Beam Load Calculator

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Reactions, maximum shear force, bending moment and deflection of simply supported and cantilever beams under a point load or UDL — for study and checking

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Enter the values

What to work out

Span (L)

Point load (P)

Distance of the load from the left support (a)

a = L/2 for a central load

Modulus of elasticity (E) — for deflection

Moment of inertia (I) — 0 to skip deflection

Result

Maximum bending moment

10kN·m

Maximum shear force

5kN

Left reaction (R_A): 5 kN
Right reaction (R_B): 5 kN
Maximum moment at (from left): 2 m

This is for study and checking hand working — not a beam design to BNBC. Design needs factored loads, load combinations and a qualified engineer's check.

Enter both E and I to see the deflection.

Working

b = L − a = 4 − 2 = 2 m
R_A = P × b ÷ L = 10 × 2 ÷ 4 = 5 kN
R_B = P × a ÷ L = 10 × 2 ÷ 4 = 5 kN
M_max = P × a × b ÷ L = 10 × 2 × 2 ÷ 4 = 10 kN·m

Formulas

SS, point load: R_A = Pb/L, R_B = Pa/L, M_max = Pab/L (= PL/4 at centre)
SS, UDL: R = wL/2, M_max = wL²/8, δ = 5wL⁴/384EI
SS, central point load: δ = PL³/48EI; off-centre: δ_max = Pb(L² − b²)^1.5 / (9√3 L EI)
Cantilever, end point load: R = P, M_max = PL, δ = PL³/3EI
Cantilever, UDL: R = wL, M_max = wL²/2, δ = wL⁴/8EI

L: span
P: point load
w: uniform load per metre
a, b: distances from the load to the left and right supports (a + b = L)
E: modulus of elasticity
I: second moment of area of the section

Assumptions

A straight, elastic, uniform beam with small deflections; the beam's own weight is not included — add it to w if needed.
The default E = 200 GPa is the textbook value for steel; enter your own for concrete or timber.
For an off-centre point load the maximum deflection uses the standard formula; it occurs in the longer segment near mid-span, not under the load.

Sources: R. S. Khurmi, Strength of Materials; S. Ramamrutham, Strength of Materials · J. M. Gere, Mechanics of Materials (deflection for an off-centre point load) · BNBC 2020 (the code that governs design)

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