Civil Engineering Reference
In-Depth Information
P
C
P
C
δ
B
O
δ
C
δ
P
B
B
Figure 5.8
Relation of the load and displacement in Region B-C.
In addition, the growth effect is involved in this region. Since the axialmember is assumed tobe a
function of the cumulative transverse plastic displacement in compression plus the cumulative
transverse plastic displacement in tension, the axial inelastic displacement of SH2 is defined as
δ
2
=
δ
Gn
P
−
P
B
ð
Þ
l
b
=
EA
ð5
:
39Þ
The parameter
δ
Gn
defined as normalized member growth by
Dicleli
and
Calik
(2008) is deter-
mined as a function of normalized cumulative plastic deformation. The inelastic behavior in
tension depends on
δ
Gn
and the plastic axial deformation
δ
p
as shown in Figure 5.1.
Substitute Eqs. (5.38) and (5.39) into Eq. (5.7), and the total inelastic displacement yields
q
l
b
2
=
12
EI
=
P
−
P
B
2
δ
00
=
Þ
=
l
b
2
+1
−4 −
m
pr
=
P
B
−
e
−
0
:
5
e
−
m
pr
=
P
B
ð
−
l
b
ð5
:
40Þ
+
δ
Gn
P
−
P
B
ð
Þ
l
b
=
EA
For a give load or input displacement, the corresponding deformation or axial force can be
solved through the combination of Eq. (5.40) and Eq. (5.6).
5.4.2 Region C-D
In this region, the tensile load
P
and the existed transverse displacement
Δ
generated a second-
order moment to satisfy static moment equilibrium. Thus, the plastic rotation behavior of the
axial member is involved. The moment of the plastic hinge formed at the middle of the member
increases in the reverse direction following the increasing of the axial load
P
in tension as
shown in Figure 5.9.
The transverse displacement of the axial member is satisfied by
=
P
y
−
P
C
Δ
=
m
pr
=
P
−
eP
y
−
P
ð5
:
41Þ
where
P
C
is the load of Point C
