Problem 5: Replace the loading by an equivalent resultant force and couple moment at point O. 0.5 m 0.7 m F= (-2i+5j-3 k) kN 0.8 m F = {8 i– 2 k} kN

Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
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**Problem 5:** Replace the loading by an equivalent resultant force and couple moment at point \( O \).

**Diagram Explanation:**

The diagram shows an L-shaped structure with a couple of forces applied to it. The structure is positioned in a 3D coordinate system with axes labeled as \( x \), \( y \), and \( z \).

- **Point \( O \):** This is located at the top of the vertical section of the structure, where the replacement of forces will be analyzed.
  
- **Dimensions:**
  - The vertical section is 0.5 meters in length.
  - The horizontal section of the L-shape is 0.7 meters in length.
  - The base section is 0.8 meters in length.

- **Forces:**
  - \( F_1 = (8i - 2k) \, \text{kN} \): This force is applied at the end of the horizontal section pointing in the direction of the axes \( i \) and \( -k \) (a combination of positive \( x \) and negative \( z \) directions).
  
  - \( F_2 = [-2i + 5j - 3k] \, \text{kN} \): This force is applied at the corner where the vertical and horizontal sections meet, with components in all three directions \( i \), \( j \), and \( k \).

The task is to combine these forces into a single resultant force and couple moment which will act at point \( O \).
Transcribed Image Text:**Problem 5:** Replace the loading by an equivalent resultant force and couple moment at point \( O \). **Diagram Explanation:** The diagram shows an L-shaped structure with a couple of forces applied to it. The structure is positioned in a 3D coordinate system with axes labeled as \( x \), \( y \), and \( z \). - **Point \( O \):** This is located at the top of the vertical section of the structure, where the replacement of forces will be analyzed. - **Dimensions:** - The vertical section is 0.5 meters in length. - The horizontal section of the L-shape is 0.7 meters in length. - The base section is 0.8 meters in length. - **Forces:** - \( F_1 = (8i - 2k) \, \text{kN} \): This force is applied at the end of the horizontal section pointing in the direction of the axes \( i \) and \( -k \) (a combination of positive \( x \) and negative \( z \) directions). - \( F_2 = [-2i + 5j - 3k] \, \text{kN} \): This force is applied at the corner where the vertical and horizontal sections meet, with components in all three directions \( i \), \( j \), and \( k \). The task is to combine these forces into a single resultant force and couple moment which will act at point \( O \).
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