Strength of Materials Methods (classical Methods)
The simplest of the three methods here discussed, the mechanics of materials method is available for simple structural members subject to specific loadings such as axially loaded bars, prismatic beams in a state of pure bending, and circular shafts subject to torsion. The solutions can under certain conditions be superimposed using the superposition principle to analyze a member undergoing combined loading. Solutions for special cases exist for common structures such as thin-walled pressure vessels.
For the analysis of entire systems, this approach can be used in conjunction with statics, giving rise to the method of sections and method of joints for truss analysis, moment distribution method for small rigid frames, and portal frame and cantilever method for large rigid frames. Except for moment distribution, which came into use in the 1930s, these methods were developed in their current forms in the second half of the nineteenth century. They are still used for small structures and for preliminary design of large structures.
The solutions are based on linear isotropic infinitesimal elasticity and Euler–Bernoulli beam theory. In other words, they contain the assumptions (among others) that the materials in question are elastic, that stress is related linearly to strain, that the material (but not the structure) behaves identically regardless of direction of the applied load, that all deformations are small, and that beams are long relative to their depth. As with any simplifying assumption in engineering, the more the model strays from reality, the less useful (and more dangerous) the result.
Read more about this topic: Structural Analysis
Famous quotes containing the words strength, materials and/or methods:
“In the mountains of truth you will never climb in vain: either you will already get further up today or you will exercise your strength so that you can climb higher tomorrow.”
—Friedrich Nietzsche (18441900)
“In how few words, for instance, the Greeks would have told the story of Abelard and Heloise, making but a sentence of our classical dictionary.... We moderns, on the other hand, collect only the raw materials of biography and history, memoirs to serve for a history, which is but materials to serve for a mythology.”
—Henry David Thoreau (18171862)
“The greatest part of our faults are more excusable than the methods that are commonly taken to conceal them.”
—François, Duc De La Rochefoucauld (16131680)