(Solved): Q.5 (a) A hollow steel shaft \( \boldsymbol{A C B} \) of outside diameter \( 50 \mathrm{~mm} \) an ...

Q.5 (a) A hollow steel shaft \( \boldsymbol{A C B} \) of outside diameter \( 50 \mathrm{~mm} \) and inside diameter 40 \( \mathrm{mm} \) is held against rotation at ends \( \boldsymbol{A} \) and \( \boldsymbol{B} \) as shown in the Figure Q5(a). Horizontal forces \( \boldsymbol{P} \) are applied at the ends of a vertical arm that is welded to the shaft at point \( \boldsymbol{C} \). (i) Determine the Polar Moment of Inertia \( J \) for the steel shaft; (3 marks) (ii) Determine the allowable value of the forces \( \boldsymbol{P} \) of the maximum permissible shear stress in the shaft is \( 55 \mathrm{MPa} \). (14 marks) Figure 05(a) (b) A steel bar \( \boldsymbol{A B C D} \), as shown in the Figure Q5(b), has a cross-sectional area of \( 600 \mathrm{~mm}^{2} \) and is loaded by forces \( \boldsymbol{P 1}=2700 \mathrm{~N}, \boldsymbol{P 2}=1800 \mathrm{~N} \) and \( \boldsymbol{P 3}= \) \( 1300 \mathrm{~N} \). (i) Assuming that the modulus of elasticity \( \boldsymbol{E}=200 \times 10^{3} \mathrm{MPa} \), calculate the change in length of the bar. Does the bar elongate or shorten? (5 marks) (ii) In order to keep the end \( \boldsymbol{D} \) of the bar in the original position, what amount should the load \( \boldsymbol{P 3} \) be increased? (3 marks)