Structural Analysis
6th Edition
ISBN: 9781337630931
Author: KASSIMALI, Aslam.
Publisher: Cengage,
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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 \( O \).](https://content.bartleby.com/qna-images/question/6177f43c-2ad1-4555-88bc-49b05c35e250/ec9164f6-a690-40cd-b1b8-aeadc304d6cd/xiakh2_processed.jpeg)
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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