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BLOCK SHEAR FAILURE IN TENSION MEMBERS

ABSTRACT

Block shear is a limit state that should be accounted for during the design of steel tension members. This failure mechanism combines a tensile failure on one plane and a shear failure on a perpendicular plane. It is important for a design equation not only to predict the capacity reliably, but also to predict accurately the failure mode.

In this study, we begin with an overview of tension members, their behaviour and design strength which is affected by yielding, fracture or block shear. Different codal provisions in IS 800: 2007 for tension members have been dealt, with a special focus on block shear and its failure mechanism. Latest specifications on block shear in AISC 2005 and Eurocode 3 have also been explained so as to provide a broader view of the standards being adopted worldwide to check failure of structures by block shear.

Recent developments in block shear research have also been discussed, both finite element analysis and experimental programs. Block shear failure is not just limited to bolted connections and keeping this in mind, research works conducted on block shear in bolted as well as welded steel sections have been presented herein.

Finally, a numerical on block shear has been solved using the provisions in IS 800, AISC 2005 and Eurocode 3. The results obtained shows the given section to be safe from block shear failure; with the Eurocode provisions predicting the lowest design strength (though more than the applied reaction), AISC value being the highest and IS 800 values somewhere in the middle range. Based on these findings and studies, a conclusion has been arrived at and presented at the end of the report.

Submitted by PRAKASH

1. INTRODUCTION

1.1 Background

Tension members with bolted ends are frequently used as principal structural members in trusses and lateral bracing systems. These members are designed to resist yielding of the gross section, rupture of the minimum net section and block shear failure during the lifetime of the structure. Block shear is known to be a potential failure mode which can control the load capacity of several different types of bolted connections, including shear connections at the ends of coped beams, tension member connections and gusset plates. A block shear failure of the connection includes shear yield or rupture through the line of bolts parallel to the applied load, and tensile yield or rupture along a plane perpendicular to the loads. In some cases, the Ëœblockâ„¢ of material bounded by these two planes may separate completely from the angle; this is the mechanism assumes by IS 800:2007 in the design of steel tension members.

High strength bolts are used extensively for connecting structural steel elements in a variety of applications, including tension member end connections and coped beam simple connections. Due to their high strength, a relatively small number of bolts are needed for a given connection, and the area bounded by these fasteners is relatively small. As a result, bolted connections can exhibit a failure mode known as block shear, wherein a Ëœblockâ„¢ of the connected element is partially driven from the remainder of the element.

1.2 Tension Members

Tension members are linear members in which axial forces act so as to elongate (stretch) the member. A rope, for example, is a tension member. Tension members carry loads most efficiently, since the entire cross section is subjected to uniform stress. Unlike compression members, they do not fail by buckling. Ties of trusses [Fig 1.1 (a)], suspenders of cable-stayed and suspension bridges [Fig.1.1 (b)], suspenders of buildings systems hanging from a central core [Fig.1.1 ©] (used in earthquake prone zones as a way of minimising inertia forces on the structure), and sag rods of roof purlins [Fig 1.1 (d)] are other examples of tension members.

Tension members are also encountered as bracings used for lateral load resistance. In X type bracings [Fig.1.1 (e)] the member which is under tension, due to lateral load acting in one direction, undergoes compressive force, when the direction of the lateral load is changed and vice versa. Hence, such members may have to be designed to resist tensile and compressive forces.

Fig. 1.1 Tension members in buildings and bridges Tension members can have a variety of cross sections. Any cross-sectional configuration may be used, because for any given material, the only determinant of the strength of a tension member is the cross-sectional area. Circular rods and rolled angle shapes are frequently used. Built-up shapes either from plates, rolled shapes, or a combination of plates and rolled shapes are sometimes used when large loads must be resisted.

The single angle and double angle sections [Fig 1.2(a)] are used in light roof trusses as in industrial buildings. The tension members in bridge trusses are made of channels or I sections, acting individually or built-up [Figs. 1.2(b) and 1.2©]. The circular rods [Fig. 1.2 (d)] are used in bracings designed to resist loads in tension only. They buckle at very low compression and are not considered effective. Steel wire ropes [Fig.1.2 (e)] are used as suspenders in the cable suspended bridges and as main stays in the cable-stayed bridges.

