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 loads. 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).
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. 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—that is the point of transition from hogging to
sagging or vice versa.
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). The concept of bending moment is very
important in engineering (particularly in Civil and mechanical engineering) and physics.
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