Introduction:
In
engineering applications, the machine parts are subjected to various forces
which may be due to either one or more of the following:
1.
Energy transmitted,
2.
Weight of machine,
3.
Frictional resistances,
4.
Inertia of reciprocating parts,
5.
Change of temperature, and
6.
Lack of balance of moving parts.
The
different forces acting on a machine part produces various types of stresses,
which is discussed in this blog.
Load
It
is defined as any external force acting
upon a machine part. The following four types of the load are important
from the subject point of view:
1.
Dead or steady load. A load is said
to be a dead or steady load, when it does not change in magnitude or direction.
2.
Live or variable load. A load is said
to be a live or variable load, when it changes continually.
3.
Suddenly applied or shock loads. A load is
said to be a suddenly applied or shock load, when it is suddenly applied or
removed.
4.
Impact load. A load is said to be an impact
load, when it is applied with some initial velocity.
Note:
A
machine part resists a dead load more easily than a live load and a live load
more easily than a shock load.
Stress
When
some external system of forces or loads act on a body, the internal forces
(equal and opposite) are set up at various sections of the body, which resist
the external forces. This internal force per unit area at any section of the
body is known as unit stress or simply a stress. It
is denoted by a Greek letter sigma (σ).
Strain
When
a system of forces or loads act on a body, it undergoes some deformation. This deformation
per unit length is known as unit strain or simply a strain.
It is denoted by a Greek letter epsilon (ε).
Tensile Stress and Strain
When
a body is subjected to two equal and opposite axial pulls P (also called
tensile load), then the stress induced at any section of the body is known as tensile
stress. A little consideration will show that due to the tensile load,
there will be a decrease in cross-sectional area and an increase in length of
the body. The ratio of the increase in length to the original length is known
as tensile strain.
Compressive
Stress and Strain
When
a body is subjected to two equal and opposite axial pushes P (also called
compressive load), then the stress induced at any section of the body is known
as compressive stress. A little consideration will show that due
to the compressive load, there will be an increase in cross-sectional area and
a decrease in length of the body. The ratio of the decrease in length to the
original length is known as compressive strain.
Shear
Stress and Strain
When
a body is subjected to two equal and opposite forces acting tangentially across
the resisting section, as a result of which the body tends to shear off the
section, then the stress induced is called shear stress.
The
corresponding strain is known as shear strain and it is measured
by the angular deformation accompanying the shear stress. The shear stress and
shear strain are denoted by the Greek letters tau (τ) and phi (φ) respectively.
Bearing
Stress
A
localized compressive stress at the surface of contact between two members of a
machine part, that are relatively at rest is known as bearing stress or
crushing stress. The bearing stress is taken into account in the
design of riveted joints, cotter joints, knuckle joints, etc. Let us consider a
riveted joint subjected to a load P It may be noted that the local compression
which exists at the surface of contact between two members of a machine part
that are in relative motion, is called bearing pressure (not the
bearing stress). This term is commonly used in the design of a journal
supported in a bearing, pins for levers, crank pins, clutch lining, etc.
Breaking
stress. After
the specimen has reached the ultimate stress, a neck is formed, which decreases
the cross-sectional area of the specimen. A little consideration will show that
the stress (or load) necessary to break away the specimen, is less than the
maximum stress. The stress is, therefore, reduced until the specimen breaks
away at point F. The stress corresponding to point F is known as
breaking stress.
Working
Stress
When
designing machine parts, it is desirable to keep the stress lower than the
maximum or ultimate stress at which failure of the material takes place. This
stress is known as the working stress or design stress. It
is also known as safe or allowable stress.
Note:
By
failure it is not meant actual breaking of the material. Some machine parts are
said to fail when they have plastic deformation set in them, and they no more
perform their function satisfactory.
Factor
of Safety
It
is defined, in general, as the ratio of the maximum stress to the working
stress.
Selection
of Factor of Safety
The
selection of a proper factor of safety to be used in designing any machine
component depends upon a number of considerations, such as the material, mode
of manufacture, type of stress, general service conditions and shape of the
parts. Before selecting a proper factor of safety, a design engineer should
consider the following points :
1.
