Page 313 - Civil Engineering Formulas

BUILDING AND STRUCTURES FORMULAS 247

example, ASCE 7-95 stipulates that the total lateral force, or base shear, V
(kips) acting in the direction of each of the principal axes of the main structural
system should be computed from
V C s W (9.139)
where C seismic response coefficient
s
W total dead load and applicable portions of other loads
The seismic coefficient, C , is determined by the following equation:
s
C s 1.2C v /RT 2/3 (9.140)
where C seismic coefficient for acceleration dependent (short period) struc-
v
tures
R response modification factor
T fundamental period, s
Alternatively, C need not be greater than
s
C s 2.5C a /R (9.141)
where C seismic coefficient for velocity dependent (intermediate and long
a
period) structures.
A rigorous evaluation of the fundamental elastic period, T, requires consid-
eration of the intensity of loading and the response of the structure to the load-
ing. To expedite design computations, T may be determined by the following:
3/4 (9.142)
T a C T h n
where C 0.035 for steel frames
T
C 0.030 for reinforced concrete frames
T
C 0.030 steel eccentrically braced frames
T
C 0.020 all other buildings
T
h height above the basic to the highest level of the building, ft
n
For vertical distribution of seismic forces, the lateral force, V, should be dis-
tributed over the height of the structure as concentrated loads at each floor level
or story. The lateral seismic force, F , at any floor level is determined by the
x
following equation:
F x C ux V (9.143)
where the vertical distribution factor is given by
k
w x h x
C ux n k (9.144)

i 1 w i h i
where w and w height from the base to level x or i
i
x
k 1 for building having period of 0.5 s or less
2 for building having period of 2.5 s or more
use linear interpolation for building periods between 0.5 and 2.5 s