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(400 - 1.5 x 349)f22 = 200f12, f22 = -0.618 f12 f22 = 1, f12 = -1.618

In mathematical terminology, natural modes , eigenvectors. ^21

f 12

f 22

shown in Fig 2.48 are called

Figure 2.48. Vibration modes; two-story example: (a) first mode; (b) second mode.

ASCE Section 9.5.6.5 states that the portion of the base shear contributed by the mth mode, Vm, shall be determined by the following equations:

where

Csm = the modal seismic design coefficient determined below Wm = the effective modal gravity load

W = the portion of the total gravity load of the structure at level i fm = the displacement amplitude at the ith level of the structure when vibrating in its mth mode

Determine Modal Mass and Participation Factors for Each Mode. Using the notation

= 1.5 kip-sec2/in (f11 + f21) = 1.5 (0.618 + 1.0) = 2.426 kip-sec2/in

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