Relatie tussen de schuifkracht en het buigmoment

Suppose a beam is subjected to a distributed load, two concentrated loads, and a couple moment. Establish the relationship between the shear and the bending moment.

Consider an elemental section of the beam and draw a free-body diagram of the section.

For the section to be in equilibrium, the moment acting on the right side of the section should be higher by a small and finite amount.

A resultant force of the distributed load is exerted at a fractional distance from the section's right end.

Using the equilibrium equation for moment, a relation between moment and shear can be obtained.

Further, by dividing it by Δx and letting Δx approach zero, the slope of the moment diagram is determined, which is equivalent to the shear.

A maximum bending moment occurs at the point where the slope of the moment and the shear are zero.

Integrating the distributed load over the elemental section, lying between two arbitrary points, a correlation between the change in the bending moment and the area under the shear diagram is obtained.