A central load of 2500 N is acting on a leaf spring. The leaf spring is to be made of 12 steel plates of 6 cm width and 5 mm thickness. If the bending stress is limited to 200 N/mm², then the length and deflection at the centre of the spring are, respectively : (Assume Modulus of elasticity as 2 × 10⁵ N/mm²)
- A660 mm; 16·08 mm
- B760 mm; 26·08 mm
- C860 mm; 36·08 mm
- D960 mm; 46·08 mmCorrect
Solution
Concept
Semi-elliptic leaf spring
Formula
σ = 3 W L / (2 n b t²); δ = 3 W L³ / (8 E n b t³)
Step-by-step solution
1. L = 2 σ n b t² / (3 W) = 2 × 200 × 12 × 60 × 25 / (3 × 2500) = 960 mm. 2. δ = 3 × 2500 × 960³ / (8 × 2×10⁵ × 12 × 60 × 5³) = 46.08 mm.
Explanation
For a simply supported (semi-elliptic) leaf spring of span L with n plates of width b and thickness t, the stress and deflection formulae give both required quantities.
Why the other options are wrong
Only a span of 960 mm gives σ = 3WL/(2nbt²) = 200 N/mm²; spans of 660, 760 and 860 mm give a lower stress for this load.
Shortcut
L = 2σ n b t² / 3W; δ = σ L² / (4 E t).
Common mistake
Taking width as 6 mm instead of 60 mm.
Correct answer: D) 960 mm; 46·08 mm