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A 16 m long cantilevered beam is supported by a fixed support at A and subjected to the loading shown. Draw the corresponding shear and bending moment diagram.

A 16 m long cantilevered beam is supported by a fixed support at A and subjected to the loading shown. Draw the corresponding shear and bending moment diagram.

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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Find reactions at A and Ma.

Give the (signed) values of the largest shear and bending moment occurring anywhere within the beam.

Draw the corresponding shear and bending moment diagram.

### Analysis of a Cantilevered Beam Subjected to Various Loads A cantilevered beam of 16 meters in length is supported by a fixed support at point \(A\) and subjected to different types of loading as illustrated in the provided diagram. #### Beam Loading Diagram The beam is subjected to: - A point load \(P\) of 40.0 kN applied downward at 1 meter from the fixed end. - A distributed load \(B\) of 20.0 kN applied over 5 meters from the fixed end. - A moment \(M\) of 60.0 kN·m applied at 1 meter from the free end of the beam. #### Shear Force Diagram (V(x)) - **Description**: The shear force diagram (V(x)) depicts the variation of the shear force along the length of the beam. - **Graph Interpretation**: - The diagram displays a constant shear force of 10 kN throughout the length of the beam. - The positive value indicates upwards for loads and reactions. #### Bending Moment Diagram (M(x)) - **Description**: The bending moment diagram (M(x)) illustrates the variation of the bending moment along the length of the beam. - **Graph Interpretation**: - The bending moment starts positive, peaking at 100 kN·m, and is linear across the entire beam. - The diagram is symmetrical about the origin (where \(M(x) = 0\)). ### Load Values - **P**: \( 40.0 \text{kN} \) - **B**: \( 20.0 \text{kN} \) - **M**: \( 60.0 \text{kN·m} \) ### Scales - The diagram uses scales of 10 kN for the shear force and 100 kN·m for the bending moment, as indicated by the labels and color codes: - Shear Force (V(x)): Red, 10 kN scaling - Bending Moment (M(x)): Purple, 100 kN·m scaling ### Conclusion The shear force and bending moment diagrams provide valuable insights into the stress distribution and bending behavior of the beam under the given loads. Understanding these diagrams is crucial for designing structural elements to ensure stability and safety.
Transcribed Image Text:### Analysis of a Cantilevered Beam Subjected to Various Loads A cantilevered beam of 16 meters in length is supported by a fixed support at point \(A\) and subjected to different types of loading as illustrated in the provided diagram. #### Beam Loading Diagram The beam is subjected to: - A point load \(P\) of 40.0 kN applied downward at 1 meter from the fixed end. - A distributed load \(B\) of 20.0 kN applied over 5 meters from the fixed end. - A moment \(M\) of 60.0 kN·m applied at 1 meter from the free end of the beam. #### Shear Force Diagram (V(x)) - **Description**: The shear force diagram (V(x)) depicts the variation of the shear force along the length of the beam. - **Graph Interpretation**: - The diagram displays a constant shear force of 10 kN throughout the length of the beam. - The positive value indicates upwards for loads and reactions. #### Bending Moment Diagram (M(x)) - **Description**: The bending moment diagram (M(x)) illustrates the variation of the bending moment along the length of the beam. - **Graph Interpretation**: - The bending moment starts positive, peaking at 100 kN·m, and is linear across the entire beam. - The diagram is symmetrical about the origin (where \(M(x) = 0\)). ### Load Values - **P**: \( 40.0 \text{kN} \) - **B**: \( 20.0 \text{kN} \) - **M**: \( 60.0 \text{kN·m} \) ### Scales - The diagram uses scales of 10 kN for the shear force and 100 kN·m for the bending moment, as indicated by the labels and color codes: - Shear Force (V(x)): Red, 10 kN scaling - Bending Moment (M(x)): Purple, 100 kN·m scaling ### Conclusion The shear force and bending moment diagrams provide valuable insights into the stress distribution and bending behavior of the beam under the given loads. Understanding these diagrams is crucial for designing structural elements to ensure stability and safety.
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