Experimental study of the strength and behaviour of reinforced coped beams

11
 Experimental study of the strength and behaviour of reinforced coped beams Michael C.H. Yam  a, , Hongwei Ma  a, b , Angus C.C. Lam  c , K.F. Chung  d a Department of Building & Real Estate, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China b Department of Civil Engineering, The South China University of Technology, Guangzhou, China c Department of Civil and Environmental Engineering, University of Macau, Macau, China d Department of Civil and Structural Engineering, The Hong Kong Polytechnic University, Hong Kong, China a b s t r a c t a r t i c l e i n f o  Article history: Received 11 February 2011 Accepted 28 April 2011 Available online 8 June 2011 Keywords: Coped beams Reinforcement details Stiffeners Testing A total of 10 full-scale tests were conducted to investigate the strength and behaviour of reinforced coped steel I-beams. The test paramet ers included the length of longitudinal stiffeners, leng th of transv erse stiffeners, combined longitudinal and transverse stiffeners, double transverse stiffeners, cope depth and cope length. For the coped beam specimens without stiffeners, local web buckling failure occurred in the cope. For the spec imen s with longi tudi nal stif fene rs only , the gene ral fail ure mod e was exu ralyield ingof thefull be am section at the location of maximum bending moment followed by web crippling at the end of the cope between the longitudinal stiffeners and the top ange of the full beam section. In contrast, the general failure mode for the specimens with combined longitu dinal and transverse stiffeners consisted of exural yielding of the full beam section at the location of maximum bending moment followed by ange local buckling near the loading position. Thetest res ults show tha t thereinf orc ement s were able toincrea se thecapac ity of thecopedbeamspeci mens signicantl y and the results also illustrat e that in additio n to cope depth, cope length also affects the behaviour and str eng th of the rei nforced cop ed beam spe cimens . Bas ed on the limite d tes t data, a modicatio n to the curre nt reinf orcem ent deta ils for cope d beams was prop osed . The prop osedreinforc emen t details accounted for the effects of various cope details. To increase the range of applicability of the proposed reinforcement details, a numerical study is currently underway to consider a wider range of cope details. © 2011 Elsevier Ltd. All rights reserved. 1. Introduction In steel structures, when secondary beams are connected to the main girders, the  anges of the beams are usually coped (notched). Because of the cope, the secondary beams are able to maintain the same top  ange elevation as that of the main girders and provide enough clearance for constructing the end connections. As shown in Fig. 1, either welded end plate or bolted clip angle connections can be used to connect the secondary beams to the main girders. Owing to the remova l of the ang e(s ), howeve r, the str eng th of the cop ed bea m section is signicantly reduced ([1], [2] and [3]). Failure modes of cope d beams incl ude  exur al yiel ding, shear yiel ding, local web buckling (Fig. 2a) and block shear of the connection (Fig. 2b). The local web buckling strength and behaviour of coped beams have bee n studied by Che ng et al. [4], Cheng and Yura [5], Aalber g and Larsen  [6], Yam et al. [7]  and others. In order to improve the strength of coped beams, Cheng et al.  [4]  proposed the set of reinforcement det ail s shown in Fi g. 3 to loc all y str eng the n the cop ed section in orde r to prevent the occurrence of local web buckling. However, the details dev elo ped were mai nly based on the resul ts of a  nite element analysis without experimental evidence. The AISC Steel Construction Manual  [8]  provides a similar set of guidelines, based on the work of Che ng et. al [4], for rei nfo rci ng cop ed bea ms.For bea m sec tions wit h h/t w 60, where h is the clear distance between  anges less the  llet and t w  is the thickne ss of the web, eithe r longi tudin al stiff ener s (Fig. 3a) or doubler plate (Fig. 3b) can be used as the reinforcement. The combined long itudi nal and trans verse stif fene rs ( Fig. 3c) ar e used when h/t w N60. For reinforced coped beams, it is necessary to check for exural yielding. Local web buckling of the coped section does not need to be checked. Yam et al.  [9]  cond uct ed tes ts and made a numerical study of the strength of reinforced coped beams, but only two coped beam spec imen s reinforced by longitudi nal stiffen ers were tested in the study. Nevertheless, the test results show that even though the coped section of the beam specimens was reinforced by a pair of longitudinal stiffeners, the web between the top  ange of the beam and the longitudinal stiffeners distorted with signi cant lateral dis pla cem ent . Lamet al. [10] also conducted tes ts on reinfo rce d cop ed beams, but the parameters examined were not suf cient to verify the effectiveness of the reinforcement details suggested by Cheng et al. [4]. The ab ove disc ussi on shows that only a few s tudie s of the stren gth and behaviour of reinforced coped beams have been made and the  Journal of Construction al Steel Research 67 (2011) 17491759  Corresponding author. E-mail address:  bsmyam@polyu .edu.hk (M.C.H. Yam). 0143-974X/$  see front matter © 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.jcsr.2011.04.015 Contents lists available at  ScienceDirect  Journal of Constructional Steel Research

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Experimental study of the strength and behaviour of reinforced coped beams

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Experimental study of the strength and behaviour of reinforced coped beams

Michael CH Yam a Hongwei Ma ab Angus CC Lam c KF Chung d

a Department of Building amp Real Estate The Hong Kong Polytechnic University Hung Hom Kowloon Hong Kong Chinab Department of Civil Engineering The South China University of Technology Guangzhou Chinac Department of Civil and Environmental Engineering University of Macau Macau Chinad Department of Civil and Structural Engineering The Hong Kong Polytechnic University Hong Kong China

a b s t r a c ta r t i c l e i n f o

Article history

Received 11 February 2011Accepted 28 April 2011

Available online 8 June 2011

Keywords

Coped beams

Reinforcement details

Stiffeners

Testing

A total of 10 full-scale tests were conducted to investigate the strength and behaviour of reinforced coped

steel I-beams The test parameters included the length of longitudinal stiffeners length of transverse

stiffeners combined longitudinal and transverse stiffeners double transverse stiffeners cope depth and cope

length For the coped beam specimens without stiffeners local web buckling failure occurred in the cope For

the specimens with longitudinal stiffeners only the general failure mode was1047298exuralyieldingof thefull beam

section at the location of maximum bending moment followed by web crippling at the end of the cope

between the longitudinal stiffeners and the top 1047298ange of the full beam section In contrast the general failure

mode for the specimens with combined longitudinal and transverse stiffeners consisted of 1047298exural yielding of

the full beam section at the location of maximum bending moment followed by 1047298ange local buckling near the

loading position

Thetest results show that thereinforcements were able to increase thecapacity of thecopedbeamspecimens

signi1047297cantly and the results also illustrate that in addition to cope depth cope length also affects the

behaviour and strength of the reinforced coped beam specimens Based on the limited test data a

modi1047297cation to the current reinforcement details for coped beams was proposed The proposedreinforcement

details accounted for the effects of various cope details To increase the range of applicability of the proposed

reinforcement details a numerical study is currently underway to consider a wider range of cope details

copy 2011 Elsevier Ltd All rights reserved

1 Introduction

In steel structures when secondary beams are connected to the

main girders the 1047298anges of the beams are usually coped (notched)

Because of the cope the secondary beams are able to maintain the

same top 1047298ange elevation as that of the main girders and provide

enough clearance for constructing the end connections As shown in

Fig 1 either welded end plate or bolted clip angle connections can be

used to connect the secondary beams to the main girders Owing to

the removal of the1047298ange(s) however the strength of the coped beam

section is signi1047297cantly reduced ([1] [2] and [3]) Failure modes of

coped beams include 1047298exural yielding shear yielding local web

buckling (Fig 2a) and block shear of the connection (Fig 2b)

The local web buckling strength and behaviour of coped beams

have been studied by Cheng et al [4] Cheng and Yura [5] Aalberg and

Larsen [6] Yam et al [7] and others In order to improve the strength

of coped beams Cheng et al [4] proposed the set of reinforcement

details shown in Fig 3 to locally strengthen the coped section in order

to prevent the occurrence of local web buckling However the details

developed were mainly based on the results of a 1047297nite element

analysis without experimental evidence The AISC Steel Construction

Manual [8] provides a similar set of guidelines based on the work

of Cheng etal [4] for reinforcing coped beamsFor beam sections with

htwle60 where h is the clear distance between 1047298anges less the 1047297llet

and tw is the thickness of the web either longitudinal stiffeners

(Fig 3a) or doubler plate (Fig 3b) can be used as the reinforcement

The combined longitudinal and transverse stiffeners (Fig 3c) are used

when htwN60 For reinforced coped beams it is necessary to check

for 1047298exural yielding Local web buckling of the coped section does not

need to be checked Yam et al [9] conducted tests and made a

numerical study of the strength of reinforced coped beams but only

two coped beam specimens reinforced by longitudinal stiffeners were

tested in the study Nevertheless the test results show that even

though the coped section of the beam specimens was reinforced by a

pair of longitudinal stiffeners the web between the top 1047298ange of the

beam and the longitudinal stiffeners distorted with signi1047297cant lateral

displacement Lamet al [10] also conducted tests on reinforced coped

beams but the parameters examined were not suf 1047297cient to verify the

effectiveness of the reinforcement details suggested by Cheng et al

[4]

The above discussion shows that only a few studies of the strength

and behaviour of reinforced coped beams have been made and the

Journal of Constructional Steel Research 67 (2011) 1749ndash1759

Corresponding author

E-mail address bsmyampolyueduhk (MCH Yam)

0143-974X$ ndash see front matter copy 2011 Elsevier Ltd All rights reserved

doi101016jjcsr201104015

Contents lists available at ScienceDirect

Journal of Constructional Steel Research

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available experimental data is insuf 1047297cient to substantiate the current

reinforcement details of coped beams Therefore the main objective

of the study presented in this paper was to provide more

experimental evidence on the strength and behaviour of reinforced

coped beams In addition a newly developed reinforcement detail

based on previous research results was also examined in this

experimental programme The experimental data will also be used

to validate a 1047297nite element model for a parametric study and the

results of that study will be reported in another research paper

2 Experimental programme

21 Test specimens

A total of 10 full-scale tests were conducted in the experimental

programme to investigate the strength and behaviour of reinforced

coped steel I-beams The main test parameters included the length of

longitudinal stiffeners (L x) length of transverse stiffeners (L y)

combined longitudinal and transverse stiffeners double transverse

stiffeners and cope details (cope depth (dc) and cope length (c)) The

test specimens are illustrated schematically in Fig 4 The measured

beam dimensions the cope details and the reinforcement details of

the specimens are shown in Table 1 The cope details and dimensions

were selected to ensure that the test results were able to illustrate the

effects of the reinforcement on strengthening the coped beam

specimens In addition the test results which considered a wide

range of cope details and dimensions can be used to properly validate

a 1047297nite element model for further parametric study Five test beam

specimens 34 m long were fabricated using the universal beam

section UB356times 127times33 (SCI Guide [11]) and Grade S355 steel (BS EN10025-2 2004 [12]) The test beam specimens were coped at both

ends with relevant reinforcement details Both ends of the test beams

were designed as separate test specimens with different cope and

reinforcement details A diagram of a typical test beam is shown in

Fig 5 Table 1 shows that two cope lengths (c approximately equal to

210 mm and 315 mm) and two cope depths (d c approximately equal

to 60 mm and105 mm) were used to form thecope details Thelength

of the longitudinal stiffeners varies approximately between 265 mm

and 412 mm corresponding to a stiffener extension (ex) ofabout one dc

beyondthe endof thecopeexcept forspecimenA3 As shown in Table 1

a stiffener extension of about 2dc was used for specimen A3 The length

(L y) of the transverse stiffeners was approximately equal to 2dc It

should be noted that the variations in the length of stiffeners the

stiffener extension and the cope details were due to fabrication errors

The width and the thickness of the stiffeners were 60 mm and 8 mm

respectively The stiffeners were welded to the beam web using a 1047297llet

weld and a partial penetration butt weld and theweld sizewas 4 mmas

shown in Fig 4 Class 42 electrodes were used to produce the welds

As shown in Table 1 specimens A1 and B1 were the control

specimens that did not have stiffeners in the cope The results for

these two specimens were compared with those of the other

specimens with various types of stiffeners in order to illustrate the

effectiveness of the reinforcement details In general a cope depth

(dc) of about 60 mm was used for the A-series specimens whereas a

cope depth of 105 mm was used for the B-series specimens as shown

in the table Specimens A2 A3 B2 and B3 were used to examine the

Cope

Bolted clip angles Welded end plate

Fig 1 Coped beam connections

(b) Block shear failure of

welded end connection

(a) Local web bucking failure

Top

flange

Buckled webBuckled web

Fig 2 Coped beam failure modes

(c) Combined longitudinal and

transverse stiffeners

(a) Longitudinal stiffeners

Shear

connection

Longitudinal stiffeners

dcdc

dc

c dc dc

(b) Doubler plate

Doubler plate

Shear

connection

c

Shear

connection

c

Transverse stiffeners

Longitudinal stiffeners

Fig 3 Coped beams reinforcement details

1750 MCH Yam et al Journal of Constructional Steel Research 67 (2011) 1749ndash1759

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effectiveness of providing longitudinal stiffeners at the cope in

improving the strength of coped beams as suggested by the previous

research results [4] The comparison of these test results was also able

to illustrate the effects of cope depth on the effectiveness of the

reinforcement details Specimen B3 which has a cope length of

315 mm (cDasymp09) was used to examine the in1047298uence of cope length

on the effectiveness of the reinforcement details Specimens A4 A5

B4 and B5 were employed to study the use of transverse stiffeners in

combination with longitudinal stiffeners in strengthening coped

beams As illustrated in Fig 4c a single pair of transverse stiffeners

was placed at the end of the cope for specimens A4 and B4 For

specimens A5 and B5 a double transverse stiffener arrangement was

used with an additional pair of transverse stiffeners placed at the end

of the longitudinal stiffeners as shown in Fig 4d This new

arrangement of transverse stiffeners is used to control the failure

mode of rigid body movement of the longitudinal stiffeners as

observed from previous test results [9]

Tension coupons were cut from the webs and the 1047298anges of the

test beams and also from the stiffeners In order to obtain the static

values of the yield strength and the ultimate strength of the materials

the stroke was held constant brie1047298y in the yield plateau the strain-

hardening range and near the ultimate strength level The average

im n A 1 n B1im n A2 A B2 n B i m n A 4 n B 4 T i l n l il fT i l l i l f i f f n ri m n A n B Fi 4 D il f im n ens)mm)(mm)Lx mmLmm x mm mm A1 3487 1253 57 83 623 2117

ndash ndash ndash ndash 061 018 A2

7182019 Experimental study of the strength and behaviour of reinforced coped beams

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static yield strength and the ultimate strength of the beams and the

stiffeners are listed in Table 2 Althoughthe samesteel grade as that of

the beam was originally requested for fabricating the stiffeners the

average yield strength and ultimate strength of the stiffeners obtained

from the tension coupon tests are signi1047297cantly lower than those of the

beams as shown in the table These lower values would be

incorporated in the calculation of the plastic moment capacity of the

reinforced section of the beams

22 Test setup

A schematic of the test setup is shown in Fig 6 The test beams

were simply supported with the coped end connected to a stub

column using M24 Grade 88 bolts Three washers (12 mm thick in

total) were used between the end plate of the beam and the column1047298ange in order to allow moderate rotation of the beam end and also to

prevent contact between the beam 1047298ange and the column 1047298ange due

to beam end rotation The end plate (10 mm thick) was welded to the

beam web using an 8 mm 1047297llet weld Typical details of the end plate

are shown in Fig 4 The beam specimens were loaded by a hydraulic

jack with a maximum capacity of 1000 kN The hydraulic jack was

located approximately 700 mm (about 2 times the beam depth) from

the stub column support This loading position was chosen in order to

prevent the concentrated load in1047298uencing the structural behaviour of

the coped region

To achieve the simply supported condition for the test beams

roller assemblies were used at the loading position and at the

supports to permit both horizontal movement and rotation of the

beam as shown in Fig 6 The test beams were prevented from lateral

movement near the loading position and near the beam ends by

lateral bracings Transverse web stiffeners were used to strengthen

the beams at the loading position and at the roller supports The

applied load and the reaction force were measured using load cells

23 Instrumentation and test procedure

The de1047298ection and movement of the test beams were measured

using linear variable differential transformers (LVDTs) The positions of

theLVDTs are shown in Fig 7 LVDTs were placed near the coped end to

record the lateral movement of the beam and to detect rigid body

movement of the longitudinal stiffeners Longitudinal strain gauges

were mounted on thebeam web near the end of thecope to record the

strain distribution across the beam depth as shown in Fig 7

The tests were conducted using load control in the early stage of

loading When the beams started to yield stroke control was used in

order to better capture the nonlinear load de1047298ection behaviour of thebeam specimens The test beams were gradually unloaded once the

maximum applied load was reached and the applied load started to

decrease signi1047297cantly Since both ends of the test beams were

designed as a test end once the test on one end of each beam was

completed the other end was then connected to the supporting stub

column for another test

3400

700 598 700699703

3 4 9

412

315 212

308 3 5 0

2 0 5

108105

Fig 5 Typical test beam

Table 2

Summary of the tension coupon test results

Coupon

specimens

Elastic

modulus E

Static yield

strength Fy

Static ultimate

strength Fu

Strain at

fracture

(MPa) (MPa) (MPa) ()

Beam 1047298ange 205000 354 484 243

Beam web 207800 366 483 241

Stiffener 199800 225 441 225

Note the values presented in the table are the average of four coupons for the webs

four coupons for the 1047298anges and two coupons for the stiffeners

Strong floor

Hydraulic

jack

Reaction frame

2000 mm (approx)

700 mm (approx)Boltedconnection

Fig 6 Test setup

1752 MCH Yam et al Journal of Constructional Steel Research 67 (2011) 1749ndash1759

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3 Test results

31 General

The test results are summarised in Table 3 The ultimate applied

load (Pu) and the corresponding in-plane de1047298ection (δ) at the loading

position are presented in the table The ultimate reaction (R u) and the

end moment (Mo) at the coped end were calculated based on the

measured applied load and the measured reaction at the other

support These end moments were caused by the small rotational

stiffness of the end plate connection However it is believed that these

end moments would not have signi1047297cant effect on the strength and

behaviour of the reinforced coped beam specimens This will be

further discussed in the following section

The general failure mode of the coped beam specimens without

stiffeners consisted of local web buckling in the cope as shown in

Fig 8a For the reinforced coped beam specimens however the 1047297nal

failure mode depended on the types of stiffener As shown in Table 3

specimens A1 and B1 (which had no stiffeners) failed in local web

buckling at the cope and the corresponding in-plane de1047298ections wereonly about 4 to 5 mm For the specimens with longitudinal stiffeners

only (A2 A3 and B2) except for specimens B3 1047298exural yielding of the

full beam section occurred at the location of maximum bending

moment and subsequently the longitudinal stiffeners moved laterally

due to web crippling near the coped end as shown in Fig 8b For

specimen B3 which had a longer cope length (c) lateral rigid body

movement of the longitudinal stiffeners occurred without signi1047297cant

yielding of the full beam section at theloading positionFor specimens

A4 A5 B4 and B5 1047298exuralyieldingof thefull beam section occurred at

the location of maximum bending moment and subsequently the

1047298ange of the beam near the loading position buckled locally as

illustrated in Fig 8c For these specimens relatively small lateral

movement of the longitudinal stiffeners was observed In particular

for specimens A5 and B5 which had double transverse stiffeners

almost no lateral movement of the longitudinal stiffeners was

observed as shown in Fig 8d

32 Load de 1047298ection behaviour

The applied load versus de1047298ection curves of specimens A1ndashA5 and

specimens B1ndashB5 are shown in Figs 9 and 10 respectively As

mentioned above the main difference between the A-series specimens

and the B-series specimens was the depth of the cope (dc) For the A-

seriesspecimensa cope depth of about 60 mmwas used whereas a cope

depth of about 150 mm wasused forthe B-seriesspecimens Bothseries

of specimensconsideredthe effects of providingstiffeners in thecope on

the strength and behaviour of coped beams

In general the applied load versus de1047298ection curves showed linear

behaviour from the beginning of loading When the applied load

reached about 80 of the ultimate loads nonlinear load de1047298ection

behaviour was observed as illustrated in Figs 9 and 10 As shown in

the 1047297gures the applied load versus de1047298ection curves of specimens A1

and B1 showed an abrupt drop in the load carrying capacity after

reaching the ultimate loads due to web buckling failure of the

specimens For the specimens reinforced with longitudinal stiffeners

(A2 A3 B2 and B3) except for specimen A3 which had a longer

stiffener extension (ex) once the ultimate loads were reached the

applied load versus de1047298ection curves descended rapidly due to web

crippling at the end of the cope together with a lateral rigid body

movement of the stiffeners For specimen A3 however the beam was

able to continue deforming without signi1047297cant drop in the load

carrying capacity after reaching the ultimate load As shown in

Table 3 the de1047298ection of specimen A3 corresponding to the ultimate

load was 215 mm which was signi1047297cantly larger than those for the

other specimens reinforced with longitudinal stiffeners

The applied load versus de1047298ection curves of the specimens whichhad both longitudinal and transverse stiffeners (specimens A4 A5 B4

and B5) show that the specimens were able to sustain larger

de1047298ections at the ultimate load levels as illustrated in Figs 9 and 10

As mentioned above these specimens failed in 1047298exural yielding of the

full beam section and theapplied load started to decrease when 1047298ange

local buckling occurred near the loading position The de1047298ections of

these specimens corresponding to the ultimate loads were generally

larger than those for the specimens with only longitudinal stiffeners

(except for specimen A3)

Applied load

Longitudinal stiffener

Strain gauge

LVDT (vertical)

LVDT (lateral)

Legend

Fig 7 Typical layout of strain gauges and LVDTs

Table 3

Summary of test results

Test specimens Ultimate load

Pu (kN)

In-plane de1047298ection

δ (mm)

Ultimate reaction

R u (kN)

Ultimate end-moment

Mo (kNm)

Stiffener type Failure mode

A1 3084 478 2019 633 Without WB

A2 4720 948 3056 354 L Y ndashR

A3 5039 215 3290 145 L Y ndashR

A4 4940 143 3275 185 L+ T Y ndashF

A5 5186 229 3403 166 L+ T Y ndashF

B1 2287 399 1495 464 Without WB

B2 4521 916 2939 684 L Y ndashR

B3 3686 804 2407 879 L R

B4 4889 171 3188 832 L+ T Y ndashF

B5 5076 235 3330 142 L+ T Y ndashF

Note L = longitudinal stiffeners T = transverse stiffeners WB = web buckling

R = rigid body movement of stiffener due to web crippling

Y ndashR = yielding of full beam section followed by rigid body movement of stiffener due to web crippling

Y ndash

F = yielding of full beam section followed by 1047298ange local buckling near loading position

1753MCH Yam et al Journal of Constructional Steel Research 67 (2011) 1749ndash1759

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33 Strain distribution

In general at least tenstrain gaugeswere mounted on the web the

top 1047298ange of the beams and the stiffeners as shown in Fig 7 Two

strain gauges were also placed on the top and bottom 1047298anges of thebeam approximately 1000 mm from the coped end support to help

monitor the loading applied to the beam Only the load versus strain

curves for the B-series specimens were used to illustrate the strain

distributions in the web at the coped end of the beam as shown in

Fig 11 The strain distributions for the A-series specimens are similar

to those of the B-series specimens

Fig 11 illustrates the elastic strain distributions in the web at an

applied load of 150 kN Asexpected it can beseen from the 1047297gure that

the longitudinal strains in the web near the top of the cope reduce

signi1047297cantly when stiffeners are used in the beam specimens The

location of the theoretical neutral axis of the reinforced section is in

reasonable agreement with the strain readings as illustrated in the

1047297gure except for specimen B4 For this specimen the corresponding

strain gauge was located very close to the transverse stiffeners andhence the readings might have been affected by the stress concen-

tration effect near the stiffeners The theoretical strain distributions of

specimen B1 (without stiffeners) and specimens B2ndashB5 (with

stiffeners) are also included in Fig 11 As can be seen from the 1047297gure

the theoretical strain distributions of specimen B1 which are

determined based on the coped beam section properties are in

general larger than those of the test results This might be due to the

fact that thestrain gaugeswere located in the web area between the

coped beam section and the full beam section and hence the

(d) No lateral movement of longitudinal

stiffeners of specimen B5

Transverse

stiffeners

Longitudinalstiffeners

(a) Buckled web of specimen A1

Top view

Buckled

web

Top

flange

Bottom

flange

Side view

Buckling line

(b) Web crippling and lateral movement of

longitudinal stiffeners of specimen B2

Lateral

movement of

stiffeners

Web

crippling

(c) Yielding of the full beam section and local flange

buckling at the loading position of specimen B5

Flange buckling

Yielding of

full beam section

Fig 8 Typical failure mode of the test specimens

0

50

100

150

200

250

300

350

400450

500

550

0 4 8 12 16 20 24 28 32 36 40 44

P

R

V

M

A1 A2 A4 A5 A3

A p p l i e d l o a d P ( k N )

Vertical deflection δ (mm)

δ

Fig 9 Load versus de1047298ection curves mdash

specimens A1ndash

A5

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strain gauge readings might have been in1047298uenced by the full beam

section Moreover the theoretical strain distributions of specimens

B2ndashB5 are in reasonable agreement with the test results as shown

in Fig 11

4 Discussion of the test results

41 General

To help discuss the test results the test maximum bending

moment at the loading position (Mmax) and at the end of the cope

(Mco) of the beam specimens were evaluated The corresponding

values are shown in Table 4 The shear capacity of the coped beam

section (R vy) the moment capacity of the coped beam section with or

without longitudinal stiffeners (Mpco) and the plastic moment

capacity of the full beam section (Mp) are also included in the table

for comparison To predict the local web buckling capacity (R wb) of

specimens A1 and B1 the design equations proposed by Yam et al [7]

were used and the predicted values are shown in Table 4 as well Theweb buckling equations for coped beams proposed by Yam et al [7]

are as follows

R Wb = τcrtW Dminusdceth THORN eth1THORN

τcr = Ks

π 2

E

12 1minusv2 tW

ho

2

eth2THORN

Ks = a

h o

c b

eth3aTHORN

a = 138minus179dc

D eth3bTHORN

b = 364 dc

D

2

336 dc

D

+ 155 eth3cTHORN

where R wb=local web buckling capacity of coped beams ks=shear

bucklingcoef 1047297cient E=elasticmodulusν =Poissons ratio ho=height

of web of T-section and other symbols have been de1047297ned above The

measureddimensionsof thebeam specimens andthe materialproperties

obtained from the tension coupon tests were used to calculate the

capacities of the specimens

As mentioned above end moments were developed in the end

plate connections In fact the ultimate end moments of the specimensvaried between 2 and 10 of the corresponding fully 1047297xed end

moment According to Vinnakota [13] for a simple shear connection

such as the end plate connection used in this study the connection

end moment may range from 5 to 20 of the fully 1047297xed moment

Therefore the ultimate end moments developed in the specimens

0

50

100

150

200

250

300

350

400

450

500

550

A p p

l i e d l o a d P ( k N )

Vertical deflection δ (mm)

0 3 3 3 6 de1047298e ct o nc ur ve ss pe cm en s B1 B 5d str but ons for the B ser es spec mens21755M C H Yam et a Journa of Construct ona Stee Research 67 (2011) 1749 1759

7182019 Experimental study of the strength and behaviour of reinforced coped beams

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were reasonable In addition as shown in Table 4 except for

specimens A1 B1 (failed in local web buckling) and B3 (with a longer

cope length) the ratio of the maximum bending moment to the

corresponding plastic moment capacity ranged from 108 to 120 and

the ultimate end moments of the specimens were only 17 to 88 of

the corresponding maximum bending moments If there was no end

moment developed at the connection the ultimate reactions of the

specimens would only be slightly decreased and the specimens could

still reach the plastic moment capacity Hence it can be seen that the

effectiveness of the reinforcement in strengthening the coped beam

specimens would not be affected due to the in1047298uence of the end

moment

42 Failure mode

The test results show that the beam specimens without stiffeners

failed in local web buckling at the cope The predicted local web

buckling capacities (R wb) of specimens A1 and B1 using the Yam

equation are in good agreement with the test results as shown in

Table 4 Neither of the two specimens reached the yield moment

capacity or the shear capacity of the coped beam section By providing

longitudinal stiffeners to reinforce the cope the failure mode of the

reinforced coped beam specimens (except for specimen B3) consisted

of 1047298exural yielding of the full beam section at the maximum bending

moment location near the loading position to be then followed byweb crippling at the end of the cope between the longitudinal

stiffeners and the top 1047298ange of the full beam section Although the

stiffener extensions (ex) of the B-series specimens were slightly

smaller than the corresponding dc (due to fabrication errors)

specimen B2 showed that the longitudinal stiffeners were able to

delay the occurrence of web crippling until the development of

1047298exuralyielding of the full beam section near the loading position had

been reached However specimen B3 which had a longer cope length

(c) of 3153 mm compared to 2072 mm of specimen B2 failed in web

crippling and the specimen did not reach the plastic moment capacity

of the full beam section near the loading position as illustrated in

Table 4 Hence it can be seen that the stiffener extension requirement

for longitudinal stiffeners should also consider the effects of cope

length in addition to cope depth

For the specimens with both longitudinal and transverse stiffeners

no web crippling was observed and the specimens were able to

develop 1047298ange buckling near the loading position after achieving the

plastic moment capacity of the full beam section It should be noted

that for the specimens which failed in 1047298exural yielding of the beam

section near the loading position the ratio of the corresponding

maximum bending moment at the loading position to the plastic

moment capacity ranges from 108 to 120 as shown in Table 4 This

high ratio is dueto thecombinedeffectsof momentgradientalong the

test beams and strain hardening of the steel material [14] It should

also be noted that the applied moment at the end of cope (M co) is less

than the corresponding moment capacity of the coped section eitherwith or without the longitudinal stiffeners (Mpco) for all of the

specimens as shown in Table 4

43 Effects of longitudinal stiffeners

As mentioned above longitudinal stiffeners are able to improve

the capacity of coped beam specimens signi1047297cantly by forcing the

occurrence of 1047298exural yielding of the full beam section near the

loading position prior to the development of webcrippling (except for

specimen B3) The ratio of the maximum bending moment at the

loading position to the plastic moment capacity of the specimens

rangesfrom 089 to 115 forthe specimenswith longitudinalstiffeners

only In order to illustrate the improved performance of thereinforcedcoped beam specimens the curves of maximum bending moment

versus beam de1047298ection at the loading position are shown in Fig 12 It

should be noted that specimens A2 B2 and B3 only have a stiffener

extension (ex) equal toabout1dc whereas specimen A3 has a stiffener

extension (ex) of about 2dc Although specimens A2 and B2 were able

to develop the plastic moment capacity of the full beam section

Fig 12 shows that the moment versus de1047298ection curves of these

specimens descend abruptly once they have reached the maximum

applied moment due to the development of web crippling However

for specimens A3 which had a stiffener extension (ex) equal to about

2dc the moment versus de1047298ection curves show a more gradual

descending branch with a signi1047297cant increase in ultimate de1047298ection

prior to the occurrence of web crippling as shown in Fig 12 In

addition Table 4 shows that for specimens A2 A3 B2 and B3 the ratio

Table 4

Summary of moment and shear capacities of specimens

Test

specimens

R u(kN)

Mmax

(kNm)

Mco

(kNm)

Mp

(kNm)

Mpco

(kNm)

R wb

(kN)

R vy(kN)

Mmax

Mp

Mco

Mpco

R uR wb

R uR vy

Stiffener

type

Failure

mode

A1 2019 1340 384 1828 430 1985 3463 073 089 102 058 Without WB

A2 3056 2095 628 1851 1224 ndash 3558 113 051 ndash 086 L Y ndashR

A3 3290 2165 579 1875 1229 ndash 3487 115 047 ndash 094 L Y ndashR

A4 3275 2096 512 1842 1193 ndash 3511 114 043 ndash 093 L+ T Y ndashF

A5 3403 2218 582 1853 1201 ndash 3516 120 048 ndash 097 L+ T Y ndashF

B1 1495 993 282 1849 322 1557 2997 054 088 096 050 Without WBB2 2939 1983 570 1834 961 ndash 2950 108 059 ndash 100 L Y ndashR

B3 2407 1600 695 1799 941 ndash 3006 089 074 ndash 080 L R

B4 3188 2137 625 1787 921 ndash 2930 120 068 ndash 109 L+ T Y ndashF

B5 3330 2186 588 1825 947 ndash 2986 120 062 ndash 112 L+ T Y ndashF

Note R u = test ultimate reaction at the coped end of the beam specimens

Mmax = test maximum bending moment of the beam specimens at the loading position

Mco = test bending moment of the beam specimens at the end of cope ( Fig 4)

Mp = plastic moment capacity of full beam section

Mpco = plastic moment capacity of the coped section with longitudinal stiffeners (specimens A2ndashA5 and B2ndashB5) or yield moment capacity of the coped section without

stiffeners (specimens A1 and B1)

R wb = local web buckling capacity of specimens without stiffeners according to Yam equations [6]

R vy = shear capacity of the coped beam section

L = longitudinal stiffeners T = transverse stiffeners WB = web buckling

R = rigid body movement of stiffener due to web crippling

Y ndashR = yielding of full beam section followed by rigid body movement of stiffener due to web crippling

Y ndashF = yielding of full beam section followed by 1047298ange local buckling near loading position

1756 MCH Yam et al Journal of Constructional Steel Research 67 (2011) 1749ndash1759

7182019 Experimental study of the strength and behaviour of reinforced coped beams

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of the ultimate reaction (R u) to the shear capacity of the coped section

ranges from 08 to 10

Based on the test results and the above discussion it can be seen

that reinforcing coped beams using a pair of longitudinal stiffeners

with a stiffener extension of 1dc is able to improve the capacity of the

beams signi1047297cantly However a longer stiffener extension (2dc used

in this test programme) was able to provide a more stable and more

gradual coped beam unloading behaviour after the full beam section

reaches its plastic moment capacity

44 Effects of combined longitudinal and transverse stiffeners

The test results show that when the specimens (A4 A5 B4 and B5)

were reinforced by both longitudinal and transverse stiffeners the

beam specimens were able to achieve the plastic moment capacity of

the full beam section with a 1047297nal failure mode of 1047298ange local buckling

near the loading position In addition the ultimate reaction (R u) of

specimens B4 and B5 reached the shear capacity of the coped sectionas shown in Table 4 The maximum bending moment versus beam

de1047298ection curves at the loading position for specimens A4 A5 B4 and

B5 are shown in Fig 13 It can be seen from the 1047297gure that all the

curves show a typical moment versus de1047298ection behaviour where the

beams are able to sustain the maximum applied moment with

considerable beam de1047298ection As shown in Table 4 the ratio of the

maximum bending moment at the loading position to the plastic

moment capacity of the specimens ranges from 114 to 120 and the

ratio of the ultimate reaction (R u) to the shear capacity of the coped

section varies between 093 and 112 Hence it can be seen that the

combined longitudinal and transverse stiffeners were able to develop

the capacity of either the coped section (except for specimen A4) or

the full beam section of the specimens and also prohibited the

occurrence of web crippling at the end of the cope Fig 14 shows the

curves of applied load versus lateral displacement of the web at the

end of the cope for specimens B4 and B5 The 1047297gure illustrates that

there is a lateral web movement of about 7 mm for specimen B4

However almost no lateral movement was observed for specimen B5

which had the double transverse stiffeners

Based on the test results and the above discussion it can be seen

that the use of combined longitudinal and transverse stiffeners in

reinforcing coped beams improves the capacity of the beams

substantially by allowing failure to occur in either the coped section

(due to shear) or the full beam section (due to moment) In addition

the reinforced coped beams were able to sustain the maximum

applied load with considerable de1047298ection Furthermore the combinedlongitudinal and double transverse stiffeners prohibit lateral move-

ment of the web at the end of the cope and hence eliminate the

possibility of web crippling

45 Effects of cope depth and cope length

All the specimens had a cope length (c) of approximately 210 mm

(cDasymp06) except for specimen B3 which had a cope length of

Vertical deflection δ (mm)

0

25

50

75

100

125

150

175200

225

250

0 3 6 9 12 15 18 21 24 27 30 33 36

M a x i m u m m o m e n t M m a x

( k N m )

P

R

V

Mmax

Mp = 1827 kNm

A4

B5

A5

B4

Fig 13 Moment versus de1047298ection curves for specimens A4 A5 B4 and B5

Vertical deflection δ (mm)

0

25

50

75

100

125

150

175

200

225

250

0 3 6 9 12 15 18 21 24 27 30 33 36

P

R

V

Mmax

A2

B2

A3

B3

Mp= 184 kNm

M a x i m u m

m o m e n t M m a x

( k N m )

Fig 12 Moment versus de1047298ection curves for specimens A2 A3 B2 and B3

1757MCH Yam et al Journal of Constructional Steel Research 67 (2011) 1749ndash1759

7182019 Experimental study of the strength and behaviour of reinforced coped beams

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315 mm (cDasymp09) The cope depth (dc) of the B-series specimens

was about 105 mm (dcDasymp03) whereas the cope depth of the A-

series specimens was about 60 mm (dcDasymp018) For specimens A1

and B1 which did not have stiffeners increasing the cope depth

causes a decrease in the web buckling capacity of the specimen as

shown in Table 4 For the specimens with stiffeners however

increasing the cope depth does not affect the capacity of the

specimens signi1047297cantly as shown in the table since the stiffeners are

able to strengthen the coped section such that web crippling does not

occur prior to the development of the full beam section plastic

moment capacity When comparing the test results of specimen B2 to

those of specimenB3 it can be seenthatincreasing the cope length by

52 (with the same stiffener extension of about 1dc) the capacity of

the beam specimens is decreased by 18 In fact the failure mode of specimen B3 is that of web crippling at the end of the cope instead of

1047298exural yielding of the full beam section near the loading position

Hence it can be seen that the reinforcement detail requirement of

coped beams should include the in1047298uence of both the cope length and

the cope depth

5 Proposed modi1047297cation to the current reinforcement details for

coped beams

As mentioned above the current reinforcement details for coped

beams are based on the work by Cheng et al [4] details which have

also been adopted by the AISC Steel Construction Manual [9] as

shown in Fig 3 According to the 1047297gure for coped beams (htwle60)

reinforced with longitudinal stiffeners the stiffener extension (ex)must be at least equal to or greater than the cope depth (d c) The

reinforced coped beam is then checked for 1047298exural yielding of the

reinforced section and a local web buckling check of the coped section

is not required

Based on the test results it can be seen that the coped beam

specimens (except for specimen B3) which were reinforced with

longitudinal stiffeners according to the current reinforcement details

were able to reach the plastic moment capacity of the full beam section

and no bending failure was observed in the reinforced section In

addition the ultimate reactions of the specimens were also close to the

shear capacity of thecoped section ForspecimenB3 which hada longer

cope length (cDasymp09 comparingto cDasymp06 of other specimens) web

crippling failure was observed prior to reaching the plastic moment

capacity of the full beam section The test results also show that

specimen A2 which had a stiffener extension of 2dc exhibited more

ductile behaviour For the specimens with both longitudinal and

transverse (single or double) stiffeners the beams were able to reach

the plastic moment capacity of the full beam section with ductile

behaviour and the ultimate reactions of the specimens were very close

to or exceeded the shear capacity of the coped section

Basedon the limited test data andtheabovediscussion a modi1047297cation

to the reinforcement details for coped beams is proposed as follows

For coped beams with htwle60 dcDle03 and cDle06 only

longitudinal stiffeners are required and the length of the

longitudinal stiffeners (L x) is

L = c + eX where eX ge 2dc

eth4THORN

For coped beams with htwle60 dcDle03 and 06lecDle09 both

longitudinal and transverse (single) stiffeners are required and the

lengths of the longitudinal (L x) and thetransverse (L y) stiffeners are

L x = c + ex where eX ge dc

L y = dc + ey where ey ge dc eth5THORN

All the symbols have been de1047297ned in Fig 4 It should be noted

that the above preliminary recommendations of the reinforcement

details for coped beam are based on limited test data Further

numerical work is underway to systematically examine the rein-

forcement requirements for a wider range of cope details in order toincrease the range of applicability of the above recommendations

6 Summary and conclusions

A total of 10 full-scale tests were conducted to investigate the

strength and behaviour of reinforced coped steel I-beams The main

test parameters included the length of longitudinal stiffeners (L x)

length of transverse stiffeners (L y) combined longitudinal and

transverse stiffeners double transverse stiffeners and the cope details

(cope depth (dc) and cope length (c)) For the coped beam specimens

without stiffeners local web buckling failure occurred in the cope For

the specimens with longitudinal stiffeners only the general failure

mode was 1047298exural yielding of the full beam section at the location of

maximum bending moment followed by web crippling at the end of

0

100

200

300

400

500

600

-2 -1 0 1 2 3 4 5 6 7 8

B5

B4

Lateral displacement of web at end of cope (mm)

A p p l i e d l o a

d

P ( k N )

P

LVDT

Specimen B4

P

LVDT

Specimen B5

Fig 14 Applied load versus lateral displacement curves for specimens B4 and B5

1758 MCH Yam et al Journal of Constructional Steel Research 67 (2011) 1749ndash1759

7182019 Experimental study of the strength and behaviour of reinforced coped beams

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the cope between the longitudinal stiffeners and the top 1047298ange of the

full beam section In contrast for the specimens with combined

longitudinal and transverse stiffeners the general failure mode was

1047298exural yielding of the full beam section at the location of maximum

bending moment followed by 1047298ange local buckling near the loading

position

Thetest results show that thereinforcementswere able to increase

the capacity of the coped beam specimens signi1047297cantly The ratio of

the maximum bending moment at the loading position to the plasticmoment capacity of the full beam section of the reinforced coped

beam specimens rangedfrom 089 to 120 andthe ratio of the ultimate

reaction (R u) to the shear capacity of the coped section varied

between 080 and 112 The test results also illustrate that in addition

to the cope depth the cope length (c) also affected the behaviour and

strength of reinforced coped beams In addition the specimens with

either a longer stiffener extension (ex) for the longitudinal stiffeners

or combined longitudinal and transverse stiffeners were able to

sustain the maximum applied load with considerable de1047298ection

Based on the limited test data a modi1047297cation to the currently

recommended reinforcement details for coped beams has been

proposed The proposed reinforcement details included the in1047298uence

of various cope details A numerical study of reinforced coped beams

is currently underway to consider a wider range of cope details in

order to increase the range of applicability of the proposed

reinforcement details for coped beams

Acknowledgements

The work described in this paper was fully supported by a

grant from the Research Grants Council of the Hong Kong Special

Administrative Region China (Project No PolyU 532908E) The

assistance of Mr TL Ip Mr CH Leong and Mr SL Meng in conduct-

ing the tests is also acknowledged

References

[1] Birkemoe PC Gilmor MI Behavior of bearing critical double-angle beamconnections Engineering Journal AISC 197815(4)109ndash15

[2] Yura JA Birkemoe PC Ricles JM Beam web shear connections an experimentalstudy Journal of the Structural Division ASCE 1982108(ST2)311ndash25

[3] Ricles JM Yura JA Strength of double-row bolted-web connections Journal of Structural Engineering ASCE 1983109(12)126ndash42[4] Cheng JJ Yura JA Johnson CP Design and behavior of coped beams Ferguson

Structural Engineering Laboratory ReportNo 84-1 Department of Civil EngineeringUniversity of Texas July 1984

[5] Cheng JJR Yura JA Local web buckling of coped beams Journal of StructuralEngineering ASCE 1986112(10)2314ndash31

[6] Aalberg A Larsen PK Local web buckling of coped beams Nordic SteelConstruction Conference NSCC 2001 Proceedings Helsinki Finland 18ndash20 June2001

[7] Yam MCH Lam ACC Iu VP Cheng JJR The local web buckling strength of coped steel I-beam Journal of Structural Engineering ASCE 2003129(1)3ndash11

[8] American Institute of Steel Construction Steel Construction Manual One EastWacker Drive Suite 700 Chicago Illinoisthird ed 2005 p 60601ndash1802

[9] Yam MCH Lam ACC Wei F Chung KF The local web buckling strength of stiffened coped steel-I-beam International Journal of Steel Structures20077(2)129ndash38

[10] LamACC Yam MCHFu CKM ExperimentalInvestigation of thelocal web buckling

strength of coped steel I-beam with and without stiffeners The 10th East Asia-Paci1047297c Conference on Structural Engineering and Construction BangkokThailand 2006 p 559ndash64 August 3ndash5

[11] InstituteSteelConstruction Steelwork Design Guideto BS5950-12000 Volume 1Section Properties Member Capacities6th ed 2001

[12] British Standards Institution (BSI) BS EN 10025-22004 Hot Rolled Products Of Structural Steels mdash Part 2 Technical Delivery Conditions for Non-Alloy StructuralSteels London 2004

[13] Vinnakota S Steel Structures Behavior and LRFD McGraw Hill 2006[14] American Society of Civil Engineers (ASCE) Welding Research Council (WRC)

Plastic Design in Steel A Guide and Commentary New York New York2nd ed 1971

1759MCH Yam et al Journal of Constructional Steel Research 67 (2011) 1749ndash1759

Page 2: Experimental study of the strength and behaviour of reinforced coped beams

7182019 Experimental study of the strength and behaviour of reinforced coped beams

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available experimental data is insuf 1047297cient to substantiate the current

reinforcement details of coped beams Therefore the main objective

of the study presented in this paper was to provide more

experimental evidence on the strength and behaviour of reinforced

coped beams In addition a newly developed reinforcement detail

based on previous research results was also examined in this

experimental programme The experimental data will also be used

to validate a 1047297nite element model for a parametric study and the

results of that study will be reported in another research paper

2 Experimental programme

21 Test specimens

A total of 10 full-scale tests were conducted in the experimental

programme to investigate the strength and behaviour of reinforced

coped steel I-beams The main test parameters included the length of

longitudinal stiffeners (L x) length of transverse stiffeners (L y)

combined longitudinal and transverse stiffeners double transverse

stiffeners and cope details (cope depth (dc) and cope length (c)) The

test specimens are illustrated schematically in Fig 4 The measured

beam dimensions the cope details and the reinforcement details of

the specimens are shown in Table 1 The cope details and dimensions

were selected to ensure that the test results were able to illustrate the

effects of the reinforcement on strengthening the coped beam

specimens In addition the test results which considered a wide

range of cope details and dimensions can be used to properly validate

a 1047297nite element model for further parametric study Five test beam

specimens 34 m long were fabricated using the universal beam

section UB356times 127times33 (SCI Guide [11]) and Grade S355 steel (BS EN10025-2 2004 [12]) The test beam specimens were coped at both

ends with relevant reinforcement details Both ends of the test beams

were designed as separate test specimens with different cope and

reinforcement details A diagram of a typical test beam is shown in

Fig 5 Table 1 shows that two cope lengths (c approximately equal to

210 mm and 315 mm) and two cope depths (d c approximately equal

to 60 mm and105 mm) were used to form thecope details Thelength

of the longitudinal stiffeners varies approximately between 265 mm

and 412 mm corresponding to a stiffener extension (ex) ofabout one dc

beyondthe endof thecopeexcept forspecimenA3 As shown in Table 1

a stiffener extension of about 2dc was used for specimen A3 The length

(L y) of the transverse stiffeners was approximately equal to 2dc It

should be noted that the variations in the length of stiffeners the

stiffener extension and the cope details were due to fabrication errors

The width and the thickness of the stiffeners were 60 mm and 8 mm

respectively The stiffeners were welded to the beam web using a 1047297llet

weld and a partial penetration butt weld and theweld sizewas 4 mmas

shown in Fig 4 Class 42 electrodes were used to produce the welds

As shown in Table 1 specimens A1 and B1 were the control

specimens that did not have stiffeners in the cope The results for

these two specimens were compared with those of the other

specimens with various types of stiffeners in order to illustrate the

effectiveness of the reinforcement details In general a cope depth

(dc) of about 60 mm was used for the A-series specimens whereas a

cope depth of 105 mm was used for the B-series specimens as shown

in the table Specimens A2 A3 B2 and B3 were used to examine the

Cope

Bolted clip angles Welded end plate

Fig 1 Coped beam connections

(b) Block shear failure of

welded end connection

(a) Local web bucking failure

Top

flange

Buckled webBuckled web

Fig 2 Coped beam failure modes

(c) Combined longitudinal and

transverse stiffeners

(a) Longitudinal stiffeners

Shear

connection

Longitudinal stiffeners

dcdc

dc

c dc dc

(b) Doubler plate

Doubler plate

Shear

connection

c

Shear

connection

c

Transverse stiffeners

Longitudinal stiffeners

Fig 3 Coped beams reinforcement details

1750 MCH Yam et al Journal of Constructional Steel Research 67 (2011) 1749ndash1759

7182019 Experimental study of the strength and behaviour of reinforced coped beams

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effectiveness of providing longitudinal stiffeners at the cope in

improving the strength of coped beams as suggested by the previous

research results [4] The comparison of these test results was also able

to illustrate the effects of cope depth on the effectiveness of the

reinforcement details Specimen B3 which has a cope length of

315 mm (cDasymp09) was used to examine the in1047298uence of cope length

on the effectiveness of the reinforcement details Specimens A4 A5

B4 and B5 were employed to study the use of transverse stiffeners in

combination with longitudinal stiffeners in strengthening coped

beams As illustrated in Fig 4c a single pair of transverse stiffeners

was placed at the end of the cope for specimens A4 and B4 For

specimens A5 and B5 a double transverse stiffener arrangement was

used with an additional pair of transverse stiffeners placed at the end

of the longitudinal stiffeners as shown in Fig 4d This new

arrangement of transverse stiffeners is used to control the failure

mode of rigid body movement of the longitudinal stiffeners as

observed from previous test results [9]

Tension coupons were cut from the webs and the 1047298anges of the

test beams and also from the stiffeners In order to obtain the static

values of the yield strength and the ultimate strength of the materials

the stroke was held constant brie1047298y in the yield plateau the strain-

hardening range and near the ultimate strength level The average

im n A 1 n B1im n A2 A B2 n B i m n A 4 n B 4 T i l n l il fT i l l i l f i f f n ri m n A n B Fi 4 D il f im n ens)mm)(mm)Lx mmLmm x mm mm A1 3487 1253 57 83 623 2117

ndash ndash ndash ndash 061 018 A2

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static yield strength and the ultimate strength of the beams and the

stiffeners are listed in Table 2 Althoughthe samesteel grade as that of

the beam was originally requested for fabricating the stiffeners the

average yield strength and ultimate strength of the stiffeners obtained

from the tension coupon tests are signi1047297cantly lower than those of the

beams as shown in the table These lower values would be

incorporated in the calculation of the plastic moment capacity of the

reinforced section of the beams

22 Test setup

A schematic of the test setup is shown in Fig 6 The test beams

were simply supported with the coped end connected to a stub

column using M24 Grade 88 bolts Three washers (12 mm thick in

total) were used between the end plate of the beam and the column1047298ange in order to allow moderate rotation of the beam end and also to

prevent contact between the beam 1047298ange and the column 1047298ange due

to beam end rotation The end plate (10 mm thick) was welded to the

beam web using an 8 mm 1047297llet weld Typical details of the end plate

are shown in Fig 4 The beam specimens were loaded by a hydraulic

jack with a maximum capacity of 1000 kN The hydraulic jack was

located approximately 700 mm (about 2 times the beam depth) from

the stub column support This loading position was chosen in order to

prevent the concentrated load in1047298uencing the structural behaviour of

the coped region

To achieve the simply supported condition for the test beams

roller assemblies were used at the loading position and at the

supports to permit both horizontal movement and rotation of the

beam as shown in Fig 6 The test beams were prevented from lateral

movement near the loading position and near the beam ends by

lateral bracings Transverse web stiffeners were used to strengthen

the beams at the loading position and at the roller supports The

applied load and the reaction force were measured using load cells

23 Instrumentation and test procedure

The de1047298ection and movement of the test beams were measured

using linear variable differential transformers (LVDTs) The positions of

theLVDTs are shown in Fig 7 LVDTs were placed near the coped end to

record the lateral movement of the beam and to detect rigid body

movement of the longitudinal stiffeners Longitudinal strain gauges

were mounted on thebeam web near the end of thecope to record the

strain distribution across the beam depth as shown in Fig 7

The tests were conducted using load control in the early stage of

loading When the beams started to yield stroke control was used in

order to better capture the nonlinear load de1047298ection behaviour of thebeam specimens The test beams were gradually unloaded once the

maximum applied load was reached and the applied load started to

decrease signi1047297cantly Since both ends of the test beams were

designed as a test end once the test on one end of each beam was

completed the other end was then connected to the supporting stub

column for another test

3400

700 598 700699703

3 4 9

412

315 212

308 3 5 0

2 0 5

108105

Fig 5 Typical test beam

Table 2

Summary of the tension coupon test results

Coupon

specimens

Elastic

modulus E

Static yield

strength Fy

Static ultimate

strength Fu

Strain at

fracture

(MPa) (MPa) (MPa) ()

Beam 1047298ange 205000 354 484 243

Beam web 207800 366 483 241

Stiffener 199800 225 441 225

Note the values presented in the table are the average of four coupons for the webs

four coupons for the 1047298anges and two coupons for the stiffeners

Strong floor

Hydraulic

jack

Reaction frame

2000 mm (approx)

700 mm (approx)Boltedconnection

Fig 6 Test setup

1752 MCH Yam et al Journal of Constructional Steel Research 67 (2011) 1749ndash1759

7182019 Experimental study of the strength and behaviour of reinforced coped beams

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3 Test results

31 General

The test results are summarised in Table 3 The ultimate applied

load (Pu) and the corresponding in-plane de1047298ection (δ) at the loading

position are presented in the table The ultimate reaction (R u) and the

end moment (Mo) at the coped end were calculated based on the

measured applied load and the measured reaction at the other

support These end moments were caused by the small rotational

stiffness of the end plate connection However it is believed that these

end moments would not have signi1047297cant effect on the strength and

behaviour of the reinforced coped beam specimens This will be

further discussed in the following section

The general failure mode of the coped beam specimens without

stiffeners consisted of local web buckling in the cope as shown in

Fig 8a For the reinforced coped beam specimens however the 1047297nal

failure mode depended on the types of stiffener As shown in Table 3

specimens A1 and B1 (which had no stiffeners) failed in local web

buckling at the cope and the corresponding in-plane de1047298ections wereonly about 4 to 5 mm For the specimens with longitudinal stiffeners

only (A2 A3 and B2) except for specimens B3 1047298exural yielding of the

full beam section occurred at the location of maximum bending

moment and subsequently the longitudinal stiffeners moved laterally

due to web crippling near the coped end as shown in Fig 8b For

specimen B3 which had a longer cope length (c) lateral rigid body

movement of the longitudinal stiffeners occurred without signi1047297cant

yielding of the full beam section at theloading positionFor specimens

A4 A5 B4 and B5 1047298exuralyieldingof thefull beam section occurred at

the location of maximum bending moment and subsequently the

1047298ange of the beam near the loading position buckled locally as

illustrated in Fig 8c For these specimens relatively small lateral

movement of the longitudinal stiffeners was observed In particular

for specimens A5 and B5 which had double transverse stiffeners

almost no lateral movement of the longitudinal stiffeners was

observed as shown in Fig 8d

32 Load de 1047298ection behaviour

The applied load versus de1047298ection curves of specimens A1ndashA5 and

specimens B1ndashB5 are shown in Figs 9 and 10 respectively As

mentioned above the main difference between the A-series specimens

and the B-series specimens was the depth of the cope (dc) For the A-

seriesspecimensa cope depth of about 60 mmwas used whereas a cope

depth of about 150 mm wasused forthe B-seriesspecimens Bothseries

of specimensconsideredthe effects of providingstiffeners in thecope on

the strength and behaviour of coped beams

In general the applied load versus de1047298ection curves showed linear

behaviour from the beginning of loading When the applied load

reached about 80 of the ultimate loads nonlinear load de1047298ection

behaviour was observed as illustrated in Figs 9 and 10 As shown in

the 1047297gures the applied load versus de1047298ection curves of specimens A1

and B1 showed an abrupt drop in the load carrying capacity after

reaching the ultimate loads due to web buckling failure of the

specimens For the specimens reinforced with longitudinal stiffeners

(A2 A3 B2 and B3) except for specimen A3 which had a longer

stiffener extension (ex) once the ultimate loads were reached the

applied load versus de1047298ection curves descended rapidly due to web

crippling at the end of the cope together with a lateral rigid body

movement of the stiffeners For specimen A3 however the beam was

able to continue deforming without signi1047297cant drop in the load

carrying capacity after reaching the ultimate load As shown in

Table 3 the de1047298ection of specimen A3 corresponding to the ultimate

load was 215 mm which was signi1047297cantly larger than those for the

other specimens reinforced with longitudinal stiffeners

The applied load versus de1047298ection curves of the specimens whichhad both longitudinal and transverse stiffeners (specimens A4 A5 B4

and B5) show that the specimens were able to sustain larger

de1047298ections at the ultimate load levels as illustrated in Figs 9 and 10

As mentioned above these specimens failed in 1047298exural yielding of the

full beam section and theapplied load started to decrease when 1047298ange

local buckling occurred near the loading position The de1047298ections of

these specimens corresponding to the ultimate loads were generally

larger than those for the specimens with only longitudinal stiffeners

(except for specimen A3)

Applied load

Longitudinal stiffener

Strain gauge

LVDT (vertical)

LVDT (lateral)

Legend

Fig 7 Typical layout of strain gauges and LVDTs

Table 3

Summary of test results

Test specimens Ultimate load

Pu (kN)

In-plane de1047298ection

δ (mm)

Ultimate reaction

R u (kN)

Ultimate end-moment

Mo (kNm)

Stiffener type Failure mode

A1 3084 478 2019 633 Without WB

A2 4720 948 3056 354 L Y ndashR

A3 5039 215 3290 145 L Y ndashR

A4 4940 143 3275 185 L+ T Y ndashF

A5 5186 229 3403 166 L+ T Y ndashF

B1 2287 399 1495 464 Without WB

B2 4521 916 2939 684 L Y ndashR

B3 3686 804 2407 879 L R

B4 4889 171 3188 832 L+ T Y ndashF

B5 5076 235 3330 142 L+ T Y ndashF

Note L = longitudinal stiffeners T = transverse stiffeners WB = web buckling

R = rigid body movement of stiffener due to web crippling

Y ndashR = yielding of full beam section followed by rigid body movement of stiffener due to web crippling

Y ndash

F = yielding of full beam section followed by 1047298ange local buckling near loading position

1753MCH Yam et al Journal of Constructional Steel Research 67 (2011) 1749ndash1759

7182019 Experimental study of the strength and behaviour of reinforced coped beams

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33 Strain distribution

In general at least tenstrain gaugeswere mounted on the web the

top 1047298ange of the beams and the stiffeners as shown in Fig 7 Two

strain gauges were also placed on the top and bottom 1047298anges of thebeam approximately 1000 mm from the coped end support to help

monitor the loading applied to the beam Only the load versus strain

curves for the B-series specimens were used to illustrate the strain

distributions in the web at the coped end of the beam as shown in

Fig 11 The strain distributions for the A-series specimens are similar

to those of the B-series specimens

Fig 11 illustrates the elastic strain distributions in the web at an

applied load of 150 kN Asexpected it can beseen from the 1047297gure that

the longitudinal strains in the web near the top of the cope reduce

signi1047297cantly when stiffeners are used in the beam specimens The

location of the theoretical neutral axis of the reinforced section is in

reasonable agreement with the strain readings as illustrated in the

1047297gure except for specimen B4 For this specimen the corresponding

strain gauge was located very close to the transverse stiffeners andhence the readings might have been affected by the stress concen-

tration effect near the stiffeners The theoretical strain distributions of

specimen B1 (without stiffeners) and specimens B2ndashB5 (with

stiffeners) are also included in Fig 11 As can be seen from the 1047297gure

the theoretical strain distributions of specimen B1 which are

determined based on the coped beam section properties are in

general larger than those of the test results This might be due to the

fact that thestrain gaugeswere located in the web area between the

coped beam section and the full beam section and hence the

(d) No lateral movement of longitudinal

stiffeners of specimen B5

Transverse

stiffeners

Longitudinalstiffeners

(a) Buckled web of specimen A1

Top view

Buckled

web

Top

flange

Bottom

flange

Side view

Buckling line

(b) Web crippling and lateral movement of

longitudinal stiffeners of specimen B2

Lateral

movement of

stiffeners

Web

crippling

(c) Yielding of the full beam section and local flange

buckling at the loading position of specimen B5

Flange buckling

Yielding of

full beam section

Fig 8 Typical failure mode of the test specimens

0

50

100

150

200

250

300

350

400450

500

550

0 4 8 12 16 20 24 28 32 36 40 44

P

R

V

M

A1 A2 A4 A5 A3

A p p l i e d l o a d P ( k N )

Vertical deflection δ (mm)

δ

Fig 9 Load versus de1047298ection curves mdash

specimens A1ndash

A5

1754 MCH Yam et al Journal of Constructional Steel Research 67 (2011) 1749ndash1759

7182019 Experimental study of the strength and behaviour of reinforced coped beams

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strain gauge readings might have been in1047298uenced by the full beam

section Moreover the theoretical strain distributions of specimens

B2ndashB5 are in reasonable agreement with the test results as shown

in Fig 11

4 Discussion of the test results

41 General

To help discuss the test results the test maximum bending

moment at the loading position (Mmax) and at the end of the cope

(Mco) of the beam specimens were evaluated The corresponding

values are shown in Table 4 The shear capacity of the coped beam

section (R vy) the moment capacity of the coped beam section with or

without longitudinal stiffeners (Mpco) and the plastic moment

capacity of the full beam section (Mp) are also included in the table

for comparison To predict the local web buckling capacity (R wb) of

specimens A1 and B1 the design equations proposed by Yam et al [7]

were used and the predicted values are shown in Table 4 as well Theweb buckling equations for coped beams proposed by Yam et al [7]

are as follows

R Wb = τcrtW Dminusdceth THORN eth1THORN

τcr = Ks

π 2

E

12 1minusv2 tW

ho

2

eth2THORN

Ks = a

h o

c b

eth3aTHORN

a = 138minus179dc

D eth3bTHORN

b = 364 dc

D

2

336 dc

D

+ 155 eth3cTHORN

where R wb=local web buckling capacity of coped beams ks=shear

bucklingcoef 1047297cient E=elasticmodulusν =Poissons ratio ho=height

of web of T-section and other symbols have been de1047297ned above The

measureddimensionsof thebeam specimens andthe materialproperties

obtained from the tension coupon tests were used to calculate the

capacities of the specimens

As mentioned above end moments were developed in the end

plate connections In fact the ultimate end moments of the specimensvaried between 2 and 10 of the corresponding fully 1047297xed end

moment According to Vinnakota [13] for a simple shear connection

such as the end plate connection used in this study the connection

end moment may range from 5 to 20 of the fully 1047297xed moment

Therefore the ultimate end moments developed in the specimens

0

50

100

150

200

250

300

350

400

450

500

550

A p p

l i e d l o a d P ( k N )

Vertical deflection δ (mm)

0 3 3 3 6 de1047298e ct o nc ur ve ss pe cm en s B1 B 5d str but ons for the B ser es spec mens21755M C H Yam et a Journa of Construct ona Stee Research 67 (2011) 1749 1759

