Page 503 - Design of Reinforced Masonry Structures

SHEAR WALLS 7.65

Wall D
R D
Wall A Wall B
R A > R B R B
CR CM M T
e
Eccentricity

Wall C
R C

Seismic force, V
FIGURE 7.28 Torsional shears caused by eccentricity, which exist because
center of mass and center of rigidity are at different locations.

When the center of mass and the center of rigidity are not coincident, horizontal tor-
sional moment is caused because the seismic force is assumed to act through the center of
mass, whereas the seismic resistance of the system acts through the center of rigidity. The
distance between the center of mass and the center of rigidity measured perpendicular to
the seismic force–resisting elements is called horizontal eccentricity, e, and the magnitude
of the torsional moment, M , is taken equal to the applied seismic force V times the eccen-
t
tricity, M = Ve. The effect of the torsional moment is to introduce torsional shears in the
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vertical seismic force–resisting elements (i.e., in shear walls). Depending on the location
of the center of rigidity with respect to the center of mass, the torsional moment can be
clockwise or counterclockwise (Fig. 7.28). Analysis of shear walls subjected to torsional
moments is discussed in Section 7.9.

7.8.6 Accidental Eccentricity and Accidental Torsion in Diaphragms
In analyzing an SFRS, it is tacitly assumed that lateral seismic force acts through the center
of mass of the system, which is easily determined from statics. The location and distribu-
tion of mass at each level required to be considered for earthquake motion response cannot
be determined with precision because of the uncertainties involved in calculation of dead

loads and centers of gravity of various structural and nonstructural elements that comprise
the mass. To account for this uncertainty, the mass at each level is assumed to be displaced
from the calculated center of mass in each direction a distance equal to 5 percent of the
building dimension at that level perpendicular to the direction of the force under consider-
ation (ASCE 7-05 Section 12.8.4.2). This distance is referred to as accidental eccentricity
and the corresponding moment as accidental horizontal torsional moment, M . According
ta
to SEOAC Bluebook [7.12], M is specified to account for uncertainties arising from fac-
ta
tors such as
1. Differences between the analytical model and actual structure
2. The real nonuniform distribution of both dead and live load