Strength Of Materials

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 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 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 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 – sectional area and subjected to some
load or force (in Newtons )

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 stress is defined as the force intensity or force per unit area. Here we use a symbol s
to represent the stress.

Here we 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 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, ‘dA' which carries a small load dP, of the total
force ‘P', Then definition of stress is

MPa = 106 Pa
GPa = 109 Pa
KPa = 103 Pa
Some times N / mm2 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 ( s )

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

Bearing Stress : When one object presses against another, it is referred to a bearing
stress ( They are in fact the compressive stresses ).

Shear stresses :
Let us consider now the situation, where the cross – sectional area of a block of material
is subject to a distribution of forces which are parallel, rather than normal, to the area
concerned. Such forces are associated with a shearing of the material, and are referred to
as shear forces. The resulting force interistes are known as shear stresses.

However, it must be borne in mind that the stress ( resultant stress ) at any point in a body
is basically resolved into two components s and t one acts perpendicular and other
parallel to the area concerned, as it is clearly defined in the following figure.

The single shear takes place on the single plane and the shear area is the cross - sectional
of the rivett, whereas the double shear takes place in the case of Butt joints of rivetts and
the shear area is the twice of the X - sectional area of the rivett.

About Admin MC3

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