Stability and strength of slender concrete deep beams - Reinforced Concrete Deep Beams - page 278

(c) If D is equal to zero (i.e. Condition 3), or more realistically, if

D is within a small tolerance of zero, 1.OE-4 say, then the

column is considered to be at incipient instability failure. That
is, the current value of is equal to, or sufficiently close to

a crit . Hence the column buckling load N crit can be calculated
from Eqn 10.4.
The steps described above assume that instability failures always precede
material failures. However, for a general computer program, the possibility
of material failure should be considered. Because of space limitation it is not
considered here.

a

10.5 Stability analysis of slender deep beams: the equivalent-column
method

Based on the method presented in Section 10.4, the buckling strength of a
deep beam is calculated as that of two Òequivalent columnsÓ, each joining a
loading block to a support reaction block, as shown in Figure 10.18 . Each
column is of rectangular cross section b by b eff , where b is the actual
thickness of the deep beam and b eff is the effective column width. As an
exploratory investigation, four effective column widths will be considered:

Case 1: (Figure 10.18a). The effective width b eff of each equivalent column

is taken as L /2, where L is the overall length of the beam. The
buckling load P of the deep beam is then taken as 2 N, where N is
the buckling load of an equivalent column. Case 1 is equivalent to
analysing the deep beam as a wide column.

Case 2: (Figure 10.18b) b eff is taken as c , where c is the width of each of

the stiff bearing blocks at the loading and support points. P= 2 N, as
in Case 1.

Case 3: (Figure 10.18c). Here the equivalent-column axis is the line joining

the loading and support reaction points, inclined at an angle f to

the vertical. b eff is taken as c cos f . The buckling load P of the

beam is taken as 2 N cos f .

Case 4: (Figure 10.18d). Cae 4 is as Case 3, except that b eff is taken as

( c +4 b ) cos , where b is the beam thickness and ( c +4 b ) is the

effective width recommended by Clause 14.2.4 of the ACI Code
(ACI Committee 318, 1983) for walls under concentrated loads.
The effective reinforcement for each equivalent column is taken as the average
amount of reinforcement in the direction of the equivalent-column axis.

f

10.6 Deep beam buckling: comparison with test results

Table 10.2 shows that the measured buckling loads of the authorsÓ 38 test
beams (Kong et al., 1986a) together with the predictions by the CIRIA