7182019 Experimental study of the strength and behaviour of reinforced coped beams

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were reasonable In addition as shown in Table 4 except for

specimens A1 B1 (failed in local web buckling) and B3 (with a longer

cope length) the ratio of the maximum bending moment to the

corresponding plastic moment capacity ranged from 108 to 120 and

the ultimate end moments of the specimens were only 17 to 88 of

the corresponding maximum bending moments If there was no end

moment developed at the connection the ultimate reactions of the

specimens would only be slightly decreased and the specimens could

still reach the plastic moment capacity Hence it can be seen that the

effectiveness of the reinforcement in strengthening the coped beam

specimens would not be affected due to the in1047298uence of the end

moment

42 Failure mode

The test results show that the beam specimens without stiffeners

failed in local web buckling at the cope The predicted local web

buckling capacities (R wb) of specimens A1 and B1 using the Yam

equation are in good agreement with the test results as shown in

Table 4 Neither of the two specimens reached the yield moment

capacity or the shear capacity of the coped beam section By providing

longitudinal stiffeners to reinforce the cope the failure mode of the

reinforced coped beam specimens (except for specimen B3) consisted

of 1047298exural yielding of the full beam section at the maximum bending

moment location near the loading position to be then followed byweb crippling at the end of the cope between the longitudinal

stiffeners and the top 1047298ange of the full beam section Although the

stiffener extensions (ex) of the B-series specimens were slightly

smaller than the corresponding dc (due to fabrication errors)

specimen B2 showed that the longitudinal stiffeners were able to

delay the occurrence of web crippling until the development of

1047298exuralyielding of the full beam section near the loading position had

been reached However specimen B3 which had a longer cope length

(c) of 3153 mm compared to 2072 mm of specimen B2 failed in web

crippling and the specimen did not reach the plastic moment capacity

of the full beam section near the loading position as illustrated in

Table 4 Hence it can be seen that the stiffener extension requirement

for longitudinal stiffeners should also consider the effects of cope

length in addition to cope depth

For the specimens with both longitudinal and transverse stiffeners

no web crippling was observed and the specimens were able to

develop 1047298ange buckling near the loading position after achieving the

plastic moment capacity of the full beam section It should be noted

that for the specimens which failed in 1047298exural yielding of the beam

section near the loading position the ratio of the corresponding

maximum bending moment at the loading position to the plastic

moment capacity ranges from 108 to 120 as shown in Table 4 This

high ratio is dueto thecombinedeffectsof momentgradientalong the

test beams and strain hardening of the steel material [14] It should

also be noted that the applied moment at the end of cope (M co) is less

than the corresponding moment capacity of the coped section eitherwith or without the longitudinal stiffeners (Mpco) for all of the

specimens as shown in Table 4

43 Effects of longitudinal stiffeners

As mentioned above longitudinal stiffeners are able to improve

the capacity of coped beam specimens signi1047297cantly by forcing the

occurrence of 1047298exural yielding of the full beam section near the

loading position prior to the development of webcrippling (except for

specimen B3) The ratio of the maximum bending moment at the

loading position to the plastic moment capacity of the specimens

rangesfrom 089 to 115 forthe specimenswith longitudinalstiffeners

only In order to illustrate the improved performance of thereinforcedcoped beam specimens the curves of maximum bending moment

versus beam de1047298ection at the loading position are shown in Fig 12 It

should be noted that specimens A2 B2 and B3 only have a stiffener

extension (ex) equal toabout1dc whereas specimen A3 has a stiffener

extension (ex) of about 2dc Although specimens A2 and B2 were able

to develop the plastic moment capacity of the full beam section

Fig 12 shows that the moment versus de1047298ection curves of these

specimens descend abruptly once they have reached the maximum

applied moment due to the development of web crippling However

for specimens A3 which had a stiffener extension (ex) equal to about

2dc the moment versus de1047298ection curves show a more gradual

descending branch with a signi1047297cant increase in ultimate de1047298ection

prior to the occurrence of web crippling as shown in Fig 12 In

addition Table 4 shows that for specimens A2 A3 B2 and B3 the ratio

Table 4

Summary of moment and shear capacities of specimens

Test

specimens

R u(kN)

Mmax

(kNm)

Mco

(kNm)

Mp

(kNm)

Mpco

(kNm)

R wb

(kN)

R vy(kN)

Mmax

Mp

Mco

Mpco

R uR wb

R uR vy

Stiffener

type

Failure

mode

A1 2019 1340 384 1828 430 1985 3463 073 089 102 058 Without WB

A2 3056 2095 628 1851 1224 ndash 3558 113 051 ndash 086 L Y ndashR

A3 3290 2165 579 1875 1229 ndash 3487 115 047 ndash 094 L Y ndashR

A4 3275 2096 512 1842 1193 ndash 3511 114 043 ndash 093 L+ T Y ndashF

A5 3403 2218 582 1853 1201 ndash 3516 120 048 ndash 097 L+ T Y ndashF

B1 1495 993 282 1849 322 1557 2997 054 088 096 050 Without WBB2 2939 1983 570 1834 961 ndash 2950 108 059 ndash 100 L Y ndashR

B3 2407 1600 695 1799 941 ndash 3006 089 074 ndash 080 L R

B4 3188 2137 625 1787 921 ndash 2930 120 068 ndash 109 L+ T Y ndashF

B5 3330 2186 588 1825 947 ndash 2986 120 062 ndash 112 L+ T Y ndashF

Note R u = test ultimate reaction at the coped end of the beam specimens

Mmax = test maximum bending moment of the beam specimens at the loading position

Mco = test bending moment of the beam specimens at the end of cope ( Fig 4)

Mp = plastic moment capacity of full beam section

Mpco = plastic moment capacity of the coped section with longitudinal stiffeners (specimens A2ndashA5 and B2ndashB5) or yield moment capacity of the coped section without

stiffeners (specimens A1 and B1)

R wb = local web buckling capacity of specimens without stiffeners according to Yam equations [6]

R vy = shear capacity of the coped beam section

L = longitudinal stiffeners T = transverse stiffeners WB = web buckling

R = rigid body movement of stiffener due to web crippling

Y ndashR = yielding of full beam section followed by rigid body movement of stiffener due to web crippling

Y ndashF = yielding of full beam section followed by 1047298ange local buckling near loading position

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7182019 Experimental study of the strength and behaviour of reinforced coped beams

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of the ultimate reaction (R u) to the shear capacity of the coped section

ranges from 08 to 10

Based on the test results and the above discussion it can be seen

that reinforcing coped beams using a pair of longitudinal stiffeners

with a stiffener extension of 1dc is able to improve the capacity of the

beams signi1047297cantly However a longer stiffener extension (2dc used

in this test programme) was able to provide a more stable and more

gradual coped beam unloading behaviour after the full beam section

reaches its plastic moment capacity

44 Effects of combined longitudinal and transverse stiffeners

The test results show that when the specimens (A4 A5 B4 and B5)

were reinforced by both longitudinal and transverse stiffeners the

beam specimens were able to achieve the plastic moment capacity of

the full beam section with a 1047297nal failure mode of 1047298ange local buckling

near the loading position In addition the ultimate reaction (R u) of

specimens B4 and B5 reached the shear capacity of the coped sectionas shown in Table 4 The maximum bending moment versus beam

de1047298ection curves at the loading position for specimens A4 A5 B4 and

B5 are shown in Fig 13 It can be seen from the 1047297gure that all the

curves show a typical moment versus de1047298ection behaviour where the

beams are able to sustain the maximum applied moment with

considerable beam de1047298ection As shown in Table 4 the ratio of the

maximum bending moment at the loading position to the plastic

moment capacity of the specimens ranges from 114 to 120 and the

ratio of the ultimate reaction (R u) to the shear capacity of the coped

section varies between 093 and 112 Hence it can be seen that the

combined longitudinal and transverse stiffeners were able to develop

the capacity of either the coped section (except for specimen A4) or

the full beam section of the specimens and also prohibited the

occurrence of web crippling at the end of the cope Fig 14 shows the

curves of applied load versus lateral displacement of the web at the

end of the cope for specimens B4 and B5 The 1047297gure illustrates that

there is a lateral web movement of about 7 mm for specimen B4

However almost no lateral movement was observed for specimen B5

which had the double transverse stiffeners

Based on the test results and the above discussion it can be seen

that the use of combined longitudinal and transverse stiffeners in

reinforcing coped beams improves the capacity of the beams

substantially by allowing failure to occur in either the coped section

(due to shear) or the full beam section (due to moment) In addition

the reinforced coped beams were able to sustain the maximum

applied load with considerable de1047298ection Furthermore the combinedlongitudinal and double transverse stiffeners prohibit lateral move-

ment of the web at the end of the cope and hence eliminate the

possibility of web crippling

45 Effects of cope depth and cope length

All the specimens had a cope length (c) of approximately 210 mm

(cDasymp06) except for specimen B3 which had a cope length of

Vertical deflection δ (mm)

0

25

50

75

100

125

150

175200

225

250

0 3 6 9 12 15 18 21 24 27 30 33 36

M a x i m u m m o m e n t M m a x

( k N m )

P

R

V

Mmax

Mp = 1827 kNm

A4

B5

A5

B4

Fig 13 Moment versus de1047298ection curves for specimens A4 A5 B4 and B5

Vertical deflection δ (mm)

0

25

50

75

100

125

150

175

200

225

250

0 3 6 9 12 15 18 21 24 27 30 33 36

P

R

V

Mmax

A2

B2

A3

B3

Mp= 184 kNm

M a x i m u m

m o m e n t M m a x

( k N m )

Fig 12 Moment versus de1047298ection curves for specimens A2 A3 B2 and B3

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7182019 Experimental study of the strength and behaviour of reinforced coped beams

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315 mm (cDasymp09) The cope depth (dc) of the B-series specimens

was about 105 mm (dcDasymp03) whereas the cope depth of the A-

series specimens was about 60 mm (dcDasymp018) For specimens A1

and B1 which did not have stiffeners increasing the cope depth

causes a decrease in the web buckling capacity of the specimen as

shown in Table 4 For the specimens with stiffeners however

increasing the cope depth does not affect the capacity of the

specimens signi1047297cantly as shown in the table since the stiffeners are

able to strengthen the coped section such that web crippling does not

occur prior to the development of the full beam section plastic

moment capacity When comparing the test results of specimen B2 to

those of specimenB3 it can be seenthatincreasing the cope length by

52 (with the same stiffener extension of about 1dc) the capacity of

the beam specimens is decreased by 18 In fact the failure mode of specimen B3 is that of web crippling at the end of the cope instead of

1047298exural yielding of the full beam section near the loading position

Hence it can be seen that the reinforcement detail requirement of

coped beams should include the in1047298uence of both the cope length and

the cope depth

5 Proposed modi1047297cation to the current reinforcement details for

coped beams

As mentioned above the current reinforcement details for coped

beams are based on the work by Cheng et al [4] details which have

also been adopted by the AISC Steel Construction Manual [9] as

shown in Fig 3 According to the 1047297gure for coped beams (htwle60)

reinforced with longitudinal stiffeners the stiffener extension (ex)must be at least equal to or greater than the cope depth (d c) The

reinforced coped beam is then checked for 1047298exural yielding of the

reinforced section and a local web buckling check of the coped section

is not required

Based on the test results it can be seen that the coped beam

specimens (except for specimen B3) which were reinforced with

longitudinal stiffeners according to the current reinforcement details

were able to reach the plastic moment capacity of the full beam section

and no bending failure was observed in the reinforced section In

addition the ultimate reactions of the specimens were also close to the

shear capacity of thecoped section ForspecimenB3 which hada longer

cope length (cDasymp09 comparingto cDasymp06 of other specimens) web

crippling failure was observed prior to reaching the plastic moment

capacity of the full beam section The test results also show that

specimen A2 which had a stiffener extension of 2dc exhibited more

ductile behaviour For the specimens with both longitudinal and

transverse (single or double) stiffeners the beams were able to reach

the plastic moment capacity of the full beam section with ductile

behaviour and the ultimate reactions of the specimens were very close

to or exceeded the shear capacity of the coped section

Basedon the limited test data andtheabovediscussion a modi1047297cation

to the reinforcement details for coped beams is proposed as follows

For coped beams with htwle60 dcDle03 and cDle06 only

longitudinal stiffeners are required and the length of the

longitudinal stiffeners (L x) is

L = c + eX where eX ge 2dc

eth4THORN

For coped beams with htwle60 dcDle03 and 06lecDle09 both

longitudinal and transverse (single) stiffeners are required and the

lengths of the longitudinal (L x) and thetransverse (L y) stiffeners are

L x = c + ex where eX ge dc

L y = dc + ey where ey ge dc eth5THORN

All the symbols have been de1047297ned in Fig 4 It should be noted

that the above preliminary recommendations of the reinforcement

details for coped beam are based on limited test data Further

numerical work is underway to systematically examine the rein-

forcement requirements for a wider range of cope details in order toincrease the range of applicability of the above recommendations

6 Summary and conclusions

A total of 10 full-scale tests were conducted to investigate the

strength and behaviour of reinforced coped steel I-beams The main

test parameters included the length of longitudinal stiffeners (L x)

length of transverse stiffeners (L y) combined longitudinal and

transverse stiffeners double transverse stiffeners and the cope details

(cope depth (dc) and cope length (c)) For the coped beam specimens

without stiffeners local web buckling failure occurred in the cope For

the specimens with longitudinal stiffeners only the general failure

mode was 1047298exural yielding of the full beam section at the location of

maximum bending moment followed by web crippling at the end of

0

100

200

300

400

500

600

-2 -1 0 1 2 3 4 5 6 7 8

B5

B4

Lateral displacement of web at end of cope (mm)

A p p l i e d l o a

d

P ( k N )

P

LVDT

Specimen B4

P

LVDT

Specimen B5

Fig 14 Applied load versus lateral displacement curves for specimens B4 and B5

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the cope between the longitudinal stiffeners and the top 1047298ange of the

full beam section In contrast for the specimens with combined

longitudinal and transverse stiffeners the general failure mode was

1047298exural yielding of the full beam section at the location of maximum

bending moment followed by 1047298ange local buckling near the loading

position

Thetest results show that thereinforcementswere able to increase

the capacity of the coped beam specimens signi1047297cantly The ratio of

the maximum bending moment at the loading position to the plasticmoment capacity of the full beam section of the reinforced coped

beam specimens rangedfrom 089 to 120 andthe ratio of the ultimate

reaction (R u) to the shear capacity of the coped section varied

between 080 and 112 The test results also illustrate that in addition

to the cope depth the cope length (c) also affected the behaviour and

strength of reinforced coped beams In addition the specimens with

either a longer stiffener extension (ex) for the longitudinal stiffeners

or combined longitudinal and transverse stiffeners were able to

sustain the maximum applied load with considerable de1047298ection

Based on the limited test data a modi1047297cation to the currently

recommended reinforcement details for coped beams has been

proposed The proposed reinforcement details included the in1047298uence

of various cope details A numerical study of reinforced coped beams

is currently underway to consider a wider range of cope details in

order to increase the range of applicability of the proposed

reinforcement details for coped beams

Acknowledgements

The work described in this paper was fully supported by a

grant from the Research Grants Council of the Hong Kong Special

Administrative Region China (Project No PolyU 532908E) The

assistance of Mr TL Ip Mr CH Leong and Mr SL Meng in conduct-

ing the tests is also acknowledged

References

[1] Birkemoe PC Gilmor MI Behavior of bearing critical double-angle beamconnections Engineering Journal AISC 197815(4)109ndash15

[2] Yura JA Birkemoe PC Ricles JM Beam web shear connections an experimentalstudy Journal of the Structural Division ASCE 1982108(ST2)311ndash25

[3] Ricles JM Yura JA Strength of double-row bolted-web connections Journal of Structural Engineering ASCE 1983109(12)126ndash42[4] Cheng JJ Yura JA Johnson CP Design and behavior of coped beams Ferguson

Structural Engineering Laboratory ReportNo 84-1 Department of Civil EngineeringUniversity of Texas July 1984

[5] Cheng JJR Yura JA Local web buckling of coped beams Journal of StructuralEngineering ASCE 1986112(10)2314ndash31

[6] Aalberg A Larsen PK Local web buckling of coped beams Nordic SteelConstruction Conference NSCC 2001 Proceedings Helsinki Finland 18ndash20 June2001

[7] Yam MCH Lam ACC Iu VP Cheng JJR The local web buckling strength of coped steel I-beam Journal of Structural Engineering ASCE 2003129(1)3ndash11

[8] American Institute of Steel Construction Steel Construction Manual One EastWacker Drive Suite 700 Chicago Illinoisthird ed 2005 p 60601ndash1802

[9] Yam MCH Lam ACC Wei F Chung KF The local web buckling strength of stiffened coped steel-I-beam International Journal of Steel Structures20077(2)129ndash38

[10] LamACC Yam MCHFu CKM ExperimentalInvestigation of thelocal web buckling

strength of coped steel I-beam with and without stiffeners The 10th East Asia-Paci1047297c Conference on Structural Engineering and Construction BangkokThailand 2006 p 559ndash64 August 3ndash5

[11] InstituteSteelConstruction Steelwork Design Guideto BS5950-12000 Volume 1Section Properties Member Capacities6th ed 2001

[12] British Standards Institution (BSI) BS EN 10025-22004 Hot Rolled Products Of Structural Steels mdash Part 2 Technical Delivery Conditions for Non-Alloy StructuralSteels London 2004

[13] Vinnakota S Steel Structures Behavior and LRFD McGraw Hill 2006[14] American Society of Civil Engineers (ASCE) Welding Research Council (WRC)

Plastic Design in Steel A Guide and Commentary New York New York2nd ed 1971

1759MCH Yam et al Journal of Constructional Steel Research 67 (2011) 1749ndash1759

Page 3: Experimental study of the strength and behaviour of reinforced coped beams

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effectiveness of providing longitudinal stiffeners at the cope in

improving the strength of coped beams as suggested by the previous

research results [4] The comparison of these test results was also able

to illustrate the effects of cope depth on the effectiveness of the

reinforcement details Specimen B3 which has a cope length of

315 mm (cDasymp09) was used to examine the in1047298uence of cope length

on the effectiveness of the reinforcement details Specimens A4 A5

B4 and B5 were employed to study the use of transverse stiffeners in

combination with longitudinal stiffeners in strengthening coped

beams As illustrated in Fig 4c a single pair of transverse stiffeners

was placed at the end of the cope for specimens A4 and B4 For

specimens A5 and B5 a double transverse stiffener arrangement was

used with an additional pair of transverse stiffeners placed at the end

of the longitudinal stiffeners as shown in Fig 4d This new

arrangement of transverse stiffeners is used to control the failure

mode of rigid body movement of the longitudinal stiffeners as

observed from previous test results [9]

Tension coupons were cut from the webs and the 1047298anges of the

test beams and also from the stiffeners In order to obtain the static

values of the yield strength and the ultimate strength of the materials

the stroke was held constant brie1047298y in the yield plateau the strain-

hardening range and near the ultimate strength level The average

im n A 1 n B1im n A2 A B2 n B i m n A 4 n B 4 T i l n l il fT i l l i l f i f f n ri m n A n B Fi 4 D il f im n ens)mm)(mm)Lx mmLmm x mm mm A1 3487 1253 57 83 623 2117

ndash ndash ndash ndash 061 018 A2

7182019 Experimental study of the strength and behaviour of reinforced coped beams

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static yield strength and the ultimate strength of the beams and the

stiffeners are listed in Table 2 Althoughthe samesteel grade as that of

the beam was originally requested for fabricating the stiffeners the

average yield strength and ultimate strength of the stiffeners obtained

from the tension coupon tests are signi1047297cantly lower than those of the

beams as shown in the table These lower values would be

incorporated in the calculation of the plastic moment capacity of the

reinforced section of the beams

22 Test setup

A schematic of the test setup is shown in Fig 6 The test beams

were simply supported with the coped end connected to a stub

column using M24 Grade 88 bolts Three washers (12 mm thick in

total) were used between the end plate of the beam and the column1047298ange in order to allow moderate rotation of the beam end and also to

prevent contact between the beam 1047298ange and the column 1047298ange due

to beam end rotation The end plate (10 mm thick) was welded to the

beam web using an 8 mm 1047297llet weld Typical details of the end plate

are shown in Fig 4 The beam specimens were loaded by a hydraulic

jack with a maximum capacity of 1000 kN The hydraulic jack was

located approximately 700 mm (about 2 times the beam depth) from

the stub column support This loading position was chosen in order to

prevent the concentrated load in1047298uencing the structural behaviour of

the coped region

To achieve the simply supported condition for the test beams

roller assemblies were used at the loading position and at the

supports to permit both horizontal movement and rotation of the

beam as shown in Fig 6 The test beams were prevented from lateral

movement near the loading position and near the beam ends by

lateral bracings Transverse web stiffeners were used to strengthen

the beams at the loading position and at the roller supports The

applied load and the reaction force were measured using load cells

23 Instrumentation and test procedure

The de1047298ection and movement of the test beams were measured

using linear variable differential transformers (LVDTs) The positions of

theLVDTs are shown in Fig 7 LVDTs were placed near the coped end to

record the lateral movement of the beam and to detect rigid body

movement of the longitudinal stiffeners Longitudinal strain gauges

were mounted on thebeam web near the end of thecope to record the

strain distribution across the beam depth as shown in Fig 7

The tests were conducted using load control in the early stage of

loading When the beams started to yield stroke control was used in

order to better capture the nonlinear load de1047298ection behaviour of thebeam specimens The test beams were gradually unloaded once the

maximum applied load was reached and the applied load started to

decrease signi1047297cantly Since both ends of the test beams were

designed as a test end once the test on one end of each beam was

completed the other end was then connected to the supporting stub

column for another test

3400

700 598 700699703

3 4 9

412

315 212

308 3 5 0

2 0 5

108105

Fig 5 Typical test beam

Table 2

Summary of the tension coupon test results

Coupon

specimens

Elastic

modulus E

Static yield

strength Fy

Static ultimate

strength Fu

Strain at

fracture

(MPa) (MPa) (MPa) ()

Beam 1047298ange 205000 354 484 243

Beam web 207800 366 483 241

Stiffener 199800 225 441 225

Note the values presented in the table are the average of four coupons for the webs

four coupons for the 1047298anges and two coupons for the stiffeners

Strong floor

Hydraulic

jack

Reaction frame

2000 mm (approx)

700 mm (approx)Boltedconnection

Fig 6 Test setup

1752 MCH Yam et al Journal of Constructional Steel Research 67 (2011) 1749ndash1759

7182019 Experimental study of the strength and behaviour of reinforced coped beams

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3 Test results

31 General

The test results are summarised in Table 3 The ultimate applied

load (Pu) and the corresponding in-plane de1047298ection (δ) at the loading

position are presented in the table The ultimate reaction (R u) and the

end moment (Mo) at the coped end were calculated based on the

measured applied load and the measured reaction at the other

support These end moments were caused by the small rotational

stiffness of the end plate connection However it is believed that these

end moments would not have signi1047297cant effect on the strength and

behaviour of the reinforced coped beam specimens This will be

further discussed in the following section

The general failure mode of the coped beam specimens without

stiffeners consisted of local web buckling in the cope as shown in

Fig 8a For the reinforced coped beam specimens however the 1047297nal

failure mode depended on the types of stiffener As shown in Table 3

specimens A1 and B1 (which had no stiffeners) failed in local web

buckling at the cope and the corresponding in-plane de1047298ections wereonly about 4 to 5 mm For the specimens with longitudinal stiffeners

only (A2 A3 and B2) except for specimens B3 1047298exural yielding of the

full beam section occurred at the location of maximum bending

moment and subsequently the longitudinal stiffeners moved laterally

due to web crippling near the coped end as shown in Fig 8b For

specimen B3 which had a longer cope length (c) lateral rigid body

movement of the longitudinal stiffeners occurred without signi1047297cant

yielding of the full beam section at theloading positionFor specimens

A4 A5 B4 and B5 1047298exuralyieldingof thefull beam section occurred at

the location of maximum bending moment and subsequently the

1047298ange of the beam near the loading position buckled locally as

illustrated in Fig 8c For these specimens relatively small lateral

movement of the longitudinal stiffeners was observed In particular

for specimens A5 and B5 which had double transverse stiffeners

almost no lateral movement of the longitudinal stiffeners was

observed as shown in Fig 8d

32 Load de 1047298ection behaviour

The applied load versus de1047298ection curves of specimens A1ndashA5 and

specimens B1ndashB5 are shown in Figs 9 and 10 respectively As

mentioned above the main difference between the A-series specimens

and the B-series specimens was the depth of the cope (dc) For the A-

seriesspecimensa cope depth of about 60 mmwas used whereas a cope

depth of about 150 mm wasused forthe B-seriesspecimens Bothseries

of specimensconsideredthe effects of providingstiffeners in thecope on

the strength and behaviour of coped beams

In general the applied load versus de1047298ection curves showed linear

behaviour from the beginning of loading When the applied load

reached about 80 of the ultimate loads nonlinear load de1047298ection

behaviour was observed as illustrated in Figs 9 and 10 As shown in

the 1047297gures the applied load versus de1047298ection curves of specimens A1

and B1 showed an abrupt drop in the load carrying capacity after

reaching the ultimate loads due to web buckling failure of the

specimens For the specimens reinforced with longitudinal stiffeners

(A2 A3 B2 and B3) except for specimen A3 which had a longer

stiffener extension (ex) once the ultimate loads were reached the

applied load versus de1047298ection curves descended rapidly due to web

crippling at the end of the cope together with a lateral rigid body

movement of the stiffeners For specimen A3 however the beam was

able to continue deforming without signi1047297cant drop in the load

carrying capacity after reaching the ultimate load As shown in

Table 3 the de1047298ection of specimen A3 corresponding to the ultimate

load was 215 mm which was signi1047297cantly larger than those for the

other specimens reinforced with longitudinal stiffeners

The applied load versus de1047298ection curves of the specimens whichhad both longitudinal and transverse stiffeners (specimens A4 A5 B4

and B5) show that the specimens were able to sustain larger

de1047298ections at the ultimate load levels as illustrated in Figs 9 and 10

As mentioned above these specimens failed in 1047298exural yielding of the

full beam section and theapplied load started to decrease when 1047298ange

local buckling occurred near the loading position The de1047298ections of

these specimens corresponding to the ultimate loads were generally

larger than those for the specimens with only longitudinal stiffeners

(except for specimen A3)

Applied load

Longitudinal stiffener

Strain gauge

LVDT (vertical)

LVDT (lateral)

Legend

Fig 7 Typical layout of strain gauges and LVDTs

Table 3

Summary of test results

Test specimens Ultimate load

Pu (kN)

In-plane de1047298ection

δ (mm)

Ultimate reaction

R u (kN)

Ultimate end-moment

Mo (kNm)

Stiffener type Failure mode

A1 3084 478 2019 633 Without WB

A2 4720 948 3056 354 L Y ndashR

A3 5039 215 3290 145 L Y ndashR

A4 4940 143 3275 185 L+ T Y ndashF

A5 5186 229 3403 166 L+ T Y ndashF

B1 2287 399 1495 464 Without WB

B2 4521 916 2939 684 L Y ndashR

B3 3686 804 2407 879 L R

B4 4889 171 3188 832 L+ T Y ndashF

B5 5076 235 3330 142 L+ T Y ndashF

Note L = longitudinal stiffeners T = transverse stiffeners WB = web buckling

R = rigid body movement of stiffener due to web crippling

Y ndashR = yielding of full beam section followed by rigid body movement of stiffener due to web crippling

Y ndash

F = yielding of full beam section followed by 1047298ange local buckling near loading position

1753MCH Yam et al Journal of Constructional Steel Research 67 (2011) 1749ndash1759

7182019 Experimental study of the strength and behaviour of reinforced coped beams

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33 Strain distribution

In general at least tenstrain gaugeswere mounted on the web the

top 1047298ange of the beams and the stiffeners as shown in Fig 7 Two

strain gauges were also placed on the top and bottom 1047298anges of thebeam approximately 1000 mm from the coped end support to help

monitor the loading applied to the beam Only the load versus strain

curves for the B-series specimens were used to illustrate the strain

distributions in the web at the coped end of the beam as shown in

Fig 11 The strain distributions for the A-series specimens are similar

to those of the B-series specimens

Fig 11 illustrates the elastic strain distributions in the web at an

applied load of 150 kN Asexpected it can beseen from the 1047297gure that

the longitudinal strains in the web near the top of the cope reduce

signi1047297cantly when stiffeners are used in the beam specimens The

location of the theoretical neutral axis of the reinforced section is in

reasonable agreement with the strain readings as illustrated in the

1047297gure except for specimen B4 For this specimen the corresponding

strain gauge was located very close to the transverse stiffeners andhence the readings might have been affected by the stress concen-

tration effect near the stiffeners The theoretical strain distributions of

specimen B1 (without stiffeners) and specimens B2ndashB5 (with

stiffeners) are also included in Fig 11 As can be seen from the 1047297gure

the theoretical strain distributions of specimen B1 which are

determined based on the coped beam section properties are in

general larger than those of the test results This might be due to the

fact that thestrain gaugeswere located in the web area between the

coped beam section and the full beam section and hence the

(d) No lateral movement of longitudinal

stiffeners of specimen B5

Transverse

stiffeners

Longitudinalstiffeners

(a) Buckled web of specimen A1

Top view

Buckled

web

Top

flange

Bottom

flange

Side view

Buckling line

(b) Web crippling and lateral movement of

longitudinal stiffeners of specimen B2

Lateral

movement of

stiffeners

Web

crippling

(c) Yielding of the full beam section and local flange

buckling at the loading position of specimen B5

Flange buckling

Yielding of

full beam section

Fig 8 Typical failure mode of the test specimens

0

50

100

150

200

250

300

350

400450

500

550

0 4 8 12 16 20 24 28 32 36 40 44

P

R

V

M

A1 A2 A4 A5 A3

A p p l i e d l o a d P ( k N )

Vertical deflection δ (mm)

δ

Fig 9 Load versus de1047298ection curves mdash

specimens A1ndash

A5

1754 MCH Yam et al Journal of Constructional Steel Research 67 (2011) 1749ndash1759

7182019 Experimental study of the strength and behaviour of reinforced coped beams

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strain gauge readings might have been in1047298uenced by the full beam

section Moreover the theoretical strain distributions of specimens

B2ndashB5 are in reasonable agreement with the test results as shown

in Fig 11

4 Discussion of the test results

41 General

To help discuss the test results the test maximum bending

moment at the loading position (Mmax) and at the end of the cope

(Mco) of the beam specimens were evaluated The corresponding

values are shown in Table 4 The shear capacity of the coped beam

section (R vy) the moment capacity of the coped beam section with or

without longitudinal stiffeners (Mpco) and the plastic moment

capacity of the full beam section (Mp) are also included in the table

for comparison To predict the local web buckling capacity (R wb) of

specimens A1 and B1 the design equations proposed by Yam et al [7]

were used and the predicted values are shown in Table 4 as well Theweb buckling equations for coped beams proposed by Yam et al [7]

are as follows

R Wb = τcrtW Dminusdceth THORN eth1THORN

τcr = Ks

π 2

E

12 1minusv2 tW

ho

2

eth2THORN

Ks = a

h o

c b

eth3aTHORN

a = 138minus179dc

D eth3bTHORN

b = 364 dc

D

2

336 dc

D

+ 155 eth3cTHORN

where R wb=local web buckling capacity of coped beams ks=shear

bucklingcoef 1047297cient E=elasticmodulusν =Poissons ratio ho=height

of web of T-section and other symbols have been de1047297ned above The

measureddimensionsof thebeam specimens andthe materialproperties

obtained from the tension coupon tests were used to calculate the

capacities of the specimens

As mentioned above end moments were developed in the end

plate connections In fact the ultimate end moments of the specimensvaried between 2 and 10 of the corresponding fully 1047297xed end

moment According to Vinnakota [13] for a simple shear connection

such as the end plate connection used in this study the connection

end moment may range from 5 to 20 of the fully 1047297xed moment

Therefore the ultimate end moments developed in the specimens

0

50

100

150

200

250

300

350

400

450

500

550

A p p

l i e d l o a d P ( k N )

Vertical deflection δ (mm)

0 3 3 3 6 de1047298e ct o nc ur ve ss pe cm en s B1 B 5d str but ons for the B ser es spec mens21755M C H Yam et a Journa of Construct ona Stee Research 67 (2011) 1749 1759

