Derive the relation between longitudinal stress and longitudinal strain
Answers
Longitudinal Strain Formula
Consider a cylinder. When that longitudinal stress acts on it, there will be a change in the length of the cylinder. Then the longitudinal strain can be mathematically expressed as follows:
LongitudinalStrain=ChangeinthelengthOriginalLength ε=ΔLL
Where,
L is the original length
ΔL change in length
Longitudinal Strain Unit
It is expressed as ε=ΔLL. Here the fundamental unit of length is the meter. Substituting it in the formula we get:
SIUnitofLongitudinalStress=mm
They cancel each other, making it unit less or dimensionless quantity.
Longitudinal stress
Stress acting along the length of thin cylinder will be termed as longitudinal stress.
If fluid is stored under pressure inside the cylindrical shell, pressure force will be acting along the length of the cylindrical shell at its two ends. Cylindrical shell will tend to burst as displayed here in following figure and stresses developed in such failure of cylindrical shell will be termed as longitudinal stress.
Answer:
A longitudinal strain is defined as
Change in the length to the original length of an object
It is caused due to longitudinal stress and is denoted by the Greek letter epsilon .
Longitudinal Strain
Longitudinal Strain Formula
Consider a cylinder. When that longitudinal stress acts on it, there will be a change in the length of the cylinder. Then the longitudinal strain can be mathematically expressed as follows:
LongitudinalStrain=ChangeinthelengthOriginalLength ε=ΔLL
Where,
L is the original length
ΔL change in length
Longitudinal Strain Unit
It is expressed as ε=ΔLL. Here the fundamental unit of length is the meter. Substituting it in the formula we get:
SIUnitofLongitudinalStress=mm
They cancel each other, making it unit less or dimensionless quantity.
Explanation:
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