A propped cantilever of span L is fixed at end A and simply supported at end B. It is subjected to a uniformly distributed load of intensity w per unit length, the reactions at A and B are
- ARA = 5wl/8, RB = 3wl/8Correct
- BRA = RB = wl/2
- CRA = 3wl/8, RB = 5wl/8
- DRA = wl/8, RB = 3wl/8
Solution
Concept
Propped cantilever reactions
Formula
Rprop = 3wL/8; Rfixed = 5wL/8
Step-by-step solution
1. Deflection at the prop due to UDL: wL⁴/8EI; due to RB: RB L³/3EI. 2. Equating: RB = 3wL/8. 3. RA = wL − 3wL/8 = 5wL/8.
Explanation
The prop reaction is found by compatibility of deflection; the fixed end then takes the larger reaction.
Why the other options are wrong
B is for a simply supported beam; C interchanges the reactions; D does not sum to wL.
Shortcut
Fixed end 5/8, prop 3/8.
Common mistake
Interchanging RA and RB.
Correct answer: A) R_A = 5wl/8, R_B = 3wl/8