Structural Load Calculator
A simply supported beam carrying a uniformly distributed load is one of the most common cases in structural statics, from floor joists to lintels. This calculator returns the total load on the span, the reaction at each support, the maximum shear force, and the maximum bending moment at midspan. All results follow directly from static equilibrium, so no empirical constant is assumed. Enter the uniform load per unit length and the span in consistent units. This is an analysis aid, not a code check: always have a licensed engineer review any real design.
Simply supported beam formula
Total load W = w * L
Reaction each support = W / 2 = w * L / 2
Max shear V = w * L / 2
Max moment M = w * L^2 / 8 (at midspan)
These are exact results from static equilibrium of a simply supported span under uniform load. The maximum moment is at midspan; the maximum shear is at the supports. Keep all inputs in consistent units so outputs are dimensionally correct.
How to use the results
- The reaction at each support equals half the total load by symmetry.
- Maximum shear occurs at the supports and equals the reaction.
- Maximum bending moment occurs at midspan for this symmetric load case.
- To size a member, compare the moment to the section modulus times allowable stress per the code.
- Deflection, load factors, and material limits are separate checks the building code requires.
Structural load: frequently asked questions
What does this beam load calculator compute?
For a simply supported beam carrying a uniformly distributed load, it returns the total load, the reaction at each support, the maximum shear force at the supports, and the maximum bending moment at midspan. These are standard results from statics for this load case.
What is the formula for maximum moment under a uniform load?
For a simply supported span of length L carrying a uniform load w per unit length, the maximum bending moment occurs at midspan and equals w times L squared, divided by 8. The maximum shear at each support equals w times L divided by 2.
Is this a design check or a code-compliant result?
It is a statics calculation, not a code check. It gives the internal forces from equilibrium. Sizing a member also requires the material strength, section properties, deflection limits, and load factors from the applicable building code. Always have a licensed engineer review structural designs.
What units should I use?
Use consistent units. If load is in pounds per foot and span is in feet, moment comes out in pound-feet and shear in pounds. If you use kilonewtons per metre and metres, moment is in kilonewton-metres. The calculator does not convert units, so keep them consistent.
Does this handle point loads or other supports?
No. This case is a single uniformly distributed load on a simply supported (pinned-roller) beam. Point loads, cantilevers, fixed ends, and continuous spans use different formulas. Use a dedicated case or a structural analysis tool for those.
Official sources
- American Society of Civil Engineers: ASCE 7 Minimum Design Loads.
- U.S. General Services Administration: structural design and engineering references.
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.