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

(9.139)

whereCsseismic response coefficient
Wtotal dead load and applicable portions of other loads

The seismic coefficient, Cs, is determined by the following equation:

(9.140)

whereCvseismic coefficient for acceleration dependent (short period) struc-
tures
Rresponse modification factor
Tfundamental period, s

Alternatively,Csneed not be greater than

(9.141)

whereCaseismic coefficient for velocity dependent (intermediate and long
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, Tmay be determined by the following:

(9.142)

whereCT0.035 for steel frames
CT0.030 for reinforced concrete frames
CT0.030 steel eccentrically braced frames
CT0.020 all other buildings
hnheight above the basic to the highest level of the building, ft

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, Fx, at any floor level is determined by the
following equation:

(9.143)

where the vertical distribution factor is given by

(9.144)

wherewxandwiheight from the base to level xori
k1 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

Cux

wxhkx

ni 1 wihki

FxCuxV

TaCThn3/4

Cs2.5Ca/R

Cs1.2Cv/RT2/3

VCsW