What load types does this calculator support?

It supports Uniformly Distributed Loads (UDL), Center Point Loads, and off-center Point Loads.

How are the reaction forces calculated for an off-center point load?

They are calculated using static equilibrium equations: RA = P * b / L and RB = P * a / L, where b is the distance from the load to the right support.

What units are used for the inputs and outputs?

Span and positions are in meters (m), loads are in kilonewtons (kN) or kilonewtons per meter (kN/m), and bending moment is in kilonewton-meters (kN·m).

Does this calculator support multiple loads on a single beam?

No, this calculator is designed for a single load configuration (either one UDL, one center point load, or one off-center point load) at a time.

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

No, the beam is assumed to be weightless unless you include its self-weight as part of the Uniformly Distributed Load (UDL).

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Beam Reaction Force Calculator (Simply Supported)

Calculate support reactions of a simply supported beam via static equilibrium. UDL: RA=RB=q·L/2. Center point load: RA=RB=P/2. Off-center point load at a: RA=P·b/L, RB=P·a/L. Also returns max shear Vmax and max moment Mmax.

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2 examples

UDL q=10 kN/m, L=10 m → RA=RB=50 kN, Mmax=125 kN·m

RA=RB=q·L/2=10·10/2=50 kN. Total load = q·L = 100 kN. Vmax = 50 kN (at supports). Mmax = q·L²/8 = 10·100/8 = 125 kN·m at midspan.

{"result":"Simply supported beam, UDL q=10 kN/m over L=10 m. RA = RB = q·L/2 = 50.00 kN. Total load = 100.00 kN. Vmax = 50.00 kN. Mmax = q·L²/8 = 125.00 kN·m at midspan.","metadata":{"input":{"loadType":"udl","L":10,"q":10},"result":{"loadType":"udl","leftReaction":50,"rightReaction":50,"reactionUnit":"kN","totalLoad":100,"maxShear":50,"maxMoment":125,"momentUnit":"kN·m"}}}

Point P=100 kN at a=3 m, L=10 m → RA=70 kN, RB=30 kN

b = L − a = 7 m. RA = P·b/L = 100·7/10 = 70 kN. RB = P·a/L = 100·3/10 = 30 kN. Vmax = max(70,30) = 70 kN (left of load). Mmax = P·a·b/L = 100·3·7/10 = 210 kN·m (under the load).

{"result":"Simply supported beam, point load P=100 kN at a=3 m from left, L=10 m (b=7 m). RA = P·b/L = 70.00 kN, RB = P·a/L = 30.00 kN. Total load = 100.00 kN. Vmax = 70.00 kN (left of load). Mmax = P·a·b/L = 210.00 kN·m under the load.","metadata":{"input":{"loadType":"point","L":10,"P":100,"a":3},"result":{"loadType":"point","leftReaction":70,"rightReaction":30,"reactionUnit":"kN","totalLoad":100,"maxShear":70,"maxShearSide":"left","maxMoment":210,"momentUnit":"kN·m","loadPositionFromLeft":3}}}

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6 options

SettingsAdjust formats, ranges, numbers, and modes.6

Load TypeselectOptionalSpan L (m)numberRequiredUniformly Distributed Load q (kN/m)numberOptionalRequired for UDL.Point Load P at Position a (kN)numberOptionalPoint load magnitude. Required for center/point modes.Load Position a from Left (m)numberOptionalDistance from left support to the point load. Required for point mode. 0 ≤ a ≤ L.Decimal PlacesnumberOptional

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Beam Reaction Force Calculator (Simply Supported)

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Examples

1. Calculating Reactions for a Floor Joist under UDL

2. Analyzing a Beam with an Off-Center Point Load

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