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Journal of Constructional Steel Research 86 (2013) 153–166

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Journal of Constructional Steel Research

Block shear strength of coped beams with single-sided bolted connection

Cheng Fang a, Angus C.C. Lam b,⁎, Michael C.H. Yam a, K.S. Seak b

a Department of Building & Real Estate, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, Chinab Department of Civil and Environmental Engineering, University of Macau, Macau SAR, China

⁎ Corresponding author. Tel.: +853 83974463; fax: +E-mail address: [email protected] (A.C.C. Lam).

0143-974X/$ – see front matter © 2013 Elsevier Ltd. Alhttp://dx.doi.org/10.1016/j.jcsr.2013.03.019

a b s t r a c t
a r t i c l e i n f o
Article history:Received 19 February 2013Accepted 31 March 2013Available online xxxx

Keywords:Block shearBolted connectionCoped beamEccentricityBeam connection

Block shear is one of the major failure modes for coped steel I-beams. While focus of previous studies on theblock shear capacity of coped steel I-beam was mainly given to the connections with double clip angles,single-sided connections, which induce out-of-plane loading eccentricity, have not been adequately considered.Ten full-scale coped steel I-beam tests were conducted to examine the effects of two main test parameters,namely, out-of-plane loading eccentricity and web block aspect ratio (ratio of shear area to tension area). Itwas found that nine test specimens failed with tension fracture along the bottom bolt row of the web, and theremaining one failed in awhole block tear-outmanner. Twisting of theweb near the copewas observed for spec-imens with single-sided connection. More importantly, the test results showed that the out-of-plane loadingeccentricity due to the single-sided connection did not have a detrimental effect on the block shear capacity ofthe specimens. Moreover, increasing the connection rotational stiffness could increase the block shear capacity.These effects are further discussed via a finite element analysis and a preliminary parametric study. Finally, thetest results are compared with four major design standards. It is found that the Canadian Standards CAN/CSA-S16-09, which gives a test-to-predicted ratio ranged from 0.93 to 1.17, provided relatively good predictionsfor the specimenswith single bolt line layout,while the predictions by other codes are too conservative. For thosespecimens with double bolt line layout, the capacities are underestimated by all the considered standards.

© 2013 Elsevier Ltd. All rights reserved.

1. Introduction

In steel construction, secondary beams are often connected to themain girder at the same elevation in order to support the slabs. Toallow enough clearance for the intersection of the beams, the flangesof the secondary beams are usually coped, as illustrated in Fig. 1(a).The cope can be located at the top flange, bottom flange, or both flangesof the beamends, depending on different construction requirements. Toconnect the coped beam end to the main girder, various connectiontypes can be used, including double clip angles, single angles, weldedplates (fin plates) or tees.

Because of the removal of the flange(s), the strength of copedbeams is reduced. The potential local failure modes of the copedbeam ends include flexural yielding, shear yielding, local web buck-ling and block shear. For the block shear failure, which is consideredin this study, the web block (which forms part of the connection) canbe torn out from the beam web, as shown in Fig. 1(b). This blockshear failure of coped beams was first observed by Birkemoe andGilmor [1]. Subsequently, Yura et al. [2] and Ricles and Yura [3]performed a series of full-scale experiments and proposed a blockshear capacity model which considered one-half of the tensilestrength on net tension area plus the shear yield strength on grossshear area. The coped beam test results from Aalberg and Larsen

853 28838314.

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[4] showed that the web block was partially torn-out with tensionfracture of the web in the vicinity of the bottom bolt hole. Kulakand Grondin [5] examined the block shear capacity equations usedby various design standards and discovered that the predictions ofthe block shear capacity of coped beams based on major standardswere generally inconsistent. Subsequently, Franchuk et al. [6,7]conducted seventeen full-scale tests to examine the effect of differ-ent geometric parameters and different bolt layouts on the blockshear behaviour of coped beams. Finite element analysis based onthe test results of Ricles and Yura [3] and Franchuk et al. [7] wasfurther conducted by Topkaya [8].

While most of the previous studies focused on coped beams withbolted double clip angle connections, the block shear response of copedbeams with single-sided connections using tees or single angles hasnot been adequately examined. Compared with double clip angle con-nections, the use of single-sided connections can simplify the procedureof shop fabrication and reduce the cost of manufacturing. However, anout-of-plane loading eccentricity is induced between the centreline ofthe beamweb and the centroid of the connectionwhen single-sided con-nections are used, as shown in Fig. 1(c). The secondary bending causedby the out-of-plane loading eccentricity may influence the block shearcapacity of the coped beam web, but test evidence is not available re-garding this concern. In addition, other factors such as bolt arrangementsand connection rotational restraints have not been sufficiently studiedin previous studies. To address these issues, ten full-scale tests wereconducted to examine the block shear behaviour and strength of coped

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Fig. 1. Illustrations of coped beams: a) typical connection types, b) typical block shear failure modes, (c) out-of-plane eccentricity of single-sided connections.

154 C. Fang et al. / Journal of Constructional Steel Research 86 (2013) 153–166

beamswith single-sided bolted connections, where different bolt layoutsand connection sizes were employed. Finite element (FE) models ofthe test specimens were subsequently established and a preliminaryparametric study was conducted to further discuss these effects. Finally,the test results were compared with the predicted block shear capacitiesaccording to various current standards, including AIJ [9], AISC-LRFD [10],EN 1993-1-8:2005 [11] and CAN/CSA-S16-09 [12], and the test-to-predict ratios were presented and discussed.

2. Experimental programme

2.1. Test specimens and setup

A total of ten full-scale tests were conducted in the experimentalprogramme, where seven specimens were connected using single-sided connections (tee or single angle) and double clip angle connec-tions were used for the remaining three specimens for comparisonpurpose. Five test beams of 3.4 m long were fabricated from the uni-versal beam section UB406 × 140 × 56 (SCI Guide [13]) with GradeS355 steel (BS EN 10025-2, 2004 [14]). The measured average width(B), height (D), and flange thickness (Tf) of the beam section dimen-sion are 142 mm, 403 mm, and 10.7 mm, respectively (Fig. 2). For thebeam web thickness (Tw), which is important for block shearstrength, the measured value is Tw = 6.6 mm for beams 1, 2, and 5,and Tw = 6.8 mm for beams 3 and 4 (nominal value = 6.8 mm).The top flange was coped and the cope depth (dc) was 35 mm for allthe specimens. The cope corners were rounded with a nominal radius

of 12.5 mm. The main test parameters included: (1) the out-of-planeloading eccentricity and (2) the web block aspect ratio (sa/ta), whichare defined schematically in Figs. 1(c) and 2(a), respectively. It shouldbe noted that the out-of-plane eccentricity was defined as: the distancebetween the centroid of the beam web to the centroid of the reactionforce(s). For the T section connection, the centroid of the two lines ofbolts (which together resist the reactions) coincides with the centroidof the tee stem, so the eccentricity is the distance from the centroidof the tee stem to the centroid of beam web. On the other hand, forthe single angle connection, only one bolt line resists the reaction, sothe eccentricity is the distance from this bolt line to the centroid ofthe beam web.

