Response Evaluation - Fundamentals of Earthquake Engineering - page 242

fundamental mode of vibration lies approximately between a straight line and a parabola (Di Sarno,
2002). Other force distributions are, however, also adopted by international seismic codes of practice
or other published recommendations to account for higher mode effects. For example, in the USA, the
seismic provisions utilize the following force pattern (FEMA 450, 2004 ):

i k

WH

i

FV = (4.38)

i B

N

∑

k

WH

j

j 1

where the power-law exponent k is related to the fundamental period T of the structural system. For
short-period structures, such as those with T ≤ 0.5 second, k = 1 and equations (4.37) and (4.38) are
equivalent. For long-period structures, e.g. T ≥ 2.5 seconds, it may be assumed that k = 2, while for
structures with a period between 0.5 and 2.5 seconds, k should be conservatively set equal to 2 or
determined by linear interpolation between 1 and 2.
Torsion is a serious problem in structures that have a non-coincident centre of mass and stiffness as
illustrated in Appendix A. The geometric eccentricity between these two centres should be considered
in the analyses of irregular or torsion-deformable structures. In addition to the geometric eccentricity,
codes specify a value of eccentricity (referred to as ' accidental eccentricity ' ) to account for uncertainty
in the calculation of the actual centre of mass and stiffness. Codes defi ne a minimum value of eccen-
tricity as a ratio of the building dimension normal to the direction of the ground motion. The value of
accidental eccentricity is frequently taken as 5%.
The steps required to perform the analysis based on the simplifi ed code procedure are summarized
in the following:

(a) Select the design earthquake spectrum. It is generally an elastic site- specifi c spectrum given in
terms of PGA and for a specifi ed value of structural damping ξ . Many codes provide spectra for
ξ = 5%, as illustrated in Section 3.4.5. This value can be considered adequate for RC and com-
posite structures. For steel structures, values of ξ equal to 2-3% should be employed. It is pos-
sible to modify spectral ordinates by using the η -factor given below (Bommer et al ., 2000 ):

10
5

η = ≥ 055 . (4.39)

+ ξ

where ξ is the viscous damping ratio, expressed in percent.
(b) Select the structural lateral force -resisting system, e.g. among those presented in Appendix A ,
material of construction and hence select the response modifi cation factor from the values pro-
vided in the code.
(c) Scale the design spectrum by using the force reduction factor selected in (b).
(d) Estimate the fundamental period of vibration of the structure T . Semi - empirical formulae or
Rayleigh's method can be used.
(e) Compute the spectral acceleration corresponding to the fundamental period T , the assumed value
of structural damping ξ and level of ductility (force reduction factor).
(f) Defi ne the importance factor of the structure.
(g) Compute the seismic weight W EQ,t . For buildings, it is suffi cient to determine the weight of each
fl oor in compliance with the rules provided in Section 4.3 .
(h) Estimate the seismic coeffi cient C and hence compute the design base shear V B from equation
(4.34) .

(i) Distribute the total seismic shear V B computed in step (h) over the main axis of the structure in

compliance with the relationship either in equation (4.37) or in equation (4.38) .