Handwritten solution please not typed ### Thermal Expansion and Force Analysis in a Rigid StructureIn 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 ExplanationThe 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.

Draw the diagram of link ABCD after heating and cooling the FC and EB respectively.

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

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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