How to Calculate Change in Length and Diameter of Steel Rod

TL;DR

To calculate the change in length and diameter of a steel rod under a tensile load, use the formulas: change in length (Δl) = (P * L) / (A * E) and lateral strain = Poisson's ratio * (Δl / original length). For a 4-meter rod with a 45 kN load, the change in length is 2.86 mm and the change in diameter is approximately 0.003575 mm.

Transcript

hello friends here in this video we will see a problem on calculation of change in length and change in diameter for that we have a question here whatever is given i'll write that in the form of data first by reading the question so let us get started a steel rod 4 meter long length is given 4 meter so it is 4000 mm and 20 mm in diameter diameter d... Read More

Key Insights

• ❓ A steel rod subjected to a tensile load will experience an increase in length and a decrease in diameter.
• 😄 The change in length can be calculated using the formula delta l = pl/ae, where p is the load, l is the length, a is the cross-sectional area, and e is Young's modulus.
• 🥳 The change in diameter can be determined using lateral strain, which is calculated using Poisson's ratio and the linear strain.
• 🥳 Poisson's ratio relates lateral strain to linear strain and is essential for finding the change in diameter.
• 👻 Young's modulus measures the stiffness of a material and allows us to calculate the change in length based on the applied load.
• 🤒 The given problem involves a steel rod with a length of 4 meters and a diameter of 20 mm subjected to a tensile load of 45 kilonewtons.
• 💬 The calculated change in length is 2.86 mm, indicating an increase in length.
• 💱 The calculated change in diameter is 3.575 x 10^-3 mm, indicating a decrease in diameter.

Questions & Answers

Q: How do you calculate the change in length of a steel rod subjected to a tensile load?

To calculate the change in length, use the formula delta l = pl/ae, where p is the load, l is the length, a is the cross-sectional area, and e is Young's modulus. Plug in the given values to find the answer.

Q: How is the change in diameter of the steel rod determined?

The change in diameter is determined using lateral strain. First, calculate the lateral strain using Poisson's ratio and the linear strain. Then, use the equation lateral strain = change in diameter/original diameter to find the change in diameter.

Q: What is the significance of Poisson's ratio in this calculation?

Poisson's ratio is used to relate lateral strain to linear strain. It allows us to determine the change in diameter of the steel rod when subjected to a tensile load parallel to its length.

Q: Can you explain the concept of Young's modulus?

Young's modulus, denoted by e, is a measure of the stiffness or elasticity of a material. It relates the stress (force per unit area) applied to a material to the resulting strain (change in length or deformation) it experiences.

Summary & Key Takeaways

• The video demonstrates how to calculate the change in length and diameter of a steel rod subjected to a tensile load.

• The formula for calculating the change in length is delta l = pl/ae, where p is the load, l is the length, a is the cross-sectional area, and e is Young's modulus.

• The lateral strain is calculated using Poisson's ratio and is used to determine the change in diameter.