7182019 Experimental study of the strength and behaviour of reinforced coped beams

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were reasonable In addition as shown in Table 4 except for

specimens A1 B1 (failed in local web buckling) and B3 (with a longer

cope length) the ratio of the maximum bending moment to the

corresponding plastic moment capacity ranged from 108 to 120 and

the ultimate end moments of the specimens were only 17 to 88 of

the corresponding maximum bending moments If there was no end

moment developed at the connection the ultimate reactions of the

specimens would only be slightly decreased and the specimens could

still reach the plastic moment capacity Hence it can be seen that the

effectiveness of the reinforcement in strengthening the coped beam

specimens would not be affected due to the in1047298uence of the end

moment

42 Failure mode

The test results show that the beam specimens without stiffeners

failed in local web buckling at the cope The predicted local web

buckling capacities (R wb) of specimens A1 and B1 using the Yam

equation are in good agreement with the test results as shown in

Table 4 Neither of the two specimens reached the yield moment

capacity or the shear capacity of the coped beam section By providing

longitudinal stiffeners to reinforce the cope the failure mode of the

reinforced coped beam specimens (except for specimen B3) consisted

of 1047298exural yielding of the full beam section at the maximum bending

moment location near the loading position to be then followed byweb crippling at the end of the cope between the longitudinal

stiffeners and the top 1047298ange of the full beam section Although the

stiffener extensions (ex) of the B-series specimens were slightly

smaller than the corresponding dc (due to fabrication errors)

specimen B2 showed that the longitudinal stiffeners were able to

delay the occurrence of web crippling until the development of

1047298exuralyielding of the full beam section near the loading position had

been reached However specimen B3 which had a longer cope length

(c) of 3153 mm compared to 2072 mm of specimen B2 failed in web

crippling and the specimen did not reach the plastic moment capacity

of the full beam section near the loading position as illustrated in

Table 4 Hence it can be seen that the stiffener extension requirement

for longitudinal stiffeners should also consider the effects of cope

length in addition to cope depth

For the specimens with both longitudinal and transverse stiffeners

no web crippling was observed and the specimens were able to

develop 1047298ange buckling near the loading position after achieving the

plastic moment capacity of the full beam section It should be noted

that for the specimens which failed in 1047298exural yielding of the beam

section near the loading position the ratio of the corresponding

maximum bending moment at the loading position to the plastic

moment capacity ranges from 108 to 120 as shown in Table 4 This

high ratio is dueto thecombinedeffectsof momentgradientalong the

test beams and strain hardening of the steel material [14] It should

also be noted that the applied moment at the end of cope (M co) is less

than the corresponding moment capacity of the coped section eitherwith or without the longitudinal stiffeners (Mpco) for all of the

specimens as shown in Table 4

43 Effects of longitudinal stiffeners

As mentioned above longitudinal stiffeners are able to improve

the capacity of coped beam specimens signi1047297cantly by forcing the

occurrence of 1047298exural yielding of the full beam section near the

loading position prior to the development of webcrippling (except for

specimen B3) The ratio of the maximum bending moment at the

loading position to the plastic moment capacity of the specimens

rangesfrom 089 to 115 forthe specimenswith longitudinalstiffeners

only In order to illustrate the improved performance of thereinforcedcoped beam specimens the curves of maximum bending moment

versus beam de1047298ection at the loading position are shown in Fig 12 It

should be noted that specimens A2 B2 and B3 only have a stiffener

extension (ex) equal toabout1dc whereas specimen A3 has a stiffener

extension (ex) of about 2dc Although specimens A2 and B2 were able

to develop the plastic moment capacity of the full beam section

Fig 12 shows that the moment versus de1047298ection curves of these

specimens descend abruptly once they have reached the maximum

applied moment due to the development of web crippling However

for specimens A3 which had a stiffener extension (ex) equal to about

2dc the moment versus de1047298ection curves show a more gradual

descending branch with a signi1047297cant increase in ultimate de1047298ection

prior to the occurrence of web crippling as shown in Fig 12 In

addition Table 4 shows that for specimens A2 A3 B2 and B3 the ratio

Table 4

Summary of moment and shear capacities of specimens

Test

specimens

R u(kN)

Mmax

(kNm)

Mco

(kNm)

Mp

(kNm)

Mpco

(kNm)

R wb

(kN)

R vy(kN)

Mmax

Mp

Mco

Mpco

R uR wb

R uR vy

Stiffener

type

Failure

mode

A1 2019 1340 384 1828 430 1985 3463 073 089 102 058 Without WB

A2 3056 2095 628 1851 1224 ndash 3558 113 051 ndash 086 L Y ndashR

A3 3290 2165 579 1875 1229 ndash 3487 115 047 ndash 094 L Y ndashR

A4 3275 2096 512 1842 1193 ndash 3511 114 043 ndash 093 L+ T Y ndashF

A5 3403 2218 582 1853 1201 ndash 3516 120 048 ndash 097 L+ T Y ndashF

B1 1495 993 282 1849 322 1557 2997 054 088 096 050 Without WBB2 2939 1983 570 1834 961 ndash 2950 108 059 ndash 100 L Y ndashR

B3 2407 1600 695 1799 941 ndash 3006 089 074 ndash 080 L R

B4 3188 2137 625 1787 921 ndash 2930 120 068 ndash 109 L+ T Y ndashF

B5 3330 2186 588 1825 947 ndash 2986 120 062 ndash 112 L+ T Y ndashF

Note R u = test ultimate reaction at the coped end of the beam specimens

Mmax = test maximum bending moment of the beam specimens at the loading position

Mco = test bending moment of the beam specimens at the end of cope ( Fig 4)

Mp = plastic moment capacity of full beam section

Mpco = plastic moment capacity of the coped section with longitudinal stiffeners (specimens A2ndashA5 and B2ndashB5) or yield moment capacity of the coped section without

stiffeners (specimens A1 and B1)

R wb = local web buckling capacity of specimens without stiffeners according to Yam equations [6]

R vy = shear capacity of the coped beam section

L = longitudinal stiffeners T = transverse stiffeners WB = web buckling

R = rigid body movement of stiffener due to web crippling

Y ndashR = yielding of full beam section followed by rigid body movement of stiffener due to web crippling

Y ndashF = yielding of full beam section followed by 1047298ange local buckling near loading position

1756 MCH Yam et al Journal of Constructional Steel Research 67 (2011) 1749ndash1759

7182019 Experimental study of the strength and behaviour of reinforced coped beams

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of the ultimate reaction (R u) to the shear capacity of the coped section

ranges from 08 to 10

Based on the test results and the above discussion it can be seen

that reinforcing coped beams using a pair of longitudinal stiffeners

with a stiffener extension of 1dc is able to improve the capacity of the

beams signi1047297cantly However a longer stiffener extension (2dc used

in this test programme) was able to provide a more stable and more

gradual coped beam unloading behaviour after the full beam section

reaches its plastic moment capacity

44 Effects of combined longitudinal and transverse stiffeners

The test results show that when the specimens (A4 A5 B4 and B5)

were reinforced by both longitudinal and transverse stiffeners the

beam specimens were able to achieve the plastic moment capacity of

the full beam section with a 1047297nal failure mode of 1047298ange local buckling

near the loading position In addition the ultimate reaction (R u) of

specimens B4 and B5 reached the shear capacity of the coped sectionas shown in Table 4 The maximum bending moment versus beam

de1047298ection curves at the loading position for specimens A4 A5 B4 and

B5 are shown in Fig 13 It can be seen from the 1047297gure that all the

curves show a typical moment versus de1047298ection behaviour where the

beams are able to sustain the maximum applied moment with

considerable beam de1047298ection As shown in Table 4 the ratio of the

maximum bending moment at the loading position to the plastic

moment capacity of the specimens ranges from 114 to 120 and the

ratio of the ultimate reaction (R u) to the shear capacity of the coped

section varies between 093 and 112 Hence it can be seen that the

combined longitudinal and transverse stiffeners were able to develop

the capacity of either the coped section (except for specimen A4) or

the full beam section of the specimens and also prohibited the

occurrence of web crippling at the end of the cope Fig 14 shows the

curves of applied load versus lateral displacement of the web at the

end of the cope for specimens B4 and B5 The 1047297gure illustrates that

there is a lateral web movement of about 7 mm for specimen B4

However almost no lateral movement was observed for specimen B5

which had the double transverse stiffeners

Based on the test results and the above discussion it can be seen

that the use of combined longitudinal and transverse stiffeners in

reinforcing coped beams improves the capacity of the beams

substantially by allowing failure to occur in either the coped section

(due to shear) or the full beam section (due to moment) In addition

the reinforced coped beams were able to sustain the maximum

applied load with considerable de1047298ection Furthermore the combinedlongitudinal and double transverse stiffeners prohibit lateral move-

ment of the web at the end of the cope and hence eliminate the

possibility of web crippling

45 Effects of cope depth and cope length

All the specimens had a cope length (c) of approximately 210 mm

(cDasymp06) except for specimen B3 which had a cope length of

Vertical deflection δ (mm)

0

25

50

75

100

125

150

175200

225

250

0 3 6 9 12 15 18 21 24 27 30 33 36

M a x i m u m m o m e n t M m a x

( k N m )

P

R

V

Mmax

Mp = 1827 kNm

A4

B5

A5

B4

Fig 13 Moment versus de1047298ection curves for specimens A4 A5 B4 and B5

Vertical deflection δ (mm)

0

25

50

75

100

125

150

175

200

225

250

0 3 6 9 12 15 18 21 24 27 30 33 36

P

R

V

Mmax

A2

B2

A3

B3

Mp= 184 kNm

M a x i m u m

m o m e n t M m a x

( k N m )

Fig 12 Moment versus de1047298ection curves for specimens A2 A3 B2 and B3

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7182019 Experimental study of the strength and behaviour of reinforced coped beams

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315 mm (cDasymp09) The cope depth (dc) of the B-series specimens

was about 105 mm (dcDasymp03) whereas the cope depth of the A-

series specimens was about 60 mm (dcDasymp018) For specimens A1

and B1 which did not have stiffeners increasing the cope depth

causes a decrease in the web buckling capacity of the specimen as

shown in Table 4 For the specimens with stiffeners however

increasing the cope depth does not affect the capacity of the

specimens signi1047297cantly as shown in the table since the stiffeners are

able to strengthen the coped section such that web crippling does not

occur prior to the development of the full beam section plastic

moment capacity When comparing the test results of specimen B2 to

those of specimenB3 it can be seenthatincreasing the cope length by

52 (with the same stiffener extension of about 1dc) the capacity of

the beam specimens is decreased by 18 In fact the failure mode of specimen B3 is that of web crippling at the end of the cope instead of

1047298exural yielding of the full beam section near the loading position

Hence it can be seen that the reinforcement detail requirement of

coped beams should include the in1047298uence of both the cope length and

the cope depth

5 Proposed modi1047297cation to the current reinforcement details for

coped beams

As mentioned above the current reinforcement details for coped

beams are based on the work by Cheng et al [4] details which have

also been adopted by the AISC Steel Construction Manual [9] as

shown in Fig 3 According to the 1047297gure for coped beams (htwle60)

reinforced with longitudinal stiffeners the stiffener extension (ex)must be at least equal to or greater than the cope depth (d c) The

reinforced coped beam is then checked for 1047298exural yielding of the

reinforced section and a local web buckling check of the coped section

is not required

Based on the test results it can be seen that the coped beam

specimens (except for specimen B3) which were reinforced with

longitudinal stiffeners according to the current reinforcement details

were able to reach the plastic moment capacity of the full beam section

and no bending failure was observed in the reinforced section In

addition the ultimate reactions of the specimens were also close to the

shear capacity of thecoped section ForspecimenB3 which hada longer

cope length (cDasymp09 comparingto cDasymp06 of other specimens) web

crippling failure was observed prior to reaching the plastic moment

capacity of the full beam section The test results also show that

specimen A2 which had a stiffener extension of 2dc exhibited more

ductile behaviour For the specimens with both longitudinal and

transverse (single or double) stiffeners the beams were able to reach

the plastic moment capacity of the full beam section with ductile

behaviour and the ultimate reactions of the specimens were very close

to or exceeded the shear capacity of the coped section

Basedon the limited test data andtheabovediscussion a modi1047297cation

to the reinforcement details for coped beams is proposed as follows

For coped beams with htwle60 dcDle03 and cDle06 only

longitudinal stiffeners are required and the length of the

longitudinal stiffeners (L x) is

L = c + eX where eX ge 2dc

eth4THORN

For coped beams with htwle60 dcDle03 and 06lecDle09 both

longitudinal and transverse (single) stiffeners are required and the

lengths of the longitudinal (L x) and thetransverse (L y) stiffeners are

L x = c + ex where eX ge dc

L y = dc + ey where ey ge dc eth5THORN

All the symbols have been de1047297ned in Fig 4 It should be noted

that the above preliminary recommendations of the reinforcement

details for coped beam are based on limited test data Further

numerical work is underway to systematically examine the rein-

forcement requirements for a wider range of cope details in order toincrease the range of applicability of the above recommendations

6 Summary and conclusions

A total of 10 full-scale tests were conducted to investigate the

strength and behaviour of reinforced coped steel I-beams The main

test parameters included the length of longitudinal stiffeners (L x)

length of transverse stiffeners (L y) combined longitudinal and

transverse stiffeners double transverse stiffeners and the cope details

(cope depth (dc) and cope length (c)) For the coped beam specimens

without stiffeners local web buckling failure occurred in the cope For

the specimens with longitudinal stiffeners only the general failure

mode was 1047298exural yielding of the full beam section at the location of

maximum bending moment followed by web crippling at the end of

0

100

200

300

400

500

600

-2 -1 0 1 2 3 4 5 6 7 8

B5

B4

Lateral displacement of web at end of cope (mm)

A p p l i e d l o a

d

P ( k N )

P

LVDT

Specimen B4

P

LVDT

Specimen B5

Fig 14 Applied load versus lateral displacement curves for specimens B4 and B5

1758 MCH Yam et al Journal of Constructional Steel Research 67 (2011) 1749ndash1759

7182019 Experimental study of the strength and behaviour of reinforced coped beams

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the cope between the longitudinal stiffeners and the top 1047298ange of the

full beam section In contrast for the specimens with combined

longitudinal and transverse stiffeners the general failure mode was

1047298exural yielding of the full beam section at the location of maximum

bending moment followed by 1047298ange local buckling near the loading

position

Thetest results show that thereinforcementswere able to increase

the capacity of the coped beam specimens signi1047297cantly The ratio of

the maximum bending moment at the loading position to the plasticmoment capacity of the full beam section of the reinforced coped

beam specimens rangedfrom 089 to 120 andthe ratio of the ultimate

reaction (R u) to the shear capacity of the coped section varied

between 080 and 112 The test results also illustrate that in addition

to the cope depth the cope length (c) also affected the behaviour and

strength of reinforced coped beams In addition the specimens with

either a longer stiffener extension (ex) for the longitudinal stiffeners

or combined longitudinal and transverse stiffeners were able to

sustain the maximum applied load with considerable de1047298ection

Based on the limited test data a modi1047297cation to the currently

recommended reinforcement details for coped beams has been

proposed The proposed reinforcement details included the in1047298uence

of various cope details A numerical study of reinforced coped beams

is currently underway to consider a wider range of cope details in

order to increase the range of applicability of the proposed

reinforcement details for coped beams

Acknowledgements

The work described in this paper was fully supported by a

grant from the Research Grants Council of the Hong Kong Special

Administrative Region China (Project No PolyU 532908E) The

assistance of Mr TL Ip Mr CH Leong and Mr SL Meng in conduct-

ing the tests is also acknowledged

References

[1] Birkemoe PC Gilmor MI Behavior of bearing critical double-angle beamconnections Engineering Journal AISC 197815(4)109ndash15

[2] Yura JA Birkemoe PC Ricles JM Beam web shear connections an experimentalstudy Journal of the Structural Division ASCE 1982108(ST2)311ndash25

[3] Ricles JM Yura JA Strength of double-row bolted-web connections Journal of Structural Engineering ASCE 1983109(12)126ndash42[4] Cheng JJ Yura JA Johnson CP Design and behavior of coped beams Ferguson

Structural Engineering Laboratory ReportNo 84-1 Department of Civil EngineeringUniversity of Texas July 1984

[5] Cheng JJR Yura JA Local web buckling of coped beams Journal of StructuralEngineering ASCE 1986112(10)2314ndash31

[6] Aalberg A Larsen PK Local web buckling of coped beams Nordic SteelConstruction Conference NSCC 2001 Proceedings Helsinki Finland 18ndash20 June2001

[7] Yam MCH Lam ACC Iu VP Cheng JJR The local web buckling strength of coped steel I-beam Journal of Structural Engineering ASCE 2003129(1)3ndash11

[8] American Institute of Steel Construction Steel Construction Manual One EastWacker Drive Suite 700 Chicago Illinoisthird ed 2005 p 60601ndash1802

[9] Yam MCH Lam ACC Wei F Chung KF The local web buckling strength of stiffened coped steel-I-beam International Journal of Steel Structures20077(2)129ndash38

[10] LamACC Yam MCHFu CKM ExperimentalInvestigation of thelocal web buckling

strength of coped steel I-beam with and without stiffeners The 10th East Asia-Paci1047297c Conference on Structural Engineering and Construction BangkokThailand 2006 p 559ndash64 August 3ndash5

[11] InstituteSteelConstruction Steelwork Design Guideto BS5950-12000 Volume 1Section Properties Member Capacities6th ed 2001

[12] British Standards Institution (BSI) BS EN 10025-22004 Hot Rolled Products Of Structural Steels mdash Part 2 Technical Delivery Conditions for Non-Alloy StructuralSteels London 2004

[13] Vinnakota S Steel Structures Behavior and LRFD McGraw Hill 2006[14] American Society of Civil Engineers (ASCE) Welding Research Council (WRC)

Plastic Design in Steel A Guide and Commentary New York New York2nd ed 1971

1759MCH Yam et al Journal of Constructional Steel Research 67 (2011) 1749ndash1759

Page 4: Experimental study of the strength and behaviour of reinforced coped beams

7182019 Experimental study of the strength and behaviour of reinforced coped beams

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static yield strength and the ultimate strength of the beams and the

stiffeners are listed in Table 2 Althoughthe samesteel grade as that of

the beam was originally requested for fabricating the stiffeners the

average yield strength and ultimate strength of the stiffeners obtained

from the tension coupon tests are signi1047297cantly lower than those of the

beams as shown in the table These lower values would be

incorporated in the calculation of the plastic moment capacity of the

reinforced section of the beams

22 Test setup

A schematic of the test setup is shown in Fig 6 The test beams

were simply supported with the coped end connected to a stub

column using M24 Grade 88 bolts Three washers (12 mm thick in

total) were used between the end plate of the beam and the column1047298ange in order to allow moderate rotation of the beam end and also to

prevent contact between the beam 1047298ange and the column 1047298ange due

to beam end rotation The end plate (10 mm thick) was welded to the

beam web using an 8 mm 1047297llet weld Typical details of the end plate

are shown in Fig 4 The beam specimens were loaded by a hydraulic

jack with a maximum capacity of 1000 kN The hydraulic jack was

located approximately 700 mm (about 2 times the beam depth) from

the stub column support This loading position was chosen in order to

prevent the concentrated load in1047298uencing the structural behaviour of

the coped region

To achieve the simply supported condition for the test beams

roller assemblies were used at the loading position and at the

supports to permit both horizontal movement and rotation of the

beam as shown in Fig 6 The test beams were prevented from lateral

movement near the loading position and near the beam ends by

lateral bracings Transverse web stiffeners were used to strengthen

the beams at the loading position and at the roller supports The

applied load and the reaction force were measured using load cells

23 Instrumentation and test procedure

The de1047298ection and movement of the test beams were measured

using linear variable differential transformers (LVDTs) The positions of

theLVDTs are shown in Fig 7 LVDTs were placed near the coped end to

record the lateral movement of the beam and to detect rigid body

movement of the longitudinal stiffeners Longitudinal strain gauges

were mounted on thebeam web near the end of thecope to record the

strain distribution across the beam depth as shown in Fig 7

The tests were conducted using load control in the early stage of

loading When the beams started to yield stroke control was used in

order to better capture the nonlinear load de1047298ection behaviour of thebeam specimens The test beams were gradually unloaded once the

maximum applied load was reached and the applied load started to

decrease signi1047297cantly Since both ends of the test beams were

designed as a test end once the test on one end of each beam was

completed the other end was then connected to the supporting stub

column for another test

3400

700 598 700699703

3 4 9

412

315 212

308 3 5 0

2 0 5

108105

Fig 5 Typical test beam

Table 2

Summary of the tension coupon test results

Coupon

specimens

Elastic

modulus E

Static yield

strength Fy

Static ultimate

strength Fu

Strain at

fracture

(MPa) (MPa) (MPa) ()

Beam 1047298ange 205000 354 484 243

Beam web 207800 366 483 241

Stiffener 199800 225 441 225

Note the values presented in the table are the average of four coupons for the webs

four coupons for the 1047298anges and two coupons for the stiffeners

Strong floor

Hydraulic

jack

Reaction frame

2000 mm (approx)

700 mm (approx)Boltedconnection

Fig 6 Test setup

1752 MCH Yam et al Journal of Constructional Steel Research 67 (2011) 1749ndash1759

7182019 Experimental study of the strength and behaviour of reinforced coped beams

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3 Test results

31 General

The test results are summarised in Table 3 The ultimate applied

load (Pu) and the corresponding in-plane de1047298ection (δ) at the loading

position are presented in the table The ultimate reaction (R u) and the

end moment (Mo) at the coped end were calculated based on the

measured applied load and the measured reaction at the other

support These end moments were caused by the small rotational

stiffness of the end plate connection However it is believed that these

end moments would not have signi1047297cant effect on the strength and

behaviour of the reinforced coped beam specimens This will be

further discussed in the following section

The general failure mode of the coped beam specimens without

stiffeners consisted of local web buckling in the cope as shown in

Fig 8a For the reinforced coped beam specimens however the 1047297nal

failure mode depended on the types of stiffener As shown in Table 3

specimens A1 and B1 (which had no stiffeners) failed in local web

buckling at the cope and the corresponding in-plane de1047298ections wereonly about 4 to 5 mm For the specimens with longitudinal stiffeners

only (A2 A3 and B2) except for specimens B3 1047298exural yielding of the

full beam section occurred at the location of maximum bending

moment and subsequently the longitudinal stiffeners moved laterally

due to web crippling near the coped end as shown in Fig 8b For

specimen B3 which had a longer cope length (c) lateral rigid body

movement of the longitudinal stiffeners occurred without signi1047297cant

yielding of the full beam section at theloading positionFor specimens

A4 A5 B4 and B5 1047298exuralyieldingof thefull beam section occurred at

the location of maximum bending moment and subsequently the

1047298ange of the beam near the loading position buckled locally as

illustrated in Fig 8c For these specimens relatively small lateral

movement of the longitudinal stiffeners was observed In particular

for specimens A5 and B5 which had double transverse stiffeners

almost no lateral movement of the longitudinal stiffeners was

observed as shown in Fig 8d

32 Load de 1047298ection behaviour

The applied load versus de1047298ection curves of specimens A1ndashA5 and

specimens B1ndashB5 are shown in Figs 9 and 10 respectively As

mentioned above the main difference between the A-series specimens

and the B-series specimens was the depth of the cope (dc) For the A-

seriesspecimensa cope depth of about 60 mmwas used whereas a cope

depth of about 150 mm wasused forthe B-seriesspecimens Bothseries

of specimensconsideredthe effects of providingstiffeners in thecope on

the strength and behaviour of coped beams

In general the applied load versus de1047298ection curves showed linear

behaviour from the beginning of loading When the applied load

reached about 80 of the ultimate loads nonlinear load de1047298ection

behaviour was observed as illustrated in Figs 9 and 10 As shown in

the 1047297gures the applied load versus de1047298ection curves of specimens A1

and B1 showed an abrupt drop in the load carrying capacity after

reaching the ultimate loads due to web buckling failure of the

specimens For the specimens reinforced with longitudinal stiffeners

(A2 A3 B2 and B3) except for specimen A3 which had a longer

stiffener extension (ex) once the ultimate loads were reached the

applied load versus de1047298ection curves descended rapidly due to web

crippling at the end of the cope together with a lateral rigid body

movement of the stiffeners For specimen A3 however the beam was

able to continue deforming without signi1047297cant drop in the load

carrying capacity after reaching the ultimate load As shown in

Table 3 the de1047298ection of specimen A3 corresponding to the ultimate

load was 215 mm which was signi1047297cantly larger than those for the

other specimens reinforced with longitudinal stiffeners

The applied load versus de1047298ection curves of the specimens whichhad both longitudinal and transverse stiffeners (specimens A4 A5 B4

and B5) show that the specimens were able to sustain larger

de1047298ections at the ultimate load levels as illustrated in Figs 9 and 10

As mentioned above these specimens failed in 1047298exural yielding of the

full beam section and theapplied load started to decrease when 1047298ange

local buckling occurred near the loading position The de1047298ections of

these specimens corresponding to the ultimate loads were generally

larger than those for the specimens with only longitudinal stiffeners

(except for specimen A3)

Applied load

Longitudinal stiffener

Strain gauge

LVDT (vertical)

LVDT (lateral)

Legend

Fig 7 Typical layout of strain gauges and LVDTs

Table 3

Summary of test results

Test specimens Ultimate load

Pu (kN)

In-plane de1047298ection

δ (mm)

Ultimate reaction

R u (kN)

Ultimate end-moment

Mo (kNm)

Stiffener type Failure mode

A1 3084 478 2019 633 Without WB

A2 4720 948 3056 354 L Y ndashR

A3 5039 215 3290 145 L Y ndashR

A4 4940 143 3275 185 L+ T Y ndashF

A5 5186 229 3403 166 L+ T Y ndashF

B1 2287 399 1495 464 Without WB

B2 4521 916 2939 684 L Y ndashR

B3 3686 804 2407 879 L R

B4 4889 171 3188 832 L+ T Y ndashF

B5 5076 235 3330 142 L+ T Y ndashF

Note L = longitudinal stiffeners T = transverse stiffeners WB = web buckling

R = rigid body movement of stiffener due to web crippling

Y ndashR = yielding of full beam section followed by rigid body movement of stiffener due to web crippling

Y ndash

F = yielding of full beam section followed by 1047298ange local buckling near loading position

1753MCH Yam et al Journal of Constructional Steel Research 67 (2011) 1749ndash1759

7182019 Experimental study of the strength and behaviour of reinforced coped beams

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33 Strain distribution

In general at least tenstrain gaugeswere mounted on the web the

top 1047298ange of the beams and the stiffeners as shown in Fig 7 Two

strain gauges were also placed on the top and bottom 1047298anges of thebeam approximately 1000 mm from the coped end support to help

monitor the loading applied to the beam Only the load versus strain

curves for the B-series specimens were used to illustrate the strain

distributions in the web at the coped end of the beam as shown in

Fig 11 The strain distributions for the A-series specimens are similar

to those of the B-series specimens

Fig 11 illustrates the elastic strain distributions in the web at an

applied load of 150 kN Asexpected it can beseen from the 1047297gure that

the longitudinal strains in the web near the top of the cope reduce

signi1047297cantly when stiffeners are used in the beam specimens The

location of the theoretical neutral axis of the reinforced section is in

reasonable agreement with the strain readings as illustrated in the

1047297gure except for specimen B4 For this specimen the corresponding

strain gauge was located very close to the transverse stiffeners andhence the readings might have been affected by the stress concen-

tration effect near the stiffeners The theoretical strain distributions of

specimen B1 (without stiffeners) and specimens B2ndashB5 (with

stiffeners) are also included in Fig 11 As can be seen from the 1047297gure

the theoretical strain distributions of specimen B1 which are

determined based on the coped beam section properties are in

general larger than those of the test results This might be due to the

fact that thestrain gaugeswere located in the web area between the

coped beam section and the full beam section and hence the

(d) No lateral movement of longitudinal

stiffeners of specimen B5

Transverse

stiffeners

Longitudinalstiffeners

(a) Buckled web of specimen A1

Top view

Buckled

web

Top

flange

Bottom

flange

Side view

Buckling line

(b) Web crippling and lateral movement of

longitudinal stiffeners of specimen B2

Lateral

movement of

stiffeners

Web

crippling

(c) Yielding of the full beam section and local flange

buckling at the loading position of specimen B5

Flange buckling

Yielding of

full beam section

Fig 8 Typical failure mode of the test specimens

0

50

100

150

200

250

300

350

400450

500

550

0 4 8 12 16 20 24 28 32 36 40 44

P

R

V

M

A1 A2 A4 A5 A3

A p p l i e d l o a d P ( k N )

Vertical deflection δ (mm)

δ

Fig 9 Load versus de1047298ection curves mdash

specimens A1ndash

A5

1754 MCH Yam et al Journal of Constructional Steel Research 67 (2011) 1749ndash1759

7182019 Experimental study of the strength and behaviour of reinforced coped beams

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strain gauge readings might have been in1047298uenced by the full beam

section Moreover the theoretical strain distributions of specimens

B2ndashB5 are in reasonable agreement with the test results as shown

in Fig 11

4 Discussion of the test results

41 General

To help discuss the test results the test maximum bending

moment at the loading position (Mmax) and at the end of the cope

(Mco) of the beam specimens were evaluated The corresponding

values are shown in Table 4 The shear capacity of the coped beam

section (R vy) the moment capacity of the coped beam section with or

without longitudinal stiffeners (Mpco) and the plastic moment

capacity of the full beam section (Mp) are also included in the table

for comparison To predict the local web buckling capacity (R wb) of

specimens A1 and B1 the design equations proposed by Yam et al [7]

were used and the predicted values are shown in Table 4 as well Theweb buckling equations for coped beams proposed by Yam et al [7]

are as follows

R Wb = τcrtW Dminusdceth THORN eth1THORN

τcr = Ks

π 2

E

12 1minusv2 tW

ho

2

eth2THORN

Ks = a

h o

c b

eth3aTHORN

a = 138minus179dc

D eth3bTHORN

b = 364 dc

D

2

336 dc

D

+ 155 eth3cTHORN

where R wb=local web buckling capacity of coped beams ks=shear

bucklingcoef 1047297cient E=elasticmodulusν =Poissons ratio ho=height

of web of T-section and other symbols have been de1047297ned above The

measureddimensionsof thebeam specimens andthe materialproperties

obtained from the tension coupon tests were used to calculate the

capacities of the specimens

As mentioned above end moments were developed in the end

plate connections In fact the ultimate end moments of the specimensvaried between 2 and 10 of the corresponding fully 1047297xed end

moment According to Vinnakota [13] for a simple shear connection

such as the end plate connection used in this study the connection

end moment may range from 5 to 20 of the fully 1047297xed moment

Therefore the ultimate end moments developed in the specimens

0

50

100

150

200

250

300

350

400

450

500

550

A p p

l i e d l o a d P ( k N )

Vertical deflection δ (mm)

0 3 3 3 6 de1047298e ct o nc ur ve ss pe cm en s B1 B 5d str but ons for the B ser es spec mens21755M C H Yam et a Journa of Construct ona Stee Research 67 (2011) 1749 1759

7182019 Experimental study of the strength and behaviour of reinforced coped beams

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were reasonable In addition as shown in Table 4 except for

specimens A1 B1 (failed in local web buckling) and B3 (with a longer

cope length) the ratio of the maximum bending moment to the

corresponding plastic moment capacity ranged from 108 to 120 and

the ultimate end moments of the specimens were only 17 to 88 of

the corresponding maximum bending moments If there was no end

moment developed at the connection the ultimate reactions of the

specimens would only be slightly decreased and the specimens could

still reach the plastic moment capacity Hence it can be seen that the

effectiveness of the reinforcement in strengthening the coped beam

specimens would not be affected due to the in1047298uence of the end

moment

42 Failure mode

The test results show that the beam specimens without stiffeners

failed in local web buckling at the cope The predicted local web

buckling capacities (R wb) of specimens A1 and B1 using the Yam

equation are in good agreement with the test results as shown in

Table 4 Neither of the two specimens reached the yield moment

capacity or the shear capacity of the coped beam section By providing

longitudinal stiffeners to reinforce the cope the failure mode of the

reinforced coped beam specimens (except for specimen B3) consisted

of 1047298exural yielding of the full beam section at the maximum bending

moment location near the loading position to be then followed byweb crippling at the end of the cope between the longitudinal

stiffeners and the top 1047298ange of the full beam section Although the

stiffener extensions (ex) of the B-series specimens were slightly

smaller than the corresponding dc (due to fabrication errors)

specimen B2 showed that the longitudinal stiffeners were able to

delay the occurrence of web crippling until the development of

1047298exuralyielding of the full beam section near the loading position had

been reached However specimen B3 which had a longer cope length

(c) of 3153 mm compared to 2072 mm of specimen B2 failed in web

crippling and the specimen did not reach the plastic moment capacity

of the full beam section near the loading position as illustrated in

Table 4 Hence it can be seen that the stiffener extension requirement

for longitudinal stiffeners should also consider the effects of cope

length in addition to cope depth

For the specimens with both longitudinal and transverse stiffeners

no web crippling was observed and the specimens were able to

develop 1047298ange buckling near the loading position after achieving the

plastic moment capacity of the full beam section It should be noted

that for the specimens which failed in 1047298exural yielding of the beam

section near the loading position the ratio of the corresponding

maximum bending moment at the loading position to the plastic

moment capacity ranges from 108 to 120 as shown in Table 4 This

high ratio is dueto thecombinedeffectsof momentgradientalong the

test beams and strain hardening of the steel material [14] It should

also be noted that the applied moment at the end of cope (M co) is less

than the corresponding moment capacity of the coped section eitherwith or without the longitudinal stiffeners (Mpco) for all of the

specimens as shown in Table 4

43 Effects of longitudinal stiffeners

As mentioned above longitudinal stiffeners are able to improve

the capacity of coped beam specimens signi1047297cantly by forcing the

occurrence of 1047298exural yielding of the full beam section near the

loading position prior to the development of webcrippling (except for

specimen B3) The ratio of the maximum bending moment at the

loading position to the plastic moment capacity of the specimens

rangesfrom 089 to 115 forthe specimenswith longitudinalstiffeners

only In order to illustrate the improved performance of thereinforcedcoped beam specimens the curves of maximum bending moment

versus beam de1047298ection at the loading position are shown in Fig 12 It

should be noted that specimens A2 B2 and B3 only have a stiffener

extension (ex) equal toabout1dc whereas specimen A3 has a stiffener

extension (ex) of about 2dc Although specimens A2 and B2 were able

to develop the plastic moment capacity of the full beam section

Fig 12 shows that the moment versus de1047298ection curves of these

specimens descend abruptly once they have reached the maximum

applied moment due to the development of web crippling However

for specimens A3 which had a stiffener extension (ex) equal to about

2dc the moment versus de1047298ection curves show a more gradual

descending branch with a signi1047297cant increase in ultimate de1047298ection

prior to the occurrence of web crippling as shown in Fig 12 In

addition Table 4 shows that for specimens A2 A3 B2 and B3 the ratio

Table 4

Summary of moment and shear capacities of specimens

Test

specimens

R u(kN)

