Quarter-elliptic Type Leaf Springs:
Figure illustrated a quarter elliptic spring carrying an end load W at free end
Z = nb t 2 / 6
M = - Wl
σb = M/ Z = 6Wl / nb2
Figure
From geometry of circles,
y (2R - y) = l × l
y = l2 / 2R
M / E I = 1 / R - 1/ R0
(- W l )/E ( n b t 3/12) = 2/ l 2 ( y - y0 )
∴ Δ= 6W l 3/ nbt 3 E
U = (½) W Δ =3W 2 l 3/ nb t 3 E