Determine the slope at B measured counterclockwise from the positive ¤ axis. Express your answer in terms of some or all of the variables E, I, P, and a. vec ? OB = Submit Request Answer Part B Determine the displacement at C measured upward. Express your answer in terms of some or all of the variables E, I, P, and a. Enter positive value if the displacement is upward and negative value if the displacement is downward.
Determine the slope at B measured counterclockwise from the positive ¤ axis. Express your answer in terms of some or all of the variables E, I, P, and a. vec ? OB = Submit Request Answer Part B Determine the displacement at C measured upward. Express your answer in terms of some or all of the variables E, I, P, and a. Enter positive value if the displacement is upward and negative value if the displacement is downward.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
Related questions
Question
Consider the beam shown in (Figure 1). EIEI is constant. Use the conjugate-beam method.
Part A:
Determine the slope at B measured counterclockwise from the positive x axis.
Express your answer in terms of some or all of the variables E, I, P, and a.
Part B
Determine the displacement at C measured upward.
Express your answer in terms of some or all of the variables E, I, P, and a.
Enter positive value if the displacement is upward and negative value if the displacement is downward.
![### Problem Statement
#### Part A
**Determine the slope at \( B \) measured counterclockwise from the positive \( x \)-axis.**
Express your answer in terms of some or all of the variables \( E \), \( I \), \( P \), and \( a \).
Input:
\[ \theta_B = \]
_Button_: **Submit**
_Button_: **Request Answer**
#### Part B
**Determine the displacement at \( C \) measured upward.**
Express your answer in terms of some or all of the variables \( E \), \( I \), \( P \), and \( a \). Enter positive value if the displacement is upward and negative value if the displacement is downward.
Input:
\[ \]
---
In this problem, you need to use your understanding of structural analysis to determine the required parameters. Here's a step-by-step guideline on how to approach the problem:
1. **Identify the Necessary Parameters**: Understand the given variables: \( E \) (Modulus of Elasticity), \( I \) (Moment of Inertia), \( P \) (Load/Force), and \( a \) (Distance/Length).
2. **Use Relevant Formulas**:
- For **slope** (\( \theta \)) at a point on a beam, you may need Euler-Bernoulli beam theory where
\(\theta = \frac{d\delta}{dx}\),
where \(\delta\) is the deflection.
- For **displacement** (\( \delta \)), use the deflection formula for beams under load.
### Explanation of Graphs/Diagrams
No graphs or diagrams are provided in the given text. Focus on the instructions and the variables provided to solve the problem.
Feel free to use the structured input area to enter terms and equations as required. Use the provided input tools to format your answer properly.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5e0c553f-25e4-4bb8-9dbb-2f691b8513ce%2Fafc39e2b-f3d6-44b1-ab78-4b081ad454ac%2Fxewsv_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Statement
#### Part A
**Determine the slope at \( B \) measured counterclockwise from the positive \( x \)-axis.**
Express your answer in terms of some or all of the variables \( E \), \( I \), \( P \), and \( a \).
Input:
\[ \theta_B = \]
_Button_: **Submit**
_Button_: **Request Answer**
#### Part B
**Determine the displacement at \( C \) measured upward.**
Express your answer in terms of some or all of the variables \( E \), \( I \), \( P \), and \( a \). Enter positive value if the displacement is upward and negative value if the displacement is downward.
Input:
\[ \]
---
In this problem, you need to use your understanding of structural analysis to determine the required parameters. Here's a step-by-step guideline on how to approach the problem:
1. **Identify the Necessary Parameters**: Understand the given variables: \( E \) (Modulus of Elasticity), \( I \) (Moment of Inertia), \( P \) (Load/Force), and \( a \) (Distance/Length).
2. **Use Relevant Formulas**:
- For **slope** (\( \theta \)) at a point on a beam, you may need Euler-Bernoulli beam theory where
\(\theta = \frac{d\delta}{dx}\),
where \(\delta\) is the deflection.
- For **displacement** (\( \delta \)), use the deflection formula for beams under load.
### Explanation of Graphs/Diagrams
No graphs or diagrams are provided in the given text. Focus on the instructions and the variables provided to solve the problem.
Feel free to use the structured input area to enter terms and equations as required. Use the provided input tools to format your answer properly.
Transcribed Image Text:### Topic: Analyzing Beams using the Conjugate-Beam Method
#### Example Problem: Analyzing a Simply Supported Beam
**Problem Statement:**
Consider the beam shown in **(Figure 1)**. \( EI \) is constant. Use the conjugate-beam method.
**Description:**
The figure shows a beam extending to the right from the free end \( C \) to the pin-supported end \( A \). The beam is roller-supported at point \( B \), which is at a distance \( a \) from \( C \). Two forces equal to \( P \) act downward on \( C \) and on a point, that is at a distance \( a \) from both \( B \) and \( A \). The distance \( x \) from \( C \) to a point on the beam is shown.
**Diagram Explanation:**
1. **Supports and Distances:**
- The beam is pin-supported at \( A \).
- The beam is roller-supported at \( B \), which is a distance \( a \) away from \( C \).
- The length of the beam from point \( C \) to point \( A \) is \( 3a \).
2. **Forces:**
- A force \( P \) acts downward on the free end \( C \).
- Another force \( P \) acts downward at a point located at distance \( a \) from both \( B \) and \( A \).
3. **Labels:**
- The beam is labeled \( A \) at the pin-supported end and \( C \) at the free end.
- \( B \) is the roller support located at a distance \( a \) from \( C \).
By using the conjugate-beam method, we can determine the deflections and slopes along the beam under the given loading conditions.
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