Structural Concrete - Hassoun

810 Chapter 20 Seismic Design of Reinforced Concrete Structures
shear force moves from center of mass to the center of rigidity, it produces a torsional moment.
The effect of torsional moment will increase horizontal forces on vertical elements. Forces are not
to be decreased due to torsional effects:
T = V x e (20.22)
where
T = torsional moment
V x = base shear at level x in any direction
E = eccentricity between center of mass and center of rigidity. It can occur in both directions:
x and y.
20.3.7 Overturning Moment
The lateral seismic force F x produces overturning moments. Overturning moment M x should be
calculated using the following equation:
n∑
M x = τ F i (h i − h x ) (20.23)
i−1
where
M x = overturning moment at level x
F i = portion of seismic base shear, V, induced at level i
h i , h x = height from base to level i and x
τ = overturning moment reduction factor
= 1.0fortop10stories
= 0.8 for twentieth story from the top and below
= linear interpolation between 1.0 and 0.8 for stories between twentieth and tenth stories
below top
Reduction factor τ is permitted to be taken as 1.0 for the full height of the structure.
20.3.8 Lateral Deformation of the Structure
The seismic lateral forces should be used in calculating deformations of the structure. The value
that is of interest for engineers is story drift—the difference between the deflections of the center
of mass at the top and the bottom of the story being considered. The value of story drift under
seismic forces is important from different perspectives: stability of the structure, potential damage
to nonstructural elements, and human comfort. The allowable values for story drift are shown in
Table 20.9 (Table 12.12-1 of ASCE 7-10).
For structures that can be designed based on simplified analysis procedure described in
Section 20.3.3, the drift can be taken as 1% of the story height unless a more exact analysis is
provided:
Δ = 0.01h x (20.24)
The value of the design story drift should be less than or equal to the value of allowable story
drift, Δ a , given in Table 20.9.
For all other structures that cannot be analyzed using the simplified analysis procedure, the
drift should be determined as follows:
1. Calculate the deflection δ x at level x from the following equation:
δ x = C dδ xe
I E
(20.25)