Civil Engineering Reference
In-Depth Information
Since the moment at PHLs #11and #12,
m
11
=
m
12
= 15103 N-m, exceeds the yield
moment
m
b
,
y
= 15000 N-m, the corrected incremental plastic rotation and the final incre-
mental moment at step
k
= 140 is
h
i
T
m
14ðÞ
=
m
14ðÞ
c
m
14ðÞ
b
m
14ðÞ
c
ð8
:
73Þ
In which
m
14ðÞ
c
½
N-m
= 17688 18178
−19647
−15103
m
14ðÞ
c
= 14695 14695 15000 15000
½
N-m
Then, the incremental plastic rotation and displacement at this step are calculated by
Eq. (8.46) as
m
−0
:
0003
0
:
0001
Δ
x
13ðÞ
=
ð8
:
74Þ
Δ
θ
00
13ðÞ
=
0
4×1
0
4×1
0
:
00015 0
:
00015 0 0
T
½
ð8
:
75Þ
Substituting Eqs. (8.59) and (8.60) into Eqs. (8.46) yields
m
−0
:
038
0
:
019
x
14ðÞ
=
ð8
:
76Þ
θ
00
14ðÞ
=
θ
00
13ðÞ
+
Δ
θ
00
13ðÞ
=
0
4×1
0
4×1
0
:
00015 0
:
00015 0 0
T
rad
½
ð8
:
77Þ
Steps 141-160
:(
k
= 141 to 160)
The procedures for solving the variables at the steps from 141 to 160 are the same as step 141
for the 2-DOFs system is always in plastic. The solution process is omitted. Thus, the solu-
tion process is omitted. Finally, the plastic hinge distribution is shown in Figure 8.7. The
0.4 m
#12
F
2,2
#11
PHL #3
#7
F
2,1
Figure 8.7
Plastic hinges distribution.
