Problem 4 on Stress, Strain - Stress and Strain - Strength of Materials

TL;DR

Calculate stress and Young's modulus for a metal rod under axial load using given dimensions and values.

Transcript

hello friends here in this video we are going to see a problem on calculation of stress and young's modulus let's have a question here a metal rod 24 mm diameter and 2 meter long is subjected to an axial pool of 40 kilo newton if the elongation of the rod is 0.5 mm find the stress induced and the value of young's modulus so this is the question we ... Read More

Key Insights

• 😵 Cross-sectional area is crucial in determining stress for materials under axial loads.
• 😵 Stress is calculated as the applied load divided by the cross-sectional area of the material.
• 🥳 Strain is the ratio of change in length to the original length of the material.
• ❓ Young's modulus relates stress and strain, providing a measure of material stiffness.
• ❓ Hooke's Law is fundamental in understanding the behavior of materials under stress.
• ❓ The elongation of a material under load can be used to calculate its modulus of elasticity.
• 🔬 Understanding stress and Young's modulus is essential in material science and engineering applications.

Questions & Answers

Q: How do you calculate the cross-sectional area of the metal rod?

The cross-sectional area is calculated using the formula A = π/4 * d^2, where d is the diameter of the rod given as 24mm.

Q: What is the formula used to calculate stress in the metal rod?

Stress is calculated as σ = Load / Area, where the load is 40 kN and the area has been determined as 4520.39 mm^2.

Q: How is strain defined in the context of the problem?

Strain is defined as the change in length divided by the original length, calculated as 0.5 mm / 2000 mm = 2.5 x 10^-4.

Q: Explain the significance of Young's modulus in materials science.

Young's modulus represents the elasticity of a material, indicating how much it will deform under stress and is crucial for material selection in engineering applications.

Summary & Key Takeaways

• Given a metal rod with a diameter of 24mm and length of 2 meters, subjected to a 40kN axial load causing an elongation of 0.5mm.

• Calculated the stress induced as 88.42 N/mm^2 and Young's modulus as 353.68 x 10^3 N/mm^2.

• Demonstrated the relationship between stress, strain, and Young's modulus in solving the problem.