Question $1($Cont$\text{'}$d$)$

$($c$)$ A bar $AB$ having length $L$ and axial rigidity $EA$ is fixed at end $A$ as shown in Fig.

Q$1($c$).$ At the other end a small gap of dimension $s$ exists between the end of the bar

and a rigid surface. A load $P$ acts on the bar at point $C,$ which is two$-$thirds of the

length from the fixed end.

i$)$ If the support reactions produced by the load $P$ are to be equal in magnitude,

what should be the size $s$ of the gap?

ii$)$ If the bar is unloaded initially and the load $P^{\text{'}}$ is increased gradually for the range

$0P^{\text{'}}P,$ determine $P^{\text{'}}$ in terms of $P$ at the moment when the gap closes.

iii$)$ Compare the magnitude of reactions at A and $B$ before and after closing of gap.

Hint: $=\frac{FL}{EA}$ using common notations.