Question

What is mean by strain and stress?

Answer 1

Hi mate.

Thanks for asking this question.

Here is your answer,


#STRESS :

Stress is defined as internal elastic

restoring force per unit cross sectional area of

body.

In Equilibrium, the applied force and internal

elastic restoring force are numerically equal,

however they are oppositely directly.


Hence,

Stress is defined as applied force per unit

cross sectional area of the body.

Thus,


$stress = \frac{applied \: force}{area}$

$stress = \frac{elastic \: restoringforce}{area}$

The S. I. unit of stress is N/ m×m or Pa and the C. G. S unit of stress is dyne/cm×cm.

The dimensions of the stress are

$( {l}^{ - 1} {m}^{1} {t}^{ - 2} )$


TYPES OF STRESS :


(1) Longitudinal / tensile stress :

The change in length of a body

when the applied force is produced then, the

stress associated is known as Longitudinal /

tensile stress

Thus,

$logitudinal \: stress = \frac{applied \: force}{area \: of \: cross \: section}$

$longitudinal \: stress = \frac{f}{a}$

$longitudinal \: stress = \frac{f}{\pi {r}^{2} }$

Therefore,

$longitudinal \: stress = \frac{mg}{\pi {r}^{2} }$

(2) Volume stress :

When applying force produces

change in volume of the body, the stress is

associated is known as volume stress.

$volume \: stress = \frac{applied \: force}{area}$

$volume \: stress = \frac{a.dp}{a}$

$volume \: stress = dp$



(3) Shearing stress :


If deforming force produces

change in shape of a body, the stress

associated is known as a shearing stress.


$shearing \: stress = \frac{tangential \: force}{area}$

$shearing \: stress = \frac{f}{a}$



# STRAIN :

Strain is defined as change in

dimensions per unit original dimensions.

Strain is dimensionless, since it is a ratio of
two similar quantities.

Strain is a pure number. So that, they have no unit.


TYPES OF STRAIN :


(1) Longitudinal / tensile stress :

Longitudinal or tensile strain is

defined as the ratio of change in length to the

original length.


$longi.\: strain = \frac{change \:in \: length}{original \: length}$


$long. \: strain = \frac{final \: length \: - \: initial \: length}{original \: legth}$

$longi. \: strain = \frac{l + (i - l)}{l}$

$longi. \: strain = \frac{i}{l}$


(2) Volume stress :


If the applied force produce

change in the volume of body, the strain is

known as volume strain.

Volume strain is defined as the ratio of

change in volume to the original volume.


$volume \: strain = \frac{Change \: in \: volume}{original \: volume}$

$volume \: strain = - \frac{dv}{v}$

Negative sign denotes that there is a

decrease in the volume with increase in

pressure by 'dp'.




(3) Shearing strain :


If the applied force produces
change in shape of a body, the strain is
associated is known as shearing strain.


Shearing strain is defined as the ratio of

relative displacement of any layer to its

perpendicular distance from fixed layer.



$shearing \: strain \: = \: \tan( \alpha )$




Thank you.




BE BRAINLY !!!!!!!!!!!!!!!!!!!

Answer 2

Stress is the initial restoring force acting per unit area and strain is defined as the ratio of change in diamention to the orginal diamention.