Journal of Constructional Steel Research 60 (2004) 16151635

Block shear is a limit state that combines a tension failure on one plane and ashear failure on a perpendicular plane. The AISC-ASD [1] and LRFD [2] specica-

12res

see front matter# 2004 Elsevier Ltd. All rights reserved. Tel.: +90-3E-mail add

0143-974X/$ -doi:10.1016/j.jcs-210-5462; fax: +90-312-210-1262.

s: ctopkaya@metu.edu.tr (C. Topkaya).r.2004.03.006tions present equations to predict the block shear rupture strength. In the AISC-ASD [1] procedure, failure is assumed to occur by simultaneous rupture of the netwww.elsevier.com/locate/jcsr

A nite element parametric study on blockshear failure of steel tension members

Cem Topkaya

Department of Civil Engineering, Middle East Technical University, 06531 Ankara, Turkey

Received 4 December 2003; accepted 26 March 2004

Abstract

Block shear is a limit state that should be accounted for during the design of steel tensionmembers. Current design equations are not based on analytical ndings and fail to predictfailure modes of tested specimens. A study has been conducted to develop simple blockshear load capacity prediction equations that are based on nite element analysis. Over athousand nonlinear analyses were performed to identify the important parameters that inu-ence block shear capacity. In addition, the eects of eccentric loading were investigated.Based on the parametric study block shear load capacity prediction equations weredeveloped. The predictions of the developed equations were compared with the experimentalndings and were found to provide estimates with acceptable accuracy.# 2004 Elsevier Ltd. All rights reserved.

Keywords: Block shear failure; Finite elements; Tension members

1. Introduction

Tension members with bolted ends are frequently encountered as principal struc-tural members in trusses and lateral bracing systems. Design of these membersshould ensure that yield of gross area, rupture of the net section and block shearfailure are precluded during the lifetime of the structure.

C. Topkaya / Journal of Constructional Steel Research 60 (2004) 161516351616tension and shear planes. The service load capacity is predicted by a single equa-tion that incorporates a factor of safety of 2.0. The ASD [1] nominal load capacitywithout the factor of safety is given in Eq. (1)

Rn FuAnt 0:6FuAnv 1where Anv is the net area subject to shear; Ant is the net area subject to tension andFu is the tensile strength of steel.On the other hand the AISCLRFD specication [2] has a more elaborate treat-

ment. The LRFD [2] procedure assumes that when one plane, either the tension orshear, reaches ultimate strength the other plane develops full yield. This assump-tion results in two possible failure mechanisms in which the controlling mode is theone having a larger fracture strength term. In the rst mechanism, it is assumedthat failure load is reached when rupture occurs along the net tension plane andfull yield is developed along the gross shear plane. On the contrary, the second fail-ure mechanism assumes that rupture occurs along the net shear plane while fullyield is developing at the gross tension plane. The nominal load capacity perAISCLRFD [2] is calculated as follows:When FuAnt 0:6FuAnv

Rn 0:6FyAgv FuAnt 0:6FuAnv FuAnt 2

When FuAnt < 0:6FuAnv

Rn 0:6FuAnv FyAgt 0:6FuAnv FuAnt 3

where Agv is the gross area subject to shear; Agt is the gross area subject to tensionand Fy is the yield stress of steel.The LRFD [2] procedure has an upper limit on the nominal strength such that

its value could not exceed the value determined by considering the simultaneousfracture at the net shear and tension planes. In order to calculate the designstrength, the nominal strength is further multiplied by a / factor which is equal to0.75.Both the ASD [1] and LRFD [2] procedures provide a reasonable level of accu-

racy in predicting load capacities while exhibiting a wide variation in experimental-to-predicted capacity ratios [3]. In addition, there are dierences between theobserved and predicted failure modes [3]. In majority of the experiments performedso far ductile rupture of the tension plane preceded by signicant necking wasobserved [3]. Rupture of the tension plane is accompanied by inelastic deforma-tions along the gross shear plane. Displacement of a block of material was seenonly when the experiment was continued until the parts separate.Both the ASD [1] and LRFD [2] block shear predictions have drawbacks in

terms of the anticipated failure mode. It is evident from the test results [3] that ten-sion and shear planes do not rupture simultaneously as assumed by the ASD speci-cation [1]. In LRFD [2] typically the equation (Eq. (3)) with shear fracture termgoverns, while experiments tend to exhibit a failure mode similar to that describedby the equation (Eq. (2)) with tensile fracture term. The current code equationsare based on simple models that do not depend on principles of mechanics. The

1617C. Topkaya / Journal of Constructional Steel Research 60 (2004) 16151635objective of this study is to develop simple block shear prediction equations basedon numerical modeling of physical systems. In this paper the use of nite elementanalysis in predicting block shear capacity of tension members is presented. Thecomparisons between nite element predictions and experimental ndings are givenfor gusset plates, angle and tee sections with nonstaggered bolted connections. Anite element parametric study was conducted to identify the important parametersthat inuence the block shear capacity. Based on the parametric study simple equa-tions to predict block shear were developed and are presented herein.

