7.8 Use of Response Spectra for Designing MDF Systems
289
Fig. 7.10 Example 7.7
(2) Compute the mode participation factors
B r =
n
i=1 m i φ
(r )
i
n
i=1 m i
φ
(r )
i
2
where n is the total number of masses.
(3) Now, each mode can be treated as a single degree of freedom system. Corresponding to the time period in each mode, S
(r )
a or S
(r )
d can be obtained from the
figure similar to Fig. 3.38.
(4) Then, either V
(r )
i
or P
(r )
i
can be computed for each mode, based on Eq. (7.54a–
7.54b) or (7.57).
(5) The last step involves the combination of various modal quantities. Usually,
the maximum values of them are of interest in design. To obtain the theoretical
exact value, timewise integrals of the ground motion are to be superimposed
with proper sign. The maximum value thus obtained may occur at any time
instant and should be picked up as the design value. The computation involved
in this case is too tedious, and a simpler procedure is adopted in design.
The maximum values of the modal quantities are calculated following steps 1 to
4. These maximum values will not occur at the same instant of time, nor their sign
will be same for each mode. As discussed in Art. 7.4, the assumption of root mean
square value of this quantity is more realistic.
Thus
V i =
V
(1)
i
2 +
V
(2)
i
2 + . . . +
V
(N)
i
2
1
2
(7.63)
Example 7.7 The three-storeyed shear building with pertinent data is shown in
Fig. 7.10. The system has 5% damping. Calculate the maximum storey shears based