The change in moment is equal to the area under the shear diagram.


When a beam is subjected to external loads, it experiences internal forces and moments that resist the applied loads. The internal moment, also known as bending moment, is the measure of the bending or flexural behavior of the beam along its length. It is due to the distribution of forces and moments acting on the beam.

To analyze the bending moment distribution along the beam, engineers often use shear and moment diagrams. The shear diagram represents the variation of shear force along the beam, while the moment diagram represents the variation of bending moment along the beam.

The shear diagram is obtained by integrating the distributed loads applied to the beam, and it shows the magnitude and direction of shear force at different points along the beam. The moment diagram is then obtained by integrating the shear diagram. It shows the magnitude and direction of bending moment at different points along the beam.

Relationship between shear and moment diagrams:

The relationship between shear and moment diagrams can be understood by considering the equilibrium of forces and moments acting on a small section of the beam. When the shear force changes along the beam, it causes a change in the bending moment.

Consider a small section of the beam with a length dx. The shear force acting on this section is given by V, and the change in shear force over the length dx is dV. The bending moment acting on this section is given by M, and the change in bending moment over the length dx is dM.

By equilibrium, the sum of forces in the vertical direction must be zero, and the sum of moments about any point must be zero. Applying this principle to the small section of the beam, we can write:

       ΣF = 0
       dV - W = 0
       dV = W

where W is the weight of the small section of the beam.

Similarly, the sum of moments about the section must be zero:

       ΣM = 0
       dM - Vdx = 0
       dM = Vdx

Substituting the value of dV from the first equation, we get:

       dM = Wdx

The change in bending moment, dM, over the length dx is equal to the weight of the small section of the beam, W, multiplied by the length dx. This means that the change in moment is directly proportional to the weight of the small section of the beam.

Area under the shear diagram:

Now, let's consider the entire beam. The shear diagram represents the distribution of shear force along the beam. The area under the shear diagram between two points represents the change in shear force between those points. Similarly, the moment diagram represents the distribution of bending moment along the beam. The area under the moment diagram between two points represents the change in bending moment between those points.

Since the change in moment is directly proportional to the weight of the small section of the beam, and the area