2. Finite element modeling

2.1. Previous studies

Finite element method was used in the past to study the behavior of structuralmembers subject to block shear and net section failure modes. Ricles and Yura [4]examined block shear failure in coped beams using a two-dimensional elasticanalysis. A modied block shear model was proposed based on the stress distri-bution around the block. Epstein and Chamarajanagar [5] studied the eects ofbolt stagger and shear lag on block shear failure of angle members. Angles weremodeled with 20 node brick elements and an elasticperfectly plastic stressstraincurve for steel was used in the analysis. A strain-based criterion was employed todetermine the failure load of members. The nondimensionalized nite elementresults were compared with the results of full scale testing. Kulak and Wu [6] stud-ied the shear lag eects on net section rupture of single and double angle tensionmembers. Angles were modeled with shell elements and multilinear isotropic hard-ening behavior was assumed for the material response. The failure load was con-sidered as the load corresponding to the last converged load step. The failure loadsobtained through the analysis were compared with the actual test results. Recently,nite element studies were conducted by Barth et al. [7] to predict the net sectionfailure of WT tension members. A very elaborate analysis method was employedwhich includes geometric and material nonlinearities as well as the surface to sur-face contact between the tee and the gusset plates. Tee sections were modeled usingeight node incompatible hexahedral elements and a trilinear true-stress true-straincurve was used to represent material nonlinear eects. The load deection curvewas traced beyond the limit point using the NewtonRaphson method. The loadcorresponding to the load limit point was considered as the failure load. Thenumerical simulation results were found to be in close agreement with the actualtest results.

2.2. Current study

As explained before nite element models with diering complexity levels wereemployed in the previous studies. This study aims to develop simple block shearcapacity prediction equations that are based on principles of mechanics. Therefore,an accurate prediction of the block shear failure load is essential. For this purposean analysis methodology similar yet less detailed than the one explained by Barth

used toIn th r plane

stress e ing 10-node te g largedeform strainbehavio arden-ing. A g genericrespons followsthe elas 02 andvaries l e ulti-mate st ere is aconstan of 0.3.The genUsua metry

plane along the length. Similarly, for cross sections that possess a symmetry plane

C. Topkaya / Journal of Constructional Steel Research 60 (2004) 161516351618like the tees, only half of the cross section is modeled. In an eort to reduce thecomputational cost, end connection details which are used to apply loading are notmodeled. In order to simulate the end reactions, nodes that lie on the half circum-ference of each hole where bolts come into contact are restrained against displace-ment in two perpendicular directions in the plane of the plate. A longitudinaldisplacement boundary condition is applied at the opposite end of the member.Throughout the analysis the NewtonRaphson method is used to trace the entire

nonlinear loaddeection response. The failure load is assumed to be the maximumload reached during the loading history. In most of the experiments failure wastriggered by signicant necking of the tension plane. In the nite element analysissubstantial amount of necking is observed near the vicinity of the leading bolt hole

Fig. 1. Generic true-stress true-strain material response for steel.] was employed. A general purpose nite element program ANSYSperform the analyses.is methodology, gusset plates are modeled using six node triangulalements. On the other hand, angles and tee sections are modeled ustrahedral elements. These element types are capable of representination geometric and material nonlinearities. The nonlinear stressr of steel is modeled using von Mises yield criterion with isotropic heneric true-stress true-strain response is used in all analyses. In thise the material behaves elastic until the yield point. A yield plateautic portion. Strain hardening commences at a true strain value of 0.inearly until the true ultimate stress is reached. The true-strain at truress is assumed to be 0.1. After the true ultimate stress is reached tht stress plateau until the material is assumed to break at a true straineric true-stress true-strain curve is given in Fig. 1.lly half length of the specimens is modeled if specimens possess a symet al. [7 [8] was

1619C. Topkaya / Journal of Constructional Steel Research 60 (2004) 16151635at the ultimate load. A representative nite element analysis on a gusset plate ispresented in Fig. 2 along with the loaddisplacement response obtained. The com-parisons of the nite element predictions with the experimental ndings will be pre-sented in the following section.

