Propped Cantilever Calculator
Reactions, fixed-end moment and max sagging moment for a propped cantilever under UDL.
INPUTS
m
kN/m
GPa
×10⁶ mm⁴
RESULTS
Reaction at fixed end
37.5 kN
Reaction at prop
22.5 kN
Fixed-end moment
-37.5 kN·m
Max sagging moment (x = 5L/8)
21.09 kN·m
Max deflection ≈ wL⁴/185EI
4.054 mm
How it works
Propping a cantilever makes it statically indeterminate — the prop force (3wL/8) is found by requiring zero deflection at the prop. The fixed end still dominates with wL²/8 hogging, but deflection collapses from wL⁴/8EI (free cantilever) to about wL⁴/185EI: a 23× improvement from one prop.
Worked example
L = 5 m, w = 12 kN/m: prop takes 3wL/8 = 22.5 kN, fixed end 5wL/8 = 37.5 kN with MA = −wL²/8 = −37.5 kN·m. Peak sagging is only 9wL²/128 = 21.1 kN·m at 5L/8 from the wall.
Frequently asked questions
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