Bridges - Wind Loading of Structures - page 301

The effective loading distribution for the root-mean-square fluctuating response, σ r ,
obtained by summing over all modes is:
(12.13)
The total root-mean-square fluctuating response is then:
which agrees with Equation (12.10).
The weighting factor for the contribution from mode j to the effective static loading
for the peak (maximum or minimum) load effect, r, in a specified time period, T, can be
written to a good approximation as:
(12.14)
where g j is an expected peak factor for the response in mode j.
Equation (12.14) can be obtained from Equation (12.12) as follows:
where g r is the peak factor for the response, which can be approximated quite accurately
by,
(12.15)
This is a weighted average of the peak factors for the various modes.
When only one mode is significant, Equation (12.14) reduces to:
(12.16)
i.e. simply the peak inertial force in the mode j .
Note that Equation (12.16) is independent of α j, and hence of the influence line I(x) .