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In the configuration shown, all members are at a uniform temperature and ABCD is vertical. Then the horizontal bars are subjected to different temperature changes: AT1= -50 K for EB and AT2= 75 K for FC. The bars EB and FC have the same length L = 1.5 m, thermal expansion coefficient a = 12 x 10-6/K, cross-sectional area = 50 mm² and Young's modulus E = 200 GPa. Assuming that the vertical bar ABCD is rigid, find the displacement at point D and the forces in bars EB and FC. The length of the rigid bar ABCD is 3 m. E D C B A

In the configuration shown, all members are at a uniform temperature and ABCD is vertical. Then the horizontal bars are subjected to different temperature changes: AT1= -50 K for EB and AT2= 75 K for FC. The bars EB and FC have the same length L = 1.5 m, thermal expansion coefficient a = 12 x 10-6/K, cross-sectional area = 50 mm² and Young's modulus E = 200 GPa. Assuming that the vertical bar ABCD is rigid, find the displacement at point D and the forces in bars EB and FC. The length of the rigid bar ABCD is 3 m. E D C B A

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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### Thermal Expansion and Force Analysis in a Rigid Structure In the configuration shown, all members are initially at a uniform temperature and the vertical bar ABCD is positioned vertically. The horizontal bars are then subjected to different temperature changes: - ΔT₁ = -50 K for bar EB - ΔT₂ = 75 K for bar FC **Properties of the Bars:** - **Length (L):** 1.5 m - **Thermal Expansion Coefficient (α):** \(12 \times 10^{-6} / K\) - **Cross-sectional Area:** \(50 \, \text{mm}^2\) - **Young's Modulus (E):** 200 GPa **Objective:** Determine the displacement at point D and calculate the forces in bars EB and FC. The length of the rigid vertical bar ABCD is 3 m. #### Diagram Explanation The diagram on the right illustrates the setup: - **ABCD** is the rigid vertical bar, 3 meters long, divided into three equal parts, each labeled "a." - Bars **EB** and **FC** are horizontal and connected at points B and C on the vertical bar, respectively. - Points E and F are fixed supports. **Analysis Strategy:** 1. **Thermal Expansion Effects:** Compute the change in length of each bar due to temperature changes using the formula for thermal expansion: \[ \Delta L = \alpha \cdot L \cdot \Delta T \] 2. **Force Calculation:** Use equilibrium equations and material properties to calculate forces in the bars. 3. **Displacement Calculation:** Determine the displacement at point D considering the effects of thermal expansion and rigidity constraints. This exercise provides a practical application of thermal expansion, material mechanics, and equilibrium in rigid body systems.
Transcribed Image Text:### Thermal Expansion and Force Analysis in a Rigid Structure In the configuration shown, all members are initially at a uniform temperature and the vertical bar ABCD is positioned vertically. The horizontal bars are then subjected to different temperature changes: - ΔT₁ = -50 K for bar EB - ΔT₂ = 75 K for bar FC **Properties of the Bars:** - **Length (L):** 1.5 m - **Thermal Expansion Coefficient (α):** \(12 \times 10^{-6} / K\) - **Cross-sectional Area:** \(50 \, \text{mm}^2\) - **Young's Modulus (E):** 200 GPa **Objective:** Determine the displacement at point D and calculate the forces in bars EB and FC. The length of the rigid vertical bar ABCD is 3 m. #### Diagram Explanation The diagram on the right illustrates the setup: - **ABCD** is the rigid vertical bar, 3 meters long, divided into three equal parts, each labeled "a." - Bars **EB** and **FC** are horizontal and connected at points B and C on the vertical bar, respectively. - Points E and F are fixed supports. **Analysis Strategy:** 1. **Thermal Expansion Effects:** Compute the change in length of each bar due to temperature changes using the formula for thermal expansion: \[ \Delta L = \alpha \cdot L \cdot \Delta T \] 2. **Force Calculation:** Use equilibrium equations and material properties to calculate forces in the bars. 3. **Displacement Calculation:** Determine the displacement at point D considering the effects of thermal expansion and rigidity constraints. This exercise provides a practical application of thermal expansion, material mechanics, and equilibrium in rigid body systems.
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