The measured dimensions of the test beams and the connectionspecimens are given in Table 1 and the corresponding symbols areshown in Fig. 2. Each specimen was designated according to the boltlayout and the type of connection for easy identification. For example,“A1-1-3-a” represents the connection using an angle section type“A1” with “1” bolt line and “3” rows of bolts. The subsequent letter“a” represents an edge distance (eh,b) of 28 mm (the letter “b” wasused for an edge distance of 50 mm). For specimen “A1-1-3-a-S”, anadditional “S” was used at the end of the designation to indicate theuse of a single angle. Generally, three kinds of bolt layout were con-sidered, namely, (1) three bolt holes in a single bolt line with anedge distance of 28 mm, (2) three bolt holes in a single bolt linewith an edge distance of 50 mm, and (3) two bolt holes in each ofthe two bolt lines with an edge distance of 28 mm. The spacing be-tween the bolt holes centres was 75 mm for all the specimens.

Fig. 2. Dimensions of specimens: a) beam details, b) connection details.

155C. Fang et al. / Journal of Constructional Steel Research 86 (2013) 153–166

Grade S355 steel plates were used for the connections (angles andtees). Two different angle sections (120 × 120 × 12 and 180 × 180 ×16)were adopted anddesignated asA1 andA2, respectively. Twodiffer-ent tee-sections, T1 and T2,were fabricated by two different sets of steelplate thickness (tw = 7.8 mm, tf = 11.9 and tw = 11.9, tf = 19.7, re-spectively) and their corresponding details and dimensions are shownin Fig. 2(b) and Table 1. Grade 12.9 M22 bolts were used for the connec-tions of all the specimens except for the specimen with the single angleconnection, where grade 12.9 M24 bolts were used. Standard hole sizeswere used in the connections. In general, the measured bolt hole

Table 1Dimensions of test beams and connections.

Beam no. Specimen designation Dimensions (mm)

eh,b g c ed,b s1 s2

1 A1-1-3-a 28 / 78 28 75 75T1-1-3-a 28 / 78 28 74 75

2 A1-1-3-b 50 / 100 27 75 75T1-1-3-b 50 / 101 28 75 75

3 T2-1-3-a 27 / 77 28 75 75T2-1-3-b 51 / 101 28 75 75

4 A2-2-2-a 28 75 153 27 75 /T1-2-2-a 28 75 153 28 75 /

5 T2-2-2-a 28 75 153 27 75 /A1-1-3-a-S 28 / 78 29 75 75

diameters on the beam webs conformed with the nominal values. Themeasured diameters varied between 23.8 mm and 24.3 mm with anaverage of 24.1 mm and a standard deviation of 0.2 mm for the24 mm diameter bolt holes. For the 26 mm diameter bolt holes, whichwere only used on the single angle connected to the column flange,the measured diameters varied between 26.0 mm and 26.3 mm withan average of 26.1 mm and a standard deviation of 0.1 mm. All theboltswere snug-tightened by hand. Table 2 summarises the comparisongroups as well as the values of the test parameters, i.e. out-of-planeloading eccentricity and web block aspect ratio. The out-of-plane

b d tw tf h t x eh,w ed,w

/ / / / 120 11.9 36 75 28178 96 7.8 11.9 / / 34 40 28/ / / / 120 11.9 36 75 28178 118 7.8 11.9 / / 34 40 28212 104 11.9 19.7 / / 51 40 28212 125 11.9 19.7 / / 51 40 28/ / / / 180 16 96 42 28178 171 7.8 11.9 / / 34 40 28212 178 11.9 19.7 / / 51 40 28/ / / / 120 11.9 60 75 28

Table 2Summary of test parameters.

Test parameter Measured value Comparison group

Out-of-plane loading eccentricity (mm) 1) 0, 7.2, 9.35, 60 1) A1-1-3-a, T1-1-3-a, T2-1-3-a, A1-1-3-a-S2) 0, 7.2, 9.35 2) A1-1-3-b, T1-1-3-b, T2-1-3-b3) 0, 7.3, 9.25 3) A2-2-2-a, T1-2-2-a, T2-2-2-a

Aspect ratio, sa/ta = shear area/tension area 1) 6.36, 3.54 1) A1-1-3-a, A1-1-3-b2) 6.32, 3.56 2) T1-1-3-a, T1-1-3-b3) 6.59, 3.49 3) T2-1-3-a, T2-1-3-b


loading eccentricity for the specimens varied between 0 mm and60 mm and the web block aspect ratio ranged from 3.49 to 6.59.

Tension coupons were cut from the webs/flanges of the test beamsand the steel plates. The coupon tests were conducted according tothe ASTM specification [15]. The average static values of the yieldstrength and the tensile strength obtained from the coupon test resultsare shown in Table 3. It should be noted that although Grade 355 steelwas originally requested for fabricating the specimens, the averagestatic yield stress and the static tensile strength of the beam flange ofthe specimens are close to 300 MPa and 450 MPa, respectively.

The test setup is illustrated in Fig. 3. Whitewash was applied onthe test beam end to illustrate the yielding pattern during testing. Aload jack with a maximum capacity of 1000 kN was used to apply thepoint load to the test beams. The loading position was located at a dis-tance of 600 mm from the test beam end. Roller assemblies were usedat the loading position and the other support end to allow in-planerotation and longitudinal movements. Lateral bracings were providedto prevent lateral movement of the beam.

2.2. Instrumentation and test procedure

The applied loads and support reactions were recorded automati-cally by the corresponding load cells. Linear variable differentialtransformers (LVDTs) were employed to measure the displacementsof the test beams. The positions of the LVDTs are shown in Fig. 3.Longitudinal strain gauges and rosettes were mounted on the beamweb near the bolt holes to record the strain distribution at the criticalregions as shown in Fig. 3. The tests were conducted by load controlin the early loading stage, where the load was applied incrementally.In the later inelastic stage, stroke control was used in order to capturethe nonlinear behaviour. The test was terminated when either thewhole web block tear-out occurred or significant unloading of thetest specimens occurred. After completing the test of one beam end,the other end of the beam was installed for the subsequent test.

