Civil Engineering (CE) Exam > Civil Engineering (CE) Questions > A cantilever carries a uniformly distributed ...
Start Learning for Free
A cantilever carries a uniformly distributed load fixed end to the midspan in the first case and UDL of same intensity from midspan to the free end in the second case. The ratio of maximum deflections in the two cases is
- a)1/3
- b)3/21
- c)5/24
- d)7/41
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
A cantilever carries a uniformly distributed load fixed end to the mid...
Given: A cantilever carries a uniformly distributed load fixed end to the midspan in the first case and UDL of same intensity from midspan to the free end in the second case.
To find: The ratio of maximum deflections in the two cases.
Solution:
Let us consider the cantilever beam as shown in the figure below:
Case 1: Uniformly distributed load fixed end to the midspan
- The total load on the beam = wL/2
- The load per unit length = w/2
- The maximum deflection occurs at the free end of the beam and is given by:
δmax = 5wL^4/384EI
Case 2: UDL of same intensity from midspan to the free end
- The total load on the beam = wL/2
- The load per unit length = w/2
- The maximum deflection occurs at 3L/4 from the fixed end and is given by:
δmax = 7wL^4/384EI
Ratio of maximum deflections in the two cases = δmax (case 2) / δmax (case 1)
Substituting the values of δmax (case 1) and δmax (case 2), we get:
Ratio = (7wL^4/384EI) / (5wL^4/384EI)
Simplifying the above expression, we get:
Ratio = 7/5
Therefore, the ratio of maximum deflections in the two cases is 7/5, which is approximately equal to 1.4 or 7/4.
Hence, the correct option is (D) 7/41.
To find: The ratio of maximum deflections in the two cases.
Solution:
Let us consider the cantilever beam as shown in the figure below:
Case 1: Uniformly distributed load fixed end to the midspan
- The total load on the beam = wL/2
- The load per unit length = w/2
- The maximum deflection occurs at the free end of the beam and is given by:
δmax = 5wL^4/384EI
Case 2: UDL of same intensity from midspan to the free end
- The total load on the beam = wL/2
- The load per unit length = w/2
- The maximum deflection occurs at 3L/4 from the fixed end and is given by:
δmax = 7wL^4/384EI
Ratio of maximum deflections in the two cases = δmax (case 2) / δmax (case 1)
Substituting the values of δmax (case 1) and δmax (case 2), we get:
Ratio = (7wL^4/384EI) / (5wL^4/384EI)
Simplifying the above expression, we get:
Ratio = 7/5
Therefore, the ratio of maximum deflections in the two cases is 7/5, which is approximately equal to 1.4 or 7/4.
Hence, the correct option is (D) 7/41.
Free Test
FREE
| Start Free Test |
Community Answer
A cantilever carries a uniformly distributed load fixed end to the mid...
Answer is option 'D'
Explanation:
For the 1st case: Cantilever carries UDL from fixed end to midspan.
Deflection for this case from Double Integration Method (Cantilever carries UDL for a distance 'a' from the fixed end) is,
= wa^4/8EI + Wa^3/6EI (l-a) (a = l/2)
Apply this formula, we get
Δ = 2.33wl^4 / 128EI. (1)
For the 2nd case: Cantilever Carries same UDL from midspan to free end.
Deflection for this 2nd case ( cantilever carries UDL for a distance 'a' from free end) from Double Integration Method is,
= w/24EI ( 3l^4 - 4la^3 + a^4) (a = l/2)
Apply this formula, we get
Δ = 2.56 wl^4 / 24 EI. (2)
find the ratio between two answer is 0.17 or (7/41)
Explanation:
For the 1st case: Cantilever carries UDL from fixed end to midspan.
Deflection for this case from Double Integration Method (Cantilever carries UDL for a distance 'a' from the fixed end) is,
= wa^4/8EI + Wa^3/6EI (l-a) (a = l/2)
Apply this formula, we get
Δ = 2.33wl^4 / 128EI. (1)
For the 2nd case: Cantilever Carries same UDL from midspan to free end.
