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.
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
Related questions
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc59a6d07-a993-40f7-b57e-cdb2ad079d78%2F38233ccd-8bf7-4023-8828-2d4832f33051%2F4u09oa_processed.png&w=3840&q=75)
Transcribed Image Text:**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.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 7 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Recommended textbooks for you
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY