Matrix analysis of rigid frames

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1951
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Virginia Tech
Abstract

The matrix power series method of inversion is impractical, since the series diverges, or converges extremely slowly, except in the analysis of very special and, usually, impractical frames.

Dwyer’s method, Zurmuhl’s method, and the method of partitioning, used with discrimination, suffice to invert any stiffness matrix with satisfactory rapidity. These methods are rapid enough to compete with moment distribution when a frame is to be analyzed for many loading conditions. This condition is met frequently enough to make a study of matrix algebra worth while for the structural engineer.

Both Dwyer’s method and Zurmuhl’s method yield reasonable accuracy when four significant figures are used in the original stiffness matrix and four decimals are used throughout the computations, provided the stiffnesses of the frame members do not differ extremely.

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