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Find the support reactions at A. Magnitude and direction.

Find the support reactions at A. Magnitude and direction.

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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Find the support reactions at A. Magnitude and direction.

### Understanding Support Reaction in a Cantilever Beam This diagram illustrates a cantilever beam setup with the objective: **"Find the support reaction at A (magnitude and direction)."** #### Diagram Details: 1. **Beam Configuration:** - A vertical cantilever beam is fixed at point A. - The beam is subject to a triangular distributed load starting from point A and tapering out over an 18-foot span. 2. **Distributed Load:** - The load is represented by a right triangle, with the base along the 18-foot length of the beam. - The maximum intensity of the load is 200 pounds per foot (lb/ft) at the farthest point from A. - Load arrows indicate the direction and distribution of force, pointing horizontally from left to right. 3. **Objective:** - To calculate the magnitude and direction of the support reaction at point A due to the triangular distributed load. This involves understanding how the load affects the stability and equilibrium of the structure at the support point. 4. **Analyzing the Load:** - The triangular distributed load can be simplified into a resultant force. The resultant of a triangular load acts at one-third the distance from the base (point A in this case). - The magnitude of the resultant force is calculated by finding the area of the triangular distribution, i.e., \( \frac{1}{2} \times \text{base} \times \text{height} \). Understanding these elements helps in the analysis and determination of the structural reactions necessary to maintain the equilibrium of the beam.
Transcribed Image Text:### Understanding Support Reaction in a Cantilever Beam This diagram illustrates a cantilever beam setup with the objective: **"Find the support reaction at A (magnitude and direction)."** #### Diagram Details: 1. **Beam Configuration:** - A vertical cantilever beam is fixed at point A. - The beam is subject to a triangular distributed load starting from point A and tapering out over an 18-foot span. 2. **Distributed Load:** - The load is represented by a right triangle, with the base along the 18-foot length of the beam. - The maximum intensity of the load is 200 pounds per foot (lb/ft) at the farthest point from A. - Load arrows indicate the direction and distribution of force, pointing horizontally from left to right. 3. **Objective:** - To calculate the magnitude and direction of the support reaction at point A due to the triangular distributed load. This involves understanding how the load affects the stability and equilibrium of the structure at the support point. 4. **Analyzing the Load:** - The triangular distributed load can be simplified into a resultant force. The resultant of a triangular load acts at one-third the distance from the base (point A in this case). - The magnitude of the resultant force is calculated by finding the area of the triangular distribution, i.e., \( \frac{1}{2} \times \text{base} \times \text{height} \). Understanding these elements helps in the analysis and determination of the structural reactions necessary to maintain the equilibrium of the beam.
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