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A rigid bar ACDB is pinned at end A and supported by vertical wires of the same material (E-210GPa) and equal cross section area (A-80 mm²) at point C and point D as shown below. The coefficient of thermal expansion of steel is alpha - 12x106/°C. The dimensions are 0.8m, d -2.4m and L - 3.0m. The vertical force P-10 kN. With this information answer the following question: C= I C -L- D 2h B P

A rigid bar ACDB is pinned at end A and supported by vertical wires of the same material (E-210GPa) and equal cross section area (A-80 mm²) at point C and point D as shown below. The coefficient of thermal expansion of steel is alpha - 12x106/°C. The dimensions are 0.8m, d -2.4m and L - 3.0m. The vertical force P-10 kN. With this information answer the following question: C= I C -L- D 2h B P

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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a. When load P is applied at room temperature what will be the tension in wire at C and D? [solve for a value in kN]

b. When load P is already applied and the room temperature is raised by 30 degrees Celsius, what will be the tensions in the wire at C and the wire at D? [solve for a value in kN]

c. What additional temperature rise is required to make the wires at C and D slack(i.e. have zero force)? [in degree Celsius]

### Transcription and Explanation for Educational Purposes **Title: Analysis of a Rigid Bar Supported by Vertical Wires** **Problem Description:** A rigid bar ACDB is pinned at end A and supported by vertical wires of the same material (E = 210 GPa) and equal cross-sectional area (A = 80 mm²) at points C and D as shown in the diagram. - The coefficient of thermal expansion of steel is \(\alpha = 12 \times 10^{-6} \, /°C\). - The dimensions are: - \(c = 0.8 \, m\), - \(d = 2.4 \, m\), - \(L = 3.0 \, m\). - The vertical force \(P = 10 \, kN\). **Diagram Explanation:** The diagram shows a horizontal rigid bar labeled ACDB, positioned with point A on the left side as the pivot point. This bar is supported vertically at points C and D by wires. A vertical force, denoted as \(P\), acts downward at point B, the rightmost end of the bar. - The length from A to C is denoted as \(c = 0.8 \, m\). - The length from C to D is denoted as \(d = 2.4 \, m\). - The total length from A to B is \(L = 3.0 \, m\). - The height between the attachment points of the wires on the bar and the fixed support above is represented as \(h\) for point C, and \(2h\) for point D, indicating that the wire at D is longer. **Objective:** Given these parameters, analyze the distribution of forces and effects of thermal expansion on the bar, using the provided mechanical properties and conditions. **Question to Explore:** - How does the rigid bar react to the applied force \(P\) and thermal expansion, considering the support and material properties? This setup could be used to understand concepts of mechanics such as equilibrium, material deformation, and the impact of thermal expansion on structural elements.
Transcribed Image Text:### Transcription and Explanation for Educational Purposes **Title: Analysis of a Rigid Bar Supported by Vertical Wires** **Problem Description:** A rigid bar ACDB is pinned at end A and supported by vertical wires of the same material (E = 210 GPa) and equal cross-sectional area (A = 80 mm²) at points C and D as shown in the diagram. - The coefficient of thermal expansion of steel is \(\alpha = 12 \times 10^{-6} \, /°C\). - The dimensions are: - \(c = 0.8 \, m\), - \(d = 2.4 \, m\), - \(L = 3.0 \, m\). - The vertical force \(P = 10 \, kN\). **Diagram Explanation:** The diagram shows a horizontal rigid bar labeled ACDB, positioned with point A on the left side as the pivot point. This bar is supported vertically at points C and D by wires. A vertical force, denoted as \(P\), acts downward at point B, the rightmost end of the bar. - The length from A to C is denoted as \(c = 0.8 \, m\). - The length from C to D is denoted as \(d = 2.4 \, m\). - The total length from A to B is \(L = 3.0 \, m\). - The height between the attachment points of the wires on the bar and the fixed support above is represented as \(h\) for point C, and \(2h\) for point D, indicating that the wire at D is longer. **Objective:** Given these parameters, analyze the distribution of forces and effects of thermal expansion on the bar, using the provided mechanical properties and conditions. **Question to Explore:** - How does the rigid bar react to the applied force \(P\) and thermal expansion, considering the support and material properties? This setup could be used to understand concepts of mechanics such as equilibrium, material deformation, and the impact of thermal expansion on structural elements.
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