Stiffness

The stiffness is a variable in engineering mechanics. Describes the resistance of an elastic body to deformation by a force or a torque.

The stiffness of a component depends on

• On the elasticity of the material ( E or G- module, depending on the load )

And

• The geometry of the component ( size and shape of cross sectional area).

Depending on the load, a distinction is different rigidities, such as stretching, bending or torsional stiffness.

The reciprocal of the stiffness is called resilience.

The stiffness is not to be confused with the strength which is a measure of the tolerable stresses of a material. This limit (e.g., tensile strength) is not dependent on a geometry, but only on the material and can therefore be looked up in material data sheets.

Rigidities

Rigidities are so listed that related parameters of the deformation result, so for example, instead of stretching length changes. This is due to the fact that the stiffness is a property of the cross-sectional geometry. However, this may change over the length of the component, so that the multiplication of the length is not always correct. The spring constant is a special case.

Axial stiffness

The axial stiffness is the product of the modulus of elasticity of the material in the loading direction and the cross -sectional area perpendicular to the loading direction ( irrespective of the shape of the cross section ):

This formulation is valid for free lateral contraction of the cross section; at the restraint of the transverse contraction Transportation Contra disabled module is used instead of the elastic modulus.

The longitudinal extension of the body is proportional to the acting axial force and inversely proportional to the axial stiffness:

With the normal stress

Bending stiffness

The flexural rigidity is the product of the modulus of elasticity of the material and geometrical moment of inertia of the cross section (which in turn depends substantially on the shape of the cross section ):

How strong is the bending or lowering of a bending stress component at a given load depends not only on the flexural strength also depends on its length and the storage conditions. The curvature of the body is proportional to the acting bending moment and inversely proportional to the flexural stiffness:

Torsional stiffness

The torsional stiffness ( also referred to as flexural rigidity ), the product of the shear modulus of the material and the torsional moment of inertia:

The torsional moment of inertia is related to the axis about which the body is twisted. It is often mistakenly claimed that it would correspond to the polar area moment of inertia of a cross section. This is true but in reality only for circular and closed circular ring cross sections. Otherwise, a closed formula can be specified for the torsional constant only in special cases.

How strong a body is rotated under a given load depends not only on the torsional moment of inertia also depends on its length L and the storage conditions. The twist per unit length is called torsion or twisting. The twist of the body is proportional to the torsional moment acting, and inversely proportional to the torsional rigidity of:

Spring constant

In practice is often the elongation, but the absolute change in length of interest. Therefore, when the spring constant of the springs will be described by the ratio of the required force for a given deflection of:

On the other hand corresponds to the spring constant of the stiffness of the spring divided by its length:

While the tensile rigidity is independent of the length of the spring, the spring constant is halved when the length of the spring is doubled.

For example, a pull rod to the cross- sectional area A = 100 mm 2 and a modulus of elasticity N/mm2 210,000 has a stiffness of E * A = 2.1 x 107 N. If the rod L = 100 mm long, as is its spring constant E · A / L = 210 000 N / mm. This calculation is valid only if the cross-section of the rod is constant over its length.