Fig. 1.2 Cross-section of typical tension members

1.3 Behaviour of Tension Members:

Fig. 1.3 Load â€œ Elongation of tension members

Since axially loaded tension members are subjected to uniform tensile stress, their load deformation behaviour [Fig.1.3] is similar to the corresponding basic material stress strain behaviour. Mild steel members exhibit an elastic range (a-b) ending at yield point (b). This is followed by yield plateau (b-c). In the yield plateau the load remains constant as the elongation increases to nearly ten times the yield strain. Under further stretching the material shows a smaller increase in tension with elongation (c-d), compared to the elastic range. This range is referred to as the strain hardening range. After reaching the ultimate load (d), the loading

decreases as the elongation increases (d-e) until rupture (e). High strength steel tension members do not exhibit a well-defined yield point and a yield plateau [Fig.1.3]. The 0.2% offset load, T, as shown in Fig. 1.3 is usually taken as the yield point in such cases.

1.4 Design Strength of Tension Members:

The strength of tension members based on IS 800:2007 is the minimum of the following three categories as stated below: Yielding of the gross section, i.e. yielding of the tension member over the member length away from the connection. Fracture of the effective net section, i.e. fracture of the tension member in the connection region. Block shear rupture, i.e. tearing out of the connection due to the combination of tensile and shear failure.

1.4.1 Design strength due to yielding of gross section:

Although steel tension members can sustain loads up to the ultimate load without failure, the elongation of the members at this load would be nearly 10-15% of the original length and the structure supported by the member would become unserviceable. Hence, in the design of tension members, the yield load is usually taken as the limiting load. The corresponding design strength in member under axial tension is given by:

Tdg = Ag fy / m0

where,

Eq. (1.1)

fy is the yield strength of the material (in MPa),

Ag is the gross area of cross section, and

m0 is the partial safety factor for failure in tension by yielding.

The value of m0 according to IS 800:2007 is 1.10.

1.4.2 Design strength due to rupture of critical section:

A tension member is often connected to the main or other members by bolts or welds. When connected using bolts, tension members have holes and hence reduced cross section, being referred to as the net area. The tensile stress in a plate at the cross section of a hole is not

uniformly distributed in the elastic range, but exhibits stress concentration adjacent to the hole [Fig. 1.4 (a)]. The ratio of the maximum elastic stress adjacent to the hole to the average stress on the net cross section is referred to as the Stress Concentration Factor. This factor is in the range of 2 to 3, depending upon the ratio of the diameter of the hole to the width of the plate normal to the direction of stress.

Fig.1.4 Stress concentration due to holes When a tension member with a hole is loaded statically, the point adjacent to the hole reaches yield stress fy first. On further loading, the stress at that point remains constant at the yield stress and the section plastifies progressively away from the hole [Fig. 1.4 (b)], until the entire net section at the hole reaches the yield stress fy [Fig. 1.4©]. Finally, the rupture (tensile failure) of the member occurs when the entire net cross section reaches the ultimate stress fu [Fig. 1.4(d)]. Here, only a small length of the member adjacent to the smallest cross section at the holes would stretch a lot at the ultimate stress, and the overall member elongation will not be large, as long as the stresses in the gross section is below the yield stress. Hence, the design strength as governed by the net cross-section at the hole is given by:

Tdn = 0.9 fu An / m1

where,

Eq. (1.2)

fu is the ultimate stress of the material,

An is the net area of the cross section after deductions for the hole, and

m1 is the partial safety factor against ultimate tension failure by rupture.

The value of m1 according to IS 800:2007 is 1.25.

1.4.3 Design strength due to block shear:

A tension member may fail along end connection due to block shear as shown in Fig. 1.5. The corresponding design strength can be evaluated using the following equations. The block shear strength, Tdb of a connection is taken as the smaller of,

T = Avg fy / v3 m0 + 0.9 Atn fu / m1

db

Eq. (1.3 a)

Or T = 0.9 Avn fu / v3 m1 + Atg fy / m0

db

Eq. (1.3 b)

where, Avg and Avn = minimum gross and net area in shear along a line of transmitted force respectively, and Atg and Atn

=

minimum gross and net area in tension from the hole to the toe of the angle perpendicular to the line of force respectively.

