Damping (DSRSS) (ratio of critical) - CAESAR II - Help

CAESAR II Users Guide

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CAESAR II
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CAESAR II Version
13

(Available for: Spectrum/DSRSS, Harmonics, and Time History)

Specifies the ratio of critical damping as described below. Typical values for piping systems, as recommended in USNRC Regulatory Guide 1.61 and ASME Code Case N-411, range from 0.01 to 0.05, based upon pipe size, earthquake severity, and the natural frequencies of the system.

Damping is not generally considered in the mathematical solutions required for spectrum or harmonic analysis. It is ignored or solved as specialized cases in most analyses and must be instead considered through adjustment of the applied loads (by generation of the response spectrum) and/or system stiffness.

For a time history analysis, damping is used explicitly, because this method uses a numeric solution to integrate the dynamic equations of motion.

For a spectrum analysis using the double sum (DSRSS) modal combination method (as defined by USNRC Regulatory Guide 1.92), the damping value is used in the calculation of the modal correlation coefficients. CAESAR II does not permit the specification of damping values for individual modes. For more information, see Modal Combination Method (Group/10%/DSRSS/ABS/SRSS).

For a harmonic analysis, this ratio is converted to Rayleigh Damping, where the damping matrix can be expressed as multiples of the mass and stiffness matrices:

[C] = a [M] + b [K]

On a modal basis, the relationship between the ratio of critical damping Cc and the constants a and b are given as:

Where:

w = undamped natural frequency of mode (radians/sec)

For many practical problems, a is extremely small, and so may be ignored, reducing the relationships to:

a = 0

b = 2 Cc / w

CAESAR II uses this implementation of damping for its harmonic analysis, with the exception that a single b is calculated for the multi-degree-of-freedom system, and the w used is that of the load forcing frequency. When the forcing frequency is in the vicinity of a modal frequency, this gives an accurate estimate of the true damping value.