Shear Member - Theory of Nonlinear Structural Analysis - page 198

6.2 Local Plastic Mechanisms in the FAM
In order to simulate the inelastic response of shear wall members in the FAM, an improvedmodel
including three local plastic mechanisms is developed here based on the above theory. In this
model, assume that the two rigid beams and the central vertical spring shown in Figure 6.1
are axially rigid and the axial deformations of the two outer vertical springs are equivalent to
a rotation degree of freedom in the RC shear wall member. Therefore, totally four degrees of
freedom, including two horizontal and two rotational degrees of freedom, x 1 , x 2 , x 3 , and x 4 ,
are retained, as shown in Figure 6.4. Then, the element stiffness matrices can be written as

2
4

3
5

K s − K s h w − h c − K s − K s h c ð Þ

2 + K e l w
2

Þ h c − K e l w
2

− K s h w − h c Þ K s h w − h c K s h w − h c Þ K s h w − h c

ð ð Þ ð ð

K e = ð6 : 8Þ

− K s K s h w − h c K s K s h c

ð Þ

Þ h c − K e l w
2

K s h c + K e l w
2

− K s h w K s h w − h c K s h c ð

in which l w is the distance between the two outer vertical springs.
The improved numerical model is illustrated in Figure 6.4, in which there are three local plastic
mechanisms, including twovertical slidinghinges (VSHs) andonehorizontal slidinghinge (HSH).

6.2.1 Displacement Decomposition
Based on the FAM, the displacements of each spring in Figure 6.2 and Figure 6.3 are expressed
as the sum of the elastic components and plastic components. Thus, there are

δ 1 = δ 0 1 + δ 0 1 ð6 : 9Þ

δ 2 = δ 0 2 + δ 0 2

ð6 : 10Þ

δ 3 = δ 0 3 + δ 0 3 ð6 : 11Þ

x 2

x 1

HSH

VSH

h w

VSH

h C

x 3

x 4

l w

Figure 6.4 Shear wall member model in the FAM.