Determine the initial radius of curvature:
A carriage spring, defiantly loaded and simply supported at its ends, has 12 steel plates each 60 mm wide by 6 mm thick. If the longest plate is 700 mm, determine the initial radius of curvature if the maximum stress is 150 N/mm2 and the plates are ultimately straight.
By neglecting loss of energy at impact, find out the height from which 200 N may be dropped centrally on the spring. E = 200 GPa.
Solution
Simply supported carriage spring :
n = 12
b = 60 mm
t = 6 mm
l = 700 mm
σb = 150 N/mm2
E = 200 GPa = 200 × 103 N/mm2
σ = 3Wl / 2 nb t2
∴ W = 3703 N
Δ= 3Wl / 8 nbt 2 E
=3 × 3703 × 7003/8 × 12 × 60 × 63 × 200 × 103 = 15.3 mm
R0 = l 2/ 8 Δ =7002/ 8 × 15.3 = 4003 mm = 4 mm
U = Change in PE
(½) × 3703 × 15.3 = 200 × (h + 15.3)
∴ h = 126 mm