Question $1$:

The beam AB in Figure $3$ is pin supported by a $20$ mm bolt at A $.$ A copper rod BC of diameter $20$ mm is attached to the beam using a $30$ mm bolt connected at B $.$ The lengths of the beam are $L_1=70**B(mm)$ and $L_2=140**B(mm),$ and the length of the rod is $L_3=90**B(mm).$ The concentrated load applied on the beam is equal to $P={1\mathrm{.}5}^{**}B(kN).$ The Young's modulus of copper is $130$ GPa and Poisson's ratio is $0\mathrm{.}33.(50$ Marks$)$

$($a$)$ Calculate reaction forces at A and the force on the rod BC$.$

$(12$ Marks$)$

$($b$)$ Determine the normal stress on the rodBC.

$(13$ Marks$)$

$($c$)$ Determine the normal strain on the rod $BC.$

$(13$ Marks$)$

$($d$)$ Calculate the total extension$/$contraction on the rod BC$.$

$(12$ Marks$)$

the B$=4\mathrm{.}9$