Civil Engineering Reference
In-Depth Information
δ
p
P
G
F
E
P
y
α
α
D
D′
C
δ
y
δ′
b
δ
b
O
O′
δ
A
2
B
A
a2
P
b
0
A
a
A
2
P
b
A
Figure 5.1
Hysteretic loop of the axial member.
appropriately depicts changing stiffness in compression. However, since the coincident initial
stiffness is required for the FAM, minor modifications are made as follows: line OA, as shown
in Figure 5.1, was divided into two parts: (1) line OA
a
, which is the opposite extension of line
OF such that the initial stiffness is the same in tension and compression, and (2) line A
a
A,
where the axial buckling load P
b
occurs at Point A, and the intermediate axial load P
b0
at Point
A
a
is set equal to half of the buckling load. In addition, the axial members under axial cycle
loads have relatively complex nonlinear displacements responses so that the model of the axial
member response is not a continuous function. In order to investigate the inelastic cyclic behav-
ior of axial members, the axial force-displacement hysteretic loop can be broken into ten
regions, O
-
A
a
,A
a
-
A, A
-
B, B
-
C, C
-
D, D
-
E, D
0
-
A
2
0
,E
-
O
0
,O
0
-
A
a2
, and A
a2
-
A
2
in first cycle
and will be discussed respectively below.
5.1.1 General Parameters
The nonlinear hysteretic behavior of axial members is usually associated with following
parameters: the axial total load P, transverse displacement
Δ
, at the middle of axial members
and axial displacement
δ
. In addition, several basic parameters representing the axial member
characteristics: the section area A, the moment of inertia for the section I, the length l
b
,
and elastic module E of the member are necessary in this model. The buckling load P
b
and
reduced plastic moment capacity m
pr
are governing parameters to depict buckling behaviors,
and the initial axial load eccentricity, e is the main cause of buckling behaviors, can be
expressed as:
m
pr
0
1
e =
−
ð
5
:
1
Þ
@
A
l
b
P
b
8EI 1+
P
b
lb
2
π
P
b
1
−
2
EI