Fig. 1.5 Typical block shear failure geometry (Representation of Atn, Atg, Avn, Avg)

It can be seen from the above two equations that according to IS 800:2007, block shear design strength is equivalent to strength of either shear yield and tensile rupture; or shear rupture and tensile yield (whicheverâ„¢s value is smaller).

1.5 Block Shear Failure Mechanism:

The design strength of tension members are not always controlled by factor of safety or by the strength of the bolts or welds with which they are connected. They may instead be controlled by block shear strength, as described below.

In block shear mode, the failure of the member occurs along a path involving tension on one plane and shear on a perpendicular plane along the fasteners. Typical block shear failure mechanism for plates and angles are shown in Fig. 1.6. The Ëœblockâ„¢ of the connected plate bounded by the bolt holes tears out in this failure mechanism, in which tensile force is developed along the section 2-3 and shear force develops along the section 1-2 and 4-3 (in case of the plate) and section 1-2 (in case of the angle section).

Fig. 1.6 Block shear failure in plates and angles When a tensile load applied to a particular connection is increased, the fracture strength of the weaker plane approaches. This plane does not fail instantly, because it is restrained by the stronger plane. The load can be increased until the fracture strength of the stronger plane is reached and during this time, the weaker plane yields. The total strength of the connection equals the fracture strength of the stronger plane plus the yield strength of the weaker plane. Thus, it is not realistic to add the fracture strength of the other plane to determine the block shear resistance of a particular member.

It is also required to check the block shear failure mode around the periphery of welded connections. Examples of block shear failures including failures in welded connections are given in Fig. 1.7. It can be observed as shown in Fig. 1.7(a) that the gusset plate may fail in tension on the net area of section a-a, and in Fig. 1.7© it may fail on the gross area of section a-a. The angle member in Fig. 1.7(a) may also separate from the gusset plate by shear on net area 1-2 combined with tension on net area 2-2 as shown in Fig. 1.7(b). A similar fracture of the welded connection of Fig. 1.7© is shown in Fig 1.7(d). The fracture of a gusset plate for a double angle member or of one of the gusset plates for an I-section [Fig. 1.7(e)] is shown in Fig. 1.7(f). All these failures [Figs. 1.7(b), (d) and (f)] are called block shear failures. However, it should be noted that no net areas are involved in the failure of welded connections [Fig. 1.7©]. Therefore, in applying Eqn. 1.3(a) Atg is to be used instead of Atn; and in Eqn. 1.3(b), Avn is to be replaced by Avg.

Fig. 1.7 Examples of block shear failure

IS 800: 2007 assumes that when one plane, either tension or shear, reaches ultimate strength the other plane develops full yield. This assumption results in two possible failure mechanisms in which the controlling mode is the one having a smaller fracture strength term. In the first mechanism, it is assumed that failure load is reached when rupture occurs along the net tension plane and full yield is developed along the gross shear plane. Conversely, the second failure mode assumes that rupture occurs along the net shear plane while full yield is developed at the gross tension plane [Refer Eqns. 1.3(a) and (b)]. Since there is no reserve of any kind beyond the ultimate resistance, an additional multiplier of 0.09 has been introduced in the said

equations. Such a high margin of safety has been traditionally used in design when considering the fracture limit state than for yielding limit state. The 0.90 factor was included in the strength equation based on a statistical evaluation of a large number of test results for net section failure of plate.

