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A 12 ft long cantilevered beam is supported by a fixed support at A and subjected to the loading shown. - find the reactions at A - Give the (signed) values of the largest shear and bending moment occuring anywhere within the beam. (Vmax and Mmax)

A 12 ft long cantilevered beam is supported by a fixed support at A and subjected to the loading shown. - find the reactions at A - Give the (signed) values of the largest shear and bending moment occuring anywhere within the beam. (Vmax and Mmax)

Elements Of Electromagnetics
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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A 12 ft long cantilevered beam is supported by a fixed support at A and subjected to the loading shown.

- find the reactions at A

- Give the (signed) values of the largest shear and bending moment occuring anywhere within the beam. (Vmax and Mmax)

### Analysis of Shear Force and Bending Moment for a Beam #### Problem Statement: Draw the shear and bending moment for the beam and loading shown. The beam is 20 meters long. #### Diagram of the Beam: The beam is supported at points A and B, which are located at the ends of the 20-meter beam. Point A is at the left end, and Point B is at the right end. The beam is horizontally aligned with three loads applied at specified points as follows: - Load at point C (5 meters from A): 130 kN directed downward. - Load at point D (10 meters from A): 50 kN directed downward. - Load at point E (15 meters from A): 130 kN directed downward. ### Loads: The loads applied to the beam are as follows: - \( C = 130 \) kN - \( D = 50 \) kN - \( E = 130 \) kN ### Scales: The scales provided in the diagram are: - 100 (red) - 500 (purple) ### Explanation of Graph Elements: 1. **V(x) Graph (Shear Force Diagram)**: - Represented in red. - This graph depicts the variation of shear force along the length of the beam. The horizontal axis represents the position \( x \) along the beam, while the vertical axis represents the magnitude of the shear force. 2. **M(x) Graph (Bending Moment Diagram)**: - Represented in purple. - This graph shows the variation of the bending moment along the beam. The horizontal axis represents the position \( x \) along the beam, and the vertical axis represents the magnitude of the bending moment. ### Points of Interest: - \( A \) and \( B \) indicate the supports at the ends of the beam. - \( C \), \( D \), and \( E \) represent the positions and magnitudes of point loads applied on the beam. - The graphs (\( V(x) \) and \( M(x) \)) start from the left support (point A) and extend to the right support (point B), indicating the shear force and bending moment values at various positions along the beam's length. This setup allows for a detailed analysis of the shear forces and bending moments distributed along a beam subjected to specific point loads, critical in the study and design of structural elements.
Transcribed Image Text:### Analysis of Shear Force and Bending Moment for a Beam #### Problem Statement: Draw the shear and bending moment for the beam and loading shown. The beam is 20 meters long. #### Diagram of the Beam: The beam is supported at points A and B, which are located at the ends of the 20-meter beam. Point A is at the left end, and Point B is at the right end. The beam is horizontally aligned with three loads applied at specified points as follows: - Load at point C (5 meters from A): 130 kN directed downward. - Load at point D (10 meters from A): 50 kN directed downward. - Load at point E (15 meters from A): 130 kN directed downward. ### Loads: The loads applied to the beam are as follows: - \( C = 130 \) kN - \( D = 50 \) kN - \( E = 130 \) kN ### Scales: The scales provided in the diagram are: - 100 (red) - 500 (purple) ### Explanation of Graph Elements: 1. **V(x) Graph (Shear Force Diagram)**: - Represented in red. - This graph depicts the variation of shear force along the length of the beam. The horizontal axis represents the position \( x \) along the beam, while the vertical axis represents the magnitude of the shear force. 2. **M(x) Graph (Bending Moment Diagram)**: - Represented in purple. - This graph shows the variation of the bending moment along the beam. The horizontal axis represents the position \( x \) along the beam, and the vertical axis represents the magnitude of the bending moment. ### Points of Interest: - \( A \) and \( B \) indicate the supports at the ends of the beam. - \( C \), \( D \), and \( E \) represent the positions and magnitudes of point loads applied on the beam. - The graphs (\( V(x) \) and \( M(x) \)) start from the left support (point A) and extend to the right support (point B), indicating the shear force and bending moment values at various positions along the beam's length. This setup allows for a detailed analysis of the shear forces and bending moments distributed along a beam subjected to specific point loads, critical in the study and design of structural elements.
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