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Propped cantilever with full-span UDL.

Calculate the compatibility-based prop reaction, fixed reaction, critical moments, and elastic deflection for a cantilever supported by a vertical prop at its free end.

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Equilibrium alone is not enough here.

A propped cantilever is statically indeterminate to the first degree. The prop reaction is obtained by requiring the free-end vertical deflection to vanish, then the remaining reactions and moments follow from equilibrium.

Governing equations

For a full-span UDL w, RA = 5wL/8 and RB = 3wL/8. The fixed-end internal moment is -wL2/8. The positive maximum moment is 9wL2/128 at x = 5L/8. The maximum deflection occurs at x = (15 - √33)L/16.

Compatibility assumptions

The coefficients assume constant EI, a rigid prop at the free end, no support settlement, and a prop that remains engaged. A flexible or yielding prop changes the compatibility equation and therefore changes the reactions.

Keep it as an elastic load-case screen.

  • The left end is fixed; the right support prevents vertical movement but does not restrain rotation.
  • The UDL covers the complete member and acts vertically downward.
  • Prop flexibility, settlement, gaps, cracking, shear deformation, stability, stress, and code limits are not checked.
  • This is elastic analysis, not propped-member design.