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A cantilever beam having 5 m length is so loaded that it develops a shearing force of 20T and a bending moment of 20 T-m at a section 2m from the free end. Maximum shearing force and maximum bending moment developed in the beam under this load are respectively 50 T and 125 T-m. The load on the beam is:
- a)25 T concentrated load at free end
- b)20T concentrated load at free end
- c)5T concentrated load at free end and 2 T/m load over entire length
- d)10 T/m udl over entire length
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A cantilever beam having 5 m length is so loaded that it develops a sh...
R
A
= 10 x 5 = 50T
M = 10 x 5 x (5/2) = 125 T.m
S.F diagram
For similar triangle
(50T/5)=(F/x) = (F/2)
\
F = 20T (at 2m from free end) and M ( at 2m from free end)
= (125 – 50 x 3 + 10 x 3 x(3/2)) T = 20 T-m
Most Upvoted Answer
A cantilever beam having 5 m length is so loaded that it develops a sh...
Given data:
Length of cantilever beam = 5m
Shearing force at a section 2m from the free end = 20T
Bending moment at a section 2m from the free end = 20 T-m
Maximum shearing force developed = 50 T
Maximum bending moment developed = 125 T-m
To find: Load on the beam
Solution:
1. Calculating the load for maximum shearing force:
Maximum shearing force developed = 50 T
As the beam is cantilever, the shearing force will be maximum at the free end
Load = Maximum shearing force
Therefore, the load on the beam for maximum shearing force = 50 T (Option A is incorrect)
2. Calculating the load for maximum bending moment:
Maximum bending moment developed = 125 T-m
As the beam is cantilever, the bending moment will be maximum at the fixed end
Maximum bending moment = (Load × Length)
Load = Maximum bending moment / Length
Load = 125 T-m / 5 m
Load = 25 T
Therefore, the load on the beam for maximum bending moment = 25 T (Option B is incorrect)
3. Calculating the actual load on the beam:
Shearing force at a section 2m from the free end = 20T
Bending moment at a section 2m from the free end = 20 T-m
Let the load at the free end be x T
As there is no load between the section 2m from the free end and the free end, the shearing force at the free end will be equal to the shearing force at the section 2m from the free end
Therefore, 20T = x T
x = 20T
Load at the free end = 20 T
Now, to find the distributed load over the entire length of the beam:
Maximum bending moment developed = 125 T-m
Load = Maximum bending moment / Length
Load = 125 T-m / 5 m
Load = 25 T
As the load at the free end is already considered, the remaining load should be distributed over the entire length of the beam
Distributed load = Load - Load at the free end
Distributed load = 25 T - 20 T
Distributed load = 5 T
Therefore, the load on the beam is 20 T concentrated load at the free end and 5 T/m UDL over the entire length (Option D is correct)
Final answer:
The load on the beam is 20 T concentrated load at the free end and 5 T/m UDL over the entire length (Option D is correct)
Length of cantilever beam = 5m
Shearing force at a section 2m from the free end = 20T
Bending moment at a section 2m from the free end = 20 T-m
Maximum shearing force developed = 50 T
Maximum bending moment developed = 125 T-m
To find: Load on the beam
Solution:
1. Calculating the load for maximum shearing force:
Maximum shearing force developed = 50 T
As the beam is cantilever, the shearing force will be maximum at the free end
Load = Maximum shearing force
Therefore, the load on the beam for maximum shearing force = 50 T (Option A is incorrect)
2. Calculating the load for maximum bending moment:
Maximum bending moment developed = 125 T-m
As the beam is cantilever, the bending moment will be maximum at the fixed end
Maximum bending moment = (Load × Length)
Load = Maximum bending moment / Length
Load = 125 T-m / 5 m
Load = 25 T
Therefore, the load on the beam for maximum bending moment = 25 T (Option B is incorrect)
3. Calculating the actual load on the beam:
Shearing force at a section 2m from the free end = 20T
Bending moment at a section 2m from the free end = 20 T-m
Let the load at the free end be x T
As there is no load between the section 2m from the free end and the free end, the shearing force at the free end will be equal to the shearing force at the section 2m from the free end
Therefore, 20T = x T
x = 20T
Load at the free end = 20 T
Now, to find the distributed load over the entire length of the beam:
Maximum bending moment developed = 125 T-m
Load = Maximum bending moment / Length
Load = 125 T-m / 5 m
Load = 25 T
As the load at the free end is already considered, the remaining load should be distributed over the entire length of the beam
Distributed load = Load - Load at the free end
Distributed load = 25 T - 20 T
Distributed load = 5 T
Therefore, the load on the beam is 20 T concentrated load at the free end and 5 T/m UDL over the entire length (Option D is correct)
Final answer:
The load on the beam is 20 T concentrated load at the free end and 5 T/m UDL over the entire length (Option D is correct)
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A cantilever beam having 5 m length is so loaded that it develops a shearing force of 20T and a bending moment of 20 T-m at a section 2m from the free end. Maximum shearing force and maximum bending moment developed in the beam under this load are respectively 50 T and 125 T-m. The load on the beam is:a)25 T concentrated load at free endb)20T concentrated load at free endc)5T concentrated load at free end and 2 T/m load over entire lengthd)10 T/m udl over entire lengthCorrect answer is option 'D'. Can you explain this answer?
