Mechanics of materials is an important topic in the study of engineering mechanics. It is normally an undergraduate subject that is taught to engineering students who have previously completed prerequisite courses in statics and dynamics. This subject is also known by other names, such as strength of materials and mechanics of deformable bodies. In simple terms, mechanics of materials is the study of how forces produce stresses in solid bodies. It is an essential topic for engineers and students who are solving problems in aerospace, aeronautical, civil, and mechanical engineering.
Static and Dynamic Loading
To determine the deformations and resulting stresses in a solid body, it is imperative that the analyst understand the applied loads. There are two types of loads that are commonly encountered in the analysis of structural members. The first load type is static which includes constant forces, pressures, moments, and dead weights. The second load type is dynamic which includes varying forces, accelerations, vibration, shock, and transient dynamic forces. Real world application of dynamic loads includes impact forces, wind loads, snow loads, and earthquake loads. In the application of any type of loading, it is essential that the analyst construct free body diagrams to determine the resolution of the applied loads. When a solid body experiences combined loading, the principle of superposition can be used to add the effect of the applied loads.
Material Properties-Stress & Strain
A critical aspect of mechanics of materials is the relationship between stress and strain. Materials that obey Hooke’s law exhibit a linear relationship between stress and strain. The resulting deformation is considered elastic when the structure retains its original shape after the applied load has been removed. When the applied load is increased, and the deformation is permanent, the material behavior is called plastic. The relationship between a material’s stress and strain determines the likelihood for a structure to survive in the real world. Stresses that occur at a point are analyzed using Mohr’s circle for two or three dimensional loading.
Types of Structural Members
Mechanics of materials provides the analyst with closed form solutions for simple structural members that experience a variety of loading conditions. Prismatic bars can be loaded axially, or in torsion. A special case of a prismatic bar is a circular shaft that is loaded in bending and torsion. Beams can be loaded axially, in pure bending, or in torsion. The beam bending case is analyzed using shear and moment diagrams. As with any axial loading, it can be either tensile or compressive. Columns are loaded axially in compression, and are normally assessed for buckling stability. Thin walled pressure vessels are typically analyzed for hoop stresses.
Preparation for Advanced Topics
Understanding the basic concepts and simplified methods in mechanics of materials prepares the student for advanced study in engineering mechanics. Analyzing real world engineering structure can be done with a background in statics, dynamics, and strength of materials. Advanced topics include machine design, vibration, advanced mechanics of materials, plates and shells, elasticity, and plasticity.