# 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**

### 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.

### Structural load

**loadloadslive load**

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.