Fig. 1.8 Block shear rupture in a gusset plate

1.6 AISC 2005 Specification for Block Shear:

The model used in the current specification (AISC 2005a) assumes that block shear failure occurs by rupture (fracture) on the shear area and rupture on the tension area. Both surfaces contribute to the total strength, and the resistance to block shear will be the sum of the strengths of the two surfaces. The shear rupture stress is taken as 60% of the tensile ultimate stress, so the nominal strength in shear is 0.6 fu Anv and the nominal strength in tension is fu Ant. This gives a nominal strength of

Rn = 0.6 fu Anv + fu Ant

Eq. (1.4)

The AISC Specification uses Eqn. 1.4 for angles and gusset plates, but for certain types of coped beam connections, the second term is reduced to account for non-uniform tensile stress. The tensile stress is non-uniform when some rotation of the block is reqired for failure to occur. For these cases,

Rn = 0.6 fu Anv + 0.5 fu Ant

Eq. (1.5)

The AISC Specification limits the 0.6 fu Anv term to 0.6 fy Agv, where 0.6fy is equal to shear field stress, and gives one equation to cover all cases as follows:

Rn = 0.6 fu Anv + Ubs fu Ant = 0.6 fy Agv + Ubs fu Ant (AISC Eqn. J4-5)

where

Eq. (1.6)

Ubs = 1.0 when the tension stress is uniform (angles, gusset plates and most coped beams)

and Ubs = 0.5 when the tension stress is non-uniform. The above specification can also be read as: Rn = Shear Rupture + Tension Rupture < Shear Yield + Tension Rupture For LRFD, the resistance factor ÃƒËœ is 0.75 and for ASD, the safety factor O is 2.0. Although AISC Eqn. J4-5 is expressed in terms of bolted connections, block shear can also occur in welded connections, especially in gusset plates.

1.7 Eurocode 3 Specification for Block Tearing:

In Eurocode 3 pr-EN 1993-1-8: 20xx, the design value for block shear (termed block tearing in the standard) for symmetric bolt groups, under centric loading is determined from the equation:

Veff,1,Rd = fu Ant / M2 + (1 / v3) fy Anv / M0

where

Eq. (1.7)

Ant = Net area subjected to tension, Anv = Net area subjected to shear, M2 = 1.25 (partial factor for resistance to breakage of cross-sections in tension), and M0 = 1.00 (partial factor for resistance of cross-sections).

For beam end with a shear force acting eccentric relative to the bolt group, the design value for block tearing Veff,2,Rd is determined from the following equation:

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Veff,2,Rd = 0.5 fu Anv / M2 + (1 / v3) fy Ant / M0

Eq. (1.8)

Thus Eqn. 1.8 considers block shear to be a combination of shear rupture and tensile yield, as evidenced from the first and second term respectively.

The tensile failure occurs along the horizontal limit of the block, and shear plastic yielding occurs along the left vertical limit of the block. The block is hatched in as shown in Fig. 1.9.

Fig. 1.9 Block Tearing

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2. LITERATURE REVIEW

2.1 Introduction

In the past, a lot of research has been carried out by eminent people on block shear failure and its properties. Along with experimental studies, finite element methods as well as statistical studies have been employed in various research works. Finite element methods have been used to study the behavior of structural members subjected to block shear and net section failure modes. Ricles and Yura examined block shear failure in coped beams using a two-dimensional elastic analysis. A modified block shear model was proposed based on the stress distribution around the block. Epstein and Chamarajanagar studied the effects of bolt stagger and shear lag on block shear failure of angle members. Angles were modeled with 20 node brick elements and an elasticâ€œperfectly plastic stressâ€œstrain curve for steel was used in the analysis. A strain-based criterion was employed to determine the failure load of members. The non-dimensionalised finite element results were compared with the results of full scale testing. Kulak and Wu studied the shear lag effects on net section rupture of single and double angle tension members. Angles were modeled with shell elements and multilinear isotropic hardening behavior was assumed for the material response. The failure load was considered as the load corresponding to the last converged load step. The failure loads obtained through the analysis were compared with the actual test results. Recently, finite element studies were conducted by Barth et al. to predict the net section failure of WT tension members. A very elaborate analysis method was employed which includes geometric and material nonlinearities as well as the surface to surface contact between the tee and the gusset plates. Tee sections were modeled using eight node incompatible hexahedral elements and a trilinear true-stress true-strain curve was used to represent material nonlinear effects. The load deflection curve was traced beyond the limit point using the Newtonâ€œRaphson method. The load corresponding to the load limit point was considered as the failure load. The numerical simulation results were found to be in close agreement with the actual test results.

