Page 76 - Advanced Design Examples of Seismic Retrofit of Structures

68 Advanced Design Examples of Seismic Retrofit of Structures

FIG. 2.38 The effects of COM-COR eccentricity of the upper diaphragm on the lower diaphragm.

forced of the upper diaphragms on the lower diaphragms. This cumulative effect
is schematically shown in Fig. 2.39.
The torsional moment of the ith story is calculated according to Eq. (2.19):
n
X

M i ¼ e ij + e aj F j (2.19)
j¼1
where:
M i ¼torsional moment of the ith story;
e ij ¼eccentricity between the center of mass of the jth level and the center of
rigidity of the ith story measured perpendicular to the direction of the applied
load. The center of mass shall be based on all floors above the story under
consideration; and
e aj ¼accidental eccentricity at the jth level which takes into account acci-
dental variation of mass and stiffness distribution of the story and also acciden-
tal variation of the shear force from torsional effects. It is a distance equal to 5%
of the horizontal dimension at the given floor level measured perpendicular to
the direction of the applied loads.
The calculations of the torsional moment in both stories from the demand
shear force in X-direction are as follows:

M UDX 2 ¼ 8:83 8:71 5% 18:15Þðð½ ð ÞÞ 1372002Š ¼ 1403Tonm