3. Test results

3.1. General

The test results showed that all the specimens failed in a block shearmanner. Typical failure modes at the end of the test are shown in Fig. 4.When the ultimate load was achieved, the web block was completely

Table 3Summary of tension coupon test results.

Coupon specimen Elastic modulus (MPa) Static yie

Beam nos. 1, 2, 5 Web 206,120 360.5Flange 218,135 302

Beam nos. 3, 4 Web 221,625 379.5Flange 224,525 295

Connection specimen 7.9 mm 207,245 40612 mm 216,668 36116 mm 211,353 36920 mm 210,180 356

Note: The values presented in the table are the average result of two coupons from the beamplates, and four coupons from 12 mm and 16 mm steel plates.

torn out for specimen T2-1-3-b, while for the other nine specimens,tension fracture of the web in the tension area (ta) with significantshear yielding in the shear area (sa) was observed at the ultimateload. Necking effect near the tension area was observed before the frac-ture of the web. In addition, for the seven specimens with single-sidedconnections, web twisting was observed near the cope. For mostcases, further loading after the initial tension fracture led to subsequentfracture of the shear area. For the double bolt line specimens, furtherloading after the ultimate load caused tension fracture of the web be-tween the first and second vertical bolt lines, and subsequently, signifi-cant shear yielding occurred near the second bolt line. Basic test results,including ultimate load, ultimate reaction, vertical in-plane deflectionat ultimate load, and failure mode, are summarised in Table 4. The ulti-mate load is the static value of the maximum load applied to the testspecimens. The corresponding ultimate reactions at the coped endwere determined based on the measured applied loads and the reac-tions at the other support. The vertical in-plane deflection (δ) wasobtained from LVDT6 (as shown in Fig. 3).

3.2. Load deflection behaviour

The load–deflection curves for all the specimens are shown inFig. 5. In general, linear responses were observed at the beginningof load. When the applied load reached around 70% of the ultimateloads, nonlinear load–deflection response started to develop. Afterthe specimens reached the ultimate loads, the load–deflection curvesshowed a sudden drop representing the initiation of fracture alongthe tension area. Subsequently, the load–deflection curves continuedwith a gradual and limited increase of the applied load. For specimenT2-1-3-b, no further load resistance was sustained beyond the ulti-mate load, which was due to the occurrence of the complete webblock tear-out. For specimens A2-2-2-a and T1-2-2-a, two loaddrops were observed. The first load drop corresponded to the firsttension fracture of the web between the edge and the first verticalbolt line, while the second drop represented the fracture of the entiretension area, i.e. tensile fracture propagated towards the secondvertical bolt line.

3.3. Strain distribution

The typical results of the tensile strain distributions are shown inFig. 6. Fig. 6(a) shows the tensile strain distributions near the bottom

ld, Fy (MPa): Static ultimate strength, Fu (MPa): Rupture strain (%)

458.5 17.7425 23.2464 14420 24.5545 17502 21.6495 21.4502 23.4

web, two coupons from the beam flange, two coupons from 7.9 mm and 20 mm steel

Fig. 3. Schematic of test setup and layouts of LVDTs and strain gauges.


bolt hole for the single bolt line specimens A1-1-3-a, T1-1-3-a,T2-1-3-a and A1-1-3-a-S under the load level of 100 kN. It is observedthat larger tensile strains were developed near the edge of the beamweb and the strains gradually decreased towards the bolt hole.Similar observations were also reported by Ricles and Yura [3]based on their finite element analysis results for similar copedbeams. In addition, it was shown that the tensile strains for specimenT2-1-3-a, which has a larger tee section (larger flange and web thick-ness), were generally smaller than those of the specimens with asmaller tee section (T1) or angle section (A1). Fig. 6(b) shows thetensile strain distributions for specimen T2-1-3-b, which has a largeredge distance of 50 mm, under different load levels. It was found thatlarge tensile strains occurred away from the beam edge at the earlyloading stage. However, as the load increased, larger tensile strainswere observed near the beam edge. For the case of double bolt linespecimens, Fig. 6(c) shows the tensile strain distributions for speci-men A2-2-2-a, and similarly, larger strains were developed near theweb edge.

Fig. 6(d) shows the shear strain distributions read from the rosettesin the web near the shear area for specimen T1-1-3-a at early loadstages (the shear strain distributions of the other specimenswith singlebolt line were similar). The shear strain distribution was non-uniform,where large shear strains were recorded near the top bolt hole. Forthe specimens with double bolt line layout, large shear strains werealso found at the top rosette, as shown in Fig. 6(e). In general, largershear deformation was exhibited adjacent to the bolt holes, especiallyin the vicinity of the top bolt hole.

4. Discussion of test results

4.1. Failure mode

Asmentioned above, the tensile strain distribution along the tensionarea was affected by the size of the connection (T1, T2, A1 and A2)and the edge distance (28 mmand 50 mm). Therefore, the types of fail-ure mode (either partial web block tear-out or complete web block

(a) Fracture of T1-1-3-a (b) Fracture of T2-1-3-b (c) Fracture of T1-2-2-a (d) Fracture of T2-2-2-a

(e) Web twisting of T1-1-3-a (f) Web twisting of T1-2-2-a

Fig. 4. Typical fracture modes and web twisting.


tear-out) at ultimate loads may be also influenced by these factors. Forthe same gauge, the connection rigidity of T2,which has a thicker flangeand web, was larger than that of T1. From Fig. 6(a), it can be seen thatfor the specimen connected by the T2 tee section, the tensile strains inthe tension area were smaller and with smaller strain gradient. Smallertensile strains might allow more shear yielding and subsequent strainhardening in the shear area to occur prior to tensile fracture. In thiscase, it would be possible for specimen T2-1-3-b to develop a completeweb block tear-out failure mode at the ultimate load. In fact, the effectsof rotational stiffness on the block shear strength of coped beamswith awelded clip angle connection have been examined by Yam et al. [16]and Wei et al. [17]. Their studies showed that the block shear strengthof the coped beams with a welded clip angle connection increasedwith increasing connection rotational stiffness. This is due to the factthat a larger connection rotational stiffness would reduce the webblock rotation because of the negative end moment generated. Hence,the tensile strains in the web near the beam edge were reduced, thusallowing the beam end to resist higher shear load prior to tensile frac-ture of the tension area. For the remaining nine specimens, because ofthe larger tensile strains at the beam edge near the tension area, tensilefracture of the tension area occurred prior to shear fracture,which led topartial web block tear-out.

