Problem 1 on Calculation of Stress in Each Material - Stress and Strain - Strength of Materials

TL;DR

Calculate the stresses in copper and steel wires, given their dimensions, length, load, and Young's modulus.

Transcript

hello friends here in this video we will see a problem on calculation of stress in each material here we have a question a copper wire 20 mm square in cross section and steel wire 30 mm square in cross section both one meter long are rigidly connected to plates on either side so i'll write them in the data here two different materials are given cop... Read More

Key Insights

• 🍽️ The copper and steel wires are rigidly connected to plates.
• 😵 The dimensions of the wires, such as cross-sectional area and length, are provided.
• 🛜 The load is equally shared between the wires.
• 👮 Hooke's law is used to calculate the stresses in the wires.

Questions & Answers

Q: How are the copper and steel wires connected in this problem?

The copper wire and steel wire are rigidly connected to plates on either side.

Q: What are the dimensions of the copper and steel wires?

The copper wire has a cross-sectional area of 20 mm square, while the steel wire has a cross-sectional area of 30 mm square.

Q: How is the load shared between the copper and steel wires?

The total load is shared equally by the copper and steel wires since they are rigidly connected.

Q: What is the equation to calculate the stress in the steel wire?

The stress in the steel wire is equal to 20 times the stress in the copper wire.

Q: How is the total load calculated?

The total load is equal to the load shared by the steel wire plus the load shared by the copper wire.

Q: How can we calculate the strain in the copper and steel wires?

Since the wires are rigidly connected and have the same length and loading conditions, their strains are equal.

Q: What is Hooke's law?

Hooke's law states that stress is equal to the product of strain and Young's modulus.

Q: What is the stress in the steel wire?

By substituting the values, the stress in the steel wire is calculated to be 258.06 newton per mm square.

Summary & Key Takeaways

• A copper wire and a steel wire, both one meter long, are rigidly connected to plates on either side.

• The wires share a load of 8 kilo newtons.

• Using the given dimensions and Young's modulus, we need to calculate the stresses produced in each material.