Vm = the total design lateral force or shear
Tm =
the modal period of vibration, in
at the base in the mth mode,
seconds, of the mth mode of the structure,
wp wx = the portion of the total gravity load,
W, located or assigned to Level i or x.
Fxm = the portion of the seismic base shear
in the mth mode, induced at Level x, and
Nxm = the displacement amplitude at the xth
level of the structure when vibrating in its mth mode,
wx = the portion of the total gravity load of
the structure, W, located or assigned to Level x. The
modal drift in a story, ) m, shall be computed as the
and
difference of the deflections, *xm, at the top and
Nim = the displacement amplitude at the ith
bottom of the story under consideration.
level of the structure when vibrating in its mth mode.
(d) Design values. The design values for
The modal deflection at each level, *xm, shall be
the modal base shear, each of the story shear,
determined by the following equations:
moment, and drift quantities, and the deflection at
each level shall be determined by combining their
*xm = Cd *xem
(3-21)
modal values as obtained above. The combination
shall be carried out by taking the square root of the
and
sum of the squares (SRSS) of each of the modal
values or by the complete quadratic combinations
g Tm Fxm
2
= 2
dxem
(3-22)
W
(CQC) technique.
4π
x
d.
Design values for sites outside the U.S.
where:
Table 3-2 in TM 5-809-10 assigns seismic zones to
selected locations outside the United States.
The
Cd =
the deflection amplification factor
seismic zones in that table are consistent with the
determined from Table 7-1,
design values in the 1991 Uniform Building Code
(UBC). Table 3-3 in this document provides spectral
the deflection of Level x in the mth
*xem
=
ordinates that have been derived to provide
mode at the center of the mass at Level x determined
comparable base shear values.
by an elastic analysis,
(1)
Algorithms to convert UBC zones to
spectral ordinates. The UBC base shear equations
m/s2),
are as follows:
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