(Solved): a) A composite bar consisting of steel and brass segments is subjected to an axial load of \( 10 \m ...

a) A composite bar consisting of steel and brass segments is subjected to an axial load of \( 10 \mathrm{kN} \) at point \( \mathrm{A} \) as shown in Figure Q5(a). The diameters of the steel and brass segments are \( 12 \mathrm{~mm} \) and \( 30 \mathrm{~mm} \) respectively. The diameter of the hollow section of the brass segment is \( 25 \mathrm{~mm} \). Given that the Young's moduli for steel and brass are \( 210 \mathrm{GPa} \) and \( 105 \mathrm{GPa} \) respectively, and the Poisson's ratio for steel is \( 0.30 \), calculate: (i) the normal stress in each segment of the composite bar (i.e. segments \( \mathrm{AB}, \mathrm{BC} \) and \( \mathrm{CD} \) ); (6 marks) (ii) the total extension of the composite bar; and (4 marks) (iii) the change in the diameter of the steel segment. (3 marks) (b) A circular rod is subjected to two torsional moments of \( 30 \mathrm{kNm} \) and \( 10 \mathrm{kNm} \) at points \( \mathrm{B} \) and \( \mathrm{C} \) respectively as shown in Figure \( Q 5(b) \). Given that the shear modulus of the rod is \( 100 \mathrm{GPa} \), determine: (i) the maximum shear stress developed in each segment of the rod; and (ii) the angle of twist in degree at the free end \( \mathrm{C} \). ( 6 marks) ( 6 marks)