Mechanics of Materials

The first four topics of the text are devoted to the analysis of the stresses and of the corresponding deformations in various structural members, considering successively axial loading, torsion, and pure bending. Each analysis is based on a few basic concepts, namely, the conditions of equilibrium of the forces exerted on the member, the relations existing between stress and strain in the material, and the conditions imposed by the supports and loading of the member. The study of each type of loading is complemented by a large number of examples designed to strengthen the students' understanding of the subject. Topic 5 is devoted to the determination of shearing stresses in beams under transverse loadings. More advanced aspects of the design of beams, such as the determination of the principal stresses at the junction of the flange and web of a W-beam, are in Topic 6. The chapter also includes the determination of stresses under combined loadings that can now include the determination of the principal stresses, principal planes, and maximum shearing stress at a given point. The determination of the deflection of beams is discussed in Topic 7. The first part of the chapter is devoted to the integration method followed by the use of singularity functions. Topic 8 is devoted to columns and includes the design of steel and aluminum columns.