Understanding beam load results
These are internal-force demands, not a beam size — they must be checked against the specific bending, shear and deflection capacities of the beam material and size being considered (see the beam deflection calculator for the serviceability check).
- Reaction, shear and moment scale linearly and quadratically (respectively) with span — doubling the span quadruples the bending moment for the same UDL, which is why long-span beams need disproportionately deeper or stronger sections.
- This calculator assumes a simply supported beam with a single uniformly distributed load. Point loads (such as a post bearing on the beam), cantilevered ends, or continuous multi-span beams require different formulas.
What does a beam load calculator compute?
A beam load calculator applies the standard equations of statics for a simply supported beam — one resting on a support at each end with no fixity or continuity — carrying a uniformly distributed load (UDL), meaning a load spread evenly along the beam's full length rather than concentrated at a point. From the UDL and span it derives the reaction force at each support, the maximum internal bending moment, the maximum internal shear force, and the total load carried.
These four values are the standard 'demand' outputs used as the starting point for beam design: the maximum moment is compared against a beam's bending capacity, the maximum shear against its shear capacity, and the reactions against what the supporting posts, walls or foundations must be able to carry.
How to use this beam load calculator
- Enter the uniformly distributed load (UDL) in kilonewtons per meter — this is the load per running meter of beam, already converted from any surface load and tributary width (see the beam span calculator if you need to derive this first).
- Enter the beam's span — the clear horizontal distance between its two supports.
- Read the end reaction (the force each support must resist), the maximum bending moment (occurring at midspan), the maximum shear (occurring at the supports) and the total load carried by the beam.
- Take these demand values to a span table, engineered-lumber design tool or licensed structural engineer to confirm or select an adequate beam size and material.
The formula behind beam load statics
For a simply supported beam under a uniformly distributed load w over span L, statics gives: each end reaction R = wL ÷ 2 (by symmetry, half the total load goes to each support); the total load = wL; the maximum shear V = wL ÷ 2 (occurring right at the supports, numerically equal to the reaction); and the maximum bending moment M = wL² ÷ 8 (occurring at the beam's midspan, where shear crosses zero).
Worked example (calculator defaults): w = 7.3 kN/m over a span L = 3.66 m. Total load = 7.3 × 3.66 ≈ 26.72 kN. End reaction R = 7.3 × 3.66 ÷ 2 ≈ 13.36 kN. Maximum shear V = 13.36 kN (same as R). Maximum moment M = 7.3 × 3.66² ÷ 8 ≈ 12.22 kN·m.
Common mistakes
- Entering a surface load (kPa) directly as the UDL (kN/m) without first multiplying by the tributary width — these are different units and the conversion step (see the beam span calculator) must not be skipped.
- Assuming the maximum moment occurs at the support rather than at midspan — for a simply supported beam under UDL, moment is zero at the supports and maximum at the center, the opposite of shear.
- Using this simply-supported UDL formula for a beam with an actual point load (e.g., a column bearing on it from above), which needs a different moment formula.
- Stopping at the load calculation without also checking deflection — a beam can pass a strength check on moment and shear yet still deflect (sag) more than is acceptable for the finishes it supports.
よくある質問
What is the formula for maximum bending moment in a simply supported beam?
For a simply supported beam under a uniformly distributed load w over span L, the maximum bending moment is M = wL² ÷ 8, occurring at the beam's midspan.
How do you calculate the reaction force on a beam?
For a simply supported beam carrying a symmetric uniformly distributed load, each end reaction equals half the total load: R = wL ÷ 2, where w is the load per unit length and L is the span.
What's the difference between shear and bending moment in a beam?
Shear is the internal force tending to slide one part of the beam vertically past an adjacent part; it is maximum at the supports for a simply supported beam under UDL. Bending moment is the internal force tending to bend (rotate) the beam; it is maximum at midspan for the same loading case.
Does a higher bending moment always mean a beam will fail?
Not by itself — the bending moment must be compared against the beam's actual moment capacity, which depends on its cross-sectional size, material and allowable bending stress. This calculator reports demand only; capacity is a separate calculation specific to the beam being considered.
Is this calculator a substitute for a structural engineer?
No. It applies standard statics formulas as an educational estimate. Final beam sizing and any load-bearing structural decision should be verified by a licensed structural engineer or checked against the applicable local building code.
参考文献
- Standard structural statics for a simply supported beam under uniformly distributed load (reaction, shear and bending moment equations), as covered in engineering statics and mechanics-of-materials textbooks.
- American Wood Council (AWC) — allowable stress design conventions for comparing bending moment and shear demand against wood beam capacity.
- International Code Council (ICC) — International Residential Code (IRC), structural design load provisions.