Structural analysis

From Freepedia

See also: structuralism.

Structural analysis is the computation of deflections, and internal forces or stresses within structures, either for design or for performance evaluation of existing structures. Structural analysis needs input data such as the applied forces or environmental effects (e.g. weight of material and , pressure of wind, temperature changes), the structure's geometry and support conditions, and the materials' properties. Output quantities may include support reactions, stresses and displacements. In design, the calculated stresses are compared to the allowable stresses for the materials used while the calculated displacements are compared to various standards for serviceability. Advanced structural analysis may include the effects of vibrations, stability and non-linear behaviours.

There are two broad classes of analysis: classical methods and matrix methods. Classical methods provide answers by means of analytical formulation, applicable mostly for simple structural models, while matrix methods are computer-oriented, applicable to structures of arbitrary size and complexity. Both approaches, however, are based on the same three fundamental relations: equilibrium, constitutive, and compatibility. The solutions are approximate when any of these relations are only approximately satisfied.

Classical methods are available for individual members such as beams, columns, shafts, and for entire structures such as trusses, frames, plates and shells. Common methods include the method of sections and method of joints for truss analysis, moment distribution 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.

Matrix methods model a structure as an assembly of elements or components with various forms of connection between them. Early application of matrix methods were for articulated frameworks with truss, beam and column elements; later and more advanced matrix methods, usually referred to as "finite element analysis" model an entire structure with one-, two-, and three-dimensional elements and can be used for articulated as well as continuous structures such as a pressure vessel, plates and shells. Commercial computer software for structural analysis typically uses matrix methods. Matrix methods themselves can be further classified into two main approaches: the displacement or stiffness method and the force or flexibility method. The stiffness method is, by far, more popular thanks to its ease of implementation as well as of formulation for advanced applications.