Short Answer:

Temperature stress is the internal stress developed in a material due to a change in temperature when its expansion or contraction is restricted. When a body is heated, it tends to expand, and when cooled, it tends to contract. If these movements are prevented, internal forces develop inside the material, causing temperature stress. This type of stress is common in bridges, rails, and engine parts where temperature variation is frequent.

In simple terms, temperature stress occurs because of the thermal expansion or contraction of materials under changing temperature conditions. It can lead to deformation or even failure if not properly managed. Engineers often use expansion joints or special materials to reduce temperature stress in structures.

Detailed Explanation :

Temperature Stress

Temperature stress is a very important concept in mechanics of materials, especially in structures and machines that are exposed to varying temperatures. Every material expands when its temperature increases and contracts when the temperature decreases. This change in length is called thermal expansion. The amount of expansion or contraction depends on the material’s coefficient of thermal expansion, which represents how much a unit length of the material changes per degree of temperature change.

However, when a material is not free to expand or contract, internal stresses are produced because of the resistance to this thermal movement. These stresses are called temperature stresses or thermal stresses. The magnitude of temperature stress depends on three main factors:

1. Temperature change (ΔT)
2. Modulus of elasticity (E)
3. Coefficient of thermal expansion (α)

If the body is free to expand, no stress is produced. But when expansion or contraction is prevented, the material experiences stress equal to what would have been required to cause that much strain mechanically.

Derivation of Temperature Stress Formula

Let a bar of original length L be subjected to a temperature change of ΔT.

• Free thermal strain produced in the bar = α × ΔT
  where,
  α = coefficient of thermal expansion (per °C),
  ΔT = change in temperature (°C).

If expansion is prevented, no change in length occurs, meaning the total strain becomes zero. Thus,
Total strain = Mechanical strain + Thermal strain = 0

Therefore,
Mechanical strain = – Thermal strain

Mechanical strain = Stress / E

Hence,

 

This equation gives the temperature stress (σ) induced in the material.

Explanation of the Formula

From the above formula,

• σ is directly proportional to the modulus of elasticity (E): Stiffer materials like steel develop higher thermal stress.
• σ is directly proportional to the coefficient of thermal expansion (α): Materials that expand more with temperature (like aluminum) develop more thermal stress when restrained.
• σ is directly proportional to temperature change (ΔT): Larger temperature differences create higher stresses.

Thus, to reduce temperature stress, engineers either allow expansion by using expansion joints or select materials with lower α or E values depending on the application.

Practical Examples

1. Railway Tracks:
   During summer, rails expand due to heat. If not provided with expansion gaps, they may buckle due to temperature stress.
2. Bridges:
   Bridges are provided with expansion joints so that the deck can expand and contract freely with temperature change without developing high stresses.
3. Piping Systems:
   Steam or hot-water pipes expand when heated. Expansion loops or flexible joints are used to absorb the expansion and prevent damage.
4. Engine Components:
   In engines, parts like pistons and cylinders operate at high temperatures, so their design considers temperature stress to avoid cracking or seizing.

Types of Temperature Stresses

1. Tensile Temperature Stress:
   When a body is cooled and contraction is prevented, the material experiences tensile stress because it tries to contract but cannot.
2. Compressive Temperature Stress:
   When a body is heated and expansion is prevented, compressive stress develops because it tries to expand but is restricted.

Effect of Temperature Stress on Structures

Temperature stress can cause several problems if not managed properly:

• Cracking in concrete structures due to restrained expansion.
• Bending or warping of metal parts in machinery.
• Misalignment of shafts or joints in mechanical systems.
• Fatigue and eventual failure under repeated temperature cycles.

To prevent these, engineers design with proper thermal allowances and use materials that can withstand such changes.

Conclusion

Temperature stress is the internal stress produced in materials when thermal expansion or contraction is restricted. It depends on the modulus of elasticity, coefficient of thermal expansion, and temperature difference. Proper understanding of temperature stress is essential in mechanical and civil engineering to design safe and durable structures. Expansion joints, flexible couplings, and thermal-resistant materials are common methods to control temperature stresses in practice.