# strength of materials basics

ISBN 978-1-56032-992-3. When a metal is subjected to a load (force), it is distorted or deformed, no matter how strong the metal or light the load. Elastic deformation refers to the ability of the material to regain its original shape after the external load is removed. g Introduction to the Thermodynamics of Materials (4th ed.). ∫ x σ d τxx = dFx/dA is the normal stress, also denoted as σx. L l This page was last edited on 26 February 2020, at 16:26. + Up to a limiting stress, a body will be able to recover its dimensions on removal of the load. − {\displaystyle {\frac {\partial \sigma _{x}}{\partial x}}+{\frac {\partial \tau }{\partial y}}=f_{x}}, ∂ It is possible to distinguish some common characteristics among the stress–strain curves of various groups of materials. The rate of change is quantified by the coefficient of linear thermal expansion, denoted by variables, CoF & α, When the stresses are removed, all the atoms return to their original positions and no permanent deformation occurs. L x According to the Hooke’s law, the stress is proportional to the strain (in the elastic region), and the slope is Young’s modulus. For components that have to withstand high pressures, such as those used in pressurized water reactors (PWRs), this criterion is not adequate. The normal stress occurs due to the infinitesimal force normal to the infinitesimal area, while shear stresses occur due to the infinitesimal force in the plane of the infinitesimal area. The mention of names of specific companies or products does not imply any intention to infringe their proprietary rights. ϵ Here L0 is called the gauge length. Strain hardening is also called work-hardening or cold-working. σ Strength of Materials in Engineering Mechanics, Introduction | Consider a rod, pulled at each end, along the longitudinal axis. τ 0 William D. Callister, David G. Rethwisch. Ashby, Michael; Hugh Shercliff; David Cebon (2007). d If the load is small, the distortion will probably disappear when the load is removed. A load applied to a mechanical member will induce internal forces within the member called stresses when those forces are expressed on a unit basis. All you need to know is: Stress, Strain, Poissions ratio, Factor of safety, SFD & BMD, Elasticity, Yeild Point & Youngs Modulus. There is also an associated stress, which is referred to as a thermal stress, however no stress is created in a member whose length changes due to a temperature change but is unconstrained. = Unlike stress in an object, which you can’t actually see, deformation is a visible and measurable quantity. ) Weakest link determination by use of three parameter Weibull statistics, Stress is defined on the average as the force divided by the area of the body over which the force acts. x {\displaystyle \left({\begin{matrix}\sigma _{x}&\tau _{xy}&\tau _{xz}\\\tau _{yx}&\sigma _{y}&\tau _{yz}\\\tau _{zx}&\tau _{zy}&\sigma _{z}\end{matrix}}\right)}. {\displaystyle \sigma =E\epsilon }. Elongation ( As already shown above, in the two-dimensional case the stress tensor has only three different components: two normal stresses and one shear stress. x + This website does not use any proprietary data. Stress is the force carried by the member per unit area, and typical units are lbf/in2 (psi) for US Customary units and N/m2 (Pa) for SI units: where F is the applied force and A is the cross-sectional area over which the force acts. {\displaystyle \Delta ={\frac {PL}{AE}}}. z These are the stress at which observable plastic deformation or “yielding” begins; the ultimate tensile strength or maximum intensity of load that can be carried in tension; and the percent elongation or strain (the amount the material will stretch) and the accompanying percent reduction of the cross-sectional area caused by stretching. Stress is the internal resistance, or counterfource, of a material to the distorting effects of an external force or load. z L This inelastic behavior is called plastic deformation. The strain defined above is called the engineering strain or the nominal strain, and is different from natural strain or true strain, which is defined as, ϵ Taylor and Francis Publishing. These shear stresses are in the plane y-z. Similarly, the shear stress is τθ = (P/A) sinθ cosθ. Note that we have considered this value of E to be the same in all directions. τ P Most polycrystalline materials have within their elastic range an almost constant relationship between stress and strain. Accordingly, in the plane stress case (taking, for instance, the plane x-y) we will have a four component stress tensor. We can extend the same idea of relating stress to strain to shear applications in the linear region, relating shear stress to shear strain to create Hooke’s law for shear stress: For isotropic materials within the elastic region, you can relate Poisson’s ratio (ν), Young’s modulus of elasticity (E), and the shear modulus of elasticity (G): The elastic moduli relevant to polycrystalline materials: If you want to get in touch with us, please do not hesitate to contact us via e-mail: The information contained in this website is for general information purposes only.

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