B) If the resultant force and couple pair is replaced by a single resultant force, where does its line of action intersects a vertical line along OB, measured from O?

Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
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For the structure and loading system shown:

B) If the resultant force and couple pair is replaced by a single resultant force, where does its line of action intersects a vertical line along OB, measured from O?

### Analysis of Forces and Resultant Movements on a Structure

#### Problem Statement:

The image shows a structural system subjected to various loads. The structure consists of two main members, arranged perpendicularly to each other.

#### Description of the Structure:

- **Horizontal Member (AB):** 
  - Point B has an applied load of 300 lb at an angle of \( \cos^{-1}(\frac{3}{5}) \) from the horizontal.
  - Point A has a downward load of 50 lb, positioned 1 ft from point B.
  - Point A also has a leftward load of 100 lb.
  - The total length between points A and B is 2 ft, with point A located 1 ft from the left end of the horizontal member.
- **Vertical Member (CD):**
  - Positioned vertically from point A to a base support at point O.
  - Point C has a downward load of 50 lb, located 1 ft from A down to C, with another 50 lb to the left at point O.
  - The length from A to C is 3 ft, with sections of 1 ft each from base O and to loading points.

#### Given Task:

B) Determine the location where a single resultant force, replacing the given forces and their moments, intersects a vertical line along the member OB, measured from point O.

#### Graphical Notation and Dimensions:

- **Coordinate Axes:**
  - The x-axis is horizontal, and the y-axis is vertical.
- **Spatial Configuration:**
  - Points on the structure are labeled as A, B, C, and O with respective distances.
  - A rigid base at point O supports the vertical member.

### Steps for Solution (Provided Explanations):

1. **Resultant Force (FR):**
   - Sum all the vertical and horizontal forces to find the components of the resultant force \( \vec{F_R} \).

2. **Moment (MR = MO):**
   - Calculate the moments caused by the distributed forces about point O to find the total moment \( M_O \).

3. **Line of Action:**
   - Determine the point where the resultant force intersects the line OB using the relationship between net force, moments, and distances from point O to give the precise location.

### Conclusion:

This analysis enables the understanding of how complex force interactions can be represented as a single resultant force and moment, simplifying the
Transcribed Image Text:### Analysis of Forces and Resultant Movements on a Structure #### Problem Statement: The image shows a structural system subjected to various loads. The structure consists of two main members, arranged perpendicularly to each other. #### Description of the Structure: - **Horizontal Member (AB):** - Point B has an applied load of 300 lb at an angle of \( \cos^{-1}(\frac{3}{5}) \) from the horizontal. - Point A has a downward load of 50 lb, positioned 1 ft from point B. - Point A also has a leftward load of 100 lb. - The total length between points A and B is 2 ft, with point A located 1 ft from the left end of the horizontal member. - **Vertical Member (CD):** - Positioned vertically from point A to a base support at point O. - Point C has a downward load of 50 lb, located 1 ft from A down to C, with another 50 lb to the left at point O. - The length from A to C is 3 ft, with sections of 1 ft each from base O and to loading points. #### Given Task: B) Determine the location where a single resultant force, replacing the given forces and their moments, intersects a vertical line along the member OB, measured from point O. #### Graphical Notation and Dimensions: - **Coordinate Axes:** - The x-axis is horizontal, and the y-axis is vertical. - **Spatial Configuration:** - Points on the structure are labeled as A, B, C, and O with respective distances. - A rigid base at point O supports the vertical member. ### Steps for Solution (Provided Explanations): 1. **Resultant Force (FR):** - Sum all the vertical and horizontal forces to find the components of the resultant force \( \vec{F_R} \). 2. **Moment (MR = MO):** - Calculate the moments caused by the distributed forces about point O to find the total moment \( M_O \). 3. **Line of Action:** - Determine the point where the resultant force intersects the line OB using the relationship between net force, moments, and distances from point O to give the precise location. ### Conclusion: This analysis enables the understanding of how complex force interactions can be represented as a single resultant force and moment, simplifying the
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