Bending moment

bendingmomentmomentsbending moments
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.wikipedia
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Beam (structure)

beambeamscrossbeam
The most common or simplest structural element subjected to bending moments is the beam. It is therefore clear that a point of zero bending moment within a beam is a point of contraflexure—that is the point of transition from hogging to sagging or vice versa.
The total effect of all the forces acting on the beam is to produce shear forces and bending moments within the beam, that in turn induce internal stresses, strains and deflections of the beam.

Bending

flexurebendbeam
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.
This bending moment resists the sagging deformation characteristic of a beam experiencing bending.

Contraflexure

It is therefore clear that a point of zero bending moment within a beam is a point of contraflexure—that is the point of transition from hogging to sagging or vice versa.
In a bending moment diagram, it is the point at which the bending moment curve intersects with the zero line.

Torque

moment armmomentlever arm
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. Moments and torques are measured as a force multiplied by a distance so they have as unit newton-metres (N·m), or pound-foot (lbf·ft).
By contrast, a lateral force on a beam produces a moment (called a bending moment), but since the angular momentum of the beam is not changing, this bending moment is not called a torque.

Newton metre

N·mNmnewton-metre
Moments and torques are measured as a force multiplied by a distance so they have as unit newton-metres (N·m), or pound-foot (lbf·ft).

Shear and moment diagram

bending moment diagramShear and moment diagramsbeam sign convention
Critical values within the beam are most commonly annotated using a bending moment diagram, where negative moments are plotted to scale above a horizontal line and positive below.
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.

Influence line

influence lines
Some of the common functions studied with influence lines include reactions (the forces that the structure’s supports must apply in order for the structure to remain static), shear, moment, and deflection (Deformation).

Stress resultants

Stress resultants in plates and shells
However, physical interpretations of bending moments in beams and plates have a straightforward interpretation as the stress resultants in a cross-section of the structural element.
These are the stress resultants (also called membrane forces, shear forces, and bending moment) that may be used to determine the detailed stress state in the structural element.

Zero-fuel weight

Maximum zero-fuel weightzero fuel weightMaximum Zero Fuel Weight
Weight in the wings does not contribute as significantly to the bending moment in the wing as does weight in the fuselage.

Structural element

structural memberList of structural elementsshell elements
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.

Force

forcesattractiveelastic force
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. Moments are calculated by multiplying the external vector forces (loads or reactions) by the vector distance at which they are applied.

Cross section (geometry)

cross sectioncross-sectioncross sections
The internal reaction loads in a cross-section of the structural element can be resolved into a resultant force and a resultant couple.

Resultant force

resultantresultant torquelinear resultant
The internal reaction loads in a cross-section of the structural element can be resolved into a resultant force and a resultant couple.

Couple (mechanics)

couplerocking coupleforce couple
The internal reaction loads in a cross-section of the structural element can be resolved into a resultant force and a resultant couple.

Dynamic equilibrium

equilibriumdynamicequilibria
The forces and moments on either side of the section must be equal in order to counteract each other and maintain a state of equilibrium so the same bending moment will result from summing the moments, regardless of which side of the section is selected.

Pound-foot (torque)

pound-footpound-feetlb-ft
Moments and torques are measured as a force multiplied by a distance so they have as unit newton-metres (N·m), or pound-foot (lbf·ft).

Engineering

engineerengineersengineered
The concept of bending moment is very important in engineering (particularly in civil and mechanical engineering) and physics.

Civil engineering

Civilcivil engineerCivil and Environmental Engineering
The concept of bending moment is very important in engineering (particularly in civil and mechanical engineering) and physics.

Mechanical engineering

mechanical engineermechanicalmechanical engineers
The concept of bending moment is very important in engineering (particularly in civil and mechanical engineering) and physics.

Physics

physicistphysicalphysicists
The concept of bending moment is very important in engineering (particularly in civil and mechanical engineering) and physics.

Tension (physics)

tensiontensiletensile force
Tensile and compressive stresses increase proportionally with bending moment, but are also dependent on the second moment of area of the cross-section of a beam (that is, the shape of the cross-section, such as a circle, square or I-beam being common structural shapes).

Stress (mechanics)

stressstressestensile stress
Tensile and compressive stresses increase proportionally with bending moment, but are also dependent on the second moment of area of the cross-section of a beam (that is, the shape of the cross-section, such as a circle, square or I-beam being common structural shapes).

Yield (engineering)

yield strengthyield stressyield
Failure in bending will occur when the bending moment is sufficient to induce tensile stresses greater than the yield stress of the material throughout the entire cross-section.

Shearing (physics)

shearingshearshear deformation
It is possible that failure of a structural element in shear may occur before failure in bending, however the mechanics of failure in shear and in bending are different.

Euclidean vector

vectorvectorsvector addition
Moments are calculated by multiplying the external vector forces (loads or reactions) by the vector distance at which they are applied.