Seismic Analysis: Equivalent Static Procedures

In many cases simplified analysis methods using equivalent static loading are used in seismic analysis. The static loading to be considered will normally be defined with reference to a design code.

Equivalent Static

The equivalent static load is based on the base shear, which in turn depends on the period of the building. This can either be specified directly or based on the code approximation. The code period is usually defined as a function of the height of the building

$$T = C(h)^n$$

The coefficients $C$ and $n$ are defined in the code.

GSA uses the details defined for the response spectrum along with the weight of the building and the period to calculate the base shear, $V$. The base shear is then distributed over the storeys, $s$, in the building based on the storey weight, $w$ and height above ground, $h$.

$$F_s = \frac{(V-F_t)w_sh_s}{\displaystyle\sum_{i=1}^nw_ih_i}$$

where $F_t$ is a concentrated force at the top defined for some of the seismic codes, but set to zero for most codes. $F_s$ represents the total force applied at the storey. This is then distributed across the nodes on that storey in proportion to the nodal masses.

Accidental Torsion

The equivalent static load procedures require accidental torsion loads to be considered. These are to represent the effect of a displacement of the centre of mass of the storeys. In GSA the accidental torsion loads are calculated so that the moment applied to the storey is proportional to the equivalent static storey forces $F_s$.

$$M_s = kdF_s$$

This depends on the building dimension d at the storey level which is determined by GSA. The factor $k$ is specified in the seismic code (typically 5%).

GSA generates a set of nodal forces that create a moment for the storey that satisfies the equation above without generating any lateral force, so that this can be used n conjunction with the equivalent static load.