In addition, web twisting effects were observed near the copeends for the specimens eccentrically connected to the tee or singleangle, and the effects were more obvious for the specimens with lon-ger cope lengths. When web twisting occurred, the web of the tee orsingle angle was twisted together with the beam web. In general,twisting of the web for the specimens with T1 connections wasmore significant than the specimens with T2 section connections.This is due to the fact that the larger size of the T2 section connectionwould provide a higher resistance against lateral bending, and thusresulting in smaller web twisting deformation.

4.2. Effect of out-of-plane loading eccentricity

There were seven specimens with load eccentricity in this study.For easier comparison, the ten test results are divided into threecomparison groups, according to the various bolt layouts, to discussthe effect of out-of-plane loading eccentricity. The first comparisongroup includes specimens A1-1-3-a, T1-1-3-a, T2-1-3-a and A1-1-3-a-S, with the nominal eccentricity values of 0 mm, 7.2 mm,9.35 mm and 60 mm, respectively. As shown in Table 4, which sum-marises the ultimate loads of all the specimens, the ultimate loadsof T1-1-3-a, T2-1-3-a and A1-1-3-a-S with out-of-plane loadingeccentricities were 9%, 17% and 4% higher than that of A1-1-3-a.For the second comparison group, where the specimens A1-1-3-b,T1-1-3-b and T2-1-3-b were considered, the nominal values of eccen-tricity were 0 mm, 7.2 mm and 9.35 mm, respectively. The ultimateloads of T1-1-3-b and T2-1-3-b with out-of-plane loading eccentrici-ties were respectively 5% and 22% higher than that of A1-1-3-b. Inthe third group, the three specimens with double bolt line layouts,i.e. A2-2-2-a, T1-2-2-a and T2-2-2-a, were compared. The nominalvalues of eccentricity of the three specimens were 0 mm, 7.3 mmand 9.25 mm, respectively. In contrast with the previous two groups,the ultimate load of specimen A2-2-2-a was 1% and 16% higher thanthat of T1-2-2-a and T2-2-2-a.

In general, inconsistent results with the change of the eccentricitywere observed, and it seems that in most cases, a larger loadingeccentricity could provide a higher block shear capacity. This unex-pected result disagrees with the initial assumption (by which thisstudy was initially driven) that the secondary bending due to theout-of-plane loading eccentricity may induce early tension fractureof the web, thus leading to a reduced block shear capacity. In anycase, the trend shown in the current tests cannot conclusively indi-cate that load eccentricity affects the block shear capacity, because

Table4

Summaryof

test

resu

ltsan

dFE

M/designpred

iction

s.

Specim

ende

sign

ation

Ultim

ateload

,P T

EST

(kN)

Ultim

ateco

nnection

reaction

(kN)

Verticalin-

plan

ede

flection

,δ(m

m)

Failu

remod

eUltim

ateload

-FEM

resu

lts,P F

EM(kN)

P TES

TP F

EMTe

st-to-pred

ictedratio

Bloc

ksh

earat

ultimateload

Web

twisting

AIJ[9]

AISC-LR

FD[10]

EN19

93-1-8

[11]

CSAS1

6-09

[12]

Topk

aya1[8]

Topk

aya2[8]

A1-1-3-a

434.3

304.7

9.10

TFNo

433.4

1.00

1.47

1.17

1.66

0.93

1.22

1.15

T1-1-3-a

471.9

331.9

9.52

TFYe

s48

1.1

0.98

1.61

1.29

1.82

1.02

1.33

1.26

A1-1-3-b

553.4

392.6

9.48

TFNo

530.0

1.04

1.43

1.21

1.81

1.01

1.30

1.19

T1-1-3-b

580.7

414.9

16.08

TFYe

s55

7.2

1.04

1.51

1.27

1.90

1.07

1.37

1.26

T2-1-3-a

509.5

358.3

11.85

TFYe

s(m

inor)

514.1

0.99

1.62

1.33

1.81

1.03

1.34

1.32

T2-1-3-b

675.7

484.6

18.23

BTYe

s63

5.6

1.06

1.63

1.41

2.05

1.17

1.47

1.39

A2-2-2-a

529.7

384.0

10.70

TFNo

547.9

0.97

1.32

1.66

1.90

1.62

1.26

1.13

T1-2-2-a

522.1

379.7

11.20

TFYe

s50

4.5

1.04

1.30

1.63

1.86

1.59

1.24

1.11

T2-2-2-a

455.4

329.0

7.45

TFYe

s(m

inor)

539.6

0.84

1.21

1.49

1.73

1.43

1.17

1.01

A1-1-3-a-S

450.7

319.2

9.19

TFYe

s(m

inor)

485.5

0.93

1.52

1.22

1.72

0.96

1.27

1.20

Mea

n=

0.99

1.46

1.37

1.83

1.18

1.30

1.20

C.O.V=

0.06

60.10

00.12

70.06

10.22

30.06

60.09

2

Note:

TF=

tens

ionfracture

inthetens

ionarea

andBT

=web

bloc

ktear-out.


the change of the connections (to provide different out-of-plane load-ing eccentricity) also influenced the connection rotational stiffness,which is another important factor that was not initially consideredas a main test parameter in this study. For example, the ultimate loadof T2-1-3-a was 17% higher than that of A1-1-3-a, but the increase ofthe ultimate load can bedue to either the eccentricity effect or the stifferrotational restraint offered by the T2 connection (or both effects).According to Yam et al. [16], the rotational stiffness of the connection,controlled by the gauge (see Fig. 2) and the connection flange thickness(see Fig. 2, t for angle & tf for tee-section), could have a significant effecton the block shear capacity of coped beams with a welded connection.Similar behaviour could happen for coped beams with bolted connec-tions, where the larger connection rotational stiffness could provide ahigher block shear capacity. To further study the influences of connec-tion eccentricity and rotational stiffness, a finite element analysis ofthe test specimens is required, which is further detailed in Section 5.

