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Cantilever beam with triangular load.

Calculate the fixed-end actions and elastic free-end movement for a load that starts at zero at the wall and rises to a peak at the free end.

read the result

Keep the triangle orientation explicit.

The load resultant is q0L/2, but its centre of action is closer to the free end because the intensity rises along the member. That changes the fixed-end moment and deflection from the uniform-load case.

Governing equations

For q(x) = q0x/L, Vfixed = q0L/2 and the internal fixed-end moment is -q0L2/3. The free-end deflection is 11q0L4/(120EI), with free-end rotation q0L3/(8EI).

Peak intensity versus resultant

Enter the maximum line load, not the total force. The calculator reports the resultant separately so the load definition can be checked before interpreting the reactions.

Keep it as an elastic load-case screen.

  • The left end is fixed and the right end is free.
  • The load is vertical, downward, zero at the fixed end, and q0 at the free end.
  • Reverse orientation, self-weight, shear deformation, stress, stability, and code limits require separate checks.
  • This is elastic analysis, not cantilever design.