f im = the displacement amplitude of the ith
Where SDS is as defined in Paragraph 3-2b, and R
level of the structure when vibrating in its mth mode.
and Tm, are as defined above.
The modal seismic response coefficient, Csm, shall be
2.
When the general design response
determined in accordance with the following
spectrum of Paragraph 3-2c(2)(a) is used for
structures where any modal period of vibration, Tm,
equation:
exceeds 4.0 seconds, the modal seismic design
coefficient, Csm, for that mode is permitted to be
S
Csm = am
(3-16)
R
determined by the following equation:
4S D1
where:
Csm =
(3-18)
2
(R)Tm
period Tm determined from either the general design
Where R, and Tm are as defined above, and SD1 is the
response spectrum of Paragraph 3-2c (2)(a), or a
design spectral response acceleration at a period of 1
site-specific response spectrum per Paragraph 3-5,
second as determined in Paragraph 3-2b.
R =
the response modification factor
(c)
Modal forces, deflections, and drifts.
determined from Table 7-1, and
The modal force, Fxm, at each level shall be
determined by the following equations:
Tm =
the modal period of vibration (in
seconds) of the mth mode of the structure.
Fxm = Cvxm Vm
(3-19)
Exceptions:
and
1. When
the general design response
w x f xm
Cvxm =
(3-20)
spectrum of Paragraph 3-2c (2)(a) is used for
n
∑ wf
i
im
structures on Site Class D, E, or F soils, the modal
i=1
seismic design coefficient, Csm, for modes other than
the fundamental mode that have periods less than
where:
0.3 seconds is permitted to be determined by the
following equation:
Cvxm = the vertical distribution factor in the
mth mode,
0.4S DS
(1.0 + 5.0Tm )
Csm =
(3-17)
R
3 - 10
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