r - The Hong Kong Polytechnic University

Table 3 Summary of the variables of parametric study
Parameters UB203×133×30 UB610×305×179 UB356×171×51 UB406×140×39
D (mm) 206.8 617.5 355.6 397.3
T (mm) 9.6 23.6 11.5 8.6
B (mm) 133.8 307 171.5 141.8
depth between fillets, d (mm) 172.4 537.3 312.2 359.7
web thickness, t w (mm) 6.3 14.1 7.3 6.3
d/t w 27.4 38.1 42.8 57.1
d c /D 0.05, 0.1, 0.15
cope depth, d c (mm) 17 21 31 31 62 93 18 36 53 20 40 60
h 0 =D-d c (mm) 190 186 176 587 556 525 338 320 302 377 358 338
c/h 0 0.1, 0.25, 0.5, 0.75, 1.0
19 19 18 59 56 52 34 32 30 38 36 34
48 47 44 147 139 131 84 80 76 94 89 84
cope length, c (mm) 95 93 88 293 278 262 169 160 151 189 179 169
143 140 132 440 417 394 253 240 227 283 268 253
190 186 176 587 556 525 338 320 302 377 358 338
In the parametric study, boundary conditions and material properties were the same as mentioned in the previous
finite element analysis. The weld contact of end plate and beam web was simulated by rigidly MPC beam
constrains (ABAQUS 6.7, 2007). For the FE models used in the parametric study, simply welded end plate was
used for the connection between the beam end and the supported column. With this modification, the effect of
clip angle to the buckling capacity of the web was eliminated. The different schematic connections of the FE
models for test specimens and the model for parametric study were illustrated in Figure 7.
Effects of Imperfection
Figure 7 Schematic of the connection of the finite element models
For the FEA of the test specimens, it is shown that the FE results compared well with the test results with the
maximum web imperfection value varied from 0.7mm to 4.0mm. In order to investigate the effect of maximum
web imperfection to the capacity of coped I-beam, a series of analysis were conducted for UB203 models with a
fixed values of c/h 0 =0.5, d c /D=0.15 and d/t w =27.4. Initial maximum web imperfections values were selected to
be 0.7, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, and 4.0 mm and the corresponding maximum capacity of the coped beam was
obtained from the FEA. The load versus deflection curve of this series of models was shown in Figure 8(a). It
was found that, the effect of initial imperfection to the load versus vertical deflection behavior in the early stage
is very limited; however, it does affect the ultimate capacity of coped beams. The ultimate capacities versus
initial maximum web imperfection values were shown in Figure 8(b). In general, as the imperfection increases,
the ultimate capacity of the coped beam deceases. It is found that the ultimate capacity decreases significantly
by 12.35% with the maximum web imperfection value increases from 0.7mm to 2.0mm. However, when the
maximum web imperfection value increased from 2.5mm to 4.0mm, the decrease of ultimate capacity becomes
less and the percentage reduction is about 4.65%. Since the decrease of ultimate capacity is not significant when
the maximum web imperfection value is larger than 2.5mm, this maximum web imperfection value was used in
the following FE analysis to obtain the effect of other parameters to the ultimate capacity of coped beam.
-469-