What Is a Bending Moment?

Bending moment is a kind of internal moment on the section of the force member. Popular saying: Bending moment is a kind of moment. Another explanation is the moment required for bending. The lower part is pulled positive (the upper part is compressed) and the upper part is pulled negative (the lower part is compressed). Its standard definition is: the resultant moment of the distributed internal force system perpendicular to the cross section.

Bending moment is a kind of internal moment on the section of the force member, that is, the resultant moment of the internal force system perpendicular to the cross section. Its size is

Moment formula:

(M _max is the maximum bending moment, F is the external force, and L is the arm).

Bending moment diagram is a kind of graph, which is used to indicate the change of bending moment along the axis in each cross section of the beam. to sum up

Figures 6-9 a, b, and c respectively show the three kinds of stresses of the same beam AB under q, M ₀ , q alone, and M ₀ alone.

Overlay schematic

When q and M _{0 work} together

V _A = ql / 2 + M ₀ / l V _S = ql / 2 + M ₀ / l

Derivation of principle

It can be seen from the calculation results that the reaction force and bending moment of the beam's support are linear functions of the load (q, M ₀ ), that is, the reaction force or bending moment has a linear relationship with the load. At this time, the reaction force or bending moment produced by g and M ₀ acting on F is equal to the algebraic sum of the reaction force or bending moment produced by g and M ₀ acting alone:

The derivation process

This relationship exists not only in this example, but also in other mechanical calculations, that is, as long as the reaction force, bending moment (or other quantity) and the load have a linear relationship, the reaction force and bending moment caused by several loads ( Or other quantities) equal to the superposition of reaction forces, bending moments (or other quantities) caused by each load alone. This relationship is called the superposition principle. The premise of applying the superposition principle is that the members are in a small deformation condition, and the effects of each load on the members are independent. ^[3]