Previous experimental studies have also been conducted to compare its findings with the predictions of block shear capacity using finite element analysis. Hardash and Bjorhovde tested 28 specimens to develop an improved design method for gusset plates. Primary variables were

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the gauge between the lines of bolts, end distance, bolt pitch and the number of bolts. Gusset plates fastened through two lines of bolts were tested in their study. A block shear model incorporating a connection length factor was developed as part of their study. Gross et al. tested 13 angle specimens that failed in block shear. Connections had two to four bolts with a hole diameter of 21 mm. The edge distance was varied between 32 mm and 50 mm in 6 mm increments and test results obtained were compared with the code predictions. Similarly, Orbison et al. tested 12 specimens that failed in block shear. Connections had two to four bolts with a hole diameter of 27 mm. A hole spacing of 76 mm and an end distance of 63.5 mm was used in all specimens. The edge distance was varied between 50.8 mm and 88.9 mm in 12.7 mm increments. Recommendations were given based on the ultimate load and the strain variation along the tension plane that was measured during the experiments.

2.2 Study of Ling et al. (2006)

Their study investigated block shear tearout (TO) failure in gusset-plate welded connections in both very high strength (VHS) tubes and structural steel hollow sections (SSHS). Twenty-five slotted gusset-plate welded connections in VHS tubes with various weld lengths were studied under tension. The existing design rules for TO failure from the American, Canadian, European and Australian standards were examined by comparing their predictions with both test results from welded connections in VHS tubes and previous tests on similar connections to SSHS. The results suggested that the existing design rules were not adequate to predict the connection strength. Therefore, five modifications to the existing design rules were examined. One of them, which used the proposed net tension area and the minimum material yield stress and tensile strength provided strength predictions that agreed best with the test results. From reliability analysis based on the first order second moment (FOSM) method, a rounded value of 0.70 was proposed for the TO capacity or resistance factor.

2.3 Study of Yam et al. (2005)

Yam et al investigated the block shear strength and behavior of coped beams with welded end connections and conducted ten full-scale coped beam tests. The failure mechanism in coped beams with welded end connections was different from that with bolted end connections, since there was no reduction in the web section area due to bolt holes. The test results showed that

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only two of the ten specimens failed by block shear mode with tension fractures. Tension fractures occurred abruptly in the beam web underneath the clip angles. No shear fractures were observed and no tear-out type of block shear occurred. Local web buckling was also a potential failure mode for coped beams with welded end connections. High compressive stresses and shear stresses were localized in the web near the end of the cope due to the combination of bending and shear in the reduced section, hence resulting in extensive yielding at the cope and inducing local web buckling. However, the specimens exhibited significant deformation of the block shear type prior to reaching their final failure mode.

The test parameters examined included the aspect ratio of the clip angles, the tension and shear area of the web block, web thickness, beam section depth, cope length and connection position. The results showed that the connection capacity increased as aspect ratio and shear area increased. A large area of tension would increase the loading eccentricity and hence generate more bending moments to the edge of the beam web region near the angle. A thin beam web and long cope length increased the susceptibility to local web buckling. The depth of the beam section and connected position did not greatly affect the connection capacity.

The design equations from current standards were used to evaluate the capacity of the specimens. It was found that the existing design standards did not provide consistent predictions of the block shear strength of coped beams with welded end connections. In addition, the rules provided by the standards could not accurately reflect the failure mode observed in the tests.

2.4 Study of Topkaya (2004)

This study reported on the experimental testing of 11 welded gusset plate specimens which were subjected to tension, and ultimately to block shear failure. In the experimental program, the effects of connection geometry and weld group configuration were investigated. Connection geometry and weld group configuration were the prime variables of the testing program. Two different weld group configurations were examined. The failure loads obtained from the experiments were compared with the predictions of resistance equations presented by the design codes. Finally, finite element analyses were conducted to predict the failure loads of the specimens and the respective load-carrying capacities of the shear and tension planes. The

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study concluded that block shear failure could be observed for connection details with and without welded tension planes; and that the mechanics of block shear failure for welded details was different when compared with the bolted details. The tension plane in the welded connection details could develop stresses in excess of the ultimate tensile strength due to the presence of stress triaxiality. Finally, design recommendations were given based on the experimental and numerical findings.

