Rate of change of bending moment is

Explanation:

The relation between shear force (V) and loading rate (w) is:

\(\frac{dV}{dx}=w\)

it means a positive slope of the shear force diagram represents an upward loading rate.

The relation between shear force (V) and bending moment (M) is:

\(\frac{dM}{dx}= V\)

it means the slope of a bending moment diagram will represent the magnitude of shear force at that section.

The relation between loading rate and shear force can be written as:

\(\frac{d^2M}{dx^2}= w\)

Additional Information

If y is the deflection then relation with moment M, shear force V and load intensity w.

\(EI\frac{d^2y}{dx^2}= M\)

\(EI\frac{d^3y}{dx^3}= V\)

\(EI\frac{d^4y}{dx^4}= w\)