Civil Engineering Reference
In-Depth Information
where
τ
Y
=0, already available from the stability analysis, are also used.
The value of the smallest coupled frequency is obtained from
τ
x
=0.74 and
(
f
3
)
2
-3.215(
f
2
)
2
+0.275
f
2
-0.000592=0
as the smallest root:
f
1
=
f
=0.047 Hz.
Knowing the values of the basic frequencies and the fact that the arrangement is
monosymmetrical, the above value could have been obtained without calculation—as
was the case with the stability analysis.
6.1.3
Maximum stresses and deformations
The torque around the shear centre is obtained from formula (5.6) where
µ
is zero as the
horizontal load is uniformly distributed:
m
z
=
q
x
y
c
+
q
y
x
c
=21.45×9=193.05 kNm/m.
As the procedure simplifies considerably for buildings subjected to uniformly distributed
load and with zero product of inertia, the simplified versions of the relevant formulae
given in section 5.7 will be used in the following.
The maximum top translations of the equivalent column are obtained from formulae
(5.98):
The maximum top rotation is calculated from formula (5.99):
