W 8x40 C 8x13.75 Find lx bf
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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![### Moment of Inertia Calculation for Composite Section
#### Diagram Description:
The diagram represents a composite section consisting of a wide flange beam (W shape) placed over a C-shaped channel.
1. **Wide Flange Beam:**
- Designation: W 8x40
- The section is shaped like the letter "H", representing a standard wide-flange beam.
2. **C-Shaped Channel:**
- Designation: C 8x13.75
- The C-shaped channel is positioned below the wide flange beam, with its open side facing downward.
#### Labels:
- Two important dimensions are labeled:
- **bf**: This likely represents the width of the flange.
- **t**: This likely represents the thickness of the web of the section.
#### Task:
- The task specified is to find \(I_x\), which is the moment of inertia about the x-axis for the composite section.
### Detailed Explanation:
To calculate the moment of inertia \(I_x\) for the composite section, follow these steps:
1. **Break Down the Section:**
- Separate the wide flange beam (W 8x40) and the C-shaped channel (C 8x13.75).
2. **Determine Individual Moments of Inertia:**
- Calculate the moment of inertia for the wide flange beam and the C-shaped channel individually, using standard formulas for these shapes.
3. **Use Parallel Axis Theorem:**
- For any component that is not centered on the x-axis, use the parallel axis theorem to find its moment of inertia relative to the x-axis of the composite section.
\[
I_{x'} = I_x + Ad^2
\]
where:
- \(I_{x'}\) is the moment of inertia about the composite centroidal x-axis.
- \(I_x\) is the moment of inertia about the component's own centroidal x-axis.
- \(A\) is the area of the component.
- \(d\) is the distance from the component's centroid to the composite centroidal x-axis.
4. **Sum of Moments of Inertia:**
- Sum the moments of inertia (including any adjustments from the parallel axis theorem) to get the total \(I_x\) for the composite section.
By following this method, one can accurately determine the moment of inertia \(I_x\) for](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6abdb772-2674-4ccf-b97c-7a87bba16f16%2F7f02ec82-713a-4e34-99e3-42b57cc2bfaf%2Fv85rrj_processed.png&w=3840&q=75)
Transcribed Image Text:### Moment of Inertia Calculation for Composite Section
#### Diagram Description:
The diagram represents a composite section consisting of a wide flange beam (W shape) placed over a C-shaped channel.
1. **Wide Flange Beam:**
- Designation: W 8x40
- The section is shaped like the letter "H", representing a standard wide-flange beam.
2. **C-Shaped Channel:**
- Designation: C 8x13.75
- The C-shaped channel is positioned below the wide flange beam, with its open side facing downward.
#### Labels:
- Two important dimensions are labeled:
- **bf**: This likely represents the width of the flange.
- **t**: This likely represents the thickness of the web of the section.
#### Task:
- The task specified is to find \(I_x\), which is the moment of inertia about the x-axis for the composite section.
### Detailed Explanation:
To calculate the moment of inertia \(I_x\) for the composite section, follow these steps:
1. **Break Down the Section:**
- Separate the wide flange beam (W 8x40) and the C-shaped channel (C 8x13.75).
2. **Determine Individual Moments of Inertia:**
- Calculate the moment of inertia for the wide flange beam and the C-shaped channel individually, using standard formulas for these shapes.
3. **Use Parallel Axis Theorem:**
- For any component that is not centered on the x-axis, use the parallel axis theorem to find its moment of inertia relative to the x-axis of the composite section.
\[
I_{x'} = I_x + Ad^2
\]
where:
- \(I_{x'}\) is the moment of inertia about the composite centroidal x-axis.
- \(I_x\) is the moment of inertia about the component's own centroidal x-axis.
- \(A\) is the area of the component.
- \(d\) is the distance from the component's centroid to the composite centroidal x-axis.
4. **Sum of Moments of Inertia:**
- Sum the moments of inertia (including any adjustments from the parallel axis theorem) to get the total \(I_x\) for the composite section.
By following this method, one can accurately determine the moment of inertia \(I_x\) for
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