Beam reactions under a uniform load
A uniformly distributed load applies the same force to every metre of a beam. Before sharing the load between supports, turn this force-per-metre into a total force.
What the formula is saying
The total load is wL and acts at the middle of the loaded length. A full-span uniform load on a simply supported beam is symmetric, so each support takes half.
Read the symbols in plain language
- w
- UDLN/m
- L
- Spanm
Sort out the units first
Use w in N/m and L in m. 4 kN/m = 4,000 N/m. Multiplying by metres cancels /m and gives a force in N.
Let’s solve one together
Read the given values, follow each operation, then check what the result means.
- w · UDL
- 4000 N/m
- L · Span
- 6 m
Convert the distributed load to total force
Every metre carries w newtons; there are L metres.
(4000) × (6) = 24000 NDivide between the two supports
The complete load is centred, so each support carries half.
(24000) ÷ 2 = 12000 N
Does this worked answer make sense?
The example’s total is 24,000 N, so the two 12,000 N reactions must add back to 24,000 N.
Now try your own values
Change a value or its unit. The same method will show your calculation, step by step.
Results update only when you calculate. The lesson example above stays unchanged.
Your turn — check your understanding
Use these new values. Work it out first, then check your answer.
- w · UDL
- 3000 N/m
- L · Span
- 4 m
Find: Reaction at each support (RA = RB)
A hint, not the answer
The total load is wL and acts at the middle of the loaded length. A full-span uniform load on a simply supported beam is symmetric, so each support takes half.
Use w in N/m and L in m. 4 kN/m = 4,000 N/m. Multiplying by metres cancels /m and gives a force in N.
Show the full practice solution
Compare the steps with your work; revealing a solution does not mark the lesson complete.
Convert the distributed load to total force
Every metre carries w newtons; there are L metres.
(3000) × (4) = 12000 NDivide between the two supports
The complete load is centred, so each support carries half.
(12000) ÷ 2 = 6000 N
Avoid the common trap
Dividing w by two without multiplying by L leaves N/m, not a support reaction. Partial-span or triangular loads need different resultants.
When this method applies — and when it does not
An ideal straight beam with the supports and load stated here. Loads are magnitudes; self-weight is omitted unless already included. This is an equilibrium result, not a check of strength, deflection or stability. Enter the nonnegative magnitude of the downward load; sign conventions for internal moments are explained separately.
For study and understanding, not approval of a real structure, site operation or design. Apply the correct standard, National Annex and professional review to actual engineering work.
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Sources & further reading
References open in a new tab and explain the underlying principles. The teaching text and examples here are SimpleFlick’s own; the source organisations have not endorsed this calculator.
Lesson updated: · Worked examples checked against the implemented formula; not an independent engineering certification.