The complete theory began with the consideration of the behavior of one and two dimensional members of structures, whose states of stress can be approximated as two dimensional, and was then generalized to three dimensions to develop a more complete theory of the elastic and plastic behavior of materials. Engineering mechanics of solids by egor p popov pdf study of strength of materials often refers to various methods of calculating the stresses and strains in structural members, such as beams, columns, and shafts. The field of strength of materials deals with forces and deformations that result from their acting on a material. A load applied to a mechanical member will induce internal forces within the member called stresses when those forces are expressed on a unit basis.
The stresses acting on the material cause deformation of the material in various manners including breaking them completely. Deformation of the material is called strain when those deformations too are placed on a unit basis. The stresses and strains that develop within a mechanical member must be calculated in order to assess the load capacity of that member. This requires a complete description of the geometry of the member, its constraints, the loads applied to the member and the properties of the material of which the member is composed. With a complete description of the loading and the geometry of the member, the state of stress and state of strain at any point within the member can be calculated. The calculated stresses may then be compared to some measure of the strength of the member such as its material yield or ultimate strength.
The calculated deflection of the member may be compared to a deflection criteria that is based on the member’s use. The calculated buckling load of the member may be compared to the applied load. The calculated stiffness and mass distribution of the member may be used to calculate the member’s dynamic response and then compared to the acoustic environment in which it will be used. Transverse loadings — Forces applied perpendicular to the longitudinal axis of a member.