r - The Hong Kong Polytechnic University

(a)
(b)
Figure 8 Load vs. deflection curves with varied imperfection
(UB203, c/h 0 =0.5, d c /D=0.15, d/t w =27.4 for all models)
Effects of Ratio of Cope Length to Reduced Beam Depth (c/h 0 )
In order to investigate the effects of the ratio of cope length to reduced beam depth (c/h 0 ) on local buckling
capacity of coped beams, models with c/h 0 varied from 0.1 to 1.0 were analyzed. The proposed c/h 0 is achieved
by designing suitable coped length and coped depth dimension for each proposed beam sections. Details of the
dimension of coped length and reduced coped depth for each beam sections are shown in Table 3. These three
series of analysis were developed on UB356 with 2.5mm initial maximum web imperfection and slenderness
ratio equals to 42.8 and the results were shown in Figure 9. In general, the ultimate reaction of coped beams was
decreased by increasing the ratio of cope length to reduced beam depth for all FE models. It is found that the
ultimate reaction of coped beam was significantly increased when the ratio of cope length to reduced beam
depth was decreased in those models. In other words, the instability of coped beams would increase by
increasing the ratio of cope length to reduced beam depth.
Additionally, it can be found from Figure 9 that the slope of curves (the curves about the effects of the ratio of
cope length to reduced beam depth) was not linear. The capacity decreases more significantly when c/h 0 is less
than 0.5. When c/h 0 varied from 0.1 to 0.5, the ultimate reaction of cope beam decreased from 484kN to 359kN,
(25.8% decreased) for the series of beams with d c /D=0.05; and the percentage decrease of the other two series of
beams with d c /D=0.1 and d c /D=0.15 were 29.1% and 29%, respectively. When c/h 0 varied from 0.5 to 1.0, the
ultimate capacity dropped from 271kN to 212kN (21.8% decreased) for the series of beams with d c /D=0.15.
Effects of the Ratio of Cope Depth to Beam Depth (d c /D)
The effect of cope depth to beam depth ratio to the capacity of coped end was investigated. Three different ratio
of cope depth to beam depth (d c /D = 0.05, 0.1 and 0.15) was designed for each beam sections. Details of the
dimension of coped depth for each beam sections are shown in Table 3. The analysis for this parameter was
carried out on five different cope length to reduced beam depth ratios (c/h 0 ) and the ratios were designed as 0.1,
0.25, 0.5, 0.75 and 1.0. It is observed from Figure 10 that, when the ratio of cope depth to beam depth increased,
the ultimate reaction decreased, however, the variation was not significant. The ultimate reaction decreased by
1%, 11.1%, 15%, 10.7%, and 6.6% for the five specified c/h 0 value, with a mean value equals to 8.9%.
Figure 9 Effects of the ratio of cope length to reduced beam depth
Figure 10 Effects of the ratio of cope depth to beam depth
-470-