Short Answer:

Stress due to temperature rise is the internal force developed within a material when it is heated but not allowed to expand freely. When a solid body is heated, it tends to expand. If this expansion is prevented by external constraints or fixed supports, internal compressive stresses are developed in the material.

This stress depends on the material’s modulus of elasticity, coefficient of thermal expansion, and temperature rise. It is an important concept in mechanical and structural engineering because excessive stress from temperature changes can cause deformation, cracks, or failure in machines and structures.

Detailed Explanation :

Stress Due to Temperature Rise

When a solid material is heated, its molecules gain energy and move apart, causing the material to expand. If the material is free to expand, there will be no stress developed because the movement is unrestricted. However, if the material is fixed at both ends or restrained in some way, the expansion cannot take place freely. In this condition, the internal molecular forces resist the expansion, and compressive stresses develop inside the material. These stresses are known as stresses due to temperature rise or thermal stresses.

This type of stress occurs commonly in engineering applications such as bridges, pipelines, boilers, and machine parts. In these systems, temperature changes happen regularly, and if not properly managed, the generated stress can cause serious structural or mechanical failures.

The magnitude of stress developed depends on three main factors:

1. The material’s modulus of elasticity (E), which measures stiffness.
2. The coefficient of thermal expansion (α), which indicates how much a material expands per degree of temperature change.
3. The temperature rise (ΔT) itself.

Formula for Stress Due to Temperature Rise

When expansion is completely restricted, the thermal stress developed in a material is given by the formula:

Where,
= Thermal stress or stress due to temperature rise (N/m² or Pa)
= Modulus of elasticity of the material (N/m²)
= Coefficient of linear expansion (per °C)
= Temperature rise (°C)

This equation shows that the thermal stress is directly proportional to the temperature rise, the material’s elasticity, and its coefficient of expansion. A larger temperature change or a stiffer material will result in higher stress if expansion is restricted.

Example:
If a steel rod is fixed at both ends and heated by 50°C, and for steel,
and , then:

Hence, a compressive stress of 120 MPa is developed in the rod.

Nature of Stress

• Compressive Stress:
  When temperature increases and expansion is restricted, compressive stress develops because the material is pushed inward.
• Tensile Stress:
  When temperature decreases and contraction is restricted, tensile stress develops because the material is pulled outward.

In this question, since we are discussing temperature rise, the stress developed is compressive in nature.

Effects of Stress Due to Temperature Rise

1. Material Deformation:
   If the stress exceeds the elastic limit, permanent deformation may occur.
2. Cracking or Failure:
   In brittle materials like glass or ceramics, high thermal stress may cause sudden cracking.
3. Distortion of Components:
   Unequal temperature rise can lead to bending or warping of parts.
4. Loosening of Joints:
   In assemblies with bolts or rivets, repeated heating and cooling may cause joints to loosen.
5. Buckling in Long Structures:
   Beams, rails, or rods may buckle if compressive stress from thermal expansion is too high.

Prevention and Control

To avoid harmful effects of stress due to temperature rise, engineers use several techniques:

• Expansion Joints: Allow free movement in bridges, rails, and pipelines.
• Proper Material Selection: Choose materials with suitable thermal expansion properties.
• Uniform Heating: Ensures even temperature distribution to reduce differential stress.
• Flexible Supports: Provide small movement freedom to components under heat.
• Thermal Insulation: Used to limit rapid temperature changes and reduce stress.

Practical Applications

1. Bridges and Railway Tracks:
   During hot weather, the steel components expand. Expansion joints are used to accommodate this expansion and prevent compressive stress buildup.
2. Engines and Turbines:
   Parts are subjected to high temperature variations. Designers calculate stress due to temperature rise to avoid mechanical failure.
3. Pressure Vessels and Boilers:
   These components face both internal pressure and thermal stress. Proper material design helps ensure safety.
4. Pipelines:
   Hot fluids flowing through metal pipes cause them to expand; flexible supports are used to absorb this movement.

Importance in Design

In mechanical and structural design, it is essential to consider stress due to temperature rise because:

• It directly affects the strength and safety of the structure.
• Ignoring it can lead to thermal fatigue or early material failure.
• It determines the need for expansion joints, insulation, and thermal allowances.

Engineers perform detailed thermal stress analysis using the given material properties and temperature conditions to ensure that the developed stresses remain within safe limits.

Conclusion

Stress due to temperature rise is the internal compressive stress that forms when a material’s expansion from heating is prevented. It depends on the modulus of elasticity, coefficient of thermal expansion, and the amount of temperature increase. If not properly managed, such stresses can lead to distortion, cracks, or failure in components. Therefore, providing expansion allowances, choosing suitable materials, and maintaining uniform temperature are essential to control and minimize the effects of thermal stress.