### 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

Determine the magnitude of the resultant of the parallel force system and it's location.

Answered: Find the resultant of the parallel…

Engineering

Civil Engineering

Find the resultant of the parallel force system below (Magnitude and Location 20 lb 5' 40 lb 6' 50 lb 8' 30 lb B

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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Concept explainers

System of Forces

A force is an external influence or agent that changes the state of a system. According to Newton's second law, the force applied to a body is proportional to the change in momentum of a body. Hence, whenever a force is applied to a body, its momentum changes. If the body is at rest, under the action of force, its state of rest changes to motion. In other words, the magnitude of the momentum of the body changes from zero to a measurable value. Similarly, if the body possesses some initial velocity, it has some associated momentum, the effect of force can cause the body to halt or come to rest, that is, the momentum reduces to zero.

Question

### 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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