# Bending

flexurebendbeambentflex can be written asbeam bendingbeamsbending rigiditybending stiffness
In applied mechanics, bending (also known as flexure) characterizes the behavior of a slender structural element subjected to an external load applied perpendicularly to a longitudinal axis of the element.wikipedia
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### Beam (structure)

beambeamscrossbeam
When the length is considerably longer than the width and the thickness, the element is called a beam.
Its mode of deflection is primarily by bending.

### Plate theory

plateplates and shellstheory of plates and shells
Therefore, to make the usage of the term more precise, engineers refer to a specific object such as; the bending of rods, the bending of beams, the bending of plates, the bending of shells and so on.
In continuum mechanics, plate theories are mathematical descriptions of the mechanics of flat plates that draws on the theory of beams.

### Bending moment

bendingmomentmoments
This bending moment resists the sagging deformation characteristic of a beam experiencing bending.
A bending moment is the reaction induced in a structural element when an external force or moment is applied to the element causing the element to bend.

### Deflection (engineering)

deflectiondeflectionsdeflect
For example, a closet rod sagging under the weight of clothes on clothes hangers is an example of a beam experiencing bending.
If, in addition, the beam is not tapered and is homogeneous, and is acted upon by a distributed load q, the above expression can be written as:

### I-beam

I beamI-beamsH-beam
Wide-flange beams (I-beams) and truss girders effectively address this inefficiency as they minimize the amount of material in this under-stressed region.
The Euler-Bernoulli beam equation shows that the I-shaped section is a very efficient form for carrying both bending and shear loads in the plane of the web.

### Neutral axis

At yield, the maximum stress experienced in the section (at the furthest points from the neutral axis of the beam) is defined as the flexural strength.
θ is the bend angle

### Bending of plates

plate bendingplate-bending
Therefore, to make the usage of the term more precise, engineers refer to a specific object such as; the bending of rods, the bending of beams, the bending of plates, the bending of shells and so on.

### Limit state design

limit stateLoad and Resistance Factor Designlimit states
This plastic hinge state is typically used as a limit state in the design of steel structures.
A structure is deemed to satisfy the ultimate limit state criterion if all factored bending, shear and tensile or compressive stresses are below the factored resistances calculated for the section under consideration.

### Euler–Bernoulli beam theory

Euler–Bernoulli beam equationbeam theoryEuler-Bernoulli beam equation
In the Euler–Bernoulli theory of slender beams, a major assumption is that 'plane sections remain plane'.

### Plastic bending

plasticPlastic Analysis
For stresses that exceed yield, refer to article plastic bending.

### Polar moment of inertia

moment of inertiapolar moments of inertiapolar-moment
where is the polar moment of inertia of the cross-section, m = \rho A is the mass per unit length of the beam, \rho is the density of the beam, A is the cross-sectional area, G is the shear modulus, and k is a shear correction factor.
Where the planar second moment of area describes an object's resistance to deflection (bending) when subjected to a force applied to a plane parallel to the central axis, the polar second moment of area describes an object's resistance to deflection when subjected to a moment applied in a plane perpendicular to the object's central axis (i.e. parallel to the cross-section).

### Truss

trusseslenticular trusschord
Wide-flange beams (I-beams) and truss girders effectively address this inefficiency as they minimize the amount of material in this under-stressed region.
Which chord carries tension and which carries compression depends on the overall direction of bending.

### Stress (mechanics)

stressstressestensile stress
These forces induce stresses on the beam.

### Contraflexure

In a bending beam, a point is known as a point of contraflexure if it is a location where bending moment is zero (changes its sign).

### Shear and moment diagram

bending moment diagramShear and moment diagramsbeam sign convention
Shear and bending moment diagrams are analytical tools used in conjunction with structural analysis to help perform structural design by determining the value of shear force and bending moment at a given point of a structural element such as a beam.

### Quartic function

quartic equationquarticquartic polynomial
:The solutions of this quartic equation are
An example arises in the Timoshenko-Rayleigh theory of beam bending.

### Sandwich theory

sandwichsandwich compositestwo thin layers of material (skins) on either side of a lightweight core

### Bending (metalworking)

bendingspringbackjoggled

### Vibration

vibrationsvibratevibrating

### Vibration of plates

vibrating plateplate vibrationsvibrations of plates

### Bending machine (manufacturing)

Bending Machine (flat metal bending)

### Applied mechanics

engineering mechanicstheoretical and applied mechanicsengineering principles
In applied mechanics, bending (also known as flexure) characterizes the behavior of a slender structural element subjected to an external load applied perpendicularly to a longitudinal axis of the element.

### Structure

structuralstructuresstructurally
In applied mechanics, bending (also known as flexure) characterizes the behavior of a slender structural element subjected to an external load applied perpendicularly to a longitudinal axis of the element.