A semi$-$elliptic leaf spring consists of two extra full$-$length leaves and eight

graduated length leaves, including the master leaf. The centre$-$to$-$centre distance

between the two eyes of the spring is $1$ m $.$ The maximum force acting on the spring

is $10$ kN and the width of each leaf is $50$ mm $.$ The spring is initially pre$-$loaded in

such a way that when the load is maximum, the stresses induced in all the leaves

are equal to $350\frac{N}{m}m2.$ The modulus of elasticity of the leaf material is $207000$

N$/$mm$2.$ Determine. $($i$)$ the thickness of leaves; and $($ii$)$ the defl ection of the spring

at maximum load. Mention Design DataBook page numbers used.