The Analysis of Shear Distribution for Multi-Cell Beams in Flexure by means of Successive Numerical Approximations

Abstract

The determination of shear distributions for multi-cell sections can conveniently be considered as two separate problems.(i)the shear flow arising from a pure torsional couple applied in the plane of the section, and(ii)the shear flow arising from a resultant shear force acting on the section so as to produce no resultant twist per unit length of that section,i.e. through the shear centre of that section.Both problems involve finding the value of one unknown shear flow for each cell, so that in multi-cell construction a set of simultaneous equations is obtained, which must be solved to obtain the shear pattern.The solution of problem (i) by successive numerical approximations has been dealt with completely by Benscoter. The present paper gives a method for problem (ii).The usefulness of the method becomes more apparent with increasing numbers of spar webs as may be envisaged for future wing sections of small thickness chord ratios. It is analogous in the procedure used to the Hardy Cross moment distribution method for continuous beams, and has similar advantages. An approximate solution of any required degree of accuracy is quickly obtainable at the design stage and the method is readily adaptable for use by a computer with no knowledge of the structural or mathematical theory involved.