Stress Calculation for Tubular Frameworks Having Continuous Longitudinals

1. In a recent paper Southwell has shown that the calculation of primary stresses for a tubular framework, generally representative of a rigid airship, is a problem which can be solved exactly by a synthesis of known “type solutions,” although the order of redundancy is such as to make it quite intractable by conventional methods. By “primary stresses” is meant those actions which would be induced in the constituent members by loads applied solely at the joints, if the joints were entirely free, so that no bending actions could came into play. It is customary to assume such freedom in stress calculation, both because the complexity of the problem is thereby reduced, and because primary stresses are in general predominent. But in proceeding to the design of the constituent members it is necessary to consider (at least in approximate fashion) what actions will be imposed as a result of rigidity in the joints; and in regard to the stressing of rigid airships it may be said that the outstanding problem (now that a technique exists for primary stress calculation) is the effect of continuity of the longitudinals. The purpose of this paper is to show that Southwell’s method can be extended so as to throw light on this question. Given the idea of a synthesis of known “type solutions,” we have only to examine the nature of these type solutions when continuous longitudinals are presumed. We shall find that their nature is unchanged, the only difference being that the ratios of the component displacements, and the rate of their variation from bulkhead to bulkhead, are slightly altered; and since it is known from experience that a close approximation can be obtained by neglecting joint rigidity, we may solve the amended equations by treating the corrections as small quantities whose squares and products can be neglected.