Question

A frame is subjected to a load P as shown in the figure. The frame has a constant value of flexible rigidity EI. The effect of axial load is neglected. The deflection at point A due to the applied load P is

• A. $\frac{4}{3}\left(\frac{P{L}^3}{EI}\right)$
• B. $\frac{P{L}^3}{EI}$
• C. $\frac{P{L}^3}{3EI}$
• D. $\frac{2}{3}\left(\frac{P{L}^3}{EI}\right)$

Answer 1

The correct option is A $\frac{4}{3}\left(\frac{P{L}^3}{EI}\right)$

$\begin{array}{cccc}\text{Member}& \text{M}& M_x& \int M{M}_{x}dx\\ \text{AB (x from A)}& \text{-Px}& \text{-x}& \underset{0}{\overset{L}{\int }}(-Px)(-x)dx=\frac{P{L}^3}{3}\\ \text{BC (x from B)}& \text{-PL}& \text{-L}& \underset{0}{\overset{L}{\int }}(-PL)(-L)dx=P{L}^3\end{array}$

${\delta }_A=\underset{0}{\overset{L}{\int }}M.\frac{\partial M/\partial P}{\left(EI\right)}dx=\underset{0}{\overset{L}{\int }}M.M_x\frac{dx}{EI}=\left(\frac{4P{L}^3}{3EI}\right)$