Problem No 5on Concept of Temperature Stresses and Strain - Stress and Strain -Strength of Materials

TL;DR

Calculate temperature stress and reaction at the clamps in a steel bar heated and allowed to cool.

Transcript

hello friends here in this video we will see a problem on temperature stress and strain here we have a question whatever is given here first i'll write that in the form of data steel bar of 30 mm diameter is heated to 80 degree celsius and then clamped at the ends it is then allowed to cool down to 30 degree celsius now so 80 degree celsius i'll ke... Read More

Key Insights

• 🤢 The problem involves calculating temperature stress and reaction in a steel bar subjected to heating and cooling.
• 🤢 The clamps attached to the steel bar prevent excessive contraction during cooling.
• ❓ The thermal strain and stress can be calculated using the prevented contraction and Young's modulus.

Questions & Answers

Q: How is the contraction prevented in the steel bar?

The contraction is prevented by clamps attached to the steel rod, which hold the bar and prevent excessive contraction.

Q: What is the thermal strain in the steel bar?

The thermal strain in the steel bar is calculated by dividing the prevented contraction (5 mm) by the original length (10,000 mm). It comes out to be 5 x 10^-4.

Q: How can the thermal stress in the steel bar be calculated?

The thermal stress is calculated by multiplying the thermal strain (5 x 10^-4) by Young's modulus (200 x 10^3). The result is 100 N/mm^2.

Q: What is the reaction at the clamps?

The reaction at the clamps can be calculated using the formula: reaction = stress x area. The stress is 100 N/mm^2 and the area is calculated using the diameter of the steel bar (30 mm). The reaction comes out to be 70.685 kN.

Summary & Key Takeaways

• The problem involves a steel bar that is heated to 80 degrees Celsius and then clamped at the ends, allowed to cool to 30 degrees Celsius.

• The contraction prevented by the clamps is 1 mm.

• Using the given values, the temperature stress and reaction at the clamps can be calculated.