Cantilever, tip point load
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About this case
How to analyze a cantilever with a tip point load
This page pre-loads a fixed-left cantilever with a point load at the free tip. Edit the length, load magnitude, section or material directly in the calculator. Results update instantly.
Textbook values: wall reaction R = P, wall moment M = PL, tip deflection δ = PL³/(3EI). Shear is constant at P along the full length; moment diagram is linear from 0 at the tip to PL at the wall.
What to watch for with tip loads
The numbers to read are the wall reaction force and wall fixing moment — together they are exactly what the bracket, weld or embedment must resist. Tip deflection against L/180 is the serviceability check; note that for the same total load, a tip load deflects 8/3 times more than a uniform load, so converting a spread-out load into a single tip value is conservative by a wide margin but useful as a bound.
Drag the load inward along the beam and both the wall moment and tip deflection fall linearly and cubically respectively; a load at three-quarters length already halves the wall moment demand. That sensitivity is worth exploiting when you can position a bracket load close to its support.
Common mistakes with this case
Modelling a genuinely distributed load as a tip load "to be safe" is defensible for a bound but can hide where the real maximum stress sits when the load actually spreads over the member. The reverse is the dangerous one: modelling a concentrated load as an equivalent UDL halves the apparent wall moment and is unconservative. Second error: applying the tip-deflection formula to a load that is not at the tip; the closed form changes, and dragging the load in the calculator shows the corrected value instantly.