Question

In the cantilever beam PQR shown in figure below, the segment PQ has flexural rigidity EI and the segment QR has infinite flexural rigidity.

The deflection and slope of the beam at 'Q' are respectively

• A. $\frac{5W{L}^3}{6EI}and\frac{3W{L}^2}{2EI}$
• B. $\frac{W{L}^3}{3EI}and\frac{W{L}^2}{2EI}$
• C. $\frac{W{L}^3}{2EI}and\frac{W{L}^2}{EI}$
• D. $\frac{W{L}^3}{3EI}and\frac{3W{L}^2}{2EI}$

Answer 1

The correct option is A $\frac{5W{L}^3}{6EI}and\frac{3W{L}^2}{2EI}$


Using standard result
Deflection at Q,
$D=\frac{W{L}^3}{3EI}+\frac{M{L}^2}{2EI}$
$=\frac{W{L}^3}{3EI}+\frac{\left(WL\right).L^2}{2EI}$
$=\frac{5W{L}^3}{6EI}$
slope at Q,
$\theta =\frac{W{L}^2}{2EI}+\frac{ML}{EI}$
$=\frac{W{L}^2}{2EI}+\frac{W{L}^2}{EI}$
$=\frac{3}{2}\frac{W{L}^2}{EI}$