Question

At the free end of a cantilever beam subjected to downward loads,

• A. slope and deflections are minimum
• B. slope and deflections are maximum
• C. slope is maximum and deflection is minimum
• D. slope is minimum and deflection is maximum

Hint:

Remember the boundary conditions for a cantilever beam (fixed at A, free at B):
- At the Fixed End (A): Deflection = 0, Slope = 0.
- At the Free End (B): Bending Moment = 0, Shear Force = 0 (unless there is a point load right at the end). Slope and Deflection are maximum.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks about the slope and deflection at the free end of a cantilever beam under downward loading.

Step 2: Detailed Explanation:
Let's consider a cantilever beam fixed at one end and free at the other. When downward loads are applied, the beam bends downwards.

• Deflection: Deflection is the vertical displacement of the beam from its original position. The fixed support cannot move, so the deflection there is zero by definition. As we move away from the fixed support towards the free end, the beam bends more and more. The largest vertical displacement will occur at the very tip, the free end. Therefore, the

deflection is maximum at the free end.

• Slope: Slope is the angle of the deflected beam with respect to the horizontal. At the fixed support, the beam is held rigidly horizontal, so the slope is zero by definition. As the beam bends, its angle with the horizontal increases, reaching its largest value at the free end. Therefore, the

slope is also maximum at the free end.



Step 3: Final Answer:
At the free end of a cantilever beam subjected to downward loads, both the slope and the deflection are maximum.