Stiffness
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- For pain and/or loss of range of motion of a joint, see joint stiffness
Stiffness is the resistance of an elastic body to deflection or deformation by an applied force. It is an extensive material property.
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[edit] Definition
The stiffness k of a body that deflects a distance δ under an applied force P is
In the International System of Units, stiffness is typically measured in newtons per metre.
As both the applied force and deflection are vectors (respectively P and δ), in general their relationship is characterised by a stiffness matrix, k where:
The deflection can, in general, refer to a point distinct from that where the force is applied and a complicated structure will not deflect purely in the same direction as an applied force. The stiffness matrix enables such systems to be characterised in straightforward terms.
The inverse of stiffness is compliance, typically measured in units of metres per newton.
[edit] Rotational stiffness
A body may also have a rotational stiffness, where the stiffness k for a rotation θ under an applied moment M is
In the S.I. system, rotational stiffness is typically measured in newton-metres per radian.
Further measures of stiffness are derived on a similar basis, including:
- shear stiffness - ratio of applied shear force to shear deformation
- torsional stiffness - ratio of applied torsion moment to angle of twist
[edit] Relationship to elasticity
In general, elastic modulus is not the same as stiffness. Elastic modulus is a property of the constituent material; stiffness is a property of a solid body. That is, the modulus is a property of the material; stiffness, on the other hand, is a property of the solid body dependent on the material and the shape and boundary conditions. For example, for an element in tension or compression, the axial stiffness is
where A is the cross-sectional area, E is the Young's modulus, and L is the length of the element. See also, stress stiffening.
For the special case of unconstrained uniaxial tension or compression, Young's modulus of elasticity can be thought of as a measure of the stiffness of a material.
[edit] Use in engineering
The stiffness of a structure is of principal importance in many engineering applications, so modulus of elasticity is often one of the primary properties considered when selecting a material. A high modulus of elasticity is sought when deflections are undesirable, while a low modulus of elasticity is required when flexibilty is needed.
