Find the resultant of the parallel force system below (Magnitude and Location 20 lb 5' 40 lb 6' 50 lb 8' 30 lb B
Find the resultant of the parallel force system below (Magnitude and Location 20 lb 5' 40 lb 6' 50 lb 8' 30 lb B
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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![### Finding the Resultant of a Parallel Force System: Magnitude and Location
#### Problem Statement:
Determine the resultant force of the parallel force system below, including both its magnitude and location.
#### Description of the Diagram:
The diagram shows a horizontal beam supported at point A with a pin support and point B with a roller support. Four vertical downward forces act on the beam at different locations. The beam is divided into segments with specified lengths.
##### Forces and Locations:
1. A 20 lb force applied downward at a distance of 4 feet from support A.
2. A 40 lb force applied downward at a distance of 9 feet from support A.
3. A 50 lb force applied downward at a distance of 15 feet from support A.
4. A 30 lb force applied downward at a distance of 23 feet from support A.
##### Beam Segment Lengths:
- Segment between A and the first force: 4 feet
- Segment between the first and second force: 5 feet
- Segment between the second and third force: 6 feet
- Segment between the third force and support B: 8 feet
#### Finding the Resultant Force:
1. **Resultant Force, \(F_R\) (Magnitude)**:
The resultant force is the sum of all the individual forces acting on the beam.
\[
F_R = 20 \text{ lb} + 40 \text{ lb} + 50 \text{ lb} + 30 \text{ lb} = 140 \text{ lb}
\]
2. **Location of the Resultant Force (Moment Calculation)**:
To find the location of the resultant force from point A, we need to balance the moments around point A.
\[
\text{Moment about A} = (20 \text{ lb} \times 4 \text{ ft}) + (40 \text{ lb} \times 9 \text{ ft}) + (50 \text{ lb} \times 15 \text{ ft}) + (30 \text{ lb} \times 23 \text{ ft})
\]
Performing the multiplication:
\[
\text{Moment about A} = (80) + (360) + (750) + (690) = 1880 \text{ lb-ft}
\]
The location of the resultant force from point A, \(x_{\text](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F24227ad7-0cee-4cb3-bf8f-36b2c099999b%2F6eea2902-0e35-4997-a42a-438a73849506%2Fm99rxw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Finding the Resultant of a Parallel Force System: Magnitude and Location
#### Problem Statement:
Determine the resultant force of the parallel force system below, including both its magnitude and location.
#### Description of the Diagram:
The diagram shows a horizontal beam supported at point A with a pin support and point B with a roller support. Four vertical downward forces act on the beam at different locations. The beam is divided into segments with specified lengths.
##### Forces and Locations:
1. A 20 lb force applied downward at a distance of 4 feet from support A.
2. A 40 lb force applied downward at a distance of 9 feet from support A.
3. A 50 lb force applied downward at a distance of 15 feet from support A.
4. A 30 lb force applied downward at a distance of 23 feet from support A.
##### Beam Segment Lengths:
- Segment between A and the first force: 4 feet
- Segment between the first and second force: 5 feet
- Segment between the second and third force: 6 feet
- Segment between the third force and support B: 8 feet
#### Finding the Resultant Force:
1. **Resultant Force, \(F_R\) (Magnitude)**:
The resultant force is the sum of all the individual forces acting on the beam.
\[
F_R = 20 \text{ lb} + 40 \text{ lb} + 50 \text{ lb} + 30 \text{ lb} = 140 \text{ lb}
\]
2. **Location of the Resultant Force (Moment Calculation)**:
To find the location of the resultant force from point A, we need to balance the moments around point A.
\[
\text{Moment about A} = (20 \text{ lb} \times 4 \text{ ft}) + (40 \text{ lb} \times 9 \text{ ft}) + (50 \text{ lb} \times 15 \text{ ft}) + (30 \text{ lb} \times 23 \text{ ft})
\]
Performing the multiplication:
\[
\text{Moment about A} = (80) + (360) + (750) + (690) = 1880 \text{ lb-ft}
\]
The location of the resultant force from point A, \(x_{\text
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