Shear Moment Diagram Example
Learn how to calculate beam reactions and draw shear force and bending moment diagrams
Medium DifficultyFE Mechanics of Materials
Problem
A simply supported beam with a length of 10 meters has the following loads:
- • Support at x = 0 m (pin support)
- • Support at x = 10 m (roller support)
- • Point load of 1000 N downward at x = 5 m
Find:
- 1. Reaction forces at the supports
- 2. Shear force diagram (SFD)
- 3. Bending moment diagram (BMD)
- 4. Maximum bending moment and its location
Step-by-Step Solution
Step 1: Draw Free Body Diagram (FBD)
First, draw the beam with all known loads and unknown reactions. Label RA, RB, and P = 1000 N.
Step 2: Apply Equilibrium Equations
ΣMA = 0 → RB = 500 N ↑
ΣFy = 0 → RA = 500 N ↑
Step 3: Draw Shear Force Diagram (SFD)
SFD: +500 N from 0 to 5 m, then -500 N from 5 to 10 m.
Step 4: Draw Bending Moment Diagram (BMD)
✓ Maximum moment = 2500 N·m at x = 5 m
Try It Yourself in PolyCalc
Use the PolyCalc Beam Calculator with this problem pre-loaded (10 m span, 1000 N at midspan).
Open Beam Calculator