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A R₁ Find R1 and R2 reactions in kg. 1000 kg. 400 kg BY 3m 1.5m 6m to C 1.5m D R₂

A R₁ Find R1 and R2 reactions in kg. 1000 kg. 400 kg BY 3m 1.5m 6m to C 1.5m D 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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**Example Problem: Beam Supported at Both Ends** **Objective:** Find R1 and R2 reactions in kg. **Diagram Explanation:** - The beam is supported at two points, A and D, with reaction forces \( R_1 \) and \( R_2 \) respectively. - The beam has a total length of \( 6 \, \text{m} \), divided into segments as follows: - Segment \( AB = 3 \, \text{m} \) - Segment \( BC = 1.5 \, \text{m} \) - Segment \( CD = 1.5 \, \text{m} \) - Two vertical loads are applied on the beam: - A load of \( 1000 \, \text{kg} \) is placed at point \( B \). - A load of \( 400 \, \text{kg} \) is placed at point \( C \). To find the reactions \( R_1 \) and \( R_2 \), use the principles of static equilibrium. **Equations:** 1. **Sum of vertical forces:** \[ R_1 + R_2 = 1400 \, \text{kg} \] 2. **Taking moments about point A:** \[ R_1 \times 0 + 1000 \times 3 + 400 \times 4.5 = R_2 \times 6 \] (Note: The distances are taken from point A) Solving these equations will provide the values of \( R_1 \) and \( R_2 \).
Transcribed Image Text:**Example Problem: Beam Supported at Both Ends** **Objective:** Find R1 and R2 reactions in kg. **Diagram Explanation:** - The beam is supported at two points, A and D, with reaction forces \( R_1 \) and \( R_2 \) respectively. - The beam has a total length of \( 6 \, \text{m} \), divided into segments as follows: - Segment \( AB = 3 \, \text{m} \) - Segment \( BC = 1.5 \, \text{m} \) - Segment \( CD = 1.5 \, \text{m} \) - Two vertical loads are applied on the beam: - A load of \( 1000 \, \text{kg} \) is placed at point \( B \). - A load of \( 400 \, \text{kg} \) is placed at point \( C \). To find the reactions \( R_1 \) and \( R_2 \), use the principles of static equilibrium. **Equations:** 1. **Sum of vertical forces:** \[ R_1 + R_2 = 1400 \, \text{kg} \] 2. **Taking moments about point A:** \[ R_1 \times 0 + 1000 \times 3 + 400 \times 4.5 = R_2 \times 6 \] (Note: The distances are taken from point A) Solving these equations will provide the values of \( R_1 \) and \( R_2 \).
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