The reliability of the properties of the material
and change of these properties during service;
2.
The reliability of test results and accuracy of
application of these results to actual machine parts;
3.
The reliability of applied load;
4.
The certainty as to exact mode of failure;
5.
The extent of simplifying assumptions;
6.
The extent of localized stresses;
7.
The extent of initial stresses set up during
manufacture;
8.
The extent of loss of life if failure occurs; and
9.
The extent of loss of property if failure occurs.
Each
of the above factors must be carefully considered and evaluated. The high
factor of safety results in unnecessary risk of failure.
Stresses
due to Change in Temperature—Thermal Stresses
Whenever
there is some increase or decrease in the temperature of a body, it causes the
body to expand or contract. A little consideration will show that if the body
is allowed to expand or contract freely, with the rise or fall of the
temperature, no stresses are induced in the body. But, if the deformation of
the body is prevented, some stresses are induced in the body. Such stresses are
known as thermal stresses.
Notes:
1.
When a body is composed of two or different
materials having different coefficient of thermal expansions, then due to the
rise in temperature, the material with higher coefficient of thermal expansion
will be subjected to compressive stress whereas the material with low
coefficient of expansion will be subjected to tensile stress.
2.
When a thin tyre is shrunk on to a wheel of diameter
D, its internal diameter d is a little less than the wheel
diameter. When the tyre is heated, its circumferance π d will increase
to π D. In this condition, it is slipped on to the wheel. When it cools,
it wants to return to its original circumference π d, but the wheel if
it is assumed to be rigid, prevents it from doing so.
Impact
Stress
Sometimes,
machine members are subjected to the load with impact. The stress produced in
the member due to the falling load is known as impact stress.
Resilience
When
a body is loaded within elastic limit, it changes its dimensions and on the
removal of the load, it regains its original dimensions. So long as it remains
loaded, it has stored energy in itself. On removing the load, the energy stored
is given off as in the case of a spring. This energy, which is absorbed in a
body when strained within elastic limit, is known as strain energy. The
strain energy is always capable of doing some work.
The
strain energy stored in a body due to external loading, within elastic limit,
is known as resilience and the maximum energy which can be stored
in a body up to the elastic limit is called proof resilience. The
proof resilience per unit volume of a material is known as modulus of
resilience.
It
is an important property of a material and gives capacity of the material to
bear impact or shocks. Sometimes machine parts are subjected to pure torsion or
bending or combination of both torsion and bending stresses.
Torsional
Shear Stress
When
a machine member is subjected to the action of two equal and opposite couples
acting in parallel planes (or torque or twisting moment), then the machine
member is said to be subjected to torsion. The stress set up by
torsion is known as torsional shear stress. It is zero at the
centroidal axis and maximum at the outer surface.
Theories
of Failure Under Static Load
It
has already been discussed in the previous chapter that strength of machine
members is based upon the mechanical properties of the materials used. Since
these properties are usually determined from simple tension or compression
tests, therefore, predicting failure in members subjected to uniaxial stress is
both simple and straight-forward. But the problem of predicting the failure
stresses for members subjected to bi-axial or tri-axial stresses is much more
complicated. In fact, the problem is so complicated that a large number of
different theories have been formulated. The principal theories of failure for
a member subjected to bi-axial stress are as follows:
1.
Maximum principal (or normal) stress theory (also
known as Rankine’s theory).
2.
Maximum shear stress theory (also known as Guest’s
or Tresca’s theory).
3.
Maximum principal (or normal) strain theory (also
known as Saint Venant theory).
4.
Maximum strain energy theory (also known as Haigh’s
theory).
5.
Maximum distortion energy theory (also known as
Hencky and Von Mises theory).
Since
ductile materials usually fail by yielding i.e. when permanent
deformations occur in the material and brittle materials fail by fracture,
therefore the limiting strength for these two classes of materials is normally
measured by different mechanical properties. For ductile materials, the
limiting strength is the stress at yield point as determined from simple
tension test and it is, assumed to be equal in tension or compression. For
brittle materials, the limiting strength is the ultimate stress in tension or
compression.
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