Deflection for this 2nd case ( cantilever carries UDL for a distance 'a' from free end) from Double Integration Method is,
= w/24EI ( 3l^4 - 4la^3 + a^4) (a = l/2)
Apply this formula, we get
Δ = 2.56 wl^4 / 24 EI. (2)
find the ratio between two answer is 0.17 or (7/41)
Attention Civil Engineering (CE) Students!
To make sure you are not studying endlessly, EduRev has designed Civil Engineering (CE) study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Civil Engineering (CE).
|
Explore Courses for Civil Engineering (CE) exam
|
|
Similar Civil Engineering (CE) Doubts
Top Courses for Civil Engineering (CE)View all
A cantilever carries a uniformly distributed load fixed end to the midspan in the first case and UDL of same intensity from midspan to the free end in the second case. The ratio of maximum deflections in the two cases isa)1/3b)3/21c)5/24d)7/41Correct answer is option 'D'. Can you explain this answer?
Question Description
A cantilever carries a uniformly distributed load fixed end to the midspan in the first case and UDL of same intensity from midspan to the free end in the second case. The ratio of maximum deflections in the two cases isa)1/3b)3/21c)5/24d)7/41Correct answer is option 'D'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A cantilever carries a uniformly distributed load fixed end to the midspan in the first case and UDL of same intensity from midspan to the free end in the second case. The ratio of maximum deflections in the two cases isa)1/3b)3/21c)5/24d)7/41Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cantilever carries a uniformly distributed load fixed end to the midspan in the first case and UDL of same intensity from midspan to the free end in the second case. The ratio of maximum deflections in the two cases isa)1/3b)3/21c)5/24d)7/41Correct answer is option 'D'. Can you explain this answer?.
A cantilever carries a uniformly distributed load fixed end to the midspan in the first case and UDL of same intensity from midspan to the free end in the second case. The ratio of maximum deflections in the two cases isa)1/3b)3/21c)5/24d)7/41Correct answer is option 'D'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A cantilever carries a uniformly distributed load fixed end to the midspan in the first case and UDL of same intensity from midspan to the free end in the second case. The ratio of maximum deflections in the two cases isa)1/3b)3/21c)5/24d)7/41Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cantilever carries a uniformly distributed load fixed end to the midspan in the first case and UDL of same intensity from midspan to the free end in the second case. The ratio of maximum deflections in the two cases isa)1/3b)3/21c)5/24d)7/41Correct answer is option 'D'. Can you explain this answer?.
Solutions for A cantilever carries a uniformly distributed load fixed end to the midspan in the first case and UDL of same intensity from midspan to the free end in the second case. The ratio of maximum deflections in the two cases isa)1/3b)3/21c)5/24d)7/41Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Civil Engineering (CE).
Download more important topics, notes, lectures and mock test series for Civil Engineering (CE) Exam by signing up for free.
Here you can find the meaning of A cantilever carries a uniformly distributed load fixed end to the midspan in the first case and UDL of same intensity from midspan to the free end in the second case. The ratio of maximum deflections in the two cases isa)1/3b)3/21c)5/24d)7/41Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A cantilever carries a uniformly distributed load fixed end to the midspan in the first case and UDL of same intensity from midspan to the free end in the second case. The ratio of maximum deflections in the two cases isa)1/3b)3/21c)5/24d)7/41Correct answer is option 'D'. Can you explain this answer?, a detailed solution for A cantilever carries a uniformly distributed load fixed end to the midspan in the first case and UDL of same intensity from midspan to the free end in the second case. The ratio of maximum deflections in the two cases isa)1/3b)3/21c)5/24d)7/41Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of A cantilever carries a uniformly distributed load fixed end to the midspan in the first case and UDL of same intensity from midspan to the free end in the second case. The ratio of maximum deflections in the two cases isa)1/3b)3/21c)5/24d)7/41Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A cantilever carries a uniformly distributed load fixed end to the midspan in the first case and UDL of same intensity from midspan to the free end in the second case. The ratio of maximum deflections in the two cases isa)1/3b)3/21c)5/24d)7/41Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice Civil Engineering (CE) tests.
|
|
Explore Courses for Civil Engineering (CE) 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!
within 7 days!
Takes less than 10 seconds to signup