P$5\mathrm{.}36$ The pin$-$connected structure shown in Figure P$5\mathrm{.}35/36$ consists of a rigid beam ABCD and two supporting bars. $\frac{?}{\text{B}\text{a}\text{r}}(1)$ is a bronze alloy $[E=105$GPa with a cross$-$sectional area of $A_1=290m{m}^2.$ Bar $(2)$ is an aluminum alloy $[E=70$GPa $]$ with a cross$-$sectional area of $A_2=650m{m}^2.$ All bars are unstressed before the load $P$ is applied; however, there is a $3-mm$ clearance in the pin connection at $A.$ If a load of $P=85kN$ is applied at $B,$ determine:

$($a$)$ the normal stresses in both bars $(1)$ and $(2).$

$($b$)$ the downward deflection of point $A$ on the rigid bar.

Ans: $16\mathrm{.}97$MPa,$83\mathrm{.}2$MPa,$3\mathrm{.}36mm$