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eplace the distributed loading shown with an equivalent resultant force, calculating both (a) the magnitude of the resultant force and (b) the location of the resultant force, as measured from point B.

eplace the distributed loading shown with an equivalent resultant force, calculating both (a) the magnitude of the resultant force and (b) the location of the resultant force, as measured from point B.

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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Replace the distributed loading shown with an equivalent resultant force, calculating both (a) the magnitude of the resultant force and (b) the location of the resultant force, as measured from point B.
### Beam Loading Diagram This diagram illustrates a cantilever beam subjected to a varying distributed load. The beam is anchored at point \( A \) and extends horizontally to point \( B \). The following details describe the load distribution and dimensions: 1. **Distributed Load**: - **At Point A**: The load intensity starts at 100 pounds per foot (lb/ft). - **At Point B**: The load intensity decreases to 50 pounds per foot (lb/ft). - The load distribution is gradually decreasing linearly from 100 lb/ft at \( A \) to 50 lb/ft at \( B \). 2. **Dimensions**: - The total length of the beam from point \( A \) to point \( B \) is 12 feet. ### Diagram Components: - **Cantilever Beam**: Shown in brown, anchored at point \( A \) and free at point \( B \). - **Distributed Load Arrows**: Black arrows pointing downwards, representing the magnitude and direction of the load. - **Load Intensities**: Numerical values at the ends of the beam to specify the load distribution. - **Linear Gradient of Load**: Illustrated by the gradually reducing size of the arrows from left to right, indicating the decrease in load intensity from point \( A \) to point \( B \). This diagram is useful for understanding the distribution of load on a beam in structural analysis and design calculations. It visually conveys how the load varies along the length of the beam and assists in determining the resultant forces and moments required for engineering analyses.
Transcribed Image Text:### Beam Loading Diagram This diagram illustrates a cantilever beam subjected to a varying distributed load. The beam is anchored at point \( A \) and extends horizontally to point \( B \). The following details describe the load distribution and dimensions: 1. **Distributed Load**: - **At Point A**: The load intensity starts at 100 pounds per foot (lb/ft). - **At Point B**: The load intensity decreases to 50 pounds per foot (lb/ft). - The load distribution is gradually decreasing linearly from 100 lb/ft at \( A \) to 50 lb/ft at \( B \). 2. **Dimensions**: - The total length of the beam from point \( A \) to point \( B \) is 12 feet. ### Diagram Components: - **Cantilever Beam**: Shown in brown, anchored at point \( A \) and free at point \( B \). - **Distributed Load Arrows**: Black arrows pointing downwards, representing the magnitude and direction of the load. - **Load Intensities**: Numerical values at the ends of the beam to specify the load distribution. - **Linear Gradient of Load**: Illustrated by the gradually reducing size of the arrows from left to right, indicating the decrease in load intensity from point \( A \) to point \( B \). This diagram is useful for understanding the distribution of load on a beam in structural analysis and design calculations. It visually conveys how the load varies along the length of the beam and assists in determining the resultant forces and moments required for engineering analyses.
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