3. Finite element analysis predictions

The prediction of block shear capacity using nite element analysis was assessed

Fig. 2. Representative nite element analysis of a gusset plate. (a) Model of half plate and (b) typical

loaddisplacement responses.by making comparisons with the experimental ndings. Block shear test results

C. Topkaya / Journal of Constructional Steel Research 60 (2004) 161516351620[911] reported on gusset plates, angles and tees by three independent researchteams were considered. Following is an overview of the properties of the specimenstested by the research groups.

3.1. Previous experimental studies

Hardash and Bjorhovde [9] tested 28 specimens to develop an improved designmethod for gusset plates. Primary variables were the gage between the lines ofbolts, end distance, bolt pitch and the number of bolts. Gusset plates fastenedthrough two lines of bolts were tested in their study. The test specimens had a gagedistance of 51 (2 in.), 76 (3 in.) and 101 mm (4 in.), an end distance of 25 (1 in.)and 38 mm (1.5 in.), and a pitch distance of 38 (1.5 in.) and 51 mm (2 in.).Connections had two to ve bolts with a hole diameter of 14 (9/16 in.) and 17 mm(11/16 in.). All of the specimens except one had a yield strength of 229 MPa(33.2 ksi) and an ultimate strength of 323 MPa (46.9 ksi). A block shear modelincorporating a connection length factor was developed as a part of the study.Gross et al. [10] tested 13 angle specimens that failed in block shear. Ten of the

specimens were made of A588 Grade 50 steel with a yield and ultimate strength of427 (62 ksi) and 545 MPa (79 ksi), respectively. The rest of the specimens weremade of A36 steel with yield and ultimate strength of 310 (45 ksi) and 469 MPa(68 ksi), respectively. Angles had 6 mm (0.25 in.) thick connected and outstandinglegs that vary between 76 (3 in.) and 101 mm (4 in.) in length. Connections hadtwo to four bolts with a hole diameter of 21 mm (13/16 in.). A hole spacing of63.5 mm (2.5 in.) and an end distance of 38 mm (1.5 in.) was used in all specimens.The edge distance was varied between 32 (1.25 in.) and 50 mm (2 in.) in 6 mm(0.25 in.) increments. The test results were compared with the code predictions.Orbison et al. [11] tested 12 specimens that failed in block shear. Three of the spe-

cimens were L 6 4 5=16 angles with yield and ultimate strength of 346 (50 ksi)and 490 MPa (71 ksi), respectively. Nine of the specimens were WT 7 11 tee sec-tions with a yield and ultimate strength of 335 (48 ksi) and 463 MPa (67 ksi), respect-ively. Connections had two to four bolts with a hole diameter of 27 mm (17/16 in.).A hole spacing of 76 mm (3 in.) and an end distance of 63.5 mm (2.5 in.) was used inall specimens. The edge distance was varied between 50.8 (2 in.) and 88.9 mm (3.5in.) in 12.7 mm (0.5 in.) increments. Recommendations were given based on the ulti-mate load and the strain variation along the tension plane that was measured duringthe experiments.

3.2. Simulation of previous experiments

For all of the above-mentioned specimens a nite element mesh was prepared.These meshes were analyzed using the same procedure explained before. Ultimateload value was documented for every analysis. Fig. 3 shows representativedeformed nite element meshes for a gusset plate and an angle specimen. The dis-placement of a block of material could be easily seen in the half plate model(Fig. 3a). In addition, the necking behavior of the tension plane is displayed in theangle model (Fig. 3b).

1621C. Topkaya / Journal of Constructional Steel Research 60 (2004) 16151635The nite element analysis predictions are presented in Fig. 4 for the 53 speci-

Fig. 3. Representative deformed shapes. (a) Half gusset plate model and (b) angle section.mens analyzed. In Fig. 4 experimental failure loads are plotted against the nite

element analysis predictions. Data points appearing below the diagonal line indi-cate tests for which the nite element analysis predictions are unconservative (loadcapacity is overestimated) while points above the line indicate conservative loadpredictions. For statistical analysis a professional factor (experimental load dividedby the predicted load) was calculated for every test. A perfect agreement betweenthe predicted and experimental failure loads are expressed by a professional factorof unity. Factors less than unity and greater than unity represent underestimateand overestimate of the failure load, respectively. The statistical analyses of thepredictions are presented in Table 1. It is evident from Fig. 4 and Table 1 that thenite element method provides excellent load capacity predictions.Similar type of comparisons were performed for the LRFD and ASD load

