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The overhanging beam, as shown in the Figure below, is supported by a pin at A. Identify the support reactions at A only. -8 m 400 N B 800 N·m 4 m 5 m

The overhanging beam, as shown in the Figure below, is supported by a pin at A. Identify the support reactions at A only. -8 m 400 N B 800 N·m 4 m 5 m

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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### Analysis of Support Reactions at Point A for an Overhanging Beam In this problem, we are presented with an overhanging beam, which is supported by a pin at point A. The objective is to determine the support reactions solely at point A. #### Figure Description: The provided figure illustrates an overhanging beam that is fixed at point A. The beam extends horizontally to the right from point A, with point B acting as an intermediate support. Here are the specific details from the figure: 1. **Forces and Moments:** - A vertical downward force of 400 N is applied on the beam at a distance of 8 meters to the right of point A. - A counterclockwise moment of 800 N·m is applied at the far right end of the beam. 2. **Dimensions:** - The total length of the beam is 12 meters, divided into two segments: 8 meters from A to B, and 4 meters from B to the end. - The height from the beam’s end where the moment is applied to the ground is 5 meters. #### Problem Statement: 1. **Find the support reactions at point A only.** - This includes any horizontal (Ax) and vertical (Ay) reaction forces and a moment (MA) at the point of support. By examining the diagram, we will need to apply concepts of static equilibrium to solve for the unknown reactions at support A. The conditions of equilibrium will include: 1. The sum of all horizontal forces must be zero. 2. The sum of all vertical forces must be zero. 3. The sum of all moments about point A must be zero. These principles will be applied to determine the support reactions at point A, ensuring that the beam remains statically balanced under the given forces and moment.
Transcribed Image Text:### Analysis of Support Reactions at Point A for an Overhanging Beam In this problem, we are presented with an overhanging beam, which is supported by a pin at point A. The objective is to determine the support reactions solely at point A. #### Figure Description: The provided figure illustrates an overhanging beam that is fixed at point A. The beam extends horizontally to the right from point A, with point B acting as an intermediate support. Here are the specific details from the figure: 1. **Forces and Moments:** - A vertical downward force of 400 N is applied on the beam at a distance of 8 meters to the right of point A. - A counterclockwise moment of 800 N·m is applied at the far right end of the beam. 2. **Dimensions:** - The total length of the beam is 12 meters, divided into two segments: 8 meters from A to B, and 4 meters from B to the end. - The height from the beam’s end where the moment is applied to the ground is 5 meters. #### Problem Statement: 1. **Find the support reactions at point A only.** - This includes any horizontal (Ax) and vertical (Ay) reaction forces and a moment (MA) at the point of support. By examining the diagram, we will need to apply concepts of static equilibrium to solve for the unknown reactions at support A. The conditions of equilibrium will include: 1. The sum of all horizontal forces must be zero. 2. The sum of all vertical forces must be zero. 3. The sum of all moments about point A must be zero. These principles will be applied to determine the support reactions at point A, ensuring that the beam remains statically balanced under the given forces and moment.
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