Structural
Point Load on Beam Calculator
Enter a concentrated load and its distance from the left support to get both reactions, the maximum moment (which occurs under the load) and the deflection at the load point. For estimation only; a licensed PE must design.
Formula
With load P at distance a from the left support and b = L - a: R1 = Pb/L, R2 = Pa/L, Mmax = Pab/L under the load, and deflection at the load Δ = Pa²b²/(3EIL), with lengths converted to inches. For a centered load this reduces to M = PL/4 and Δ = PL³/(48EI).
Worked example
A 2,000 lb load 4 ft from the left end of a 12 ft span: b = 8 ft, R1 = 2,000 × 8 ÷ 12 = 1,333 lb, R2 = 667 lb, M = 2,000 × 4 × 8 ÷ 12 = 5,333 ft-lb. With E = 1,600,000 psi and I = 177.98 in⁴: Δ = 2,000 × 48² × 96² ÷ (3 × 1,600,000 × 177.98 × 144) = 0.35 in.
Assumptions and limits
- Single concentrated load, simple supports, beam self-weight ignored (use the uniform load calculator and superimpose).
- Maximum deflection occurs slightly toward the midspan side of an off-center load; the value at the load is close to but not exactly the maximum.
- For estimation only. A licensed Professional Engineer (PE) must design and stamp any structural, foundation or life-safety element.
Frequently asked questions
Where is the maximum moment for a point load?
Directly under the load. For a load at midspan it is PL/4, the largest possible moment for a single load on a simple span.
Can I combine a point load and a uniform load?
Yes. For linear elastic beams, moments, reactions and deflections from separate loads can be added (superposition), though the maximums may occur at different points.
What is a typical point load in a house?
Posts carrying a beam or a girder truss bearing on a header are common examples. Their loads must be traced down to a footing by the designer.