Civil Engineering Reference
In-Depth Information
(a)
(b)
(c)
τ″
x
′
x
1
″
F
F
F
SH
L
L
L
SH
SH
θ″
RH
m
RH
m
m
RH
Figure 4.5
Determination of the displacements in the FAM: (a) Elastic displacement; (b) Plastic
bending displacement; (c) Plastic shear displacement.
4.2.2 Plastic Bending Displacement x
0
1
Assuming that there is no elastic displacement and the SH is locked, as shown in Figure 4.5(b),
the RH rotates
θ
00
, which is the plastic rotation due to bending behavior, while other parts of the
system remain rigid. According to the kinematic relationship, the plastic bending displacement
x
1
00
can be written as:
x
0
1
=
θ
00
L
ð4
:
10Þ
4.2.3 Plastic Shear Displacement x
0
2
Similar to the procedure for
x
00
1
, as shown in Figure 4.5(c), assume that there is no elastic
displacement of the system and the RH is locked. The SH begins to slide due to the lateral
load
F
, while other parts of the SDOF system remain rigid. Then the plastic shear displacement
x
0
2
equals to the sliding
τ
00
of SH, which is the plastic shear deformation due to shear
behavior as:
x
0
2
=
τ
00
ð4
:
11Þ
4.2.4 Combination of the Bending and Shear Behaviors
The displacement decomposition and inelastic mechanisms of the SDOF system subjected to
the lateral load
F
are illustrated in Figure 4.6, in which the displacement
x
contains the elastic
