| Strength Of Materials |
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| materials science | |
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Strength of materials is the scientific area of Materials Science for the study of the strength of engineering materials and their mechanical behavior in general (such as Stress , Deformation , Strain and stress-strain relations). Strength is considered in terms of ''' Compressive Strength ''', ''' Tensile Strength ''', and ''' Shear Strength ''', namely the limit states of Compressive Stress , Tensile Stress and Shear Stress respectively. DEFINITIONS Stress terms '' Stress '' is the internal distribution of forces within a body that balances and reacts to the loads applied to it. It is a complicated Tensor quantity that can be broken down into simpler elements for engineering purposes;
Strength terms '' Compressive Strength '' is a limit state of Compressive Stress that leads to compressive failure in the manner of ductile failure (infinite theoretically yield) or in the manner of brittle failure (rupture as the result of crack propagation, or sliding among a weak plane - see Shear Strength ). '' Tensile Strength '' is a limit state of Tensile Stress that leads to tensile failure in the manner of ductile failure (yield as the first stage of failure, some hardening in the second stage and break after a possible "neck" formation) or in the manner of brittle failure (sudden breaking in two or more pieces with a low stress state). Strain - deformation terms '' Deformation '' of the material is the change in geometry when stress is applied (in the form of force loading, gravitational field, acceleration, thermal expansion, etc.). Deformation is expressed by the displacement field of the material. '' Strain '' or ''reduced deformation'' is a mathematical term to express the trend of the deformation change among the material field. For uniaxial loadings - displacements of a specimen (for example a bar element) it is expressed as the quotient of the displacement and the length of the specimen. For 3D displacement fields it is expressed as derivates of displacement functions in terms of a second order Tensor (with 6 independent elements). '' Deflection '' is a term to describe the magnitude to which a construction or structural element bends under a load. STRESS - STRAIN RELATIONS '' Elasticity '' is the ability of a material to return to its previous shape after stress is released. In some materials, the relation between applied stress and the resulting strain is directly proportional (up to a certain limit), and a graph representing those two quantities is a straight line. Hooke's Law describes such relationships and is valuable in the study of springs. (see Solid Mechanics ). In other materials, the relation is not linear. In steel, the most common material for making springs, most of the elastic range is linear, though the relation becomes non-linear at the extreme end, just before the material begins to deform plastically. '' Plasticity '' is the property of materials to deform permanently after force is applied and released. Most solid materials behave elastically when relatively low amounts of force are applied, and plastically under higher amounts of force. DESIGN TERMS Ultimate strength is an attribute directly related to a material, rather than just specific specimen of the material, and as such is quoted force per unit of cross section area (). For example, Ultimate Tensile Strength (UTS) of mild steel is . It is useful to remember that . (or stress) and UTS: the Ultimate force (or stress). For example to achieve a factor of safety of 4, the allowable stress in a mild steel component can be worked out as . SUGGESTED READING
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