### Pipe Assembly AnalysisThe pipe assembly in the figure is supported by a fixed support at point A. A couple-moment and a force are applied at points B and C, respectively. In Cartesian coordinates:- The applied couple-moment is \(\mathbf{M}_{B} = -150 \, \mathbf{k} \, \text{N-m}\).- The applied force is \(\mathbf{F}_{C} = +200 \, \mathbf{j} \, \text{Newtons}\).The weight of the pipe assembly is negligible for this analysis.#### Steps to Solve for the Reactions at Point A**1. Draw a Free Body Diagram (FBD):** - Create a suitable FBD to identify the unknown force and moment reactions at the fixed support, Point A. You may use the existing drawing, ensuring it clearly shows the force and moment reaction vectors. - **Important:** Use double arrowheads to distinguish moment vectors from force vectors.**2. Calculate \(\mathbf{F}_{C}\mathbf{M}_{A}\):** - Determine the moment generated at point A due to the force applied at point C.**3. Write the Equations of Equilibrium:** - Solve these equations to find the reactions at Point A. Specifically, determine the force-reaction vector \(\mathbf{A}\) and the moment-reaction vector \(\mathbf{R}_{M_{A}}\).#### Detailed Explanation:1. **Drawing Free Body Diagram (FBD):** - Identify the forces and moments acting on the pipe assembly. - Represent the applied couple-moment \(\mathbf{M}_{B}\) and force \(\mathbf{F}_{C}\) accurately. - Include the reaction forces and moments at the fixed support A, typically represented as \(\mathbf{A}\) for the force-reaction vector, and \(\mathbf{R}_{M_{A}}\) for the moment-reaction vector.2. **Moment Calculation:** - Use the cross-product rule to calculate the moments: \[ \mathbf{M}_{A} = \mathbf{r}_{A \text{ to } C} \times \mathbf{F}_{C} \] - Ensure to consider the distances and orientation correctly to get the accurate moment value at point A.3. **Equilibrium Equations:** - **Translational Equilibrium ### Analysis of a Force and Moment Diagram in a Piping System#### Description:This diagram represents a segment of a piping system subjected to both a force and a moment. The system is defined in a three-dimensional coordinate system (x, y, z). The following elements and properties are depicted in the diagram:1. **Coordinates and Dimensions:** - **Point A** to **Point B**: A horizontal pipe extending 2 meters along the x-axis. - **Point B** to a vertical elbow joint**: A pipe section that extends 1 meter along the y-axis. - **The elbow at Point B**: Connecting to the vertical assembly. - **Vertical section** from **Point B** to C: Extends 2 meters down along the z-axis. - **Horizontal section** from **Point C**: Extending 2.5 meters along the y-axis.2. **Applied Forces and Moments:** - An external moment (**\( M_B \)**) of magnitude 150 N·m is applied at Point B, acting in the negative z-direction. - An external force (**\( F_C \)**) of magnitude 200 N is applied at Point C, directed parallel to the positive y-axis.#### Key Points:- **Understanding Moment (\( M \)) and Force (\( F \))** - A **moment** is a rotational force that can cause an object to rotate about a specific point or axis. The moment \( M_B \) at Point B is likely intended to simulate the effect of external torque applied to the pipe section. - A **force** is a vector quantity that produces a change in the motion of an object. The force \( F_C \) at Point C could represent an axial load applied to the piping system that might affect its stability or alignment.- **Applications in Engineering:** - Such diagrams are essential in mechanical and structural engineering for analyzing the stresses and strains within a piping system. - The given moment and force will impose stresses on the pipes, which must be properly accounted for in the design to ensure integrity and functionality under operational conditions.#### Visual Representation:- The **x, y, and z axes** provide a 3D perspective of the piping structure.- **Lengths** along each part of the piping are given to scale (2 m, 1 m, 2.5 m, 2 m), which helps in

A fixed support will exert both horizontal and vertical components of reaction force along with the…

The pipe assembly of the figure is supported by a fixed support at point A. A couple-moment and a force are applied at points B and C, respectively. In Cartesian coordinates, the applied couple-moment is MR = -150 k N-m, and the applied force is Fc = + 200ĵ`Newtons. You may neglect the weight of the pipe assembly. 1. Draw a FBD which is suitable for solution of this problem, when seeking the unknown force and moment reactions at the fixed support, Point A. You may use the existing drawing given below. Your FBD must clearly/correctly show the force and moment reaction vectors. Use double arrowheads to distinguish moment vectors from force vectors. 2. Calculate F°MA, which is the moment generated at A due to the force applied at Point C. 3. Write the equations of equilibrium and solve to find the reactions at Point A. Specifically, find the force-reaction vector, A and the moment-reaction vector, *MA.

The pipe assembly of the figure is supported by a fixed support at point A. A couple-moment and a force are applied at points B and C, respectively. In Cartesian coordinates, the applied couple-moment is MR = -150 k N-m, and the applied force is Fc = + 200ĵ`Newtons. You may neglect the weight of the pipe assembly. 1. Draw a FBD which is suitable for solution of this problem, when seeking the unknown force and moment reactions at the fixed support, Point A. You may use the existing drawing given below. Your FBD must clearly/correctly show the force and moment reaction vectors. Use double arrowheads to distinguish moment vectors from force vectors. 2. Calculate F°MA, which is the moment generated at A due to the force applied at Point C. 3. Write the equations of equilibrium and solve to find the reactions at Point A. Specifically, find the force-reaction vector, A and the moment-reaction vector, *MA.

