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The bracket ABCDE is hinged at A and has a roller support resting on the angled surface, with a = 35°. The load, P = 250 lbs is applied at both places shown. Solve for reactions at A and E. 3 in. 10 in.- A В 3 in. C 5 in. E D - 8 in.

The bracket ABCDE is hinged at A and has a roller support resting on the angled surface, with a = 35°. The load, P = 250 lbs is applied at both places shown. Solve for reactions at A and E. 3 in. 10 in.- A В 3 in. C 5 in. E D - 8 in.

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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**Educational Content: Analyzing Bracket Reactions** --- **Problem Statement:** The bracket \( ABCDE \) is hinged at point \( A \) and has a roller support resting on an angled surface at point \( E \). The angle of the surface is \( \alpha = 35^\circ \). A load, \( P = 250 \, \text{lbs} \), is applied at both locations shown in the diagram. Your task is to solve for the reactions at points \( A \) and \( E \). **Diagram Explanation:** - The illustration presents a bracket \( ABCDE \) consisting of segments connected at angles. - Point \( A \) is affixed with a hinge, connecting the bracket to a vertical surface. - The bracket extends horizontally from \( A \) to \( B \), a distance of 10 inches. - From \( B \), the bracket moves vertically downward to point \( E \), and it is supported by a roller on an inclined plane. - The inclined plane creates an angle \( \alpha = 35^\circ \) with the horizontal. - A force \( P = 250 \, \text{lbs} \) acts vertically downward at 3 inches to the right of point \( B \). - Another force \( P = 250 \, \text{lbs} \) acts horizontally to the right at a point 3 inches below and 5 inches left of \( D \). - The lower horizontal segment from \( D \) to \( E \) measures 8 inches in length. **Objective:** Determine the reaction forces at the hinge \( A \) and roller support \( E \). **Approach:** To solve for the reactions at \( A \) and \( E \), consider the following steps: 1. Analyze the forces and moments acting on the bracket. 2. Apply equilibrium conditions (sum of forces and sum of moments equal zero). 3. Calculate reactions using trigonometry and equilibrium equations. This problem provides an excellent opportunity to apply principles of statics, such as equilibrium analysis and trigonometry, to solve for unknown reactions—a common task in engineering mechanics.
Transcribed Image Text:**Educational Content: Analyzing Bracket Reactions** --- **Problem Statement:** The bracket \( ABCDE \) is hinged at point \( A \) and has a roller support resting on an angled surface at point \( E \). The angle of the surface is \( \alpha = 35^\circ \). A load, \( P = 250 \, \text{lbs} \), is applied at both locations shown in the diagram. Your task is to solve for the reactions at points \( A \) and \( E \). **Diagram Explanation:** - The illustration presents a bracket \( ABCDE \) consisting of segments connected at angles. - Point \( A \) is affixed with a hinge, connecting the bracket to a vertical surface. - The bracket extends horizontally from \( A \) to \( B \), a distance of 10 inches. - From \( B \), the bracket moves vertically downward to point \( E \), and it is supported by a roller on an inclined plane. - The inclined plane creates an angle \( \alpha = 35^\circ \) with the horizontal. - A force \( P = 250 \, \text{lbs} \) acts vertically downward at 3 inches to the right of point \( B \). - Another force \( P = 250 \, \text{lbs} \) acts horizontally to the right at a point 3 inches below and 5 inches left of \( D \). - The lower horizontal segment from \( D \) to \( E \) measures 8 inches in length. **Objective:** Determine the reaction forces at the hinge \( A \) and roller support \( E \). **Approach:** To solve for the reactions at \( A \) and \( E \), consider the following steps: 1. Analyze the forces and moments acting on the bracket. 2. Apply equilibrium conditions (sum of forces and sum of moments equal zero). 3. Calculate reactions using trigonometry and equilibrium equations. This problem provides an excellent opportunity to apply principles of statics, such as equilibrium analysis and trigonometry, to solve for unknown reactions—a common task in engineering mechanics.
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