A cantilever beam subjected to two different point loads is shown in the figure [Fixed at A, 10 kN at B (2 m from A), 20 kN at free end C (1 m from B)]. Calculate the slope at fixed end A. Take 'EI' as constant throughout its length.
- AZeroCorrect
- B13.33 / EI
- C85 / EI
- D105 / EI
Solution
Concept
At a fixed support, the beam cannot rotate or move, so slope and deflection there are zero.
Formula
At fixed end: θA = 0, yA = 0
Step-by-step solution
1. End A is a fixed support. 2. A fixed support stops both rotation and vertical movement. 3. So slope at A, θA = 0, for any loads on the beam. 4. Answer: Zero.
Explanation
A fixed end holds the beam fully, so the beam cannot turn at that point. The slope at a fixed end is always zero, whatever the loads are. The loads only cause slope and deflection away from the support, with the maximum at the free end C.
Why the other options are wrong
B, C and D are non-zero values. They look like slope or deflection results at B or C, not at fixed end A.
Shortcut
Fixed end means slope = 0 and deflection = 0. No calculation needed.
Common mistake
Students calculate the slope at free end C and mark it as the slope at A.
Correct answer: A) Zero