The relationship between load intensity (W), shear force (S) and bending moment (M) is given by

Explanation:

Shear Force:

Shear force at any section is the summation of all transverse loading, either to the left or to the right of any section.

Bending Moment:

A bending moment at any section is a resultant algebraic sum of moments caused by transverse forces either from the left or right of the section.

Relationship between bending moment, shear force, and loading:

• The rate of change of shear force at any section is equal to load intensity at that section.

i.e. Change of shear force between two sections is equal to the area under the load intensity diagram between those two sections.

• The rate of change of bending moment at any section is equal to shear force at that section.​

i.e. Change of bending moment between two sections is equal to the area under the shear force diagram between those two sections

The presence of a concentrated couple leads to a sudden rise or fall of the Bending moment diagram depending upon the sign and direction of the couple.