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when they are initially pinned to a straight, rigid, horizontal beam BF. Subsequentially, heating of the rods causes them to elongate and leaves the beam in the position denoted by B*D*F*. Point D moves vertically downward by a distance 8p = 0.24 in., and the inclination angle of the beam is 0 = 0.5° in the counterclockwise sense, as indicated on Fig. P2.3-8. Determine the strains e₁, 2, and e, in the three rods. VEXE Jc E O 6 ft (2) (3) B 3 8p -3 ft BL D* P2.3-8 2 ft- F* 4 ft 10

when they are initially pinned to a straight, rigid, horizontal beam BF. Subsequentially, heating of the rods causes them to elongate and leaves the beam in the position denoted by B*D*F*. Point D moves vertically downward by a distance 8p = 0.24 in., and the inclination angle of the beam is 0 = 0.5° in the counterclockwise sense, as indicated on Fig. P2.3-8. Determine the strains e₁, 2, and e, in the three rods. VEXE Jc E O 6 ft (2) (3) B 3 8p -3 ft BL D* P2.3-8 2 ft- F* 4 ft 10

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 2.3-8: **Description:** Vertical rods (1), (2), and (3) are all strain-free when they are initially pinned to a straight, rigid, horizontal beam BF. Subsequently, heating of the rods causes them to elongate and leaves the beam in the position denoted by B*D*F*. Point D moves vertically downward by a distance \( \delta_D = 0.24 \) in., and the inclination angle of the beam is \( \theta = 0.5^\circ \) in the counterclockwise sense, as indicated on Fig. P2.3-8. Determine the strains \( \epsilon_1 \), \( \epsilon_2 \), and \( \epsilon_3 \) in the three rods. **Diagram Explanation:** The diagram accompanying the problem shows three vertical rods labeled (1), (2), and (3). These rods are attached to a horizontal beam BF at positions B, D, and F, respectively. After heating, the new positions of these points are indicated as B*, D*, and F*, depicting the beam's deformed state. Measurements provided in the diagram: - The height of rods (1) and (3) are 6 ft and 4 ft, respectively. - The distance between points B and D is 3 ft. - The distance between points D and F is 2 ft. - The vertical displacement \( \delta_D \) is 0.24 inches. - The beam's inclination angle \( \theta \) post-heating is 0.5° counterclockwise. ### Determination of Strains: To determine the strains \( \epsilon_1 \), \( \epsilon_2 \), and \( \epsilon_3 \), we apply the principles of deformation due to thermal expansion. **Strain Calculation Steps:** 1. **Calculate the displacement in rod 1 and rod 3 due to the beam's tilt and vertical movement:** - \(\tan(\theta) = \frac{\Delta y}{\Delta x}\) - Vertical displacement at B (\(\Delta y_B\)): \(\delta_B = \delta_D - 3 ft \times \tan(\theta)\) - Vertical displacement at F (\(\Delta y_F\)): \(\delta_F = \delta_D + 2 ft \times \tan(\theta)\) 2. **Determine the total length change
Transcribed Image Text:### Problem 2.3-8: **Description:** Vertical rods (1), (2), and (3) are all strain-free when they are initially pinned to a straight, rigid, horizontal beam BF. Subsequently, heating of the rods causes them to elongate and leaves the beam in the position denoted by B*D*F*. Point D moves vertically downward by a distance \( \delta_D = 0.24 \) in., and the inclination angle of the beam is \( \theta = 0.5^\circ \) in the counterclockwise sense, as indicated on Fig. P2.3-8. Determine the strains \( \epsilon_1 \), \( \epsilon_2 \), and \( \epsilon_3 \) in the three rods. **Diagram Explanation:** The diagram accompanying the problem shows three vertical rods labeled (1), (2), and (3). These rods are attached to a horizontal beam BF at positions B, D, and F, respectively. After heating, the new positions of these points are indicated as B*, D*, and F*, depicting the beam's deformed state. Measurements provided in the diagram: - The height of rods (1) and (3) are 6 ft and 4 ft, respectively. - The distance between points B and D is 3 ft. - The distance between points D and F is 2 ft. - The vertical displacement \( \delta_D \) is 0.24 inches. - The beam's inclination angle \( \theta \) post-heating is 0.5° counterclockwise. ### Determination of Strains: To determine the strains \( \epsilon_1 \), \( \epsilon_2 \), and \( \epsilon_3 \), we apply the principles of deformation due to thermal expansion. **Strain Calculation Steps:** 1. **Calculate the displacement in rod 1 and rod 3 due to the beam's tilt and vertical movement:** - \(\tan(\theta) = \frac{\Delta y}{\Delta x}\) - Vertical displacement at B (\(\Delta y_B\)): \(\delta_B = \delta_D - 3 ft \times \tan(\theta)\) - Vertical displacement at F (\(\Delta y_F\)): \(\delta_F = \delta_D + 2 ft \times \tan(\theta)\) 2. **Determine the total length change
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