×

Close

Type:
**Note**Institute:
**
West Bengal University of technology
**Course:
**
B.Tech
**Specialization:
**Mechanical Engineering**Offline Downloads:
**7**Views:
**308**Uploaded:
**3 months ago**

INTRODUCTION AND REVIEW
Preamble
Engineering science is usually subdivided into number of topics such as
1. Solid Mechanics
2. Fluid Mechanics
3. Heat Transfer
4. Properties of materials and soon Although there are close links between them in terms of the physical
principles involved and methods of analysis employed.
The solid mechanics as a subject may be defined as a branch of applied mechanics that deals with
behaviours of solid bodies subjected to various types of loadings. This is usually subdivided into further two
streams i.e Mechanics of rigid bodies or simply Mechanics and Mechanics of deformable solids.
The mechanics of deformable solids which is branch of applied mechanics is known by several names i.e.
strength of materials, mechanics of materials etc.
Mechanics of rigid bodies:
The mechanics of rigid bodies is primarily concerned with the static and dynamic behaviour 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.
Mechanics of deformable solids :
Mechanics of solids:
The mechanics of deformable solids is more concerned with the internal forces and associated changes in
the geometry of the components involved. Of particular 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 an equal roles in this field.
Analysis of stress and strain :
Concept of stress : Let us introduce the concept of stress as we know that the main problem of
engineering mechanics of material is the investigation of the internal resistance of the body, i.e. the nature of
forces set up within a body to balance the effect of the externally applied forces.
The externally applied forces are termed as loads. These externally applied forces may be due to any one of
the reason.
(i) due to service conditions
(ii) due to environment in which the component works

(iii) through contact with other members
(iv) due to fluid pressures
(v) due to gravity or inertia forces.
As we
e know that in mechanics of deformable solids, externally applied forces acts on a body and body
suffers a deformation. From equilibrium point of view, this action should be opposed or reacted by internal
forces which are set up within the particles of material due to cohesion.
These
he internal forces give rise to a concept of stress. Therefore, let us define a stress Therefore, let us
define a term stress
Stress:
Let us consider a rectangular bar of some cross
Newtons )
sectional area and subjected to some load or force (in
Let us imagine that the same rectangular bar is assumed to be cut into two halves at section XX. The each
portion of this rectangular bar is in equilibrium under the action of load P and the internal forces acting at the
section XX has been shown
Now sstress is defined as the force intensity or force per unit area. Here we use a symbol σ to represent the
stress.
Where A is the area of the X
section
ec

Here we
e are using an assumption that the total force or total load carried by the rectangular bar is uniformly
distributed over its cross section.
But the stress distributions may be for from uniform, with local regions of high stress known as
a stress
concentrations.
If the force carried by a component is not uniformly distributed over its cross sectional area, A, we must
consider a small area, δA' wh
hich carries a small load δP, of the total force P', Then definition of stress is
As a particular stress generally holds true only at a point, therefore it is defined mathematically as
Units :
2
The
he basic units of stress in S.I units i.e. (International system) are N / m (or Pa)
6
MPa = 10 Pa
9
GPa = 10 Pa
3
KPa = 10 Pa
2
Some times N / mm units are also used, because this is an equivalent to MPa. While US customary unit is
pound per square inch psi.
TYPES OF STRESSES :
only two basic stresses exists : (1) normal stress and (2) shear shear stress. Other stresses either are
similar to these basic stresses or are a combination of these e.g. bending stress is a combination tensile,
compressive and shear stresses. Torsional stress, as encountered in twisting of a shaft is a shearing stress.
Let us define the normal stresses and shear stresses in the following sections.
Normal stresses : We have defined stress as force per unit area. If the stresses are normal to the areas
concerned, then these are termed as normal stresses. The normal stresses are generally denoted by a
Greek letter ( σ )

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 acts as shown in the
figures below :
Tensile or compressive stresses :
The normal stresses can be either tensile or compressive whether the stresses acts out of the area or into
the area

## Leave your Comments