2.5 Study of Gupta and Gupta (2004)

Their study examined the block shear capacity of steel angles (single as well as double angles), for bolt holes in one or more rows, and with staggered and non-staggered holes. Only those specimens that follow all provisions regarding minimum pitch, edge and end distances were included in the study. Angles composed of high strength steel were not included in their study. An improved approach to compute the block gross shear area of specimens that had bolt holes staggered such that the end distance along the row of bolts towards the heel was relatively more, was suggested. The area as per their improved approach was termed as effective block gross shear area and was somewhat less than the block gross shear area, as per current practice. There was a considerable improvement in values of professional factors when the concept of effective block gross shear area was used in the computations. Based on the findings, they proposed a simple equation to give adequate results for single as well as double angles, for bolt holes in one or more rows, and with staggered and non-staggered holes.

Fig. 2.1 Non-uniform stress distribution along the block gross shear plane

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2.6 Study of Epstein and McGinnis (2000)

The goal of their study was to accurately model structural tee specimens using the finite element method in order to predict the failure mode. In this way, it was believed that future tests might be designed based on finite element results and the results of their tests might be correlated with finite element results. The finite element models were accurate in predicting failure mode, especially when compared to the results of the physical tests, and normalized failure load plots showed similar shapes. Noteworthy was the strong analytical evidence for the formation of the block shear failure mode on the alternative path as observed in many of the models. Another interesting result was the unexpected formation of a compressive zone in the web of the tension members at the leading set of bolt holes. In terms of behavior, it was noted that an eccentric tension member was subjected not only to an axial force but also to a moment due to the connection eccentricity. Opposing moments were also present, created by the reaction shears at the bolt holes. During the work on failure mode matching, it appeared that better matches were made when the U factor was included in the code equations. Further, when trying to match the experimental results, the plots of normalized failure load versus depth also seemed to show the appropriateness of adding the U factor to the code equations, perhaps in some modified form.

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3. NUMERICAL EXAMPLE

3.1 Problem Statement

An ISMB 600 is connected to a column by web cleats with a single row of bolts. The applied reaction is 350 kN and there are four 20-mm-diameter bolts through the web as shown in Fig. 3.1. Now, this section will be checked for block shear failure using provisions of the IS 800:2007; AISC Specification 2005 (both LRFD and ASD); and Eurocode 3 (all of which have been discussed in previous sections).

Fig. 3.1 ISMB 600

3.2 Solution

Yield stress of the material = fy = 250 N/mm2 Ultimate stress of the material = fu = 410 N/mm2

Plate or web thickness (ISMB 600) = 12 mm

Net length of shear face = (3 * 50 + 75) â€œ (3.5 * 22) = 148 mm Net length of tension face = 60 â€œ (0.5 * 22) = 49 mm Avg = 12 * (50 + 50 + 50 + 75) = 2700 mm2 Avn = 12 * 148 = 1776 mm2 Atg = 12 * 60 = 720 mm2 Atn = 12 * 49 = 588 mm2

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Computing block shear strength using IS 800: 2007

m0 = 1.10 m1 = 1.25 T = Avg fy / v3 m0 + 0.9 Atn fu / m1

= [2700 * 250 / (v3 * 1.1) + 0.9 * 588 * 410 / 1.25] / 1000 kN = 527.86 kN or

db1

db2

= 0.9 Avn fu / v3 m1 + Atg fy / m0

= [0.9 * 1776 * 410 / (v3 * 1.25) + 720 * 250 / 1.1] / 1000 kN = 466.32 kN

Since T

db2

< Tdb1

Therefore, Tdb = 466.32 kN The value of Tdb = 466.32 kN is much higher than the applied reaction of 350 kN and hence the section will not fail by block shear.

