Spatial or Modal Combination First - CAESAR II - Help

CAESAR II Users Guide

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CAESAR II
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CAESAR II Version
12

(Available for: Spectrum)

Specifies the method for combining load case results as described below. Select Spatial to first combine spatial components of the load case. Select Modal to first combine modal components of the load case.

In a spectrum analysis, each of the modal responses must be summed. In addition, if multiple shocks have been applied to the structure in multiple directions, the results must be combined, such as spatially combining the X-direction, Y-direction, and Z-direction results. A difference in the final results (spatial first versus modal first) arises whenever different methods are used for the spatial and modal combinations. The combination of spatial components first implies that the shock loads are dependent, while the combination of modal components first implies that the shock loads are independent.

Dependent and independent refer to the time relationship between the X, Y, and Z components of the earthquake. With a dependent shock case, the X, Y, and Z components of the earthquake have a direct relationship. A change in the shock along one direction produces a corresponding change in the other directions. For example, an earthquake acts along a specific direction, having components in more than one axis with a fault at a 30° angle between the X- and Z-axes. The Z-direction load is scaled by a factor of tan 30°, but the identical version of the X-direction load is used. In this example, spatial combinations should be made first.

An independent shock has X, Y, and Z time histories producing related frequency spectra but completely unrelated time histories. The Independent type of earthquake is far more common, so in most cases the modal components should be combined first.

For example, IEEE 344-1975 (IEEE Recommended Practices for Seismic Qualification of Class 1E Equipment for Nuclear Power Generating Stations) states:

"Earthquakes produce random ground motions which are characterized by simultaneous but statistically INDEPENDENT horizontal and vertical components."

This is usually less of an issue for force spectrum combinations. Normally there are no separate spatial components to combine because X- Y- and Z-shocks are not acting simultaneously. When there is more than one potential force load, the spatial combination method may be used to indicate the independence of the loadings. For example, select Modal if two independent relief valves may or may not fire simultaneously and the two shocks are defined as being in different directions (such as X and Y). If the two valves are dependent and will open simultaneously, select Spatial. Otherwise, the direction defined for a force spectrum loading has no meaning.

  • Nuclear Regulatory Guide 1.92 (published in February 1976) describes the requirements for combining spatial components when performing seismic response spectra analysis for nuclear power plants.

  • Because all time history combinations are done algebraically (in-phase), this option has no effect on time history results.