Page 296 - Advanced Design Examples of Seismic Retrofit of Structures

Example of a Steel Frame Building Retrofitted Chapter 5 287

The complete set of requirements of determination of the irregularity of the
buildings in plan and height are presented in Section 2.5.4 in Chapter 2.

l Coordinates of center of mass (CoM) and center of rigidity (CoR) are shown
in Table 5.4. Based on the results of this table, the main building has the dis-
tance of CoM and CoR is less than 20% of the external dimension of the build-
ing in each direction; however, this is not the case for the sports building.
l According to Table 5.5, the maximum interstory displacement (by inclusion
of accidental torsion) of the main building is larger than 20% of the average
interstory displacement of the two story ends. The opposite condition exists
for the sports building.
l The difference between the stiffness of the diaphragms in adjacent stories is
larger than 50% in the main building because the system if the diaphragms in
the upper and lower stories are lightweight and jack-arch roof, respectively.
The single-story sports building is not subjected to irregularity in height.
l None of the buildings has discontinued load-bearing members in height.
l Although the total mass of the first story in the main building is not within
50% difference with that of the floor story, the building is not irregular in this
regard because one of these stories is the roof of the building. The single-story
sports building is not subjected to irregularity in height.
l For the main building, the only lateral load-bearing elements are infill walls
and their stiffness in the floor story is not less than 70% of that in the first
story. The single-story sports building is not subjected to irregularity in
height.
l In the main building, the sum of the shear strengths of the seismic-force-
resisting system in the floor story in each direction is not less than 80%
of the strength in the first story. The single-story sports building is not sub-
jected to irregularity in height.

5.4.2 Diaphragms
Based on ASCE 41 [1], a diaphragm with horizontal deformation along its
length less than half the average story drift is regarded as rigid. In a flexible
diaphragm, horizontal deformation along its length is larger than two times
the average story drift. The semi-rigid diaphragm is between the thresholds
of the rigid and flexible diaphragms. In order to determine the maximum hor-
izontal deformation of a diaphragm, the equivalent beam can be used [2]. Defor-
mation of this beam (Δ story ) is divided into flexural deformation (Δ f ) and shear
deformation (Δ s ).

Δ story ¼ Δ f + Δ s (5.1)
5ωL 4
Δ f ¼ (5.2)
384EI