A uniform beam is simply supported at both ends x = 0 and x = L. Find the shape of the center line of the beam, given the weight per unit Length is w.....
A uniform beam is simply supported at both ends x = 0 and x = L. Find the shape of the center line of the beam, given the weight per unit Length is w.....
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Question
![**Problem Statement:**
A uniform beam is simply supported at both ends \( x = 0 \) and \( x = L \). Find the shape of the center line of the beam, given that the weight per unit length is \( w \).
**Possible Solutions:**
a. \[
y(x) = \frac{w}{24EI} \left[ 7L^4 x - 10L^3 x^3 + 3x^5 \right]
\]
b. \[
y(x) = \frac{w}{24EI} \left[ L^4 - 10L^2 x^3 + 3x^5 \right]
\]
c. \[
y(x) = \frac{w}{24EI} \left[ x^4 - 2L x^3 + L^3 x \right]
\]
d. \[
y(x) = \frac{w}{24EI} \left[ 2x^4 - 5L x^3 + 3L^2 x^4 \right]
\]
e. \[
y(x) = \frac{w}{24EI} \left[ 2L^4 x - 10L^3 x^3 + 3L x^5 \right]
\]
Where:
- \( y(x) \) is the deflection of the beam at a distance \( x \) from one end.
- \( w \) is the weight per unit length of the beam.
- \( E \) is the modulus of elasticity of the beam material.
- \( I \) is the moment of inertia of the beam cross-section about its neutral axis.
- \( L \) is the total length of the beam.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc59b3e01-f4fe-4ed0-a002-b05c91db4102%2Ff5e3c422-b9d4-4d67-a07a-bb423a4acdf6%2F390w32e_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
A uniform beam is simply supported at both ends \( x = 0 \) and \( x = L \). Find the shape of the center line of the beam, given that the weight per unit length is \( w \).
**Possible Solutions:**
a. \[
y(x) = \frac{w}{24EI} \left[ 7L^4 x - 10L^3 x^3 + 3x^5 \right]
\]
b. \[
y(x) = \frac{w}{24EI} \left[ L^4 - 10L^2 x^3 + 3x^5 \right]
\]
c. \[
y(x) = \frac{w}{24EI} \left[ x^4 - 2L x^3 + L^3 x \right]
\]
d. \[
y(x) = \frac{w}{24EI} \left[ 2x^4 - 5L x^3 + 3L^2 x^4 \right]
\]
e. \[
y(x) = \frac{w}{24EI} \left[ 2L^4 x - 10L^3 x^3 + 3L x^5 \right]
\]
Where:
- \( y(x) \) is the deflection of the beam at a distance \( x \) from one end.
- \( w \) is the weight per unit length of the beam.
- \( E \) is the modulus of elasticity of the beam material.
- \( I \) is the moment of inertia of the beam cross-section about its neutral axis.
- \( L \) is the total length of the beam.
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