QUESTION ONE $(20$marks$)$

a$)$ A $100$ mm diameter off$-$set link is transmitting an axial pull of $30$ kN as shown in the Figure$-1.$ Find the stresses at points A and $B.(8$marks$)$

Figure $1$

b$)$ A shaft is loaded by a torque of $5$ kNm $.$ The material has a yield point of $350$ MPa $.$ Find the required diameter using the distortion energy theory. Take a factor of safety of $2\mathrm{.}5$

${}_1,{}_2=(\frac{{}_x+{}_y}{2})+-\sqrt[\phantom{2}]{(\frac{{}_x-{}_y}{2}{)}^2+({}_x{)}^2},J=\frac{d^4}{32}$

$(12$marks$)$

Distortion energy theory: ${}^{\text{'}}=({}_1^2-{}_1{}_2+{}_2^2{)}^{\frac{1}{2}}$