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Bar AB in the three-hinged arch is horizontal. (Assume that the +x-axis is to the right and the +y-axis is up along the page. 2.1 kips A B 3.2 kips 10 ft 4 ft→< 8 ft -4 ft><4 ft>

Bar AB in the three-hinged arch is horizontal. (Assume that the +x-axis is to the right and the +y-axis is up along the page. 2.1 kips A B 3.2 kips 10 ft 4 ft→< 8 ft -4 ft><4 ft>

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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**Diagram Explanation:** The diagram shows a three-hinged arch with points A, B, and C. Bar AB is horizontal. The following features are present: - Point A is a support on the left side with an unknown force \( A_x \) (horizontal) and \( A_y \) (vertical). - A vertical load of 2.1 kips is applied at point B. - A vertical load of 3.2 kips is applied at the end of the inclined section, 10 feet above point C. - Point C is a support on the right side with an unknown force \( C_x \) (horizontal) and \( C_y \) (vertical). **Dimensions:** - Distance from A to B is 8 feet. - Distance from B to C horizontally is 8 feet. - Vertical height from the horizontal line through A and B to the load at C is 10 feet. **Calculations Required:** 1. **Determine the reactions at A and C in pounds:** - For \( A_x \) and \( C_x \): Input magnitude; directions are shown with arrows. - For \( A_y \) and \( C_y \): Input magnitude; directions are shown with arrows. 2. **Determine the forces pin B exerts on each member in pounds:** - \( B_x \) for the horizontal component. - \( B_y \) for the vertical component. These values must comply with the equilibrium conditions of a static system: - Sum of horizontal forces = 0 - Sum of vertical forces = 0 - Sum of moments about any point = 0 This setup is used to solve for forces in a statically determinate structure, often seen in structural engineering problems.
Transcribed Image Text:**Diagram Explanation:** The diagram shows a three-hinged arch with points A, B, and C. Bar AB is horizontal. The following features are present: - Point A is a support on the left side with an unknown force \( A_x \) (horizontal) and \( A_y \) (vertical). - A vertical load of 2.1 kips is applied at point B. - A vertical load of 3.2 kips is applied at the end of the inclined section, 10 feet above point C. - Point C is a support on the right side with an unknown force \( C_x \) (horizontal) and \( C_y \) (vertical). **Dimensions:** - Distance from A to B is 8 feet. - Distance from B to C horizontally is 8 feet. - Vertical height from the horizontal line through A and B to the load at C is 10 feet. **Calculations Required:** 1. **Determine the reactions at A and C in pounds:** - For \( A_x \) and \( C_x \): Input magnitude; directions are shown with arrows. - For \( A_y \) and \( C_y \): Input magnitude; directions are shown with arrows. 2. **Determine the forces pin B exerts on each member in pounds:** - \( B_x \) for the horizontal component. - \( B_y \) for the vertical component. These values must comply with the equilibrium conditions of a static system: - Sum of horizontal forces = 0 - Sum of vertical forces = 0 - Sum of moments about any point = 0 This setup is used to solve for forces in a statically determinate structure, often seen in structural engineering problems.
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