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| {{about||pain and/or loss of range of motion of a joint|joint stiffness|the term regarding the stability of a differential equation|stiff equation}}
| | Wilber Berryhill is the name his parents gave him and he totally digs that title. One of the extremely best things in the globe for him is performing ballet and he'll be beginning something else alongside with it. Distributing production is how he makes a living. I've always cherished residing in Kentucky but now I'm contemplating other choices.<br><br>Stop by my website - [http://beauty.thuvienbao.com/profile.php?u=MaBrandenb free psychic readings] |
| {{redirect|Flexibility}}
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| [[File:Beam bending.svg|thumb|right]]
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| '''Stiffness''' is the rigidity of an object — the extent to which it resists [[deformation (mechanics)|deformation]] in response to an applied [[force]].<ref>{{cite journal
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| | title = Stiffness--an unknown world of mechanical science?
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| | journal = Injury
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| | author = Baumgart F.
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| | year = 2000
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| | volume = 31
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| | publisher = Elsevier
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| | quote = “Stiffness” = “Load” divided by “Deformation”
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| | url = http://www.sciencedirect.com/science/article/pii/S0020138300800406
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| | accessdate = 2012-05-04
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| | doi=10.1016/S0020-1383(00)80040-6}}</ref> The complementary concept is '''flexibility''' or pliability: the more flexible an object is, the less stiff it is.<ref>{{citation |page=126 |chapter=Stiffness and flexibility |title=200 science investigations for young students |author=Martin Wenham |year=2001 |isbn=978-0-7619-6349-3}}</ref>
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| ==Calculations==
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| '''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 [[Degrees of freedom (mechanics)|degree of freedom]] (for example, stretching or compression of a rod), the stiffness is defined as
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| :<math>k=\frac {F} {\delta} </math>
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| where,
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| :''F'' is the force applied on the body
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| :δ is the [[displacement field (mechanics)|displacement]] produced by the force along the same degree of freedom (for instance, the change in length of a stretched spring)
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| In the [[International System of Units]], stiffness is typically measured in [[Newton (unit)|newton]]s per metre.
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| In Imperial units, stiffness is typically measured in [[Pound (force)|pound]]s(lbs) per inch.
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| Generally speaking, [[Deflection (engineering)|deflections]] (or motions) of an infinitesimal element (which is viewed as a point) in an elastic body can occur along multiple [[Degrees of freedom (mechanics)|degrees of freedom]] (maximum of six DOF at a point). For example, a point on a horizontal [[Euler–Bernoulli beam equation|beam]] can undergo both a vertical [[Displacement (vector)|displacement]] and a rotation relative to its undeformed axis. When there are M degrees of freedom a M x M [[Matrix (mathematics)|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.
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| It is noted that for a body with multiple DOF, the equation above generally does not apply since the applied force generates not only the deflection along its own direction (or degree of freedom), but also those along other directions.
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| For a body with multiple DOF, in order to calculate a particular direct-related stiffness (the diagonal terms), the corresponding DOF is left free while the remaining should be constrained. Under such a condition, the above equation can be used to obtain the direct-related stiffness for the degree of freedom which is unconstrained. The ratios between the reaction forces (or moments) and the produced deflection are the coupling stiffnesses.
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| == Compliance ==
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| The [[Multiplicative inverse|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]].
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| == Rotational stiffness ==<!-- [[Torsional rigidity]] redirects here -->
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| A body may also have a rotational stiffness, ''k'', given by
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| :<math>k=\frac {M} {\theta} </math>
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| where
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| : ''M'' is the applied [[moment (physics)|moment]]
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| : ''θ'' is the rotation
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| In the SI system, rotational stiffness is typically measured in [[newton-metre]]s per [[radian]].
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| In the SAE system, rotational stiffness is typically measured in inch-[[Pound (force)|pound]]s per [[degree (angle)|degree]].
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| Further measures of stiffness are derived on a similar basis, including:
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| * shear stiffness - ratio of applied [[shear stress|shear]] force to shear deformation
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| * torsional stiffness - ratio of applied [[torsion (mechanics)|torsion]] moment to angle of twist
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| == Relationship to elasticity ==
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| 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 structure. 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 [[compression (physical)|compression]], the axial stiffness is
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| :<math>k=\frac {AE} {L} </math> | |
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| where
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| :''A'' is the cross-sectional area,
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| :''E'' is the (tensile) elastic modulus (or [[Young's modulus]]),
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| :''L'' is the length of the element.
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| Similarly, the rotational stiffness is
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| :<math>k=\frac {nGI} {L} </math>
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| where
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| :"I" is the polar moment of inertia,
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| :"n" is an integer depending on the boundary condition (=4 for fixed ends)
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| :"G" is the rigidity modulus of the material
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| For the special case of unconstrained uniaxial tension or compression, [[Young's modulus]] ''can'' be thought of as a measure of the stiffness of a material.
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| == Use in engineering ==
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| 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 (engineering)|deflection]] is undesirable, while a low modulus of elasticity is required when flexibility is needed.
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| == See also == | |
| *[[Elasticity (physics)]]
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| *[[Elastic modulus]]
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| *[[Mechanical impedance]]
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| *[[Hardness]]
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| *[[Hooke's law]]
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| *[[Moment of inertia]]
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| *[[Stiffness (mathematics)]]
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| *[[Young's modulus]]
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| *[[Compliant mechanism]]
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| == References ==
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| {{Reflist}}
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| [[Category:Physical quantities]]
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| [[Category:Continuum mechanics]]
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| [[Category:Structural analysis]]
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Wilber Berryhill is the name his parents gave him and he totally digs that title. One of the extremely best things in the globe for him is performing ballet and he'll be beginning something else alongside with it. Distributing production is how he makes a living. I've always cherished residing in Kentucky but now I'm contemplating other choices.
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