Mmax

(kNm)

Mco

(kNm)

Mp

(kNm)

Mpco

(kNm)

R wb

(kN)

R vy(kN)

Mmax

Mp

Mco

Mpco

R uR wb

R uR vy

Stiffener

type

Failure

mode

A1 2019 1340 384 1828 430 1985 3463 073 089 102 058 Without WB

A2 3056 2095 628 1851 1224 ndash 3558 113 051 ndash 086 L Y ndashR

A3 3290 2165 579 1875 1229 ndash 3487 115 047 ndash 094 L Y ndashR

A4 3275 2096 512 1842 1193 ndash 3511 114 043 ndash 093 L+ T Y ndashF

A5 3403 2218 582 1853 1201 ndash 3516 120 048 ndash 097 L+ T Y ndashF

B1 1495 993 282 1849 322 1557 2997 054 088 096 050 Without WBB2 2939 1983 570 1834 961 ndash 2950 108 059 ndash 100 L Y ndashR

B3 2407 1600 695 1799 941 ndash 3006 089 074 ndash 080 L R

B4 3188 2137 625 1787 921 ndash 2930 120 068 ndash 109 L+ T Y ndashF

B5 3330 2186 588 1825 947 ndash 2986 120 062 ndash 112 L+ T Y ndashF

Note R u = test ultimate reaction at the coped end of the beam specimens

Mmax = test maximum bending moment of the beam specimens at the loading position

Mco = test bending moment of the beam specimens at the end of cope ( Fig 4)

Mp = plastic moment capacity of full beam section

Mpco = plastic moment capacity of the coped section with longitudinal stiffeners (specimens A2ndashA5 and B2ndashB5) or yield moment capacity of the coped section without

stiffeners (specimens A1 and B1)

R wb = local web buckling capacity of specimens without stiffeners according to Yam equations [6]

R vy = shear capacity of the coped beam section

L = longitudinal stiffeners T = transverse stiffeners WB = web buckling

R = rigid body movement of stiffener due to web crippling

Y ndashR = yielding of full beam section followed by rigid body movement of stiffener due to web crippling

Y ndashF = yielding of full beam section followed by 1047298ange local buckling near loading position

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of the ultimate reaction (R u) to the shear capacity of the coped section

ranges from 08 to 10

Based on the test results and the above discussion it can be seen

that reinforcing coped beams using a pair of longitudinal stiffeners

with a stiffener extension of 1dc is able to improve the capacity of the

beams signi1047297cantly However a longer stiffener extension (2dc used

in this test programme) was able to provide a more stable and more

gradual coped beam unloading behaviour after the full beam section

reaches its plastic moment capacity

44 Effects of combined longitudinal and transverse stiffeners

The test results show that when the specimens (A4 A5 B4 and B5)

were reinforced by both longitudinal and transverse stiffeners the

beam specimens were able to achieve the plastic moment capacity of

the full beam section with a 1047297nal failure mode of 1047298ange local buckling

near the loading position In addition the ultimate reaction (R u) of

specimens B4 and B5 reached the shear capacity of the coped sectionas shown in Table 4 The maximum bending moment versus beam

de1047298ection curves at the loading position for specimens A4 A5 B4 and

B5 are shown in Fig 13 It can be seen from the 1047297gure that all the

curves show a typical moment versus de1047298ection behaviour where the

beams are able to sustain the maximum applied moment with

considerable beam de1047298ection As shown in Table 4 the ratio of the

maximum bending moment at the loading position to the plastic

moment capacity of the specimens ranges from 114 to 120 and the

ratio of the ultimate reaction (R u) to the shear capacity of the coped

section varies between 093 and 112 Hence it can be seen that the

combined longitudinal and transverse stiffeners were able to develop

the capacity of either the coped section (except for specimen A4) or

the full beam section of the specimens and also prohibited the

occurrence of web crippling at the end of the cope Fig 14 shows the

curves of applied load versus lateral displacement of the web at the

end of the cope for specimens B4 and B5 The 1047297gure illustrates that

there is a lateral web movement of about 7 mm for specimen B4

However almost no lateral movement was observed for specimen B5

which had the double transverse stiffeners

Based on the test results and the above discussion it can be seen

that the use of combined longitudinal and transverse stiffeners in

reinforcing coped beams improves the capacity of the beams

substantially by allowing failure to occur in either the coped section

(due to shear) or the full beam section (due to moment) In addition

the reinforced coped beams were able to sustain the maximum

applied load with considerable de1047298ection Furthermore the combinedlongitudinal and double transverse stiffeners prohibit lateral move-

ment of the web at the end of the cope and hence eliminate the

possibility of web crippling

45 Effects of cope depth and cope length

All the specimens had a cope length (c) of approximately 210 mm

(cDasymp06) except for specimen B3 which had a cope length of

Vertical deflection δ (mm)

0

25

50

75

100

125

150

175200

225

250

0 3 6 9 12 15 18 21 24 27 30 33 36

M a x i m u m m o m e n t M m a x

( k N m )

P

R

V

Mmax

Mp = 1827 kNm

A4

B5

A5

B4

Fig 13 Moment versus de1047298ection curves for specimens A4 A5 B4 and B5

Vertical deflection δ (mm)

0

25

50

75

100

125

150

175

200

225

250

0 3 6 9 12 15 18 21 24 27 30 33 36

P

R

V

Mmax

A2

B2

A3

B3

Mp= 184 kNm

M a x i m u m

m o m e n t M m a x

( k N m )

Fig 12 Moment versus de1047298ection curves for specimens A2 A3 B2 and B3

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315 mm (cDasymp09) The cope depth (dc) of the B-series specimens

was about 105 mm (dcDasymp03) whereas the cope depth of the A-

series specimens was about 60 mm (dcDasymp018) For specimens A1

and B1 which did not have stiffeners increasing the cope depth

causes a decrease in the web buckling capacity of the specimen as

shown in Table 4 For the specimens with stiffeners however

increasing the cope depth does not affect the capacity of the

specimens signi1047297cantly as shown in the table since the stiffeners are

able to strengthen the coped section such that web crippling does not

occur prior to the development of the full beam section plastic

moment capacity When comparing the test results of specimen B2 to

those of specimenB3 it can be seenthatincreasing the cope length by

52 (with the same stiffener extension of about 1dc) the capacity of

the beam specimens is decreased by 18 In fact the failure mode of specimen B3 is that of web crippling at the end of the cope instead of

1047298exural yielding of the full beam section near the loading position

Hence it can be seen that the reinforcement detail requirement of

coped beams should include the in1047298uence of both the cope length and

the cope depth

5 Proposed modi1047297cation to the current reinforcement details for

coped beams

As mentioned above the current reinforcement details for coped

beams are based on the work by Cheng et al [4] details which have

also been adopted by the AISC Steel Construction Manual [9] as

shown in Fig 3 According to the 1047297gure for coped beams (htwle60)

reinforced with longitudinal stiffeners the stiffener extension (ex)must be at least equal to or greater than the cope depth (d c) The

reinforced coped beam is then checked for 1047298exural yielding of the

reinforced section and a local web buckling check of the coped section

is not required

Based on the test results it can be seen that the coped beam

specimens (except for specimen B3) which were reinforced with

longitudinal stiffeners according to the current reinforcement details

were able to reach the plastic moment capacity of the full beam section

and no bending failure was observed in the reinforced section In

addition the ultimate reactions of the specimens were also close to the

shear capacity of thecoped section ForspecimenB3 which hada longer

cope length (cDasymp09 comparingto cDasymp06 of other specimens) web

crippling failure was observed prior to reaching the plastic moment

capacity of the full beam section The test results also show that

specimen A2 which had a stiffener extension of 2dc exhibited more

ductile behaviour For the specimens with both longitudinal and

transverse (single or double) stiffeners the beams were able to reach

the plastic moment capacity of the full beam section with ductile

behaviour and the ultimate reactions of the specimens were very close

to or exceeded the shear capacity of the coped section

Basedon the limited test data andtheabovediscussion a modi1047297cation

to the reinforcement details for coped beams is proposed as follows

For coped beams with htwle60 dcDle03 and cDle06 only

longitudinal stiffeners are required and the length of the

longitudinal stiffeners (L x) is

L = c + eX where eX ge 2dc

eth4THORN

For coped beams with htwle60 dcDle03 and 06lecDle09 both

longitudinal and transverse (single) stiffeners are required and the

lengths of the longitudinal (L x) and thetransverse (L y) stiffeners are

L x = c + ex where eX ge dc

L y = dc + ey where ey ge dc eth5THORN

All the symbols have been de1047297ned in Fig 4 It should be noted

that the above preliminary recommendations of the reinforcement

details for coped beam are based on limited test data Further

numerical work is underway to systematically examine the rein-

forcement requirements for a wider range of cope details in order toincrease the range of applicability of the above recommendations

6 Summary and conclusions

A total of 10 full-scale tests were conducted to investigate the

strength and behaviour of reinforced coped steel I-beams The main

test parameters included the length of longitudinal stiffeners (L x)

length of transverse stiffeners (L y) combined longitudinal and

transverse stiffeners double transverse stiffeners and the cope details

(cope depth (dc) and cope length (c)) For the coped beam specimens

without stiffeners local web buckling failure occurred in the cope For

the specimens with longitudinal stiffeners only the general failure

mode was 1047298exural yielding of the full beam section at the location of

maximum bending moment followed by web crippling at the end of

0

100

200

300

400

500

600

-2 -1 0 1 2 3 4 5 6 7 8

B5

B4

Lateral displacement of web at end of cope (mm)

A p p l i e d l o a

d

P ( k N )

P

LVDT

Specimen B4

P

LVDT

Specimen B5

Fig 14 Applied load versus lateral displacement curves for specimens B4 and B5

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the cope between the longitudinal stiffeners and the top 1047298ange of the

full beam section In contrast for the specimens with combined

longitudinal and transverse stiffeners the general failure mode was

1047298exural yielding of the full beam section at the location of maximum

bending moment followed by 1047298ange local buckling near the loading

position

Thetest results show that thereinforcementswere able to increase

the capacity of the coped beam specimens signi1047297cantly The ratio of

the maximum bending moment at the loading position to the plasticmoment capacity of the full beam section of the reinforced coped

beam specimens rangedfrom 089 to 120 andthe ratio of the ultimate

reaction (R u) to the shear capacity of the coped section varied

between 080 and 112 The test results also illustrate that in addition

to the cope depth the cope length (c) also affected the behaviour and

strength of reinforced coped beams In addition the specimens with

either a longer stiffener extension (ex) for the longitudinal stiffeners

or combined longitudinal and transverse stiffeners were able to

sustain the maximum applied load with considerable de1047298ection

Based on the limited test data a modi1047297cation to the currently

recommended reinforcement details for coped beams has been

proposed The proposed reinforcement details included the in1047298uence

of various cope details A numerical study of reinforced coped beams

is currently underway to consider a wider range of cope details in

order to increase the range of applicability of the proposed

reinforcement details for coped beams

Acknowledgements

The work described in this paper was fully supported by a

grant from the Research Grants Council of the Hong Kong Special

Administrative Region China (Project No PolyU 532908E) The

assistance of Mr TL Ip Mr CH Leong and Mr SL Meng in conduct-

ing the tests is also acknowledged

References

[1] Birkemoe PC Gilmor MI Behavior of bearing critical double-angle beamconnections Engineering Journal AISC 197815(4)109ndash15

[2] Yura JA Birkemoe PC Ricles JM Beam web shear connections an experimentalstudy Journal of the Structural Division ASCE 1982108(ST2)311ndash25

[3] Ricles JM Yura JA Strength of double-row bolted-web connections Journal of Structural Engineering ASCE 1983109(12)126ndash42[4] Cheng JJ Yura JA Johnson CP Design and behavior of coped beams Ferguson

Structural Engineering Laboratory ReportNo 84-1 Department of Civil EngineeringUniversity of Texas July 1984

[5] Cheng JJR Yura JA Local web buckling of coped beams Journal of StructuralEngineering ASCE 1986112(10)2314ndash31

[6] Aalberg A Larsen PK Local web buckling of coped beams Nordic SteelConstruction Conference NSCC 2001 Proceedings Helsinki Finland 18ndash20 June2001

[7] Yam MCH Lam ACC Iu VP Cheng JJR The local web buckling strength of coped steel I-beam Journal of Structural Engineering ASCE 2003129(1)3ndash11

[8] American Institute of Steel Construction Steel Construction Manual One EastWacker Drive Suite 700 Chicago Illinoisthird ed 2005 p 60601ndash1802

[9] Yam MCH Lam ACC Wei F Chung KF The local web buckling strength of stiffened coped steel-I-beam International Journal of Steel Structures20077(2)129ndash38

[10] LamACC Yam MCHFu CKM ExperimentalInvestigation of thelocal web buckling

strength of coped steel I-beam with and without stiffeners The 10th East Asia-Paci1047297c Conference on Structural Engineering and Construction BangkokThailand 2006 p 559ndash64 August 3ndash5

[11] InstituteSteelConstruction Steelwork Design Guideto BS5950-12000 Volume 1Section Properties Member Capacities6th ed 2001

[12] British Standards Institution (BSI) BS EN 10025-22004 Hot Rolled Products Of Structural Steels mdash Part 2 Technical Delivery Conditions for Non-Alloy StructuralSteels London 2004

[13] Vinnakota S Steel Structures Behavior and LRFD McGraw Hill 2006[14] American Society of Civil Engineers (ASCE) Welding Research Council (WRC)

Plastic Design in Steel A Guide and Commentary New York New York2nd ed 1971

1759MCH Yam et al Journal of Constructional Steel Research 67 (2011) 1749ndash1759

Page 5: Experimental study of the strength and behaviour of reinforced coped beams

7182019 Experimental study of the strength and behaviour of reinforced coped beams

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3 Test results

31 General

The test results are summarised in Table 3 The ultimate applied

load (Pu) and the corresponding in-plane de1047298ection (δ) at the loading

position are presented in the table The ultimate reaction (R u) and the

end moment (Mo) at the coped end were calculated based on the

measured applied load and the measured reaction at the other

support These end moments were caused by the small rotational

stiffness of the end plate connection However it is believed that these

end moments would not have signi1047297cant effect on the strength and

behaviour of the reinforced coped beam specimens This will be

further discussed in the following section

The general failure mode of the coped beam specimens without

stiffeners consisted of local web buckling in the cope as shown in

Fig 8a For the reinforced coped beam specimens however the 1047297nal

failure mode depended on the types of stiffener As shown in Table 3

specimens A1 and B1 (which had no stiffeners) failed in local web

buckling at the cope and the corresponding in-plane de1047298ections wereonly about 4 to 5 mm For the specimens with longitudinal stiffeners

only (A2 A3 and B2) except for specimens B3 1047298exural yielding of the

full beam section occurred at the location of maximum bending

moment and subsequently the longitudinal stiffeners moved laterally

due to web crippling near the coped end as shown in Fig 8b For

specimen B3 which had a longer cope length (c) lateral rigid body

movement of the longitudinal stiffeners occurred without signi1047297cant

yielding of the full beam section at theloading positionFor specimens

A4 A5 B4 and B5 1047298exuralyieldingof thefull beam section occurred at

the location of maximum bending moment and subsequently the

1047298ange of the beam near the loading position buckled locally as

illustrated in Fig 8c For these specimens relatively small lateral

movement of the longitudinal stiffeners was observed In particular

for specimens A5 and B5 which had double transverse stiffeners

almost no lateral movement of the longitudinal stiffeners was

observed as shown in Fig 8d

32 Load de 1047298ection behaviour

The applied load versus de1047298ection curves of specimens A1ndashA5 and

specimens B1ndashB5 are shown in Figs 9 and 10 respectively As

mentioned above the main difference between the A-series specimens

and the B-series specimens was the depth of the cope (dc) For the A-

seriesspecimensa cope depth of about 60 mmwas used whereas a cope

depth of about 150 mm wasused forthe B-seriesspecimens Bothseries

of specimensconsideredthe effects of providingstiffeners in thecope on

the strength and behaviour of coped beams

In general the applied load versus de1047298ection curves showed linear

behaviour from the beginning of loading When the applied load

reached about 80 of the ultimate loads nonlinear load de1047298ection

behaviour was observed as illustrated in Figs 9 and 10 As shown in

the 1047297gures the applied load versus de1047298ection curves of specimens A1

and B1 showed an abrupt drop in the load carrying capacity after

reaching the ultimate loads due to web buckling failure of the

specimens For the specimens reinforced with longitudinal stiffeners

(A2 A3 B2 and B3) except for specimen A3 which had a longer

stiffener extension (ex) once the ultimate loads were reached the

applied load versus de1047298ection curves descended rapidly due to web

crippling at the end of the cope together with a lateral rigid body

movement of the stiffeners For specimen A3 however the beam was

able to continue deforming without signi1047297cant drop in the load

carrying capacity after reaching the ultimate load As shown in

Table 3 the de1047298ection of specimen A3 corresponding to the ultimate

load was 215 mm which was signi1047297cantly larger than those for the

other specimens reinforced with longitudinal stiffeners

The applied load versus de1047298ection curves of the specimens whichhad both longitudinal and transverse stiffeners (specimens A4 A5 B4

and B5) show that the specimens were able to sustain larger

de1047298ections at the ultimate load levels as illustrated in Figs 9 and 10

As mentioned above these specimens failed in 1047298exural yielding of the

full beam section and theapplied load started to decrease when 1047298ange

local buckling occurred near the loading position The de1047298ections of

these specimens corresponding to the ultimate loads were generally

larger than those for the specimens with only longitudinal stiffeners

(except for specimen A3)

Applied load

Longitudinal stiffener

Strain gauge

LVDT (vertical)

LVDT (lateral)

Legend

Fig 7 Typical layout of strain gauges and LVDTs

Table 3

Summary of test results

Test specimens Ultimate load

Pu (kN)

In-plane de1047298ection

δ (mm)

Ultimate reaction

R u (kN)

Ultimate end-moment

Mo (kNm)

Stiffener type Failure mode

A1 3084 478 2019 633 Without WB

A2 4720 948 3056 354 L Y ndashR

A3 5039 215 3290 145 L Y ndashR

A4 4940 143 3275 185 L+ T Y ndashF

A5 5186 229 3403 166 L+ T Y ndashF

B1 2287 399 1495 464 Without WB

B2 4521 916 2939 684 L Y ndashR

B3 3686 804 2407 879 L R

B4 4889 171 3188 832 L+ T Y ndashF

B5 5076 235 3330 142 L+ T Y ndashF

Note L = longitudinal stiffeners T = transverse stiffeners WB = web buckling

R = rigid body movement of stiffener due to web crippling

Y ndashR = yielding of full beam section followed by rigid body movement of stiffener due to web crippling

Y ndash

F = yielding of full beam section followed by 1047298ange local buckling near loading position

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33 Strain distribution

In general at least tenstrain gaugeswere mounted on the web the

top 1047298ange of the beams and the stiffeners as shown in Fig 7 Two

strain gauges were also placed on the top and bottom 1047298anges of thebeam approximately 1000 mm from the coped end support to help

monitor the loading applied to the beam Only the load versus strain

curves for the B-series specimens were used to illustrate the strain

distributions in the web at the coped end of the beam as shown in

Fig 11 The strain distributions for the A-series specimens are similar

to those of the B-series specimens

Fig 11 illustrates the elastic strain distributions in the web at an

applied load of 150 kN Asexpected it can beseen from the 1047297gure that

the longitudinal strains in the web near the top of the cope reduce

signi1047297cantly when stiffeners are used in the beam specimens The

location of the theoretical neutral axis of the reinforced section is in

reasonable agreement with the strain readings as illustrated in the

1047297gure except for specimen B4 For this specimen the corresponding

strain gauge was located very close to the transverse stiffeners andhence the readings might have been affected by the stress concen-

tration effect near the stiffeners The theoretical strain distributions of

specimen B1 (without stiffeners) and specimens B2ndashB5 (with

stiffeners) are also included in Fig 11 As can be seen from the 1047297gure

the theoretical strain distributions of specimen B1 which are

determined based on the coped beam section properties are in

general larger than those of the test results This might be due to the

fact that thestrain gaugeswere located in the web area between the

coped beam section and the full beam section and hence the

(d) No lateral movement of longitudinal

stiffeners of specimen B5

Transverse

stiffeners

Longitudinalstiffeners

(a) Buckled web of specimen A1

Top view

Buckled

web

Top

flange

Bottom

flange

Side view

Buckling line

(b) Web crippling and lateral movement of

longitudinal stiffeners of specimen B2

Lateral

movement of

stiffeners

Web

crippling

(c) Yielding of the full beam section and local flange

buckling at the loading position of specimen B5

Flange buckling

Yielding of

full beam section

Fig 8 Typical failure mode of the test specimens

0

50

100

150

200

250

300

350

400450

500

550

0 4 8 12 16 20 24 28 32 36 40 44

P

R

V

M

A1 A2 A4 A5 A3

A p p l i e d l o a d P ( k N )

Vertical deflection δ (mm)

δ

Fig 9 Load versus de1047298ection curves mdash

specimens A1ndash

A5

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strain gauge readings might have been in1047298uenced by the full beam

section Moreover the theoretical strain distributions of specimens

B2ndashB5 are in reasonable agreement with the test results as shown

in Fig 11

4 Discussion of the test results

41 General

To help discuss the test results the test maximum bending

moment at the loading position (Mmax) and at the end of the cope

(Mco) of the beam specimens were evaluated The corresponding

values are shown in Table 4 The shear capacity of the coped beam

section (R vy) the moment capacity of the coped beam section with or

without longitudinal stiffeners (Mpco) and the plastic moment

capacity of the full beam section (Mp) are also included in the table

for comparison To predict the local web buckling capacity (R wb) of

specimens A1 and B1 the design equations proposed by Yam et al [7]

were used and the predicted values are shown in Table 4 as well Theweb buckling equations for coped beams proposed by Yam et al [7]

are as follows

R Wb = τcrtW Dminusdceth THORN eth1THORN

τcr = Ks

π 2

E

12 1minusv2 tW

ho

2

eth2THORN

Ks = a

h o

c b

eth3aTHORN

a = 138minus179dc

D eth3bTHORN

b = 364 dc

D

2

336 dc

D

+ 155 eth3cTHORN

where R wb=local web buckling capacity of coped beams ks=shear

bucklingcoef 1047297cient E=elasticmodulusν =Poissons ratio ho=height

of web of T-section and other symbols have been de1047297ned above The

measureddimensionsof thebeam specimens andthe materialproperties

obtained from the tension coupon tests were used to calculate the

capacities of the specimens

As mentioned above end moments were developed in the end

plate connections In fact the ultimate end moments of the specimensvaried between 2 and 10 of the corresponding fully 1047297xed end

moment According to Vinnakota [13] for a simple shear connection

such as the end plate connection used in this study the connection

end moment may range from 5 to 20 of the fully 1047297xed moment

Therefore the ultimate end moments developed in the specimens

0

50

100

150

200

250

300

350

400

450

500

550

A p p

l i e d l o a d P ( k N )

Vertical deflection δ (mm)

0 3 3 3 6 de1047298e ct o nc ur ve ss pe cm en s B1 B 5d str but ons for the B ser es spec mens21755M C H Yam et a Journa of Construct ona Stee Research 67 (2011) 1749 1759

7182019 Experimental study of the strength and behaviour of reinforced coped beams

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were reasonable In addition as shown in Table 4 except for

specimens A1 B1 (failed in local web buckling) and B3 (with a longer

cope length) the ratio of the maximum bending moment to the

corresponding plastic moment capacity ranged from 108 to 120 and

the ultimate end moments of the specimens were only 17 to 88 of

the corresponding maximum bending moments If there was no end

moment developed at the connection the ultimate reactions of the

specimens would only be slightly decreased and the specimens could

still reach the plastic moment capacity Hence it can be seen that the

effectiveness of the reinforcement in strengthening the coped beam

specimens would not be affected due to the in1047298uence of the end

moment

42 Failure mode

The test results show that the beam specimens without stiffeners

failed in local web buckling at the cope The predicted local web

buckling capacities (R wb) of specimens A1 and B1 using the Yam

equation are in good agreement with the test results as shown in

Table 4 Neither of the two specimens reached the yield moment

capacity or the shear capacity of the coped beam section By providing

longitudinal stiffeners to reinforce the cope the failure mode of the

reinforced coped beam specimens (except for specimen B3) consisted

of 1047298exural yielding of the full beam section at the maximum bending

moment location near the loading position to be then followed byweb crippling at the end of the cope between the longitudinal

stiffeners and the top 1047298ange of the full beam section Although the

stiffener extensions (ex) of the B-series specimens were slightly

smaller than the corresponding dc (due to fabrication errors)

specimen B2 showed that the longitudinal stiffeners were able to

delay the occurrence of web crippling until the development of

1047298exuralyielding of the full beam section near the loading position had

been reached However specimen B3 which had a longer cope length

(c) of 3153 mm compared to 2072 mm of specimen B2 failed in web

crippling and the specimen did not reach the plastic moment capacity

of the full beam section near the loading position as illustrated in

Table 4 Hence it can be seen that the stiffener extension requirement

for longitudinal stiffeners should also consider the effects of cope

length in addition to cope depth

For the specimens with both longitudinal and transverse stiffeners

no web crippling was observed and the specimens were able to

develop 1047298ange buckling near the loading position after achieving the

plastic moment capacity of the full beam section It should be noted

that for the specimens which failed in 1047298exural yielding of the beam

section near the loading position the ratio of the corresponding

maximum bending moment at the loading position to the plastic

moment capacity ranges from 108 to 120 as shown in Table 4 This

high ratio is dueto thecombinedeffectsof momentgradientalong the

test beams and strain hardening of the steel material [14] It should

also be noted that the applied moment at the end of cope (M co) is less

than the corresponding moment capacity of the coped section eitherwith or without the longitudinal stiffeners (Mpco) for all of the

specimens as shown in Table 4

43 Effects of longitudinal stiffeners

As mentioned above longitudinal stiffeners are able to improve

the capacity of coped beam specimens signi1047297cantly by forcing the

occurrence of 1047298exural yielding of the full beam section near the

loading position prior to the development of webcrippling (except for

specimen B3) The ratio of the maximum bending moment at the

loading position to the plastic moment capacity of the specimens

rangesfrom 089 to 115 forthe specimenswith longitudinalstiffeners

only In order to illustrate the improved performance of thereinforcedcoped beam specimens the curves of maximum bending moment

versus beam de1047298ection at the loading position are shown in Fig 12 It

should be noted that specimens A2 B2 and B3 only have a stiffener

extension (ex) equal toabout1dc whereas specimen A3 has a stiffener

extension (ex) of about 2dc Although specimens A2 and B2 were able

to develop the plastic moment capacity of the full beam section

Fig 12 shows that the moment versus de1047298ection curves of these

specimens descend abruptly once they have reached the maximum

applied moment due to the development of web crippling However

for specimens A3 which had a stiffener extension (ex) equal to about

2dc the moment versus de1047298ection curves show a more gradual

descending branch with a signi1047297cant increase in ultimate de1047298ection

prior to the occurrence of web crippling as shown in Fig 12 In

addition Table 4 shows that for specimens A2 A3 B2 and B3 the ratio

Table 4

Summary of moment and shear capacities of specimens

Test

specimens

R u(kN)

Mmax

(kNm)

Mco

(kNm)

Mp

(kNm)

Mpco

(kNm)

R wb

(kN)

R vy(kN)

Mmax

Mp

Mco

Mpco

R uR wb

R uR vy

Stiffener

type

Failure

mode

A1 2019 1340 384 1828 430 1985 3463 073 089 102 058 Without WB

A2 3056 2095 628 1851 1224 ndash 3558 113 051 ndash 086 L Y ndashR

A3 3290 2165 579 1875 1229 ndash 3487 115 047 ndash 094 L Y ndashR

A4 3275 2096 512 1842 1193 ndash 3511 114 043 ndash 093 L+ T Y ndashF

A5 3403 2218 582 1853 1201 ndash 3516 120 048 ndash 097 L+ T Y ndashF

B1 1495 993 282 1849 322 1557 2997 054 088 096 050 Without WBB2 2939 1983 570 1834 961 ndash 2950 108 059 ndash 100 L Y ndashR

B3 2407 1600 695 1799 941 ndash 3006 089 074 ndash 080 L R

B4 3188 2137 625 1787 921 ndash 2930 120 068 ndash 109 L+ T Y ndashF

B5 3330 2186 588 1825 947 ndash 2986 120 062 ndash 112 L+ T Y ndashF

Note R u = test ultimate reaction at the coped end of the beam specimens

Mmax = test maximum bending moment of the beam specimens at the loading position

Mco = test bending moment of the beam specimens at the end of cope ( Fig 4)

Mp = plastic moment capacity of full beam section

Mpco = plastic moment capacity of the coped section with longitudinal stiffeners (specimens A2ndashA5 and B2ndashB5) or yield moment capacity of the coped section without

stiffeners (specimens A1 and B1)

R wb = local web buckling capacity of specimens without stiffeners according to Yam equations [6]

R vy = shear capacity of the coped beam section

L = longitudinal stiffeners T = transverse stiffeners WB = web buckling

R = rigid body movement of stiffener due to web crippling

Y ndashR = yielding of full beam section followed by rigid body movement of stiffener due to web crippling

Y ndashF = yielding of full beam section followed by 1047298ange local buckling near loading position

1756 MCH Yam et al Journal of Constructional Steel Research 67 (2011) 1749ndash1759

7182019 Experimental study of the strength and behaviour of reinforced coped beams

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of the ultimate reaction (R u) to the shear capacity of the coped section

ranges from 08 to 10

Based on the test results and the above discussion it can be seen

that reinforcing coped beams using a pair of longitudinal stiffeners

with a stiffener extension of 1dc is able to improve the capacity of the

beams signi1047297cantly However a longer stiffener extension (2dc used

in this test programme) was able to provide a more stable and more

gradual coped beam unloading behaviour after the full beam section

reaches its plastic moment capacity

44 Effects of combined longitudinal and transverse stiffeners

The test results show that when the specimens (A4 A5 B4 and B5)

were reinforced by both longitudinal and transverse stiffeners the

beam specimens were able to achieve the plastic moment capacity of

the full beam section with a 1047297nal failure mode of 1047298ange local buckling

near the loading position In addition the ultimate reaction (R u) of

specimens B4 and B5 reached the shear capacity of the coped sectionas shown in Table 4 The maximum bending moment versus beam

de1047298ection curves at the loading position for specimens A4 A5 B4 and

B5 are shown in Fig 13 It can be seen from the 1047297gure that all the

curves show a typical moment versus de1047298ection behaviour where the

beams are able to sustain the maximum applied moment with

considerable beam de1047298ection As shown in Table 4 the ratio of the

maximum bending moment at the loading position to the plastic

moment capacity of the specimens ranges from 114 to 120 and the

ratio of the ultimate reaction (R u) to the shear capacity of the coped

section varies between 093 and 112 Hence it can be seen that the

combined longitudinal and transverse stiffeners were able to develop

the capacity of either the coped section (except for specimen A4) or

the full beam section of the specimens and also prohibited the

occurrence of web crippling at the end of the cope Fig 14 shows the

curves of applied load versus lateral displacement of the web at the

end of the cope for specimens B4 and B5 The 1047297gure illustrates that

there is a lateral web movement of about 7 mm for specimen B4

However almost no lateral movement was observed for specimen B5

which had the double transverse stiffeners

Based on the test results and the above discussion it can be seen

that the use of combined longitudinal and transverse stiffeners in

reinforcing coped beams improves the capacity of the beams

substantially by allowing failure to occur in either the coped section

(due to shear) or the full beam section (due to moment) In addition

the reinforced coped beams were able to sustain the maximum

applied load with considerable de1047298ection Furthermore the combinedlongitudinal and double transverse stiffeners prohibit lateral move-

ment of the web at the end of the cope and hence eliminate the

possibility of web crippling

45 Effects of cope depth and cope length

All the specimens had a cope length (c) of approximately 210 mm

(cDasymp06) except for specimen B3 which had a cope length of

Vertical deflection δ (mm)

