**Problem 5.73: Analysis of Thick-Walled Cylinders****Description:**Two thick-walled cylinders are mated with no gap or interference. Initially, the inner cylinder has an inner radius \(a\) and outer radius \(b\), while the outer cylinder has an inner radius \(b\) and outer radius \(c\). The inner cylinder is made of a material with a modulus of elasticity \(E_i\) and a Poisson’s ratio \(\nu_i\). The outer cylinder is made of a material with a modulus of elasticity \(E_o\) and a Poisson’s ratio \(\nu_o\). The interior of the inner cylinder is then subjected to a pressure \(p_i\).**Tasks:**(a) **Determine the equation for the resulting interface pressure at \( r = b \).**(b) **Given:** - Internal pressure, \(p_i = 1 \, \text{MPa}\) - Modulus of elasticity of inner cylinder, \(E_i = 210 \, \text{GPa}\) - Poisson’s ratio of inner cylinder, \(\nu_i = 0.3\) - Modulus of elasticity of outer cylinder, \(E_o = 105 \, \text{GPa}\) - Poisson’s ratio of outer cylinder, \(\nu_o = 0.32\) - Inner radius, \(a = 100 \, \text{mm}\) - Interface radius, \(b = 150 \, \text{mm}\) - Outer radius, \(c = 200 \, \text{mm}\)**Objective:** Determine and plot the tangential and radial stresses in each cylinder.**Graph/Diagram Explanation:** Not applicable as there is no graph or diagram provided in the text.

Answered: Image /qna-images/answer/778b6906-814f-4ec9-a329-9fa38afd0ee0.jpg

[wo thick-walled cylinders are mated with no gap or interference. Initial he inner cylinder has an inner radius a and outer radius b, whereas the out cylinder has an inner radius b and outer radius c. The inner cylinder is of material with a modulus of elasticity E; and a Poisson's ratio v;, whereas t outer cylinder is of a material with a modulus of elasticity E, and a Poisson ratio vp. The inside of the inner cylinder is then subjected to a pressure p¡. a) Determine the equation for the resulting interface pressure p at r = b. b) If p; = 1 MPa, E; = 210 GPa, v; = 0.3, E, = 105 GPa, v, = 0.32, a = 200 mm, determine and plot the 100 mm, b = 150 mm, and c

[wo thick-walled cylinders are mated with no gap or interference. Initial he inner cylinder has an inner radius a and outer radius b, whereas the out cylinder has an inner radius b and outer radius c. The inner cylinder is of material with a modulus of elasticity E; and a Poisson's ratio v;, whereas t outer cylinder is of a material with a modulus of elasticity E, and a Poisson ratio vp. The inside of the inner cylinder is then subjected to a pressure p¡. a) Determine the equation for the resulting interface pressure p at r = b. b) If p; = 1 MPa, E; = 210 GPa, v; = 0.3, E, = 105 GPa, v, = 0.32, a = 200 mm, determine and plot the 100 mm, b = 150 mm, and c

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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Axial Load

When a bar of the uniform cross-section is acted by a load, such that the load acts along the longitudinal axis of the bar, such kinds of loadings are known as axial loadings. In general terms, a load is an external force acting on a component. An axial load acts perpendicular to the geometric cross-section of the component. Based on the direction of the application of the load, an axial load can be tensile or compressive. The analysis of bodies under the action of axial loads is generally studied under the branch of mechanics, known as statics.

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**Problem 5.73: Analysis of Thick-Walled Cylinders**

**Description:**
Two thick-walled cylinders are mated with no gap or interference. Initially, the inner cylinder has an inner radius \(a\) and outer radius \(b\), while the outer cylinder has an inner radius \(b\) and outer radius \(c\). The inner cylinder is made of a material with a modulus of elasticity \(E_i\) and a Poisson’s ratio \(\nu_i\). The outer cylinder is made of a material with a modulus of elasticity \(E_o\) and a Poisson’s ratio \(\nu_o\). The interior of the inner cylinder is then subjected to a pressure \(p_i\).

**Tasks:**

(a) **Determine the equation for the resulting interface pressure at \( r = b \).**

(b) **Given:**
- Internal pressure, \(p_i = 1 \, \text{MPa}\)
- Modulus of elasticity of inner cylinder, \(E_i = 210 \, \text{GPa}\)
- Poisson’s ratio of inner cylinder, \(\nu_i = 0.3\)
- Modulus of elasticity of outer cylinder, \(E_o = 105 \, \text{GPa}\)
- Poisson’s ratio of outer cylinder, \(\nu_o = 0.32\)
- Inner radius, \(a = 100 \, \text{mm}\)
- Interface radius, \(b = 150 \, \text{mm}\)
- Outer radius, \(c = 200 \, \text{mm}\)

**Objective:** Determine and plot the tangential and radial stresses in each cylinder.

**Graph/Diagram Explanation:**
Not applicable as there is no graph or diagram provided in the text.

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