# Rigidity

the rigidity is a size of, those the connection between the load, which affects a body and whose deformation describes. The rigidity of a body depends on its material as well as geometry. Depending upon type of load one differentiates differentRigidities, e.g. Bending extension or torsional rigidity. The reciprocal value of the rigidity is called indulgence.

The rigidity belongs with the tear tenacity, firmness, ductility, hardness, density and the fusing temperature to the material properties of a material.

## rigidities

rigidities always consist of a material and a geometry term. Which material size is used - thus modulus of elasticity or thrust - depends on the demand, thosethe outside load causes. Rigidities are noted in such a way that referred deformation sizes result, thus e.g. Stretches instead of length variations. This is justified in the fact that the rigidity is a characteristic of the cross section. Cross section geometry can itself however over the length of a construction unitchange, so that the multiplication with the length is not always correct. The spring rate is a special case.

### extension rigidity

the extension rigidity is the product of the modulus of elasticity of the material in load direction times the cross-section area perpendicular to the load direction. It is independently of the form of the cross section, depends it on its surface.

[itex] E \ cdot A< /math> for example in [itex] \ mathrm {N}< /math>

Above formulation applies to free lateral contraction of the cross section. With handicapped Querkontration for the modulus of elasticity the querkontrationsbehinderte module is used. The longitudinal expansion[itex] \ epsilon< /math> the body is the attacking normal force [itex] F< /math> as well as the extension rigidity proportionally.

[itex] \ epsilon = \ frac {F} {I/O}< /math>

### flexural rigidity

the flexural rigidity is the product of modulus of elasticity and area moment 2. Degree [itex] I< /math> the cross section. The area moment 2. Degree hangs substantially ofthe form of the cross section off.

[itex] E \ cdot I< /math> for example in [itex] \ mathrm {N mm^2}< /math>

Like strongly the deflection and/or. Sinking of a bend-stressed construction unit with given load is, depends apart from the flexural rigidity also on its length and the conditions of support. The curvature[itex] \ kappa< /math> the body is the attacking bending moment [itex] M_ {\ mathrm {B}}< /math> as well as the flexural rigidity proportionally.

[itex] \ kappa = \ frac {M_ {\ mathrm {B}}} {EGG}< /math>

### torsional rigidity

the torsional rigidity is the product of the polar area moment 2. Degree [itex] I_ {\ mathrm {p}}< /math> and shear modulus [itex] the G< /math> the material. The polar area momentis related to the axle, around which the body is tordiert.

[itex] G \ cdot I_ {\ mathrm {p}}< /math> for example in [itex] \ mathrm {N mm^2}< /math>

As strong, i.e. around like much degree, a body under a certain load rotated, hangs beside polar area moment 2.Order also from its length and the conditions of support. The Drillung [itex] \ vartheta'< /math> the body is the attacking twisting moment [itex] M_ {\ mathrm {T}}< /math> as well as the torsional rigidity proportionally.

[itex] \ vartheta' = \ frac {M_ {\ mathrm {T}}} {GI_ {\ mathrm {p}}}< /math>

## spring rate

in practice is often not the stretch [itex] \ epsilon< /math> separatethe absolute length variation [itex] \ delta L< /math> of interest. Therefore the spring rate becomes by the relationship of the necessary Kraft math F [/itex] with< feathers/springs> for a certain deflection [itex] \ delta L< /math> described. The spring rate consists of the rigidity of the feather/spring, divided by their length. Duringthe extension rigidity of the length of the feather/spring is independent, halves themselves the spring rate, if the length of the feather/spring is doubled.

Example: A tension member with the cross section A =100mm 2 and a modulus of elasticity of 210,000 N/mm 2 has a rigidityof E·A = 2,1×10 7 N. The staff is L =100mm amounts to its spring rate E long in such a way·A / L = 210,000 N/mm. The computation applies then only if the cross section of the staff is constant.

## rigidity and firmness

rigidity are with firmness to be confounded. The firmness is a measure for the yieldable loads of a material. As a body is not rigid has anything with its firmness to do.