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 for the statement of the Second Moment-Area Theorem.

Step 2: Key Concept (Alternate):
Theorem 1: Change in slope between two points = area of M/EI diagram between those points. Theorem 2: Vertical deviation of one point from tangent at another point = moment of M/EI diagram area about the deviating point.

Step 3: Detailed Explanation:
To find vertical intercept at B from tangent at A: take M/EI diagram between A and B, find its area, multiply by horizontal distance from centroid of that area to point B. This gives the tangential deviation. The question describes exactly this: vertical intercept equals moment of bending moment diagram area about the point under consideration.

Step 4: Final Answer:
The vertical intercept at a point between tangents from two points equals the moment of the area of the bending moment diagram about that point, divided by EI.