Short Answer:
Temperature strain is the change in length per unit original length of a material due to a change in temperature. When a material is heated, it expands, and when it is cooled, it contracts. This change in dimension per unit length caused by temperature variation is called temperature strain.
In simple words, temperature strain represents the thermal deformation experienced by a material when its temperature changes. If the body is allowed to expand or contract freely, it develops only temperature strain and no stress. However, if expansion or contraction is restricted, thermal stresses are developed.
Detailed Explanation:
Temperature Strain
Definition and Meaning:
Temperature strain is the strain produced in a material due to a change in temperature. Every material expands when it is heated and contracts when it is cooled. The amount of expansion or contraction depends on the coefficient of thermal expansion of the material and the temperature difference applied.
If the body is free to expand or contract, only a change in length (strain) occurs without any stress. But if the body is restricted, the strain leads to internal thermal stresses. Hence, temperature strain is an essential concept in the study of thermal deformation and thermal stress in materials and structures.
Derivation of Temperature Strain
Let us derive the expression for temperature strain developed in a material due to temperature change.
- Consider a uniform bar:
- Original length of the bar =
- Change in temperature = (°C or K)
- Coefficient of linear expansion = (/°C)
When the temperature changes by , the change in length of the bar is given by:
Here,
- = change in length,
- = coefficient of linear expansion,
- = temperature change.
- Definition of strain:
Strain () is defined as the change in length per unit original length:
Substitute the value of :
Simplifying,
This is the basic equation for temperature strain, also called thermal strain.
Explanation of the Formula
- — Coefficient of linear expansion:
It represents the amount of expansion per unit length per degree rise in temperature. Different materials have different values of . For example, steel has a smaller value compared to aluminum, which expands more with temperature. - — Temperature difference:
It is the change between the final and initial temperature of the material. A greater temperature difference produces a larger strain. - — Temperature strain:
It is a dimensionless quantity since it is the ratio of two lengths. It shows the proportional deformation due to temperature variation.
Thus, temperature strain depends only on the material property () and the temperature change (), not on the original dimensions of the object.
Units of Temperature Strain
Since strain is the ratio of two lengths, it is dimensionless (no unit).
However, it can be represented as microstrain (µε), where:
Example:
If , it can be written as .
Example Calculation
A steel rod of 2 m length is heated by 50°C.
Given:
Temperature strain is given by:
So, the temperature strain = 0.0006, meaning the rod elongates by 0.06% of its original length when heated by 50°C.
Effect of Temperature Strain
- Free Expansion:
- If a material is free to expand or contract, only temperature strain occurs.
- No internal stress is developed.
- Example: A freely hanging metal rod elongates when heated but returns to original length when cooled.
- Restricted Expansion:
- If expansion or contraction is restricted, temperature strain is partially or fully prevented.
- This prevention results in thermal stresses in the material.
- Example: A steel beam fixed at both ends in a building develops compressive stress when heated.
- Non-uniform Temperature:
- When different parts of a structure experience different temperatures, uneven temperature strain causes thermal distortion or warping.
Factors Affecting Temperature Strain
- Temperature Difference ():
The larger the temperature change, the greater the strain. - Material Property ():
Materials with higher coefficients of thermal expansion undergo more strain for the same temperature change. - Temperature Distribution:
Uniform heating results in uniform strain, while non-uniform heating leads to bending or distortion. - Constraint Conditions:
If the material is constrained, thermal strain results in the development of thermal stress. - Shape and Size:
Long members show more noticeable thermal strain compared to short members for the same temperature rise.
Practical Examples of Temperature Strain
- Bridges and Railway Tracks:
Expansion joints are provided to accommodate temperature strain caused by daily temperature changes. - Pipes and Boilers:
Metallic pipes carrying hot fluids expand and contract continuously due to temperature strain. - Concrete Structures:
Concrete expands and contracts due to temperature changes, leading to cracks if temperature strain is not managed. - Bimetallic Strips:
Used in thermostats — two metals with different values bend when heated because of unequal temperature strain. - Aerospace and Engines:
Components experience severe temperature variations, requiring careful design to control thermal strain.
Difference Between Thermal Strain and Thermal Stress
- Thermal Strain: Change in length per unit length due to temperature change.
Occurs when the body is free to expand or contract.
- Thermal Stress: Internal resistance developed when expansion/contraction is prevented.
Thermal stress always occurs because of thermal strain under constraint conditions.
Importance of Temperature Strain in Engineering
- Helps in predicting deformation in machine and structural components due to temperature variation.
- Essential for designing bridges, pipelines, engines, and turbines exposed to high temperatures.
- Prevents failure, distortion, and cracking caused by temperature effects.
- Assists in material selection for thermal applications (choosing materials with low values).
Conclusion:
Temperature strain is the strain produced due to a change in temperature, expressed as . It represents the expansion or contraction per unit length of a material when subjected to heating or cooling. If the body is free, only temperature strain occurs; if restricted, it generates thermal stress. Understanding temperature strain is vital in mechanical and civil engineering design to ensure structures and machines can withstand temperature variations safely and efficiently.