6 2 0 2 + 8- 1. Determine the area of the shape 2. Determine the moment of inertia about the y-axis. 3. Determine the radius of gyration with respect to the y-axis.
6 2 0 2 + 8- 1. Determine the area of the shape 2. Determine the moment of inertia about the y-axis. 3. Determine the radius of gyration with respect to the y-axis.
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
Related questions
Question
According to the answer key, the answers should be-
1. A = 34 mm2
2. Iy = 1011 mm4
3. ky = 5.45 mm
![### Engineering Mechanics: Composite Shape Analysis
#### Problem Set
For problems 1-3, use the following information. A composite shape is drawn to scale below. Grid units are [mm].
![Composite Shape Diagram]
The diagram represents a composite shape on a grid. Each square on the grid represents an area of 1 mm². The composite shape has sections extending from coordinates (0,6) to (2-4) horizontally, then angling downward to (6-0) and horizontally again to (8,6).
### Tasks:
1. **Determine the area of the shape**
- Calculate the total area covered by the shaded portions.
2. **Determine the moment of inertia about the y-axis**
- Use the parallel axis theorem and formulas for calculating the moment of inertia for basic shapes to find the composite moment of inertia about the y-axis.
3. **Determine the radius of gyration with respect to the y-axis**
- The radius of gyration is defined as \( k = \sqrt{\frac{I}{A}} \), where \(I\) is the moment of inertia and \(A\) is the area.
### Detailed Diagram Analysis:
##### Graph/Diagram Description:
- The graph displays a composite shape consisting of rectangular sections assembled in a 'U' like configuration.
- The shape extends from (0,0) to (0,6), and each block on the grid represents a 1 mm x 1 mm square.
- The vertical sections rise to 6 mm height with a width extending from 0 mm to 2 mm and again from 6 mm to 8 mm.
- The bottom section of the ‘U’ is at 0 mm height, stretching from 2 mm to 6 mm horizontally.
### Calculation Approach:
1. **Area Calculation**:
- Divide the composite shape into simpler rectangles and calculate the area of each, summing them up to get the total area.
2. **Moment of Inertia Calculation**:
- Use the formula for the moment of inertia of rectangles and aggregate them considering the distance from the y-axis.
3. **Radius of Gyration Calculation**:
- Apply the formula for the radius of gyration given the calculated moment of inertia and total area.
By following the calculation steps, you can determine the required properties (area, moment of inertia, and radius of gyration) for the composite shape using basic principles of engineering mechanics.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F848bc833-9fb3-4eda-a7de-b585ddd0b1dc%2Fbe8efe15-187b-4de4-b552-6af36b671771%2F8y4nsdto_processed.png&w=3840&q=75)
Transcribed Image Text:### Engineering Mechanics: Composite Shape Analysis
#### Problem Set
For problems 1-3, use the following information. A composite shape is drawn to scale below. Grid units are [mm].
![Composite Shape Diagram]
The diagram represents a composite shape on a grid. Each square on the grid represents an area of 1 mm². The composite shape has sections extending from coordinates (0,6) to (2-4) horizontally, then angling downward to (6-0) and horizontally again to (8,6).
### Tasks:
1. **Determine the area of the shape**
- Calculate the total area covered by the shaded portions.
2. **Determine the moment of inertia about the y-axis**
- Use the parallel axis theorem and formulas for calculating the moment of inertia for basic shapes to find the composite moment of inertia about the y-axis.
3. **Determine the radius of gyration with respect to the y-axis**
- The radius of gyration is defined as \( k = \sqrt{\frac{I}{A}} \), where \(I\) is the moment of inertia and \(A\) is the area.
### Detailed Diagram Analysis:
##### Graph/Diagram Description:
- The graph displays a composite shape consisting of rectangular sections assembled in a 'U' like configuration.
- The shape extends from (0,0) to (0,6), and each block on the grid represents a 1 mm x 1 mm square.
- The vertical sections rise to 6 mm height with a width extending from 0 mm to 2 mm and again from 6 mm to 8 mm.
- The bottom section of the ‘U’ is at 0 mm height, stretching from 2 mm to 6 mm horizontally.
### Calculation Approach:
1. **Area Calculation**:
- Divide the composite shape into simpler rectangles and calculate the area of each, summing them up to get the total area.
2. **Moment of Inertia Calculation**:
- Use the formula for the moment of inertia of rectangles and aggregate them considering the distance from the y-axis.
3. **Radius of Gyration Calculation**:
- Apply the formula for the radius of gyration given the calculated moment of inertia and total area.
By following the calculation steps, you can determine the required properties (area, moment of inertia, and radius of gyration) for the composite shape using basic principles of engineering mechanics.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Step 1: Split the given area into three basic areas as shown.
VIEWStep 2: Evaluate areas and centroid distances.
VIEWStep 3: Evaluate area moment of inertia of each shape about y-axis
VIEWStep 4: Evaluate area moment of inertia of shaded region about y-axis.
VIEWStep 5: Evaluate radius of gyration about y-axis.
VIEWSolution
VIEW
Trending now
This is a popular solution!
Step by step
Solved in 6 steps with 39 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Recommended textbooks for you
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY