A hollow mast of circular section as shown is to be stiffened by bonding two strips of the same material and of rectangular section to the mast throughout its length. Determine the proper dimension h of each near-rectangle which will exactly double the stiffness of the mast to bending in the y-z plane. (Stiffness in the y-z plane is proportional to the area moment of inertia about the x-axis.) Take the inner boundary of each strip to be a straight line. Assume d = 130 mm, D = 255 mm, w = 60 mm. W || In |_w_ W Answer: hi - x mm
A hollow mast of circular section as shown is to be stiffened by bonding two strips of the same material and of rectangular section to the mast throughout its length. Determine the proper dimension h of each near-rectangle which will exactly double the stiffness of the mast to bending in the y-z plane. (Stiffness in the y-z plane is proportional to the area moment of inertia about the x-axis.) Take the inner boundary of each strip to be a straight line. Assume d = 130 mm, D = 255 mm, w = 60 mm. W || In |_w_ W Answer: hi - x mm
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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![### Determining the Stiffness of a Hollow Mast with Rectangular Strips
**Problem Statement:**
A hollow mast of circular section, as shown in the accompanying diagram, is to be stiffened by bonding two strips of the same material and of rectangular section to the mast throughout its length. The task is to determine the proper dimension \( h \) of each near-rectangle, which will exactly double the stiffness of the mast to bending in the y-z plane. Note that stiffness in the y-z plane is proportional to the area moment of inertia about the x-axis. The inner boundary of each strip is to be a straight line.
**Given:**
- Inner diameter of the hollow mast, \( d = 130 \) mm
- Outer diameter of the hollow mast, \( D = 255 \) mm
- Width of each strip, \( w = 60 \) mm
**Accompanying Diagram Description:**
The diagram features a hollow circular mast with two bonded rectangular strips.
- The mast's central circle represents the cross-section of the hollow part.
- Two rectangular strips are symmetrically bonded to the exterior of the mast along the y-axis.
- Labels indicate dimensions such as:
- \( d \): Inner diameter of the mast
- \( D \): Outer diameter of the mast
- \( w \): Width of each rectangular strip
- \( h \): Height of each rectangular strip (unknown value to be determined)
The y-axis runs vertically in the diagram, and the x-axis runs horizontally. The strips are aligned along the y-axis.
**Objective:**
Determine the value of \( h \) such that the stiffness of the mast to bending in the y-z plane is doubled.
**Formula and Calculation Approach:**
1. Compute the area moment of inertia \( I_{x} \) of the hollow circular section about the x-axis.
2. Add the area moment of inertia contributed by the bonded rectangular strips.
3. Solve for \( h \) such that the total area moment of inertia about the x-axis is doubled.
**Answer**:
Provide the value of \( h \) after solving the equation to double the stiffness.
**Answer Box:**
\[ h = \ \boxed{} \ \text{mm} \]
This educational content is structured to provide a comprehensive approach to understanding the stiffness enhancement of a hollow circular mast when additional rectangular strips are added. Users are encouraged to follow the given](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc59a6d07-a993-40f7-b57e-cdb2ad079d78%2F006dec1f-aadf-46f6-a703-a6f8883f214d%2Fqfn36ds_processed.png&w=3840&q=75)
Transcribed Image Text:### Determining the Stiffness of a Hollow Mast with Rectangular Strips
**Problem Statement:**
A hollow mast of circular section, as shown in the accompanying diagram, is to be stiffened by bonding two strips of the same material and of rectangular section to the mast throughout its length. The task is to determine the proper dimension \( h \) of each near-rectangle, which will exactly double the stiffness of the mast to bending in the y-z plane. Note that stiffness in the y-z plane is proportional to the area moment of inertia about the x-axis. The inner boundary of each strip is to be a straight line.
**Given:**
- Inner diameter of the hollow mast, \( d = 130 \) mm
- Outer diameter of the hollow mast, \( D = 255 \) mm
- Width of each strip, \( w = 60 \) mm
**Accompanying Diagram Description:**
The diagram features a hollow circular mast with two bonded rectangular strips.
- The mast's central circle represents the cross-section of the hollow part.
- Two rectangular strips are symmetrically bonded to the exterior of the mast along the y-axis.
- Labels indicate dimensions such as:
- \( d \): Inner diameter of the mast
- \( D \): Outer diameter of the mast
- \( w \): Width of each rectangular strip
- \( h \): Height of each rectangular strip (unknown value to be determined)
The y-axis runs vertically in the diagram, and the x-axis runs horizontally. The strips are aligned along the y-axis.
**Objective:**
Determine the value of \( h \) such that the stiffness of the mast to bending in the y-z plane is doubled.
**Formula and Calculation Approach:**
1. Compute the area moment of inertia \( I_{x} \) of the hollow circular section about the x-axis.
2. Add the area moment of inertia contributed by the bonded rectangular strips.
3. Solve for \( h \) such that the total area moment of inertia about the x-axis is doubled.
**Answer**:
Provide the value of \( h \) after solving the equation to double the stiffness.
**Answer Box:**
\[ h = \ \boxed{} \ \text{mm} \]
This educational content is structured to provide a comprehensive approach to understanding the stiffness enhancement of a hollow circular mast when additional rectangular strips are added. Users are encouraged to follow the given
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