Determine the maximum stress:
A laminated spring of the quarter elliptic type, 0.6 m long, is to give a static deflection of 80 mm under an end load of 2000 N. If the leaf material is 60 mm wide and 5 mm thick, determine the number of leaves needed and the maximum stress.
From what height may the load be dropped on to the undeflected spring to cause of maximum stress of 8000 N/mm^{2}? E = 200 GPa.
Solution
Quarter Elliptic Leaf Spring l = 0.6 m
Δ = 80 mm
W = 2000 N
b = 60 mm
t = 5 mm
n = ?
σ_{b} = ?
Δ= 6W l ^{3}/ nbt ^{3} E
⇒ 80 = 3 × 2000 × 600^{3} / n × 60 × 5^{3} × 200 × 10^{3}
∴ n = 21.6 (say 22 leaves)
σ = 6Wl / nbt
= 6 × 2000 × 600 /22 Δ× 60 × 5^{2}
= 369 N/mm^{2}
For maximum stress of 800 N/mm^{2}
800 = 6 × W × 600 / 22 × 60 × 52
⇒ W = 7333.3 N
Corresponding deflection = 6 × 7333.3 × 600^{3}/22 × 60 × 5^{3} × 200 × 10^{3}
= 288 mm
Loss of PE = Gain of KE
2000 (h + 288) = (½) × 7333.3 × 288
∴ h = 240 mm