Stiffness
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- For pain and/or loss of range of motion of a joint, see joint stiffness
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[edit] Overview
Stiffness is the resistance of an elastic body to deflection or deformation by an applied force. It is an intensive material property.
The stiffness k of a body that deflects a distance δ under an applied force P is
In the S.I. system, 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:
- P = k δ.
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 one dimension, Young's modulus of elasticity can be thought of as a measure of the stiffness of a material.
For solid bodies, the stiffness is proportional to the elastic modulus, but also dependent on an element's dimensions. 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 and k is stiffness of material . The unit of k is Nm-1
[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.