capacity predictions. In calculating the LRFD and ASD failure loads bolt holesizes were taken as 2 mm (1/16 in.) greater than the nominal bolt hole diameter.LRFD and ASD load capacity predictions are presented in Figs. 5 and 6, and thestatistical measures of the predictions are given in Table 1. It is worthwhile to notethat in almost all of the 53 tests considered, fracture occurred at the net tensionplane. On the other hand, in all of the LRFD predictions except three cases, theequation with the shear fracture term governed. It is obvious from this discussionthat LRFD predictions do not capture the failure mode of the specimens.Based on the tests considered both LRFD and ASD procedures oer on averagea conservative estimate of the failure load. On the other hand, the nite element

C. Topkaya / Journal of Constructional Steel Research 60 (2004) 161516351622analysis predictions give much closer results with less scatter compared to the codeequations. The nite element procedure explained earlier is promising in terms ofestimating the failure loads. This procedure will be employed for the rest of thisstudy to develop simple block shear load capacity prediction equations.

4. Parametric study

4.1. Concentric connections

A parametric study has been conducted to develop simple equations for predict-ing block shear load capacities. The procedure explained before was used in all

Table 1

Professional factor statistics for nite element analysisLRFDASD predictions

Professional factor

Finite element AISCLRFD AISCASD

Mean 0.990 1.174 1.150

Standard deviation 0.068 0.138 0.128

Maximum 1.123 1.458 1.458

Minimum 0.840 0.925 0.925Fig. 4. Comparison of nite element analysis predictions with experimental ndings.analyses. Initially, edge distance, end distance, number of bolts, bolt pitch, yield

Fig. 5. Comparison of LRFD procedure predictions with experimental ndings.

1623C. Topkaya / Journal of Constructional Steel Research 60 (2004) 16151635Fig. 6. Comparison of ASD procedure predictions with experimental ndings.

cases for two boundary conditions had equal share. For all analyses connectionswith single line of bolts in the half plate model were considered. The analyzed spe-

C. Topkaya / Journal of Constructional Steel Research 60 (2004) 161516351624cimens had an end distance of 25 (1 in.), 38 (1.5 in.), 50 (2 in.) and 64 mm (2.5 in.)and an edge distance of 25 (1 in.), 38 (1.5 in.), 50 (2 in.), 64 (2.5 in.) and 76 mm(3 in.). Plates connected with two, three or four bolts were modeled in which14 (0.56 in.) and 27 mm (1.06 mm) diameter bolt holes were considered. In allmodels a bolt pitch greater than or equal to three times the bolt diameter waschosen to satisfy the minimum hole spacing provisions. Bolt pitch values of 38(1.5 in.), 50 (2 in.), 64 (2.5 in.) and 76 mm (3 in.) were used. The resulting geome-tries have connection lengths from 64 (2.5 in.) to 292 mm (11.5 in.). For these 504cases the ultimate strength of the plate material was held constant at a value of352 MPa (50.4 ksi). Yield stress values of 210 (30 ksi), 252 (36 ksi), and 293 MPa(42 ksi) were considered. The combinations of the variables considered in the studyare given in Table 2.

Fig. 7. Edge boundary conditions for the parametric study.stress (Fy), ultimate strength (Fu), bolt diameter and edge boundary conditionswere considered as the prime variables. In order to reduce the computational costtwo-dimensional plane stress models were analyzed. Two typical edge boundaryconditions were considered in the analysis namely, boundary condition 1 (BC1)and boundary condition 2 (BC2) (Fig. 7). Boundary condition 1 (BC1) representsthe case of a gusset plate where half of the member is modeled and rollers areplaced along the side which is close to the bolt holes. On the other hand, BC2represents the case of a splice plate used to join the anges of W-shapes. Since thebolts are symmetrically placed on both sides, only half of the plate is modeled androllers are placed along the side which is farther away from the bolt holes. The pri-mary dierence between the two boundary conditions is, in the case of a gussetplate, fracture of tension plane is between two bolt holes and in the case of a spliceplate, the fracture of the tension plane is between a bolt hole and a free edge.A total of 504 nonlinear nite element analyses were performed in which the

1625C. Topkaya / Journal of Constructional Steel Research 60 (2004) 16151635Table 2

Combinations of the variables used in parametric study

End distance Edge distance Pitch distance Fu/Fy

Hole diameter (14 mm)

