find the net change in length if ,value of a is 100mm^2 and E=200×10^9
Answers
SIMPLE STRESSES AND STRAINS
INTRODUCTION
Within elastic stage, the resisting force equals applied load. This resisting force per unit area
is called stress or intensity of stress.
STRESS
The force of resistance per unit area, offered by a body against deformation is known as
stress. The external force acting on the body is called the load or force. The load is applied on the
body while the stress is induced in the material of the body. A loaded member remains in equilibrium
when the resistance offered by the member against the deformation and the applied load are equal.
Mathematically stress is written as,
A
P
σ
where = Stress (also called intensity of stress),
P = Cross-Sectional or load, and
A = Cross-Sectional area.
In the S.I. Units, the force is expressed in newtons (Written as N) and area is expressed as m2
. Hence,
unit stress becomes as N/m2
. The area is also expressed in millimetre square then unit of force
becomes as N/mm2
.
1 N/m2
= 1 N/(100cm)2
= 1 N/104
cm3
= 104 N/cm2
or 10-6N/mm2
2 2 2
10
1 1
cm mm
STRAIN
When a body is subjected to some external force, there is some change of dimension of the
body. The ratio of change of dimension of the body to the original dimension is known as strain.
Strain is dimensionless.
e
δl - Change in length in mm
l - original length in mm
Strain may be:-
1. Tensile strain, 2. Compressive strain
2. Volumetric strain, and 4. Shear strain
If there is some increase in length of a body due to external force, then the ratio of increase of
length to the original length of body is known as tensile strain. But if there is some decrease in length
of the body, then the ratio of decrease of the length of the body to the original length is known as
compressive strain. The ratio of change of volume of the body to the original volume is known as
volumetric strain. The strain produced by shear stress is known as shear strain.
TYPES OF STRESSES
The stress may be normal stress or a shear stress.
Normal stress is the stress which acts in a direction perpendicular to the areas. It is represented by
(sigma). The normal stress is further divided into tensile stress and compressive stress.
Tensile Stress. The stress induced in a body, when subjected to two equal and opposite pulls as
shown in Fig.1.1 () as a result of which there is an increase in length, is known as tensile stress. The
ratio of increase in length to the original length is known as tensile strain. The tensile stress acts
normal to the area and it pulls on the area.