**Problem Description: Steel Pipe Compression Analysis**A steel pipe is given with the following parameters:- Length \( L = 4.0 \) ft- Outside diameter \( d_2 = 6.0 \) in- Inside diameter \( d_1 = 4.5 \) inThis pipe is subjected to an axial compressive force \( P = 140 \) kip. The material properties are as follows:- Modulus of elasticity \( E = 30,000 \) ksi- Poisson’s ratio \( \nu = 0.30 \)**Objective:**Determine the following quantities for the pipe:(a) The shortening \( \delta \)(b) The lateral strain \( \epsilon_{\text{lat}} \)(c) The increase in the outer diameter \( \Delta d_2 \)(d) The modulus of rigidity \( G \)**Diagram Explanation:**The diagram depicts a cylindrical steel pipe positioned vertically, with a downward axial force \( P \) applied at the top. The diagram shows:- The length \( L \) of the cylinder.- The outer diameter \( d_2 \) and inner diameter \( d_1 \).- The pipe is compressed from the top, which potentially shortens its height and changes its diameter.**Note:**- \( \text{ksi} = 1000 \) psi- \( \text{kip} = 1000 \) lbf

Answered: Image /qna-images/answer/959d9387-1354-47cc-841a-6111af5d8b30.jpg

A steel pipe of length L = 4.0 ft, outside diameter d₂ = 6.0 in., and inside diameter d₁ = 4.5 in. is compressed by an axial force P = 140 kip. The material has a modulus of elasticity E = 30,000 ksi and Poisson's ratio v = 0.30. Determine the following quantities for the pipe: (a) the shortening 6, (b) the lateral strain € lat, (c) the increase in the outer diameter 4d₂ (e) the modulus of rigidity G Reminder: ksi = 1000 psi, and kip = 1000 lbf P -d₁-

A steel pipe of length L = 4.0 ft, outside diameter d₂ = 6.0 in., and inside diameter d₁ = 4.5 in. is compressed by an axial force P = 140 kip. The material has a modulus of elasticity E = 30,000 ksi and Poisson's ratio v = 0.30. Determine the following quantities for the pipe: (a) the shortening 6, (b) the lateral strain € lat, (c) the increase in the outer diameter 4d₂ (e) the modulus of rigidity G Reminder: ksi = 1000 psi, and kip = 1000 lbf P -d₁-

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Strain energy

The term strain indicates the variation in an object's length, area, and volume when the object is subjected to an external force. The external force may be of normal, shear, moment, torque, etc. The strain in an object depends on the types of external force and cross-section of the object. Mathematically, the evaluation of strain can be obtained with the help of elastic constants.

Question

**Problem Description: Steel Pipe Compression Analysis**

A steel pipe is given with the following parameters:
- Length \( L = 4.0 \) ft
- Outside diameter \( d_2 = 6.0 \) in
- Inside diameter \( d_1 = 4.5 \) in

This pipe is subjected to an axial compressive force \( P = 140 \) kip. The material properties are as follows:
- Modulus of elasticity \( E = 30,000 \) ksi
- Poisson’s ratio \( \nu = 0.30 \)

**Objective:**

Determine the following quantities for the pipe:
(a) The shortening \( \delta \)
(b) The lateral strain \( \epsilon_{\text{lat}} \)
(c) The increase in the outer diameter \( \Delta d_2 \)
(d) The modulus of rigidity \( G \)

**Diagram Explanation:**

The diagram depicts a cylindrical steel pipe positioned vertically, with a downward axial force \( P \) applied at the top. The diagram shows:
- The length \( L \) of the cylinder.
- The outer diameter \( d_2 \) and inner diameter \( d_1 \).
- The pipe is compressed from the top, which potentially shortens its height and changes its diameter.

**Note:**

- \( \text{ksi} = 1000 \) psi
- \( \text{kip} = 1000 \) lbf

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