### Calculating Support Reactions for a Loaded BeamIn this example, we will calculate the support reactions at points \(A\) and \(B\) for the loaded beam.#### Given Data:- Force \(P = 143 \text{ lb}\)- Distributed Load \(w = 92 \text{ lb/ft}\)- Distance \(a = 3.2 \text{ ft}\)- Distance \(b = 7.0 \text{ ft}\)#### Diagram Explanation:The diagram provided illustrates a beam supported at two points, \(A\) (fixed support) and \(B\) (roller support). The following elements are depicted:- **Support at A:** This support can provide reactions in both the horizontal (\(A_x\)) and vertical (\(A_y\)) directions.- **Support at B:** This is a roller support that provides a vertical reaction (\(B_y\)).- **Point Load \(P\)** applied vertically downward at a distance \(a\) from support \(A\).- **Distributed Load \(w\):** The load varies linearly across the span from point \(A\) to point \(B\).- **Coordinates:** \(x\) represents the horizontal axis, while \(y\) represents the vertical axis.#### Calculation Objective:We need to compute the reactions at the supports \(A_x\), \(A_y\), and \(B_y\).#### Calculation Steps:1. **Sum of Horizontal Forces:** \[ \Sigma F_x = 0 \] \[ A_x = 0 \] 2. **Sum of Vertical Forces:** \[ \Sigma F_y = 0 \] \[ A_y + B_y - P - w \times (a + b) = 0 \] 3. **Moment Around Point A:** \[ \Sigma M_A = 0 \] \[ -P \times a - \left( \frac{w \times (a + b) \times (a + b/2)}{2} \right) + B_y \times (a + b) = 0 \]By solving these equations, the values for \(A_y\) and \(B_y\) can be determined. Insert these computed values:#### Answers:- \( A_x = \)- \( A_y = \)-

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Answered: Calculate the support reactions at A…

Calculate the support reactions at A and B for the loaded beam. Assume P = 143 lb, w = 92 lb/ft, a = 3.2 ft, and b = 7.0 ft. L A _a. P b W B

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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