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

(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)