Question

A simply supported beam of uniform flexural rigidity is loaded as shown in the given figure. The rotation of the end A is

• A. $\frac{P{L}^2}{9EI}$
• B. $\frac{P{L}^2}{6EI}$
• C. $\frac{P{L}^2}{18EI}$
• D. $\frac{P{L}^2}{12EI}$

Answer 1

The correct option is A $\frac{P{L}^2}{9EI}$

The M/EI diagram of beam is




The slope at mid point is zero. The difference between the slope at two points is M/EI area between those points. So slope at A

${\theta }_A=\frac{PL}{3EI}\times (\frac{1}{2}\times \frac{L}{3}+\frac{L}{6})=\frac{P{L}^2}{9EI}$