This document describes an experiment to determine the stiffness of an open and closed coil spring and the modulus of rigidity of the spring material. A spring testing machine is used to apply loads to the springs and measure the deflection. The stiffness and modulus of rigidity are calculated based on equations that relate the applied load, spring geometry, and measured deflection. Test procedures are outlined for performing compression and tension tests on open and closed coil springs. Measurements of spring dimensions, number of coils, and load-deflection data are collected and used to calculate values for stiffness, shear stress, strain energy, and modulus of rigidity.

1. Expt No:
Date :
SPRING TEST (OPEN & CLOSED COIL SPRING)
AIM:
To find the stiffness of spring and the modulus of rigidity of the materials
of the specimen.
APPARATUS:
Spring testing machine, spring for tension or compression test, vernier
caliper & balance.
PRINCIPLE:
A helical spring is formed when a wire of solid circular cross section is
wound on a circular core in a spiral form. Under the axial load the spring is
subjected to both bending and twist. At any point in the coil tangent to
helical centers line is not perpendicular to axial force. If ‘w’ is the force
component parallel to tangent at any point (wSin α) produces the bending
moment M and the component perpendicular to the tangent (wCos α)
produces a torque ‘t’, where α is the angle of helix.
M = wR Sin α
T = wR Cos α
Where, R = mean radius of coil
Angle of helix, α = pitch / 2πR
Equating work done by the axial load to the total strain energy in bending
& torsion we obtain,
δ = (64wR3n Sec α /d4) × (Cos2α /N+ 2Sin2α /E)
Where,
E = 2N(1+1/m), assume 1/m = 0.3
N = (64wR3n Sec α/d4δ) × (Cos2α+2Sin2α /2.6)
When coils are wound very closely, angle of helix becomes very small. Hence
effect of ‘wSinα’ may be neglected.
δ = 64 wR3n / Nd4
Open coiled springs are those for which the effect of angle of helix cannot

2. OBSERVATIONS & CALCULATIONS:
Sl.
No
Load
in
kg w
Compression scale reading
Load in
kg w
Extension scale reading
Load
increasing
(mm)
Load
decreasing
(mm)
Mean
deflection
d
(mm)
Load
increasing
(mm)
Load
decreasing
(mm)
Mean
deflection
d in
(mm)
Closed
coil
Open
coil
Diameter of the wire,d (mm)
Mean radius of the coil, R
(mm)
R = D1+ D2/4
D1 = outer diameter of coil
(mm)
D2 = inner diameter of coil
(mm)
No. of turns, n
Length of wire, l(mm)
Pitch, p = (l/n)
tan α = p/(2πR)
α

3. be neglected under the action of axial load, both torsional & bending moments
are to be considered. If the effect of helix is negligible, they are known as
closed coiled helical spring. Hence only the effect of torsion is considered.
Shear stress max., Zmax =16wRcosα/ πd3
TEST SET UP:
The spring testing machine consists of graduated scales with a sliding
vernier fitted to a metallic angle frame. One end of the spring is passed through
the hook of the sliding vernier and the other end is suspended from an
adjustable hook fitted to the metallic frame. Another hook is provided at the
bottom of the sliding arm on which a pan is attached to and weight.
PROCEDURE:
1. Suspend the spring between sliding vernier and adjustable hook.
2. Adjust the top hook so that zero of the vernier coincides exactly with zero of
graduated
scale.
3. Suspend the pan of known weight from bottom hook of sliding vernier and
note
the deflection.
4. Gradually add weights to the pan and note the corresponding deflection. Note
the
deflection on removing the weights one by one. Find the mean deflection.
5. Draw a curve for load verses deflection. A straight-line curve proves that
deflection
is proportional to the load.
6. The procedure is repeated for tension test and compression test.
7. Measure the diameter‘d’ of the wire, internal and external diameter ‘D1’ and
‘D2’
of the coil, number of turns of the spring, length of the spring etc.
8.’w’ and δ are obtained from the graph.

4. Open coil (Compression) Closed coil (Tension)
Load
(kg)
Shear stress
I=16×w×R/
(πd3
)
(kg/ cm2
)
Stiffness
y = w /δ
(kg/ cm)
Strain
energy
u=wδ/2
(kgcm2
s-2
)
Load
(kg)
Shear stress
I=16×w×R/
(πd3
)
(kg/cm2
)
Stiffness
y=w/δ
(kg/cm)
Strain
energy
u=wδ/2
(kgcm2
s-2
)
Slope of load Vs deflection graph (Open coil) = kg/mm
Stiffness of spring (compression) = N/mm
= N/mm
Slope of load Vs deflection graph (Closed coil ) = kg/mm
Stiffness of spring (compression) = N/mm
= N/mm
Modulus of rigidity of spring , N (Open coil under compression )
N = (64wR3
n Sec α/d4
δ ) × (cos2
α + 2Sin2
α/2.6)

5. RESULT:
Modulus of rigidity of the material of spring under tension =
Stiffness of spring under tension =
Modulus of rigidity of the material of spring under compression =
Stiffness of spring under compression =
Modulus of rigidity of spring , N (Closed coil under tension )
N =