Civil Engineering Reference
In-Depth Information
5.4.5 Region E-F
The load-displacement relation in this region is again associated with the elastic behavior as
shown in Figure 5.12, therefore, the transverse displacement and plastic displacement like
region O-F are
Δ
=0
ð5
:
49Þ
δ
00
=0
ð5
:
50Þ
P
=
α
k
b
δ
−
δ
ð Þ+
P
E
ð5
:
51Þ
in which,
δ
E
and P
E
are the axial total displacement and load at Point E.
5.4.6 Region A
a2
-
A
2
The behavior of the axial member in this region is similar to that in the region A
a
-A, see
Figure 5.13. The transverse displacement is expressed as
l
b
2
P
b
0
e
8
E
t
I
1+
P
b
0
l
b
2
π
P
P
b
0
−
1
2
Δ
= −2
ð5
:
52Þ
2
E
t
I
Substituting Eq. (5.52) into Eq. (5.8) yields
=
8
E
t
I
= −
m
pr
=
P
b
0
−
e
−
l
b
2
P
b
0
e
1+
P
b
0
l
b
2
2
E
t
I
=
π
ð5
:
53Þ
where
E
t
is defined as elastic modulus considering Baushinger effect degradation by
Dicleli
and
Calik
(2008) is determined as a function of normalized cumulative plastic deformation. The
buckling load
P
0
b
in the second cyclic loop is the solution of Eq. (5.53).
P
P
E
E
δ
A
a
2
F
O
δ
F
δ
E
δ
A
a2
A
2
Figure 5.12
Relation of the load and displacement in Region E-F.
