### 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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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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Concept explainers

Bending Moment

In general, we can define the bending moment as the reaction induced when a certain amount of load or force is applied to an element which makes it bend.

Question

### 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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