Flexural rigidity

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Flexural rigidity

Flexural rigidity is defined as the force

Force

In physics, a force is that which can cause an object with mass to change its velocity. Force has both Euclidean_vector#Length of a vector and Direction , making it a Vector quantity....
couple

Couple (mechanics)

A Couple is a system of forces with a resultant moment but no resultant force. Another term for a couple is a pure moment. Its effect is to create rotation without Translation_....
required to bend a rigid

Rigid

In mathematics, a rigid collection C of mathematical objects is one in which every c ? C is uniquely determined by less information about c than one would expect....
structure to a unit curvature

Curvature

In mathematics, curvature refers to any of a number of loosely related concepts in different areas of geometry. Intuitively, curvature is the amount by which a geometric object deviates from being flat, or straight in the case of a line , but this is defined in different ways depending on the context....
.

In a beam

Beam (structure)

A beam is a List of structural elements that is capable of withstanding Structural load primarily by resisting bending. The bending force induced into the material of the beam as a result of the external loads, own weight and external reactions to these loads is called a bending moment....
or rod

Cylinder (geometry)

A cylinder is one of the most curvilinear basic geometric shapes: the surface formed by the points at a fixed distance from a given straight line, the axis of the cylinder....
, flexural rigidity varies along the length as a function of x shown in the following equation:

where E is the modulus of elasticity

Young's modulus

In solid mechanics, Young's modulus is a measure of the stiffness of an isotropic elastic material. It is also known as the Young modulus, modulus of elasticity, elastic modulus or tensile modulus....
, I is the 2nd moment of inertia, y is the transverse displacement of the beam at x, and M(x) is the bending moment

Moment (physics)

In physics, the term "moment" can refer to many different concepts:*Moment of force is a synonym for torque, an important basic concept in physics, civil engineering, and mechanical engineering....
at x.

Flexural rigidity has SI units of Pa

Pascal (unit)

The pascal is the SI derived unit of pressure, stress , Young's modulus and tensile strength. It is a measure of force per unit area i.e. equivalent to one newton per square meter or one joule per cubic meter....
·m⁴ (which also equals N

Newton

The newton is the International System of Units SI derived unit of force, named after Isaac Newton in recognition of his work on classical mechanics....
·m²).

Flexure of the lithosphere
The thin lithospheric plates which cover the surface of the Earth are also subject to flexure, when a load or force is applied to them.

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Encyclopedia

Flexural rigidity is defined as the force

Force

In physics, a force is that which can cause an object with mass to change its velocity. Force has both Euclidean_vector#Length of a vector and Direction , making it a Vector quantity....
couple

Couple (mechanics)

Rigid

In mathematics, a rigid collection C of mathematical objects is one in which every c ? C is uniquely determined by less information about c than one would expect....
structure to a unit curvature

Curvature

Beam (structure)

Cylinder (geometry)

Young's modulus

Moment (physics)

Pascal (unit)

Newton

The newton is the International System of Units SI derived unit of force, named after Isaac Newton in recognition of his work on classical mechanics....
·m²).

Flexure of the lithosphere

The thin lithospheric plates which cover the surface of the Earth are also subject to flexure, when a load or force is applied to them. On a geological timescale, the lithosphere behaves, elastically (in first approach) and can therefore bend under loading by mountain chains, volcanoes and so on.

The flexure of the plate depends on:

1. The plate thickness (usually referred to as elastic thickness of the lithosphere).
2. The elastic properties of the plate
3. The applied load or force

As flexural rigidity of the plate is determined by the Young's modulus, Poisson's ratio and cube of the plates elastic thickness, it is a governing factor in both (1) and (2).

Flexural rigidity

Flexure of the lithosphere

See also