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Prob. 2.3-4. A "rigid" beam BC of length L is supported by a fixed pin at C and by an extensible rod AB, whose original length is also L. When 0= 45°, rod AB is horizontal and strain free, that is, e(0 = 45°) = 0. (a) Determine an expression for e(0), the strain in rod AB, as a function of the angle shown in Fig. P2.3-4, valid for 45° 0 ≤ 90°. (b) Write a computer program and use it to plot the expres- sion for e(0) for the range 45° 0 ≤ 90°. B Rigid

Prob. 2.3-4. A "rigid" beam BC of length L is supported by a fixed pin at C and by an extensible rod AB, whose original length is also L. When 0= 45°, rod AB is horizontal and strain free, that is, e(0 = 45°) = 0. (a) Determine an expression for e(0), the strain in rod AB, as a function of the angle shown in Fig. P2.3-4, valid for 45° 0 ≤ 90°. (b) Write a computer program and use it to plot the expres- sion for e(0) for the range 45° 0 ≤ 90°. B Rigid

Elements Of Electromagnetics
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 2.3-4: Analysis of Strain in an Extensible Rod **Problem Statement:** A "rigid" beam BC of length \(L\) is supported by a fixed pin at \(C\) and by an extensible rod \(AB\), whose original length is also \(L\). When \(\theta = 45^\circ\), rod \(AB\) is horizontal and strain-free, that is, \(\epsilon(\theta = 45^\circ) = 0\). #### Objectives: (a) Determine an expression for \(\epsilon(\theta)\), the strain in rod \(AB\), as a function of the angle \(\theta\) shown in Fig. P2.3-4, valid for \(45^\circ \leq \theta \leq 90^\circ\). (b) Write a computer program and use it to plot the expression for \(\epsilon(\theta)\) for the range \(45^\circ \leq \theta \leq 90^\circ\). #### Explanation of Diagram: The diagram in Fig. P2.3-4 shows a beam-rod assembly where: - Point \(C\) is the fixed pin support. - Point \(A\) is where the extensible rod is fixed to a wall. - \(A\)B is the extensible rod of original length \(L\). - \(B\)C is the rigid beam also of length \(L\). - The angle \(\theta\) represents the rotation of beam \(BC\) from the horizontal axis. When the system is in a strain-free state, \(\theta = 45^\circ\). Understanding the setup and behavior of this mechanical system is crucial for applications related to mechanical engineering and material science, particularly in analyzing how structural components deform under various conditions. **Steps to Solve:** 1. **Derive the Expression for \(\epsilon(\theta)\):** - Utilize geometric relationships and trigonometry to express the change in length of rod \(AB\) as a function of angle \(\theta\). - Consider both the initial (strain-free) state and the deformed states. 2. **Develop a Computer Program:** - Implement the derived mathematical expression in a programming environment (e.g., Python, MATLAB). - Generate a plot of \(\epsilon(\theta)\) over the specified range of angles. This problem
Transcribed Image Text:### Problem 2.3-4: Analysis of Strain in an Extensible Rod **Problem Statement:** A "rigid" beam BC of length \(L\) is supported by a fixed pin at \(C\) and by an extensible rod \(AB\), whose original length is also \(L\). When \(\theta = 45^\circ\), rod \(AB\) is horizontal and strain-free, that is, \(\epsilon(\theta = 45^\circ) = 0\). #### Objectives: (a) Determine an expression for \(\epsilon(\theta)\), the strain in rod \(AB\), as a function of the angle \(\theta\) shown in Fig. P2.3-4, valid for \(45^\circ \leq \theta \leq 90^\circ\). (b) Write a computer program and use it to plot the expression for \(\epsilon(\theta)\) for the range \(45^\circ \leq \theta \leq 90^\circ\). #### Explanation of Diagram: The diagram in Fig. P2.3-4 shows a beam-rod assembly where: - Point \(C\) is the fixed pin support. - Point \(A\) is where the extensible rod is fixed to a wall. - \(A\)B is the extensible rod of original length \(L\). - \(B\)C is the rigid beam also of length \(L\). - The angle \(\theta\) represents the rotation of beam \(BC\) from the horizontal axis. When the system is in a strain-free state, \(\theta = 45^\circ\). Understanding the setup and behavior of this mechanical system is crucial for applications related to mechanical engineering and material science, particularly in analyzing how structural components deform under various conditions. **Steps to Solve:** 1. **Derive the Expression for \(\epsilon(\theta)\):** - Utilize geometric relationships and trigonometry to express the change in length of rod \(AB\) as a function of angle \(\theta\). - Consider both the initial (strain-free) state and the deformed states. 2. **Develop a Computer Program:** - Implement the derived mathematical expression in a programming environment (e.g., Python, MATLAB). - Generate a plot of \(\epsilon(\theta)\) over the specified range of angles. This problem
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