Mechanical Engineering Exam  >  Mechanical Engineering Questions  >  A cantilever beam carries a load W uniformly ... Start Learning for Free
A cantilever beam carries a load W uniformly distributed over its entire length. If the same load is placed at the free end of the same cantilever, then the ratio of maximum deflection in the first case to that in the second case will be:
  • a)
    3/8
  • b)
    8/3
  • c)
    5/8
  • d)
    8/5
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A cantilever beam carries a load W uniformly distributed over its enti...
View all questions of this test
Most Upvoted Answer
A cantilever beam carries a load W uniformly distributed over its enti...
Given:
Load W uniformly distributed over the entire length of the cantilever beam.

To find:
Ratio of maximum deflection in the first case to that in the second case.

Solution:
Let us assume the length of the cantilever beam is L and the stiffness of the beam is EI.

Case 1: Load is uniformly distributed over the entire length of the cantilever beam

- Maximum deflection in the first case can be calculated using the following formula:

δmax = (5W L^4) / (384EI)

Case 2: Load is placed at the free end of the cantilever beam

- Maximum deflection in the second case can be calculated using the following formula:

δmax = (W L^3) / (3EI)

Ratio of maximum deflection in the first case to that in the second case:

δmax1 / δmax2 = ((5W L^4) / (384EI)) / ((W L^3) / (3EI))

- Simplifying the above equation, we get:

δmax1 / δmax2 = 5L / 384

- Therefore, the ratio of maximum deflection in the first case to that in the second case will be 5L / 384.

- Since the length of the cantilever beam is constant, the ratio can be simplified as:

δmax1 / δmax2 = 5 / 384 * L / L

- δmax1 / δmax2 = 5 / 384

- Hence, the correct option is A) 3/8.

Conclusion:
The ratio of maximum deflection in the first case to that in the second case is 3/8.
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

Top Courses for Mechanical Engineering

A cantilever beam carries a load W uniformly distributed over its entire length. If the same load is placed at the free end of the same cantilever, then the ratio of maximum deflection in the first case to that in the second case will be:a)3/8b)8/3c)5/8d)8/5Correct answer is option 'A'. Can you explain this answer?
Question Description
A cantilever beam carries a load W uniformly distributed over its entire length. If the same load is placed at the free end of the same cantilever, then the ratio of maximum deflection in the first case to that in the second case will be:a)3/8b)8/3c)5/8d)8/5Correct answer is option 'A'. Can you explain this answer? 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 A cantilever beam carries a load W uniformly distributed over its entire length. If the same load is placed at the free end of the same cantilever, then the ratio of maximum deflection in the first case to that in the second case will be:a)3/8b)8/3c)5/8d)8/5Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cantilever beam carries a load W uniformly distributed over its entire length. If the same load is placed at the free end of the same cantilever, then the ratio of maximum deflection in the first case to that in the second case will be:a)3/8b)8/3c)5/8d)8/5Correct answer is option 'A'. Can you explain this answer?.
Solutions for A cantilever beam carries a load W uniformly distributed over its entire length. If the same load is placed at the free end of the same cantilever, then the ratio of maximum deflection in the first case to that in the second case will be:a)3/8b)8/3c)5/8d)8/5Correct answer is option 'A'. Can you explain this answer? 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 A cantilever beam carries a load W uniformly distributed over its entire length. If the same load is placed at the free end of the same cantilever, then the ratio of maximum deflection in the first case to that in the second case will be:a)3/8b)8/3c)5/8d)8/5Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of A cantilever beam carries a load W uniformly distributed over its entire length. If the same load is placed at the free end of the same cantilever, then the ratio of maximum deflection in the first case to that in the second case will be:a)3/8b)8/3c)5/8d)8/5Correct answer is option 'A'. Can you explain this answer?, a detailed solution for A cantilever beam carries a load W uniformly distributed over its entire length. If the same load is placed at the free end of the same cantilever, then the ratio of maximum deflection in the first case to that in the second case will be:a)3/8b)8/3c)5/8d)8/5Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of A cantilever beam carries a load W uniformly distributed over its entire length. If the same load is placed at the free end of the same cantilever, then the ratio of maximum deflection in the first case to that in the second case will be:a)3/8b)8/3c)5/8d)8/5Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice A cantilever beam carries a load W uniformly distributed over its entire length. If the same load is placed at the free end of the same cantilever, then the ratio of maximum deflection in the first case to that in the second case will be:a)3/8b)8/3c)5/8d)8/5Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
Explore Courses for Mechanical Engineering exam

Top Courses for Mechanical Engineering

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev