 

  1.13   AISC eV  99.

[( F p ,C  1.5 N/1.13)]

e  max eV , e N 

Fp,C is the preload force, expressed as the fraction Kn of the bolt’s ultimate load; fu,b is the bolt ultimate stress; Ares is the net area of the threading; V is the maximum computed shear;  is the coefficient of friction;  is hole coefficient; eV > 1 means the limit value is exceeded, resulting in a slip of connection.

Anchor bolts If a bolt layout is classed as an anchor, the pull-out checks are used to supplement the normal strength checks made on the layout. In practice, the pull-out force N on each bolt is compared with a limit value Fd, thus generating a utilisation index. This utilisation index is associated with the bolt layout, not the constraint block on which the bolt layout is presumably anchored. As in the other cases, this index is compared with that obtained for the bolt layout after the other checks and, if larger, is stored along with the cause which gave rise to it. In detail the rule is the following:

E

N Fd

Fd 

FL



where the safety factor  is equal to 2 for AISC-ASD. This check is omitted if a compression is present, as it is assumed that there will be a bearing surface to react it. The calculation of limit pull-out force FL depends on the kind of the anchor defined by the user and on some parameters. It is possible to define 5 different kinds of anchor, that are checked in 5 different ways.

Kind 1 The bond stress between the bar and concrete is responsible for the resistance. The rule is:

    f bd   l   FL   2     n 1       a   fbd

is the design tangential bond stress between the bar and concrete;  it is the bar diameter a it is the minimum distance between the bar and the free surface of the constraint block (end of concrete) ln it is the straight length of anchor Kind 2 Similar to kind 1 but also a hook is resisting, which increases the pull-out force. The rule is:

    f bd   ln  7.4  r  3.5  l2      FL   2     1      a  fbd

is the design tangential bond stress between the bar and concrete;  it is the bar diameter a it is the minimum distance between the bar and the free surface of the constraint block (end of concrete) ln it is the straight length of anchor r l2

is the hook radius is the length of the straight part of the bar, after the hook

Kind 3 Similar to kind 1, but also a washer circular plate is present. The rule is:

      f  bd   l      f    r 2  FL   n cd 2   1           a      fbd fcd



is the design tangential bond stress between the bar and concrete; is the design compressive stress of concrete it is the bar diameter

a it is the minimum distance between the bar and the free surface of the constraint block (end of concrete) ln it is the straight length of anchor r is the washer radius Kind 4 Similar to kind 3, but the resisting mechanism use concrete cone detachment from constraint block. Basically the formula provided in Eurocode 2, §6.2 is assumed, considering the maximum force guaranteed by such mechanism and checking that specific limit between dimensions are met. The rule is:

FL  3  f cd    r 2

ln  2  r a  3 r fcd is the design compressive stress of concrete a it is the minimum distance between the bar and the free surface of the constraint block (end of concrete) ln it is the straight length of anchor r is the washer radius The program checks also that the dimensions meet the necessary inequalities, and thus also a, r and ln are used. Kind 5 If the user wishes to directly input the limit pull-out force (unfactored) he/she may wish to input directly the value of FL (that will be later divided by  to get Fd).

Pins The resistance checks of a pin are generally different from those of a bolt. The pin shaft is always computed keeping into account the computed bending, no matter the choice to neglect "parasitic bending" in bolt layouts. The checks of the pin shaft are different from those of a bolt for three main reasons: 1. the limit allowable stress due to axial force is set equal to 1N/mm 2 (1MPa). If the axial force is higher than the value 1MPa x r2, the pin does not pass the check. If it is lower, the force is discarded. 2. The limit tangential stress allowable for torsion Mt is equal to 1N/mm 2. If the torque applied is higher than this limit (equal to 1MPa x r3/2), the shear V in the shaft of the pin is notionally set equal to 1x1012N and consequently the pin will not pass the check. 3. The combination rule of the effects due to shear V and bending M for some standard is different from that of the bolts. Therefore the expected forces carried by a pin are shear V and bending M, while axial force N and torque Mt, should be negligible.

eM 

M 0.75  0.5 f u  Wcomp

eV 

V 0.5  0.5 f u A

if (eV  1.e  3) AND (eM  1.e  3)e  eM elseif (eV  1.e  3) AND (e N  1.e  3)e  max{ eV , eM } elseif (eM  1.e  3) AND (eV  1.e  3)e  eV else e  eM2  eV2 Note well: pin's torsional inertia moment is theoretically null; in order to prevent large displacements in case of very small offsets multiplied by high forces, a fictitious torsional inertia moment is assigned to the pin (Jt,pin). Conventionally, it is equal to 1/1000 of shaft circle's torsional inertia moment.

J t , pin 

J t ,circle 1000



 r4 2

1  1000

American Standard AISC-LRFD (Load and Resistance Factor Design) Bolts Resistance check formulae for bolts not being slip-resistant are given below. The presence of a pre-load does not affect the computation.

eN 

N M  kM  0.75  0.75 f u Ares 0.75  0.75 f u  Wcomp

eV 

V (total ); 0.75  0.5 f u A

eV 

V (threaded ); 0.75  0.4 f u Ares

if (eV  1.e  3) AND (e N  1.e  3)e  e N elseif (eV  1.e  3) AND (e N  1.e  3)e  max{ eV , e N } elseif (e N  1.e  3) AND (eV  1.e  3)e  eV else e  e N2  eV2 if (total )

Wcomp  W

elseif (threaded ) Wcomp  Wres In previous formulae, if parasitic bending has been neglected, we have kM=0, otherwise kM=1.

Slip-resistant bolts

A slip-resistant joint can be associated with a bolt layout. In this case, resistance checks on the bolt layout take account of tension only, which is necessarily going to be present, and not shear. Instead, the latter is divided by a suitable limit shear value, which depends on the effective tension in the bolt, and also of course on the active standard and the settings specified for the bolt layout: pre-load, coefficient of friction, etc. If the joint is slip-resistant then bearing stress checks do not apply. The bolt layout is subject to two checks: the tension check in the shaft, and the shear check. If parasitic moments in the shaft have not been neglected, the stress associated with them is then added to the stress due to the tension. The part of component total utilisation associated to axial force ( e N ) is the same one already explained in bolts resistance checks. If a bolt layout is just-shear and slip-resistant, bendings on the layout cause axial forces in bolts, not bending. Check formulae are the following:

F p ,C  K n  f ub  Ares eV 

V

1.5 N   0.85   F p ,C     1 . 13     1.13   AISC eV  99.

[( F p ,C  1.5 N/1.13), N with sign]

[( F p ,C  1.5 N/1.13)]

e  max eV , e N 

Fp,C is the preload force, expressed as the fraction Kn of the bolt’s ultimate load; fu,b is the bolt ultimate stress; Ares is the net area of the threading; V is the maximum computed shear;  is the coefficient of friction;  is hole coefficient; eV > 1 means the limit value is exceeded, resulting in a slip of connection.

Anchor bolts If a bolt layout is classed as an anchor, the pull-out checks are used to supplement the normal strength checks made on the layout. In practice, the pull-out force N on each bolt is compared with a limit value Fd, thus generating a utilisation index. This utilisation index is associated with the bolt layout, not the constraint block on which the bolt layout is presumably anchored. As in the other cases, this index is compared with that obtained for the bolt layout after the other checks and, if larger, is stored along with the cause which gave rise to it. In detail the rule is the following:

E

N Fd

Fd 

FL



where the safety factor  is equal to 1.333 for AISC-LRFD. This check is omitted if a compression is present, as it is assumed that there will be a bearing surface to react it. The calculation of limit pull-out force FL depends on the kind of the anchor defined by the user and on some parameters. It is possible to define 5 different kinds of anchor, that are checked in 5 different ways.

Kind 1 The bond stress between the bar and concrete is responsible for the resistance. The rule is:

    f bd   l   FL   2     n 1       a   fbd

is the design tangential bond stress between the bar and concrete;  it is the bar diameter a it is the minimum distance between the bar and the free surface of the constraint block (end of concrete) ln it is the straight length of anchor Kind 2 Similar to kind 1 but also a hook is resisting, which increases the pull-out force. The rule is:

    f bd   ln  7.4  r  3.5  l2      FL   2     1      a  fbd

is the design tangential bond stress between the bar and concrete;  it is the bar diameter a it is the minimum distance between the bar and the free surface of the constraint block (end of concrete) ln it is the straight length of anchor r l2

is the hook radius is the length of the straight part of the bar, after the hook

Kind 3 Similar to kind 1, but also a washer circular plate is present. The rule is:

      f  bd   l      f    r 2  FL   n cd 2   1           a      fbd fcd



is the design tangential bond stress between the bar and concrete; is the design compressive stress of concrete it is the bar diameter

a it is the minimum distance between the bar and the free surface of the constraint block (end of concrete) ln it is the straight length of anchor r is the washer radius Kind 4 Similar to kind 3, but the resisting mechanism use concrete cone detachment from constraint block. Basically the formula provided in Eurocode 2, §6.2 is assumed, considering the maximum force guaranteed by such mechanism and checking that specific limit between dimensions are met. The rule is:

FL  3  f cd    r 2

ln  2  r a  3 r fcd is the design compressive stress of concrete a it is the minimum distance between the bar and the free surface of the constraint block (end of concrete) ln it is the straight length of anchor r is the washer radius The program checks also that the dimensions meet the necessary inequalities, and thus also a, r and ln are used. Kind 5 If the user wishes to directly input the limit pull-out force (unfactored) he/she may wish to input directly the value of FL (that will be later divided by  to get Fd). Pins The resistance checks of a pin are generally different from those of a bolt. The pin shaft is always computed keeping into account the computed bending, no matter the choice to neglect "parasitic bending" in bolt layouts. The checks of the pin shaft are different from those of a bolt for three main reasons: 1. the limit allowable stress due to axial force is set equal to 1N/mm 2 (1MPa). If the axial force is higher than the value 1MPa x r2, the pin does not pass the check. If it is lower, the force is discarded. 2. The limit tangential stress allowable for torsion Mt is equal to 1N/mm 2. If the torque applied is higher than this limit (equal to 1MPa x r3/2), the shear V in the shaft of the pin is notionally set equal to 1x1012N and consequently the pin will not pass the check. 3. The combination rule of the effects due to shear V and bending M for some standard is different from that of the bolts. Therefore the expected forces carried by a pin are shear V and bending M, while axial force N and torque Mt, should be negligible.

eM 

M 0.75  0.75 f u  Wcomp

eV 

V 0.75  0.5 f u A

if ( eV  1.e  3) AND ( eM  1.e  3)e  eM elseif ( eV  1.e  3) AND ( eM  1.e  3)e  max{ eV ,eM } elseif ( eM  1.e  3) AND ( eV  1.e  3)e  eV else e  eM2  eV2 Note well: pin's torsional inertia moment is theoretically null; in order to prevent large displacements in case of very small offsets multiplied by high forces, a fictitious torsional inertia moment is assigned to the pin (Jt,pin). Conventionally, it is equal to 1/1000 of shaft circle's torsional inertia moment.

J t , pin 

J t ,circle 1000



 r4 2



1 1000

Italian Standard CNR 10011 AS (Allowable Stresses) Bolts Resistance check formulae for bolts not being slip-resistant are given below. The presence of a pre-load does not affect the computation.

  kN 

N M  kM Ares Wcomp

V Acomp

f kN  min 0,7 f u , f y  e  1,5 e  1,5

 f KN 2 f kN

if (e  1.e  3)e  e elseif (e  1.e  3)e  e else e  e2  e2 if (total )

Acomp  A

elseif (threaded ) Acomp  Ares if (total )

Wcomp  W

elseif (threaded ) Wcomp  Wres In previous formulae, if parasitic bending has been neglected, we have kN=1.25 and kM=0, otherwise kN=1 and kM=1.

Slip-resistant bolts

A slip-resistant joint can be associated with a bolt layout. In this case, resistance checks on the bolt layout take account of tension only, which is necessarily going to be present, and not shear. Instead, the latter is divided by a suitable limit shear value, which depends on the effective tension in the bolt, and also of course on the active standard and the settings specified for the bolt layout: pre-load, coefficient of friction, etc. If the joint is slip-resistant then bearing stress checks do not apply. The bolt layout is subject to two checks: the tension check in the shaft, and the shear check. If parasitic moments in the shaft have not been neglected, the stress associated with them is then added to the stress due to the tension. The part of component total utilisation associated to axial force ( e N ) is the same one already explained in bolts resistance checks. If a bolt layout is just-shear and slip-resistant, bendings on the layout cause axial forces in bolts, not bending. Check formulae are the following:

F p ,C  K n  f ub  Ares eV  1.5  1.25

V [( F p ,C  N), N with sign] Fp,C  N 

eV  99.

[( F p ,C  N)]

e  max eV , e N 

Fp,C is the preload force, expressed as the fraction Kn of the bolt’s ultimate load; fu,b is the bolt ultimate stress; Ares is the net area of the threading; V is the maximum computed shear;  is the coefficient of friction; eV > 1 means the limit value is exceeded, resulting in a slip of connection.

Anchor bolts If a bolt layout is classed as an anchor, the pull-out checks are used to supplement the normal strength checks made on the layout. In practice, the pull-out force N on each bolt is compared with a limit value Fd, thus generating a utilisation index. This utilisation index is associated with the bolt layout, not the constraint block on which the bolt layout is presumably anchored. As in the other cases, this index is compared with that obtained for the bolt layout after the other checks and, if larger, is stored along with the cause which gave rise to it. In detail the rule is the following:

E

N Fd

Fd 

FL



where the safety factor  is equal to 1.5 for CNR-AS. This check is omitted if a compression is present, as it is assumed that there will be a bearing surface to react it. The calculation of limit pull-out force FL depends on the kind of the anchor defined by the user and on some parameters. It is possible to define 5 different kinds of anchor, that are checked in 5 different ways.

Kind 1 The bond stress between the bar and concrete is responsible for the resistance. The rule is:

    f bd   l   FL   2     n 1       a   fbd

is the design tangential bond stress between the bar and concrete;  it is the bar diameter a it is the minimum distance between the bar and the free surface of the constraint block (end of concrete) ln it is the straight length of anchor Kind 2 Similar to kind 1 but also a hook is resisting, which increases the pull-out force. The rule is:

    f bd   ln  7.4  r  3.5  l2      FL   2     1      a  fbd

is the design tangential bond stress between the bar and concrete;  it is the bar diameter a it is the minimum distance between the bar and the free surface of the constraint block (end of concrete) ln it is the straight length of anchor r is the hook radius l2 is the length of the straight part of the bar, after the hook Kind 3 Similar to kind 1, but also a washer circular plate is present. The rule is:

      f bd   2 FL    l      f    r  n cd 2   1           a      fbd fcd

is the design tangential bond stress between the bar and concrete; is the design compressive stress of concrete  it is the bar diameter a it is the minimum distance between the bar and the free surface of the constraint block (end of concrete) ln it is the straight length of anchor r is the washer radius Kind 4 Similar to kind 3, but the resisting mechanism use concrete cone detachment from constraint block. Basically the formula provided in Eurocode 2, §6.2 is assumed, considering the maximum force guaranteed by such mechanism and checking that specific limit between dimensions are met. The rule is:

FL  3  f cd    r 2

ln  2  r a  3 r fcd is the design compressive stress of concrete a it is the minimum distance between the bar and the free surface of the constraint block (end of concrete) ln it is the straight length of anchor r is the washer radius The program checks also that the dimensions meet the necessary inequalities, and thus also a, r and ln are used. Kind 5 If the user wishes to directly input the limit pull-out force (unfactored) he/she may wish to input directly the value of FL (that will be later divided by  to get Fd).

Pins The resistance checks of a pin are generally different from those of a bolt. The pin shaft is always computed keeping into account the computed bending, no matter the choice to neglect "parasitic bending" in bolt layouts. The checks of the pin shaft are different from those of a bolt for three main reasons: 1. the limit allowable stress due to axial force is set equal to 1N/mm 2 (1MPa). If the axial force is higher than the value 1MPa x r2, the pin does not pass the check. If it is lower, the force is discarded. 2. The limit tangential stress allowable for torsion Mt is equal to 1N/mm 2. If the torque applied is higher than this limit (equal to 1MPa x r3/2), the shear V in the shaft of the pin is notionally set equal to 1x1012N and consequently the pin will not pass the check. 3. The combination rule of the effects due to shear V and bending M for some standard is different from that of the bolts.

Therefore the expected forces carried by a pin are shear V and bending M, while axial force N and torque Mt, should be negligible.



M Wgp



V Agp

f kN  min 0,7 f u , f y  e  1,5 e  1,5

 f KN 2 f kN

if ( e  1.e  3)e  e elseif ( e  1.e  3)e  e else e  e2  e2 Note well: pin's torsional inertia moment is theoretically null; in order to prevent large displacements in case of very small offsets multiplied by high forces, a fictitious torsional inertia moment is assigned to the pin (Jt,pin). Conventionally, it is equal to 1/1000 of shaft circle's torsional inertia moment.

J t , pin 

J t ,circle 1000



 r4 2



1 1000

Italian Standard CNR 10011 LS (Limit States) Bolts Resistance check formulae for bolts not being slip-resistant are given below. The presence of a pre-load does not affect the computation.

N M  kM Ares Wcomp

  kN 

V Acomp

f kN  min 0,7 f u , f y  e  e 

 f KN 2 f kN

if (e  1.e  3)e  e elseif (e  1.e  3)e  e else e  e2  e2 if (total )

Acomp  A

elseif (threaded ) Acomp  Ares if (total )

Wcomp  W

elseif (threaded ) Wcomp  Wres In previous formulae, if parasitic bending has been neglected, we have kN=1.25 and kM=0, otherwise kN=1 and kM=1.

Slip-resistant bolts

A slip-resistant joint can be associated with a bolt layout. In this case, resistance checks on the bolt layout take account of tension only, which is necessarily going to be present, and not shear. Instead, the latter is divided by a suitable limit shear value, which depends on the effective tension in the bolt, and also of course on the active standard and the settings specified for the bolt layout: pre-load, coefficient of friction, etc. If the joint is slip-resistant then bearing stress checks do not apply. The bolt layout is subject to two checks: the tension check in the shaft, and the shear check. If parasitic moments in the shaft have not been neglected, the stress associated with them is then added to the stress due to the tension. The part of component total utilisation associated to axial force ( e N ) is the same one already explained in bolts resistance checks. If a bolt layout is just-shear and slip-resistant, bendings on the layout cause axial forces in bolts, not bending. Check formulae are the following:

F p ,C  K n  f ub  Ares eV  1.25

V [( F p ,C  N), N with sign] Fp,C  N 

eV  99.

[( F p ,C  N)]

e  max eV , e N 

Fp,C is the preload force, expressed as the fraction Kn of the bolt’s ultimate load; fu,b is the bolt ultimate stress; Ares is the net area of the threading; V is the maximum computed shear;  is the coefficient of friction; eV > 1 means the limit value is exceeded, resulting in a slip of connection.

Anchor bolts If a bolt layout is classed as an anchor, the pull-out checks are used to supplement the normal strength checks made on the layout. In practice, the pull-out force N on each bolt is compared with a limit value Fd, thus generating a utilisation index. This utilisation index is associated with the bolt layout, not the constraint block on which the bolt layout is presumably anchored. As in the other cases, this index is compared with that obtained for the bolt layout after the other checks and, if larger, is stored along with the cause which gave rise to it. In detail the rule is the following:

E

N Fd

Fd 

FL



where the safety factor  is equal to 1 for CNR-LS. This check is omitted if a compression is present, as it is assumed that there will be a bearing surface to react it. The calculation of limit pull-out force FL depends on the kind of the anchor defined by the user and on some parameters. It is possible to define 5 different kinds of anchor, that are checked in 5 different ways.

Kind 1 The bond stress between the bar and concrete is responsible for the resistance. The rule is:

    f bd   l   FL   2     n 1       a   fbd

is the design tangential bond stress between the bar and concrete;  it is the bar diameter a it is the minimum distance between the bar and the free surface of the constraint block (end of concrete) ln it is the straight length of anchor Kind 2 Similar to kind 1 but also a hook is resisting, which increases the pull-out force. The rule is:

    f bd   ln  7.4  r  3.5  l2      FL   2     1      a  fbd

is the design tangential bond stress between the bar and concrete;  it is the bar diameter a it is the minimum distance between the bar and the free surface of the constraint block (end of concrete) ln it is the straight length of anchor r is the hook radius l2 is the length of the straight part of the bar, after the hook Kind 3 Similar to kind 1, but also a washer circular plate is present. The rule is:

      f bd   2 FL    l      f    r  n cd 2   1           a      fbd fcd

is the design tangential bond stress between the bar and concrete; is the design compressive stress of concrete  it is the bar diameter a it is the minimum distance between the bar and the free surface of the constraint block (end of concrete) ln it is the straight length of anchor r is the washer radius Kind 4 Similar to kind 3, but the resisting mechanism use concrete cone detachment from constraint block. Basically the formula provided in Eurocode 2, §6.2 is assumed, considering the maximum force guaranteed by such mechanism and checking that specific limit between dimensions are met. The rule is:

FL  3  f cd    r 2

ln  2  r a  3 r fcd is the design compressive stress of concrete a it is the minimum distance between the bar and the free surface of the constraint block (end of concrete) ln it is the straight length of anchor r is the washer radius The program checks also that the dimensions meet the necessary inequalities, and thus also a, r and ln are used. Kind 5 If the user wishes to directly input the limit pull-out force (unfactored) he/she may wish to input directly the value of FL (that will be later divided by  to get Fd).

Pins The resistance checks of a pin are generally different from those of a bolt. The pin shaft is always computed keeping into account the computed bending, no matter the choice to neglect "parasitic bending" in bolt layouts. The checks of the pin shaft are different from those of a bolt for three main reasons: 1. the limit allowable stress due to axial force is set equal to 1N/mm 2 (1MPa). If the axial force is higher than the value 1MPa x r2, the pin does not pass the check. If it is lower, the force is discarded. 2. The limit tangential stress allowable for torsion Mt is equal to 1N/mm 2. If the torque applied is higher than this limit (equal to 1MPa x r3/2), the shear V in the shaft of the pin is notionally set equal to 1x1012N and consequently the pin will not pass the check. 3. The combination rule of the effects due to shear V and bending M for some standard is different from that of the bolts.

Therefore the expected forces carried by a pin are shear V and bending M, while axial force N and torque Mt, should be negligible.



M Wgp



V Agp

f kN  min 0,7 f u , f y  e  e 

 f KN 2 f kN

if ( e  1.e  3)e  e elseif ( e  1.e  3)e  e else e  e2  e2 Note well: pin's torsional inertia moment is theoretically null; in order to prevent large displacements in case of very small offsets multiplied by high forces, a fictitious torsional inertia moment is assigned to the pin (Jt,pin). Conventionally, it is equal to 1/1000 of shaft circle's torsional inertia moment.

J t , pin 

Welds checks

Fillet welds EN1993-1-8 IS 800:2007-WS (Working Stress) IS 800:2007-LS (Limit States) AISC-ASD (Allowable Stress Design)

J t ,circle 1000



 r4 2



1 1000

AISC-LRFD (Load and Resistance Factor Design) CNR 10011 AS (Allowable Stresses) CNR 10011 SL (Limit States)

Eurocode 3 - EN1993-1-8 CSE implements the method set out in EN 1993-1-8, paragraph 4.5.3.3:

Fw, Ed  Fw, Rd

Fw,Ed is the design value of the force in the weld per unit length, that is

Fw, Ed  a n 2per  t 2par  t 2per Fw,Rd is the design strength of the weld per unit length, and which, regardless of the orientation of the plane of the throat section relative to the force applied, is equal to

Fw, Rd  f vw.d a

where a is the throat section of the weld and fvw.d is the design shear strength of the seam, which is equal to:

f vw.d 

fu / 3

 w M 2

fu is the ultimate stress of the least resistant material among those of the connected entities w is a correlation factor which can be obtained from the following table depending on the material (EN 1993-1-8, Table 4.1)

EN 1993-1-8, Table 4.1

IS800:2007WS CSE implements the following method:

Fw, Ed  Fw, Rd Fw,Ed is the design value of the force in the weld per unit length, that is

Fw, Ed  a n 2per  t 2par  t 2per Fw,Rd is the design strength of the weld per unit length, and which, regardless of the orientation of the plane of the throat section relative to the force applied, is equal to

fu

Fw, Rd  a  0.6 

3

a is the throat section of the weld fu is the ultimate stress of the least resistant material among those of the connected entities

IS800:2007LS CSE implements the following method:

Fw, Ed  Fw, Rd

Fw,Ed is the design value of the force in the weld per unit length, that is

Fw, Ed  a n 2per  t 2par  t 2per Fw,Rd is the design strength of the weld per unit length, and which, regardless of the orientation of the plane of the throat section relative to the force applied, is equal to

fu

Fw, Rd  a  Fw, Rd  a 

3   m,w fu 1.2  3   m , w

for shop welds for site welds

a is the throat section of the weld fu is the ultimate stress of the least resistant material among those of the connected entities

AISC-ASD CSE implements the following method:

Fw, Ed  Fw, Rd

Fw,Ed is the design value of the force in the weld per unit length, that is

Fw, Ed  a n 2per  t 2par  t 2per

Fw,Rd is the design strength of the weld per unit length, and which, regardless of the orientation of the plane of the throat section relative to the force applied, is equal to

Fw,Rd  a  0.3 fu

a is the throat section of the weld fu is the ultimate stress of the least resistant material among those of the connected entities

AISC-LRFD CSE implements the following method:

Fw, Ed  Fw, Rd

Fw,Ed is the design value of the force in the weld per unit length, that is

Fw, Ed  a n 2per  t 2par  t 2per Fw,Rd is the design strength of the weld per unit length, and which, regardless of the orientation of the plane of the throat section relative to the force applied, is equal to

Fw, Rd  a  0.45  f u

a is the throat section of the weld fu is the ultimate stress of the least resistant material among those of the connected entities

Italian Standard CNR 10011 AS (Allowable Stresses) (Note: in the standard, nper, tpar and tper are referred to respectively as ┴, || and ┴) “Any tensile or compressive stresses || present in the transverse section of the weld, understood as part of the resistance-section of the member, must not be taken into consideration for the purposes of checking the actual weld.” Consider the components ┴, || and ┴ of the projected throat section. For the allowable stress checks, the following must apply:  when ┴, || and ┴are all present:

 0.85 adm for steel grade S235      0.70 adm for steel grades S275 and S355 2 

2 

2 ||

(1)

  

 adm for steel grade S235  0.85 adm for steel grades S275 and S355 (2)

 when only the components ┴ and ┴are present: expression (2) must hold, and the following must also apply:



 0.85 adm for steel grade S235  0.70 adm for steel grades S275 and S355



 0.85 adm for steel grade S235  0.70 adm for steel grades S275 and S355

 when only the components || and ┴, or ┴, and ||, or only one of the three components are present: expression (1) must hold

Italian Standard CNR 10011 LS (Limit States) (Note: in the standard, nper, tpar and tper are referred to respectively as ┴, || and ┴) “Any tensile or compressive stresses || present in the transverse section of the weld, understood as part of the resistance-section of the member, must not be taken into consideration for the purposes of checking the actual weld.” Consider the components ┴, || and ┴ of the projected throat section. For the limit state checks, the following must apply:  when ┴, || and ┴are all present:

 0.85 f d for steel grade S235       0.70 f d for steel grades S275 and S355 2 

2 

2 ||

  

 f d for steel grade S235  0.85 f d for steel grades S275 and S355

(1)

(2)

 when only the components ┴ and ┴are present: expression (2) must hold, and the following must also apply:



 0.85 f d for steel grade S235  0.70 f d for steel grades S275 and S355



 0.85 f d for steel grade S235  0.70 f d for steel grades S275 and S355

 when only the components || and ┴, or ┴, and ||, or only one of the three components are present: expression (1) must hold

Penetration welds For penetration weld layouts, the checks are carried out by projecting the thickness onto the common plane of the two welded faces, and then considering the section obtained by joining the rectangles thus obtained. The section in question is computed as an ordinary section subject to combined compression and bending or tension and bending, with shears and torsion, and the ideal Von Mises stress compared with the limit design tension. A simplified approach is used to take account of the effects of the shear and torsion. If the thickness of the penetration welds is such that the available thickness is completely filled (complete penetration welding), then the strength of the weld will be equivalent to that of the thinner of the plates which it joins (full-strength welds). This can be achieved both with a single seam of the necessary thickness and with two seams making up the full thickness between them. This choice affects the type of work process. The torsional strength can be determined using either the polar moment of inertia model or the model that computes Jt as the sum of the contributions of type (1/3)Lt3.

Components checks Bolt bearing pressure check

In non slip-resistant bolt layouts, once the shear in bolts has been computed, it acts on the thicknesses of joined components. This implies a bearing pressure, whose limits depend on the Standard and the distance from considered bolt to the edges (see for instance EN1993-1-8:2005, par. 3.6.1). Punching shear check

Head and nut of bolts in tension produce bearing pressure on joined plates, which are subjected to possible punching shear failure. Once the force in each bolt has been computed, known bolts size and plates thickness it is possible to automatically check this failure mode according to the relevant code rule. Bearing surface check

When bolt layouts are computed using a bearing surface, the maximum compressive stress on that surface is checked, according to a stress distribution which guarantees equilibrium. Maximum compressive stress on

the surface is compared to the maximum stress that can be carried by the component to which the surface belongs. When bearing surface is defined, user defines also the component to which it belongs. The utilisation index computed through this check will be assigned to that component. Block tearing check

When a bolt layout is connected to a component, it is possible to find a plate having a number of holes equal to the number of bolts belonging to that layout. Each bolt produce a shear force different from those of the other bolts. Under all those forces, a part of the plate can be torn away from the other one: in n is bolts total number, the first part will contain x bolts and the second part will contain n-x bolts. The program searches, for all sets of x bolts, and for all x so that 2