Beam Load Calculator
What This Beam Load Calculator Estimates
This calculator estimates the allowable central point load on a simply supported beam when bending stress is the controlling limit. It uses the span length, section modulus, and allowable bending stress to solve for the point load that produces the selected stress at midspan.
The model is useful for early sizing, classroom calculations, and quick sanity checks. It assumes a single point load at the middle of a simply supported span. Distributed loads, cantilevers, continuous beams, shear capacity, deflection, lateral-torsional buckling, bearing, and connection design require separate checks.
Formula
For a simply supported beam with a central point load, the maximum bending moment is:
Bending stress is moment divided by section modulus:
Solving those two relationships for the allowable point load gives:
The form accepts span in meters, section modulus in cubic centimeters, and allowable stress in MPa. With those units, the calculator reports load in kilonewtons using PkN = 4 σ Z / (1000 L).
Worked Example
Suppose a simply supported beam spans 4.0 m, has a section modulus of 300 cm³, and the selected allowable bending stress is 150 MPa. The allowable central point load is:
P = 4 × 150 × 300 / (1000 × 4.0) = 45 kN
If the actual point load is larger than 45 kN, bending stress exceeds the selected allowable stress. If the load is well below that value, bending stress has reserve capacity, although shear and deflection still need their own checks.
How Inputs Affect the Result
| Change | Effect on allowable point load | Reason |
|---|---|---|
| Longer span | Lower allowable load | Moment rises with span for the same point load. |
| Higher section modulus | Higher allowable load | More section modulus reduces bending stress. |
| Higher allowable stress | Higher allowable load | The material or design limit permits more moment. |
Design Notes
Use an allowable stress that already reflects the material, code method, and safety factor you intend to apply. For structural work, compare this quick bending estimate with governing design standards and check serviceability deflection. A beam can satisfy bending stress and still be unacceptable because it sags too much, buckles laterally, crushes at supports, or lacks adequate connections.
Before using the result in a real design, confirm that the span condition matches a simply supported beam with a concentrated midspan load. If the load is off center, spread over an area, repeated dynamically, or applied to a beam with fixed or continuous supports, the moment pattern changes and this simplified load limit may be misleading.
Beam Guard Mini-Game
Dial in temporary shoring to keep the live load ratio under the midspan limit while crews roll carts, stack pallets, and pull weight away. Staying inside the safe band links every adjustment to so the calculator’s formula becomes muscle memory.
Enter span, section modulus, and allowable stress to seed the safe load before starting a run.