Beam Load Calculator
Calculate deflection, stress, moment, and shear for structural beams based on loads and material properties.
Enter beam dimensions and load details to see results.
How It Works
How This Calculator Works
This calculator determines beam deflection, stress, bending moment, and shear force based on standard beam theory for rectangular beams. It supports both simply-supported and cantilever beams with point or distributed loads, and includes common materials with their elastic modulus values.
The Formulas
Moment of Inertia:
I = bh³/12 (for rectangular sections)
For simply-supported beams with point load:
Deflection = PL³/(48EI)
Moment = PL/4
Shear = P/2
For simply-supported beams with distributed load:
Deflection = 5wL⁴/(384EI)
Moment = wL²/8
Shear = wL/2
For cantilever beams with point load:
Deflection = PL³/(3EI)
Moment = PL
Shear = P
For cantilever beams with distributed load:
Deflection = wL⁴/(8EI)
Moment = wL²/2
Shear = wL
Bending stress calculation:
σ = Mc/I (where c = h/2)
Material Properties
| Material | Elastic Modulus (E) | Units |
|---|---|---|
| Structural Steel | 29,000,000 | psi |
| Aluminum | 10,000,000 | psi |
| Douglas Fir | 1,900,000 | psi |
| Southern Pine | 1,600,000 | psi |
| Oak | 1,800,000 | psi |
| Concrete | 3,600,000 | psi |
Important Considerations
- This calculator assumes linear elastic behavior and small deflections
- For point loads, the load is assumed to be at the center for simply-supported beams, and at the free end for cantilever beams
- For distributed loads, the load is assumed to be uniformly distributed over the entire beam length
- For complex loading or irregular cross-sections, consult a structural engineer
- Results can be affected by support conditions, which may differ from idealized models
Frequently Asked Questions
What is beam deflection?
Beam deflection is the displacement of a beam from its original position when subjected to loads. It is an important consideration in structural design as excessive deflection can lead to cracking in supported materials, aesthetic issues, or even structural failure if severe enough.
What's the difference between simply-supported and cantilever beams?
A simply-supported beam is supported at both ends, allowing rotation but not vertical movement at the supports. A cantilever beam is fixed at one end and free at the other, like a diving board. Cantilever beams generally experience larger deflections and stresses for the same load compared to simply-supported beams.
How do I know if my beam's deflection is acceptable?
Building codes typically specify maximum allowable deflection limits. A common rule of thumb is that the maximum deflection should not exceed span/360 for floor beams or span/240 for roof beams under live loads. For precise limits, consult your local building code or a structural engineer.
Can I use this calculator for steel I-beams or other shapes?
This calculator is designed specifically for rectangular cross-sections. For I-beams, T-beams, or other non-rectangular sections, you would need to use the appropriate moment of inertia values for those shapes. For standard steel shapes, consult the AISC Steel Construction Manual or other reference materials for section properties.