resultant moment and express as a Cartesian vector. 2021 Cathy Zupke M₁ X Z M3 M₂ L5 LA- y
resultant moment and express as a Cartesian vector. 2021 Cathy Zupke M₁ X Z M3 M₂ L5 LA- y
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Question
![**Description of the Problem:**
A pipe intersection has moments on three of its branches as depicted in the figure and parameter table. Your task is to calculate the resultant moment and express it as a Cartesian vector.
**Diagram Explanation:**
The diagram shows a 3D coordinate system with three moments, \( M_1 \), \( M_2 \), and \( M_3 \), acting along different branches of the pipe:
- \( M_1 \) acts along the negative x-direction.
- \( M_2 \) acts in a plane involving x and y axes, oriented at an angle in the positive y-direction.
- \( M_3 \) acts in the negative z-direction.
**Parameter Table:**
| Parameter | Value | Units |
|-----------|-------|---------|
| \( L_1 \) | 1 | ft |
| \( L_2 \) | 4 | ft |
| \( L_3 \) | 3 | ft |
| \( L_4 \) | 2.5 | ft |
| \( L_5 \) | 3 | ft |
| \( M_1 \) | 200 | lb·ft |
| \( M_2 \) | 250 | lb·ft |
| \( M_3 \) | 200 | lb·ft |
**Calculation Instructions:**
To find the resultant moment as a Cartesian vector, decompose each moment vector into its i, j, and k components using the given lengths (\( L_1 \), \( L_2 \), etc.) and angles implied in the diagram.
**Note:**
Use \( i, j, k \) for the unit vectors \( \hat{i}, \hat{j}, \hat{k} \).
The resultant moment should be expressed in the following format:
\[ \text{Resultant moment} = \text{(calculated vector)} \, \text{lb·ft} \]
Fill in the box provided with the calculated resultant moment in Cartesian vector form.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6e7ba281-dd87-4688-be97-9abf26130e05%2Fc82aac9e-8c62-470d-8adb-ef631fd46f29%2F987wud8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Description of the Problem:**
A pipe intersection has moments on three of its branches as depicted in the figure and parameter table. Your task is to calculate the resultant moment and express it as a Cartesian vector.
**Diagram Explanation:**
The diagram shows a 3D coordinate system with three moments, \( M_1 \), \( M_2 \), and \( M_3 \), acting along different branches of the pipe:
- \( M_1 \) acts along the negative x-direction.
- \( M_2 \) acts in a plane involving x and y axes, oriented at an angle in the positive y-direction.
- \( M_3 \) acts in the negative z-direction.
**Parameter Table:**
| Parameter | Value | Units |
|-----------|-------|---------|
| \( L_1 \) | 1 | ft |
| \( L_2 \) | 4 | ft |
| \( L_3 \) | 3 | ft |
| \( L_4 \) | 2.5 | ft |
| \( L_5 \) | 3 | ft |
| \( M_1 \) | 200 | lb·ft |
| \( M_2 \) | 250 | lb·ft |
| \( M_3 \) | 200 | lb·ft |
**Calculation Instructions:**
To find the resultant moment as a Cartesian vector, decompose each moment vector into its i, j, and k components using the given lengths (\( L_1 \), \( L_2 \), etc.) and angles implied in the diagram.
**Note:**
Use \( i, j, k \) for the unit vectors \( \hat{i}, \hat{j}, \hat{k} \).
The resultant moment should be expressed in the following format:
\[ \text{Resultant moment} = \text{(calculated vector)} \, \text{lb·ft} \]
Fill in the box provided with the calculated resultant moment in Cartesian vector form.
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