# The rate of change of bending moment is equal to

By BYJU'S Exam Prep

Updated on: October 17th, 2023

(a) Shear force at that section

(b) Deflection at that section

(d) Slope of that section

The rate of change of bending moment is equal to Shear force at that section. The relation between shear force (V) and loading rate (w) is: dv/dx = w. It means a positive slope of the shear force diagram represents an upward loading rate.

### Rate of Change of Bending Moment

• The relation between shear force (V) and bending moment (M) is: 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: d2M/dx2 = w
• If y is the deflection then relation with moment M, shear force V and load intensity w.
• EI d2y/dx2 = M
• EI d3y/dx3 = V
• EI d4y/dx4 = w
• Therefore, the rate of change of bending moment is equal to shear force at that section

Summary:

## The rate of change of bending moment is equal to (a) Shear force at that section (b) Deflection at that section (c) Loading at that section (d) Slope of that section

Shear force at that section is equal to the rate of change of bending moment. The reaction produced in a structural element when an external force or moment is applied to the element is referred to as bending moment.

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