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(a) Determine R₁ and R₂. (b) Write the equations of the shear and moment. (c) Draw shear and bending moment diagrams. 20 kN/m R₁ 1m 3 m 80 kN/m * 1 1m R₂

(a) Determine R₁ and R₂. (b) Write the equations of the shear and moment. (c) Draw shear and bending moment diagrams. 20 kN/m R₁ 1m 3 m 80 kN/m * 1 1m R₂

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 Statement #### Tasks: (a) **Determine \( R_1 \) and \( R_2 \).** (b) **Write the equations of the shear and moment.** (c) **Draw shear and bending moment diagrams.** ### Diagram Analysis - The diagram represents a beam of total length 5 meters. - It is supported by two reactions: \( R_1 \) at the left end and \( R_2 \) at the right end. - The beam has two types of loads applied along its length: - A triangular distributed load starts at 20 kN/m on the left and increases linearly to 80 kN/m over a 4-meter span. - The length of the beam is divided into three sections: 1 meter on the left end, 3 meters in the middle, and 1 meter on the right end. ### Explanation of Loads 1. **Triangular Distributed Load:** - Begins at 20 kN/m and increases to 80 kN/m over a distance of 4 meters. - This type of load linearly varies, creating a triangular shape in the load distribution graph. ### Steps to Solve 1. **Determine Support Reactions \( R_1 \) and \( R_2 \):** - Utilize equilibrium equations for statics, such as summing moments about one point to solve for the reactions at supports. 2. **Write Equations of Shear and Moment:** - Use the calculated reactions and applied loads to derive expressions for shear force and bending moment along the length of the beam. - Develop piecewise functions to account for changes in loading conditions across different sections. 3. **Draw Diagrams:** - **Shear Force Diagram (SFD):** Illustrates how shear force varies across the beam; typically, it will start from zero, increase or decrease according to the loads, and return to zero at the supports. - **Bending Moment Diagram (BMD):** Shows the bending moment variation, shaped typically as curves between the points of zero moment, with maximum or minimum values occurring where shear force crosses zero or load discontinuity points. These diagrams help understand where maximum shear and bending stresses occur, crucial for structural analysis and design.
Transcribed Image Text:### Problem Statement #### Tasks: (a) **Determine \( R_1 \) and \( R_2 \).** (b) **Write the equations of the shear and moment.** (c) **Draw shear and bending moment diagrams.** ### Diagram Analysis - The diagram represents a beam of total length 5 meters. - It is supported by two reactions: \( R_1 \) at the left end and \( R_2 \) at the right end. - The beam has two types of loads applied along its length: - A triangular distributed load starts at 20 kN/m on the left and increases linearly to 80 kN/m over a 4-meter span. - The length of the beam is divided into three sections: 1 meter on the left end, 3 meters in the middle, and 1 meter on the right end. ### Explanation of Loads 1. **Triangular Distributed Load:** - Begins at 20 kN/m and increases to 80 kN/m over a distance of 4 meters. - This type of load linearly varies, creating a triangular shape in the load distribution graph. ### Steps to Solve 1. **Determine Support Reactions \( R_1 \) and \( R_2 \):** - Utilize equilibrium equations for statics, such as summing moments about one point to solve for the reactions at supports. 2. **Write Equations of Shear and Moment:** - Use the calculated reactions and applied loads to derive expressions for shear force and bending moment along the length of the beam. - Develop piecewise functions to account for changes in loading conditions across different sections. 3. **Draw Diagrams:** - **Shear Force Diagram (SFD):** Illustrates how shear force varies across the beam; typically, it will start from zero, increase or decrease according to the loads, and return to zero at the supports. - **Bending Moment Diagram (BMD):** Shows the bending moment variation, shaped typically as curves between the points of zero moment, with maximum or minimum values occurring where shear force crosses zero or load discontinuity points. These diagrams help understand where maximum shear and bending stresses occur, crucial for structural analysis and design.
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