### Problem 4.125**Description:**The rigid L-shaped member \(ABF\) is supported by a ball-and-socket joint at \(A\) and by three cables. For the loading shown, determine the tension in each cable and the reaction at \(A\).**Diagram Explanation:**1. **Member Structure:** - The structure is a rigid L-shaped member \(ABF\). - It is supported at point \(A\) by a ball-and-socket joint and extends to point \(F\).2. **Coordinate System:** - The diagram uses a 3D Cartesian coordinate system with \(x\), \(y\), and \(z\) axes. - The member layout follows the x-axis towards point \(F\) and the z-axis towards point \(G\).3. **Dimensions:** - The member spans 16 inches from \(A\) to \(H\) along the z-axis, and continues from \(H\) to \(J\) for an additional 16 inches along the y-axis. - The sections \(BG\), \(CD\), \(DE\), and \(EF\) all measure 8 inches along the x-axis.4. **Loads:** - The member experiences three downward forces of 24 lbs each at points \(B\), \(C\), and \(D\).5. **Cables:** - Cable \(H\) connects from point \(H\) to point \(C\). - Cable \(J\) connects from point \(J\) to point \(F\).**Objective:**- **Tension Analysis:** Calculate the tension in each of the cables.- **Reaction Forces:** Determine the reaction forces at the ball-and-socket joint at \(A\).This problem requires applying principles of static equilibrium to solve for unknown forces using vector mechanics.

4.125 The rigid L-shaped member ABF is supported by a ball-and-socket joint at A and by three cables. For the loading shown, determine the tension in each cable and the reaction at A. Z 16 in. 12 in. 9 in. A 16 in. B H 8 in. 16 in. 24 lb 8 in. y D E 8 in. 24 lb 8 in. F X

4.125 The rigid L-shaped member ABF is supported by a ball-and-socket joint at A and by three cables. For the loading shown, determine the tension in each cable and the reaction at A. Z 16 in. 12 in. 9 in. A 16 in. B H 8 in. 16 in. 24 lb 8 in. y D E 8 in. 24 lb 8 in. F X

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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Question

### Problem 4.125

**Description:**

The rigid L-shaped member \(ABF\) is supported by a ball-and-socket joint at \(A\) and by three cables. For the loading shown, determine the tension in each cable and the reaction at \(A\).

**Diagram Explanation:**

1. **Member Structure:**
- The structure is a rigid L-shaped member \(ABF\).
- It is supported at point \(A\) by a ball-and-socket joint and extends to point \(F\).

2. **Coordinate System:**
- The diagram uses a 3D Cartesian coordinate system with \(x\), \(y\), and \(z\) axes.
- The member layout follows the x-axis towards point \(F\) and the z-axis towards point \(G\).

3. **Dimensions:**
- The member spans 16 inches from \(A\) to \(H\) along the z-axis, and continues from \(H\) to \(J\) for an additional 16 inches along the y-axis.
- The sections \(BG\), \(CD\), \(DE\), and \(EF\) all measure 8 inches along the x-axis.

4. **Loads:**
- The member experiences three downward forces of 24 lbs each at points \(B\), \(C\), and \(D\).

5. **Cables:**
- Cable \(H\) connects from point \(H\) to point \(C\).
- Cable \(J\) connects from point \(J\) to point \(F\).

**Objective:**

- **Tension Analysis:** Calculate the tension in each of the cables.
- **Reaction Forces:** Determine the reaction forces at the ball-and-socket joint at \(A\).

This problem requires applying principles of static equilibrium to solve for unknown forces using vector mechanics.

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