Furthermore, it is unexpected in the third comparison group thatthe ultimate load of specimen T2-2-2-a is much lower than that ofspecimen T1-2-2-a, noting that T2 section is larger than T1 section.Although the lower ultimate load for specimen T2-2-2-amay be partiallydue to the different material properties between the test beam no. 4(for A2-2-2-a and T1-2-2-a) and beam no. 5 (for T2-2-2-a), where thestrength of beam no. 5 is slightly lower, the significantly decreased ulti-mate load of specimen T2-2-2-a still exceeds expectation. As noted inTable 4, the vertical in-plane deflection (δ) for specimen T2-2-2-a at ulti-mate load was only 7.45 mm, which was evidently smaller than that ofthe other two specimens within the comparison group (10.7 mm forA2-2-2-a and 11.2 mm for T1-2-2-a). This implies that the lower ulti-mate load of specimen T2-2-2-a may be due to possible initial imperfec-tions of the specimen (especially around the bolt holes) or erratic testsetup, but further confirmation via finite element analysis is needed, aspresented in Section 5.

4.3. Effect of aspect ratio

Three comparison groups can be considered to study the effectof the aspect ratio, i.e. A1-1-3-a & A1-1-3-b, T1-1-3-a & T1-1-3-b,and T2-1-3-a & T2-1-3-b. For each group, the net tension area wasincreased by 137.5%, while the shear area is the same. The ultimateload of 1-3-b specimens was in average 27% higher than that of 1-3-aspecimens. The increase of the ultimate loads can be demonstratedvia a basic block shear model Pr = 1.0FuAnt + 0.6FyAgv (Fu = tensilestrength, Ant = net tension area, Fy = yield strength, and Agv = grossshear area). Using the equation, the increased Pr for the consideredcomparison pair is 22%, which is slightly lower but comparable to thetest results. This implies that the major contribution for the increaseof the ultimate load could be attributed by the change of the tensionarea. More comprehensive comparisons between the test results andthe major standards are presented in Section 6.

5. Finite element analysis

As discussed in the previous section, the influences of connectioneccentricity and connection rotational stiffness need further supple-mentary investigations. With this aim, finite element models ofthe ten test specimens were established first, and the models werevalidated through comparisons with the corresponding test results.A preliminary parametric studywas subsequently conducted to explainsome observations from the tests. The general FE programme ABAQUS[18], which is capable of simulating both material nonlinearity andgeometric nonlinearity, was used in this study. A typical FE modelbuilt in ABAQUS is shown in Fig. 7(a). For the beamweb, where fractureis expected to occur, freemesh solid elements C3D10Mwere employed;for the remaining structural parts, more computational efficient solidelements C3D8R were used. A friction coefficient of 0.2 (Class D slipfactor for untreated hot roll steel, Eurocode 3 [11]) was employed for

Fig. 5. Load deflection curves for the specimens.


all hard contacts since the surfaces of the specimens, angles andtee-sections were generally untreated. These contacts included: 1) thecontact between the beam web and the connected plates (tee stem orangle leg); 2) the contact between the bolts and bolt holes; and 3) thecontact between the bolt head and one side of the beam web (fortee and single angle connections only). In order to achieve good numer-ical convergence, the bolt diameter was considered to be the same asthe bolt hole diameter, such that a full contact between them wasestablished initially. The values of true stress and true plastic strain ofmaterial were input into the ABAQUS model. Since no material testwas performed on bolts, nominal values for modulus of elasticity(210 GPa), yield strength (1080 MPa) and tensile strength (1200 MPa)were employed. A bilinear stress–strain curve was used assuming astrain of 15% for the tensile strength. Bolt preload was not consideredin the FE model since the bolts were only snug-tightened by hand inthe testing programme.

To simulate the fracture of the beam web, the damage modeloffered by ABAQUS for modelling the progressive damage of ductilemetals was employed. The progressive damage models allow for asmooth degradation of the material stiffness. Two basic parameterswere considered to control the progress of material damage, namely,a damage initiation criterion and a damage evolution response. Thedamage initiation criterion describes the maximum strain which ini-tiates damage, i.e. the starting point of the decreasing branch of thestress–strain curve. This strain causes material stiffness degradation,where the value can be obtained from the coupon test. The damageevolution law describes the rate of degradation of the material

stiffness once the corresponding initiation criterion has been reached.This strain value has insignificant effect on the ultimate load, but mayslightly affect the deflection at ultimate load and the load decreasingrate after ultimate load. In the current model, a linear damage evolu-tion law was considered, and a strain of 5% beyond the damage initi-ation strain was employed to allow the damage evolution (from theinitiation of damage to a complete loss of the element stiffness).This strain was employed to achieve a reasonable numerical conver-gence, and the ultimate load of the FEmodel is not sensitive to this strain.It should be noted that when the material exhibits strain-softening be-haviour, the stress–strain relationship no longer accurately representsthe material's behaviour. Continuing to use the stress–strain relationintroduces a strong mesh dependency. In ABAQUS all of the availabledamage evolution models use a formulation intended to alleviate themesh dependency. This is accomplished by introducing a characteristiclength into the formulation, which in ABAQUS is related to the elementsize, and expressing the softening part of the constitutive law as astress–displacement relation. More details of the material damagemodel used in ABAQUS can be found in [18]. For the remaining part ofthe specimens where no fracture is expected, normal elasto-plasticmaterial models were considered, where the material is assumed tobehave linearly at the elastic range, followed by a multi-linear strainhardening response.

Quasi-static displacement was applied onto the loading point tosimulate the applied load. For the boundary conditions, lateral restraintswere applied along the beam flange edge to prevent lateral movement.Vertical support (but free to move horizontally) was applied at the

Fig. 6. Strain distributions: a) tensile strain of A1-1-3-a, T1-1-3-a, T2-1-3-a, and A1-1-3-a-S under P = 100 kN, b) tensile strain of T2-1-3-b, c) tensile strain of A2-2-2-a, d) shearstrain of T1-1-3-a, e) shear strain of A2-2-2-a.


uncoped beam end to simulate simply-supported condition. For theangles or tees at the other end, the bolt holes that were connected tothe column face were fixed in the horizontal direction, while verticalsprings were applied in the inner areas of these bolt holes to considerthe additional vertical displacement caused by bolt slip and local bearingdeformation of the bolt hole. Since it is difficult to accurately measurethe effect of bolt slippage and possible slight support deformation, atrial-and-error procedure was adopted to determine the spring stiffness.Using this procedure, the spring stiffness was gradually adjusted untilthe initial stiffness of the analytical load–deflection curves generallymatched the test curves. It was found that adopting an overall stiffnessbetween 35 kN/mm and 50 kN/mm of the vertical spring assemblygenerally correlated well with the test results. The effect of the stiffnessof the vertical springs due to bolt slippage and bolt hole deformationcan be assessed via FE models. Fig. 8 shows an example of specimenA1-1-3-a with different vertical springs. It can be seen that the verticalsprings did not have a significant effect on the ultimate load.

