Subtopic: Measurement of force, stress, torque, speed, displacement and acceleration on machine elements – shafts, couplings, keys, bearings and knuckle joints
Question Statement:
A semi-elliptic leaf spring for a farm trailer has 10 leaves of width $60\text{ mm}$ and thickness $8\text{ mm}$. The effective span length of the spring between supports is $1.0\text{ m}$. If the spring carries a central load of $12\text{ kN}$, calculate the maximum bending stress in the spring leaves in $\text{MPa}$.
Answer Key:
468.75
Step-by-Step Solution & Explanation
For a semi-elliptic leaf spring of span $2L = 1.0\text{ m}$ ($L = 0.5\text{ m} = 500\text{ mm}$):
Total central load $2W = 12\text{ kN}$, so load on each cantilever half is $W = 6\text{ kN} = 6000\text{ N}$.
Number of leaves $n = 10$, width $b = 60\text{ mm}$, thickness $t = 8\text{ mm}$.
Maximum bending stress:
$\sigma_b = \frac{6 W L}{n b t^2} = \frac{6 \times 6000 \times 500}{10 \times 60 \times 8^2} = \frac{18000000}{38400} = 468.75\text{ MPa}$