Beam Deflection Calculator Formula
Understand the math behind the beam deflection calculator. Each variable explained with a worked example.
Formulas Used
Max Deflection
max_deflection = elastic_modulus > 0 && moment_of_inertia > 0 ? 5 * load_pli * pow(span_in, 4) / (384 * elastic_modulus * moment_of_inertia) : 0Span/Deflection Ratio
span_ratio = elastic_modulus > 0 && moment_of_inertia > 0 && (5 * load_pli * pow(span_in, 4) / (384 * elastic_modulus * moment_of_inertia)) > 0 ? span_in / (5 * load_pli * pow(span_in, 4) / (384 * elastic_modulus * moment_of_inertia)) : 0L/360 Limit
limit_360 = span_in / 360Variables
| Variable | Description | Default |
|---|---|---|
span | Beam Span(ft) | 12 |
load_plf | Uniform Load(lb/ft) | 200 |
elastic_modulus | Modulus of Elasticity (E)(psi) | 1700000 |
moment_of_inertia | Moment of Inertia (I)(in^4) | 98 |
span_in | Derived value= span * 12 | calculated |
load_pli | Derived value= load_plf / 12 | calculated |
How It Works
Simply Supported Beam Deflection
Delta_max = 5wL^4 / (384EI)
Where w is the load per inch, L is the span in inches, E is the modulus of elasticity, and I is the moment of inertia. Common deflection limits are L/360 for floors and L/240 for roofs.
Worked Example
12 ft beam, 200 lb/ft load, E = 1,700,000 psi, I = 98 in^4.
span = 12load_plf = 200elastic_modulus = 1700000moment_of_inertia = 98
- 01w = 200/12 = 16.67 lb/in
- 02L = 144 in
- 03Delta = 5 x 16.67 x 144^4 / (384 x 1,700,000 x 98)
- 04Delta = 0.283 in
- 05L/360 = 0.40 in; deflection is within limits.
Ready to run the numbers?
Open Beam Deflection Calculator