Stiffness - Wikipedia, the free encyclopediaPage 1 of 4 Stiffness From Wikipedia, the free encyclopedia Stiffness is the rigidity of an object — the extent to which it resists deformation in response to an applied force.[1] The complementary concept is flexibility or pliability: the more flexible an object is, the less stiff it is.[2] Contents ◾ ◾ ◾ ◾ ◾ ◾ ◾ 1 2 3 4 5 6 7 Calculations Compliance Rotational stiffness Relationship to elasticity Applications See also References Calculations The stiffness, k, of a body is a measure of the resistance offered by an elastic body to deformation. For an elastic body with a single degree of freedom (DOF) (for example, stretching or compression of a rod), the stiffness is defined as where, F is the force applied on the body δ is the displacement produced by the force along the same degree of freedom (for instance, the change in length of a stretched spring) In the International System of Units, stiffness is typically measured in newtons per meter. In Imperial units, stiffness is typically measured in pounds(lbs) per inch. Generally speaking, deflections (or motions) of an infinitesimal element (which is viewed as a point) in an elastic body can occur along multiple DOF (maximum of six DOF at a point). For example, a point on a horizontal beam can undergo both a vertical displacement and a rotation relative to its undeformed axis. When there are M degrees of freedom a M x M matrix must be used to describe the stiffness at the point. The diagonal terms in the matrix are the direct-related stiffnesses (or simply stiffnesses) along the same degree of freedom and the off-diagonal terms are the coupling stiffnesses between two different degrees of freedom (either at the same or different points) or the same degree of freedom at two different points. In industry, the term influence coefficient is sometimes used to refer to the coupling stiffness. https://en.wikipedia.org/wiki/Stiffness 31/03/2016 the corresponding DOF is left free while the remaining should be constrained. 1/Pa.Stiffness . but also those along other directions.Wikipedia. Further measures of stiffness are derived on a similar basis. the axial stiffness is https://en. is an extensive property of the solid body dependent on the material and the shape and boundary conditions.[3] and so take the units of reciprocal stress. In the SAE system. the modulus is an intensive property of the material. The ratios between the reaction forces (or moments) and the produced deflection are the coupling stiffnesses. rotational stiffness is typically measured in newton-metres per radian. stiffness. the above equation can be used to obtain the direct-related stiffness for the degree of freedom which is unconstrained. given by where M is the applied moment θ is the rotation In the SI system. in order to calculate a particular direct-related stiffness (the diagonal terms).wikipedia. For a body with multiple DOF. stiffness is a property of a structure. including: ◾ shear stiffness . That is. rotational stiffness is typically measured in inch-pounds per degree.ratio of applied shear force to shear deformation ◾ torsional stiffness . In rheology it may be defined as the ratio of strain to stress. e.org/wiki/Stiffness 31/03/2016 . typically measured in units of metres per newton. the free encyclopedia Page 2 of 4 It is noted that for a body with multiple DOF. Elastic modulus is a property of the constituent material. for an element in tension or compression. elastic modulus is not the same as stiffness.ratio of applied torsion moment to angle of twist Relationship to elasticity In general. the equation above generally does not apply since the applied force generates not only the deflection along its own direction (or degree of freedom). Rotational stiffness A body may also have a rotational stiffness. on the other hand. For example.g. Under such a condition. Compliance The inverse of stiffness is compliance (or sometimes elastic modulus). A description including all possible stretch and shear parameters is given by the elasticity tensor. k. Young's modulus can be thought of as a measure of the stiffness of a material. 126. the stiffness of the extracellular matrix is important for guiding the migration of cells in a phenomenon called durotaxis. 51 (4): pp.Stiffness . July/August 2007.php?title=Stiffness&oldid=706816523" https://en. For the special case of unconstrained uniaxial tension or compression.org/wiki/Stiffness 31/03/2016 . Applications The stiffness of a structure is of principal importance in many engineering applications. In biology. (2000). the rotational stiffness of a straight section is where "J" is the torsion constant for the section. "G" is the rigidity modulus of the material Note that in SI. Retrieved from "https://en. so the modulus of elasticity is often one of the primary properties considered when selecting a material. Retrieved 2012-05-04.. "Delayed flow in thermo-reversible colloidal gels". the free encyclopedia Page 3 of 4 where A is the cross-sectional area. these units yield . p. Similarly. 623–644.S.1016/S0020-1383(00)80040-6. Journal of Rheology. Martin Wenham (2001). E is the (tensile) elastic modulus (or Young's modulus). Baumgart F. U.Wikipedia. ISBN 978-0-7619-6349-3 3. while a low modulus of elasticity is required when flexibility is needed.wikipedia.wikipedia. See also ◾ ◾ ◾ ◾ ◾ ◾ Elasticity (physics) Elastic modulus Mechanical impedance Hardness Hooke's law Moment of inertia ◾ ◾ ◾ ◾ ◾ ◾ Stiffness (mathematics) Young's modulus Compliant mechanism Shore durometer Elastography Tactile Imaging References 1. Society of Rheology. GOPALAKRISHNAN and CHARLES F. 200 science investigations for young students. L is the length of the element. doi:10. "Stiffness--an unknown world of mechanical science?". ZUKOSKI.org/w/index. Injury (Elsevier) 31.A. "Stiffness and flexibility". "“Stiffness” = “Load” divided by “Deformation”" 2. V. A high modulus of elasticity is sought when deflection is undesirable. Wikipedia® is a registered trademark of the Wikimedia Foundation.wikipedia. By using this site. https://en. additional terms may apply. the free encyclopedia Page 4 of 4 Categories: Physical quantities Continuum mechanics Structural analysis ◾ This page was last modified on 25 February 2016. Inc.Stiffness . at 13:04.org/wiki/Stiffness 31/03/2016 . you agree to the Terms of Use and Privacy Policy. ◾ Text is available under the Creative Commons Attribution-ShareAlike License..Wikipedia. a non-profit organization.