Civil Engineering Reference
In-Depth Information
(a)
(b)
F
F
F
SH
L
L
=
+
m
RH
m
m
Figure 4.4
The flexural member: (a) Cantilever column; (b) Equivalent SDOF system.
deformation varies with the moment along the length of the column, and is usually assumed
to be concentrated at the column end. However, the shear deformation, unlike the bending
behavior, is generated along the column, so the deformation of the shear effect can be
considered as a sliding mechanism. As a result, in the FAM, the flexural member shown in
Figure 4.4(a) can be simplified to the system shown in Figure 4.4(b). As illustration,
a rotation hinge (RH) is assembled at the column end to represent the plastic rotation due to
the bending behavior and a slide hinge (SH) is assigned to the column to represent the lateral
plastic deformation due to the shear behavior. The two hinges, RH and SH, are the local plastic
mechanisms.
In addition, the total lateral displacement
x
of the flexural member is the sum of the elastic
displacement
x
0
and the inelastic displacement
x
00
:
x
=
x
0
+
x
00
ð4
:
7Þ
where
x
00
is the sum of the plastic bending displacement
x
0
1
due to RH and plastic shear displace-
ment
x
0
2
due to SH:
x
00
=
x
0
1
+
x
0
2
ð4
:
8Þ
4.2.1 Elastic Displacement x
0
In order to obtain the elastic displacement
x
0
, the RH and SH should be locked as shown in
Figure 4.5(a), and the relationship between the lateral load
F
and the elastic displacement
x
0
is satisfied by
F
=
k
0
x
0
ð4
:
9Þ
where
k
0
is the initial elastic stiffness.
