How to use this calculator
Enter the span, up to three point loads with their distances from the left support, and an optional uniform load over part or all of the span. Leave unused loads at 0.
Formulas
ReactionsRB = ΣPiaiL RA = ΣP − RB
Shear and momentV(x) = RA − (loads left of x) M(x) = ∫0x V dx
Maximum momentoccurs where V crosses zero
Worked example
6 m beam with 10 kN at 2 m, 5 kN at 4.5 m and 2 kN/m everywhere (the default)
- Resultant of the distributed load: 12 kN at 3 m.
- ΣMA: RB = (10×2 + 5×4.5 + 12×3)/6 = 13.08 kN; RA = 27 − 13.08 = 13.92 kN.
- Shear drops from 13.92 − 2×2 = 9.92 kN to −0.08 kN at x = 2 m, so it crosses zero there.
- Mmax = 13.92 × 2 − 2 × 2²/2 = 23.83 kN·m at x = 2 m.
Frequently asked questions
How do I draw these by hand?
Start at the left with V = RA. Step down at each point load, slope down by w under distributed loads. The moment diagram is the running area under the shear diagram, and it is zero at both supports.
What about cantilevers or overhangs?
This calculator covers simple supports. For a cantilever with an end load or full uniform load, use the cantilever beam calculator.