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Development of Modern Structural Mechanics

Development of Modern Structural Mechanics - Development of...

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Development of Structural Mechanics Structural Mechanics is a branch of structural engineering concerned with applying Newtonian mechanics to the analysis of deformations, internal forces and stresses within framed and/or continuum structural elements and sub-assemblages, either for design or for performance evaluation of existing structures. Structural mechanics limits the scope of study from solid mechanics which deals with the deformation and motion of solids including microscopic analysis of viscoelastic and hereditary materials. Advanced structural analysis may include the effects of dynamic, stability, and non-linear behavior. There are three approaches to structural analysis: the strength of materials approach, the elasticity theory approach, and the finite element approach. The first two methods make use of analytical formulations leading to closed-form solutions. The third, a numerical method of solving field problems such as displacement field and stress field, etc., is very widely used for structural analysis. The equations needed for the formulation of the finite element method are based on theories of mechanics such as elasticity theory and strength of materials. Analytical formulations apply mostly to simple linear elastic problems, while the finite element method is computer oriented, applicable to structures of great complexity. Regardless of approach, structural analysis is based on the same fundamental relations: equilibrium, constitutive, compatibility, and strain-deformation. The solutions are approximate when any of these relations are only approximately satisfied, or only represent an approximation of reality (Wikipedia, 2006). Strength of materials approach - Being the simplest of the three discussed, the strength of materials approach is applicable to simple structural members subjected to specific loadings. Except for the moment distribution method developed by Cross (1930), the basic strength of 1
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materials methods were available in their current forms in the second half of the nineteenth century. They are still widely used for small structures and for preliminary design of large structures. The solutions are based on linear isotropic infinitesimal elasticity and Euler-Bernoulli elementary beam theory. The simplifying assumptions include that the materials 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 the members are idealized with one-dimensional entities. Solutions for special cases exist for certain structures such as thin-walled pressure vessels. As with any simplifying assumptions in engineering, the more the model deviates from reality, the less useful (and more dangerous) the result becomes.
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