Experiment No. 3
Spring Test
Shiva Yadav
Aerospace Engineering, 3rd Sem
(Dated: August 10, 2022)
This report is a summary of the experiment known as the Spring Test used to determine the
Modulus of rigidity of a given spring. The values of the Stiffness and Modulus of Rigidity
are successfully obtained. The value of rigidity of a material obtained through such experiment is
very useful in determining possible applications of the material in various industries such that the
products are less prone to mechanical failure.
I. INTRODUCTION
Springs are an integral part of a vast array of prod-
ucts and devices, from automotive and aerospace to
medical devices and consumer products. From key-
boards to cars, it’s virtually impossible to spend a
day in the modern world without interacting with
many springs. Springs are designed around spe-
cific types of mechanical motion, including tension,
compression, and torsion, and they cover a range of
forces from fractions of a pound to hundreds of thou-
sands of pounds. Any change in a spring, whether
size, shape, or material, will impact the mechanical
properties and therefore performance of the device.
Mechanical performance needs to be carefully mea-
sured during product design and development as well
as monitoring in a production environment. Equip-
ment designed to test springs must have the appro-
priate mechanical motion control and force measure-
ment. capability.
II. THEORY
The spring constant of a spring is the change in
force it experiences per unit change in extension or
compression. It is a constant that depends upon
the length, radius of turns, number of turns and
material of spring. When force is applied spring
is compressed or elongated but the deformation
comes due to the bending deformation of the
spring wire. Hooke’s Law is the law which gives the
mathematical relationship between the applied force
on the spring and the elongation or compression in
the spring’s length. It states that within the elastic
limit of the material the change produced in the
length of the spring will be directly proportional
to the applied tensile or compressive force on the
spring. Generally, the Hooke’s Law condition is
satisfied well for length changes which are small in
comparison to the natural length of the spring.
Mathematically,
F=−kx
Where,
Fis applied force,
kis the spring constant,
xis the change in the length of the spring.
Angle of Helix (α)
It is the ratio of the pitch of the spring to the
mean circumference of the helix and is given by the
relation,
tan α=L
2πRN
Where,
L= Length of the spring
R= Mean radius of the spring,
N=number of turns in the spring.
Helical Springs are very helpful for practical pur-
poses due to their shock absorbing and load bearing
properties. There are two types of helical springs
when distinguished in terms of their load bearing
capacity, the Open Coiled and Closed Coiled Helical
Springs.
A. Open coiled Helical spring
The open coiled helical springs are designed to re-
sist compression and hence are also known as com-
pression springs. These are not wound tightly and
thus have a higher pitch. For these springs, the mod-
ulus of rigidity can be found by the equation below.
G=64kR3nsec α
d4(cos2α+sin2α
1+µ)
