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 units such as newton.metres (N.m) and foot.pounds (ft.lb). The concept of bending moment is very important in engineering and physics. It has been suggested that this article or section be merged with torque. ... Engineering is the discipline of acquiring and applying knowledge of design, analysis, and/or construction of works for practical purposes. ... A magnet levitating above a high-temperature superconductor demonstrates the Meissner effect. ...

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. Tensile stress (or tension) is the stress state leading to expansion; that is, the length of a material tends to increase in the tensile direction. ... Compressive stress is the stress applied to materials resulting in their compaction (decrease of volume). ... The second moment of area, also known as the area moment of inertia or second moment of inertia, is a property of a shape that is used to predict its resistance to bending and deflection which are directly proportional. ... Yield strength, or the yield point, is defined in engineering and materials science as the stress at which a material begins to plastically deform. ... Shearing in continuum mechanics refers to the occurrence of a shear strain, which is a deformation of a material substance in which parallel internal surfaces slide past one another. ...

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. A dynamic equilibrium occurs when two reversible processes occur at the same rate. ...

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. This article is about vectors that have a particular relation to the spatial coordinates. ... For other uses, see Force (disambiguation). ... This article is about vectors that have a particular relation to the spatial coordinates. ...

If clockwise bending moments are taken as negative, then a negative bending moment within an element will cause "sagging", and a clockwise moment will cause "hogging". 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. A statically determinate beam, bending under an evenly distributed load. ... The point or points of contraflexure are the places in the beam where no bending occurs in the beam. ...

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

See also

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