Info

2% 0.64 0.64 0.59 0.37 0.30 0.24 0.20 0.17 0.15 0.13 0.17 0.10

5% 0.50 0.50 0.48 0.30 0.24 0.192 0.16 0.137 0.12 0.107 0.096 0.08

7% 0.44 0.44 0.44 0.28 0.22 0.18 0.15 0.13 0.11 0.10 0.09 0.07

10% 0.38 0.38 0.38 0.25 0.20 0.16 0.13 0.11 0.10 0.09 0.08 0.066

20% 0.27 0.27 0.27 0.20 0.16 0.12 0.10 0.09 0.08 0.07 0.06 0.05

Figure 2.56. Response spectrum for seven-story building example: (a) acceleration spectrum; (b) tripartite diagram; (c) response spectra numerical representation.

Figure 2.57. Seven-story building; modal analysis to determine base shears.

Solution. From the modal analysis results shown in Fig. 2.57, the sum of the participation factors, PFxm and am, add up to 1.08 and 0.986, respectively. These values being close to 1.0 indicates that most of the modal participation is included in the three modes considered in the example. The story accelerations and the base shears are combined by the square-root-of-the-sum-of-the-squares (SRSS). The modal base shears are 2408 kips, 632 kips, and 200 kips for the first, second, and third modes, respectively. These are used in Fig. 2.61 to determine story forces. The SRSS base shear is 2498 kips.

Story Forces, Accelerations, and Displacements. Figures 2.57-2.60 are set up in a manner similar to the static design procedure described previously. In the static lateral procedure, Wh/XWh is used to distribute the force on the assumption of a straight line mode shape. In the dynamic analysis, the more representative Wf/XWf distribution is used to distribute the forces. The story shears and overturning moments are determined in the same manner for each method. Modal story accelerations are determined by dividing the story force by the story weight. Modal story displacements are calculated from the accelerations and the period by using the following equations:

where

Sxm = lateral displacement at level x for mode m

Sam = spectral displacement for mode m calculated from response spectrum

Tm = modal period of vibration

Modal interstory drifts AS are calculated by taking the difference between the S values of adjacent stories. The values shown in Figs. 2.58-2.60 are summarized in Fig. 2.61.

The fundamental period of vibration as determined from a computer analysis is 0.88 sec. The periods of the second and third modes of vibration are 0.288 sec and 0.164 sec, respectively. From Figs. 2.56, using a response curve with 5% of critical damping

Modal base shear V = 2408 kips

(1)

(2)

(3)

(4)

(5) (6)

(7)

(8)

(9)

(10)

(11)

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