0

25

50

75

100

125

150

175200

225

250

0 3 6 9 12 15 18 21 24 27 30 33 36

M a x i m u m m o m e n t M m a x

( k N m )

P

R

V

Mmax

Mp = 1827 kNm

A4

B5

A5

B4

Fig 13 Moment versus de1047298ection curves for specimens A4 A5 B4 and B5

Vertical deflection δ (mm)

0

25

50

75

100

125

150

175

200

225

250

0 3 6 9 12 15 18 21 24 27 30 33 36

P

R

V

Mmax

A2

B2

A3

B3

Mp= 184 kNm

M a x i m u m

m o m e n t M m a x

( k N m )

Fig 12 Moment versus de1047298ection curves for specimens A2 A3 B2 and B3

1757MCH Yam et al Journal of Constructional Steel Research 67 (2011) 1749ndash1759

7182019 Experimental study of the strength and behaviour of reinforced coped beams

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315 mm (cDasymp09) The cope depth (dc) of the B-series specimens

was about 105 mm (dcDasymp03) whereas the cope depth of the A-

series specimens was about 60 mm (dcDasymp018) For specimens A1

and B1 which did not have stiffeners increasing the cope depth

causes a decrease in the web buckling capacity of the specimen as

shown in Table 4 For the specimens with stiffeners however

increasing the cope depth does not affect the capacity of the

specimens signi1047297cantly as shown in the table since the stiffeners are

able to strengthen the coped section such that web crippling does not

occur prior to the development of the full beam section plastic

moment capacity When comparing the test results of specimen B2 to

those of specimenB3 it can be seenthatincreasing the cope length by

52 (with the same stiffener extension of about 1dc) the capacity of

the beam specimens is decreased by 18 In fact the failure mode of specimen B3 is that of web crippling at the end of the cope instead of

1047298exural yielding of the full beam section near the loading position

Hence it can be seen that the reinforcement detail requirement of

coped beams should include the in1047298uence of both the cope length and

the cope depth

5 Proposed modi1047297cation to the current reinforcement details for

coped beams

As mentioned above the current reinforcement details for coped

beams are based on the work by Cheng et al [4] details which have

also been adopted by the AISC Steel Construction Manual [9] as

shown in Fig 3 According to the 1047297gure for coped beams (htwle60)

reinforced with longitudinal stiffeners the stiffener extension (ex)must be at least equal to or greater than the cope depth (d c) The

reinforced coped beam is then checked for 1047298exural yielding of the

reinforced section and a local web buckling check of the coped section

is not required

Based on the test results it can be seen that the coped beam

specimens (except for specimen B3) which were reinforced with

longitudinal stiffeners according to the current reinforcement details

were able to reach the plastic moment capacity of the full beam section

and no bending failure was observed in the reinforced section In

addition the ultimate reactions of the specimens were also close to the

shear capacity of thecoped section ForspecimenB3 which hada longer

cope length (cDasymp09 comparingto cDasymp06 of other specimens) web

crippling failure was observed prior to reaching the plastic moment

capacity of the full beam section The test results also show that

specimen A2 which had a stiffener extension of 2dc exhibited more

ductile behaviour For the specimens with both longitudinal and

transverse (single or double) stiffeners the beams were able to reach

the plastic moment capacity of the full beam section with ductile

behaviour and the ultimate reactions of the specimens were very close

to or exceeded the shear capacity of the coped section

Basedon the limited test data andtheabovediscussion a modi1047297cation

to the reinforcement details for coped beams is proposed as follows

For coped beams with htwle60 dcDle03 and cDle06 only

longitudinal stiffeners are required and the length of the

longitudinal stiffeners (L x) is

L = c + eX where eX ge 2dc

eth4THORN

For coped beams with htwle60 dcDle03 and 06lecDle09 both

longitudinal and transverse (single) stiffeners are required and the

lengths of the longitudinal (L x) and thetransverse (L y) stiffeners are

L x = c + ex where eX ge dc

L y = dc + ey where ey ge dc eth5THORN

All the symbols have been de1047297ned in Fig 4 It should be noted

that the above preliminary recommendations of the reinforcement

details for coped beam are based on limited test data Further

numerical work is underway to systematically examine the rein-

forcement requirements for a wider range of cope details in order toincrease the range of applicability of the above recommendations

6 Summary and conclusions

A total of 10 full-scale tests were conducted to investigate the

strength and behaviour of reinforced coped steel I-beams The main

test parameters included the length of longitudinal stiffeners (L x)

length of transverse stiffeners (L y) combined longitudinal and

transverse stiffeners double transverse stiffeners and the cope details

(cope depth (dc) and cope length (c)) For the coped beam specimens

without stiffeners local web buckling failure occurred in the cope For

the specimens with longitudinal stiffeners only the general failure

mode was 1047298exural yielding of the full beam section at the location of

maximum bending moment followed by web crippling at the end of

0

100

200

300

400

500

600

-2 -1 0 1 2 3 4 5 6 7 8

B5

B4

Lateral displacement of web at end of cope (mm)

A p p l i e d l o a

d

P ( k N )

P

LVDT

Specimen B4

P

LVDT

Specimen B5

Fig 14 Applied load versus lateral displacement curves for specimens B4 and B5

1758 MCH Yam et al Journal of Constructional Steel Research 67 (2011) 1749ndash1759

7182019 Experimental study of the strength and behaviour of reinforced coped beams

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the cope between the longitudinal stiffeners and the top 1047298ange of the

full beam section In contrast for the specimens with combined

longitudinal and transverse stiffeners the general failure mode was

1047298exural yielding of the full beam section at the location of maximum

bending moment followed by 1047298ange local buckling near the loading

position

Thetest results show that thereinforcementswere able to increase

the capacity of the coped beam specimens signi1047297cantly The ratio of

the maximum bending moment at the loading position to the plasticmoment capacity of the full beam section of the reinforced coped

beam specimens rangedfrom 089 to 120 andthe ratio of the ultimate

reaction (R u) to the shear capacity of the coped section varied

between 080 and 112 The test results also illustrate that in addition

to the cope depth the cope length (c) also affected the behaviour and

strength of reinforced coped beams In addition the specimens with

either a longer stiffener extension (ex) for the longitudinal stiffeners

or combined longitudinal and transverse stiffeners were able to

sustain the maximum applied load with considerable de1047298ection

Based on the limited test data a modi1047297cation to the currently

recommended reinforcement details for coped beams has been

proposed The proposed reinforcement details included the in1047298uence

of various cope details A numerical study of reinforced coped beams

is currently underway to consider a wider range of cope details in

order to increase the range of applicability of the proposed

reinforcement details for coped beams

Acknowledgements

The work described in this paper was fully supported by a

grant from the Research Grants Council of the Hong Kong Special

Administrative Region China (Project No PolyU 532908E) The

assistance of Mr TL Ip Mr CH Leong and Mr SL Meng in conduct-

ing the tests is also acknowledged

References

[1] Birkemoe PC Gilmor MI Behavior of bearing critical double-angle beamconnections Engineering Journal AISC 197815(4)109ndash15

[2] Yura JA Birkemoe PC Ricles JM Beam web shear connections an experimentalstudy Journal of the Structural Division ASCE 1982108(ST2)311ndash25

[3] Ricles JM Yura JA Strength of double-row bolted-web connections Journal of Structural Engineering ASCE 1983109(12)126ndash42[4] Cheng JJ Yura JA Johnson CP Design and behavior of coped beams Ferguson

Structural Engineering Laboratory ReportNo 84-1 Department of Civil EngineeringUniversity of Texas July 1984

[5] Cheng JJR Yura JA Local web buckling of coped beams Journal of StructuralEngineering ASCE 1986112(10)2314ndash31

[6] Aalberg A Larsen PK Local web buckling of coped beams Nordic SteelConstruction Conference NSCC 2001 Proceedings Helsinki Finland 18ndash20 June2001

[7] Yam MCH Lam ACC Iu VP Cheng JJR The local web buckling strength of coped steel I-beam Journal of Structural Engineering ASCE 2003129(1)3ndash11

[8] American Institute of Steel Construction Steel Construction Manual One EastWacker Drive Suite 700 Chicago Illinoisthird ed 2005 p 60601ndash1802

[9] Yam MCH Lam ACC Wei F Chung KF The local web buckling strength of stiffened coped steel-I-beam International Journal of Steel Structures20077(2)129ndash38

[10] LamACC Yam MCHFu CKM ExperimentalInvestigation of thelocal web buckling

strength of coped steel I-beam with and without stiffeners The 10th East Asia-Paci1047297c Conference on Structural Engineering and Construction BangkokThailand 2006 p 559ndash64 August 3ndash5

[11] InstituteSteelConstruction Steelwork Design Guideto BS5950-12000 Volume 1Section Properties Member Capacities6th ed 2001

[12] British Standards Institution (BSI) BS EN 10025-22004 Hot Rolled Products Of Structural Steels mdash Part 2 Technical Delivery Conditions for Non-Alloy StructuralSteels London 2004

[13] Vinnakota S Steel Structures Behavior and LRFD McGraw Hill 2006[14] American Society of Civil Engineers (ASCE) Welding Research Council (WRC)

Plastic Design in Steel A Guide and Commentary New York New York2nd ed 1971

1759MCH Yam et al Journal of Constructional Steel Research 67 (2011) 1749ndash1759

Page 6: Experimental study of the strength and behaviour of reinforced coped beams

7182019 Experimental study of the strength and behaviour of reinforced coped beams

httpslidepdfcomreaderfullexperimental-study-of-the-strength-and-behaviour-of-reinforced-coped-beams 611

33 Strain distribution

In general at least tenstrain gaugeswere mounted on the web the

top 1047298ange of the beams and the stiffeners as shown in Fig 7 Two

strain gauges were also placed on the top and bottom 1047298anges of thebeam approximately 1000 mm from the coped end support to help

monitor the loading applied to the beam Only the load versus strain

curves for the B-series specimens were used to illustrate the strain

distributions in the web at the coped end of the beam as shown in

Fig 11 The strain distributions for the A-series specimens are similar

to those of the B-series specimens

Fig 11 illustrates the elastic strain distributions in the web at an

applied load of 150 kN Asexpected it can beseen from the 1047297gure that

the longitudinal strains in the web near the top of the cope reduce

signi1047297cantly when stiffeners are used in the beam specimens The

location of the theoretical neutral axis of the reinforced section is in

reasonable agreement with the strain readings as illustrated in the

1047297gure except for specimen B4 For this specimen the corresponding

strain gauge was located very close to the transverse stiffeners andhence the readings might have been affected by the stress concen-

tration effect near the stiffeners The theoretical strain distributions of

specimen B1 (without stiffeners) and specimens B2ndashB5 (with

stiffeners) are also included in Fig 11 As can be seen from the 1047297gure

the theoretical strain distributions of specimen B1 which are

determined based on the coped beam section properties are in

general larger than those of the test results This might be due to the

fact that thestrain gaugeswere located in the web area between the

coped beam section and the full beam section and hence the

(d) No lateral movement of longitudinal

stiffeners of specimen B5

Transverse

stiffeners

Longitudinalstiffeners

(a) Buckled web of specimen A1

Top view

Buckled

web

Top

flange

Bottom

flange

Side view

Buckling line

(b) Web crippling and lateral movement of

longitudinal stiffeners of specimen B2

Lateral

movement of

stiffeners

Web

crippling

(c) Yielding of the full beam section and local flange

buckling at the loading position of specimen B5

Flange buckling

Yielding of

full beam section

Fig 8 Typical failure mode of the test specimens

0

50

100

150

200

250

300

350

400450

500

550

0 4 8 12 16 20 24 28 32 36 40 44

P

R

V

M

A1 A2 A4 A5 A3

A p p l i e d l o a d P ( k N )

Vertical deflection δ (mm)

δ

Fig 9 Load versus de1047298ection curves mdash

specimens A1ndash

A5

1754 MCH Yam et al Journal of Constructional Steel Research 67 (2011) 1749ndash1759

7182019 Experimental study of the strength and behaviour of reinforced coped beams

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strain gauge readings might have been in1047298uenced by the full beam

section Moreover the theoretical strain distributions of specimens

B2ndashB5 are in reasonable agreement with the test results as shown

in Fig 11

4 Discussion of the test results

41 General

To help discuss the test results the test maximum bending

moment at the loading position (Mmax) and at the end of the cope

(Mco) of the beam specimens were evaluated The corresponding

values are shown in Table 4 The shear capacity of the coped beam

section (R vy) the moment capacity of the coped beam section with or

without longitudinal stiffeners (Mpco) and the plastic moment

capacity of the full beam section (Mp) are also included in the table

for comparison To predict the local web buckling capacity (R wb) of

specimens A1 and B1 the design equations proposed by Yam et al [7]

were used and the predicted values are shown in Table 4 as well Theweb buckling equations for coped beams proposed by Yam et al [7]

are as follows

R Wb = τcrtW Dminusdceth THORN eth1THORN

τcr = Ks

π 2

E

12 1minusv2 tW

ho

2

eth2THORN

Ks = a

h o

c b

eth3aTHORN

a = 138minus179dc

D eth3bTHORN

b = 364 dc

D

2

336 dc

D

+ 155 eth3cTHORN

where R wb=local web buckling capacity of coped beams ks=shear

bucklingcoef 1047297cient E=elasticmodulusν =Poissons ratio ho=height

of web of T-section and other symbols have been de1047297ned above The

measureddimensionsof thebeam specimens andthe materialproperties

obtained from the tension coupon tests were used to calculate the

capacities of the specimens

As mentioned above end moments were developed in the end

plate connections In fact the ultimate end moments of the specimensvaried between 2 and 10 of the corresponding fully 1047297xed end

moment According to Vinnakota [13] for a simple shear connection

such as the end plate connection used in this study the connection

end moment may range from 5 to 20 of the fully 1047297xed moment

Therefore the ultimate end moments developed in the specimens

0

50

100

150

200

250

300

350

400

450

500

550

A p p

l i e d l o a d P ( k N )

Vertical deflection δ (mm)

0 3 3 3 6 de1047298e ct o nc ur ve ss pe cm en s B1 B 5d str but ons for the B ser es spec mens21755M C H Yam et a Journa of Construct ona Stee Research 67 (2011) 1749 1759

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were reasonable In addition as shown in Table 4 except for

specimens A1 B1 (failed in local web buckling) and B3 (with a longer

cope length) the ratio of the maximum bending moment to the

corresponding plastic moment capacity ranged from 108 to 120 and

the ultimate end moments of the specimens were only 17 to 88 of

the corresponding maximum bending moments If there was no end

moment developed at the connection the ultimate reactions of the

specimens would only be slightly decreased and the specimens could

still reach the plastic moment capacity Hence it can be seen that the

effectiveness of the reinforcement in strengthening the coped beam

specimens would not be affected due to the in1047298uence of the end

moment

42 Failure mode

The test results show that the beam specimens without stiffeners

failed in local web buckling at the cope The predicted local web

buckling capacities (R wb) of specimens A1 and B1 using the Yam

equation are in good agreement with the test results as shown in

Table 4 Neither of the two specimens reached the yield moment

capacity or the shear capacity of the coped beam section By providing

longitudinal stiffeners to reinforce the cope the failure mode of the

reinforced coped beam specimens (except for specimen B3) consisted

of 1047298exural yielding of the full beam section at the maximum bending

moment location near the loading position to be then followed byweb crippling at the end of the cope between the longitudinal

stiffeners and the top 1047298ange of the full beam section Although the

stiffener extensions (ex) of the B-series specimens were slightly

smaller than the corresponding dc (due to fabrication errors)

specimen B2 showed that the longitudinal stiffeners were able to

delay the occurrence of web crippling until the development of

1047298exuralyielding of the full beam section near the loading position had

been reached However specimen B3 which had a longer cope length

(c) of 3153 mm compared to 2072 mm of specimen B2 failed in web

crippling and the specimen did not reach the plastic moment capacity

of the full beam section near the loading position as illustrated in

Table 4 Hence it can be seen that the stiffener extension requirement

for longitudinal stiffeners should also consider the effects of cope

length in addition to cope depth

For the specimens with both longitudinal and transverse stiffeners

no web crippling was observed and the specimens were able to

develop 1047298ange buckling near the loading position after achieving the

plastic moment capacity of the full beam section It should be noted

that for the specimens which failed in 1047298exural yielding of the beam

section near the loading position the ratio of the corresponding

maximum bending moment at the loading position to the plastic

moment capacity ranges from 108 to 120 as shown in Table 4 This

high ratio is dueto thecombinedeffectsof momentgradientalong the

test beams and strain hardening of the steel material [14] It should

also be noted that the applied moment at the end of cope (M co) is less

than the corresponding moment capacity of the coped section eitherwith or without the longitudinal stiffeners (Mpco) for all of the

specimens as shown in Table 4

43 Effects of longitudinal stiffeners

As mentioned above longitudinal stiffeners are able to improve

the capacity of coped beam specimens signi1047297cantly by forcing the

occurrence of 1047298exural yielding of the full beam section near the

loading position prior to the development of webcrippling (except for

specimen B3) The ratio of the maximum bending moment at the

loading position to the plastic moment capacity of the specimens

rangesfrom 089 to 115 forthe specimenswith longitudinalstiffeners

only In order to illustrate the improved performance of thereinforcedcoped beam specimens the curves of maximum bending moment

versus beam de1047298ection at the loading position are shown in Fig 12 It

should be noted that specimens A2 B2 and B3 only have a stiffener

extension (ex) equal toabout1dc whereas specimen A3 has a stiffener

extension (ex) of about 2dc Although specimens A2 and B2 were able

to develop the plastic moment capacity of the full beam section

Fig 12 shows that the moment versus de1047298ection curves of these

specimens descend abruptly once they have reached the maximum

applied moment due to the development of web crippling However

for specimens A3 which had a stiffener extension (ex) equal to about

2dc the moment versus de1047298ection curves show a more gradual

descending branch with a signi1047297cant increase in ultimate de1047298ection

prior to the occurrence of web crippling as shown in Fig 12 In

addition Table 4 shows that for specimens A2 A3 B2 and B3 the ratio

Table 4

Summary of moment and shear capacities of specimens

Test

specimens

R u(kN)

Mmax

(kNm)

Mco

(kNm)

Mp

(kNm)

Mpco

(kNm)

R wb

(kN)

R vy(kN)

Mmax

Mp

Mco

Mpco

R uR wb

R uR vy

Stiffener

type

Failure

mode

A1 2019 1340 384 1828 430 1985 3463 073 089 102 058 Without WB

A2 3056 2095 628 1851 1224 ndash 3558 113 051 ndash 086 L Y ndashR

A3 3290 2165 579 1875 1229 ndash 3487 115 047 ndash 094 L Y ndashR

A4 3275 2096 512 1842 1193 ndash 3511 114 043 ndash 093 L+ T Y ndashF

A5 3403 2218 582 1853 1201 ndash 3516 120 048 ndash 097 L+ T Y ndashF

B1 1495 993 282 1849 322 1557 2997 054 088 096 050 Without WBB2 2939 1983 570 1834 961 ndash 2950 108 059 ndash 100 L Y ndashR

B3 2407 1600 695 1799 941 ndash 3006 089 074 ndash 080 L R

B4 3188 2137 625 1787 921 ndash 2930 120 068 ndash 109 L+ T Y ndashF

B5 3330 2186 588 1825 947 ndash 2986 120 062 ndash 112 L+ T Y ndashF

Note R u = test ultimate reaction at the coped end of the beam specimens

Mmax = test maximum bending moment of the beam specimens at the loading position

Mco = test bending moment of the beam specimens at the end of cope ( Fig 4)

Mp = plastic moment capacity of full beam section

Mpco = plastic moment capacity of the coped section with longitudinal stiffeners (specimens A2ndashA5 and B2ndashB5) or yield moment capacity of the coped section without

stiffeners (specimens A1 and B1)

R wb = local web buckling capacity of specimens without stiffeners according to Yam equations [6]

R vy = shear capacity of the coped beam section

L = longitudinal stiffeners T = transverse stiffeners WB = web buckling

R = rigid body movement of stiffener due to web crippling

Y ndashR = yielding of full beam section followed by rigid body movement of stiffener due to web crippling

Y ndashF = yielding of full beam section followed by 1047298ange local buckling near loading position

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of the ultimate reaction (R u) to the shear capacity of the coped section

ranges from 08 to 10

Based on the test results and the above discussion it can be seen

that reinforcing coped beams using a pair of longitudinal stiffeners

with a stiffener extension of 1dc is able to improve the capacity of the

beams signi1047297cantly However a longer stiffener extension (2dc used

in this test programme) was able to provide a more stable and more

gradual coped beam unloading behaviour after the full beam section

reaches its plastic moment capacity

44 Effects of combined longitudinal and transverse stiffeners

The test results show that when the specimens (A4 A5 B4 and B5)

were reinforced by both longitudinal and transverse stiffeners the

beam specimens were able to achieve the plastic moment capacity of

the full beam section with a 1047297nal failure mode of 1047298ange local buckling

near the loading position In addition the ultimate reaction (R u) of

specimens B4 and B5 reached the shear capacity of the coped sectionas shown in Table 4 The maximum bending moment versus beam

de1047298ection curves at the loading position for specimens A4 A5 B4 and

B5 are shown in Fig 13 It can be seen from the 1047297gure that all the

curves show a typical moment versus de1047298ection behaviour where the

beams are able to sustain the maximum applied moment with

considerable beam de1047298ection As shown in Table 4 the ratio of the

maximum bending moment at the loading position to the plastic

moment capacity of the specimens ranges from 114 to 120 and the

ratio of the ultimate reaction (R u) to the shear capacity of the coped

section varies between 093 and 112 Hence it can be seen that the

combined longitudinal and transverse stiffeners were able to develop

the capacity of either the coped section (except for specimen A4) or

the full beam section of the specimens and also prohibited the

occurrence of web crippling at the end of the cope Fig 14 shows the

curves of applied load versus lateral displacement of the web at the

end of the cope for specimens B4 and B5 The 1047297gure illustrates that

there is a lateral web movement of about 7 mm for specimen B4

However almost no lateral movement was observed for specimen B5

which had the double transverse stiffeners

Based on the test results and the above discussion it can be seen

that the use of combined longitudinal and transverse stiffeners in

reinforcing coped beams improves the capacity of the beams

substantially by allowing failure to occur in either the coped section

(due to shear) or the full beam section (due to moment) In addition

the reinforced coped beams were able to sustain the maximum

applied load with considerable de1047298ection Furthermore the combinedlongitudinal and double transverse stiffeners prohibit lateral move-

ment of the web at the end of the cope and hence eliminate the

possibility of web crippling

45 Effects of cope depth and cope length

All the specimens had a cope length (c) of approximately 210 mm

(cDasymp06) except for specimen B3 which had a cope length of

Vertical deflection δ (mm)

0

25

50

75

100

125

150

175200

225

250

0 3 6 9 12 15 18 21 24 27 30 33 36

M a x i m u m m o m e n t M m a x

( k N m )

P

R

V

Mmax

Mp = 1827 kNm

A4

B5

A5

B4

Fig 13 Moment versus de1047298ection curves for specimens A4 A5 B4 and B5

Vertical deflection δ (mm)

0

25

50

75

100

125

150

175

200

225

250

0 3 6 9 12 15 18 21 24 27 30 33 36

P

R

V

Mmax

A2

B2

A3

B3

Mp= 184 kNm

M a x i m u m

m o m e n t M m a x

( k N m )

Fig 12 Moment versus de1047298ection curves for specimens A2 A3 B2 and B3

1757MCH Yam et al Journal of Constructional Steel Research 67 (2011) 1749ndash1759

7182019 Experimental study of the strength and behaviour of reinforced coped beams

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315 mm (cDasymp09) The cope depth (dc) of the B-series specimens

was about 105 mm (dcDasymp03) whereas the cope depth of the A-

series specimens was about 60 mm (dcDasymp018) For specimens A1

and B1 which did not have stiffeners increasing the cope depth

causes a decrease in the web buckling capacity of the specimen as

shown in Table 4 For the specimens with stiffeners however

increasing the cope depth does not affect the capacity of the

specimens signi1047297cantly as shown in the table since the stiffeners are

able to strengthen the coped section such that web crippling does not

occur prior to the development of the full beam section plastic

moment capacity When comparing the test results of specimen B2 to

those of specimenB3 it can be seenthatincreasing the cope length by

52 (with the same stiffener extension of about 1dc) the capacity of

the beam specimens is decreased by 18 In fact the failure mode of specimen B3 is that of web crippling at the end of the cope instead of

1047298exural yielding of the full beam section near the loading position

Hence it can be seen that the reinforcement detail requirement of

coped beams should include the in1047298uence of both the cope length and

the cope depth

5 Proposed modi1047297cation to the current reinforcement details for

coped beams

As mentioned above the current reinforcement details for coped

beams are based on the work by Cheng et al [4] details which have

also been adopted by the AISC Steel Construction Manual [9] as

shown in Fig 3 According to the 1047297gure for coped beams (htwle60)

reinforced with longitudinal stiffeners the stiffener extension (ex)must be at least equal to or greater than the cope depth (d c) The

reinforced coped beam is then checked for 1047298exural yielding of the

reinforced section and a local web buckling check of the coped section

is not required

Based on the test results it can be seen that the coped beam

specimens (except for specimen B3) which were reinforced with

longitudinal stiffeners according to the current reinforcement details

were able to reach the plastic moment capacity of the full beam section

and no bending failure was observed in the reinforced section In

addition the ultimate reactions of the specimens were also close to the

shear capacity of thecoped section ForspecimenB3 which hada longer

cope length (cDasymp09 comparingto cDasymp06 of other specimens) web

crippling failure was observed prior to reaching the plastic moment

capacity of the full beam section The test results also show that

specimen A2 which had a stiffener extension of 2dc exhibited more

ductile behaviour For the specimens with both longitudinal and

transverse (single or double) stiffeners the beams were able to reach

the plastic moment capacity of the full beam section with ductile

behaviour and the ultimate reactions of the specimens were very close

to or exceeded the shear capacity of the coped section

Basedon the limited test data andtheabovediscussion a modi1047297cation

to the reinforcement details for coped beams is proposed as follows

For coped beams with htwle60 dcDle03 and cDle06 only

longitudinal stiffeners are required and the length of the

longitudinal stiffeners (L x) is

L = c + eX where eX ge 2dc

eth4THORN

For coped beams with htwle60 dcDle03 and 06lecDle09 both

longitudinal and transverse (single) stiffeners are required and the

lengths of the longitudinal (L x) and thetransverse (L y) stiffeners are

L x = c + ex where eX ge dc

L y = dc + ey where ey ge dc eth5THORN

All the symbols have been de1047297ned in Fig 4 It should be noted

that the above preliminary recommendations of the reinforcement

details for coped beam are based on limited test data Further

numerical work is underway to systematically examine the rein-

forcement requirements for a wider range of cope details in order toincrease the range of applicability of the above recommendations

6 Summary and conclusions

A total of 10 full-scale tests were conducted to investigate the

strength and behaviour of reinforced coped steel I-beams The main

test parameters included the length of longitudinal stiffeners (L x)

length of transverse stiffeners (L y) combined longitudinal and

transverse stiffeners double transverse stiffeners and the cope details

(cope depth (dc) and cope length (c)) For the coped beam specimens

without stiffeners local web buckling failure occurred in the cope For

the specimens with longitudinal stiffeners only the general failure

mode was 1047298exural yielding of the full beam section at the location of

maximum bending moment followed by web crippling at the end of

0

100

200

300

400

500

600

-2 -1 0 1 2 3 4 5 6 7 8

B5

B4

Lateral displacement of web at end of cope (mm)

A p p l i e d l o a

d

P ( k N )

P

LVDT

Specimen B4

P

LVDT

Specimen B5

Fig 14 Applied load versus lateral displacement curves for specimens B4 and B5

1758 MCH Yam et al Journal of Constructional Steel Research 67 (2011) 1749ndash1759

7182019 Experimental study of the strength and behaviour of reinforced coped beams

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the cope between the longitudinal stiffeners and the top 1047298ange of the

full beam section In contrast for the specimens with combined

longitudinal and transverse stiffeners the general failure mode was

1047298exural yielding of the full beam section at the location of maximum

bending moment followed by 1047298ange local buckling near the loading

position

Thetest results show that thereinforcementswere able to increase

the capacity of the coped beam specimens signi1047297cantly The ratio of

the maximum bending moment at the loading position to the plasticmoment capacity of the full beam section of the reinforced coped

beam specimens rangedfrom 089 to 120 andthe ratio of the ultimate

reaction (R u) to the shear capacity of the coped section varied

between 080 and 112 The test results also illustrate that in addition

to the cope depth the cope length (c) also affected the behaviour and

strength of reinforced coped beams In addition the specimens with

either a longer stiffener extension (ex) for the longitudinal stiffeners

or combined longitudinal and transverse stiffeners were able to

sustain the maximum applied load with considerable de1047298ection

Based on the limited test data a modi1047297cation to the currently

recommended reinforcement details for coped beams has been

proposed The proposed reinforcement details included the in1047298uence

of various cope details A numerical study of reinforced coped beams

is currently underway to consider a wider range of cope details in

order to increase the range of applicability of the proposed

reinforcement details for coped beams

Acknowledgements

The work described in this paper was fully supported by a

grant from the Research Grants Council of the Hong Kong Special

Administrative Region China (Project No PolyU 532908E) The

assistance of Mr TL Ip Mr CH Leong and Mr SL Meng in conduct-

ing the tests is also acknowledged

References

[1] Birkemoe PC Gilmor MI Behavior of bearing critical double-angle beamconnections Engineering Journal AISC 197815(4)109ndash15

[2] Yura JA Birkemoe PC Ricles JM Beam web shear connections an experimentalstudy Journal of the Structural Division ASCE 1982108(ST2)311ndash25

[3] Ricles JM Yura JA Strength of double-row bolted-web connections Journal of Structural Engineering ASCE 1983109(12)126ndash42[4] Cheng JJ Yura JA Johnson CP Design and behavior of coped beams Ferguson

Structural Engineering Laboratory ReportNo 84-1 Department of Civil EngineeringUniversity of Texas July 1984

[5] Cheng JJR Yura JA Local web buckling of coped beams Journal of StructuralEngineering ASCE 1986112(10)2314ndash31

[6] Aalberg A Larsen PK Local web buckling of coped beams Nordic SteelConstruction Conference NSCC 2001 Proceedings Helsinki Finland 18ndash20 June2001

[7] Yam MCH Lam ACC Iu VP Cheng JJR The local web buckling strength of coped steel I-beam Journal of Structural Engineering ASCE 2003129(1)3ndash11

[8] American Institute of Steel Construction Steel Construction Manual One EastWacker Drive Suite 700 Chicago Illinoisthird ed 2005 p 60601ndash1802

[9] Yam MCH Lam ACC Wei F Chung KF The local web buckling strength of stiffened coped steel-I-beam International Journal of Steel Structures20077(2)129ndash38

[10] LamACC Yam MCHFu CKM ExperimentalInvestigation of thelocal web buckling

strength of coped steel I-beam with and without stiffeners The 10th East Asia-Paci1047297c Conference on Structural Engineering and Construction BangkokThailand 2006 p 559ndash64 August 3ndash5

