The simply supported steel beam shown is fabricated from an American Standard S18 x 54.7 section. F -4/₂- Given: • L = 10 ft • 9o = 4 kip/ft F = 8 kip . B₁ B₂ B3 = number (rtol=0.01, atol=1e-05) C₁ = number (rtol=0.01, atol=1e-05) C₂ number (rtol=0.01, atol=1e-05) Write an elastic curve equation valid for the entire beam in the following form: y(x) =B₁³ + B₂ < x-5>³ + B₁ < x-5>¹ + ₁ + €₂] Place the coordinate system origin (x = 0) at the left end of the beam. Give values for the missing terms, in the units listed. || || || number (rtol=0.01, atol=1e-05) number (rtol=0.01, atol=1e-05) Determine the deflection and slope at x = 1.5 ft. Yx = Yz L number (rtol=0.01, atol=1e-05) number (rtol=0.01, atol=1e-05) kip kip kip/ft kip. ft² kip. ft³ qo in
The simply supported steel beam shown is fabricated from an American Standard S18 x 54.7 section. F -4/₂- Given: • L = 10 ft • 9o = 4 kip/ft F = 8 kip . B₁ B₂ B3 = number (rtol=0.01, atol=1e-05) C₁ = number (rtol=0.01, atol=1e-05) C₂ number (rtol=0.01, atol=1e-05) Write an elastic curve equation valid for the entire beam in the following form: y(x) =B₁³ + B₂ < x-5>³ + B₁ < x-5>¹ + ₁ + €₂] Place the coordinate system origin (x = 0) at the left end of the beam. Give values for the missing terms, in the units listed. || || || number (rtol=0.01, atol=1e-05) number (rtol=0.01, atol=1e-05) Determine the deflection and slope at x = 1.5 ft. Yx = Yz L number (rtol=0.01, atol=1e-05) number (rtol=0.01, atol=1e-05) kip kip kip/ft kip. ft² kip. ft³ qo in
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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![## HW6.2: Deformation of a Steel I-Beam
### Description
The simply supported steel beam shown is fabricated from an American Standard S18 x 54.7 section.
#### Diagram Explanation
The diagram illustrates a beam with:
- A length \( L \), divided into two equal sections of \( L/2 \).
- A point load \( F \) applied at the center.
- A uniformly distributed load \( q_o \) acting along part of the beam's length.
- Supports at both ends of the beam.
### Given:
- \( L = 10 \) ft
- \( q_o = 4 \) kip/ft
- \( F = 8 \) kip
### Task
Write an elastic curve equation valid for the entire beam in the following form:
\[
y(x) = \frac{1}{EI} [\beta_1 x^3 + \beta_2 \langle x - 5 \rangle^3 + \beta_3 \langle x - 5 \rangle^4 + C_1 x + C_2]
\]
- Place the coordinate system origin (\( x = 0 \)) at the left end of the beam.
- Provide values for the missing terms in the units listed below.
#### Unknown Variables:
- \( \beta_1 = \) [number (rtol=0.01, atol=1e-05)] kip
- \( \beta_2 = \) [number (rtol=0.01, atol=1e-05)] kip
- \( \beta_3 = \) [number (rtol=0.01, atol=1e-05)] kip/ft
- \( C_1 = \) [number (rtol=0.01, atol=1e-05)] kip⋅ft\(^2\)
- \( C_2 = \) [number (rtol=0.01, atol=1e-05)] kip⋅ft\(^3\)
### Determine the deflection and slope at \( x = 1.5 \) ft:
- \( y_{x} = \) [number (rtol=0.01, atol=1e-05)] in
- \( y'_{x} = \) [number (rtol=0.01, atol=1e-05)] °](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F12ae3db2-d1ea-4786-8934-352b9e22afb1%2F256dd1d8-86c7-4bd6-bd6f-efab938a2ef9%2Flm60qx_processed.png&w=3840&q=75)
Transcribed Image Text:## HW6.2: Deformation of a Steel I-Beam
### Description
The simply supported steel beam shown is fabricated from an American Standard S18 x 54.7 section.
#### Diagram Explanation
The diagram illustrates a beam with:
- A length \( L \), divided into two equal sections of \( L/2 \).
- A point load \( F \) applied at the center.
- A uniformly distributed load \( q_o \) acting along part of the beam's length.
- Supports at both ends of the beam.
### Given:
- \( L = 10 \) ft
- \( q_o = 4 \) kip/ft
- \( F = 8 \) kip
### Task
Write an elastic curve equation valid for the entire beam in the following form:
\[
y(x) = \frac{1}{EI} [\beta_1 x^3 + \beta_2 \langle x - 5 \rangle^3 + \beta_3 \langle x - 5 \rangle^4 + C_1 x + C_2]
\]
- Place the coordinate system origin (\( x = 0 \)) at the left end of the beam.
- Provide values for the missing terms in the units listed below.
#### Unknown Variables:
- \( \beta_1 = \) [number (rtol=0.01, atol=1e-05)] kip
- \( \beta_2 = \) [number (rtol=0.01, atol=1e-05)] kip
- \( \beta_3 = \) [number (rtol=0.01, atol=1e-05)] kip/ft
- \( C_1 = \) [number (rtol=0.01, atol=1e-05)] kip⋅ft\(^2\)
- \( C_2 = \) [number (rtol=0.01, atol=1e-05)] kip⋅ft\(^3\)
### Determine the deflection and slope at \( x = 1.5 \) ft:
- \( y_{x} = \) [number (rtol=0.01, atol=1e-05)] in
- \( y'_{x} = \) [number (rtol=0.01, atol=1e-05)] °
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Step 1: Consider the FBD of the beam.
VIEWStep 2: Apply Macaulay's method.
VIEWStep 3: Evaluate slope and deflection using double integration method.
VIEWStep 4: Evaluate constants of integration using boundary conditions.
VIEWStep 5: Compare given elastic curve equation with equation (2a).
VIEWStep 6: Evaluate slope and deflection at x=1.5 ft.
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