Civil Engineering Reference
In-Depth Information
buckling. The continuous load is obtained by distributing the concentrated forces
of this unconservative manoeuvre can be accounted for by applying Dunkerley's summation
theorem (cf. section 3.1.1) which leads to the introduction of the reduction factor
(9.8)
This phenomenon is similar to the one discussed in section 3.1.1 and values for the
reduction factor
r
s
are given there, in
Table 3.1
, as a function of the number of
storeys
n
.
The full-height bending of the whole structure normally plays an important
role in the behaviour and it has a significant effect on the value of the overall
critical load.
The shear stiffness which, by definition, also represents the shear critical load, is
linked to the shear deformation of the structure. The shear deformation is characterized
by lateral sway which is mainly resisted by the stiffening effect of the beams (
Fig. 9.1/
c;
Fig. 9.2/a
)
. The shear deformation and shear stiffness are associated by two
phenomena: full-height sway (due to the stiffening effect of the beams over the height
of the framework) and storey-height sway (because the stiffening effect is only
concentrated on storey levels). Consequently, the corresponding shear critical load
originates from two sources and its value is obtained in two steps.
First, in assuming that the stiffening effect of the beams is continuously
distributed over the height and there is no additional sway between the beams
(
Fig. 9.2/b
)
, the part critical load which is associated with this full-height shear
deformation is obtained as
(9.9)
where
E
b,i
, I
b,i
and
l
i
are the modulus of elasticity, the second moment of area and the
length of the ith beam and
h
is the storey height.
Second, in assuming that the structure only develops sway between the storey
levels, a storey-height section of the structure is investigated. Assuming frameworks
on fixed supports, each storey behaves in the same way
(
Fig. 9.2/c
)
and the part critical
load which characterizes this storey-height shear deformation is obtained as
