Beam Load Calculator
Reactions, peak shear and peak moment for the four classic cases — the statics ledger every other beam check draws from.
Beam Load Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- Four idealised cases; symmetric loading only
- Single spans — no continuity
In short: A 6 m simply supported span at 10 kN/m leans on each support with 30.000 kN, carries a peak shear of 30.000 kN at the supports, and bends under a peak moment of 45.000 kN·m at midspan — wL² over 8. That 45 is the number the bending-stress page consumes, and the 30 kN reactions are what the bearings or columns below must be designed for: a beam check is never just about the beam.
Formula
M = wL²/8 (SS+UDL) · PL/4 (SS+P) · PL (cant+P) · wL²/2 (cant+UDL) ··· V = wL/2 or P/2
Equilibrium is the whole story: the supports push back exactly what the load pushes down, and the internal shear and moment follow from cutting the beam and summing one side. The moment constants change with the case — an eighth, a quarter, one, a half — because the load's lever arm does. A cantilever carries the same load at a moment four times a simply supported span's, which is why the free end is a luxury the fixed end pays for.
Worked Example
- Pick the case that matches the real structure.
- Enter the load and the span.
- Read the reactions, peak shear and peak moment.
- Hand the moment to the bending-stress page and the reactions to whatever is underneath.
Defaults: case 1, 10 kN/m over 6 m → reactions 30.000 kN, V 30.000 kN, M 45.000 kN·m. The centre-point check: 20 kN on the same span → 10.000 kN reactions, M 30.000 kN·m. The cantilever warning: the same UDL on a cantilever peaks at 180.000 kN·m — fourfold.
Strengths & Limits Of This Model
Where this engine is strong
- Reactions, shear and moment from one entry
- Case constants shown in the arithmetic
Where it stops
- No moving or pattern loads
- No envelope or combination logic
Practical Use Cases
Preliminary sizing
the three numbers that size everything
Bearing and column loads
the reactions card
Teaching
cut the beam, sum one side
Methodology & Editorial Standards
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Beam Load Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
Why is the cantilever moment four times worse?
Same load, same span — wL²/2 against wL²/8. Every bit of a cantilever's load acts at leverage all the way back to the fixed end, while a simply supported beam's load splits its leverage toward two shared supports. The arithmetic of the lever arm is the oldest lesson in the field: where the load sits relative to restraint matters more than how heavy it is.
My beam is neither simply supported nor fixed at all — which case do I pick?
Pick the one that is safe-sided: real bearings sit between ideal pins and fixes, and partial rotational restraint lands between the two answers. Choose the case with the larger moment for strength checks and treat the page's numbers as the bracket your real beam lives inside. The four ideal cases exist so a first pass takes seconds; the second pass is a frame analysis.
Are the two reactions always equal?
For these symmetric cases, yes — the load sits at the span's centre of symmetry, so each support carries half. An off-centre point load shares the load in proportion to the spans beside it, and the page's idealised set keeps to the symmetric half-dozen for exactly the reason hand-checks love them: you can feel when the number is wrong.
Where does the peak shear live?
At the supports for simply supported cases and at the fixed end for cantilevers — wherever the load first hands its force into structure. The shear diagram is flat or triangular between those points for these cases, which is why the shear-stress page only needs one number from here: the peak.
Does the beam's own weight count in w?
Add it — self-weight is a UDL the beam carries whether or not anything else shows up. Convert the section's area to kN/m (steel at about 77 kN per cubic metre per square metre of section) and add it to the applied load. Long spans frequently govern on self-weight alone, which surprises nobody who has watched a crane lift a roof truss.
What do I do with the reactions?
Design what is underneath them — the pad, the column, the holding-down bolts. Every load is a relay: the beam hands its reactions to the columns, the columns to the foundation, the foundation to the ground. A beam check that stops at the beam is half a check.
Why does the moment peak where shear crosses zero?
Because moment is the running sum of shear — it keeps climbing while shear is positive and turns over exactly where shear passes through zero. For the symmetric cases that crossing is midspan, which is why the closed forms all point there. The shears and moments are one diagram read twice, not two facts.
Is this safe for continuous beams over several supports?
No — and the page refuses to pretend: continuity redistributes both moments and reactions, midspan relief and support spikes that the single-span cases cannot see. Continuous beams need the three-moment equation or frame software. Use these numbers as the isolated-span bracket, not the verdict.