1) Derive the shear and bending moment diagram for the following beam loading: A 0000 500 N 500 N B 0.4 m- -0.4 m C D -0.4 m- 2400 N/m 0.3 m a) Using the method of cutting the beam at several points at distance x from A b) Using a method that uses the following relationships between V, w, and M: dv dx = -W V = E dM dx
1) Derive the shear and bending moment diagram for the following beam loading: A 0000 500 N 500 N B 0.4 m- -0.4 m C D -0.4 m- 2400 N/m 0.3 m a) Using the method of cutting the beam at several points at distance x from A b) Using a method that uses the following relationships between V, w, and M: dv dx = -W V = E dM dx
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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![### Shear and Bending Moment Diagrams
#### Objective:
Derive the shear force and bending moment diagram for the provided beam loading.
#### Beam Loading Description:
- The beam has a hinge support at point A and a roller support at point D.
- Point loads of 500 N are applied downward at points B and C.
- A uniformly distributed load of 2400 N/m is applied between points D and E.
#### Beam Specifications:
- Length between supports A and B: 0.4 m
- Length between supports B and C: 0.4 m
- Length between supports C and D: 0.4 m
- Length between supports D and E: 0.3 m
#### Steps:
##### a) Using the method of cutting the beam at several points at distance \( x \) from A:
1. **Calculate Reactions at Supports**:
- Sum of vertical forces and moments to determine the reaction forces at supports A and D.
2. **Shear Force and Bending Moment Calculations**:
- Divide the beam into segments (AB, BC, CD, DE).
- Write equilibrium equations for each segment to determine the shear force (V) and bending moment (M) for the beam.
##### b) Using the relationship between V, w, and M:
Given the relationships:
\[ \frac{dV}{dx} = -w \]
\[ V = \frac{dM}{dx} \]
1. **Shear and Moment Distribution**:
- Use the differential relationships to derive the expressions for shear force (V) and bending moment (M) along the beam.
#### Explanation of Graphs and Diagrams:
- The **Shear Force Diagram (V)** typically plots the shear force values along the length of the beam.
- The **Bending Moment Diagram (M)** plots the bending moment values along the length of the beam.
- Transitions and discontinuities in these diagrams occur at points of applied loads and supports.
**Note on Diagrams**:
- The diagrams should illustrate the changes in shear force and bending moment at each segment of the beam.
- The vertical loads will create downward spikes in the shear force diagram.
- Support reactions will cause upward spikes in the shear force diagram.
- In the bending moment diagram, moments are highest where shear changes sign (zero-crossings).
The objective is to comprehend the distribution of internal forces resulting from external loads and to use](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F06728e89-3f8b-48c3-ace6-581691a0e4c4%2F6aba90e3-fee0-4a35-af6e-fd2d73ec5d9f%2F1ygqhj9_processed.png&w=3840&q=75)
Transcribed Image Text:### Shear and Bending Moment Diagrams
#### Objective:
Derive the shear force and bending moment diagram for the provided beam loading.
#### Beam Loading Description:
- The beam has a hinge support at point A and a roller support at point D.
- Point loads of 500 N are applied downward at points B and C.
- A uniformly distributed load of 2400 N/m is applied between points D and E.
#### Beam Specifications:
- Length between supports A and B: 0.4 m
- Length between supports B and C: 0.4 m
- Length between supports C and D: 0.4 m
- Length between supports D and E: 0.3 m
#### Steps:
##### a) Using the method of cutting the beam at several points at distance \( x \) from A:
1. **Calculate Reactions at Supports**:
- Sum of vertical forces and moments to determine the reaction forces at supports A and D.
2. **Shear Force and Bending Moment Calculations**:
- Divide the beam into segments (AB, BC, CD, DE).
- Write equilibrium equations for each segment to determine the shear force (V) and bending moment (M) for the beam.
##### b) Using the relationship between V, w, and M:
Given the relationships:
\[ \frac{dV}{dx} = -w \]
\[ V = \frac{dM}{dx} \]
1. **Shear and Moment Distribution**:
- Use the differential relationships to derive the expressions for shear force (V) and bending moment (M) along the beam.
#### Explanation of Graphs and Diagrams:
- The **Shear Force Diagram (V)** typically plots the shear force values along the length of the beam.
- The **Bending Moment Diagram (M)** plots the bending moment values along the length of the beam.
- Transitions and discontinuities in these diagrams occur at points of applied loads and supports.
**Note on Diagrams**:
- The diagrams should illustrate the changes in shear force and bending moment at each segment of the beam.
- The vertical loads will create downward spikes in the shear force diagram.
- Support reactions will cause upward spikes in the shear force diagram.
- In the bending moment diagram, moments are highest where shear changes sign (zero-crossings).
The objective is to comprehend the distribution of internal forces resulting from external loads and to use
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VIEWStep 3: SF and BM calculation at distance x form point A
VIEWStep 4: Shear force and bending moment diagram and Part B
VIEWStep 5: Shear force and bending moment calculation for Part B using given information
VIEWStep 6: Shear force and bending moment diagram
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