A 30 ft tall column has a cross section of 8" x 8" with 1" thick walls, (i.e., it has a 6" x 6" hole in the middle). The material has a Young's Modulus E = 2,000,000 psi, and an axial yield stress of 1600 psi. Using a crushing FOS of 1.67 and a buckling FOS of 1.9, compute the following: a) What is the LARGEST axial load this column can sustain? Dection A b) If the column is braced (in both directions) at 10 feet above the ground, what is the maximum axial load the column can sustain?
A 30 ft tall column has a cross section of 8" x 8" with 1" thick walls, (i.e., it has a 6" x 6" hole in the middle). The material has a Young's Modulus E = 2,000,000 psi, and an axial yield stress of 1600 psi. Using a crushing FOS of 1.67 and a buckling FOS of 1.9, compute the following: a) What is the LARGEST axial load this column can sustain? Dection A b) If the column is braced (in both directions) at 10 feet above the ground, what is the maximum axial load the column can sustain?
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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![### Column Load Analysis Problem
**Problem Statement:**
A 30 ft tall column has a cross-section of 8" x 8" with 1" thick walls (i.e., it has a 6" x 6" hole in the middle). The material has a Young's Modulus \( E = 2,000,000 \) psi, and an axial yield stress of 1600 psi. Using a crushing Factor of Safety (FOS) of 1.67 and a buckling FOS of 1.9, compute the following:
#### Questions:
a) What is the LARGEST axial load this column can sustain?
b) If the column is braced (in both directions) at 10 feet above the ground, what is the maximum axial load the column can sustain?
---
**Approach Explanation:**
For this type of problem, we typically need to consider two major failure mechanisms: crushing and buckling.
1. **Crushing:** Occurs when the stress in the column exceeds the material's yield stress.
- Calculate the cross-sectional area.
- Determine the ultimate crushing load using the yield stress and cross-sectional area.
- Apply the Factor of Safety to find the safe crushing load.
2. **Buckling:** Happens when the column bends sideways under compressive load.
- Compute the moment of inertia based on the column's cross-section.
- Use Euler's buckling formula to determine the critical buckling load.
- Apply the Factor of Safety to find the safe buckling load.
### Detailed Solution Steps:
1. **Crushing Load:**
- Calculate the cross-sectional area \( A \).
- Use the crushing FOS to determine the safe load.
2. **Buckling Load:**
- Calculate the moment of inertia \( I \) for the cross-section.
- Use Euler's formula:
\[
P_{cr} = \frac{\pi^2 E I}{(K L)^2}
\]
where \( K \) is the effective length factor, and \( L \) is the length of the column.
- Adjust \( K \) and \( L \) if the column is braced.
### Solving the Problem:
_To be completed with detailed equations and calculations based on the given material properties and column dimensions._
By understanding and using these principles, students or engineers can determine the maximum safe load a column can sustain](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fefe8e5bf-0d01-40a5-8bfd-713b940a86f2%2Fde0c2ce9-d0a6-4c8d-bc01-1528e0219c40%2Fh8s5ve8_processed.png&w=3840&q=75)
Transcribed Image Text:### Column Load Analysis Problem
**Problem Statement:**
A 30 ft tall column has a cross-section of 8" x 8" with 1" thick walls (i.e., it has a 6" x 6" hole in the middle). The material has a Young's Modulus \( E = 2,000,000 \) psi, and an axial yield stress of 1600 psi. Using a crushing Factor of Safety (FOS) of 1.67 and a buckling FOS of 1.9, compute the following:
#### Questions:
a) What is the LARGEST axial load this column can sustain?
b) If the column is braced (in both directions) at 10 feet above the ground, what is the maximum axial load the column can sustain?
---
**Approach Explanation:**
For this type of problem, we typically need to consider two major failure mechanisms: crushing and buckling.
1. **Crushing:** Occurs when the stress in the column exceeds the material's yield stress.
- Calculate the cross-sectional area.
- Determine the ultimate crushing load using the yield stress and cross-sectional area.
- Apply the Factor of Safety to find the safe crushing load.
2. **Buckling:** Happens when the column bends sideways under compressive load.
- Compute the moment of inertia based on the column's cross-section.
- Use Euler's buckling formula to determine the critical buckling load.
- Apply the Factor of Safety to find the safe buckling load.
### Detailed Solution Steps:
1. **Crushing Load:**
- Calculate the cross-sectional area \( A \).
- Use the crushing FOS to determine the safe load.
2. **Buckling Load:**
- Calculate the moment of inertia \( I \) for the cross-section.
- Use Euler's formula:
\[
P_{cr} = \frac{\pi^2 E I}{(K L)^2}
\]
where \( K \) is the effective length factor, and \( L \) is the length of the column.
- Adjust \( K \) and \( L \) if the column is braced.
### Solving the Problem:
_To be completed with detailed equations and calculations based on the given material properties and column dimensions._
By understanding and using these principles, students or engineers can determine the maximum safe load a column can sustain
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