2 bolt case

25 25/38 38/50/64 1.68/1.4/1.2

38 25/38 38/50 1.68/1.4/1.2

50 25/38 38 1.68/1.4/1.2

3 bolt case

25 25/50 38/50/64 1.68/1.4/1.238 25/50 38/50/64 1.68/1.4/1.2

50 25/50 38/50/64 1.68/1.4/1.2

1.68/1.4/1.2eective shear stress developing at the gross shear plane. If this eective shearstress could be determined from the parametric study then a simplied equationbased on numerical analysis could be found.mate stress at failure. Based on this discussion the only unknown would be theprediction equation should consider the contributions of the tension and shearplanes and should be based on the premise that the net tension plane reaches ulti-that there should be a single equation to predict the block shear load capacity. The

These observations are in agreement with the experimental ndings [3] and suggest

ure load while there were signicant amounts of yielding at the gross shear plane.

In all nite element analyses the net tension plane reached ultimate stress at fail-All dimensions are in mm.cases for two BCTotal number of 108Total number of cases 5464 50/64/76 76 1.68/1.4/1.24 bolt case

50 50/64/76 76 1.68/1.4/1.264 50/64/76 76 1.68/1.4/1.250 50/64/76 76 1.68/1.4/1.23 bolt case64 50/64/76 76 1.68/1.4/1.250 50/64/76 76 1.68/1.4/1.22 bolt casecases for two BC

Hole diameter (27 mm)Total number of 396Total number of cases 19850 25/50/76 38/50/64/76 1.68/1.4/1.238 25/50/76 38/50/64/764 bolt case

25 25/50/76 38/50/64/76 1.68/1.4/1.2

function of connection length and ultimate-to-yield ratio.

C. Topkaya / Journal of Constructional Steel Research 60 (2004) 161516351626Fig. 8. Eect of boundary conditions on eective stress.Eective shear stress values were calculated for each analysis case using the ulti-

mate load values. A careful examination of the data reveals that the eective shear

stress does not depend much on the end and edge distances for centric loading.

However, the dependence is much more pronounced when connection length,

boundary conditions and ultimate-to-yield ratio are considered. In Fig. 8 a generic

plot for the dependence of eective shear stress normalized by yield stress

(Fy 252 MPa 36 ksi) is given as a function of the connection length. Similartype of plots could be obtained if other yield stress values are considered. It is evi-

dent from Fig. 8 that the eective shear stress decreases as the connection length

increases. This phenomenon was pointed out by Hardash and Bjorhovde [9] earlier.

It is interesting to note that the slope of this decreasing trend is dierent for two

boundary conditions. For the case of gusset plates represented by the BC1 the

decrease in eective shear stress is much more pronounced than the case of splice

plates which were represented by the BC2. This observation initially suggests that

there should be dierent prediction equations for each structural member type.

Although it is possible to derive such equations based on the analysis results, it is

not necessary for practical purposes. The dierence in eective shear stress between

two boundary conditions stays below 10%. This observation suggests that the eect

of the dierence between boundary conditions could be ignored and the two

boundary conditions could be used together to represent the general variation as a

mate- g toboth withconne orth-while . Forhigh ctionlength tion,accor ate-to-yie ng isa fun FDspeciFor th of

the m e-to-yield iousobser werecondu ksi).Yield ulti-mate- 216analy f theresult th isthe same for materials possessing the same ultimate-to-yield ratio. The ndings

1627C. Topkaya / Journal of Constructional Steel Research 60 (2004) 16151635presented so far will be used in developing block shear prediction equations thatare functions of ultimate-to-yield ratio and connection length.

Fig. 9. Variation of eective shear stress with connection length and ultimate-to-yield ratio.variation of eective shear stress as a function of connection length andto-yield ratio is presented in Fig. 9. In this gure data points that belonboundary conditions are included. The decrease in eective shear stressction length is observed for all three yield stress values. However, it is wto note that the slope of the trendlines for three sets of data are dierentultimate-to-yield ratio the decrease in eective shear stress with conneis much more pronounced than the low ultimate-to-yield ratio. In addi

ding to Fig. 9 the eective shear stress on gross area varies with the ultimld ratio. For a given connection length the eective shear stress developiction of the yield stress. A single value (0.6 Fy) like the one used in the LRcation could not be used if more accurate predictions are required.the 504 previously mentioned nite element analyses the ultimate strengaterial was kept constant and the yield stress was varied to get ultimatvalues of 1.68, 1.4 and 1.2. In order to investigate the validity of prevvations for other ultimate strength values a set of additional analysescted. The ultimate strength of the material was taken as 472 MPa (68.4stress values of 279 (40.5 ksi) and 393 MPa (57 ksi) that produce anto-yield ratio of 1.68 and 1.2, respectively were considered. A total ofses were performed for the two boundary conditions. Examination os revealed that the variation in eective shear stress with connection lengThe ulti-

