What load types does this calculator support?

It supports Uniformly Distributed Loads (UDL), mid-span point loads, and point loads placed at any arbitrary position along the span.

What units should I use for inputs?

Input span lengths and positions in millimeters (mm), uniformly distributed loads in Newtons per millimeter (N/mm), and point loads in Newtons (N).

How is the maximum bending moment calculated for an offset point load?

It uses the formula M_max = (P * a * b) / L, where 'a' is the distance from support A, 'b' is the distance to support B (L - a), and 'L' is the total span.

Does this calculator account for the self-weight of the beam?

No, the calculator only computes forces based on the external loads you input. You must add the beam's self-weight as a UDL if you wish to include it.

Where does the maximum shear force occur?

For simply supported beams under these load configurations, the maximum shear force occurs at the supports.

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Simply Supported Beam Calculator

Calculate the maximum bending moment M_max, maximum shear force V_max and support reactions for a simply supported beam under a uniformly distributed load, a mid-span point load, or a point load at an arbitrary position. UDL: M_max = qL²/8; mid-span: M_max = PL/4; offset: M_max = P·a·b/L.

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2 examples

UDL: q=10 N/mm, L=4000 mm → M_max = 2.0×10⁷ N·mm

R_A = R_B = qL/2 = 20000 N. V_max = qL/2 = 20000 N. M_max = qL²/8 = 10·4000²/8 = 2.0×10⁷ N·mm = 20000 N·m at mid-span.

{"result":"Simply supported beam, UDL q=10 N/mm, L=4000 mm. Reactions R_A = R_B = qL/2 = 20000 N. V_max = qL/2 = 20000 N at supports. M_max = qL²/8 = 2.0e+7 N·mm (20000 N·m) at mid-span (x = L/2 = 2000 mm).","metadata":{"input":{"loadType":"udl","q":10,"L":4000},"result":{"loadType":"udl","M_max":20000000,"M_max_Nm":20000,"V_max":20000,"R_A":20000,"R_B":20000,"location":"mid-span (x = L/2 = 2000 mm)"}}}

Point load at a: P=8000 N, a=1500 mm, L=4000 mm → M_max = 7.5×10⁶ N·mm

b = L − a = 2500 mm. R_A = P·b/L = 5000 N, R_B = P·a/L = 3000 N. V_max = max(R_A,R_B) = 5000 N. M_max = P·a·b/L = 8000·1500·2500/4000 = 7.5×10⁶ N·mm at x = a = 1500 mm.

{"result":"Simply supported beam, point load P=8000 N at a=1500 mm, L=4000 mm. b = L−a = 2500 mm. R_A = P·b/L = 5000 N, R_B = P·a/L = 3000 N. V_max = max(R_A,R_B) = 5000 N. M_max = P·a·b/L = 7500000 N·mm (7500 N·m) at x = a = 1500 mm.","metadata":{"input":{"loadType":"pointOffset","P":8000,"L":4000,"a":1500},"result":{"loadType":"pointOffset","M_max":7500000,"M_max_Nm":7500,"V_max":5000,"R_A":5000,"R_B":3000,"location":"x = a = 1500 mm"}}}

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6 options

SettingsAdjust formats, ranges, numbers, and modes.6

Load TypeselectOptionalUniformly Distributed Load q (N/mm)numberOptionalUsed in 'Uniformly Distributed Load' mode.Point Load P (N)numberOptionalUsed in 'Mid-span Point Load' and 'Point Load at a' modes.Span Length L (mm)numberRequiredLoad Position a (mm)numberOptionalUsed only in 'Point Load at a' mode. Must satisfy 0 < a < L.Decimal PlacesnumberOptional

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Simply Supported Beam Calculator

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Examples

1. Uniformly Distributed Load Analysis for a Floor Joist

2. Offset Point Load Calculation for a Crane Runway Beam

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