﻿

# Bending moment

A bending moment exists in a structural element when a moment is applied to the element so that the element bends. Moments and torques are measured as a force multiplied by a distance so they have as unit newton-metres (N·m) , or foot-pounds force (ft·lbf). The concept of bending moment is very important in engineering (particularly in Civil and Mechanical Engineering) and physics.

When a bending moment exists in a structural element it induces tensile stresses and compressive stresses in the element. Tensile stresses and compressive stresses increase proportionally with bending moment, but are also dependent on the second moment of area of the cross-section of the structural element. Failure in bending will occur when the bending moment is sufficient to induce tensile stresses greater than the yield stress of the material. 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.

The bending moment at a section through a structural element may be defined as "the sum of the moments about that section of all external forces acting to one side of that section". 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.

Moments are calculated by multiplying the external vector forces (loads or reactions) by the vector distance at which they are applied. When analysing an entire element, it is sensible to calculate moments at both ends of the element, at the beginning, centre and end of any uniformly distributed loads, and directly underneath any point loads. Of course any "pin-joints" within a structure allow free rotation, and so zero moment occurs at these points as there is no way of transmitting turning forces from one side to the other.

If clockwise bending moments are taken as negative, then a negative bending moment within an element will cause "sagging", and a positive moment will cause "hogging". It is therefore clear that a point of zero bending moment within a beam is a point of contraflexure&mdash;that is the point of transition from hogging to sagging or vice versa.

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. Bending moment varies linearly over unloaded sections, and parabolically over uniformly loaded sections.

To resist higher bending moment, the beam shall be deeper.

*First moment of area
*Second moment of area
*Wing bending relief

Wikimedia Foundation. 2010.

### Look at other dictionaries:

• Bending moment — Bending moment. См. Изгибающий момент. (Источник: «Металлы и сплавы. Справочник.» Под редакцией Ю.П. Солнцева; НПО Профессионал , НПО Мир и семья ; Санкт Петербург, 2003 г.) …   Словарь металлургических терминов

• bending moment — lenkimo momentas statusas T sritis fizika atitikmenys: angl. bending moment; flexural moment; flexural torque vok. Biegemoment, n; Biegungsmoment, n rus. изгибающий момент, m; момент изгиба, m pranc. moment de flexion, m; moment fléchissant, m …   Fizikos terminų žodynas

• bending moment — noun physics : the resultant moment about the neutral axis of any cross section of a rod or beam of the system of forces that produce bending * * * Physics. the algebraic sum of the moments about the neutral axis of any cross section of a beam.… …   Useful english dictionary

• bending moment — a system of internal forces whose resultant is a moment. This term is most commonly used to refer to internal forces in beams …   Mechanics glossary

• bending moment — Physics. the algebraic sum of the moments about the neutral axis of any cross section of a beam. [1855 60] * * * …   Universalium

• Moment — Moment(s) may refer to: Moment (time) Contents 1 Science, engineering, and mathematics 2 Art and entertainment …   Wikipedia

• Moment redistribution — refers to the behavior of statically indeterminate structures that are not completely elastic, but have some reserve plastic capacity. When one location first yields, further load to the structure causes bending moment to redistribute differently …   Wikipedia

• Bending — For other uses, see Bending (disambiguation). Flexure redirects here. For joints that bend, see living hinge. For bearings that operate by bending, see flexure bearing. Continuum mechanics …   Wikipedia

• Moment distribution method — The moment distribution method (not to be confused with moment redistribution) is a structural analysis method for statically indeterminate beams and frames developed by Hardy Cross. It was published in 1930 in an ASCE journal.[1] The method only …   Wikipedia

• Bending stiffness — The bending stiffness E I of a beam (or a plate) relates the applied bending moment to the resulting deflection of the beam. It is the product of the elastic modulus E of the beam material and the area moment of inertia I of the beam cross… …   Wikipedia