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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),
Rigidity is the property of a structure that it does not bend or flex under an applied force. The opposite of rigidity is flexibility.In structural rigidity theory, structures are formed by collections of objects that are themselves rigid bodies, often assumed to take simple geometric forms such as straight rods (line segments), with pairs of objects connected by flexible hinges.
is the elastic modulus and is the second moment of area, the product of these giving the flexural rigidity of the beam. This equation is very common in engineering practice: it describes the deflection of a uniform, static beam. Successive derivatives of have important meanings:
G is the modulus of rigidity (shear modulus) of the material J is the torsional constant. Inverting the previous relation, we can define two quantities; the torsional rigidity, = with SI units N⋅m 2 /rad. And the torsional stiffness,
The elastic modulus of a material is not the same as the stiffness of a component made from that material. Elastic modulus is a property of the constituent material; stiffness is a property of a structure or component of a structure, and hence it is dependent upon various physical dimensions that describe that component.
Quantities used in the definition of the section modulus of a beam. The maximum tensile stress at a cross-section is at the location = and the maximum compressive stress is at the location = where the height of the cross-section is = +. These stresses are
Flexural rigidity is defined as the force couple required to bend a fixed non-rigid structure by one unit of curvature, or as the resistance offered by a structure while undergoing bending. Flexural rigidity of a beam
Structural rigidity, a mathematical theory of the stiffness of ensembles of rigid objects connected by hinges; Rigidity (electromagnetism), the resistance of a charged particle to deflection by a magnetic field; Rigidity (mathematics), a property of a collection of mathematical objects (for instance sets or functions)