### Problem Statement:A pressure vessel is exposed to a combination of loads as shown below. The vessel (diameter 100 mm) has a wall thickness of 3 mm. Address the following:1. If the yield strength of the material is 144 MPa, determine the largest tension force $ P $ with respect to a factor of safety of 2 applied to the distortional energy theory.### Diagram Explanation:- **Description**: A cylindrical pressure vessel is depicted, showing the points where external forces and moments are acting.- **Forces and Moments**: - The internal pressure $ p = 3.5 $ MPa. - There is a twisting moment $ T = 450 $ N-m applied along the axis of the cylinder. - The axial tension force $ P $ is applied horizontally at both ends of the cylinder.This educational content focuses on understanding the application of mechanical properties and safety factors in engineering design using a practical example of a pressure vessel subject to combined loading scenarios.

Answered: A pressure vessel is exposed to a…

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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### Problem Statement:
A pressure vessel is exposed to a combination of loads as shown below. The vessel (diameter 100 mm) has a wall thickness of 3 mm. Address the following:

1. If the yield strength of the material is 144 MPa, determine the largest tension force $ P $ with respect to a factor of safety of 2 applied to the distortional energy theory.

### Diagram Explanation:
- **Description**: A cylindrical pressure vessel is depicted, showing the points where external forces and moments are acting.
- **Forces and Moments**:
- The internal pressure $ p = 3.5 $ MPa.
- There is a twisting moment $ T = 450 $ N-m applied along the axis of the cylinder.
- The axial tension force $ P $ is applied horizontally at both ends of the cylinder.

This educational content focuses on understanding the application of mechanical properties and safety factors in engineering design using a practical example of a pressure vessel subject to combined loading scenarios.

Expert Solution

Step 1: Determine the given variables

Given data:

$table row straight d equals cell 100 space mm end cell row straight t equals cell 3 space mm end cell row cell Pressure space comma space straight p end cell equals cell 3.5 space MPa end cell row cell Torque space comma space straight T end cell equals cell 450 space Nm end cell row cell Force space end cell equals cell space straight P end cell row cell left parenthesis straight a right parenthesis space straight sigma subscript straight y end cell equals cell 144 space MPa comma space FOS equals 2 end cell row cell left parenthesis straight b right parenthesis space FOS end cell equals cell 1.75 end cell end table$

To find:

(a) The tension force P according to distortional energy theory.

(b) The minimum wall thickness.

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