Computing block shear strength using AISC 2005

Since stress distribution in I section is uniform, Ubs = 1.0

Nominal block shear strength Rn = 0.6 fu Anv + Ubs fu Ant = [(0.6 * 410 * 1776) + (1.0 * 410 * 588)] / 1000 = 677.98 kN with an upper limit of 0.6 fy Agv + Ubs fu Ant = [(0.6 * 250 * 2700) + (1.0 * 410 * 588)] / 1000 = 646.08 kN The nominal block shear strength is therefore 646.08 kN. Resistance factor = ÃƒËœ = 0.75 The design strength for LRFD = ÃƒËœ Rn = 0.75 * 646.08 = 484.56 kN

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Considering the design strength value obtained, we can see that it is greater than the applied reaction of 350 kN and hence the section will not fail in block shear.

Computing block shear strength using Eurocode 3

M0 = 1.00 M2 = 1.25

For centric loading and symmetrical bolt group, the design value for block shear is

Veff,1,Rd = fu Ant / M2 + (1 / v3) fy Anv / M0

= [(410 * 588 / 1.25) + (250 * 1776 / v3 * 1.0)] / 1000 = 367.7 kN

Since the design value of 367.7 kN is higher than the 350 kN applied reaction, there will be no block shear failure in the section.

Hence, the design block shear strength for different codes arranged in increasing order is: Eurocode 3 < IS 800:2007 < AISC 2005 (LRFD value) i.e. 367.7 kN < 466.32 kN < 484.56 kN Thus, all the three standards give the design block shear strength which is greater than the applied reaction of 350 kN.

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4. CONCLUSION

Block shear failure is the important limit state that should be considered during the design of steel tension members. When the steel tension member connections are relatively short, block shear failure is usually the governing failure mode. A comparison of the various design standards used for calculating block shear strength has revealed that there exist inconsistencies in predicting the accurate design value.

Although the results obtained from the numerical shows that the considered section is safe from block shear failure, the design capacities differ from each other by as much as 116.86 kN if we compare the end extreme values (i.e. 367.7 kN from Eurocode 3 and 484.56 kN from AISC 2005). This can be explained from the fact that different standards consider different modes of failure. For instance, IS 800 assumes block shear design strength to be equivalent to the strength of either shear yield and tensile rupture; or shear rupture and tensile yield (whicheverâ„¢s value is smaller). AISC Specification can be read as: the summation of shear rupture and tension rupture is less than shear yield and tension rupture combined. Also Eurocode 3 takes a different view and considers block shear to be a combination of shear rupture and tensile yield only.

While calculating design strength, IS 800 does not incorporate factors like eccentricity (but considered in Eurocode 3) and also does not check whether the tension stress is uniform or non-uniform (but this is done in AISC 2005). Also, from previous research studies, it was noted that eccentric tension members are subjected not only to axial forces but also to moments due to connection eccentricities. Presence of in-plane eccentricity can reduce the block shear load capacity by 10% for longer connections. Moreover, shear lag reduction coefficient Ubs has been incorporated only in the AISC Specification. Stress concentrations, connection geometries and other factors that may contribute to yield or rupture of the tension plane without affecting the shear plane can also be expected to reduce block shear load capacity. Equations having high safety indices than the traditional target for connections can result in uneconomical connections. Thus, there exists considerable scope for improvement and analytical work together with some statistically meaningful experimentation could help designers optimize connection geometries, and may influence the framers of future codes.

Submitted to the DEPARTMENT OF APPLIED MECHANICS In partial fulfillment of the requirements for the award of the degree of BACHELOR OF TECHNOLOGY IN CIVIL ENGINEERING Submitted by PRAKASH AGARWAL Guided by Prof. A J SHAH

DEPARTMENT OF APPLIED MECHANICS S V NATIONAL INSTITUTE OF TECHNOLOGY SURAT - 395007 GUJARAT DECEMBER 2009

CERTIFICATE

This is to certify that the seminars entitled ËœBLOCK SHEAR FAILURE IN TENSION MEMBERSâ„¢ submitted by PRAKASH AGARWAL in partial fulfillment of the requirement for the award of the degree in BACHELOR OF TECHNOLOGY IN CIVIL ENGINEERING of Sardar Vallabhbhai National Institute of Technology, Surat is the record of his own work carried out under my supervision and guidance. The matter embodied in the seminars has not been submitted elsewhere for the award of any degree or diploma.

