Civil Engineering Reference
In-Depth Information
methods are very conservative. An equivalent-column method is also
proposed for more accurate prediction of deep beam buckling loads.
10.2
Slender deep beam behaviour
10.2.1
Elastic behaviour
There is very little information on the elastic behaviour of slender deep
beams in the literature (Albritton, 1965; Andrews, 1978; CIRIA, 1977). It is
reasonable to expect that the buckling behaviour of a slender deep beam
with free vertical edges is comparable to that of a slender wall
(
Figure 10.1
a
and b). Similarly, the buckling behaviour of a slender deep beam with lateral
restraint along four edges can be expected to be comparable to that of a thin
plate (Figures 10.1 c and d). Using the finite element program PAFEC, the
specimens shown in Figure 10.1 were modelled by three layers of Brick
elements, and their lateral deflections were determined and compared.
Figure 10.1e shows that the maximum deflections of the wall (i.e. wide
column) in Figure 10.1a and those of the deep beam in Figure. 10.1b always
occurred at around mid-height. Figure 10.1e also shows that the mid-height
deflections of the column were practically the same at Sections A-A, B-B,
and C-C, but those of the deep beam decreased markedly from A-A to C-C:
over the support (Section A-A), the mid-height deflection of the deep beam
was about 20% higher than that of the column; at the quarter-span (Section
B-B), the mid-height deflection of the deep beam and that of the column
were almost the same; at mid-span (Section C-C), the mid height deflection
of the deep beam was about 20% less than that of the column. Therefore,
Figure 10.1e suggests that, for a slender deep beam with unrestrained
vertical edges (Figure 10.lb), buckling failure is likely to occur at mid-
height by horizontal cracks, initialised from the vertical edges where the
lateral deflections are maximum; this seemed to agree with the authorsÓ tests
(Wong, 1987a). Figure 10.1e shows that when the vertical edges of the
slender deep beam in Figure 10.1 b were restrained (Figure 10.1d), its lateral
deflections were considerably reduced, and were always less than those of
the column in Figure 10.1a and the plate in Figure 10.1e. Figure 10.1e also
shows that the buckling failure mode of the deep beam in Figure 10.1d
would be in biaxial curvature, as that of the plate in Figure 10.1c.
The above comparison is based on elastic analysis, which assumes an
isotropic material obeying HookeÓs law, and hence provides no information
on the post-cracking behaviour and inadequate guidance of the ultimate load
behaviour under the influence of the slenderness effect.
10.2.2
Ultimate load behaviour
Experiments on slender concrete deep beams are comparatively difficult to
carry out and require attention to details to prevent injury to personnel or
