Mechanical Engineering Exam > Mechanical Engineering Questions > Determine slope and deflection at D for the b...
Start Learning for Free
Determine slope and deflection at D for the beam and loading shown in fig.1 and take the flexural rigidity of the beam as?
Most Upvoted Answer
Determine slope and deflection at D for the beam and loading shown in ...
Given:
- The beam has a length of L
- The beam has a rectangular cross-section with width b and height d
- The beam is simply supported at points A and C
- The beam is subjected to a uniformly distributed load w over its entire length
To find:
- The slope at point D
- The deflection at point D
Assumptions:
- The beam is made of a homogeneous and isotropic material
- The beam is in the linear elastic range
- The beam is loaded within its elastic limit
- The beam has a constant flexural rigidity (EI) along its length
Procedure:
1. Determine the reaction forces at points A and C:
- Since the beam is simply supported at points A and C, the vertical reaction forces at these points will be equal to half of the total load acting on the beam.
- The total load acting on the beam is equal to the product of the uniformly distributed load w and the length of the beam L.
- Therefore, the reaction forces at points A and C can be calculated as:
- RA = RC = (w * L) / 2
2. Calculate the bending moment at point D:
- The bending moment at point D can be determined by considering the equilibrium of moments about point D.
- Since the beam is symmetrically loaded and supported, the bending moment at point D will be zero.
3. Determine the slope at point D:
- The slope at point D can be calculated by considering the equation for the slope of a beam subjected to a bending moment.
- The slope at any point along the beam can be given by the equation: θ = M(x) / (EI)
- Since the bending moment at point D is zero, the slope at point D will also be zero.
4. Calculate the deflection at point D:
- The deflection at point D can be determined by integrating the equation for the slope of the beam.
- The equation for the deflection of the beam can be given by: δ = ∫(θ(x)) dx
- Since the slope at point D is zero, the deflection at point D will also be zero.
Conclusion:
- The slope at point D is zero.
- The deflection at point D is zero.
- This means that point D remains undeformed under the given loading condition.
- The flexural rigidity of the beam (EI) does not affect the slope or deflection at point D in this case.
- The beam has a length of L
- The beam has a rectangular cross-section with width b and height d
- The beam is simply supported at points A and C
- The beam is subjected to a uniformly distributed load w over its entire length
To find:
- The slope at point D
- The deflection at point D
Assumptions:
- The beam is made of a homogeneous and isotropic material
- The beam is in the linear elastic range
- The beam is loaded within its elastic limit
- The beam has a constant flexural rigidity (EI) along its length
Procedure:
1. Determine the reaction forces at points A and C:
- Since the beam is simply supported at points A and C, the vertical reaction forces at these points will be equal to half of the total load acting on the beam.
- The total load acting on the beam is equal to the product of the uniformly distributed load w and the length of the beam L.
- Therefore, the reaction forces at points A and C can be calculated as:
- RA = RC = (w * L) / 2
2. Calculate the bending moment at point D:
- The bending moment at point D can be determined by considering the equilibrium of moments about point D.
- Since the beam is symmetrically loaded and supported, the bending moment at point D will be zero.
3. Determine the slope at point D:
- The slope at point D can be calculated by considering the equation for the slope of a beam subjected to a bending moment.
- The slope at any point along the beam can be given by the equation: θ = M(x) / (EI)
- Since the bending moment at point D is zero, the slope at point D will also be zero.
4. Calculate the deflection at point D:
- The deflection at point D can be determined by integrating the equation for the slope of the beam.
- The equation for the deflection of the beam can be given by: δ = ∫(θ(x)) dx
- Since the slope at point D is zero, the deflection at point D will also be zero.
Conclusion:
- The slope at point D is zero.
- The deflection at point D is zero.
- This means that point D remains undeformed under the given loading condition.
- The flexural rigidity of the beam (EI) does not affect the slope or deflection at point D in this case.
Attention Mechanical Engineering Students!
To make sure you are not studying endlessly, EduRev has designed Mechanical Engineering study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Mechanical Engineering.
|
Explore Courses for Mechanical Engineering exam
|
|
Similar Mechanical Engineering Doubts
Top Courses for Mechanical EngineeringView all
Determine slope and deflection at D for the beam and loading shown in fig.1 and take the flexural rigidity of the beam as?
Question Description
Determine slope and deflection at D for the beam and loading shown in fig.1 and take the flexural rigidity of the beam as? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Determine slope and deflection at D for the beam and loading shown in fig.1 and take the flexural rigidity of the beam as? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Determine slope and deflection at D for the beam and loading shown in fig.1 and take the flexural rigidity of the beam as?.
Determine slope and deflection at D for the beam and loading shown in fig.1 and take the flexural rigidity of the beam as? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Determine slope and deflection at D for the beam and loading shown in fig.1 and take the flexural rigidity of the beam as? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Determine slope and deflection at D for the beam and loading shown in fig.1 and take the flexural rigidity of the beam as?.
Solutions for Determine slope and deflection at D for the beam and loading shown in fig.1 and take the flexural rigidity of the beam as? in English & in Hindi are available as part of our courses for Mechanical Engineering.
Download more important topics, notes, lectures and mock test series for Mechanical Engineering Exam by signing up for free.
Here you can find the meaning of Determine slope and deflection at D for the beam and loading shown in fig.1 and take the flexural rigidity of the beam as? defined & explained in the simplest way possible. Besides giving the explanation of
Determine slope and deflection at D for the beam and loading shown in fig.1 and take the flexural rigidity of the beam as?, a detailed solution for Determine slope and deflection at D for the beam and loading shown in fig.1 and take the flexural rigidity of the beam as? has been provided alongside types of Determine slope and deflection at D for the beam and loading shown in fig.1 and take the flexural rigidity of the beam as? theory, EduRev gives you an
ample number of questions to practice Determine slope and deflection at D for the beam and loading shown in fig.1 and take the flexural rigidity of the beam as? tests, examples and also practice Mechanical Engineering tests.
|
|
Explore Courses for Mechanical Engineering exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup