Civil Engineering Reference
In-Depth Information
columns of the framework cannot 'utilize' their own bending stiffness. As a rule, the
approximation is also justified with frameworks on fixed supports as the bending
stiffness of the individual columns is normally insignificant compared to the 'global'
bending stiffness in structural engineering practice and therefore can be ignored as a
conservative approximation. However, if for some reason it is necessary to take into
consideration the 'local' bending stiffness of the columns or/and if the distribution of
the load is different from the uniformly distributed case, a more sophisticated (and
more complicated) method can be used which was developed by Hegedüs and Kollár
[1984] for the buckling analysis of sandwich columns with thick faces subjected to
axial load of arbitrary distribution.
Fig. 9.6
Origination and analysis of the sandwich model. a) Frame, b) sandwich,
c) buckled shape, d) elementary section.
The governing differential equation of the problem is obtained by considering the
equilibrium of an elementary section of the sandwich column (Fig. 9.6/c/d) which is
characterized by the 'global' bending stiffness and the shear stiffness of the system
[Zalka and Armer, 1992]:
(9.20)
In the governing differential equation
q
represents the intensity of the uniformly
distributed vertical load,
E
c
I
g
is the 'global' bending stiffness of the columns,
r
s
is the
modifier as defined by formula (9.8) and given in
Table 3.1
and
K
is the shear stiffness
of the system.
