What is Bending Moment?
A bending moment is the internal moment that causes a structural element to bend when subjected to external forces. It is the algebraic sum of the moments of all forces acting on one side of a section about that section. Understanding bending moments is essential for designing beams, frames, and other structural elements that resist flexural loads.
The bending moment varies along the length of a beam and depends on the type of loading, support conditions, and the position being analyzed. Engineers use bending moment diagrams (BMD) to visualize the variation of bending moment along a beam.
Bending Moment Formulas
Sign Convention
| Condition | Sign | Effect |
|---|---|---|
| Sagging (concave up) | Positive (+) | Bottom fibers in tension |
| Hogging (concave down) | Negative (-) | Top fibers in tension |
| Clockwise shear | Positive (+) | Left side up, right side down |
| Counter-clockwise shear | Negative (-) | Left side down, right side up |
Frequently Asked Questions
How do I draw a bending moment diagram?
First, calculate the support reactions. Then, starting from one end, calculate the bending moment at key points (supports, load locations, and positions of zero shear). The bending moment is zero at simple supports and reaches maximum where shear force is zero. Plot these values to create the BMD.
What is the relationship between shear force and bending moment?
The shear force is the derivative of the bending moment: V = dM/dx. This means the bending moment is maximum where the shear force is zero (or changes sign). A uniformly distributed load produces a linearly varying shear force and a parabolic bending moment.
How does bending moment relate to bending stress?
Bending stress is calculated as sigma = M*y/I, where M is the bending moment, y is the distance from the neutral axis, and I is the moment of inertia. Maximum stress occurs at the extreme fibers (top and bottom of the cross-section) where y is maximum.