**Replacement of Original Loading System with Equivalent System****Description of the Problem:**The frame depicted has an original loading system consisting of four applied forces and one couple moment. Your task is to replace this loading system with an equivalent resultant force and couple moment, both acting at point B.**Diagrams:**1. **Original System:** - The force \( F_1 \) acts at the left end of the horizontal member at point \( A \), with a distance \( d_1 \) to point \( B \). - The force \( F_2 \) acts to the right of \( F_1 \), with a distance \( d_2 \) to point \( B \). - The force \( F_3 \) acts downward at \( B \). - The force \( F_4 \) acts downward on the vertical member at a distance \( d_3 \) below point \( B \). - The couple moment \( M_A \) acts at point \( A \).2. **Equivalent System:** - A resultant force \( (F_R) \) acts at point \( B \). - A resultant couple moment \( (M_R) \) acts at point \( B \).**Given Data:**- Distance Values: - \( d_1 = 0.990 \, \text{m} \) - \( d_2 = 1.14 \, \text{m} \) - \( d_3 = 0.540 \, \text{m} \) - \( d_4 = 2.08 \, \text{m} \)- Force Values: - \( F_1 = 502 \, \text{N} \) - \( F_2 = 300 \, \text{N} \) - \( F_3 = 508 \, \text{N} \) - \( F_4 = 402 \, \text{N} \)- Moment Value: - \( M_A = 1507 \, \text{N} \cdot \text{m} \)**Objective:**Express the Cartesian components of the resultant force and the couple moment at point \( B \) in newtons and newton-meters to three significant figures.**Solution Format:**\[(F_R)_x,

Solution: Consider the equilibrium in x-direction : The direction of the force will be rightward.…

The frame has an original loading system of four applied forces and one applied couple moment. Replace this loading system by an equivalent resultant force and couple moment acting at point B. (FR), (M2)», F3 B A (FR), dz ¥F4 Original System Equivalent System Assume the following values: d1 = 0.990 m , d2 = 1.14 m , d3 = 0.540 m , d4 = 2.08 m , F1 = 502 N , F2 = 300 N , F3 = 508 N , F4 = 402 N , and MA = 1507 N · m . Express the Cartesian components of the resultant force and the couple moment in newtons and newton-meters to three significant figures separated by commas.

The frame has an original loading system of four applied forces and one applied couple moment. Replace this loading system by an equivalent resultant force and couple moment acting at point B. (FR), (M2)», F3 B A (FR), dz ¥F4 Original System Equivalent System Assume the following values: d1 = 0.990 m , d2 = 1.14 m , d3 = 0.540 m , d4 = 2.08 m , F1 = 502 N , F2 = 300 N , F3 = 508 N , F4 = 402 N , and MA = 1507 N · m . Express the Cartesian components of the resultant force and the couple moment in newtons and newton-meters to three significant figures separated by commas.

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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Concept explainers

Types of loading

In mechanical terminology, the term load indicates that external force/weight, either constant or variable, acts on a mechanical member/structure. The weight of an object of a specific material is also an external load, and the external force that works on a structure comes under the categories of loading. The external load generates its effects as stress and strain in the structure.

Question

**Replacement of Original Loading System with Equivalent System**

**Description of the Problem:**
The frame depicted has an original loading system consisting of four applied forces and one couple moment. Your task is to replace this loading system with an equivalent resultant force and couple moment, both acting at point B.

**Diagrams:**

1. **Original System:**
- The force \( F_1 \) acts at the left end of the horizontal member at point \( A \), with a distance \( d_1 \) to point \( B \).
- The force \( F_2 \) acts to the right of \( F_1 \), with a distance \( d_2 \) to point \( B \).
- The force \( F_3 \) acts downward at \( B \).
- The force \( F_4 \) acts downward on the vertical member at a distance \( d_3 \) below point \( B \).
- The couple moment \( M_A \) acts at point \( A \).

2. **Equivalent System:**
- A resultant force \( (F_R) \) acts at point \( B \).
- A resultant couple moment \( (M_R) \) acts at point \( B \).

**Given Data:**
- Distance Values:
- \( d_1 = 0.990 \, \text{m} \)
- \( d_2 = 1.14 \, \text{m} \)
- \( d_3 = 0.540 \, \text{m} \)
- \( d_4 = 2.08 \, \text{m} \)
- Force Values:
- \( F_1 = 502 \, \text{N} \)
- \( F_2 = 300 \, \text{N} \)
- \( F_3 = 508 \, \text{N} \)
- \( F_4 = 402 \, \text{N} \)
- Moment Value:
- \( M_A = 1507 \, \text{N} \cdot \text{m} \)

**Objective:**
Express the Cartesian components of the resultant force and the couple moment at point \( B \) in newtons and newton-meters to three significant figures.

**Solution Format:**
\[
(F_R)_x,

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