A J SHAH

Lecturer Faculty Supervisor Dept. of Applied Mechanics SVNIT, SURAT

Anant M Parghi

Lecturer Seminar Coordinator Dept. of Applied Mechanics SVNIT, SURAT

Dr A K Desai

Associate professor Head of the department Dept. of Applied Mechanics SVNIT, SURAT

EXAMINERâ„¢S CERTIFICATE OF APPROVAL

The seminars entitled ËœBLOCK SHEAR FAILURE IN TENSION MEMBERSâ„¢ submitted by PRAKASH AGARWAL in partial fulfillment for the award of the degree in Bachelor of Technology in Civil Engineering of Sardar Vallabhbhai National Institute of Technology, Surat is hereby approved for the award of the degree.

Examiners:

1.

2.

ACKNOWLEDGEMENT

This seminars work would not have been possible without the valuable guidance of Prof. A J Shah of Applied Mechanics Department, SVNIT, Surat. I hereby take this opportunity to express my deep sense of gratitude and indebtedness to him. His kind cooperation and the interactive environment ensured the successful completion of this work. I am also thankful to our teaching and non-teaching staff members and all my friends who helped me avail the necessary information for the completion of this seminars work.

CONTENTS

ABSTRACT LIST OF FIGURES NOMENCLATURE (i) (ii) (iii)

1.0 INTRODUCTION 1.1 Background 1.2 Tension Members 1.3 Behaviour of Tension Members 1.4 Design Strength of Tension Members 1.5 Block Shear Failure Mechanism 1.6 AISC 2005 Specification for Block Shear 1.7 Eurocode 3 Specification for Block Tearing

1 1 1 3 4 7 9 10

2.0 LITERATURE REVIEW 2.1 Introduction 2.2 Study of Ling et al. (2007) 2.3 Study of Yam et al (2007) 2.4 Study of Topkaya (2004) 2.5 Study of Gupta and Gupta (2004) 2.6 Study of Epstein and McGinnis (2000) 3.0 NUMERICAL EXAMPLE 3.1 Problem Statement 3.2 Solution

12 12 13 13 14 15 16 17 17 17

4.0 CONCLUSION REFERENCES

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LIST OF FIGURES

Sl. No. TITLE Page No.

Fig. 1.1 Fig. 1.2 Fig. 1.3 Fig. 1.4 Fig. 1.5 Fig. 1.6 Fig. 1.7 Fig. 1.8 Fig. 1.9 Fig. 2.1 Fig. 3.1

Tension members in buildings and bridges Cross-section of typical tension members Load â€œ Elongation of tension members Stress concentration due to holes Typical block shear failure geometry Block shear failure in plates and angles Examples of block shear failure Block shear rupture in a gusset plate Block Tearing Non-uniform stress distribution along the gross shear plane ISMB 600

2 3 3 5 6 7 8 9 11 15 17

ii

NOMENCLATURE

Ag An Atg

- Gross cross-sectional area - Net area of the total cross-section - Gross cross-sectional in tension from the centre of the hole to the toe of the angle section / channel section, etc perpendicular to the line of force.

Atn

- Net sectional in tension from the centre of the hole to the toe of the angle perpendicular to the line of force.

Avg Avn fy fu Rn Tdg Tdn Tdb Ubs

- Gross cross-sectional area in shear along the line of transmitted force - Net cross-sectional area in shear along the line of transmitted force - Characteristic yield stress - Characteristic ultimate tensile stress - Nominal resistance (AISC 2005) - Yielding strength of gross section under axial tension - Rupture strength of net section under axial tension - Block shear strength at end connection - Reduction factor in block shear (AISC 2005)

Veff, 1, Rd - Block shear strength for centric loading (Eurocode 3) Veff, 2, Rd - Block shear strength for eccentric loading (Eurocode 3)

m0 m1 M0 M2

ÃƒËœ O

- Partial safety factor for failure in tension by yielding (IS 800: 2007)

- Partial safety factor against ultimate tensile failure by rupture (IS 800: 2007) - Partial factor for resistance of cross-sections (Eurocode 3) - Partial factor for resistance to breakage of cross-sections in tension (Eurocode 3)

Resistance factor (AISC 2005 LRFD) Safety factor (AISC 2005 ASD)

iii