Question

In the structure shown in the figure below, what is the distance through which the point A move towards each other ?

• A. $4P{a}^3/EI$
• B. $16P{a}^3/3EI$
• C. $28P{a}^3/3EI$
• D. $6P{a}^3/EI$

Answer 1

The correct option is C $28P{a}^3/3EI$

(c) Joints B and C are rigid, hence can act as fixed supports. Hence BA will act as a cantilever with point load at A

$\therefore {\delta }_P=\frac{P(2a{)}^3}{3EI}=\frac{8P{a}^3}{3EI}$

Now at ends B and C moements of magnitude 2Pa will act respectively.

$\therefore {\theta }_B={\theta }_C=\frac{2Pa\times a}{2EI}=\frac{P{a}^2}{EI}$

$and{\delta }_M={\theta }_B\times 2a=\frac{P{a}^2}{EI}\times 2a=\frac{2P{a}^3}{EI}$

$\therefore Totaldeflection=2({\delta }_P+{\delta }_M)$

$=2(\frac{8P{a}^3}{3EI}+\frac{2P{a}^3}{EI})=\frac{28P{a}^3}{3EI}$