C. Topkaya / Journal of Constructional Steel Research 60 (2004) 161516351628Fig. 10. Eect of in-plane eccentricity on block shear load capacity.4.2. Connection eccentricity

4.2.1. In-plane eccentricitySeveral analyses were performed in order to investigate the eects of eccentric

loading on block shear load capacity. The parametric study results presented so faronly encompassed the case of centric loading. In order to simulate in-plane eccen-tricity similar type of two-dimensional plate models were analyzed without anyedge boundary conditions. In other words, the cases that were analyzed using BC2(Fig. 7) were analyzed again by removing the roller boundary condition (Fig. 10a).The amount of eccentricity could be quantied by the distance between the line ofbolts and the centerline of the plate. The same variables used for the parametricstudy were used for eccentric loading analyses. The resulting eccentricities variedbetween 20% and 40% of the depth of the member. To be able to assess the impor-tance of in-plane eccentricity the results of 198 additional analyses were comparedwith the results pertaining to the cases with BC2. Analyses with the second bound-ary condition were accepted as the basis and provide an upper bound becausebending is not present and the bolts are close to the free edge.

there is no reduction in capacity for connections less than 150 mm (6 in.) in length.For some very short connections the eccentricity seems to increase the strength by

results obtained from these three-dimensional analysis were compared with

1629C. Topkaya / Journal of Constructional Steel Research 60 (2004) 16151635the two-dimensional models in which no eccentricity is present. Examination of thecomparisons revealed that out-of-plane eccentricity has no signicant eect onthe block shear load capacity. Results for connections with out-of-plane eccen-tricity are at most 5% dierent than the connections without eccentricity. Theconclusion of block shear load capacity unaected by out-of-plane eccentricity is inagreement with the earlier observations of Orbison et al. [11].

5. Development of block shear load capacity prediction equations

Equations that are based on applying numerical results to a theoretical modelwere developed to predict the block shear load capacity of tension members.The aforementioned 504 two-dimensional analyses results constitute the basis ofstatistical analysis. As explained before, the aim of the study is to develop a singleequation to predict the block shear load capacity. In this equation, it is assumedthat the net tension plane reaches ultimate strength while the gross shear plane2%. This might be attributable to the numerical details adopted and may not hap-pen in practice. For connections longer than 150 mm (6 in.) reductions up to 15%could be obtained. Since the reduction is applied to longer connections and mostof the reduction values stayed below 10%, the eects of in-plane eccentricity wasnot studied further. During the design stage the block shear capacity can bereduced by 10% for longer connections if desired.

4.2.2. Out-of-plane eccentricitySixteen three-dimensional nite element models were analyzed to investigate the

eects of out-of-plane eccentricity on block shear. The three-dimensional modelsrepresent the case of a channel section fastened through two lines of bolts locatedon the web. The ctitious channel section was 5 mm (0.2 in.) thick and had a depthof 305 mm (12 in.) and a ange width of 152 mm (6 in.). This kind of a connectiondetail has out-of-plane eccentricity while having no in-plane eccentricity. In thesenew set of analyses, material properties were kept constant to have an ultimate-to-yield ratio of 1.2 while the geometric properties were varied. Two, three and fourbolt congurations were considered which resulted in connection lengths between89 (3.5 in.) and 280 mm (11 in.). End distance was kept constant at 50.8 mm (2 in.)while the edge distance was varied between 25.4 (1 in.) and 50.8 mm (2 in.). TheExamination of the data gathered from this additional analyses revealed that forsome connections presence of eccentricity reduces the block shear load capacity.The amount of reduction in the capacity is mostly inuenced by the connectionlength. The amount of eccentricity, other geometric and material properties do notsignicantly aect the loss of capacity. Fig. 10b presents the nominal block shearload capacity of 198 eccentrically loaded connections normalized by their capacityunder centric loading as a function of the connection length. Fig. 10b shows that

C. Topkaya / Journal of Constructional Steel Research 60 (2004) 161516351630develops an eective shear stress which is represented as a percentage of yieldstress. The aim of this section is to quantify the value of eective shear stress basedon geometric and material properties. Examination of analytical ndings revealsthat the eective shear stress is mostly inuenced by the ultimate-to-yield ratio andthe connection length. Several forms of equations were tried and the ones whichare simple to use in design are represented here. If the eective shear stress is basedon both the ultimate-to-yield ratio and the connection length Eq. (4) could befound by regression analysis and rounding o the coecients.

