30 KN A 1m B 3 m 50 KN 2 m D
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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Beam loaded as shown in Fig. below. Determine the Following:
Reaction support at point B.
a. 56KN (Downward Direction)
b. 56KN (Upward Direction)
c. 35KN (Downward Direction)
d. 35KN (Upward Direction)
Reaction support at point D.
a. 26 KN (Downward Direction)
b. 26 KN (Upward Direction)
c. 24KN (Downward Direction)
d. 24KN (Upward Direction)
Shear force equation of section AB.
a. -30KN
b. 30KN
c. -32KN
d. 32KN
Shear force equation of section CD.
a. -24KN
b. 24KN
c. -28KN
d. 28KN
Bending moment equation of section BC.
a. 26KN(x)+56KN.m
b. 26KN(x)-56KN.m
c. -26KN(x)+56KN.m
d. None of the above.
Maximum bending moment of the beam.
a. 47KN.m
b. 46KN.m
c. 48KN.m
d. None of the above
Transcribed Image Text:### Equilibrium of Forces in a Simple Beam System
This diagram provides a visual representation of the equilibrium of forces in a simple beam system. Let's break down the different components and forces in this setup:
#### Components:
- **Beam (ABCD):** This is the horizontal element that is subjected to external forces.
- **Supports (B and D):** These are the points at which the beam is supported. Support at point B looks like a hinge (or pin) support, and support at point D is a roller support.
#### External Forces:
- **Point A:** A downward force of 30 kN is applied.
- **Point C:** A downward force of 50 kN is applied.
#### Distances:
- **Distance AB:** 1 meter from point A to the first support at B.
- **Distance BC:** 3 meters between supports B and C.
- **Distance CD:** 2 meters from the second load at point C to the support at D.
### Detailed Explanation:
1. **Loading Conditions:**
- **A (30 kN):** Point A is subjected to a concentrated load of 30 kN acting vertically downward.
- **C (50 kN):** Point C is subjected to a concentrated load of 50 kN acting vertically downward.
2. **Supports and Reactions:**
- **Support B:** Hinge (pin) support at point B allows rotation but restricts translations in both horizontal and vertical directions.
- **Support D:** Roller support at point D allows rotation and horizontal translation but restricts vertical translation.
3. **Force Distribution:**
- The beam is supported at two points which means the reaction forces at points B and D will balance the applied loads to satisfy the equilibrium conditions.
### Equilibrium Conditions:
For the beam to be in equilibrium, the following conditions must be satisfied:
1. **Sum of Vertical Forces:** The sum of the vertical forces must be zero.
2. **Sum of Moments:** The sum of the moments about any point must be zero, typically calculated about a support.
#### Calculation of Reactions:
To find the reactions at supports (B and D), use the equilibrium equations:
- \( \Sigma F_y = 0 \) (sum of vertical forces)
- \( \Sigma M_{any point} = 0 \) (sum of moments about any point, usually around one of the supports to simplify calculations)
By solving these equations,
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Follow-up Question
Solve for the Following:
Shear force equation of section CD.
a. -24KN
b. 24KN
c. -28KN
d. 28KN
Bending moment equation of section BC.
a. 26KN(x)+56KN.m
b. 26KN(x)-56KN.m
c. -26KN(x)+56KN.m
d. None of the above.
Maximum bending moment of the beam.
a. 47KN.m
b. 46KN.m
c. 48KN.m
d. None of the above
![### Structural Analysis of a Simply Supported Beam with Point Loads
The diagram demonstrates a simply supported beam subjected to two point loads. The beam is horizontal and rests on two supports located at points B and D, which are assumed to be pin and roller supports respectively. Here is a detailed explanation of the configuration:
1. **Support Locations and Distance:**
- Point A to Point B: The distance between point A and support B is 1 meter.
- Point B to Point C: The distance between support B and point C is 3 meters.
- Point C to Point D: The distance between point C and support D is 2 meters.
2. **Load Application:**
- A vertical point load of 30 kN is applied downward at point A.
- Another vertical point load of 50 kN is applied downward at point C.
3. **Support Types:**
- Support at Point B: This is a pin support, which allows rotation but prevents translation in any direction.
- Support at Point D: This is a roller support, which allows horizontal translation but prevents vertical movement.
### Explanation of Forces and Reactions
When analyzing such a beam, the reactions at the supports (B and D) must be determined to ensure equilibrium. The steps typically include:
1. **Summing up the vertical forces:**
\[ \sum F_y = 0 \quad \Rightarrow \quad R_B + R_D - 30\, \text{kN} - 50\, \text{kN} = 0 \]
2. **Taking moments about one of the supports to solve for the reactions:**
For instance, taking moments about point B:
\[ \sum M_B = 0 \quad \Rightarrow \quad -30\, \text{kN} \times 1\, \text{m} + R_D \times 5\, \text{m} - 50\, \text{kN} \times 4\, \text{m} = 0 \]
3. **Solving these equations will give the reactions at the supports:**
- \( R_B \) is the reaction at the pin support B.
- \( R_D \) is the reaction at the roller support D.
Analyzing this beam is crucial in structural engineering to ensure that it can withstand the applied loads without failure. Understanding the types of supports and the nature of loads acting](https://content.bartleby.com/qna-images/question/0ef7dced-e510-451b-b91a-a720e02ad23a/ee964b19-ec7f-4d36-9ab9-55085addc17a/3kk9hqt_processed.png)
Transcribed Image Text:### Structural Analysis of a Simply Supported Beam with Point Loads
The diagram demonstrates a simply supported beam subjected to two point loads. The beam is horizontal and rests on two supports located at points B and D, which are assumed to be pin and roller supports respectively. Here is a detailed explanation of the configuration:
1. **Support Locations and Distance:**
- Point A to Point B: The distance between point A and support B is 1 meter.
- Point B to Point C: The distance between support B and point C is 3 meters.
- Point C to Point D: The distance between point C and support D is 2 meters.
2. **Load Application:**
- A vertical point load of 30 kN is applied downward at point A.
- Another vertical point load of 50 kN is applied downward at point C.
3. **Support Types:**
- Support at Point B: This is a pin support, which allows rotation but prevents translation in any direction.
- Support at Point D: This is a roller support, which allows horizontal translation but prevents vertical movement.
### Explanation of Forces and Reactions
When analyzing such a beam, the reactions at the supports (B and D) must be determined to ensure equilibrium. The steps typically include:
1. **Summing up the vertical forces:**
\[ \sum F_y = 0 \quad \Rightarrow \quad R_B + R_D - 30\, \text{kN} - 50\, \text{kN} = 0 \]
2. **Taking moments about one of the supports to solve for the reactions:**
For instance, taking moments about point B:
\[ \sum M_B = 0 \quad \Rightarrow \quad -30\, \text{kN} \times 1\, \text{m} + R_D \times 5\, \text{m} - 50\, \text{kN} \times 4\, \text{m} = 0 \]
3. **Solving these equations will give the reactions at the supports:**
- \( R_B \) is the reaction at the pin support B.
- \( R_D \) is the reaction at the roller support D.
Analyzing this beam is crucial in structural engineering to ensure that it can withstand the applied loads without failure. Understanding the types of supports and the nature of loads acting
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