Theweb twisting effect of the FEmodel using a single tee connection(scale factor = 3.0) is shown in Fig. 7(b). The deformation shape iswellpredicted through comparisons with the test results given in Fig. 4.Typical fracture behaviour of the FE model is shown in Fig. 7(c). Thecontour indicates the ‘damage initiation index’ which is an outputvariable that increases monotonically with plastic deformation, and avalue exceeding 1.0 indicates the initiation of material damage. It isclearly shown that complete tensile fracture with significant shearyielding governs the failuremode,which is in linewith the test observa-tions. In addition, it is shown thatmore significant yielding occurs alongthe shear area immediately above the bolt holes, which may be due tothe combined effects of shear and bearing. The load–deflection curvesfrom the FE analysis for the ten specimens are shown in Fig. 5, andthe corresponding ultimate loads are listed in Table 4. In general, theFE predictions correlate reasonably well with the test results, thus

indicating the reliability of the FE models. In addition, the FE resultsshow that the presence of loading eccentricity does not decrease theultimate load, which is consistent with the finding from the tests. Thetest-to-predicted ratio ranges between 0.844 and 1.063, where the dis-crepancies are within 10% for most specimens except for T2-2-2-a. Forspecimen T2-2-2-a, the test ultimate load is very low, which is only84.4% of the FE prediction. As discussed in the previous section, thetest ultimate load of specimen T2-2-2-a was significantly smaller thanthat of T1-2-2-a, noting that T1 section is even smaller than T2 section.The FE result, which is inconsistent with the test result, seems to give amore reasonable prediction, i.e. the predicted ultimate load of T2-2-2-ais larger than that of T1-2-2-a. Based on this supplementary FE analysis,the authors deduce that the low test ultimate load of specimen T2-2-2-amay be due to the combined effects of lower material strength, initialimperfections of the test specimen, and/or possible erratic test setupalignment.

The comparisons between elastic strains recorded by the straingauges and the corresponding FE predictions are shown in Fig. 6.Reasonable correlations are generally found, particularly for the spec-imens with tee connections. A certain level of discrepancy is found forthe specimens with double angle connections. The main reason canbe due to the fact that for these specimens, the strain gauges mountedon the beam web have to be placed between the angle plate andbeam web. Contact between the two plates, which can induce fric-tions, may influence the readings of the strain gauges. Notwithstand-ing, the trends for strain gradient are still well reflected.

To further study the effects of loading eccentricity and rotationalrestraint on the block shear strength and behaviour of coped beams, apreliminary parametric study was conducted. Three types of bolt lay-outs, namely, A-1-3-a/T-1-3-a, A-1-3-b/T-1-3-b, and A-2-2-a/T-2-2-a,are considered. The designation of the FE model is similar to thatused for the test specimens. For example, model A-1-3-a and T-1-3-a

Fig. 7. Finite element model in ABAQUS: a) typical model and mesh, b) web twisting effect—scale factor = 3.0, c) fracture behaviour.


represent the specimenswith the bolt layout of “1” bolt line, “3” rows ofbolts, and an edge distance (eh,b) of 28 mm connected by double angleand single tee, respectively. For each comparison group, the same con-nection flange plate thickness (20 mm) is used for the tee and angle,and thus the end rotational restraint of the connections is only con-trolled by the gauge, i.e. the end rotational restraint is increased via

Fig. 8. Influence of vertical springs on ultimate load capacity.

decreasing the gauge. Three conditions of end rotational restraint areconsidered, which are ‘gauge = 150 mm’, ‘gauge = 75 mm’, and‘rigid in rotation’. In this study, the gauge represents the ‘net gaugeLng’, as illustrated in Fig. 9(a). For the case of ‘rigid in rotation’, theflangeof the tee or angle is fully restrained against bending. Employing eachcondition of gauge, the behaviour of the FE models using double clipangles and single tee were compared to consider the effect of loadingeccentricity.

The ultimate loads of the parametrically varied FE models areshown in Fig. 9(a). It is shown that increasing the end rotationalrestraint tends to increase the ultimate load. This is in line with thefindings of [16,17] for coped beams with welded end connections.On the other hand, when the same gauge is employed, the modelwith a single tee can achieve a slightly higher ultimate load thanthat with double angles (except the case of A-2-2-a/T-2-2-a withgauge = 150 mm). This implies that for most cases the out-of-planeloading eccentricity may have no detrimental effect on the blockshear capacity, and the eccentricity could even increase slightly thecapacity. This observation partially explains the unexpected test re-sults, where it was found that for most cases the ultimate loads forthe test specimens with tees were slightly higher than those withdouble angles, although other combined factors such as the influenceof end rotation restraints (due to varied gauges) may also contributeto this phenomenon. To explain the possible reason for this increaseof ultimate load, a section through the deformed shape (scale factor =

Fig. 9. Results of numerical study: a) influences of rotational restraint stiffness and loading eccentricity, b) cut view of web twisting—scale factor = 3.0, c) web twisting of specimenwith double bolt line—scale factor = 3.0.


3.0) of the FE model (with a single tee connection) due to web twisting,as shown in Fig. 9(b), is examined. When web twisting occurs, the axialline of the bolts (especially for the top bolt) starts to incline. As illustratedin the figure, when the beam web tends to move downward, the slightincline of the bolt head could help to ‘support’ the beam web via thevertical component of the normal contact force between the bolt headand the beam web. This minor vertical force component, which canalso lead to an increase of plate-contact friction, may alleviate the forcedirectly resisted by the web block, and hence may slightly increase theblock shear capacity. In addition, it can be seen from Figs. 7(b) and9(b) that the out-of-plane deformation caused by web twisting is onlylocalised near the upper area of the cope, therefore the tensile fracturearea that normally governs the ultimate load is not significantly affectedby theweb out-of-plane twisting. In otherwords, the potential beneficialeffect caused by the additional friction as mentioned above, along withthe negligible influence on the tensile fracture area due to web twisting,could increase the ultimate load as a result.

