UNIT-5

SPRINGS

1. A close coiled helical compression spring of 16 active coils has a spring

stiffness of 10 N/mm. It is cut into two springs having 7 and 9 turns.
Determine the spring stiffness of resulting springs.
2. A bus is provided with four leaf springs each having 9 leaves and
supports are 2m a part and section of leaf is 50 mm x 6mm. The full
capacity load for springs amounts to 10000N. The rear axle takes 80% of
load, breaking strength 12,000. Check the dimensions.
3. A Rail wagon weighing 300kN is moving with a velocity of 2m/sec. It is
to be brought to rest by two buffers with springs of 300mm diameter.
The maximum deflection of spring is 300mm, allowable shear stress in
the spring = 600 N/mm2. Design the spring.
4. Design the spring for an elevator at the bottom of which 8 identical
springs are set in parallel to absorb the shock of the elevator in case of
failure. The weight of the elevator is 20 kN and has a free fall of 1.2 m
from rest. The spring is made of 20 mm dia wire and has a spring index
of 5.5. Each spring has 12 active turns. Neglect the effect of counter
weight.
5. A railway car weighing 20 kN and moving with a velocity of 15 kmph is
to be stopped by a buffer consisting of 4 helical compression springs in
which the maximum compression allowed is 0.3 m. Find the no. of
active turns required if the spring is made of 20 mm diameter wire and
160 mm mean coil diameter. Also find the maximum shear stress
induced in the coils.
6. A semi elliptical laminated spring is to carry of load of 5000N and
consists 8 leaves 46mm wide, two of the leaves being of full length. The
spring is to be made 1000mm between the eyes and is held at the center
by a 60mm wide band. Assume that the spring is initially stressed so as
to induce an equal stress of 500N/mm2 when fully loaded. Design the
spring

