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F4-30. Replace the loading system by an equivalent resultant force and couple moment acting at point O. F1 = 100 N M. = 75 N•m 0.3 m F2 200 N 0.4 m 0.5 m y

F4-30. Replace the loading system by an equivalent resultant force and couple moment acting at point O. F1 = 100 N M. = 75 N•m 0.3 m F2 200 N 0.4 m 0.5 m y

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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**F4–30.** Replace the loading system by an equivalent resultant force and couple moment acting at point \( O \). **Description of Diagram:** The diagram shows a three-dimensional structure with two forces and a couple moment. The key components are as follows: 1. **Coordinate Axes:** - The origin \( O \) is marked, with axes extending in the \( x \), \( y \), and \( z \) directions. 2. **Forces:** - \( F_1 = 100 \, \text{N} \) acts in the vertical plane downward along the negative \( z \)-axis, 0.3 meters from the origin \( O \). - \( F_2 = 200 \, \text{N} \) acts diagonally in the direction shown, 0.4 meters in the \( y \)-direction from the origin \( O \). 3. **Moment:** - \( M_c = 75 \, \text{N} \cdot \text{m} \) acts in the clockwise direction around the axis of the upper part of the structure. 4. **Dimensions:** - The distance from \( O \) along the \( x \)-axis to the vertical force \( F_1 \) is 0.5 meters. - The distance from \( O \) along the \( y \)-axis to the line of action of \( F_2 \) is 0.4 meters. The goal is to determine an equivalent system of this loading that consists of a single resultant force and a couple moment at the point \( O \).
Transcribed Image Text:**F4–30.** Replace the loading system by an equivalent resultant force and couple moment acting at point \( O \). **Description of Diagram:** The diagram shows a three-dimensional structure with two forces and a couple moment. The key components are as follows: 1. **Coordinate Axes:** - The origin \( O \) is marked, with axes extending in the \( x \), \( y \), and \( z \) directions. 2. **Forces:** - \( F_1 = 100 \, \text{N} \) acts in the vertical plane downward along the negative \( z \)-axis, 0.3 meters from the origin \( O \). - \( F_2 = 200 \, \text{N} \) acts diagonally in the direction shown, 0.4 meters in the \( y \)-direction from the origin \( O \). 3. **Moment:** - \( M_c = 75 \, \text{N} \cdot \text{m} \) acts in the clockwise direction around the axis of the upper part of the structure. 4. **Dimensions:** - The distance from \( O \) along the \( x \)-axis to the vertical force \( F_1 \) is 0.5 meters. - The distance from \( O \) along the \( y \)-axis to the line of action of \( F_2 \) is 0.4 meters. The goal is to determine an equivalent system of this loading that consists of a single resultant force and a couple moment at the point \( O \).
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