$($c$)$ A $100$mm$\backslash$times $12$mm thick tie$-$bar is connected to another by fillet welds around the end of the bar and inside a slot machined in it as shown in Figure Q$5.$

Figure Q$5$

Calculate the size of the fillet if the working stresses are $110$M$($N$)/($m$^(2))$ for the transverse welds and $80$M$($N$)/($m$^(2))$ for longitudinal welds. The working stress for the tie$-$bar is $120$M$($N$)/($m$^(2))$ and the value of k is $0\mathrm{.}7.$

$[8$ marks$]$