### Solving for the Resultant Force in a Parallel Force SystemIn this problem, we will determine the resultant force, along with its magnitude and location, for a given parallel force system.### Problem DescriptionThe figure provided illustrates a simply supported beam with two point loads and a uniformly distributed load. The beam has supports at points \( A \) and \( B \).The forces acting on the beam are as follows:1. A concentrated load of 3 kips located 3 ft from the support at \( A \).2. A concentrated load of 10 kips located 7 ft from the support at \( A \).3. A uniformly distributed load of 2 kips/ft acting over a span of 6 ft starting 13 ft from the support at \( A \).### Force Diagram Explanation- **Support Points**: - \( A \): Pin support. - \( B \): Roller support, located 12 feet from the pin support at \( A \).- **Loads**: - **3 kips Load**: Applied vertically downward, located 3 ft from point \( A \). - **10 kips Load**: Applied vertically downward, located 7 ft from point \( A \). - **Uniform Load**: Distributed load of 2 kips/ft over a span of 6 ft, starting 13 ft from point \( A \).### Steps to Solve the Problem1. **Calculate the Resultant (Magnitude) of the Forces**: - Sum the concentrated loads. - Determine the equivalent point load for the uniformly distributed load.2. **Determine the Position (Location \( x \)) of the Resultant Force**: - Calculate the moment of each force about point \( A \). - Compute the resultant moment using the principle of moments.### Solving for the Magnitude of the Resultant Force- **Resultant Force from Concentrated Loads**: \( F_{\text{resultant}} = 3 \text{ kips} + 10 \text{ kips} = 13 \text{ kips} \)- **Resultant Force from Uniformly Distributed Load**: \( F_{\text{uniform}} = 2 \text{ kips/ft} \times 6 \text{ ft} = 12 \text{ kips} \)- **Total Resultant Force**: \(

To find:The magnitude and location of the resultant.

Answered: Solve for the Resultant (Magnitude and…

Solve for the Resultant (Magnitude and Location x) for the parallel force system below. A 3 ft 3 kips 4 ft 10 kips 5 ft -2 kips/ft m B 6 ft

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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Graphical Methods

The graphical method is a method of solving equations involving more than one variable using the Cartesian coordinate system. In civil engineering, the use of the graphical method is limited to the problems involving two variables. The graphical method has a great impact in solving the questions regarding engineering mechanics.

Question

### Solving for the Resultant Force in a Parallel Force System

In this problem, we will determine the resultant force, along with its magnitude and location, for a given parallel force system.

### Problem Description

The figure provided illustrates a simply supported beam with two point loads and a uniformly distributed load. The beam has supports at points \( A \) and \( B \).

The forces acting on the beam are as follows:

1. A concentrated load of 3 kips located 3 ft from the support at \( A \).
2. A concentrated load of 10 kips located 7 ft from the support at \( A \).
3. A uniformly distributed load of 2 kips/ft acting over a span of 6 ft starting 13 ft from the support at \( A \).

### Force Diagram Explanation

- **Support Points**:
- \( A \): Pin support.
- \( B \): Roller support, located 12 feet from the pin support at \( A \).

- **Loads**:
- **3 kips Load**: Applied vertically downward, located 3 ft from point \( A \).
- **10 kips Load**: Applied vertically downward, located 7 ft from point \( A \).
- **Uniform Load**: Distributed load of 2 kips/ft over a span of 6 ft, starting 13 ft from point \( A \).

### Steps to Solve the Problem

1. **Calculate the Resultant (Magnitude) of the Forces**:
- Sum the concentrated loads.
- Determine the equivalent point load for the uniformly distributed load.

2. **Determine the Position (Location \( x \)) of the Resultant Force**:
- Calculate the moment of each force about point \( A \).
- Compute the resultant moment using the principle of moments.

### Solving for the Magnitude of the Resultant Force

- **Resultant Force from Concentrated Loads**:
\( F_{\text{resultant}} = 3 \text{ kips} + 10 \text{ kips} = 13 \text{ kips} \)

- **Resultant Force from Uniformly Distributed Load**:
\( F_{\text{uniform}} = 2 \text{ kips/ft} \times 6 \text{ ft} = 12 \text{ kips} \)

- **Total Resultant Force**:
\(

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