Challenges for the Next Generation of Seismic Codes - Earthquake Engineering for Structural Design - page 509

The frame was analyzed under the pulse type excitation using the time-history
method, for velocities corresponding to moderate earthquakes. The first analysis
considered the frame loaded by a velocity pulse of 50 cm/sec corresponding to the
first vibration mode (Tp =T 1= 1.01 sec) (Fig. 10.30a). Large lateral displacements
(until 25 cm) occur and the global mechanism is formed. For the velocity pulse of
60 cm/sec and pulse period corresponding to second vibration mode (Tp = T2 =
0.328 sec), Figure 10.30b shows a maximum displacement of 4.5 cm, 5.6 times
smaller than the displacement corresponding to the first vibration mode. The
displacement profile corresponds to the second vibration mode. The collapse
mechanism is formed at the top story. The response to the third ground motion
(Fig. 10.30c) corresponds to a pulse with period equal to the third vibration mode
(Tp = T3 = 0.172 sec) and velocity of 100 cm/sec. The maximum displacement is
3 cm, 8.3 times smaller than the one for the first vibration mode and the
displacement profile corresponds to third vibration mode. The collapse mechanism
involves the middle frame story.
These results demonstrate that the traditional analysis methods, mainly based
on the predominance of the first vibration mode, cannot detect the effects of higher
vibration mode, in case of ground motion characteristics which excite the building
into higher vibration modes. The main effects are the formation of local
mechanisms in the superior part of structure (Goel and Chopra, 2005). This is
clearly the case of frames situated in low to moderate seismic regions, where the
velocity pulse periods are always smaller than the first vibration periods of
structures.
The force distributions corresponding to the formation of collapse
mechanisms for the first three vibration modes are presented in Figure 10.31a. The
first mode distribution produces a global plastic mechanism and the increasing
force intensity can cause the building to rotate as a rigid body around its base. The
second mode force distribution causes a local plastic mechanism in the third story
and the increasing force intensity can cause the third story to rotate as a rigid body
around the second floor. The third mode force distribution causes a collapse
mechanism at the second story, which rotates as a rigid body over the first story .
The corresponding moments for the three distributions are presented in Figure
10.31b. One can see that the formation of a plastic mechanism requires that the
applied lateral forces must be 2.8 and 3.68 times the ones of the second and third
mode, respectively, in comparison with the first mode. This remark is a
justification of the results of frame analyses, which show that a structure, designed
for the first vibration mode, reaches the collapse of the top stories for accelerations
higher than the design ones.