Elastic Deflection of Beams and frames Using Dream Method

Abstract

This paper presents a new graphical method for the analysis of linear elastic structures called Dream Method. The method states that the strain energy of a linear elastic multi-member structure undergoing small deformation is the sum of moment of area of the bending moment diagrams of the individual members each about its own diagram base divided by the flexural rigidity of the member. The displacement at any point on the structure is equal to the partial derivative of the total strain energy with respect to the load at that point. The method is applied successfully in the analysis of a built-in stepped beam, a beam on three supports, and a four-member frame.