haw bong lworuld thei pole need to be to buck'le nder elf weighe? CONSTANTS 1= % *, A=rr;, E • 200 E9 fe, 8= 700 kgh? g = 9.81 m/st re 0.01 m
haw bong lworuld thei pole need to be to buck'le nder elf weighe? CONSTANTS 1= % *, A=rr;, E • 200 E9 fe, 8= 700 kgh? g = 9.81 m/st re 0.01 m
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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![### Analysis of Pole Buckling Under Self-Weight
**Objective:**
Determine the length at which a vertical pole will buckle under its own weight.
**Given Diagram:**
A vertical pole fixed at the base, showing forces acting due to self-weight.
**Constants:**
- **Moment of Inertia (I):**
\[
I = \frac{\pi}{4}r^4
\]
- **Cross-sectional Area (A):**
\[
A = \pi r^2
\]
- **Modulus of Elasticity (E):**
\[
E = 200 \times 10^9 \, \text{Pa}
\]
- **Density (β):**
\[
\beta = 7800 \, \text{kg/m}^3
\]
- **Acceleration due to Gravity (g):**
\[
g = 9.81 \, \text{m/s}^2
\]
- **Radius (r):**
\[
r = 0.01 \, \text{m}
\]
This setting and information enable calculations concerning the buckling behavior under given conditions of material and geometry.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe3b63b44-9302-458a-a5f0-5e786e8527ac%2F6dcb6e53-7054-44c9-9a27-a9a8f8407a08%2Frcbcy7g_processed.png&w=3840&q=75)
Transcribed Image Text:### Analysis of Pole Buckling Under Self-Weight
**Objective:**
Determine the length at which a vertical pole will buckle under its own weight.
**Given Diagram:**
A vertical pole fixed at the base, showing forces acting due to self-weight.
**Constants:**
- **Moment of Inertia (I):**
\[
I = \frac{\pi}{4}r^4
\]
- **Cross-sectional Area (A):**
\[
A = \pi r^2
\]
- **Modulus of Elasticity (E):**
\[
E = 200 \times 10^9 \, \text{Pa}
\]
- **Density (β):**
\[
\beta = 7800 \, \text{kg/m}^3
\]
- **Acceleration due to Gravity (g):**
\[
g = 9.81 \, \text{m/s}^2
\]
- **Radius (r):**
\[
r = 0.01 \, \text{m}
\]
This setting and information enable calculations concerning the buckling behavior under given conditions of material and geometry.
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