An analytical technique for obtaining an expected equivalent damping coefficient for a single-degree-of-freedom structure under random loading is discussed and illustrated. The expected energy dissipation is determined by integration of the product of the inelastic deformation energy and the amplitude probability density throughout the range of displacements. The technique is applied in detail to an elastic-perfectly plastic model subjected to excitation simulating the El Centro and Golden Gate earthquakes. A maximum expected equivalent damping ratio of only 0.117625 occurs when the mean displacement equals 2.765 times the yielding displacement under the following conditions: (a) the response peak amplitudes are Rayleigh distributed, (b) the excitation is a wide band random process, and (c) the material is elastic-perfectly plastic.

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