Strength of Materials & Engineering Mechanics - UNIT 1.pdf

20AG302
STRENGTH OF MATERIALS
AND
ENGINEERING MECHANICS
Handled by,
Dr. P. DINESHKUMAR M.E., Ph.D.,
Assistant Professor,
Department of Agricultural Engineering,
KongunaduCollege of Engineering andTechnology

UNIT – 1
STRESS, STRAIN AND DEFORMATION OF SOLIDS
Rigid bodies and deformable solids – Tension,
Compression and Shear Stresses – Deformation of
simple and compound bars – Thermal stresses – Elastic
constants – Volumetric strains –Stresses on inclined
planes – principal stresses and principal planes –
Mohr’s circle of stress.

INTRODUCTION
Engineering science is usually subdivided into number of topics
such as
1. Solid Mechanics.
2. Fluid Mechanics.
3. Heat Transfer.
4. Properties of materials.

SOLID MECHANICS
The solid mechanics as a subject may be defined as a branch of
applied mechanics that deals with behaviors of solid bodies
subjected to various types of loadings.
This is usually subdivided into further two streams
1. Mechanics of Rigid bodies or simply Mechanics
2. Mechanics of Deformable solids.

MECHANICSOF RIGID BODIES
The mechanics of rigid bodies is primarily concerned with the static
and dynamic behavior under external forces of engineering
components and systems which are treated as infinitely strong and
undeformable, primarily we deal here with the forces and motions
associated with particles and rigid bodies.
“A rigid body is defined as a body on which the distance between
two points never changes whatever be the force applied on it”
For example: A bridge does not deform under the weight of a single man but it may
deform under the load of a truck or ten trucks. However, the deformation is small.

MECHANICSOF DEFORMABLE SOLIDS
• The mechanics of deformable solids is more concerned with the
internal forces and associated changes in the geometry of the
components involved.
• The importance are the properties of the materials used, the strength of
which will determine whether the components fail by breaking in
service, and the stiffness of which will determine whether the amount
of deformation they suffer is acceptable.
• Therefore, the subject of mechanics of materials or strength of
materials is central to the whole activity of engineering design.
• Usually the objectives in analysis here will be the determination of the
stresses, strains, and deflections produced by loads. Theoretical
analyses and experimental results have equal roles in this field.

TYPES OF STRESSES
1. Normal Stress
2. Shear stress

NORMAL STRESS
Normal stress is stress which acts in a direction perpendicular to the
area. The normal stress is further divided into
•Tensile stress
•Compressive stress

This is also known as uniaxial state of stress, because the stresses acts only in
one direction however, such a state rarely exists, therefore we have biaxial and
triaxial state of stresses where either the two mutually perpendicular normal
stresses acts or three mutually perpendicular normal stresses.
Uni – axial Stress Bi - axial Stress Tri - axial Stress

TENSILE STRESS
The stress induced in a body, when subjected to two equal and
opposite pulls as a result of which there is an increase in length is
known as tensile stress.

COMPRESSIVE STRESS
The stress induced in a body, when subjected to two equal and
opposite pushes as a result of which there is an decrease in length is
known as compressive stress.

SHEAR STRESS
The shear stress induced in a body, when subjected to two equal and
opposite forces which are acting tangentially across the resisting
action as a result of which the body tends to shear off across the
section is known as shear stress. It is denoted by τ.

ELASTICITY
When an external force acts on a body, the body tends to undergo
some deformation. If the external force is removed and the body
comes back to its original shape and size (which means the
deformation disappears completely), the body is known as elastic
body. The property is called elasticity.

ELASTIC LIMIT
The body will regain its pervious shape and size only when the
deformation caused by the external force, is within a certain limit.
Thus there is a limiting value of force up ti and within which, the
deformation completely disappears on the removal of the force. The
value of stress corresponding to this limiting force is known as the
elastic limit of the material.

HOOKE’S LAW
Hooke’s law states that when a material is loaded within proportional
limit, the stress is proportional to the strain.
This means the ratio of the stress to the corresponding strain is a
constant within the proportional limit.
This constant is known as Modulus of Elasticity (or) Modulus of
Rigidity.

When a body is subjected to an axial tensile load, there is an increase
in the length of the body. But at the same time there is a decrease in
other dimensions of the body at right angles to the line of action of
the applied load. Thus the body is having axial deformation and also
deformation at right angles to the line of action of the applied load.

LONGITUDINAL STRAIN
The ratio of axial deformation to the original length of the
body is known as longitudinal (or linear) strain.

LATERAL STRAIN
The strain at right angles to the direction of applied load is known as
lateral strain.

POISSON’S RATIO
The ratio of lateral strain to longitudinal strain is a constant for a
given material, when the material is stressed within proportional
limit. This ratio is called Poisson’s ratio.

Strength of Materials & Engineering Mechanics - UNIT 1.pdf

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