Relatie tussen de verdeelde belasting en de dwarskracht.

Consider a beam experiencing a distributed load, two concentrated loads, and a couple moment. Establish the relationship between the shear and the distributed load.

First, consider an elemental section on the beam free from any concentrated load or couple moment and draw a free-body diagram of the section.

To maintain equilibrium, the shear force acting on the right-hand side of the section should be incremented by a small and finite amount.

The resultant force of the distributed load acts at a fractional distance from the right end of the section.

Using the equation of equilibrium for vertical force, a relation between shear and load is obtained.

Next, by dividing both sides of the equation by Δx and letting Δx approach zero, the slope of the shear force can be determined, which is equal to the distributed load intensity.

Finally, rearranging the equation and integrating the distributed load over the elemental section between two arbitrary points leads to a relation between the change in shear and the area under the load curve.