Elements Of Electromagnetics
7th Edition
ISBN: 9780190698614
Author: Sadiku, Matthew N. O.
Publisher: Oxford University Press
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![### Calculating Support Reactions for a Loaded Beam
In this example, we will calculate the support reactions at points \(A\) and \(B\) for the loaded beam.
#### Given Data:
- Force \(P = 143 \text{ lb}\)
- Distributed Load \(w = 92 \text{ lb/ft}\)
- Distance \(a = 3.2 \text{ ft}\)
- Distance \(b = 7.0 \text{ ft}\)
#### Diagram Explanation:
The diagram provided illustrates a beam supported at two points, \(A\) (fixed support) and \(B\) (roller support). The following elements are depicted:
- **Support at A:** This support can provide reactions in both the horizontal (\(A_x\)) and vertical (\(A_y\)) directions.
- **Support at B:** This is a roller support that provides a vertical reaction (\(B_y\)).
- **Point Load \(P\)** applied vertically downward at a distance \(a\) from support \(A\).
- **Distributed Load \(w\):** The load varies linearly across the span from point \(A\) to point \(B\).
- **Coordinates:** \(x\) represents the horizontal axis, while \(y\) represents the vertical axis.
#### Calculation Objective:
We need to compute the reactions at the supports \(A_x\), \(A_y\), and \(B_y\).
#### Calculation Steps:
1. **Sum of Horizontal Forces:**
\[ \Sigma F_x = 0 \]
\[ A_x = 0 \]
2. **Sum of Vertical Forces:**
\[ \Sigma F_y = 0 \]
\[ A_y + B_y - P - w \times (a + b) = 0 \]
3. **Moment Around Point A:**
\[ \Sigma M_A = 0 \]
\[ -P \times a - \left( \frac{w \times (a + b) \times (a + b/2)}{2} \right) + B_y \times (a + b) = 0 \]
By solving these equations, the values for \(A_y\) and \(B_y\) can be determined. Insert these computed values:
#### Answers:
- \( A_x = \)
- \( A_y = \)
-](https://content.bartleby.com/qna-images/question/c59a6d07-a993-40f7-b57e-cdb2ad079d78/3a2cb088-d692-45df-b7e8-6db44b13e449/yuifht9_processed.png)
Transcribed Image Text:### Calculating Support Reactions for a Loaded Beam
In this example, we will calculate the support reactions at points \(A\) and \(B\) for the loaded beam.
#### Given Data:
- Force \(P = 143 \text{ lb}\)
- Distributed Load \(w = 92 \text{ lb/ft}\)
- Distance \(a = 3.2 \text{ ft}\)
- Distance \(b = 7.0 \text{ ft}\)
#### Diagram Explanation:
The diagram provided illustrates a beam supported at two points, \(A\) (fixed support) and \(B\) (roller support). The following elements are depicted:
- **Support at A:** This support can provide reactions in both the horizontal (\(A_x\)) and vertical (\(A_y\)) directions.
- **Support at B:** This is a roller support that provides a vertical reaction (\(B_y\)).
- **Point Load \(P\)** applied vertically downward at a distance \(a\) from support \(A\).
- **Distributed Load \(w\):** The load varies linearly across the span from point \(A\) to point \(B\).
- **Coordinates:** \(x\) represents the horizontal axis, while \(y\) represents the vertical axis.
#### Calculation Objective:
We need to compute the reactions at the supports \(A_x\), \(A_y\), and \(B_y\).
#### Calculation Steps:
1. **Sum of Horizontal Forces:**
\[ \Sigma F_x = 0 \]
\[ A_x = 0 \]
2. **Sum of Vertical Forces:**
\[ \Sigma F_y = 0 \]
\[ A_y + B_y - P - w \times (a + b) = 0 \]
3. **Moment Around Point A:**
\[ \Sigma M_A = 0 \]
\[ -P \times a - \left( \frac{w \times (a + b) \times (a + b/2)}{2} \right) + B_y \times (a + b) = 0 \]
By solving these equations, the values for \(A_y\) and \(B_y\) can be determined. Insert these computed values:
#### Answers:
- \( A_x = \)
- \( A_y = \)
-
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- question 6arrow_forwardDetermine the reactions present at the pin A and roller B required for equilibrium of the beam. (Final Answers – signs depend on FBD: Ay = 2230 N, Ax = 0, B = 2170Narrow_forwardDraw the F.B.D. for the beam shown in fig * ? and then find the reactions at A and B 2 kN/m 1.5 kN y 30° L--x 1.2 m 0.6 1.2 m 1.8 m 1.2 marrow_forward
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