Stiffness

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. Joint stiffness may be either the Symptom of pain on moving a joint the Symptom of loss of range of motion or the physical sign of reduced range of motion A material is said to be elastic if it deforms under stress (e In Materials science, deformation is a change in the shape or size of an object due to an applied force. In Physics, a force is whatever can cause an object with Mass to Accelerate. It is an extensive material property. In the Physical sciences an intensive property (also called a bulk property) is a Physical property of a system that does not depend on the

1 Definition
2 Rotational stiffness
3 Relationship to elasticity
4 Use in engineering
5 See also

Definition

The stiffness, k, of a body is

$k=\frac {P} {\delta}$

where

P is the applied force

δ is the deflected distance

In the International System of Units, stiffness is typically measured in newtons per metre. The newton (symbol N) is the SI derived unit of Force, named after Isaac Newton in recognition of his work on Classical The metre or meter is a unit of Length. It is the basic unit of Length in the Metric system and in the International

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:

$P=k \delta \,$

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.

Rotational stiffness

A body may also have a rotational stiffness, k, given by

$k=\frac {M} {\theta}$

where

M is the applied moment

θ is the rotation

In the SI system, rotational stiffness is typically measured in newton-metres per radian. In Physics, the moment of force (often just moment, though there are other quantities of that name such as Moment of inertia) is a Pseudovector Newton metre is the unit of moment ( Torque) in the SI system The radian is a unit of plane Angle, equal to 180/ π degrees, or about 57

In the SAE system, rotational stiffness is typically measured in inch-pounds per degree. Inches redirects here To see the Les Savy Fav album see Inches. This article deals with the unit of force For the unit of mass see Pound (mass. This article describes the unit of angle For other meanings see Degree.

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

Relationship to elasticity

In general, elastic modulus is not the same as stiffness. A shear stress, denoted \tau\ ( Tau) is defined as a stress which is applied Parallel or tangential to a face of a material In Solid mechanics, torsion is the twisting of an object due to an applied Torque. An elastic modulus, or modulus of elasticity, is the mathematical description of an object or substance's tendency to be deformed elastically (i Elastic modulus is a property of the constituent material; stiffness is a property of a solid body. That is, the modulus is an intensive property of the material; stiffness, on the other hand, is an extensive property of the solid body dependent on the material and the shape and boundary conditions. In the Physical sciences an intensive property (also called a bulk property) is a Physical property of a system that does not depend on the In the Physical sciences an intensive property (also called a bulk property) is a Physical property of a system that does not depend on the For example, for an element in tension or compression, the axial stiffness is

$k=\frac {AE} {L}$

where

A is the cross-sectional area,

E is the Young's modulus,

L is the length of the element. In Physics String Tension is the magnitude of the pulling force exerted by a string cable chain or similar object on another object Physical compression is the result of the subjection of a material to Compressive stress, resulting in reduction of Volume. In Solid mechanics, Young's modulus (E is a measure of the Stiffness of an isotropic elastic material

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. In Solid mechanics, Young's modulus (E is a measure of the Stiffness of an isotropic elastic 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. An elastic modulus, or modulus of elasticity, is the mathematical description of an object or substance's tendency to be deformed elastically (i A high modulus of elasticity is sought when deflections are undesirable, while a low modulus of elasticity is required when flexibility is needed. An elastic modulus, or modulus of elasticity, is the mathematical description of an object or substance's tendency to be deformed elastically (i

Dictionary

-noun

rigidity or a measure of rigidity
inflexibility or a measure of inflexibility

© 2009 citizendia.org; parts available under the terms of GNU Free Documentation License, from http://en.wikipedia.org
network: | |

Contents

Definition

Rotational stiffness

Relationship to elasticity

Use in engineering

See also

Dictionary

stiffness

-noun