Rn 0:25 0:35 FuFy

Cl2800

FyAgv FuAnt 4

where Cl is the connection length (distance from the center of the leading bolt holeto the end of the plate).The coecient of determination (r2) for the eective shear stress normalized by

yield stress is 0.87 if the coecients of Eq. (4) are used. The upper limit on eectiveshear stress is 0.6 Fu if Eq. (4) is used. In Eq. (4), Cl is expressed in millimeters andif another system of units is used, the coecient for connection length should beadjusted accordingly.A more simplied equation could be developed if the eective shear stress is

based only on the ultimate-to-yield ratio. Regression analysis with rounding o thecoecients revealed that Eq. (5) could also be a simple alternative to Eq. (4).

Rn 0:20 0:35 FuFy

FyAgv FuAnt 5

The coecient of determination (r2) for the eective shear stress normalized byyield stress is 0.81 if the coecients of Eq. (5) are used.A careful examination of the data reveals that an equation in which eective

shear stress is based solely on the ultimate strength could be developed. Two dier-ent ultimate strength values were used in the parametric study. For the 720 analy-ses cases the eective shear stress is normalized by ultimate strength and the datapoints are presented in Fig. 11. According to this gure the eective shear stressvalues fall within a band that is bounded by 4055% of ultimate strength averaginga value of 48%. Based on this observation a very simple prediction equation wasdeveloped and is presented in Eq. (6).

Rn 0:48FuAgv FuAnt 6All the equations derived so far were for cases where loading was centric. As

explained before out-of-plane eccentricity has no signicant eect on the blockshear capacity. On the other hand, in-plane eccentricity might cause a smallreduction in the values. Therefore, for cases where in-plane eccentricity is presentdesigners might reduce the block shear load capacity by 10% for longer connec-tions.The quality of the prediction equations were assessed by making comparisons

with the experimental ndings. Three sets of experimental data that were men-tioned before were used for comparison purposes. In calculating net areas for ten-

1631C. Topkaya / Journal of Constructional Steel Research 60 (2004) 16151635sion, hole diameters were increased by 2 mm (1/16 in.) to account for damageallowance. The comparisons of load predictions and test results are presented inFigs. 1214 and the statistical measures of the predictions are given in Table 3.It is evident from the gures and the statistical measures that the developed

equations predict block shear load capacities with acceptable accuracy. The aver-

Fig. 11. Eective shear stress as a function of ultimate strength.age professional factor for all three equations is close to unity and the standard

factors amin-ation o ith agusset redic-tion eq . Thedata po de [9]in deve If thisdata po redic-tion woFigs. or the

angle s rengthpredict y wasinvestig niteelemen res inthe ang r fail-ure. G earingcontinu . Thisobserva ced acombinon is close to 10%. According to the maximum and minimum profes, predictions of 25% understrength and overstrength are possible. Exf the predictions show that maximum understrength is associated wplate specimen with a very short connection length (66 mm (2.6 in.)). Puations fail to provide better estimates for this particular specimenint related with this specimen was discarded by Hardash and Bjorhovloping a block shear capacity prediction equation for gusset plates.int is discarded from the data set then the maximum understrength puld stay below 17% for the three equations.1214 suggest that all three equations have unconservative estimates fpecimens tested by Gross et al. [10]. In addition, the maximum overstion belongs to this set of specimens. The reason of this discrepancated further by examining the stress patterns at failure throught analysis. This detailed investigation suggested that some of the failule specimens were due to a combination of net section and block sheaross et al. [10] also observed that for some of the specimens ted at an angle from the shear plane after the tension plane rupturetion strengthens the assertion that some of these specimens experiendeviati sionaled failure mode in which the developed equations fail to predict.

Fig. 12. Comparison of Eq. (4) predictions with experimental ndings.

C. Topkaya / Journal of Constructional Steel Research 60 (2004) 161516351632Fig. 13. Comparison of Eq. (5) predictions with experimental ndings.

