**Problem Statement:**Determine the reactions at the supports of the beam which is loaded as shown. Assume \( w_1 = 660 \, \text{N/m} \), \( w_2 = 400 \, \text{N/m} \), \( a = 6.6 \, \text{m} \), \( b = 1.2 \, \text{m} \).**Diagram Description:**The diagram shows a beam supported at two points: \( A \) and \( B \). Point \( A \) is on the left end of the beam and is supported by a pin support, while point \( B \) is to the right of point \( A \) and is supported by a roller support. The beam is subjected to a trapezoidal distributed load, with \( w_1 \) at the leftmost end of the beam, reducing linearly to \( w_2 \) just before point \( B \). Lengths are denoted as follows:- Distance \( a \) from point \( A \) to the vertical position just before point \( B \), where the supports and the distributed load are also depicted.- Distance \( b \) from the endpoint of the load until point \( B \).**Calculations Section:***Answers* (Reactions at supports):- \( A_x \) \( = \) [Input Field] N- \( A_y \) \( = \) [Input Field] N- \( B_y \) \( = \) [Input Field] N**Instructions for Students:**To solve this problem, consider the following steps:1. Determine the equivalent point loads of the distributed load.2. Apply the equilibrium equations to the beam to find the reactions at the supports: - Sum of Vertical Forces (\( \sum F_y = 0 \)) - Sum of Horizontal Forces (\( \sum F_x = 0 \)) - Sum of Moments about a point (\( \sum M = 0 \))3. Use the given dimensions and loads to find reactions at points \(A\) and \(B\).Ensure to show all your workings and check your results for accuracy.

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Answered: Determine the reactions at the supports…

Determine the reactions at the supports of the beam which is loaded as shown. Assume w₁ = 660 N/m, w₂ = 400 N/m, a = 6.6 m, b = 1.2 m.

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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Concept explainers

Types of loading

In mechanical terminology, the term load indicates that external force/weight, either constant or variable, acts on a mechanical member/structure. The weight of an object of a specific material is also an external load, and the external force that works on a structure comes under the categories of loading. The external load generates its effects as stress and strain in the structure.

Question

**Problem Statement:**

Determine the reactions at the supports of the beam which is loaded as shown. Assume \( w_1 = 660 \, \text{N/m} \), \( w_2 = 400 \, \text{N/m} \), \( a = 6.6 \, \text{m} \), \( b = 1.2 \, \text{m} \).

**Diagram Description:**

The diagram shows a beam supported at two points: \( A \) and \( B \). Point \( A \) is on the left end of the beam and is supported by a pin support, while point \( B \) is to the right of point \( A \) and is supported by a roller support. The beam is subjected to a trapezoidal distributed load, with \( w_1 \) at the leftmost end of the beam, reducing linearly to \( w_2 \) just before point \( B \).

Lengths are denoted as follows:
- Distance \( a \) from point \( A \) to the vertical position just before point \( B \), where the supports and the distributed load are also depicted.
- Distance \( b \) from the endpoint of the load until point \( B \).

**Calculations Section:**

*Answers* (Reactions at supports):

- \( A_x \) \( = \) [Input Field] N
- \( A_y \) \( = \) [Input Field] N
- \( B_y \) \( = \) [Input Field] N

**Instructions for Students:**

To solve this problem, consider the following steps:
1. Determine the equivalent point loads of the distributed load.
2. Apply the equilibrium equations to the beam to find the reactions at the supports:
- Sum of Vertical Forces (\( \sum F_y = 0 \))
- Sum of Horizontal Forces (\( \sum F_x = 0 \))
- Sum of Moments about a point (\( \sum M = 0 \))
3. Use the given dimensions and loads to find reactions at points \(A\) and \(B\).

Ensure to show all your workings and check your results for accuracy.

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