Beam distributed-load reactions calculator

Calculate reaction at each support and maximum sagging moment with your own figures.

Your numbers

Use the units shown. Results update as you change valid inputs.

Use reaction at each support and maximum sagging moment to compare changes to your inputs. The method and limits below explain the scope.

Examples

Examples

Try the starting example

Simply-supported span (m)
6
Uniform downward load (kN/m)
5
Profile intervals (count)
10
Reaction at each support (kN)
15
Maximum sagging moment (kN m)
22.5
Position/shear/moment profile (JSON)
[[0,15,0],[0.6,12,8.1],[1.2,9,14.4],[1.8,6,18.9],[2.4,3,21.6],[3,0,22.5],[3.6,-3,21.6],[4.2,-6,18.9],[4.8,-9,14.4],[5.4,-12,8.1],[6,-15,0]]

Try another scenario

Simply-supported span (m)
7
Uniform downward load (kN/m)
5
Profile intervals (count)
10
Reaction at each support (kN)
17.5
Maximum sagging moment (kN m)
30.625
Position/shear/moment profile (JSON)
[[0,17.5,0],[0.7,14,11.025],[1.4,10.5,19.6],[2.1,7,25.725],[2.8,3.5,29.4],[3.5,0,30.625],[4.2,-3.5,29.4],[4.9,-7,25.725],[5.6,-10.5,19.6],[6.3,-14,11.025],[7,-17.5,0]]
Calculation method

Calculation method

Reaction at each support (kN)

Uniform load over full simply-supported span; V=R−wx and M=Rx−wx²/2.

Maximum sagging moment (kN m)

Uniform load over full simply-supported span; V=R−wx and M=Rx−wx²/2.

Position/shear/moment profile (JSON)

Uniform load over full simply-supported span; V=R−wx and M=Rx−wx²/2.

Symbols and units
a
Simply-supported span (m)
b
Uniform downward load (kN/m)
c
Profile intervals (count)

Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.

Assumptions & limits

Assumptions & limits

  • User-supplied measurements and assumptions; Uniform load over full simply-supported span; V=R−wx and M=Rx−wx²/2. Supported limits: Finite numeric values bounded to 1e9 magnitude; lists and tables contain 1–100 records unless a stricter bound is stated. Inputs use the units shown. Lists explicitly paired by a method must have matching lengths; independent polynomial coefficient vectors may differ. Respect stated physical, interpolation, policy and computational domain limits.
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Further reading

Method reference ↗

Background reading; this does not imply endorsement or independent review of SumFizz.

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