Stiffness 475008 225772253 2008-07-15T09:40:23Z 128.250.80.15 reflist {{for|pain and/or loss of range of motion of a joint|joint stiffness}} '''Stiffness''' is the resistance of an [[Elasticity (physics)|elastic]] body to [[deflection]] or [[deformation]] by an applied [[force]]. It is an [[intensive and extensive properties|extensive material property]]. ==Definition== The stiffness, ''k'', of a body is :<math>k=\frac {P} {\delta} </math> where :''P'' is the applied force :&delta; is the deflected distance In the [[International System of Units]], stiffness is typically measured in [[newton]]s per [[metre]]. As both the applied force and [[deflection#Construction|deflection]] are [[vector (spatial)|vector]]s (respectively '''''P''''' and '''&delta;'''), in general their relationship is characterised by a stiffness matrix, '''''k''''', where: :<math> P=k \delta \,</math> 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. In rheology it may be defined as the ratio of strain to stress <ref>V. GOPALAKRISHNAN and CHARLES F. ZUKOSKI; “Delayed flow in thermo-reversible colloidal gels”; Journal of Rheology; Society of Rheology, U.S.A.; July/August 2007; 51 (4): pp. 623–644.</ref>, and so take the units of reciprocal stress, ''e.g''. 1/[[pascal (unit)|Pa]]. == Rotational stiffness == A body may also have a rotational stiffness, ''k'', given by :<math>k=\frac {M} {\theta} </math> where : ''M'' is the applied [[moment (physics)|moment]] : ''&theta;'' is the rotation In the SI system, rotational stiffness is typically measured in [[newton-metre]]s per [[radian]]. In the SAE system, rotational stiffness is typically measured in [[inch]]-[[pound-force|pound]]s per [[degree (angle)|degree]]. Further measures of stiffness are derived on a similar basis, including: * shear stiffness - ratio of applied [[shear stress|shear]] force to shear deformation * torsional stiffness - ratio of applied [[torsion (mechanics)|torsion]] moment to angle of twist == 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 an [[intensive and extensive properties|intensive property]] of the material; stiffness, on the other hand, is an [[intensive and extensive properties|extensive property]] of the solid body dependent on the material ''and'' the shape and boundary conditions. For example, for an element in [[tension (mechanics)|tension]] or [[physical compression|compression]], the axial stiffness is :<math>k=\frac {AE} {L} </math> where :''A'' is the cross-sectional area, :''E'' is the [[Young's modulus]], :''L'' is the length of the element. For the special case of unconstrained uniaxial tension or compression, [[Young's modulus|Young's modulus of elasticity]] ''can'' be thought of as a measure of the stiffness of a material. == Use in engineering == The stiffness of a structure is of principal importance in many engineering applications, so the [[modulus of elasticity]] is often one of the primary properties considered when selecting a material. A high modulus of elasticity is sought when [[deflection|deflections]] are undesirable, while a low [[modulus of elasticity]] is required when flexibility is needed. == References == {{Reflist}} == See also == *[[Elasticity (physics)|Elasticity]] *[[Elastic modulus]] *[[Hardness]] *[[Moment of inertia]] *[[Young's modulus]] *[[Hooke's law]] [[Category:Physical quantity]] [[Category:Classical mechanics]] [[bs:Krutost]] [[ca:Rigidesa]] [[de:Steifigkeit]] [[es:Rigidez]] [[it:Rigidezza]] [[nl:Stijfheid]] [[ja:剛性]] [[pt:Rigidez]] [[ru:Жёсткость]] [[zh:剛度]]