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Strength of materials

The strength of materials is determined using various methods of calculating the stresses and strains in structural members, such as beams, columns, and shafts. The methods employed to predict the response of a structure under loading and its susceptibility to various failure modes takes into account the properties of the materials, such as yield strength, ultimate strength, Young's modulus, and Poisson's ratio.

Yield (engineering)Yield (engineering)In materials science and engineering, the yield point is the point on a stress–strain curve that indicates the limit of elastic behavior and the beginning of plastic behavior. Below the yield point, a material will deform elastically and will return to its original shape when the applied stress is removed. Once the yield point is passed, some fraction of the deformation will be permanent and non-reversible and is known as plastic deformation.Compressive stressCompressive stressCompressive stresses are generated in objects when they are subjected to forces that push inward, causing the material to shorten or compress. These stresses occur when an object is squeezed or pressed from opposite directions. In everyday life, compressive stresses are common in many structures and materials. For instance, the weight of a building creates compressive stresses in its walls and foundations.Stress concentrationStress concentrationIn solid mechanics, a stress concentration (also called a stress raiser or a stress riser or notch sensitivity) is a location in an object where the stress is significantly greater than the surrounding region. Stress concentrations occur when there are irregularities in the geometry or material of a structural component that cause an interruption to the flow of stress. This arises from such details as holes, grooves, notches and fillets.Shear stressShear stressShear stress (often denoted by τ, Greek: tau) is the component of stress coplanar with a material cross section. It arises from the shear force, the component of force vector parallel to the material cross section. Normal stress, on the other hand, arises from the force vector component perpendicular to the material cross section on which it acts.Deformation (engineering)Deformation (engineering)In engineering, deformation is the change in size or shape of an object when subjected to force, and may be elastic or plastic depending on whether the deformation is reversible when the actuating force is removed. An object's intrinsic resistance to deformation is known as its stiffness or rigidity. If the deformation is negligible under stress, the object is said to be rigid; conversely, it is said to be flexible or pliable.Stress (mechanics)Stress (mechanics)Physical quantity that expresses internal forces in a continuous material StressResidual stresses inside a plastic protractor are revealed by polarized light.Common symbolsσSI unitpascalOther unitspsi, barIn SI base unitsPa = kg⋅m−1⋅s−2Dimension L − 1 M T − 2 {\displaystyle {\mathsf {L}}^{-1}{\mathsf {M}}{\mathsf {T}}^{-2}} Part of a series onContinuum mechanics J = − D d φ d x {\displaystyle J=-D{\frac {d\varphi }{dx}}} Fick's laws of diffusion Laws Conservations Mass Momentum Energy Inequalities Clausius–Duhem (entropy) Solid mechanics Deformation Elasticity linear Plasticity Hooke's law Stress Strain Finite strain Infinitesimal strain Compatibility Bending Contact mechanics frictional Material failure theory Fracture mechanics Fluid mechanics Fluids Statics · Dynamics Archimedes' principle · Bernoulli's principle Navier–Stokes equations Poiseuille equation · Pascal's law Viscosity (Newtonian · non-Newtonian) Buoyancy · Mixing · Pressure Liquids Adhesion Capillary action Chromatography Cohesion (chemistry) Surface tension Gases Atmosphere Boyle's law Charles's law Combined gas law Fick's law Gay-Lussac's law Graham's law Plasma Magnetohydrodynamics Rheology Viscoelasticity Rheometry Rheometer Smart fluids Electrorheological Magnetorheological Ferrofluids Scientists Bernoulli Boyle Cauchy Charles Euler Fick Gay-Lussac Graham Hooke Newton Navier Noll Pascal Stokes Truesdell vte In continuum mechanics, stress is a physical quantity that describes forces present during deformation.Ultimate tensile strengthUltimate tensile strengthUltimate tensile strength (also called UTS, tensile strength, TS, ultimate strength or Ftu{\displaystyle F_{\text{tu}}} in notation) is the maximum stress that a material can withstand while being stretched or pulled before breaking. In brittle materials, the ultimate tensile strength is close to the yield point, whereas in ductile materials, the ultimate tensile strength can be higher.Young's modulusYoung's modulusYoung's modulus (or the Young modulus) is a mechanical property of solid materials that measures the tensile or compressive stiffness when the force is applied lengthwise. It is the elastic modulus for tension or axial compression. Young's modulus is defined as the quotient of the stress (force per unit area) applied to the object and the resulting axial strain (a dimensionless quantity that quantifies relative deformation) in the linear elastic region of the material.Poisson's ratioPoisson's ratioIn materials science and solid mechanics, Poisson's ratio (symbol: ν (nu)) is a measure of the Poisson effect, the deformation (expansion or contraction) of a material in directions perpendicular to the specific direction of loading. The value of Poisson's ratio is the negative of the ratio of transverse strain to axial strain. For small values of these changes, ν is the amount of transversal elongation divided by the amount of axial compression.Strain (mechanics)Strain (mechanics)Relative deformation of a physical body StrainOther namesStrain tensorSI unit1Other units%In SI base unitsm/mBehaviour undercoord transformationtensorDimension 1 {\displaystyle 1} Part of a series onContinuum mechanics J = − D d φ d x {\displaystyle J=-D{\frac {d\varphi }{dx}}} Fick's laws of diffusion Laws Conservations Mass Momentum Energy Inequalities Clausius–Duhem (entropy) Solid mechanics Deformation Elasticity linear Plasticity Hooke's law Stress Strain Finite strain Infinitesimal strain Compatibility Bending Contact mechanics frictional Material failure theory Fracture mechanics Fluid mechanics Fluids Statics · Dynamics Archimedes' principle · Bernoulli's principle Navier–Stokes equations Poiseuille equation · Pascal's law Viscosity (Newtonian · non-Newtonian) Buoyancy · Mixing · Pressure Liquids Adhesion Capillary action Chromatography Cohesion (chemistry) Surface tension Gases Atmosphere Boyle's law Charles's law Combined gas law Fick's law Gay-Lussac's law Graham's law Plasma Magnetohydrodynamics Rheology Viscoelasticity Rheometry Rheometer Smart fluids Electrorheological Magnetorheological Ferrofluids Scientists Bernoulli Boyle Cauchy Charles Euler Fick Gay-Lussac Graham Hooke Newton Navier Noll Pascal Stokes Truesdell vte In mechanics, strain is defined as relative deformation, compared to a reference position configuration.Stephen TimoshenkoStephen TimoshenkoStepan Prokopovich Timoshenko (Ukrainian: Степан Прокопович Тимошенко, romanized: Stepan Prokopovych Tymoshenko, Ukrainian pronunciation:; Russian: Степан Прокофьевич Тимошенко, romanized: Stepan Prokofyevich Timoshenko, ; 22 December [O.S. 10 December] 1878 – May 29, 1972), later known as Stephen Timoshenko, was a Ukrainian and later an American engineer and academician.

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