i)Thickness of leaves

ii) Eye diameter

iii) Length of leaves

iv) Maximum deflection and camber. Assume E = 2.1×105 N/mm2

7. At the bottom of a mine shaft, a group of 10 identical close coiled helical

springs are set in parallel to absorb. The shock caused by the falling of
the cage in case of a failure. The loaded cage weighs 75KN, while the
counter weight has a weight of 15KN. If the loaded cage falls through a
height of 50 meters from rest, find the maximum stress induced in each
spring if it is made of 50mm diameter steel rod. The spring index is 6
and the number of active turn in each spring is 20. Modulus of rigidity
G= 80KNmm2.
8. A helical compression spring made of oil tempered carbon steel, is
subjected to a load which varies from 400 N to 1000 N. The spring index
is 6 and the design factor of safety is 1.25. If the yield stress in shear is
770MPa and endurance stress in shear is 350MPa, find: i). Size of the
spring wire, ii). Diameters of the spring, iii). Number of turns of the
spring, and 4. Free length of the spring. The compression of the spring at
 the maximum load is 30 mm. The modulus of rigidity for the spring
material may be taken as 80kN/mm2.
9. Find the maximum shear stress and deflection induced in a helical spring
of the following specifications, if it has to absorb 1000 N-m of energy.
Mean diameter of spring = 100 mm; Diameter of steel wire, used for
making the spring = 20 mm;Number of coils = 30; Modulus of rigidity
of steel = 85 kN/mm2.
10. Design a compression helical spring to carry a load of 500 N with a
deflection of 25 mm. The spring index may be taken as 8. Assume the
following values of the spring material: Permissible shear stress=350
Mpa Modulus of rigidity =84 KN/mm2 Wahl’s factor =(4C-1)/(4C-4)
+0.615/C, where C is spring index.
11.At the bottom of an elevator shaft a group of 8 identical springs are set
in Parallel to absorb the shock of the elevator in the case of failure. The
elevator Weighs 40 kN. Assuming the elevator has a free fall of 1.5 m
from rest; determine the maximum stress in each spring is made of 30
mm diameter rod. For each spring, the spring index is 8 and the number
of active coils is 12. Take G=83 GN/m2.
12.Design a spring for spring loaded safety valve for the following
Conditions: Operating pressure 100 N/cm2. Diameter of valve seat 100
mm. Design shear stress for the spring is 400
N/mm2,G=0.86×105N/mm2. The spring is to be kept in a casing of 120
mm inner diameter and 400 mm long. The spring should be at maximum
lift of 6 mm when the pressure is 107.5 N/cm2.
13.A rail carriage weighing 200kN and running at 5 km/hour is brought to
rest by four buffer springs of close coiled helical type during connection
with another carriage which is already at rest. The mean coil diameter is
 5 times the wire diameter. The deflection of each spring is 220 mm, to
bring the carriage to rest. Safe shear stress for the spring material is 400
N/mm2. Calculate the maximum load on the spring, diameter of wire
and coil, number of turns and free length of spring. Assume the ends of
spring are squared and ground. Take G= 0.8×104N/mm2.
14.A lift system is provided with cushion springs at the bottom of lift. The
lift is free to fall. Springs are set in parallel. Specify the required number
of springs if the lift has free fall of 1.5m from rest.
Weight of lift = 30kN
Allowable deflection per spring = 370 mm
Number of active turns = 15
Spring mean coil diameter = 30 mm
Spring wire diameter = 30mm
Modulus of rigidity for spring = 80Gpa.
15.Design a helical compression spring for a maximum load of 1000 N for
a deflection of 25mm using the value of spring index as 5. The
maximum permissible shear stress for spring wire is 420 MPa and
modulus of rigidity is 84 kN/mm2
16. Find the maximum shear stress and deflection induced in a helical
spring of the following specifications, if it has to absorb 1000 N-m of
energy. Mean diameter of spring = 100 mm; Diameter of steel wire, used
for making the spring = 20 mm; Number of coils = 30; Modulus of
rigidity of steel = 85 kN/mm2.
17.Design a spring for a balance to measure 0 to 1000 N over a scale of
length 80 mm. The spring is to be enclosed in a casing of 25 mm
diameter. The approximate number of turns is 30. The modulus of
 rigidity is 85 kN/mm2. Also calculate the maximum shear stress
induced.
18.A helical compression spring made of oil tempered carbon steel, is
subjected to a load which varies from 400 N to 1000 N. The spring index
is 6 and the design factor of safety is 1.25.If the yield stress in shear is
770 MPa and endurance stress in shear is 350MPa. Find: 1) Size of the
spring wire 2) Diameters of the spring 3) Number of turns of the spring
and 4) Free length of the spring. The compression of the spring at the
maximum load is 30 mm. The modulus of rigidity for the spring material
may be taken as 80 kN/mm2.
19.Design a helical spring for a spring loaded safety valve for the following
conditions: Diameter of valve seat = 65 mm, operating pressure = 0.7
N/mm2, Maximum pressure when the valve blows off freely = 0.75
N/mm2, Maximum lift of the valve when the pressure rises from 0.7 to
0.75 N/mm2 = 3.5 mm, Maximum allowable stress = 550 MPa, Modulus
of rigidity = 84 KN/mm2, Spring index = 6.
20.A truck spring has 12 number of leaves, two of which are full length
leaves. The spring supports are 1.05 m apart and the central band is 85
mm wide. The central load is to be 5.4 KN with a permissible stress of
280 MPa. Determine the thickness and width of the steel spring leaves.
The ratio of the total depth to the width of the spring is 3.Also determine
the deflection of the spring.
21. A mechanism used in printing machinery consists of a tension spring
assembled with a preload of 30N. The wire diameter of spring is 2mm
with a spring index of 6. The spring has 18 active coils. The spring wire
is hard drawn and oil tempered having the shear stress 680MPa and
modulus of rigidity 80kN/mm2. Determine the initial torsional shear
stress in the wire, spring rate and the force to cause the body of the
spring to its yield strength.