Position of the last point load variable method-writing bending moment’s expressions

Résumé

This paper presents the use of the P.L.P.L. method to solve a system of a simply supported straight beam loaded by a convoy. It is the result of our own research that we have presented in thesis. Here, we make a highlight on the writing of bending moment’s expressions. For vulgarization, we act to show the process and we convince to prove the ease offered by this method. We define in this paper, the aim of the use, which consists in determining the bending moments and the shear forces in the beam. We describe the model, then we present the general formula used to establish the expressions of bending moments under each load of the convoy. Thus, after describing all parameters related to the structure and those related to the loads, we show the expressions of bending moments in an abacus, which is shown as a table. This abacus would be used easily by those in charge of calculation. We show a case study of bridge where we present a program, on EXCEL, for writing bending moment’s expressions. Then we show curves resulting from the expressions previously determined and we determine dangerous cross-section and also the dangerous position of the convoy on the beam. Thus after that we are able to calculate the maximum value of bending moment. We prove that the use of the method is simple, easy and leads to reliable results. In the future we will use the results of this research to solve a system of continuous beam loaded with a convoy.