The Conjugate Method for Solving Mono-Axial Frames

Abstract

This paper discusses materials for a course on ‘Strength of materials and mechanics of solids’, addressed to students of second-year mechanical engineering, ocean engineering, civil engineering and aerospace engineering. In particular, the problem of the evaluation of the deflection and of the axial displacement of elastic mono-axial frames is considered. This problem is solved by the use of a generalization of the classical conjugate beam method, that here is defined conjugate mono-axial frame method. It lies on the similarity between all three kinematic differential equations governing the elastic deflection and axial displacement of the mono-axial frame and all three static differential equations governing its equilibrium. This implies some comparisons and theorems that are reported in the present paper. The mode of presentation of this material is by lecture, within a regular course, of 3–4 hours, with 2–3 revision hours. The material must be presented after the classical elastic beam and frame problem has been treated. The material helps students to analyse the important relationships between the kinematics and the statics of any elastic structure.