The fundamental problem of structural analysis is the prediction of the ability of
machine components to provide reliable service under its applied loads and temperature. The basis of the solution is the calculation of certain performance indices, such
as stress (force per unit area), strain (deformation per unit length), or gross deformation, which can then be compared to allowable values of these parameters. The allowable values of the parameters are determined by the component function (deformation
constraints) or by the material limitations (yield strength, ultimate strength, fatigue
strength, etc.). Further constraints on the allowable values of the performance indices
are often imposed through the application of factors of safety.
Strength of materials, also know as mechanics of materials, is focused on analyzing stresses and deflections in materials under load. Knowledge of stresses and deflections allows for the safe design of structures that are capable of supporting their intended loads.
When dealing with mechanics of materials, choosing the correct formula to calculate the stress at a given point can be difficult. Normal and shear stresses come in a wide variety of applications, each stress application with its own calculation formula. The most common stress types you deal with in basic mechanics of materials fall into several major categories