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FIND THE ouAFORT EACTIONS ArT 2K/ft 30

FIND THE ouAFORT EACTIONS ArT 2K/ft 30

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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Find the support reactions at A and B

**Title: Analysis of Support Reactions in Structural Beams** **Objective:** Determine the support reactions at points \( A \) and \( B \) in a beam system subjected to a combination of forces. **Diagram Explanation:** The diagram illustrates a beam with the following characteristics: - **Support Types:** - Point \( A \) is supported by a pin, which provides vertical and horizontal reaction components. - Point \( B \) is supported by a roller, providing only a vertical reaction component. - **Applied Forces:** - A concentrated force of \( 5 \, \text{kips} \) is acting at an angle of \( 30^\circ \) from the horizontal, positioned 5 feet from point \( A \). - A uniform distributed load of \( 2 \, \text{kips/ft} \) spans a length of 10 feet, starting 5 feet from point \( A \) and ending at point \( B \). **Beam Dimensions:** - The total length of the beam from \( A \) to \( B \) is 20 feet, with distances marked at 5 feet intervals from \( A \). **Solution Approach:** 1. Resolve the angled force into horizontal and vertical components. 2. Apply equilibrium equations (\(\Sigma F_x = 0\), \(\Sigma F_y = 0\), \(\Sigma M = 0\)) to solve for unknown reactions at \( A \) and \( B \). This analysis provides foundational knowledge required to calculate forces in static beam systems, essential for ensuring structural integrity and safety in engineering designs.
Transcribed Image Text:**Title: Analysis of Support Reactions in Structural Beams** **Objective:** Determine the support reactions at points \( A \) and \( B \) in a beam system subjected to a combination of forces. **Diagram Explanation:** The diagram illustrates a beam with the following characteristics: - **Support Types:** - Point \( A \) is supported by a pin, which provides vertical and horizontal reaction components. - Point \( B \) is supported by a roller, providing only a vertical reaction component. - **Applied Forces:** - A concentrated force of \( 5 \, \text{kips} \) is acting at an angle of \( 30^\circ \) from the horizontal, positioned 5 feet from point \( A \). - A uniform distributed load of \( 2 \, \text{kips/ft} \) spans a length of 10 feet, starting 5 feet from point \( A \) and ending at point \( B \). **Beam Dimensions:** - The total length of the beam from \( A \) to \( B \) is 20 feet, with distances marked at 5 feet intervals from \( A \). **Solution Approach:** 1. Resolve the angled force into horizontal and vertical components. 2. Apply equilibrium equations (\(\Sigma F_x = 0\), \(\Sigma F_y = 0\), \(\Sigma M = 0\)) to solve for unknown reactions at \( A \) and \( B \). This analysis provides foundational knowledge required to calculate forces in static beam systems, essential for ensuring structural integrity and safety in engineering designs.
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