Shear Force and Bending Moment Diagrams
How beams carry internal shear and bending along their length
Difficulty
Intermediate
Read time
10 min
Review status
Needs review
Concept sketch
Beam load, shear diagram, moment diagram
Simplified beam example
Overview
Shear force and bending moment diagrams show how internal forces vary along a beam. They help students find where loads create the largest internal shear, where bending is critical, and where stress or deflection calculations should focus.
How to read it
- Read the horizontal axis as position along the beam.
- Look for jumps in shear at point loads and changes in slope under distributed loads.
- Use zero-shear locations as candidates for maximum or minimum bending moment.
- Check that moment is zero at pins, rollers, or free ends when the support cannot resist a moment.
When to use it
- Beam reaction and internal force problems.
- Finding critical locations for bending stress.
- Preparing for beam deflection or design calculations.
- Checking whether a beam problem setup makes physical sense.
What the diagrams show
A shear diagram plots the internal shear force V along the beam. A bending moment diagram plots the internal bending moment M along the beam. These are not applied loads; they are internal resultants that appear when the beam is cut and one segment is placed in equilibrium.
Start with reactions
Before drawing shear and moment diagrams, solve support reactions using equilibrium. If the reactions are wrong, every later region of the diagram will be wrong. This is why beam problems usually begin with a full free-body diagram of the entire beam.
How loads change the curves
Point loads create jumps in the shear diagram. Distributed loads create slopes in the shear diagram. The bending moment diagram changes according to the shear: where shear is constant, moment changes linearly; where shear varies linearly, moment is curved.
Why engineers use them
The largest bending moment often controls bending stress, while large shear can matter near supports or concentrated loads. The diagrams help identify critical sections before doing detailed stress, deflection, or design checks.