1633C. Topkaya / Journal of Constructional Steel Research 60 (2004) 161516356. F

S sti-gati

. T redh gsto ndm

. O orefa ereo ityp as

Eq. (4) Eq. (5) Eq. (6)

Stan

devia

Max

Minuture research needs

everal factors that were not considered in this study require further inveon. These can be summarized as follows:

his study focused on block shear failure of tension members with nonstaggeoles. Further research is needed to determine the applicability of these ndinblock shear failure of beams and of connections having staggered holes aultiple bolt lines.nly block shear failure type was considered. However, as mentioned befilures due to a combination of net section and block shear failure wbserved in the tests [10]. Future research should focus on developing capacrediction equations for this type of failure mode, which is usually termed

n 0.997 0.988 1.009

dard

tion

0.100 0.106 0.102

imum 1.219 1.250 1.269

imum 0.786 0.754 0.789MeaProfessional factor statistics for developed equations

Professional factorTable 3Fig. 14. Comparison of Eq. (6) predictions with experimental ndings.

cularly the dierences in the yield plateau and strain hardening regions, need to

connection length and boundary conditions.

C. Topkaya / Journal of Constructional Steel Research 60 (2004) 161516351634. Presence of in-plane eccentricity can reduce the block shear load capacity by10% for longer connections.

. Presence of out-of-plane eccentricity does not signicantly aect the response.

. The developed equations provide load capacity estimates with acceptable accu-racy. These equations could be alternatives to more traditional code equations.

References

[1] AISC. Allowable stress design specication for structural steel buildings, 9th ed. Chicago (IL):

American Institute of Steel Construction; 1989.

[2] AISC. Load and resistance factor design specication for structural steel buildings, 3rd ed. Chicago

(IL): American Institute of Steel Construction; 2001.

[3] Cunnigham TJ, Orbison JG, Ziemian RD. Assessment of American block shear load capacity pre-

dictions. Journal of Constructional Steel Research 1995;35:32338.

[4] Ricles JM, Yura JA. Strength of double-row bolted-web connections. ASCE Journal of Structural

Engineering 1983;109(1):12642.be studied.. In this study, the failure was quantied by the ultimate load reached during theanalysis. Other failure measures based on local strains could be used to quantifyultimate loads and eventually to develop similar load capacity prediction expres-sions.

7. Conclusions

A comprehensive analytical study on block shear failure of steel tension mem-bers was presented. A nite element analysis methodology was developed to pre-dict the block shear failure load capacities. Specimens tested by three independentresearch teams were modeled and analyzed with this method. Finite element analy-sis was found to predict the failure loads of test specimens with acceptable accu-racy. A parametric study was conducted to identify the important parameters thatinuence the block shear response. Simple block shear load capacity predictionequations were developed based on the analysis results and their quality is assessedby making comparisons with experimental ndings.The following can be concluded from this study:

. Block shear load capacity is mostly inuenced by the ultimate-to-yield ratio,partial net section rupture [7]. The detailed modeling technique presented byBarth et al. [7] could be used to study this behavior.

. For gusset plates the loading was assumed to be parallel to one of the principalaxes of the plate. Additional studies are required to nd out the behavior ofthese members under inclined loading.

. The study was based on an assumed yield criterion and a generic stressstraincurve. The eect of using a dierent yield criterion such as Tresca criterion needsfurther investigation. In addition, the eects of stressstrain behavior, parti-

[5] Epstein HI, Chamarajanagar R. Finite element studies for correlation with block shear tests. Com-

puters and Structures 1996;61(5):96774.

[6] Kulak GL, Wu EY. Shear lag in bolted angle tension members. ASCE Journal of Structural Engin-

eering 1997;123(9):114452.

[7] Barth KE, Orbison JG, Nukala R. Behavior of steel tension members subjected to uniaxial loading.

Journal of Constructional Steel Research 2002;58:110320.

[8] ANSYS. Version 6.1 on-line users manual; 2001.

[9] Hardash SG, Bjorhovde R. New design criteria for gusset plates in tension. AISC Engineering

Journal 1985;22(2):7794.

[10] Gross JM, Orbison JG, Ziemian RD. Block shear tests in high-strength steel angles. AISC Engin-

eering Journal 1995;32(3):11722.

[11] Orbison JG, Wagner ME, Fritz WP. Tension plane behavior in single-row bolted connections sub-

ject to block shear. Journal of Constructional Steel Research 1999;49:22539.

1635C. Topkaya / Journal of Constructional Steel Research 60 (2004) 16151635

A finite element parametric study on block shear failure of steel tension membersIntroductionFinite element modelingPrevious studiesCurrent study

Finite element analysis predictionsPrevious experimental studiesSimulation of previous experiments

Parametric studyConcentric connectionsConnection eccentricityIn-plane eccentricityOut-of-plane eccentricity

Development of block shear load capacity prediction equationsFuture research needsReferences