Static Force Method of Seismic Analysis

DOE-STD-1020-2002

that do not necessarily occur simultaneously. It should be understood that the strict application

of modal analysis assumes elastic response (stiffness remains constant) of the structure.

C.4.2

Static Force Method of Seismic Analysis

Seismic provisions in model building codes are based on a method that permits

earthquake behavior of facilities to be translated into a relatively simple set of formulas. From

these formulas, equivalent static seismic loads that may affect structures, systems, or components

can be approximated to provide a basis for design or evaluation. Equivalent static force methods

apply only to relatively simple structures with nearly regular, symmetrical geometry and

essentially uniform mass and stiffness distribution. More complex structures require a more

rigorous approach to determine the distribution of seismic forces throughout the structure, as

described in Section C.6.

Key elements of equivalent static force seismic evaluation methods are formulas that

provide (1) total base shear; (2) fundamental period of vibration; (3) distribution of seismic

forces with height of the structure; and (4) distribution of story forces to individual resisting

elements including torsional considerations. These formulas are based on the response of

structures with regular distribution of mass and stiffness over height in the fundamental mode of

vibration. The IBC provisions (Reference C-28) include, in their equation for total base shear,

terms corresponding to maximum ground acceleration, spectral amplification as a function of

natural period, a factor of conservatism based on the importance of the facility, and a reduction

factor that accounts for energy absorption capacity. Very simple formulas estimate fundamental

period by relating period to structure dimensions with coefficients for different materials or by a

slightly more complex formula based on Rayleigh's method. The IBC defines the distribution of

lateral forces of various floor levels. The overturning moment is calculated as the static effect of

the forces acting at each floor level. Story shears are distributed to the various resisting elements

in proportion to their rigidities, considering diaphragm rigidity. Increased shears due to actual

and accidental torsion must be accounted for.

Seismic forces in members determined from the above approach are combined with

forces due to other loadings using code defined load factors and are compared to code defined

strength or stress levels in order to evaluate whether or not the design is adequate for earthquake

loads. In addition, in buildings, deflections are computed from the lateral forces and compared

to story drift limitations to provide for control of potential damage and overall structural frame

stability from P-delta effects.

C.4.3 Soil-Structure Interaction

When massive stiff structures are founded on or embedded in a soil foundation media,

both the frequency and amplitude of the response due to seismic excitation can be affected by

soil-structure interaction (SSI), including spatial variation of the ground motion. For rock sites,

the effects of the SSI are much less pronounced. It is recommended that the effects of SSI be

considered for major structures for all sites with a median soil stiffness at the foundation base

C-23