A New Method for Solving the Integrals of the Mohr-Maxwell Method for Displacements Calculus of Bent Straight Bars

The paper presents a new way of solving the integrals that appear in the Mohr-Maxwell energy method for calculating the displacements or rotations of straight bars subjected to bending. The method proposed by the authors, studied and tested for many years in the Military Technical Academy in the Strength of Materials group led by Col. Prof. Vasile Palacianu, eliminates the need to build effort diagrams. To solve the integral on a certain domain, a formula is applied that takes into consideration only the value of the moments at the ends of the integration interval. The well-known restriction for Veresceaghin grapho-analytical integration is maintained: on the integration domain, the variation of the bending moment produced by the generalized load equal to unity must vary linearly. Therefore, the method proposed by the authors cannot be applied to curved bars. Our new method can be used for a beam and also for a beams system. After the presentation of the theoretical foundations of the method and the establishment of the calculation relationship in three variants: without the load distributed over the integration interval, with the load uniformly distributed and with the load distributed according to a linear law, some edifying examples are presented, which highlight the efficiency of the method and the modality for work.