A semi-elliptical laminated vehicle spring to carry a load 8500 kgf is to consist of seven leaves 10 cm wide, two of the leaves extending the full length of the spring. The spring is to be 110 cm in length and attached to the axle by two U-bolts 10 cm apart. The bolts hold the central portion of the spring so rigidly that they may be considered equivalent to a band having a width equal to the distance between bolts. The leaves are to be silico-manganese steel. Assuming an allowable stress of 3500 kgf/cm^{2}. determine :

- Thicknes of the leaves
- Deflection of the spring
- Diameter of the eye
- Length of the leaves
- Radius to which leaves should be initially bent

Assume modulus of elasticity as 2,1 x 10^{6} kgf/cm^{2}.

Solution

- 2W = 8500 kgf
- n = 7 (total number of leaves)
- nf = 2 (number of full length leaves)
- ng = 5 (number of graduated leaves)
- b = 10 cm (width of the leaves)
- 2L
_{1}_{ }= 110 cm (length of span) - l = 10 cm (distance between centres of
- U-bolts)
- σ = 3500 kgf/cm
^{2}

**1. Thickness of leaves**

the effective length of the spring

2L = 2L1 – l = 110 – 10 = 90

L = 90/2 =45 cm

assuming that the leaves are not initially stressed, the maximum stress (σ = σf)

**2. Deflection of spring**

**3. Diameter of eye**

Assuming bearing preasure on the pin which may 10 kgf/cm^{2}.

** **

**4. Lenfgth of leaves**

Ineffective length of the spring is 80 mm

Length of the smallest leaf:

**5. Radius of which the leaves should be initially bent**