Before sizing a beam you need to know how much load each support carries and how large the bending moment gets. For a simply supported beam the reactions follow from two equilibrium equations: the vertical forces balance and the moments about either support sum to zero. The largest moment occurs under one of the point loads or where the shear crosses zero.
How to use the Beam Load Calculator
- Span
- Point load 1
- Position of load 1 (from left)
- Point load 2
- Position of load 2
- Point load 3
- Position of load 3
- Uniform load
Results update as you type, and every field accepts the units shown in its menu.
How it works
Enter the span, up to three point loads with their distance from the left support (set unused loads to zero) and any uniform load. The calculator returns both reactions and the bending moment at each load and at mid-span.
Tips for an accurate estimate
- Keep units consistent – the calculator handles conversions, but check every field’s unit before reading a result.
- Use values from standards, data sheets or test pieces whenever you have them; typical values are only a starting point.
- Apply appropriate safety factors and have structural, electrical and pressure work checked by a qualified professional.
- Record the inputs you used so the calculation can be reviewed later.
Common mistakes to avoid
- Confusing diameter and radius, or nominal and actual sizes.
- Using allowable stresses and ultimate strengths interchangeably.
- Treating rule-of-thumb results as a substitute for code tables or an engineered design.
Inputs explained
| Field | What to enter |
|---|---|
| Span | Units: m, ft, cm, in, yd |
| Point load 1 | Units: N, kN, lbf, kip, kgf |
| Position of load 1 (from left) | Units: m, ft, cm, in, yd |
| Point load 2 | Units: N, kN, lbf, kip, kgf |
| Position of load 2 | Units: m, ft, cm, in, yd |
| Point load 3 | Units: N, kN, lbf, kip, kgf |
| Position of load 3 | Units: m, ft, cm, in, yd |
| Uniform load | Units: kN/m, N/m, lbf/ft, lbf/in |
What each result means
- Reaction at right support B = ([Point load 1]×[Position of load 1 (from left)] + [Point load 2]×[Position of load 2] + [Point load 3]×[Position of load 3] + [Uniform load]×[Span]^2÷2)÷[Span]
- Reaction at left support A = [Point load 1] + [Point load 2] + [Point load 3] + [Uniform load]×[Span] – [Reaction at right support B]
- Largest of these moments = max([Moment under load 1], [Moment under load 2], [Moment under load 3], [Moment at mid-span])
Example values
How the main result changes when Span changes and everything else stays at the example values above:
| Span (m) | Reaction at left support A (N) |
|---|---|
| 3 | 3,166.67 |
| 4.5 | 8,361.11 |
| 6 | 11,333.33 |
| 7.5 | 13,416.67 |
| 9 | 15,055.56 |
| 12 | 17,666.67 |
Formula
R_B = (Σ Pᵢ aᵢ + w L² ÷ 2) ÷ LR_A = Σ Pᵢ + w L − R_BM(x) = R_A x − Σ Pᵢ (x − aᵢ) for aᵢ < x − w x² ÷ 2Worked example
Inputs — Span: 6 m; Point load 1: 10,000 N; Position of load 1 (from left): 2 m; Point load 2: 5,000 N; Position of load 2: 4 m; Point load 3: 0 N; Position of load 3: 5 m; Uniform load: 1 kN/m.
Results — Reaction at right support B = 9,666.67 N; Reaction at left support A = 11,333.33 N; Moment under load 1 = 20,666.67 N·m; Moment under load 2 = 17,333.33 N·m; Moment under load 3 = 9,166.67 N·m; Moment at mid-span = 19,500 N·m; Largest of these moments = 20,666.67 N·m.
Frequently asked questions
How do I calculate beam reactions?
Take moments about one support: R_B × L = Σ (load × distance from A). Then R_A = total load − R_B.
Where is the maximum bending moment?
Under a point load or where the shear force changes sign; for a single central load it is at mid-span, PL/4.
Does the calculator include the beam's self-weight?
Add it to the uniform load (weight per metre of the beam).
What formula does the Beam Load Calculator use?
R_B = (Σ Pᵢ aᵢ + w L² ÷ 2) ÷ L.