Question

The vertical deflection at the free end of a quadrantal ring (Radius \( R \) with uniform flexural rigidity \( EI \)) which is fixed at the base and subjected to a vertically downward load \( W \) at the free end is

• A. \( \frac{WR^3 \pi}{4EI} \)
• B. \( \frac{WR^3 \pi}{2EI} \)
• C. \( \frac{WR^3 \pi}{3EI} \)
• D. \( \frac{WR^3 \pi}{EI} \)

Hint:

- The deflection at a free end of a curved beam depends on the radius \( R \) and flexural rigidity \( EI \).

Answer 1

The Correct Option is B

Step 1: Applying deflection formula for a quadrantal ring. - The deflection \( \delta \) at the free end of a quadrantal ring due to a point load \( W \) at the tip is: \[ \delta = \frac{WR^3 \pi}{2EI} \] Step 2: Selecting the correct option. Since the formula matches with option (B), the correct answer is (B).