Question

Consider a 250 mm $\times$ 15 mm $\times$ 10 mm steel bar which is free to expand is heated from $15^\circ$C to $40^\circ$C. What will be developed?

• A. Compressive stress
• B. Tensile stress
• C. Shear stress
• D. No stress

Hint:

Thermal stress develops only when expansion or contraction is restrained. Free expansion produces strain but no stress.

Answer 1

The Correct Option is D

Step 1: Understand thermal expansion.
When a material is heated, it tends to expand. Thermal stress develops only if this expansion is restrained.
Step 2: Analyze the given condition.
The steel bar is stated to be free to expand. This means there is no external restraint preventing its thermal expansion.
Step 3: Apply the concept of thermal stress.
Thermal stress is given by:
\[ \sigma = E \alpha \Delta T \]
This formula applies only when expansion is fully or partially restrained.
Since the bar is free, no resistance is offered against expansion.
Step 4: Conclusion.
As there is no restraint, no stress is developed in the bar.