Civil Engineering Reference
In-Depth Information
Table 4.6
Numerical results of the RC column subjected to cyclic loadings
Plastic deformations
Forces
Input displacements
x
(mm)
Elastic displacements
x
0
(mm)
θ
00
(rad)
τ
00
(mm)
Branches
m
(kN-m)
V
(kN)
Elastic
0
0
0
0
0
0
0.10
0.10
0
0
29.46
20.00
0.20
0.20
0
0
58.93
40.00
0.30
0.30
0
0
88.39
60.00
Hardening
0.40
0.31
0.000037
0.000037
90.73
61.59
0.50
0.32
0.000075
0.000074
93.08
63.18
.
.
.
.
.
.
1.80
0.42
0.00056
0.00055
123.50
83.83
1.90
0.43
0.00060
0.00059
125.84
85.42
Unloading
1.80
0.39
0.00056
0.00059
114.76
77.90
1.70
0.35
0.00052
0.00058
103.70
70.39
.
.
.
.
.
.
0.90
0.051
0.00019
0.00057
15.12
10.26
0.80
0.014
0.00015
0.00056
4.04
2.74
Reloading
0.70
−
0.018
0.00013
0.00053
−
5.27
−
3.58
0.60
−
0.046
0.00011
0.00048
−
13.60
−
9.23
.
.
.
.
.
.
−0.20
−0.27
0.000013
0.000053
−80.08
−54.36
−0.30
−0.30
0
0.00
−88.39
−60.00
Hardening
−0.40
−0.31
−0.000037
−0.000037
−90.73
−61.59
−0.50
−0.32
−0.000075
−0.000074
−93.08
−63.18
.
.
.
.
.
.
−1.80
−0.42
−0.00056
−0.00055
−123.50
−83.83
−1.90
−0.43
−0.00060
−0.00059
−125.84
−85.42
Unloading
−0.18
−0.39
−0.00056
−0.00059
−114.76
−77.90
−0.17
−0.35
−0.00052
−0.00058
−103.70
−70.39
.
.
.
.
.
.
−0.90
−0.051
−0.00019
−0.00057
−15.12
−10.26
−0.80
−0.014
−0.00015
−0.00056
−4.04
−2.74
.
.
.
.
.
.
.
versus plastic deformation relationships for RHs and SHs, respectively, should be involved for
solving the 2(
q
f
+
q
s
) unknowns uniquely. Once
f
k
+1
and
d
Λ
00
are solved, the plastic deforma-
tion at time step
k
+1
Λ
k
+1
00
can be obtained using Eq. (4.112). Then the plastic displacement
x
0
k
+1
can be calculated as:
x
0
k
+1
=
K
−1
K
0
Λ
0
k
+1
ð4
:
114Þ
