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EXAMPLE
The nonlinear static analysis method based on displacement is illustrated with two examples: Ex. A is a
storey shear model. Ex. B is a structure that collapses from 7 th storey to 13 th storey in Tang Shan
earthquake.
EX.A
Its structural parameters are shown in Table 1. The structure is in region of VII. The characteristic
period value is 0.30 second. The nonlinear static analysis method based on displacement is carried out
with 5 steps. Data at each step are shown in Table 2. The inter-storey drift at each step is shown in Fig
1, and displacement of top floor versus the acceleration of ground motion in Fig 2.
^\
1 st floor
2 na floor
3 ra floor
4 m floor
Mass
(xlO 6^)
7.8
7.0
6.8
5.0
Stiffiiess
(xW*N/m)
3.86314
4.03524
3.03524
2.24514
Table 1: structural parameters
Post stiffness
(xlQ 7 #/w)
7.72628
8.07048
6.07048
4.49028
Inter-storey
yield drift (m)
0.0101
0.0080
0.0080
0.0080
Inter-storey
limited drift (m)
0.0910
0.0720
0.0720
0.0720
\^
1 st step
2 nd step
3 rd step
4 th step
5 m step
Floor
9 nd
i st
3 ra
4 m
^nd
Table 2: Frequency and damage states at each step
State
Yield
Yield
Yield
Yield
Utmost
Acceleration of
ground motion( mis 2 }
1.0065
1.0889
1.1266
1.7323
1.7311
1 st
2.6809
1.7751
1.3350
1.2268
1.1989
Frequency (rad/sec)
ond
3 rd
6.7741 10.1263
6.7537 7.9907
4.4852 7.1603
3.4175 5.6160
3.0295 4.5286
4th
13.0079
11.1671
11.1592
9.0872
5.8173
EX.B
The height of every floor of Ex. B is 4m except 4.5m at both 11 th and 12 th floor, and 3m at 13 th floor.
The height from the base of structure is 52.0m. The span between columns is 6.0m. The cross-sections
of columns decrease from 600 x 800mm(at 1 st floor) to 300 x 300mm (at 13 th floor). The cross-section
of beams is 300 x 700mm. The grade of concrete is C20. The structure is in region of VIIL The
characteristic period value is 0.40 second. The elevation of the frame structure is shown by Fig 3. The
Giberson model is adopted in analysis, so yields of members occur only at the ends of elements. Fig 4
shows the damage formation pattern of the structure. It is clear that members* deformation limitation