The seismic analysis of complex piping systems is often carried out by the response spectrum method. The maximum probable responses are calculated as the square root of the sum of the squares (SRSS) of the responses obtained in various modes of vibration for the three components of earthquake. A coupling matrix is introduced in case of modes with closely spaced frequencies. The ASME strength criterion for the pipes is based on maximum shear stress which can be calculated from the two orthogonal bending moments and the torsional moment acting on the cross section. Strictly speaking, one should know the combination of these three moments acting simultaneously which would give the maximum shear stress at the section being designed. However, the response spectrum method gives the maximum probable values which in general do not occur simultaneously. Often the pipe is conservatively designed as if these probable maximum values were occurring simultaneously. It can be shown that this procedure may overestimate the maximum shear stress by as much as 73 percent. To overcome this problem a new method is applied by which simultaneous variation in the three moments can be predicted to cause the extreme probable effect. The new method is “exact” within the framework of existing procedures and assumptions.

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