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For the beam shown, find the reactions at the supports and plot the shear-force and bending-moment diagrams. Label the diagrams properly and provide values at all key points. 1.2 m R₁ 12 kN A 1 m 1 m B R₂ 14 kN C X

For the beam shown, find the reactions at the supports and plot the shear-force and bending-moment diagrams. Label the diagrams properly and provide values at all key points. 1.2 m R₁ 12 kN A 1 m 1 m B R₂ 14 kN C X

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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### Problem Description For the beam shown in the diagram below, find the reactions at the supports and plot the shear-force and bending-moment diagrams. Label the diagrams properly and provide values at all key points. ### Beam Diagram and Specifications ![Beam Diagram](image.png) A horizontal beam is shown with the following details: - Support \(O\) is at one end with reaction \(R_1\). - Support \(B\) is in the middle with reaction \(R_2\). - The left section \(OA\) is 1.2 meters long. - Point \(A\) is 1 meter from support \(B\). - Point \(C\) is 1 meter from support \(B\). - A 2 kN load is applied vertically downward at point \(A\). - A 4 kN load is applied vertically downward at point \(C\). ### Step-by-Step Solution 1. **Identify the Supports and Loads:** - Supports: \(O\) (with reaction \(R_1\)) and \(B\) (with reaction \(R_2\)). - Loads: 2 kN downward at \(A\), 4 kN downward at \(C\). 2. **Equilibrium Equations:** - Sum of vertical forces \( \sum F_y = 0 \): \( R_1 + R_2 - 2 \text{kN} - 4 \text{kN} = 0 \) - Taking moments about point \(O\): \( \sum M_O = 0 \): \( 1.2R_2 - 1.2 \cdot 2 \text{kN} - 2.2 \cdot 4 \text{kN} = 0 \) 3. **Solve for Reactions:** - Compute reactions \(R_1\) and \(R_2\). 4. **Shear-force Diagram (SFD):** - Calculate shear forces at key points: \(O\), \(A\), \(B\), \(C\). 5. **Bending-moment Diagram (BMD):** - Calculate moments at key points: \(O\), \(A\), \(B\), \(C\). ### Explanation of Diagrams - **Shear-force Diagram (SFD):** The SFD will illustrate how shear force varies
Transcribed Image Text:### Problem Description For the beam shown in the diagram below, find the reactions at the supports and plot the shear-force and bending-moment diagrams. Label the diagrams properly and provide values at all key points. ### Beam Diagram and Specifications ![Beam Diagram](image.png) A horizontal beam is shown with the following details: - Support \(O\) is at one end with reaction \(R_1\). - Support \(B\) is in the middle with reaction \(R_2\). - The left section \(OA\) is 1.2 meters long. - Point \(A\) is 1 meter from support \(B\). - Point \(C\) is 1 meter from support \(B\). - A 2 kN load is applied vertically downward at point \(A\). - A 4 kN load is applied vertically downward at point \(C\). ### Step-by-Step Solution 1. **Identify the Supports and Loads:** - Supports: \(O\) (with reaction \(R_1\)) and \(B\) (with reaction \(R_2\)). - Loads: 2 kN downward at \(A\), 4 kN downward at \(C\). 2. **Equilibrium Equations:** - Sum of vertical forces \( \sum F_y = 0 \): \( R_1 + R_2 - 2 \text{kN} - 4 \text{kN} = 0 \) - Taking moments about point \(O\): \( \sum M_O = 0 \): \( 1.2R_2 - 1.2 \cdot 2 \text{kN} - 2.2 \cdot 4 \text{kN} = 0 \) 3. **Solve for Reactions:** - Compute reactions \(R_1\) and \(R_2\). 4. **Shear-force Diagram (SFD):** - Calculate shear forces at key points: \(O\), \(A\), \(B\), \(C\). 5. **Bending-moment Diagram (BMD):** - Calculate moments at key points: \(O\), \(A\), \(B\), \(C\). ### Explanation of Diagrams - **Shear-force Diagram (SFD):** The SFD will illustrate how shear force varies
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