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A cantilever beam having 5 m length is so loaded that it develops a shearing force of 20T and a bending moment of 20 T-m at a section 2m from the free end. Maximum shearing force and maximum bending moment developed in the beam under this load are respectively 50 T and 125 T-m. The load on the beam is:a)25 T concentrated load at free endb)20T concentrated load at free endc)5T concentrated load at free end and 2 T/m load over entire lengthd)10 T/m udl over entire lengthCorrect answer is option 'D'. 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 having 5 m length is so loaded that it develops a shearing force of 20T and a bending moment of 20 T-m at a section 2m from the free end. Maximum shearing force and maximum bending moment developed in the beam under this load are respectively 50 T and 125 T-m. The load on the beam is:a)25 T concentrated load at free endb)20T concentrated load at free endc)5T concentrated load at free end and 2 T/m load over entire lengthd)10 T/m udl over entire lengthCorrect answer is option 'D'. 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 having 5 m length is so loaded that it develops a shearing force of 20T and a bending moment of 20 T-m at a section 2m from the free end. Maximum shearing force and maximum bending moment developed in the beam under this load are respectively 50 T and 125 T-m. The load on the beam is:a)25 T concentrated load at free endb)20T concentrated load at free endc)5T concentrated load at free end and 2 T/m load over entire lengthd)10 T/m udl over entire lengthCorrect answer is option 'D'. Can you explain this answer?.
A cantilever beam having 5 m length is so loaded that it develops a shearing force of 20T and a bending moment of 20 T-m at a section 2m from the free end. Maximum shearing force and maximum bending moment developed in the beam under this load are respectively 50 T and 125 T-m. The load on the beam is:a)25 T concentrated load at free endb)20T concentrated load at free endc)5T concentrated load at free end and 2 T/m load over entire lengthd)10 T/m udl over entire lengthCorrect answer is option 'D'. 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 having 5 m length is so loaded that it develops a shearing force of 20T and a bending moment of 20 T-m at a section 2m from the free end. Maximum shearing force and maximum bending moment developed in the beam under this load are respectively 50 T and 125 T-m. The load on the beam is:a)25 T concentrated load at free endb)20T concentrated load at free endc)5T concentrated load at free end and 2 T/m load over entire lengthd)10 T/m udl over entire lengthCorrect answer is option 'D'. 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 having 5 m length is so loaded that it develops a shearing force of 20T and a bending moment of 20 T-m at a section 2m from the free end. Maximum shearing force and maximum bending moment developed in the beam under this load are respectively 50 T and 125 T-m. The load on the beam is:a)25 T concentrated load at free endb)20T concentrated load at free endc)5T concentrated load at free end and 2 T/m load over entire lengthd)10 T/m udl over entire lengthCorrect answer is option 'D'. Can you explain this answer?.
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A cantilever beam having 5 m length is so loaded that it develops a shearing force of 20T and a bending moment of 20 T-m at a section 2m from the free end. Maximum shearing force and maximum bending moment developed in the beam under this load are respectively 50 T and 125 T-m. The load on the beam is:a)25 T concentrated load at free endb)20T concentrated load at free endc)5T concentrated load at free end and 2 T/m load over entire lengthd)10 T/m udl over entire lengthCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for A cantilever beam having 5 m length is so loaded that it develops a shearing force of 20T and a bending moment of 20 T-m at a section 2m from the free end. Maximum shearing force and maximum bending moment developed in the beam under this load are respectively 50 T and 125 T-m. The load on the beam is:a)25 T concentrated load at free endb)20T concentrated load at free endc)5T concentrated load at free end and 2 T/m load over entire lengthd)10 T/m udl over entire lengthCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of A cantilever beam having 5 m length is so loaded that it develops a shearing force of 20T and a bending moment of 20 T-m at a section 2m from the free end. Maximum shearing force and maximum bending moment developed in the beam under this load are respectively 50 T and 125 T-m. The load on the beam is:a)25 T concentrated load at free endb)20T concentrated load at free endc)5T concentrated load at free end and 2 T/m load over entire lengthd)10 T/m udl over entire lengthCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A cantilever beam having 5 m length is so loaded that it develops a shearing force of 20T and a bending moment of 20 T-m at a section 2m from the free end. Maximum shearing force and maximum bending moment developed in the beam under this load are respectively 50 T and 125 T-m. The load on the beam is:a)25 T concentrated load at free endb)20T concentrated load at free endc)5T concentrated load at free end and 2 T/m load over entire lengthd)10 T/m udl over entire lengthCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
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