On a Grillage Supported at Four Corners

Abstract

A matrix analysis of a grillage simply supported at four corners under joint loadings is presented with a new approach. The beams of the grillage may be of variable stiffness with unequal spacing, and their intersections need not be orthogonal. However, the stiffness of all transverse or longitudinal beams must be the same. The joints of the grillage are assumed to transmit only compression and tension. The matrix equation of the grillage leads to the form AX+XB=E, in which matrices A and B may be singular, and the unknown matrix X is rectangular. A method of solution is developed and illustrated by a numerical example.