Introduction - STD-102020020135

DOE-STD-1020-2002

(C-8)

where W is the inertial weight applied at each story of the structure, δΤ is the total displacement

relative to the base of each story corresponding to the permissible total distortion occurring in

the critical story, and δQ is the elastic displacement relative to the base corresponding to a unit

value of the ratio of the elastic demand to the capacity for the critical story. For a single story,

Equation C-8 simplifies down to a story ductility, Fs of:

s =

(C-9)

where δΤ is the total permissible story displacement and δy is the yield displacement

(Demand/Capacity equals unity). However, for multistory structures, F from Equation C-8 is

always less than Fs from Equation C-9 except when the nonlinear distortions are spread

throughout the structure which is very unlikely. The following equation can be used to relate F

to Fs :

(C-10)

where Fk is a reduction factor to convert a story ductility estimate to a system ductility estimate.

For a well designed structure in which the ratio of the demand to the capacity does not differ by

more than a factor of about l.3 over the structure height, Fk will typically range from 0.5 to 0.75.

In these cases, Equation C-10 may be used with a conservatively estimated Fk of 0.5 in lieu of

Equation C-8 or nonlinear time history analyses.

Once the permissible system ductility has been established, many approaches can be

used for estimating F. For broad, smooth input spectra and moment-frame structures with

essentially full elasto-plastic nonlinear hysteretic loops, either the Newmark-Hall (Reference

C-15) or Riddell-Newmark (Reference C-12) approach is commonly used. However, for

concrete shear wall structures or braced frames which have severely pinched hysteretic loops,

Kennedy, et.al. (Reference C-24) has shown that these approaches are likely to be slightly

nonconservative. For such structures, the approach of Reference C-24 is preferred.

C-35