# 2.5.2 Earthquake Loading in Piping Stress Analysis

Earthquakes may be analyzed using either dynamic or static methods. Dynamic earthquake analyses, which will be covered in depth later, are not discussed here.

Static earthquake loads are determined and applied in a manner very similar to static wind loads. The static loading magnitude is considered to be in direct proportion to the element's weight. Earthquake load magnitudes are given in terms of the gravitational acceleration constant, i.e. g's. If an earthquake is modeled as having a 0.5 g load in the X direction, then a force equal to one-half of the system's weight is applied to the pipe uniformly in the X direction.

Earthquake static load cases are set up and determined exactly as they are for wind occasional loads, i.e. by considering the same load case, non linearity, and directional sensitivity logic. In some cases the client specifies the magnitude of the earthquake loading in g's and the direction(s). In others, the analysis is left to the sole discretion of the engineer. It is not unusual to see only X or X-Y components of an earthquake. It is not uncommon to see Y only components, or X, Y and Z simultaneous components.

When not provided by the client, there are a number of sources for obtaining the seismic g-factors:

**Response spectrum:** If seismic response spectra are available for the piping system, then, given the natural frequency of the lowest mode of vibration of a piping system, the analyst can find a corresponding acceleration from one of the curves. If this acceleration lies on the right side of the peak, this acceleration may be conservatively used an overall g-factor. For more information on seismic response spectra, refer to Sections 4 and 5 of these seminar notes.

**Building code:** Building codes provide ways to calculate seismic g-factors, based upon earthquake potential, structure type, and structure fundamental frequency. For example, the Uniform Building Code and the BOCA Basic/National Building Code calculates:

### g = ZKCT

Where:

g = static equivalent g-factor to use for seismic design, multiples of gravity Z = seismic coefficient based on earthquake zone, equal to 0.0 for Zone 0,0.25 or Zone 1, 0.5 for Zone 2, and 1.0 for Zone 3 K = structure type constant, ranging from 0.67 to 3.0, dimensionless C = 0.05/T^(1/3), but not greater than 0.1 T = fundamental period (inverse of frequency) of structure, sec

**ASCE #7**: This standard calculates seismic g-factors in a manner similar to those of the building codes, based upon earthquake potential, structure importance, structure type, structure fundamental frequency, and soil parameters. The requirement is:

### V = ZIKCSW

Where:

V = total lateral force or shear at the base, lb Z = seismic zone coefficient:

I = occupancy importance factor:

K = structure type constant from Table 24 of ANSI A58.1, ranging from 0.67 to 2.5 (use K=2.0 for structures other than buildings) C = 1/[15 T^(1/2)], not greater than 0.12 T = fundamental period (inverse of frequency) of structure, sec S = soil type coefficient from Table 25 of ANSI A58.1, ranging from 1.0 to 1.5 (note that the product of C and S need not exceed the value 0.14, so this value should be used as a conservative maximum). W = total dead load

The "g"' factor can be found be dividing both sides of this equation by W, so:

### g = V/W = ZIKCS

For piping, the generic equation for the maximum g-factor is:

g = Z (1.0) (2.0) (0.14)

and, for the various values of Z

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