Cantilever Column Calculator: Base Reactions, Shear and Moment for Wind and Load
Base axial force, shear and moment of a tower or post for a top load, self-weight and wind loads, with a moment diagram.
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How this calculator works
Enter the height, the load on top, the self-weight per metre, a horizontal point load at the top and a horizontal load per metre along the height. The base takes the total vertical load as an axial force, the total horizontal load as a shear, and the sum of the wind forces times their lever arms as a bending moment.
It also gives the forces at any height you choose, and for a round section, the axial and bending stress at the base. The bending moment diagram shows how the moment builds up towards the base.
Use it for water towers, sign posts, light poles, flag poles, chimneys and similar. Work the wind loads out to AS/NZS 1170.2 first.
Formulas used
- N = P + wH
- V = F + qH
- M = FH + \frac{qH^2}{2}
Worked example
With the default numbers in the calculator above:
- Axial force at the base (load plus self-weight): 75.00 kN (compression)
- Shear force at the base: 5.00 kN
- Bending moment at the base: 40.00 kN·m
- Forces at 5.00 m above the base: 67.50 kN, 4.00 kN, 17.50 kN·m
Change the numbers in the calculator to see the full working, every step, for your own case.
Common questions
Why does the axial force rise towards the base?
Each part of the column carries its own weight and all the weight above it, so it adds up to the base.
Where is the bending moment greatest?
At the base, where the lever arms are longest.
Are second-order effects included?
No. The load on top acting on the sideways sway adds a bit more moment, which matters for slender columns.
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Further reading: Any statics text (cantilever reactions); AS/NZS 1170.2 (wind actions).
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