Cantilever moment from a load at the free end
A cantilever is fixed at one end and free at the other. A downward tip load creates the largest bending-moment magnitude at the fixed end, where its lever arm is longest.
What the formula is saying
Take moments about the fixed end. The load P acts a perpendicular distance L away, so the required resisting moment has magnitude PL.
Read the symbols in plain language
- P
- Point loadN
- L
- Lengthm
Sort out the units first
Use N and m for N·m. The calculator returns a magnitude; the usual sagging-positive convention would label this bending as hogging (negative).
Let’s solve one together
Read the given values, follow each operation, then check what the result means.
- P · Point load
- 5000 N
- L · Length
- 2 m
Identify the perpendicular lever arm
For a vertical tip load on a horizontal beam, the arm is the full span.
(2) = 2 mMultiply force by distance
Report the maximum moment magnitude at the fixed end.
(5000) × (2) = 10000 N·m
Does this worked answer make sense?
The moment falls to zero at the unloaded free-end side of the tip. The fixed-end magnitude in this example is 10 kN·m.
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.
- P · Point load
- 8000 N
- L · Length
- 3 m
Find: Cantilever moment from a load at the free end
A hint, not the answer
Take moments about the fixed end. The load P acts a perpendicular distance L away, so the required resisting moment has magnitude PL.
Use N and m for N·m. The calculator returns a magnitude; the usual sagging-positive convention would label this bending as hogging (negative).
Show the full practice solution
Compare the steps with your work; revealing a solution does not mark the lesson complete.
Identify the perpendicular lever arm
For a vertical tip load on a horizontal beam, the arm is the full span.
(3) = 3 mMultiply force by distance
Report the maximum moment magnitude at the fixed end.
(8000) × (3) = 24000 N·m
Avoid the common trap
Do not divide by four as for a simply supported centre load. Do not mistake the positive magnitude for a signed sagging moment.
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.