On the other hand, the comparison group A-2-2-a/T-2-2-a withgauge = 150 mm is an exception, where the ultimate load of modelA-2-2-a is higher. This may be due the fact that compared with the

‘1-3-a’ or ‘1-3-b’ bolt layouts, longer cope length was used for the‘2-2-a’ layout, as shown in Fig. 9(c), which could lead to a more signif-icant out-of-plane bending. Moreover, the tension area (which is im-portant in determining the block shear capacity) for the ‘2-2-a’ boltlayout is also closer to the top of the cope; therefore, the tensionarea can be more easily affected by web twisting, leading to a reducedultimate load. It is worth noting that only the case of gauge =150 mm shows a decreased ultimate load of model T-2-2-a comparedwith A-2-2-a. This is due to the fact that the increase of gauge not onlydecreases the in-plane connection rigidity, but also decreases theout-of-plane bending rigidity of the connection. Therefore, morelateral movement of the web plate of the tee can be induced when alarger gauge (e.g. 150 mm) is employed, which may further enlargethe web twisting effect. As a result, the possible beneficial effect offriction for model T-2-2-a is counteracted by the detrimental influ-ence of web twisting, thus leading to a lower ultimate load than itscounterpart.

To further discuss the influence of friction on the ultimate load,Fig. 10(a) shows the contour of friction force distribution of the beamweb with double angle and single tee connection under an applied

Fig. 10. Influence of friction: a) typical friction force distribution, b) resisting force contributed by friction and bolt-hole bearing, c) influence of friction coefficient for A-1-3-a andT-1-3-a.


load of 400 kN, where the case of A-1-3-a/T-1-3-a with gauge =150 mm is considered. For the beam web connected by the single tee,more friction is induced, particularly on the ‘bolt side’, where significantcontact force between the beamweband bolt head is developed. For thebeamweb connected by the double clip angles, friction force is also ob-served, which can be largely due to the deformation of the bolts undershear and minor bending. Fig. 10(b) further illustrates the resistingforce distribution of the beam web contributed by bolt-hole bearing

and total friction. Under an applied load of 100 kN (leading to a beamend reaction of approximately 70 kN), the total friction forces inducedon the beam web for the model connected by double clip angles andsingle tee are close, which are 10.02 kN and 10.98 kN, respectively. Asthe load increases to 400 kN, where evident web twisting occurs forthe model with the single tee, the proportion of friction force for themodel with the single tee is clearly larger than that with the doubleclip angles. The larger friction force can be helpful to alleviate the


force directly resisted by the whole block. Fig. 10(c) confirms the bene-ficial influence of friction through comparing the ultimate loads of thetwo models with different friction coefficients. It is clearly found thatwhen the friction coefficient is reduced from 0.2 to 0.0, the ultimateloads for the models with double angle and single tee tend to be veryclose. This implies that the increased ultimate loads observed in thisstudy for the specimens with tee connections can be largely due tothe friction effects.

6. Comparison of test results with design equations

6.1. General

The current design standards from Japan (AIJ [9]), America(AISC-LRFD [10]), Europe (EN 1993-1-8:2005 [11]), and Canada(CAN/CSA-S16-09 [12]) were chosen to compare with the test results.In addition, Topkaya [8] proposed two alternative block shear modelsbased on an extensive parametric study, and these were also includedfor discussion. The design equations in these standards and researchpapers for block shear of coped beams were initially based on theresearch of bolted double clip angle connections (with no loadingeccentricity). The comparison of the capacities between these designmethods and the test results is summarised in Table 4. The predictedcapacities are calculated based on the measured geometries and ma-terial properties. The resistance factor (or partial factor) in the designequations is taken as 1.0 for calculating the predicted capacities.

6.2. Architectural Institute of Japan, AIJ (1990)

The AIJ [9] provides two equations for predicting the block shearcapacity of coped beams with bolted connections as below:

Pr ¼ ϕ FuAnt þ 1=ffiffiffi3

p� �FyAnv

h ior Pr ¼ ϕ FyAnt þ 1=

ffiffiffi3

p� �FuAnv

h ið1Þ

where Pr = factored ultimate connection capacity; ϕ = resistancefactor; Fu = tensile strength; Fy = yield strength; Ant = net tensionarea; Anv = net shear area. The smaller value predicted from thetwo equations governs the design capacity.

As shown in Table 4, the two equations underestimate the blockshear capacities of all the test specimens, especially for the single boltline layouts. The average test-to-predicted for all the ten specimens is1.46, and the associated C.O.V. is 0.1; among these, the average test-to-predicted ratios for the specimens with single and double bolt linelayouts are 1.54 and 1.28, respectively. The conservative prediction bythe standard can be due to the underestimation of the contribution bythe shear area. As observed from the test, shear yielding occurs alongthe gross shear area, but AIJ [9] conservatively assumes that only thenet shear area takes action.

6.3. AISC-LRFD (2005)

AISC-LRFD [10] assumes that block shear is governed by tensionfracture on the net tension area, combined with shear yielding on thegross shear area or shear rupture on the net shear area, as expressedbelow:

Pr ¼ ϕ UbsFuAnt þ 0:6FuAnvð Þ≤ϕ UbsFuAnt þ 0:6FyAgv

� �ð2Þ

where Ubs = 1.0 if the tensile stress is uniform (single bolt line);Ubs = 0.5 if the tensile stress is non-uniform (double or multiple boltlines); and Agv = gross shear area. The other symbols are similar tothose defined in Section 6.2. Eq. (5) indicates that in combination withtension fracture, either gross yielding or net rupture on the shear areamay govern the capacity. AISC-LRFD provides the predictions of blockshear capacity for single bolt line connections with a mean test-to-

predicted ratio of 1.27. More conservative predictions are given fordouble bolt line connections, where a mean test-to-predicted ratio of1.59 is obtained. This implies that Ubs = 0.5 may be overly conservativefor the specimens with double or multiple vertical bolt lines.

6.4. EN 1993-1-8:2005

Eurocode 3 (EN 1993-1-8:2005) [11] employs a single equation toconsider the block shear capacity, which is governed by tension frac-ture on the net tension area and shear yielding on the net shear area:

Pr ¼ 0:5FuAnt=γM2 þ 1=ffiffiffi3

p� �FyAnv=γM0 ð3Þ

where γM0 = the partial safety factor for resistance of cross-section;γM2 = the partial safety factor for resistance of cross-section in tensionto fracture. Eurocode 3 provides the most conservative estimations forboth single and double line connections with mean test-to-predictedratios of 1.82 and 1.73, respectively. The main reason is due to the factthat a factor of 0.5 is applied to the tensile fracture resistance, regardlessof the bolt layouts. In addition, the assumption of shear yielding overthe net section in Eurocode 3 also underestimates the block shearcapacity.

