Understanding Beam Calculations
This calculator analyzes a simply supported beam under point or uniformly distributed loads, providing reaction forces, maximum bending moment, and deflection. It supports both imperial and metric units for structural design.
Proper beam sizing ensures structural integrity, preventing excessive deflection or failure. The modulus of elasticity (E) and moment of inertia (I) are critical for deflection calculations. Typical E values: Steel (29,000 ksi or 200 GPa), Wood (1,900 ksi or 13 GPa).
Example Beam Calculation Results
| Parameter | Imperial | Metric | Scenario |
|---|---|---|---|
| Load | 1000 lb (point) | 4448 N (point) | Point load at midspan |
| Reaction Forces | 500 lb (each) | 2224 N (each) | 10 ft (3.048 m) beam |
| Max Moment | 2500 lb-ft | 3389 N-m | At midspan |
| Max Deflection | 0.02 in. | 0.51 mm | Steel, 4x8 in. section |
| Moment of Inertia | 170.67 in⁴ | 7.1e7 mm⁴ | Rectangular section |
How to Use the Beam Calculator
- Select the unit system (imperial or metric).
- Enter beam length and material (steel, wood, or custom modulus of elasticity).
- Choose section type (rectangular or I-beam) and enter dimensions.
- Select load type (point, UDL, or combined) and enter load details.
- Click "Calculate Beam Parameters" to view reaction forces, maximum moment, deflection, and moment of inertia.
Beam Deflection Curve
Deflection along beam length for selected load and section.
Frequently Asked Questions
What is a simply supported beam?
A simply supported beam is supported at both ends (one pinned, one roller), allowing rotation but not vertical movement, ideal for simple structural analysis.
How is maximum deflection calculated?
Deflection depends on load, beam length, modulus of elasticity, and moment of inertia. For a point load, it’s calculated as δ = P a (L - a) (L² - a (L - a)) / (6 E I L); for UDL, δ = 5 w L⁴ / (384 E I).