r - The Hong Kong Polytechnic University

The 5th Cross-strait Conference on Structural and Geotechnical Engineering (SGE-5)
Hong Kong, China, 13-15 July 2011
FINITE ELEMENT STUDY OF INELASTIC LOCAL WEB BUCKLING CAPACITY
OF COPED STEEL I-BEAM
Y. Qin 1 , C. C. Lam 2 , V. P. Iu 3 , and K. P. Kou 4
1,2,3,4 Department of Civil and Environmental Engineering,
University of Macau, Macau SAR, China.
2 Email: fstccl@umac.mo
ABSTRACT
In steel construction, beams often have to be coped at the flange to provide clearance for the framing beams or
to maintain the main beam and the secondary beam at the same level. When the beams are coped, the local web
buckling capacity of the beams at the coped region may be reduced. Depending on the cope details, the local
web buckling capacity can be classified as elastic and inelastic web buckling. For coped beam with relatively
short coped length and depth, part or the whole section of the web may yield before local web buckling occurs.
In this paper, non-linear finite element analyze, which included both material and geometric nonlinearities, of
the inelastic local web buckling capacity of coped steel I-beam is presented. The effects of different parameters,
such as (1) web slenderness (d/t w ), (2) cope depth to beam depth ratio (d c /D), (3) cope length to reduced web
depth ratio (c/h o ) and (4) initial imperfection of web section, to the web buckling capacity of coped steel I-beam
were studied. The current finite element results showed that local web buckling capacity decreased with
increased initial imperfection. Meanwhile, for beams with the smallest beam depth to web thickness ratio, both
shear yielding capacity and elastic web buckling capacity gave conservative prediction when c/h o is larger than
0.5. On the other hand, for beams with largest beam depth to web thickness ratio, the predicted elastic web
buckling capacity was closed to the finite element results for c/h o larger than 0.75. However, the prediction of
both shear yielding capacity and elastic web buckling capacity gave conservative prediction when c/h o is smaller
than 0.75 for most of the cases in this study.
KEYWORDS
Cope beam; finite element method; inelastic analysis; local web buckling; steel structures.
INTRODUCTION
In order to make the beam flanges at the same elevation, in practical steel construction, beam flanges often have to
be cut away from the major part to provide enough clearance for supports. The cope can be at the top (as shown in
Figure 1), the bottom, or both flanges in combination. As a result, due to the coped flanges, the corresponding
lateral-torsional buckling capacity and the local web buckling (LWB) capacity of the beam may be reduced. For
the beams with lateral support, block shear failure of the connection at beam end and local web buckling were two
potential failure modes. For thin webs, failure could occur by local web buckling at the coped region. The global
lateral-torsional buckling behavior and the elastic local web buckling strength of coped steel-I beam were studied
both experimentally and analytically by Cheng et al. (1984). Further studies of the design and behavior of coped I
beams were also conducted by some researchers (Cheng and Yura 1986; Lam et al. 2000; Yam et al. 2000; Johan
Maljaars et al. 2002; Yam et al. 2007). Based on the experimental and numerical investigations of the local web
buckling strength of coped section, Yam et al. (2003) proposed a modified plate buckling equation that considered
the shear buckling phenomenon for predicting the elastic local web buckling capacity of coped steel I-beam. It is
proposed that the critical elastic web buckling reaction (R cr ) can be predicted by Eqs. (1) to (3).
k
s
b
0
,
⎛ h ⎞
= a⎜
⎟
⎝ c ⎠
R
cr
=τ t D − d )
(1)
cr
w ( c
2
2
π E ⎛ tw
⎞
τ = k
2
12( 1 )
⎜
⎟
(2)
cr s
−υ
⎝ h0
⎠
2
d
c
a = 1.38
−1.79
,
⎛ dc ⎞ ⎛ dc
⎞
b = 3.64⎜
⎟ − 3.36⎜
⎟ + 1. 55
(3)
D ⎝ D ⎠ ⎝ D ⎠
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