6.5. CSA-S16-09 (2009)

CAN/CSA-S16-09 [12] employs a single equation for the design ofblock shear in coped beams:

Pr ¼ ϕu UtFuAnt þ 0:6Agv Fy þ Fu� �

=2h i

ð4Þ

where ϕu = the resistance factor; and Ut = the efficiency factor.Ut = 0.9 for coped beams with one bolt line; Ut = 0.3 for copedbeams with two bolt lines. The efficiency factor was obtained accordingto the study of Franchuk et al. [6]. Eq. (4) considers that the block shearcapacity is governed by fracture of the net tension area combiningwiththe failure of the gross shear area with the average yield and ultimateshear strengths. The use of the average shear strengthmay better reflectthe observations from the test results that shear strain hardening couldoccur before tension fracture of the web block. The test-to-predictedratios predicted by CAN/CSA-S16-09 range from 0.93 to 1.17 for singlebolt line connections. The corresponding mean test-to-predicted ratiois 1.03. This indicates that CAN/CSA-S16-09 can provide good predic-tions for the specimens with single bolt line layouts. For the doublebolt line specimens, on the other hand, the CAN/CSA-S16-09 predictionsare more conservative with a mean test-to-predicted ratio of 1.47. Theconservative predictions can be due to the underestimated efficiencyfactor Ut = 0.3 for the double line connections. An efficiency factor of0.5 may lead to a less conservative prediction.

6.6. Topkaya (2007)

Topkaya [8] presented a nonlinear FE analysis study on block shear ofcoped beams, and the methodology was adopted for a parametric studycomprising ninety analyses. Based on the available test data and theparametric study, two alternative block shear models were developed,as given by:

Pr ¼ FyAnt þ 0:5FyAgv or Pr ¼ FuAnt þ 0:4FuAgv ð5Þ

where the former equationwas based on the critical tension plane yieldcriterion, and the latter was based on the maximum fracture load crite-rion. As shown in Table 4 (Topkaya 1 and Topkaya 2 are the predictionsbased on the former and the latter equations, respectively), both equa-tions could give reasonable predictionswith themean test-to-predictedratio above unity and the associated C.O.V. less than 0.1. Comparedwith


the former equation, which is more conservative, the latter equationcould provide the test-to-predicted ratio closer to unity, although theC.O.V. is slightly larger.

In view of the above, it is found that AIJ [9], AISC-LRFD [10], andEN1993-1-8:2005 [11] are quite conservative in predicting the blockshear strength of cope beams. The predictions based on the equationsproposed by Topkaya [8] are also on the conservative side for thespecimens with single bolt line connections, but it seems that theultimate loads of the specimens with double bolt line connectionscan be better predicted. CAN/CSA-S16-09 [12] produces good predic-tions of the block shear capacity of coped beams with single bolt lineconnections. The reasonable use of the average value of the shearyield strength and shear ultimate strength in CAN/CSA-S16-09 leadsto a good correlation with the observations from the tests. However,the predictions for coped beams with double bolt line connectionsare conservative. More tests on coped beams using double bolt lineconnections with different aspect ratios of web block need to beperformed to further verify the Ut value.

7. Summary and conclusions

A total of ten full-scale tests were conducted to investigate the blockshear strength and behaviour of coped beamswith single-sided connec-tions and double clip angle connection. The failure mechanisms of allthe test specimens were block shear when the ultimate loads wereachieved, where only specimen T2-1-3-b failed in whole block tear-out while the other specimens failed in tension fracture (partial tear-out) of the beam web and excessive shear yielding in the shear area.Further loading could induce a complete tear-out of the web block forthose specimens exhibiting partial tear-out under the ultimate load.In addition, the specimens with a single-sided connection exhibitedtwisting of the web near the cope. More significant web twisting wasobserved for the specimens with longer cope length and smaller thick-ness of the connected web of tee or angle.

Themain test parameters in this experimental programme includedthe out-of-plane loading eccentricity and the aspect ratio of web block.It was observed that the presence of out-of-plane loading eccentricityshowed no detrimental effect on the block shear strength of copedbeams; however, this finding could not conclusively reflect the soleeffect of out-of-plane loading eccentricity due to the combined influ-ence of connection rigidity, which can be beneficial for improving theblock shear capacity. In view of this, a FE analysis, which supplementedthe test results, was conducted to preliminarily investigate the effectsof out-of-plane loading eccentricity and connection rigidity. It wasreconfirmed that the loading eccentricity could slightly increase theblock shear capacity, and it was subsequently found that the possiblebeneficial effect of out-of-plane loading eccentricity can be explainedby the influence of friction: the secondary bending (twisting) of thebeam web caused by the out-of-plane loading eccentricity is onlylocalised near the upper area of the coped region, and normally thesecondary bending could not affect the tension area which is criticalin determining the block shear capacity; when secondary bending oc-curs,more frictional action is induced, which alleviates the load resistedby the block. The parametric study also showed that when friction wasexcluded, the ultimate loads for the models with double clip angle orsingle tee connections could be close. However, for the case of doublebolt line with smaller connection rigidity, detrimental effects inducedby loading eccentricity became evident. In view of the above, it is sug-gested that for most cases, no reduction of block shear capacity maybe required for the coped beams with single-sided bolted connections,but attention should be paid to the case where the tension fracture

area is relatively close to the top of the cope, combining with the con-current condition of small connection rigidity. Extensive parametricstudies, taking account of more varied connection types and boltlayouts, are required towards a conclusive design recommendation.Furthermore, it was found that a decrease in aspect ratio (increase intension area) could provide a higher block shear capacity of copedbeams.

Finally, the test results were compared with various design speci-fications. In general, only the Canadian Standards CAN/CSA-S16-09can provide good predictions of the block shear capacity of copedbeams for the single bolt line specimens. Other specifications suchas AIJ, AISC-LRFD, and Eurocode3 were shown to provide inconsistentand conservative estimations. For the double bolt line specimens, theequations proposed by Topkaya [8] seem to provide reasonable predic-tions. More study for double bolt line specimens is needed since none ofthe design standards can give favourable predictions for the block shearcapacities. The experimental results reported in this study obviouslyform an important basis of more extensive parametric studies via finiteelement analyses in future.

Acknowledgements

Thework described in this paper was supported by a grant providedby The Hong Polytechnic University, Central Research Grant (ProjectNo. G-U754). The assistance of the technical staff in the StructuralLaboratory of the University of Macau is also acknowledged.

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