[11] InstituteSteelConstruction Steelwork Design Guideto BS5950-12000 Volume 1Section Properties Member Capacities6th ed 2001

[12] British Standards Institution (BSI) BS EN 10025-22004 Hot Rolled Products Of Structural Steels mdash Part 2 Technical Delivery Conditions for Non-Alloy StructuralSteels London 2004

[13] Vinnakota S Steel Structures Behavior and LRFD McGraw Hill 2006[14] American Society of Civil Engineers (ASCE) Welding Research Council (WRC)

Plastic Design in Steel A Guide and Commentary New York New York2nd ed 1971

1759MCH Yam et al Journal of Constructional Steel Research 67 (2011) 1749ndash1759

Page 7: Experimental study of the strength and behaviour of reinforced coped beams

7182019 Experimental study of the strength and behaviour of reinforced coped beams

httpslidepdfcomreaderfullexperimental-study-of-the-strength-and-behaviour-of-reinforced-coped-beams 711

strain gauge readings might have been in1047298uenced by the full beam

section Moreover the theoretical strain distributions of specimens

B2ndashB5 are in reasonable agreement with the test results as shown

in Fig 11

4 Discussion of the test results

41 General

To help discuss the test results the test maximum bending

moment at the loading position (Mmax) and at the end of the cope

(Mco) of the beam specimens were evaluated The corresponding

values are shown in Table 4 The shear capacity of the coped beam

section (R vy) the moment capacity of the coped beam section with or

without longitudinal stiffeners (Mpco) and the plastic moment

capacity of the full beam section (Mp) are also included in the table

for comparison To predict the local web buckling capacity (R wb) of

specimens A1 and B1 the design equations proposed by Yam et al [7]

were used and the predicted values are shown in Table 4 as well Theweb buckling equations for coped beams proposed by Yam et al [7]

are as follows

R Wb = τcrtW Dminusdceth THORN eth1THORN

τcr = Ks

π 2

E

12 1minusv2 tW

ho

2

eth2THORN

Ks = a

h o

c b

eth3aTHORN

a = 138minus179dc

D eth3bTHORN

b = 364 dc

D

2

336 dc

D

+ 155 eth3cTHORN

where R wb=local web buckling capacity of coped beams ks=shear

bucklingcoef 1047297cient E=elasticmodulusν =Poissons ratio ho=height

of web of T-section and other symbols have been de1047297ned above The

measureddimensionsof thebeam specimens andthe materialproperties

obtained from the tension coupon tests were used to calculate the

capacities of the specimens

As mentioned above end moments were developed in the end

plate connections In fact the ultimate end moments of the specimensvaried between 2 and 10 of the corresponding fully 1047297xed end

moment According to Vinnakota [13] for a simple shear connection

such as the end plate connection used in this study the connection

end moment may range from 5 to 20 of the fully 1047297xed moment

Therefore the ultimate end moments developed in the specimens

0

50

100

150

200

250

300

350

400

450

500

550

A p p

l i e d l o a d P ( k N )

Vertical deflection δ (mm)

0 3 3 3 6 de1047298e ct o nc ur ve ss pe cm en s B1 B 5d str but ons for the B ser es spec mens21755M C H Yam et a Journa of Construct ona Stee Research 67 (2011) 1749 1759

7182019 Experimental study of the strength and behaviour of reinforced coped beams

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were reasonable In addition as shown in Table 4 except for

specimens A1 B1 (failed in local web buckling) and B3 (with a longer

cope length) the ratio of the maximum bending moment to the

corresponding plastic moment capacity ranged from 108 to 120 and

the ultimate end moments of the specimens were only 17 to 88 of

the corresponding maximum bending moments If there was no end

moment developed at the connection the ultimate reactions of the

specimens would only be slightly decreased and the specimens could

still reach the plastic moment capacity Hence it can be seen that the

effectiveness of the reinforcement in strengthening the coped beam

specimens would not be affected due to the in1047298uence of the end

moment

42 Failure mode

The test results show that the beam specimens without stiffeners

failed in local web buckling at the cope The predicted local web

buckling capacities (R wb) of specimens A1 and B1 using the Yam

equation are in good agreement with the test results as shown in

Table 4 Neither of the two specimens reached the yield moment

capacity or the shear capacity of the coped beam section By providing

longitudinal stiffeners to reinforce the cope the failure mode of the

reinforced coped beam specimens (except for specimen B3) consisted

of 1047298exural yielding of the full beam section at the maximum bending

moment location near the loading position to be then followed byweb crippling at the end of the cope between the longitudinal

stiffeners and the top 1047298ange of the full beam section Although the

stiffener extensions (ex) of the B-series specimens were slightly

smaller than the corresponding dc (due to fabrication errors)

specimen B2 showed that the longitudinal stiffeners were able to

delay the occurrence of web crippling until the development of

1047298exuralyielding of the full beam section near the loading position had

been reached However specimen B3 which had a longer cope length

(c) of 3153 mm compared to 2072 mm of specimen B2 failed in web

crippling and the specimen did not reach the plastic moment capacity

of the full beam section near the loading position as illustrated in

Table 4 Hence it can be seen that the stiffener extension requirement

for longitudinal stiffeners should also consider the effects of cope

length in addition to cope depth

For the specimens with both longitudinal and transverse stiffeners

no web crippling was observed and the specimens were able to

develop 1047298ange buckling near the loading position after achieving the

plastic moment capacity of the full beam section It should be noted

that for the specimens which failed in 1047298exural yielding of the beam

section near the loading position the ratio of the corresponding

maximum bending moment at the loading position to the plastic

moment capacity ranges from 108 to 120 as shown in Table 4 This

high ratio is dueto thecombinedeffectsof momentgradientalong the

test beams and strain hardening of the steel material [14] It should

also be noted that the applied moment at the end of cope (M co) is less

than the corresponding moment capacity of the coped section eitherwith or without the longitudinal stiffeners (Mpco) for all of the

specimens as shown in Table 4

43 Effects of longitudinal stiffeners

As mentioned above longitudinal stiffeners are able to improve

the capacity of coped beam specimens signi1047297cantly by forcing the

occurrence of 1047298exural yielding of the full beam section near the

loading position prior to the development of webcrippling (except for

specimen B3) The ratio of the maximum bending moment at the

loading position to the plastic moment capacity of the specimens

rangesfrom 089 to 115 forthe specimenswith longitudinalstiffeners

only In order to illustrate the improved performance of thereinforcedcoped beam specimens the curves of maximum bending moment

versus beam de1047298ection at the loading position are shown in Fig 12 It

should be noted that specimens A2 B2 and B3 only have a stiffener

extension (ex) equal toabout1dc whereas specimen A3 has a stiffener

extension (ex) of about 2dc Although specimens A2 and B2 were able

to develop the plastic moment capacity of the full beam section

Fig 12 shows that the moment versus de1047298ection curves of these

specimens descend abruptly once they have reached the maximum

applied moment due to the development of web crippling However

for specimens A3 which had a stiffener extension (ex) equal to about

2dc the moment versus de1047298ection curves show a more gradual

descending branch with a signi1047297cant increase in ultimate de1047298ection

prior to the occurrence of web crippling as shown in Fig 12 In

addition Table 4 shows that for specimens A2 A3 B2 and B3 the ratio

Table 4

Summary of moment and shear capacities of specimens

Test

specimens

R u(kN)

Mmax

(kNm)

Mco

(kNm)

Mp

(kNm)

Mpco

(kNm)

R wb

(kN)

R vy(kN)

Mmax

Mp

Mco

Mpco

R uR wb

R uR vy

Stiffener

type

Failure

mode

A1 2019 1340 384 1828 430 1985 3463 073 089 102 058 Without WB

A2 3056 2095 628 1851 1224 ndash 3558 113 051 ndash 086 L Y ndashR

A3 3290 2165 579 1875 1229 ndash 3487 115 047 ndash 094 L Y ndashR

A4 3275 2096 512 1842 1193 ndash 3511 114 043 ndash 093 L+ T Y ndashF

A5 3403 2218 582 1853 1201 ndash 3516 120 048 ndash 097 L+ T Y ndashF

B1 1495 993 282 1849 322 1557 2997 054 088 096 050 Without WBB2 2939 1983 570 1834 961 ndash 2950 108 059 ndash 100 L Y ndashR

B3 2407 1600 695 1799 941 ndash 3006 089 074 ndash 080 L R

B4 3188 2137 625 1787 921 ndash 2930 120 068 ndash 109 L+ T Y ndashF

B5 3330 2186 588 1825 947 ndash 2986 120 062 ndash 112 L+ T Y ndashF

Note R u = test ultimate reaction at the coped end of the beam specimens

Mmax = test maximum bending moment of the beam specimens at the loading position

Mco = test bending moment of the beam specimens at the end of cope ( Fig 4)

Mp = plastic moment capacity of full beam section

Mpco = plastic moment capacity of the coped section with longitudinal stiffeners (specimens A2ndashA5 and B2ndashB5) or yield moment capacity of the coped section without

stiffeners (specimens A1 and B1)

R wb = local web buckling capacity of specimens without stiffeners according to Yam equations [6]

R vy = shear capacity of the coped beam section

L = longitudinal stiffeners T = transverse stiffeners WB = web buckling

R = rigid body movement of stiffener due to web crippling

Y ndashR = yielding of full beam section followed by rigid body movement of stiffener due to web crippling

Y ndashF = yielding of full beam section followed by 1047298ange local buckling near loading position

1756 MCH Yam et al Journal of Constructional Steel Research 67 (2011) 1749ndash1759

7182019 Experimental study of the strength and behaviour of reinforced coped beams

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of the ultimate reaction (R u) to the shear capacity of the coped section

ranges from 08 to 10

Based on the test results and the above discussion it can be seen

that reinforcing coped beams using a pair of longitudinal stiffeners

with a stiffener extension of 1dc is able to improve the capacity of the

beams signi1047297cantly However a longer stiffener extension (2dc used

in this test programme) was able to provide a more stable and more

gradual coped beam unloading behaviour after the full beam section

reaches its plastic moment capacity

44 Effects of combined longitudinal and transverse stiffeners

The test results show that when the specimens (A4 A5 B4 and B5)

were reinforced by both longitudinal and transverse stiffeners the

beam specimens were able to achieve the plastic moment capacity of

the full beam section with a 1047297nal failure mode of 1047298ange local buckling

near the loading position In addition the ultimate reaction (R u) of

specimens B4 and B5 reached the shear capacity of the coped sectionas shown in Table 4 The maximum bending moment versus beam

de1047298ection curves at the loading position for specimens A4 A5 B4 and

B5 are shown in Fig 13 It can be seen from the 1047297gure that all the

curves show a typical moment versus de1047298ection behaviour where the

beams are able to sustain the maximum applied moment with

considerable beam de1047298ection As shown in Table 4 the ratio of the

maximum bending moment at the loading position to the plastic

moment capacity of the specimens ranges from 114 to 120 and the

ratio of the ultimate reaction (R u) to the shear capacity of the coped

section varies between 093 and 112 Hence it can be seen that the

combined longitudinal and transverse stiffeners were able to develop

the capacity of either the coped section (except for specimen A4) or

the full beam section of the specimens and also prohibited the

occurrence of web crippling at the end of the cope Fig 14 shows the

curves of applied load versus lateral displacement of the web at the

end of the cope for specimens B4 and B5 The 1047297gure illustrates that

there is a lateral web movement of about 7 mm for specimen B4

However almost no lateral movement was observed for specimen B5

which had the double transverse stiffeners

Based on the test results and the above discussion it can be seen

that the use of combined longitudinal and transverse stiffeners in

reinforcing coped beams improves the capacity of the beams

substantially by allowing failure to occur in either the coped section

(due to shear) or the full beam section (due to moment) In addition

the reinforced coped beams were able to sustain the maximum

applied load with considerable de1047298ection Furthermore the combinedlongitudinal and double transverse stiffeners prohibit lateral move-

ment of the web at the end of the cope and hence eliminate the

possibility of web crippling

45 Effects of cope depth and cope length

All the specimens had a cope length (c) of approximately 210 mm

(cDasymp06) except for specimen B3 which had a cope length of

Vertical deflection δ (mm)

0

25

50

75

100

125

150

175200

225

250

0 3 6 9 12 15 18 21 24 27 30 33 36

M a x i m u m m o m e n t M m a x

( k N m )

P

R

V

Mmax

Mp = 1827 kNm

A4

B5

A5

B4

Fig 13 Moment versus de1047298ection curves for specimens A4 A5 B4 and B5

Vertical deflection δ (mm)

0

25

50

75

100

125

150

175

200

225

250

0 3 6 9 12 15 18 21 24 27 30 33 36

P

R

V

Mmax

A2

B2

A3

B3

Mp= 184 kNm

M a x i m u m

m o m e n t M m a x

( k N m )

Fig 12 Moment versus de1047298ection curves for specimens A2 A3 B2 and B3

1757MCH Yam et al Journal of Constructional Steel Research 67 (2011) 1749ndash1759

7182019 Experimental study of the strength and behaviour of reinforced coped beams

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315 mm (cDasymp09) The cope depth (dc) of the B-series specimens

was about 105 mm (dcDasymp03) whereas the cope depth of the A-

series specimens was about 60 mm (dcDasymp018) For specimens A1

and B1 which did not have stiffeners increasing the cope depth

causes a decrease in the web buckling capacity of the specimen as

shown in Table 4 For the specimens with stiffeners however

increasing the cope depth does not affect the capacity of the

specimens signi1047297cantly as shown in the table since the stiffeners are

able to strengthen the coped section such that web crippling does not

occur prior to the development of the full beam section plastic

moment capacity When comparing the test results of specimen B2 to

those of specimenB3 it can be seenthatincreasing the cope length by

52 (with the same stiffener extension of about 1dc) the capacity of

the beam specimens is decreased by 18 In fact the failure mode of specimen B3 is that of web crippling at the end of the cope instead of

1047298exural yielding of the full beam section near the loading position

Hence it can be seen that the reinforcement detail requirement of

coped beams should include the in1047298uence of both the cope length and

the cope depth

5 Proposed modi1047297cation to the current reinforcement details for

coped beams

As mentioned above the current reinforcement details for coped

beams are based on the work by Cheng et al [4] details which have

also been adopted by the AISC Steel Construction Manual [9] as

shown in Fig 3 According to the 1047297gure for coped beams (htwle60)

reinforced with longitudinal stiffeners the stiffener extension (ex)must be at least equal to or greater than the cope depth (d c) The

reinforced coped beam is then checked for 1047298exural yielding of the

reinforced section and a local web buckling check of the coped section

is not required

Based on the test results it can be seen that the coped beam

specimens (except for specimen B3) which were reinforced with

longitudinal stiffeners according to the current reinforcement details

were able to reach the plastic moment capacity of the full beam section

and no bending failure was observed in the reinforced section In

addition the ultimate reactions of the specimens were also close to the

shear capacity of thecoped section ForspecimenB3 which hada longer

cope length (cDasymp09 comparingto cDasymp06 of other specimens) web

crippling failure was observed prior to reaching the plastic moment

capacity of the full beam section The test results also show that

specimen A2 which had a stiffener extension of 2dc exhibited more

ductile behaviour For the specimens with both longitudinal and

transverse (single or double) stiffeners the beams were able to reach

the plastic moment capacity of the full beam section with ductile

behaviour and the ultimate reactions of the specimens were very close

to or exceeded the shear capacity of the coped section

Basedon the limited test data andtheabovediscussion a modi1047297cation

to the reinforcement details for coped beams is proposed as follows

For coped beams with htwle60 dcDle03 and cDle06 only

longitudinal stiffeners are required and the length of the

longitudinal stiffeners (L x) is

L = c + eX where eX ge 2dc

eth4THORN

For coped beams with htwle60 dcDle03 and 06lecDle09 both

longitudinal and transverse (single) stiffeners are required and the

lengths of the longitudinal (L x) and thetransverse (L y) stiffeners are

L x = c + ex where eX ge dc

L y = dc + ey where ey ge dc eth5THORN

All the symbols have been de1047297ned in Fig 4 It should be noted

that the above preliminary recommendations of the reinforcement

details for coped beam are based on limited test data Further

numerical work is underway to systematically examine the rein-

forcement requirements for a wider range of cope details in order toincrease the range of applicability of the above recommendations

6 Summary and conclusions

A total of 10 full-scale tests were conducted to investigate the

strength and behaviour of reinforced coped steel I-beams The main

test parameters included the length of longitudinal stiffeners (L x)

length of transverse stiffeners (L y) combined longitudinal and

transverse stiffeners double transverse stiffeners and the cope details

(cope depth (dc) and cope length (c)) For the coped beam specimens

without stiffeners local web buckling failure occurred in the cope For

the specimens with longitudinal stiffeners only the general failure

mode was 1047298exural yielding of the full beam section at the location of

maximum bending moment followed by web crippling at the end of

0

100

200

300

400

500

600

-2 -1 0 1 2 3 4 5 6 7 8

B5

B4

Lateral displacement of web at end of cope (mm)

A p p l i e d l o a

d

P ( k N )

P

LVDT

Specimen B4

P

LVDT

Specimen B5

Fig 14 Applied load versus lateral displacement curves for specimens B4 and B5

1758 MCH Yam et al Journal of Constructional Steel Research 67 (2011) 1749ndash1759

7182019 Experimental study of the strength and behaviour of reinforced coped beams

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the cope between the longitudinal stiffeners and the top 1047298ange of the

full beam section In contrast for the specimens with combined

longitudinal and transverse stiffeners the general failure mode was

1047298exural yielding of the full beam section at the location of maximum

bending moment followed by 1047298ange local buckling near the loading

position

Thetest results show that thereinforcementswere able to increase

the capacity of the coped beam specimens signi1047297cantly The ratio of

the maximum bending moment at the loading position to the plasticmoment capacity of the full beam section of the reinforced coped

beam specimens rangedfrom 089 to 120 andthe ratio of the ultimate

reaction (R u) to the shear capacity of the coped section varied

between 080 and 112 The test results also illustrate that in addition

to the cope depth the cope length (c) also affected the behaviour and

strength of reinforced coped beams In addition the specimens with

either a longer stiffener extension (ex) for the longitudinal stiffeners

or combined longitudinal and transverse stiffeners were able to

sustain the maximum applied load with considerable de1047298ection

Based on the limited test data a modi1047297cation to the currently

recommended reinforcement details for coped beams has been

proposed The proposed reinforcement details included the in1047298uence

of various cope details A numerical study of reinforced coped beams

is currently underway to consider a wider range of cope details in

order to increase the range of applicability of the proposed

reinforcement details for coped beams

Acknowledgements

The work described in this paper was fully supported by a

grant from the Research Grants Council of the Hong Kong Special

Administrative Region China (Project No PolyU 532908E) The

assistance of Mr TL Ip Mr CH Leong and Mr SL Meng in conduct-

ing the tests is also acknowledged

References

[1] Birkemoe PC Gilmor MI Behavior of bearing critical double-angle beamconnections Engineering Journal AISC 197815(4)109ndash15

[2] Yura JA Birkemoe PC Ricles JM Beam web shear connections an experimentalstudy Journal of the Structural Division ASCE 1982108(ST2)311ndash25

[3] Ricles JM Yura JA Strength of double-row bolted-web connections Journal of Structural Engineering ASCE 1983109(12)126ndash42[4] Cheng JJ Yura JA Johnson CP Design and behavior of coped beams Ferguson

Structural Engineering Laboratory ReportNo 84-1 Department of Civil EngineeringUniversity of Texas July 1984

[5] Cheng JJR Yura JA Local web buckling of coped beams Journal of StructuralEngineering ASCE 1986112(10)2314ndash31

[6] Aalberg A Larsen PK Local web buckling of coped beams Nordic SteelConstruction Conference NSCC 2001 Proceedings Helsinki Finland 18ndash20 June2001

[7] Yam MCH Lam ACC Iu VP Cheng JJR The local web buckling strength of coped steel I-beam Journal of Structural Engineering ASCE 2003129(1)3ndash11

[8] American Institute of Steel Construction Steel Construction Manual One EastWacker Drive Suite 700 Chicago Illinoisthird ed 2005 p 60601ndash1802

[9] Yam MCH Lam ACC Wei F Chung KF The local web buckling strength of stiffened coped steel-I-beam International Journal of Steel Structures20077(2)129ndash38

[10] LamACC Yam MCHFu CKM ExperimentalInvestigation of thelocal web buckling

strength of coped steel I-beam with and without stiffeners The 10th East Asia-Paci1047297c Conference on Structural Engineering and Construction BangkokThailand 2006 p 559ndash64 August 3ndash5

[11] InstituteSteelConstruction Steelwork Design Guideto BS5950-12000 Volume 1Section Properties Member Capacities6th ed 2001

[12] British Standards Institution (BSI) BS EN 10025-22004 Hot Rolled Products Of Structural Steels mdash Part 2 Technical Delivery Conditions for Non-Alloy StructuralSteels London 2004

[13] Vinnakota S Steel Structures Behavior and LRFD McGraw Hill 2006[14] American Society of Civil Engineers (ASCE) Welding Research Council (WRC)

Plastic Design in Steel A Guide and Commentary New York New York2nd ed 1971

1759MCH Yam et al Journal of Constructional Steel Research 67 (2011) 1749ndash1759

Page 8: Experimental study of the strength and behaviour of reinforced coped beams

7182019 Experimental study of the strength and behaviour of reinforced coped beams

httpslidepdfcomreaderfullexperimental-study-of-the-strength-and-behaviour-of-reinforced-coped-beams 811

were reasonable In addition as shown in Table 4 except for

specimens A1 B1 (failed in local web buckling) and B3 (with a longer

cope length) the ratio of the maximum bending moment to the

corresponding plastic moment capacity ranged from 108 to 120 and

the ultimate end moments of the specimens were only 17 to 88 of

the corresponding maximum bending moments If there was no end

moment developed at the connection the ultimate reactions of the

specimens would only be slightly decreased and the specimens could

still reach the plastic moment capacity Hence it can be seen that the

effectiveness of the reinforcement in strengthening the coped beam

specimens would not be affected due to the in1047298uence of the end

moment

42 Failure mode

The test results show that the beam specimens without stiffeners

failed in local web buckling at the cope The predicted local web

buckling capacities (R wb) of specimens A1 and B1 using the Yam

equation are in good agreement with the test results as shown in

Table 4 Neither of the two specimens reached the yield moment

capacity or the shear capacity of the coped beam section By providing

longitudinal stiffeners to reinforce the cope the failure mode of the

reinforced coped beam specimens (except for specimen B3) consisted

of 1047298exural yielding of the full beam section at the maximum bending

moment location near the loading position to be then followed byweb crippling at the end of the cope between the longitudinal

stiffeners and the top 1047298ange of the full beam section Although the

stiffener extensions (ex) of the B-series specimens were slightly

smaller than the corresponding dc (due to fabrication errors)

specimen B2 showed that the longitudinal stiffeners were able to

delay the occurrence of web crippling until the development of

1047298exuralyielding of the full beam section near the loading position had

been reached However specimen B3 which had a longer cope length

(c) of 3153 mm compared to 2072 mm of specimen B2 failed in web

crippling and the specimen did not reach the plastic moment capacity

of the full beam section near the loading position as illustrated in

Table 4 Hence it can be seen that the stiffener extension requirement

for longitudinal stiffeners should also consider the effects of cope

length in addition to cope depth

For the specimens with both longitudinal and transverse stiffeners

no web crippling was observed and the specimens were able to

develop 1047298ange buckling near the loading position after achieving the

plastic moment capacity of the full beam section It should be noted

that for the specimens which failed in 1047298exural yielding of the beam

section near the loading position the ratio of the corresponding

maximum bending moment at the loading position to the plastic

moment capacity ranges from 108 to 120 as shown in Table 4 This

high ratio is dueto thecombinedeffectsof momentgradientalong the

test beams and strain hardening of the steel material [14] It should

also be noted that the applied moment at the end of cope (M co) is less

than the corresponding moment capacity of the coped section eitherwith or without the longitudinal stiffeners (Mpco) for all of the

specimens as shown in Table 4

43 Effects of longitudinal stiffeners

As mentioned above longitudinal stiffeners are able to improve

the capacity of coped beam specimens signi1047297cantly by forcing the

occurrence of 1047298exural yielding of the full beam section near the

loading position prior to the development of webcrippling (except for

specimen B3) The ratio of the maximum bending moment at the

loading position to the plastic moment capacity of the specimens

rangesfrom 089 to 115 forthe specimenswith longitudinalstiffeners

only In order to illustrate the improved performance of thereinforcedcoped beam specimens the curves of maximum bending moment

versus beam de1047298ection at the loading position are shown in Fig 12 It

should be noted that specimens A2 B2 and B3 only have a stiffener

extension (ex) equal toabout1dc whereas specimen A3 has a stiffener

extension (ex) of about 2dc Although specimens A2 and B2 were able

to develop the plastic moment capacity of the full beam section

Fig 12 shows that the moment versus de1047298ection curves of these

specimens descend abruptly once they have reached the maximum

applied moment due to the development of web crippling However

for specimens A3 which had a stiffener extension (ex) equal to about

2dc the moment versus de1047298ection curves show a more gradual

descending branch with a signi1047297cant increase in ultimate de1047298ection

prior to the occurrence of web crippling as shown in Fig 12 In

addition Table 4 shows that for specimens A2 A3 B2 and B3 the ratio

Table 4

Summary of moment and shear capacities of specimens

Test

specimens

R u(kN)

Mmax

(kNm)

Mco

(kNm)

Mp

(kNm)

Mpco

(kNm)

R wb

(kN)

R vy(kN)

Mmax

Mp

Mco

Mpco

R uR wb

R uR vy

Stiffener

type

Failure

mode

A1 2019 1340 384 1828 430 1985 3463 073 089 102 058 Without WB

A2 3056 2095 628 1851 1224 ndash 3558 113 051 ndash 086 L Y ndashR

A3 3290 2165 579 1875 1229 ndash 3487 115 047 ndash 094 L Y ndashR

A4 3275 2096 512 1842 1193 ndash 3511 114 043 ndash 093 L+ T Y ndashF

A5 3403 2218 582 1853 1201 ndash 3516 120 048 ndash 097 L+ T Y ndashF

B1 1495 993 282 1849 322 1557 2997 054 088 096 050 Without WBB2 2939 1983 570 1834 961 ndash 2950 108 059 ndash 100 L Y ndashR

B3 2407 1600 695 1799 941 ndash 3006 089 074 ndash 080 L R

B4 3188 2137 625 1787 921 ndash 2930 120 068 ndash 109 L+ T Y ndashF

B5 3330 2186 588 1825 947 ndash 2986 120 062 ndash 112 L+ T Y ndashF

Note R u = test ultimate reaction at the coped end of the beam specimens

Mmax = test maximum bending moment of the beam specimens at the loading position

Mco = test bending moment of the beam specimens at the end of cope ( Fig 4)

Mp = plastic moment capacity of full beam section

Mpco = plastic moment capacity of the coped section with longitudinal stiffeners (specimens A2ndashA5 and B2ndashB5) or yield moment capacity of the coped section without

stiffeners (specimens A1 and B1)

R wb = local web buckling capacity of specimens without stiffeners according to Yam equations [6]

R vy = shear capacity of the coped beam section

L = longitudinal stiffeners T = transverse stiffeners WB = web buckling

R = rigid body movement of stiffener due to web crippling

Y ndashR = yielding of full beam section followed by rigid body movement of stiffener due to web crippling

Y ndashF = yielding of full beam section followed by 1047298ange local buckling near loading position

1756 MCH Yam et al Journal of Constructional Steel Research 67 (2011) 1749ndash1759

7182019 Experimental study of the strength and behaviour of reinforced coped beams

httpslidepdfcomreaderfullexperimental-study-of-the-strength-and-behaviour-of-reinforced-coped-beams 911

of the ultimate reaction (R u) to the shear capacity of the coped section

ranges from 08 to 10

Based on the test results and the above discussion it can be seen

that reinforcing coped beams using a pair of longitudinal stiffeners

with a stiffener extension of 1dc is able to improve the capacity of the

beams signi1047297cantly However a longer stiffener extension (2dc used

in this test programme) was able to provide a more stable and more

gradual coped beam unloading behaviour after the full beam section

reaches its plastic moment capacity

44 Effects of combined longitudinal and transverse stiffeners

The test results show that when the specimens (A4 A5 B4 and B5)

were reinforced by both longitudinal and transverse stiffeners the

beam specimens were able to achieve the plastic moment capacity of

the full beam section with a 1047297nal failure mode of 1047298ange local buckling

near the loading position In addition the ultimate reaction (R u) of

specimens B4 and B5 reached the shear capacity of the coped sectionas shown in Table 4 The maximum bending moment versus beam

de1047298ection curves at the loading position for specimens A4 A5 B4 and

B5 are shown in Fig 13 It can be seen from the 1047297gure that all the

curves show a typical moment versus de1047298ection behaviour where the

beams are able to sustain the maximum applied moment with

considerable beam de1047298ection As shown in Table 4 the ratio of the

maximum bending moment at the loading position to the plastic

moment capacity of the specimens ranges from 114 to 120 and the

ratio of the ultimate reaction (R u) to the shear capacity of the coped

section varies between 093 and 112 Hence it can be seen that the

combined longitudinal and transverse stiffeners were able to develop

the capacity of either the coped section (except for specimen A4) or

the full beam section of the specimens and also prohibited the

occurrence of web crippling at the end of the cope Fig 14 shows the

curves of applied load versus lateral displacement of the web at the

end of the cope for specimens B4 and B5 The 1047297gure illustrates that

there is a lateral web movement of about 7 mm for specimen B4

However almost no lateral movement was observed for specimen B5

which had the double transverse stiffeners

Based on the test results and the above discussion it can be seen

that the use of combined longitudinal and transverse stiffeners in

reinforcing coped beams improves the capacity of the beams

substantially by allowing failure to occur in either the coped section

(due to shear) or the full beam section (due to moment) In addition

the reinforced coped beams were able to sustain the maximum

applied load with considerable de1047298ection Furthermore the combinedlongitudinal and double transverse stiffeners prohibit lateral move-

ment of the web at the end of the cope and hence eliminate the

possibility of web crippling

45 Effects of cope depth and cope length

All the specimens had a cope length (c) of approximately 210 mm

(cDasymp06) except for specimen B3 which had a cope length of

Vertical deflection δ (mm)

0

25

50

75

100

125

150

175200

225

250

0 3 6 9 12 15 18 21 24 27 30 33 36

M a x i m u m m o m e n t M m a x

( k N m )

P

R

V

Mmax

Mp = 1827 kNm

A4

B5

A5

B4

Fig 13 Moment versus de1047298ection curves for specimens A4 A5 B4 and B5

Vertical deflection δ (mm)

0

25

50

75

100

125

150

175

200

225

250

0 3 6 9 12 15 18 21 24 27 30 33 36

P

R

V

Mmax

A2

B2

A3

B3

Mp= 184 kNm

M a x i m u m

m o m e n t M m a x

( k N m )

Fig 12 Moment versus de1047298ection curves for specimens A2 A3 B2 and B3

1757MCH Yam et al Journal of Constructional Steel Research 67 (2011) 1749ndash1759

7182019 Experimental study of the strength and behaviour of reinforced coped beams

httpslidepdfcomreaderfullexperimental-study-of-the-strength-and-behaviour-of-reinforced-coped-beams 1011

315 mm (cDasymp09) The cope depth (dc) of the B-series specimens

was about 105 mm (dcDasymp03) whereas the cope depth of the A-

series specimens was about 60 mm (dcDasymp018) For specimens A1

and B1 which did not have stiffeners increasing the cope depth

causes a decrease in the web buckling capacity of the specimen as

shown in Table 4 For the specimens with stiffeners however

increasing the cope depth does not affect the capacity of the

specimens signi1047297cantly as shown in the table since the stiffeners are

able to strengthen the coped section such that web crippling does not

occur prior to the development of the full beam section plastic

moment capacity When comparing the test results of specimen B2 to

those of specimenB3 it can be seenthatincreasing the cope length by

52 (with the same stiffener extension of about 1dc) the capacity of

the beam specimens is decreased by 18 In fact the failure mode of specimen B3 is that of web crippling at the end of the cope instead of

