Strengths Misc Notes

# Strengths Misc Notes - Useful solutions to standard...

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Useful solutions to standard problems in Introduction and synopsis Modelling is a key part of design. In the early stage, approximate modelling establishes whether the concept will work at all, and identifies the combination of material properties which maximize performance. At the embodiment stage, more accurate modelling brackets values for the forces, the displacements, the velocities, the heat fluxes and the dimensions of the components. And in the final stage, modelling gives precise values for stresses, strains and failure probability in key components; power, speed, efficiency and so forth. Many components with simple geometries and loads have been modelled already. Many more complex components can be modelled approximately by idealizing them as one of these. There is no need to reinvent the beam or the column or the pressure vessel; their behaviour under all common types of loading has already been analysed. The important thing is to know that the results exist and where to find them. This appendix summarizes the results of modelling a number of standard problems. Their useful- ness cannot be overstated. Many problems of conceptual design can be treated, with adequate precision, by patching together the solutions given here; and even the detailed analysis of non- critical components can often be tackled in the same way. Even when this approximate approach is not sufficiently accurate, the insight it gives is valuable. The appendix contains 15 double page sections which list, with a short commentary, results for constitutive equations; for the loading of beams, columns and torsion bars; for contact stresses, cracks and other stress concentrations; for pressure vessels, vibrating beams and plates; and for the flow of heat and matter. They are drawn from numerous sources, listed under Further reading in Section A.16.

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376 Materials Selection in Mechanical Design A.l Constitutive equations for mechanical response The behaviour of a component when it is loaded depends on the mechanism by which it deforms. A beam loaded in bending may deflect elastically; it may yield plastically; it may deform by creep; and it may fracture in a brittle or in a ductile way. The equation which describes the material response is known as a constitutive equation. Each mechanism is characterized by a different constitutive equation. The constitutive equation contains one or more than one material property : Young’s modulus, E, and Poisson’s ratio, II, are the material properties which enter the constitutive equation for linear-elastic deformation; the yield strength, uy, is the material property which enters the constitutive equation for plastic flow; creep constants, EO, a0 and n enter the equation for creep; the fracture toughness, IC[,-, enters that for brittle fracture.
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## This note was uploaded on 09/19/2009 for the course CEE 372 taught by Professor Siddharthan during the Spring '08 term at Nevada.

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Strengths Misc Notes - Useful solutions to standard...

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