Civil Engineering Reference
In-Depth Information
=
sEI
=
L scEI
=
L
scEI
=
L sEI
=
L
1718
:
1 1076
:
0
1076
:
0 1718
:
1
K
0
o
=
ð7
:
138bÞ
Then, the governing equations of the FAM in Eqs. (7.128) and (7.129) become
=
x
k
+1
−
Δθ
0
1
Δθ
0
2
θ
0
1
θ
0
2
m
1
m
2
1718
:
1 1076
:
0
1076
:
0 1718
:
1
698
:
5
698
:
5
1718
:
1 1076
:
0
1076
:
0 1718
:
1
+
k
+1
k
ð7
:
139Þ
θ
0
1
θ
0
2
1
224
:
3
698
:
5
x
0
k
+1
=
½
698
:
5
ð7
:
140Þ
k
+1
At the axial compressive force of
P
= 500 kN, assume that the yieldmoments are
m
y
1
= 200 kNm
and
m
y
2
= 220 kNm. Let both plastic hinges exhibit bilinear kinematic hardening behavior with
K
t
1
= 300 kNm/rad and
K
t
2
= 200 kNm/rad, then the corresponding moment versus plastic rota-
tion relationships can be written as:
θ
0
1
=0
m
1
= 200 + 300 ×
θ
0
1
m
1
≤ 200
m
1
> 200
,
ð7
:
141aÞ
if
then
θ
0
2
=0
m
2
= 220 + 200 ×
θ
0
2
m
2
≤ 220
if
m
2
> 220
,
then
ð7
:
141bÞ
60
300
Inelastic
Elastic
Inelastic
Elastic
40
200
20
100
0
0
-20
-100
-40
-200
-60
-80
-300
0
5
10
15
20
0
5
10
15
20
Time (s)
Time (s)
1.5
5
Inelastic
Elastic
0
1
-5
-10
0.5
-15
0
-20
-25
-0.5
-30
-35
-1
-40
-1.5
-45
0
5
10
15
20
0
5
10
15
20
Time (s)
Time (s)
Figure 7.14
Global responses of the SDOF column with geometric nonlinearity.