1047298exural yielding of the full beam section near the loading position

Hence it can be seen that the reinforcement detail requirement of

coped beams should include the in1047298uence of both the cope length and

the cope depth

5 Proposed modi1047297cation to the current reinforcement details for

coped beams

As mentioned above the current reinforcement details for coped

beams are based on the work by Cheng et al [4] details which have

also been adopted by the AISC Steel Construction Manual [9] as

shown in Fig 3 According to the 1047297gure for coped beams (htwle60)

reinforced with longitudinal stiffeners the stiffener extension (ex)must be at least equal to or greater than the cope depth (d c) The

reinforced coped beam is then checked for 1047298exural yielding of the

reinforced section and a local web buckling check of the coped section

is not required

Based on the test results it can be seen that the coped beam

specimens (except for specimen B3) which were reinforced with

longitudinal stiffeners according to the current reinforcement details

were able to reach the plastic moment capacity of the full beam section

and no bending failure was observed in the reinforced section In

addition the ultimate reactions of the specimens were also close to the

shear capacity of thecoped section ForspecimenB3 which hada longer

cope length (cDasymp09 comparingto cDasymp06 of other specimens) web

crippling failure was observed prior to reaching the plastic moment

capacity of the full beam section The test results also show that

specimen A2 which had a stiffener extension of 2dc exhibited more

ductile behaviour For the specimens with both longitudinal and

transverse (single or double) stiffeners the beams were able to reach

the plastic moment capacity of the full beam section with ductile

behaviour and the ultimate reactions of the specimens were very close

to or exceeded the shear capacity of the coped section

Basedon the limited test data andtheabovediscussion a modi1047297cation

to the reinforcement details for coped beams is proposed as follows

For coped beams with htwle60 dcDle03 and cDle06 only

longitudinal stiffeners are required and the length of the

longitudinal stiffeners (L x) is

L = c + eX where eX ge 2dc

eth4THORN

For coped beams with htwle60 dcDle03 and 06lecDle09 both

longitudinal and transverse (single) stiffeners are required and the

lengths of the longitudinal (L x) and thetransverse (L y) stiffeners are

L x = c + ex where eX ge dc

L y = dc + ey where ey ge dc eth5THORN

All the symbols have been de1047297ned in Fig 4 It should be noted

that the above preliminary recommendations of the reinforcement

details for coped beam are based on limited test data Further

numerical work is underway to systematically examine the rein-

forcement requirements for a wider range of cope details in order toincrease the range of applicability of the above recommendations

6 Summary and conclusions

A total of 10 full-scale tests were conducted to investigate the

strength and behaviour of reinforced coped steel I-beams The main

test parameters included the length of longitudinal stiffeners (L x)

length of transverse stiffeners (L y) combined longitudinal and

transverse stiffeners double transverse stiffeners and the cope details

(cope depth (dc) and cope length (c)) For the coped beam specimens

without stiffeners local web buckling failure occurred in the cope For

the specimens with longitudinal stiffeners only the general failure

mode was 1047298exural yielding of the full beam section at the location of

maximum bending moment followed by web crippling at the end of

0

100

200

300

400

500

600

-2 -1 0 1 2 3 4 5 6 7 8

B5

B4

Lateral displacement of web at end of cope (mm)

A p p l i e d l o a

d

P ( k N )

P

LVDT

Specimen B4

P

LVDT

Specimen B5

Fig 14 Applied load versus lateral displacement curves for specimens B4 and B5

1758 MCH Yam et al Journal of Constructional Steel Research 67 (2011) 1749ndash1759

7182019 Experimental study of the strength and behaviour of reinforced coped beams

httpslidepdfcomreaderfullexperimental-study-of-the-strength-and-behaviour-of-reinforced-coped-beams 1111

the cope between the longitudinal stiffeners and the top 1047298ange of the

full beam section In contrast for the specimens with combined

longitudinal and transverse stiffeners the general failure mode was

1047298exural yielding of the full beam section at the location of maximum

bending moment followed by 1047298ange local buckling near the loading

position

Thetest results show that thereinforcementswere able to increase

the capacity of the coped beam specimens signi1047297cantly The ratio of

the maximum bending moment at the loading position to the plasticmoment capacity of the full beam section of the reinforced coped

beam specimens rangedfrom 089 to 120 andthe ratio of the ultimate

reaction (R u) to the shear capacity of the coped section varied

between 080 and 112 The test results also illustrate that in addition

to the cope depth the cope length (c) also affected the behaviour and

strength of reinforced coped beams In addition the specimens with

either a longer stiffener extension (ex) for the longitudinal stiffeners

or combined longitudinal and transverse stiffeners were able to

sustain the maximum applied load with considerable de1047298ection

Based on the limited test data a modi1047297cation to the currently

recommended reinforcement details for coped beams has been

proposed The proposed reinforcement details included the in1047298uence

of various cope details A numerical study of reinforced coped beams

is currently underway to consider a wider range of cope details in

order to increase the range of applicability of the proposed

reinforcement details for coped beams

Acknowledgements

The work described in this paper was fully supported by a

grant from the Research Grants Council of the Hong Kong Special

Administrative Region China (Project No PolyU 532908E) The

assistance of Mr TL Ip Mr CH Leong and Mr SL Meng in conduct-

ing the tests is also acknowledged

References

[1] Birkemoe PC Gilmor MI Behavior of bearing critical double-angle beamconnections Engineering Journal AISC 197815(4)109ndash15

[2] Yura JA Birkemoe PC Ricles JM Beam web shear connections an experimentalstudy Journal of the Structural Division ASCE 1982108(ST2)311ndash25

[3] Ricles JM Yura JA Strength of double-row bolted-web connections Journal of Structural Engineering ASCE 1983109(12)126ndash42[4] Cheng JJ Yura JA Johnson CP Design and behavior of coped beams Ferguson

Structural Engineering Laboratory ReportNo 84-1 Department of Civil EngineeringUniversity of Texas July 1984

[5] Cheng JJR Yura JA Local web buckling of coped beams Journal of StructuralEngineering ASCE 1986112(10)2314ndash31

[6] Aalberg A Larsen PK Local web buckling of coped beams Nordic SteelConstruction Conference NSCC 2001 Proceedings Helsinki Finland 18ndash20 June2001

[7] Yam MCH Lam ACC Iu VP Cheng JJR The local web buckling strength of coped steel I-beam Journal of Structural Engineering ASCE 2003129(1)3ndash11

[8] American Institute of Steel Construction Steel Construction Manual One EastWacker Drive Suite 700 Chicago Illinoisthird ed 2005 p 60601ndash1802

[9] Yam MCH Lam ACC Wei F Chung KF The local web buckling strength of stiffened coped steel-I-beam International Journal of Steel Structures20077(2)129ndash38

[10] LamACC Yam MCHFu CKM ExperimentalInvestigation of thelocal web buckling

strength of coped steel I-beam with and without stiffeners The 10th East Asia-Paci1047297c Conference on Structural Engineering and Construction BangkokThailand 2006 p 559ndash64 August 3ndash5

[11] InstituteSteelConstruction Steelwork Design Guideto BS5950-12000 Volume 1Section Properties Member Capacities6th ed 2001

[12] British Standards Institution (BSI) BS EN 10025-22004 Hot Rolled Products Of Structural Steels mdash Part 2 Technical Delivery Conditions for Non-Alloy StructuralSteels London 2004

[13] Vinnakota S Steel Structures Behavior and LRFD McGraw Hill 2006[14] American Society of Civil Engineers (ASCE) Welding Research Council (WRC)

Plastic Design in Steel A Guide and Commentary New York New York2nd ed 1971

1759MCH Yam et al Journal of Constructional Steel Research 67 (2011) 1749ndash1759

Page 9: Experimental study of the strength and behaviour of reinforced coped beams

7182019 Experimental study of the strength and behaviour of reinforced coped beams

httpslidepdfcomreaderfullexperimental-study-of-the-strength-and-behaviour-of-reinforced-coped-beams 911

of the ultimate reaction (R u) to the shear capacity of the coped section

ranges from 08 to 10

Based on the test results and the above discussion it can be seen

that reinforcing coped beams using a pair of longitudinal stiffeners

with a stiffener extension of 1dc is able to improve the capacity of the

beams signi1047297cantly However a longer stiffener extension (2dc used

in this test programme) was able to provide a more stable and more

gradual coped beam unloading behaviour after the full beam section

reaches its plastic moment capacity

44 Effects of combined longitudinal and transverse stiffeners

The test results show that when the specimens (A4 A5 B4 and B5)

were reinforced by both longitudinal and transverse stiffeners the

beam specimens were able to achieve the plastic moment capacity of

the full beam section with a 1047297nal failure mode of 1047298ange local buckling

near the loading position In addition the ultimate reaction (R u) of

specimens B4 and B5 reached the shear capacity of the coped sectionas shown in Table 4 The maximum bending moment versus beam

de1047298ection curves at the loading position for specimens A4 A5 B4 and

B5 are shown in Fig 13 It can be seen from the 1047297gure that all the

curves show a typical moment versus de1047298ection behaviour where the

beams are able to sustain the maximum applied moment with

considerable beam de1047298ection As shown in Table 4 the ratio of the

maximum bending moment at the loading position to the plastic

moment capacity of the specimens ranges from 114 to 120 and the

ratio of the ultimate reaction (R u) to the shear capacity of the coped

section varies between 093 and 112 Hence it can be seen that the

combined longitudinal and transverse stiffeners were able to develop

the capacity of either the coped section (except for specimen A4) or

the full beam section of the specimens and also prohibited the

occurrence of web crippling at the end of the cope Fig 14 shows the

curves of applied load versus lateral displacement of the web at the

end of the cope for specimens B4 and B5 The 1047297gure illustrates that

there is a lateral web movement of about 7 mm for specimen B4

However almost no lateral movement was observed for specimen B5

which had the double transverse stiffeners

Based on the test results and the above discussion it can be seen

that the use of combined longitudinal and transverse stiffeners in

reinforcing coped beams improves the capacity of the beams

substantially by allowing failure to occur in either the coped section

(due to shear) or the full beam section (due to moment) In addition

the reinforced coped beams were able to sustain the maximum

applied load with considerable de1047298ection Furthermore the combinedlongitudinal and double transverse stiffeners prohibit lateral move-

ment of the web at the end of the cope and hence eliminate the

possibility of web crippling

45 Effects of cope depth and cope length

All the specimens had a cope length (c) of approximately 210 mm

(cDasymp06) except for specimen B3 which had a cope length of

Vertical deflection δ (mm)

0

25

50

75

100

125

150

175200

225

250

0 3 6 9 12 15 18 21 24 27 30 33 36

M a x i m u m m o m e n t M m a x

( k N m )

P

R

V

Mmax

Mp = 1827 kNm

A4

B5

A5

B4

Fig 13 Moment versus de1047298ection curves for specimens A4 A5 B4 and B5

Vertical deflection δ (mm)

0

25

50

75

100

125

150

175

200

225

250

0 3 6 9 12 15 18 21 24 27 30 33 36

P

R

V

Mmax

A2

B2

A3

B3

Mp= 184 kNm

M a x i m u m

m o m e n t M m a x

( k N m )

Fig 12 Moment versus de1047298ection curves for specimens A2 A3 B2 and B3

1757MCH Yam et al Journal of Constructional Steel Research 67 (2011) 1749ndash1759

7182019 Experimental study of the strength and behaviour of reinforced coped beams

httpslidepdfcomreaderfullexperimental-study-of-the-strength-and-behaviour-of-reinforced-coped-beams 1011

315 mm (cDasymp09) The cope depth (dc) of the B-series specimens

was about 105 mm (dcDasymp03) whereas the cope depth of the A-

series specimens was about 60 mm (dcDasymp018) For specimens A1

and B1 which did not have stiffeners increasing the cope depth

causes a decrease in the web buckling capacity of the specimen as

shown in Table 4 For the specimens with stiffeners however

increasing the cope depth does not affect the capacity of the

specimens signi1047297cantly as shown in the table since the stiffeners are

able to strengthen the coped section such that web crippling does not

occur prior to the development of the full beam section plastic

moment capacity When comparing the test results of specimen B2 to

those of specimenB3 it can be seenthatincreasing the cope length by

52 (with the same stiffener extension of about 1dc) the capacity of

the beam specimens is decreased by 18 In fact the failure mode of specimen B3 is that of web crippling at the end of the cope instead of

1047298exural yielding of the full beam section near the loading position

Hence it can be seen that the reinforcement detail requirement of

coped beams should include the in1047298uence of both the cope length and

the cope depth

5 Proposed modi1047297cation to the current reinforcement details for

coped beams

As mentioned above the current reinforcement details for coped

beams are based on the work by Cheng et al [4] details which have

also been adopted by the AISC Steel Construction Manual [9] as

shown in Fig 3 According to the 1047297gure for coped beams (htwle60)

reinforced with longitudinal stiffeners the stiffener extension (ex)must be at least equal to or greater than the cope depth (d c) The

reinforced coped beam is then checked for 1047298exural yielding of the

reinforced section and a local web buckling check of the coped section

is not required

Based on the test results it can be seen that the coped beam

specimens (except for specimen B3) which were reinforced with

longitudinal stiffeners according to the current reinforcement details

were able to reach the plastic moment capacity of the full beam section

and no bending failure was observed in the reinforced section In

addition the ultimate reactions of the specimens were also close to the

shear capacity of thecoped section ForspecimenB3 which hada longer

cope length (cDasymp09 comparingto cDasymp06 of other specimens) web

crippling failure was observed prior to reaching the plastic moment

capacity of the full beam section The test results also show that

specimen A2 which had a stiffener extension of 2dc exhibited more

ductile behaviour For the specimens with both longitudinal and

transverse (single or double) stiffeners the beams were able to reach

the plastic moment capacity of the full beam section with ductile

behaviour and the ultimate reactions of the specimens were very close

to or exceeded the shear capacity of the coped section

Basedon the limited test data andtheabovediscussion a modi1047297cation

to the reinforcement details for coped beams is proposed as follows

For coped beams with htwle60 dcDle03 and cDle06 only

longitudinal stiffeners are required and the length of the

longitudinal stiffeners (L x) is

L = c + eX where eX ge 2dc

eth4THORN

For coped beams with htwle60 dcDle03 and 06lecDle09 both

longitudinal and transverse (single) stiffeners are required and the

lengths of the longitudinal (L x) and thetransverse (L y) stiffeners are

L x = c + ex where eX ge dc

L y = dc + ey where ey ge dc eth5THORN

All the symbols have been de1047297ned in Fig 4 It should be noted

that the above preliminary recommendations of the reinforcement

details for coped beam are based on limited test data Further

numerical work is underway to systematically examine the rein-

forcement requirements for a wider range of cope details in order toincrease the range of applicability of the above recommendations

6 Summary and conclusions

A total of 10 full-scale tests were conducted to investigate the

strength and behaviour of reinforced coped steel I-beams The main

test parameters included the length of longitudinal stiffeners (L x)

length of transverse stiffeners (L y) combined longitudinal and

transverse stiffeners double transverse stiffeners and the cope details

(cope depth (dc) and cope length (c)) For the coped beam specimens

without stiffeners local web buckling failure occurred in the cope For

the specimens with longitudinal stiffeners only the general failure

mode was 1047298exural yielding of the full beam section at the location of

maximum bending moment followed by web crippling at the end of

0

100

200

300

400

500

600

-2 -1 0 1 2 3 4 5 6 7 8

B5

B4

Lateral displacement of web at end of cope (mm)

A p p l i e d l o a

d

P ( k N )

P

LVDT

Specimen B4

P

LVDT

Specimen B5

Fig 14 Applied load versus lateral displacement curves for specimens B4 and B5

1758 MCH Yam et al Journal of Constructional Steel Research 67 (2011) 1749ndash1759

7182019 Experimental study of the strength and behaviour of reinforced coped beams

httpslidepdfcomreaderfullexperimental-study-of-the-strength-and-behaviour-of-reinforced-coped-beams 1111

the cope between the longitudinal stiffeners and the top 1047298ange of the

full beam section In contrast for the specimens with combined

longitudinal and transverse stiffeners the general failure mode was

1047298exural yielding of the full beam section at the location of maximum

bending moment followed by 1047298ange local buckling near the loading

position

Thetest results show that thereinforcementswere able to increase

the capacity of the coped beam specimens signi1047297cantly The ratio of

the maximum bending moment at the loading position to the plasticmoment capacity of the full beam section of the reinforced coped

beam specimens rangedfrom 089 to 120 andthe ratio of the ultimate

reaction (R u) to the shear capacity of the coped section varied

between 080 and 112 The test results also illustrate that in addition

to the cope depth the cope length (c) also affected the behaviour and

strength of reinforced coped beams In addition the specimens with

either a longer stiffener extension (ex) for the longitudinal stiffeners

or combined longitudinal and transverse stiffeners were able to

sustain the maximum applied load with considerable de1047298ection

Based on the limited test data a modi1047297cation to the currently

recommended reinforcement details for coped beams has been

proposed The proposed reinforcement details included the in1047298uence

of various cope details A numerical study of reinforced coped beams

is currently underway to consider a wider range of cope details in

order to increase the range of applicability of the proposed

reinforcement details for coped beams

Acknowledgements

The work described in this paper was fully supported by a

grant from the Research Grants Council of the Hong Kong Special

Administrative Region China (Project No PolyU 532908E) The

assistance of Mr TL Ip Mr CH Leong and Mr SL Meng in conduct-

ing the tests is also acknowledged

References

[1] Birkemoe PC Gilmor MI Behavior of bearing critical double-angle beamconnections Engineering Journal AISC 197815(4)109ndash15

[2] Yura JA Birkemoe PC Ricles JM Beam web shear connections an experimentalstudy Journal of the Structural Division ASCE 1982108(ST2)311ndash25

[3] Ricles JM Yura JA Strength of double-row bolted-web connections Journal of Structural Engineering ASCE 1983109(12)126ndash42[4] Cheng JJ Yura JA Johnson CP Design and behavior of coped beams Ferguson

Structural Engineering Laboratory ReportNo 84-1 Department of Civil EngineeringUniversity of Texas July 1984

[5] Cheng JJR Yura JA Local web buckling of coped beams Journal of StructuralEngineering ASCE 1986112(10)2314ndash31

[6] Aalberg A Larsen PK Local web buckling of coped beams Nordic SteelConstruction Conference NSCC 2001 Proceedings Helsinki Finland 18ndash20 June2001

[7] Yam MCH Lam ACC Iu VP Cheng JJR The local web buckling strength of coped steel I-beam Journal of Structural Engineering ASCE 2003129(1)3ndash11

[8] American Institute of Steel Construction Steel Construction Manual One EastWacker Drive Suite 700 Chicago Illinoisthird ed 2005 p 60601ndash1802

[9] Yam MCH Lam ACC Wei F Chung KF The local web buckling strength of stiffened coped steel-I-beam International Journal of Steel Structures20077(2)129ndash38

[10] LamACC Yam MCHFu CKM ExperimentalInvestigation of thelocal web buckling

strength of coped steel I-beam with and without stiffeners The 10th East Asia-Paci1047297c Conference on Structural Engineering and Construction BangkokThailand 2006 p 559ndash64 August 3ndash5

[11] InstituteSteelConstruction Steelwork Design Guideto BS5950-12000 Volume 1Section Properties Member Capacities6th ed 2001

[12] British Standards Institution (BSI) BS EN 10025-22004 Hot Rolled Products Of Structural Steels mdash Part 2 Technical Delivery Conditions for Non-Alloy StructuralSteels London 2004

[13] Vinnakota S Steel Structures Behavior and LRFD McGraw Hill 2006[14] American Society of Civil Engineers (ASCE) Welding Research Council (WRC)

Plastic Design in Steel A Guide and Commentary New York New York2nd ed 1971

1759MCH Yam et al Journal of Constructional Steel Research 67 (2011) 1749ndash1759

Page 10: Experimental study of the strength and behaviour of reinforced coped beams

7182019 Experimental study of the strength and behaviour of reinforced coped beams

httpslidepdfcomreaderfullexperimental-study-of-the-strength-and-behaviour-of-reinforced-coped-beams 1011

315 mm (cDasymp09) The cope depth (dc) of the B-series specimens

was about 105 mm (dcDasymp03) whereas the cope depth of the A-

series specimens was about 60 mm (dcDasymp018) For specimens A1

and B1 which did not have stiffeners increasing the cope depth

causes a decrease in the web buckling capacity of the specimen as

shown in Table 4 For the specimens with stiffeners however

increasing the cope depth does not affect the capacity of the

specimens signi1047297cantly as shown in the table since the stiffeners are

able to strengthen the coped section such that web crippling does not

occur prior to the development of the full beam section plastic

moment capacity When comparing the test results of specimen B2 to

those of specimenB3 it can be seenthatincreasing the cope length by

52 (with the same stiffener extension of about 1dc) the capacity of

the beam specimens is decreased by 18 In fact the failure mode of specimen B3 is that of web crippling at the end of the cope instead of

1047298exural yielding of the full beam section near the loading position

Hence it can be seen that the reinforcement detail requirement of

coped beams should include the in1047298uence of both the cope length and

the cope depth

5 Proposed modi1047297cation to the current reinforcement details for

coped beams

As mentioned above the current reinforcement details for coped

beams are based on the work by Cheng et al [4] details which have

also been adopted by the AISC Steel Construction Manual [9] as

shown in Fig 3 According to the 1047297gure for coped beams (htwle60)

reinforced with longitudinal stiffeners the stiffener extension (ex)must be at least equal to or greater than the cope depth (d c) The

reinforced coped beam is then checked for 1047298exural yielding of the

reinforced section and a local web buckling check of the coped section

is not required

Based on the test results it can be seen that the coped beam

specimens (except for specimen B3) which were reinforced with

longitudinal stiffeners according to the current reinforcement details

were able to reach the plastic moment capacity of the full beam section

and no bending failure was observed in the reinforced section In

addition the ultimate reactions of the specimens were also close to the

shear capacity of thecoped section ForspecimenB3 which hada longer

cope length (cDasymp09 comparingto cDasymp06 of other specimens) web

crippling failure was observed prior to reaching the plastic moment

capacity of the full beam section The test results also show that

specimen A2 which had a stiffener extension of 2dc exhibited more

ductile behaviour For the specimens with both longitudinal and

transverse (single or double) stiffeners the beams were able to reach

the plastic moment capacity of the full beam section with ductile

behaviour and the ultimate reactions of the specimens were very close

to or exceeded the shear capacity of the coped section

Basedon the limited test data andtheabovediscussion a modi1047297cation

to the reinforcement details for coped beams is proposed as follows

For coped beams with htwle60 dcDle03 and cDle06 only

longitudinal stiffeners are required and the length of the

longitudinal stiffeners (L x) is

L = c + eX where eX ge 2dc

eth4THORN

For coped beams with htwle60 dcDle03 and 06lecDle09 both

longitudinal and transverse (single) stiffeners are required and the

lengths of the longitudinal (L x) and thetransverse (L y) stiffeners are

L x = c + ex where eX ge dc

L y = dc + ey where ey ge dc eth5THORN

All the symbols have been de1047297ned in Fig 4 It should be noted

that the above preliminary recommendations of the reinforcement

details for coped beam are based on limited test data Further

numerical work is underway to systematically examine the rein-

forcement requirements for a wider range of cope details in order toincrease the range of applicability of the above recommendations

6 Summary and conclusions

A total of 10 full-scale tests were conducted to investigate the

strength and behaviour of reinforced coped steel I-beams The main

test parameters included the length of longitudinal stiffeners (L x)

length of transverse stiffeners (L y) combined longitudinal and

transverse stiffeners double transverse stiffeners and the cope details

(cope depth (dc) and cope length (c)) For the coped beam specimens

without stiffeners local web buckling failure occurred in the cope For

the specimens with longitudinal stiffeners only the general failure

mode was 1047298exural yielding of the full beam section at the location of

maximum bending moment followed by web crippling at the end of

0

100

200

300

400

500

600

-2 -1 0 1 2 3 4 5 6 7 8

B5

B4

Lateral displacement of web at end of cope (mm)

A p p l i e d l o a

d

P ( k N )

P

LVDT

Specimen B4

P

LVDT

Specimen B5

Fig 14 Applied load versus lateral displacement curves for specimens B4 and B5

1758 MCH Yam et al Journal of Constructional Steel Research 67 (2011) 1749ndash1759

7182019 Experimental study of the strength and behaviour of reinforced coped beams

httpslidepdfcomreaderfullexperimental-study-of-the-strength-and-behaviour-of-reinforced-coped-beams 1111

the cope between the longitudinal stiffeners and the top 1047298ange of the

full beam section In contrast for the specimens with combined

longitudinal and transverse stiffeners the general failure mode was

1047298exural yielding of the full beam section at the location of maximum

bending moment followed by 1047298ange local buckling near the loading

position

Thetest results show that thereinforcementswere able to increase

the capacity of the coped beam specimens signi1047297cantly The ratio of

the maximum bending moment at the loading position to the plasticmoment capacity of the full beam section of the reinforced coped

beam specimens rangedfrom 089 to 120 andthe ratio of the ultimate

reaction (R u) to the shear capacity of the coped section varied

between 080 and 112 The test results also illustrate that in addition

to the cope depth the cope length (c) also affected the behaviour and

strength of reinforced coped beams In addition the specimens with

either a longer stiffener extension (ex) for the longitudinal stiffeners

or combined longitudinal and transverse stiffeners were able to

sustain the maximum applied load with considerable de1047298ection

Based on the limited test data a modi1047297cation to the currently

recommended reinforcement details for coped beams has been

proposed The proposed reinforcement details included the in1047298uence

of various cope details A numerical study of reinforced coped beams

is currently underway to consider a wider range of cope details in

order to increase the range of applicability of the proposed

reinforcement details for coped beams

Acknowledgements

The work described in this paper was fully supported by a

grant from the Research Grants Council of the Hong Kong Special

Administrative Region China (Project No PolyU 532908E) The

assistance of Mr TL Ip Mr CH Leong and Mr SL Meng in conduct-

ing the tests is also acknowledged

References

[1] Birkemoe PC Gilmor MI Behavior of bearing critical double-angle beamconnections Engineering Journal AISC 197815(4)109ndash15

[2] Yura JA Birkemoe PC Ricles JM Beam web shear connections an experimentalstudy Journal of the Structural Division ASCE 1982108(ST2)311ndash25

[3] Ricles JM Yura JA Strength of double-row bolted-web connections Journal of Structural Engineering ASCE 1983109(12)126ndash42[4] Cheng JJ Yura JA Johnson CP Design and behavior of coped beams Ferguson

Structural Engineering Laboratory ReportNo 84-1 Department of Civil EngineeringUniversity of Texas July 1984

[5] Cheng JJR Yura JA Local web buckling of coped beams Journal of StructuralEngineering ASCE 1986112(10)2314ndash31

[6] Aalberg A Larsen PK Local web buckling of coped beams Nordic SteelConstruction Conference NSCC 2001 Proceedings Helsinki Finland 18ndash20 June2001

[7] Yam MCH Lam ACC Iu VP Cheng JJR The local web buckling strength of coped steel I-beam Journal of Structural Engineering ASCE 2003129(1)3ndash11

[8] American Institute of Steel Construction Steel Construction Manual One EastWacker Drive Suite 700 Chicago Illinoisthird ed 2005 p 60601ndash1802

[9] Yam MCH Lam ACC Wei F Chung KF The local web buckling strength of stiffened coped steel-I-beam International Journal of Steel Structures20077(2)129ndash38

[10] LamACC Yam MCHFu CKM ExperimentalInvestigation of thelocal web buckling

strength of coped steel I-beam with and without stiffeners The 10th East Asia-Paci1047297c Conference on Structural Engineering and Construction BangkokThailand 2006 p 559ndash64 August 3ndash5

[11] InstituteSteelConstruction Steelwork Design Guideto BS5950-12000 Volume 1Section Properties Member Capacities6th ed 2001

[12] British Standards Institution (BSI) BS EN 10025-22004 Hot Rolled Products Of Structural Steels mdash Part 2 Technical Delivery Conditions for Non-Alloy StructuralSteels London 2004

[13] Vinnakota S Steel Structures Behavior and LRFD McGraw Hill 2006[14] American Society of Civil Engineers (ASCE) Welding Research Council (WRC)

Plastic Design in Steel A Guide and Commentary New York New York2nd ed 1971

1759MCH Yam et al Journal of Constructional Steel Research 67 (2011) 1749ndash1759

Page 11: Experimental study of the strength and behaviour of reinforced coped beams

7182019 Experimental study of the strength and behaviour of reinforced coped beams

httpslidepdfcomreaderfullexperimental-study-of-the-strength-and-behaviour-of-reinforced-coped-beams 1111

the cope between the longitudinal stiffeners and the top 1047298ange of the

full beam section In contrast for the specimens with combined

longitudinal and transverse stiffeners the general failure mode was

1047298exural yielding of the full beam section at the location of maximum

bending moment followed by 1047298ange local buckling near the loading

position

Thetest results show that thereinforcementswere able to increase

the capacity of the coped beam specimens signi1047297cantly The ratio of

the maximum bending moment at the loading position to the plasticmoment capacity of the full beam section of the reinforced coped

beam specimens rangedfrom 089 to 120 andthe ratio of the ultimate

reaction (R u) to the shear capacity of the coped section varied

between 080 and 112 The test results also illustrate that in addition

to the cope depth the cope length (c) also affected the behaviour and

strength of reinforced coped beams In addition the specimens with

either a longer stiffener extension (ex) for the longitudinal stiffeners

or combined longitudinal and transverse stiffeners were able to

sustain the maximum applied load with considerable de1047298ection

Based on the limited test data a modi1047297cation to the currently

recommended reinforcement details for coped beams has been

proposed The proposed reinforcement details included the in1047298uence

of various cope details A numerical study of reinforced coped beams

is currently underway to consider a wider range of cope details in

order to increase the range of applicability of the proposed

reinforcement details for coped beams

Acknowledgements

The work described in this paper was fully supported by a

grant from the Research Grants Council of the Hong Kong Special

Administrative Region China (Project No PolyU 532908E) The

assistance of Mr TL Ip Mr CH Leong and Mr SL Meng in conduct-

ing the tests is also acknowledged

References

[1] Birkemoe PC Gilmor MI Behavior of bearing critical double-angle beamconnections Engineering Journal AISC 197815(4)109ndash15

[2] Yura JA Birkemoe PC Ricles JM Beam web shear connections an experimentalstudy Journal of the Structural Division ASCE 1982108(ST2)311ndash25

[3] Ricles JM Yura JA Strength of double-row bolted-web connections Journal of Structural Engineering ASCE 1983109(12)126ndash42[4] Cheng JJ Yura JA Johnson CP Design and behavior of coped beams Ferguson

Structural Engineering Laboratory ReportNo 84-1 Department of Civil EngineeringUniversity of Texas July 1984

[5] Cheng JJR Yura JA Local web buckling of coped beams Journal of StructuralEngineering ASCE 1986112(10)2314ndash31

[6] Aalberg A Larsen PK Local web buckling of coped beams Nordic SteelConstruction Conference NSCC 2001 Proceedings Helsinki Finland 18ndash20 June2001

[7] Yam MCH Lam ACC Iu VP Cheng JJR The local web buckling strength of coped steel I-beam Journal of Structural Engineering ASCE 2003129(1)3ndash11

[8] American Institute of Steel Construction Steel Construction Manual One EastWacker Drive Suite 700 Chicago Illinoisthird ed 2005 p 60601ndash1802

[9] Yam MCH Lam ACC Wei F Chung KF The local web buckling strength of stiffened coped steel-I-beam International Journal of Steel Structures20077(2)129ndash38

[10] LamACC Yam MCHFu CKM ExperimentalInvestigation of thelocal web buckling

strength of coped steel I-beam with and without stiffeners The 10th East Asia-Paci1047297c Conference on Structural Engineering and Construction BangkokThailand 2006 p 559ndash64 August 3ndash5

[11] InstituteSteelConstruction Steelwork Design Guideto BS5950-12000 Volume 1Section Properties Member Capacities6th ed 2001

[12] British Standards Institution (BSI) BS EN 10025-22004 Hot Rolled Products Of Structural Steels mdash Part 2 Technical Delivery Conditions for Non-Alloy StructuralSteels London 2004

[13] Vinnakota S Steel Structures Behavior and LRFD McGraw Hill 2006[14] American Society of Civil Engineers (ASCE) Welding Research Council (WRC)

Plastic Design in Steel A Guide and Commentary New York New York2nd ed 1971

1759MCH Yam et al Journal of Constructional Steel Research 67 (2011) 1749ndash1759