Experimental study of the strength and behaviour of reinforced coped beams
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7182019 Experimental study of the strength and behaviour of reinforced coped beams
httpslidepdfcomreaderfullexperimental-study-of-the-strength-and-behaviour-of-reinforced-coped-beams 111
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
7182019 Experimental study of the strength and behaviour of reinforced coped beams
httpslidepdfcomreaderfullexperimental-study-of-the-strength-and-behaviour-of-reinforced-coped-beams 211
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
httpslidepdfcomreaderfullexperimental-study-of-the-strength-and-behaviour-of-reinforced-coped-beams 311
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
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
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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
7182019 Experimental study of the strength and behaviour of reinforced coped beams
httpslidepdfcomreaderfullexperimental-study-of-the-strength-and-behaviour-of-reinforced-coped-beams 211
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
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
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
7182019 Experimental study of the strength and behaviour of reinforced coped beams
httpslidepdfcomreaderfullexperimental-study-of-the-strength-and-behaviour-of-reinforced-coped-beams 311
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
httpslidepdfcomreaderfullexperimental-study-of-the-strength-and-behaviour-of-reinforced-coped-beams 411
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
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
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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
7182019 Experimental study of the strength and behaviour of reinforced coped beams
httpslidepdfcomreaderfullexperimental-study-of-the-strength-and-behaviour-of-reinforced-coped-beams 411
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
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
7182019 Experimental study of the strength and behaviour of reinforced coped beams
httpslidepdfcomreaderfullexperimental-study-of-the-strength-and-behaviour-of-reinforced-coped-beams 511
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
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
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
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
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
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
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
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
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
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
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