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

Plane Trusses

It is defined as, two or more elements like beams or any two or more force members, which when assembled together, behaves like a complete structure or as a single structure. They generally consist of two force member which means any component structure where the force is applied only at two points. The point of contact of joints of truss are known as nodes. They are generally made up of triangular patterns. Nodes are the points where all the external forces and the reactionary forces due to them act and shows whether the force is tensile or compressive. There are various characteristics of trusses and are characterized as Simple truss, planar truss or the Space Frame truss.

Equilibrium Equations

If a body is said to be at rest or moving with a uniform velocity, the body is in equilibrium condition. This means that all the forces are balanced in the body. It can be understood with the help of Newton's first law of motion which states that the resultant force on a system is null, where the system remains to be at rest or moves at uniform motion. It is when the rate of the forward reaction is equal to the rate of the backward reaction.

Force Systems

When a body comes in interaction with other bodies, they exert various forces on each other. Any system is under the influence of some kind of force. For example, laptop kept on table exerts force on the table and table exerts equal force on it, hence the system is in balance or equilibrium. When two or more materials interact then more than one force act at a time, hence it is called as force systems.

Question

### Pipe Assembly Analysis

The pipe assembly in the figure is supported by a fixed support at point A. A couple-moment and a force are applied at points B and C, respectively.

In Cartesian coordinates:
- The applied couple-moment is \(\mathbf{M}_{B} = -150 \, \mathbf{k} \, \text{N-m}\).
- The applied force is \(\mathbf{F}_{C} = +200 \, \mathbf{j} \, \text{Newtons}\).

The weight of the pipe assembly is negligible for this analysis.

#### Steps to Solve for the Reactions at Point A

**1. Draw a Free Body Diagram (FBD):**
- Create a suitable FBD to identify the unknown force and moment reactions at the fixed support, Point A. You may use the existing drawing, ensuring it clearly shows the force and moment reaction vectors.
- **Important:** Use double arrowheads to distinguish moment vectors from force vectors.

**2. Calculate \(\mathbf{F}_{C}\mathbf{M}_{A}\):**
- Determine the moment generated at point A due to the force applied at point C.

**3. Write the Equations of Equilibrium:**
- Solve these equations to find the reactions at Point A. Specifically, determine the force-reaction vector \(\mathbf{A}\) and the moment-reaction vector \(\mathbf{R}_{M_{A}}\).

#### Detailed Explanation:

1. **Drawing Free Body Diagram (FBD):**
- Identify the forces and moments acting on the pipe assembly.
- Represent the applied couple-moment \(\mathbf{M}_{B}\) and force \(\mathbf{F}_{C}\) accurately.
- Include the reaction forces and moments at the fixed support A, typically represented as \(\mathbf{A}\) for the force-reaction vector, and \(\mathbf{R}_{M_{A}}\) for the moment-reaction vector.

2. **Moment Calculation:**
- Use the cross-product rule to calculate the moments:
\[
\mathbf{M}_{A} = \mathbf{r}_{A \text{ to } C} \times \mathbf{F}_{C}
\]
- Ensure to consider the distances and orientation correctly to get the accurate moment value at point A.

3. **Equilibrium Equations:**
- **Translational Equilibrium

### Analysis of a Force and Moment Diagram in a Piping System

#### Description:

This diagram represents a segment of a piping system subjected to both a force and a moment. The system is defined in a three-dimensional coordinate system (x, y, z). The following elements and properties are depicted in the diagram:

1. **Coordinates and Dimensions:**
- **Point A** to **Point B**: A horizontal pipe extending 2 meters along the x-axis.
- **Point B** to a vertical elbow joint**: A pipe section that extends 1 meter along the y-axis.
- **The elbow at Point B**: Connecting to the vertical assembly.
- **Vertical section** from **Point B** to C: Extends 2 meters down along the z-axis.
- **Horizontal section** from **Point C**: Extending 2.5 meters along the y-axis.

2. **Applied Forces and Moments:**
- An external moment (**\( M_B \)**) of magnitude 150 N·m is applied at Point B, acting in the negative z-direction.
- An external force (**\( F_C \)**) of magnitude 200 N is applied at Point C, directed parallel to the positive y-axis.

#### Key Points:

- **Understanding Moment (\( M \)) and Force (\( F \))**
- A **moment** is a rotational force that can cause an object to rotate about a specific point or axis. The moment \( M_B \) at Point B is likely intended to simulate the effect of external torque applied to the pipe section.
- A **force** is a vector quantity that produces a change in the motion of an object. The force \( F_C \) at Point C could represent an axial load applied to the piping system that might affect its stability or alignment.

- **Applications in Engineering:**
- Such diagrams are essential in mechanical and structural engineering for analyzing the stresses and strains within a piping system.
- The given moment and force will impose stresses on the pipes, which must be properly accounted for in the design to ensure integrity and functionality under operational conditions.

#### Visual Representation:

- The **x, y, and z axes** provide a 3D perspective of the piping structure.
- **Lengths** along each part of the piping are given to scale (2 m, 1 m, 2.5 m, 2 m), which helps in

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