A semi-elliptic multi-leaf spring is needed for the suspension of the rear axle of a truck. It consists of two extra full-length leaves and ten graduated length leaves including the master leaf. The centre - tocentre distance between the spring eyes is 1.2 m. The leaves are build of steel 55Si2Mo90 (Syt = 1500 n/mm2 and E = 207000 N/mm2) and the factor of safety is 2.5. The spring is to be designed for a maximum force of 30 KN. The leaves are pre-stressed so as to same stresses in all leaves. Evaluate :
(i) The cross-section of leaves, and
(ii) the deflection at the end of the spring.