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Visvesvaraya Technological University VTU
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Page-1

- Simple Stresses And Strains - ( 1 - 4 )
- Hooke's law - ( 5 - 5 )
- Young's modulus - ( 6 - 18 )
- Saint venant's priciple - ( 19 - 34 )
- Thin And Thick Cylinders - ( 35 - 44 )
- Thick cylinder theory - ( 45 - 51 )
- Bending Moment And Shear Forces - ( 52 - 107 )
- Columns And Struts - ( 108 - 120 )
- Typical failure of coloums - ( 121 - 139 )
- Euler's theory - ( 140 - 147 )
- Theories Of Failure - ( 148 - 160 )

Topic:

Strength of Materials (15CV 32)
Module 1 : Simple Stresses and Strains
Dr. H. Ananthan, Professor, VVIET,MYSURU
8/21/2017
Introduction, Definition and concept and of stress and strain. Hooke’s law, Stress-Strain
diagrams for ferrous and non-ferrous materials, factor of safety, Elongation of tapering bars
of circular and rectangular cross sections, Elongation due to self-weight. Saint Venant’s
principle, Compound bars, Temperature stresses, Compound section subjected to temperature
stresses, state of simple shear, Elastic constants and their relationship.

1.1 Introduction
In civil engineering structures, we frequently encounter structural elements such as tie members,
cables, beams, columns and struts subjected to external actions called forces or loads. These
elements have to be designed such that they have adequate strength, stiffness and stability.
The strength of a structural component is its ability to withstand applied forces without failure
and this depends upon the sectional dimensions and material characteristics. For instance a steel
rod can resist an applied tensile force more than an aluminium rod with similar diameter. Larger
the sectional dimensions or stronger is the material greater will be the force carrying capacity.
Stiffness influences the deformation as a consequence of stretching, shortening, bending, sliding,
buckling, twisting and warping due to applied forces as shown in the following figure. In a
deformable body, the distance between two points changes due to the action of some kind of
forces acting on it.
A weight suspended by two
cables causes stretching of the
cables. Cables are in axial
tension.
Inclined members undergo
shortening, and stretching will
be induced in the horizontal
member. Inclined members
are in axial compression and
horizontal member is in axial
tension.
Bolt connecting the plates is subjected to
sliding along the failure plane. Shearing
Cantilever beam subjected to
bending due to transverse loads
results in shortening in the
bottom half and stretching in
the top half of the beam.
Cantilever beam subjected to
twisting and warping due to
Buckling of long compression members
due to axial load.
torsional moments.
forces are induced.

Such deformations also depend upon sectional dimensions, length and material characteristics.
For instance a steel rod undergoes less of stretching than an aluminium rod with similar diameter
and subjected to same tensile force.
Stability refers to the ability to maintain its original configuration. This again depends upon
sectional dimensions, length and material characteristics. A steel rod with a larger length will
buckle under a compressive action, while the one with smaller length can remain stable even
though the sectional dimensions and material characteristics of both the rods are same.
The subject generally called Strength of Materials includes the study of the distribution of
internal forces, the stability and deformation of various elements. It is founded both on the
results of experiments and the application of the principles of mechanics and mathematics. The
results obtained in the subject of strength of materials form an important part of the basis of
scientific and engineering designs of different structural elements. Hence this is treated as subject
of fundamental importance in design engineering. The study of this subject in the context of
civil engineering refers to various methods of analyzing deformation behaviour of structural
elements such as plates, rods, beams, columns, shafts etc.,.
1.2 Concepts and definitions
A load applied to a structural member will induce internal forces within the member called stress
resultants and if computed based on unit cross sectional area then they are termed as intensity of
stress or simply stress in the member.
The stresses induced in the structural member will cause different types of deformation in the
member. If such deformations are computed based on unit dimensions then they are termed as
strain in the member.
The stresses and strains that develop within a structural member must be calculated in order to
assess its strength, deformations and stability. This requires a complete description of the
geometry, constraints, applied loads and the material properties of the member.
The calculated stresses may then be compared to some measure of the strength of the material
established through experiments. The calculated deformations in the member may be compared
with respect limiting criteria established based on experience. The calculated buckling load of

the member may be compared with the applied load and the safety of the member can be
assessed.
It is generally accepted that analytical methods coupled with experimental observations can
provide solutions to problems in engineering with a fair degree of accuracy. Design solutions are
worked out by a proper analysis of deformation of bodies subjected to surface and body forces
along with material properties established through experimental investigations.
1.3 Simple Stress
Consider the suspended bar of original length L0 and uniform cross sectional area A0 with a force
or load P applied to its end as shown in the following figure (a). Let us imagine that the bar is
cut in to two parts by a section x-x and study the equilibrium of the lower portion of the bar as
shown in figure (b). At the lower end, we have the applied force P
It can be noted that, the external force applied to a body in equilibrium is reacted by internal
forces set up within the material. If a bar is subjected to an axial tension or compression, P, then
the internal forces set up are distributed uniformly and the bar is said to be subjected to a uniform
direct or normal or simple stress. The stress being defined as
( )
( )
( )
Note
i.
This is expressed as N/mm2 or MPa.
ii.
Stress may thus be compressive or tensile depending on the nature of the load.
iii.
In some cases the stress may vary across any given section, and in such cases the stress at any
point is given by the limiting value of P/A as A tends to zero.

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