METHODS FOR HANDLING CONCENTRATED LOADS IN BENDING DEFORMATION PROBLEMS IN MATERIAL MECHANICS

The concentration of force and moment is widespread in practical mechanical problems. However, when deriving the differential relationships between load intensity, shear force, and bending moment, the differential segments extracted do not include concentrated loads. Solving the equations for internal forces and bending deformations often requires artificial segmentation of the beam, making the solution process exceptionally intricate. This paper introduces singular functions to transform concentrated loads into distributed loads and provides load intensity equations under any loading conditions. Through calculus relationships, equations for internal forces, rotations, and deflections are derived. This approach enhances students' comprehension of a mechanical model in which, during the derivation of differential relationships, the differential segments solely consist of distributed loads. The solution to bending deformations also eliminates the need for beam segmentation, significantly simplifies the calculation process and makes it suitable for computer programming.