Equivalent Static Lateral Forces

The concept employed in equivalent static lateral force procedures is to place static loads on a structure with magnitudes and direction that closely approximate the effects of dynamic loading caused by earthquakes. Concentrated lateral forces due to dynamic loading tend to occur at floor and ceiling/roof levels in buildings, where concentration of mass is the highest. Furthermore, concentrated lateral forces tend to be larger at higher elevations in a structure. Thus, the greatest lateral displacements and the largest lateral forces often occur at the top level of a structure (particularly for tall buildings). These effects are modeled in equivalent static lateral force procedures of the IBC and UBC by placing a force at each story level in a structure, as shown below:

where V = base shear force associated with ground motion at the base of the structure
          Fx = lateral story force applied at each story level of the structure
          Ft = additional lateral force applied at the top level of the structure (per the UBC)

<IMG SRC="newseismic_movie.swf" WIDTH=550 HEIGHT=450 BORDER=0>

In general, the distribution of lateral story forces is associated with the first (fundamental) mode of vibration of a cantilevered structure. (In this case, a typical structure is idealized as a “vertical cantilever” rigidly attached to the ground.) The effects of higher modes of vibration are approximated in the UBC by considering an additional lateral force, Ft, applied to the top level of a structure. In the IBC, the effects of higher modes of vibration are addressed when calculating story forces, Fx, by utilizing a “distribution exponent”, 1 < k < 2, that can vary based on the natural (fundamental) period of vibration of the structure.

In both the IBC and the UBC, the summation of the lateral story forces (plus the additional lateral force at the top, Ft, in the UBC) must be equivalent to the base shear (V) force applied to the structure due to seismic ground motion.