Civil Engineering Reference
In-Depth Information
that the CIRIA methods could lead to designs with a factor of safety
exceeding 60; the authors believe that BS8110Ós slender column
recommendations are unsuitable for use in predicting the buckling loads of
slender concrete deep beams. Though the CIRIA methods can be grossly
inaccurate, the concept of an equivalent-column is attractive. In this section,
a computer-aided method (Kong
et al.
, 1986b; Kong and Wong, 1987;
Wong, 1987a) is presented for the detailed stability analysis of slender
concrete columns. The method is applied to slender deep beams in Section
10.5 and compared with CIRIAÓs methods in Section 10.6.
10.4.1
Theoretical background
Consider the slender column in Figure 10.6a; let the moment-deflection (
M
Î
e
add
) curve be as shown in Figure 10.6b. The total external moment
M
t
at the
mid-height due to the load
N
is M
t
=
N
(
e
+
e
add
).
Figure 10.6
Simplified moment-deflection curve
For any given value of
N,
the relation between Mt and
e
add
can be
represented on Figure 10.6b as a straight line having a slope equal to
N
and
passing through the point
A
at a distance
e
to the left of the origin
O
.
Suppose for the time being it is crudely assumed that the
MÎe
add
curve is
independent of the load
N.
Let
N
crit
be the value of
N
at which instability
failure of the column occurs. Then a line such as Line 1, with a slope less
than
N
crit
, will intersect the
M
Î
e
add
curve. At the point of intersection,
B,
the
external moment
M
t
[=
N
(
e+e
add
)] is in equilibrium with the internal moment
M
. If this equilibrium is disturbed by slightly increasing
e
add
, then
M
t
becomes less than
M
. Hence the equilibrium at
B
is stable.
