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The shear modulus is one of several quantities for measuring the stiffness of materials. All of them arise in the generalized Hooke's law: . Young's modulus E describes the material's strain response to uniaxial stress in the direction of this stress (like pulling on the ends of a wire or putting a weight on top of a column, with the wire getting longer and the column losing height),
Other names are sometimes employed for one or both parameters, depending on context. For example, the parameter μ is referred to in fluid dynamics as the dynamic viscosity of a fluid (not expressed in the same units); whereas in the context of elasticity, μ is called the shear modulus, [2]: p.333 and is sometimes denoted by G instead of μ.
In physics, Hooke's law is an empirical law which states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance—that is, F s = kx, where k is a constant factor characteristic of the spring (i.e., its stiffness), and x is small compared to the total possible deformation of the spring.
Elastic properties describe the reversible deformation (elastic response) of a material to an applied stress.They are a subset of the material properties that provide a quantitative description of the characteristics of a material, like its strength.
The shear modulus or modulus of rigidity (G or Lamé second parameter) describes an object's tendency to shear (the deformation of shape at constant volume) when acted upon by opposing forces; it is defined as shear stress over shear strain. The shear modulus is part of the derivation of viscosity. The bulk modulus (K) describes volumetric ...
The bulk modulus (which is usually positive) can be formally defined by the equation K = − V d P d V , {\displaystyle K=-V{\frac {dP}{dV}},} where P {\displaystyle P} is pressure, V {\displaystyle V} is the initial volume of the substance, and d P / d V {\displaystyle dP/dV} denotes the derivative of pressure with respect to volume.
The shear is constant in absolute value: it is half the central load, P / 2. It changes sign in the middle of the beam. The bending moment varies linearly from one end, where it is 0, and the center where its absolute value is PL / 4, is where the risk of rupture is the most important.
The formulas are organized into tables in a hierarchical format: chapter, table, case, subcase, and each case and subcase is accompanied by diagrams. The main topics of the book include: • The behavior of bodies under stress • Analytical, numerical, and experimental methods • Tension, compression, shear, and combined stress