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Learning Goal: To replace force-couple systems with an equivalent force by specifying the magnitude and direction of the equivalent force and the location where the force needs to be applied. Certain force-couple systems can be replaced by a single force. The requirement is that the lines of action of the resultant force, FR, and the resultant couple moment, (MR)o, are perpendicular to each other. This is equivalent to saying the following types of force systems can be simplified to a single force: Figure M 30° X 3 ft A B 2 ft < 2 of 3

Learning Goal: To replace force-couple systems with an equivalent force by specifying the magnitude and direction of the equivalent force and the location where the force needs to be applied. Certain force-couple systems can be replaced by a single force. The requirement is that the lines of action of the resultant force, FR, and the resultant couple moment, (MR)o, are perpendicular to each other. This is equivalent to saying the following types of force systems can be simplified to a single force: Figure M 30° X 3 ft A B 2 ft < 2 of 3

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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**Learning Goal:** To replace force-couple systems with an equivalent force by specifying the magnitude and direction of the equivalent force and the location where the force needs to be applied. Certain force-couple systems can be replaced by a single force. The requirement is that the lines of action of the resultant force, \( F_R \), and the resultant couple moment, \( (M_R)_O \), are perpendicular to each other. This is equivalent to saying the following types of force systems can be simplified to a single force. **Figure:** The diagram shows an L-shaped structure with forces and dimensions indicated on it. It includes: - A vertical section labeled as \( A \) to \( B \), with a height of \( 2 \, \text{ft} \) and an extension continuing to \( C \) totaling \( 4 \, \text{ft} \). - A horizontal section from \( B \) to \( C \) measuring \( 3 \, \text{ft} \). - A force \( F_1 \) acting upwards at an angle towards the horizontal top of the vertical section. It is directed \( 5 \) units in the vertical direction and \( 3 \) units in the horizontal. - A force \( F_2 \) acting towards the middle of the horizontal section with a given angle of \( 30^\circ \) from the horizontal. - A couple moment \( M \) represented by a curved arrow at the corner \( C \) indicating a counterclockwise rotation. - An \( xy \)-axis at the top section aligns with the forces and structure, denoting orientation and reference for vector directions and projections.
Transcribed Image Text:**Learning Goal:** To replace force-couple systems with an equivalent force by specifying the magnitude and direction of the equivalent force and the location where the force needs to be applied. Certain force-couple systems can be replaced by a single force. The requirement is that the lines of action of the resultant force, \( F_R \), and the resultant couple moment, \( (M_R)_O \), are perpendicular to each other. This is equivalent to saying the following types of force systems can be simplified to a single force. **Figure:** The diagram shows an L-shaped structure with forces and dimensions indicated on it. It includes: - A vertical section labeled as \( A \) to \( B \), with a height of \( 2 \, \text{ft} \) and an extension continuing to \( C \) totaling \( 4 \, \text{ft} \). - A horizontal section from \( B \) to \( C \) measuring \( 3 \, \text{ft} \). - A force \( F_1 \) acting upwards at an angle towards the horizontal top of the vertical section. It is directed \( 5 \) units in the vertical direction and \( 3 \) units in the horizontal. - A force \( F_2 \) acting towards the middle of the horizontal section with a given angle of \( 30^\circ \) from the horizontal. - A couple moment \( M \) represented by a curved arrow at the corner \( C \) indicating a counterclockwise rotation. - An \( xy \)-axis at the top section aligns with the forces and structure, denoting orientation and reference for vector directions and projections.
**Analyzing the Force-Couple System on a Bracket** For the bracket shown in the diagram, the forces are given as \( F_1 = 162 \, \text{lb} \), \( F_2 = 54 \, \text{lb} \), and the moment \( M = 550 \, \text{lb} \cdot \text{ft} \). The task is to replace this force and couple system with an equivalent force by specifying: - The magnitude of the force. - The direction in which the force acts. - The intersection point of the force's line of action with member \( AB \), as measured from point \( A \). **Instructions:** - Express your answers as three separate values separated by commas, each to three significant digits. - The angle should be measured counterclockwise from the positive x-axis (which is parallel to segment \( CB \)). **Input Format:** - Provide the equivalent force \( F_R \), the angle \( \theta_R \), and the distance \( d \) in the specific field. **Example Input:** - Example: \( F_R \), \( \theta_R \), \( d \) = [Force in lb, Angle in degrees, Distance in ft] The functionality allows entering values directly into the input fields for automated assessment, and feedback is available via the "View Available Hint(s)" option. **Diagram Explanation:** - The diagram is a detailed figure (referred to as Figure 2) showing the forces acting on the bracket and their points of application. The depiction emphasizes force vectors, moment arms, and relevant geometrical features that aid in calculating the equivalent force and the system's resultant behavior.
Transcribed Image Text:**Analyzing the Force-Couple System on a Bracket** For the bracket shown in the diagram, the forces are given as \( F_1 = 162 \, \text{lb} \), \( F_2 = 54 \, \text{lb} \), and the moment \( M = 550 \, \text{lb} \cdot \text{ft} \). The task is to replace this force and couple system with an equivalent force by specifying: - The magnitude of the force. - The direction in which the force acts. - The intersection point of the force's line of action with member \( AB \), as measured from point \( A \). **Instructions:** - Express your answers as three separate values separated by commas, each to three significant digits. - The angle should be measured counterclockwise from the positive x-axis (which is parallel to segment \( CB \)). **Input Format:** - Provide the equivalent force \( F_R \), the angle \( \theta_R \), and the distance \( d \) in the specific field. **Example Input:** - Example: \( F_R \), \( \theta_R \), \( d \) = [Force in lb, Angle in degrees, Distance in ft] The functionality allows entering values directly into the input fields for automated assessment, and feedback is available via the "View Available Hint(s)" option. **Diagram Explanation:** - The diagram is a detailed figure (referred to as Figure 2) showing the forces acting on the bracket and their points of application. The depiction emphasizes force vectors, moment arms, and relevant geometrical features that aid in calculating the equivalent force and the system's resultant behavior.
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