Bending moment

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. The most common or simplest structural element subjected to bending moments is the beam. The example shows a beam which is simply supported at both ends. Simply supported means that each end of the beam can rotate; therefore each end support has no bending moment. The ends can only react to the shear load. Other beams can have both ends fixed; therefore each end support has both bending moment and shear reaction loads. Beams can also have one end fixed and one end simply supported. The simplest type of beam is the cantilever, which is fixed at one end and is free at the other end (neither simple or fixed). In reality, beam supports are usually neither absolutely fixed nor absolutely rotating freely.

The internal reaction loads in a cross-section of the structural element can be resolved into a resultant force and a resultant couple. For equilibrium, the moment created by external forces (and external moments) must be balanced by the couple induced by the internal loads. The resultant internal couple is called the bending moment while the resultant internal force is called the shear force (if it is transverse to the plane of element) or the normal force (if it is along the plane of the element).