GATE Exam > GATE Questions > A three hinged semicircular arch of radius R ...
Start Learning for Free
A three hinged semicircular arch of radius R carries a uniformly distributed load w per unit run over the whole span. The horizontal thrust is
- a)wR
- b)wR/2
- c)4wR/3π
- d)2wR/3π
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A three hinged semicircular arch of radius R carries a uniformly distr...
The horizontal thrust in a three-hinged arch is given by the formula:
H = (wL^2)/(8R)
where w is the uniformly distributed load, L is the span of the arch, and R is the radius of curvature.
In this case, the span of the arch is half of the circumference of the circle, which is πR. Therefore, L = πR/2.
Substituting these values into the formula, we get:
H = (w(πR/2)^2)/(8R) = (wπR^2)/32R = wRπ/32
Simplifying further, we get:
H = wR(π/32)
Therefore, the horizontal thrust is option (a) wRπ/32.
H = (wL^2)/(8R)
where w is the uniformly distributed load, L is the span of the arch, and R is the radius of curvature.
In this case, the span of the arch is half of the circumference of the circle, which is πR. Therefore, L = πR/2.
Substituting these values into the formula, we get:
H = (w(πR/2)^2)/(8R) = (wπR^2)/32R = wRπ/32
Simplifying further, we get:
H = wR(π/32)
Therefore, the horizontal thrust is option (a) wRπ/32.
Community Answer
A three hinged semicircular arch of radius R carries a uniformly distr...
The horizontal thrust in a three-hinged semicircular arch is given by the expression:
H = (5/8)*wR
Therefore, option c) 4wR/3 is not correct.
The derivation of the above formula is as follows:
Consider a small element of length dx at a distance x from the left support. The load on this element is w*dx. Let the vertical reaction at the left support be R1, and the vertical reactions at the hinges be R2 and R3, respectively.
Taking moments about the left support, we get:
R2*R2x + R3*R3x = w*x*dx/2 + R1*R1x
where R2x and R3x are the horizontal distances of the hinges from the left support, and R1x is the horizontal distance of the left support from the left end of the arch.
Since the arch is symmetrical, we have R2x = R3x = R/2 and R1x = R.
Substituting these values, we get:
R2^2 + R3^2 = w*x*dx/2 + R1*R
Taking moments about the hinge at the crown, we get:
R1*R1x + R2*R2x = R3*R3x
Substituting the values of R2x, R3x, and R1x, we get:
R1*R + R2*R/2 = R3*R/2
Solving these two equations for R2 and R3, we get:
R2 = (5/8)*w*x*dx*R/R1
R3 = (3/8)*w*x*dx*R/R1
Integrating these expressions over the span of the arch, we get:
H = R2 + R3 = (5/8)*w*R
Therefore, option a) wR and option b) wR/2 are not correct, and the correct answer is option c) 5wR/8.
H = (5/8)*wR
Therefore, option c) 4wR/3 is not correct.
The derivation of the above formula is as follows:
Consider a small element of length dx at a distance x from the left support. The load on this element is w*dx. Let the vertical reaction at the left support be R1, and the vertical reactions at the hinges be R2 and R3, respectively.
Taking moments about the left support, we get:
R2*R2x + R3*R3x = w*x*dx/2 + R1*R1x
where R2x and R3x are the horizontal distances of the hinges from the left support, and R1x is the horizontal distance of the left support from the left end of the arch.
Since the arch is symmetrical, we have R2x = R3x = R/2 and R1x = R.
Substituting these values, we get:
R2^2 + R3^2 = w*x*dx/2 + R1*R
Taking moments about the hinge at the crown, we get:
R1*R1x + R2*R2x = R3*R3x
Substituting the values of R2x, R3x, and R1x, we get:
R1*R + R2*R/2 = R3*R/2
Solving these two equations for R2 and R3, we get:
R2 = (5/8)*w*x*dx*R/R1
R3 = (3/8)*w*x*dx*R/R1
Integrating these expressions over the span of the arch, we get:
H = R2 + R3 = (5/8)*w*R
Therefore, option a) wR and option b) wR/2 are not correct, and the correct answer is option c) 5wR/8.
|
Explore Courses for GATE exam
|
|
Top Courses for GATEView all
Question Description
A three hinged semicircular arch of radius R carries a uniformly distributed load w per unit run over the whole span. The horizontal thrust isa)wRb)wR/2c)4wR/3πd)2wR/3πCorrect answer is option 'B'. Can you explain this answer? for GATE 2025 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A three hinged semicircular arch of radius R carries a uniformly distributed load w per unit run over the whole span. The horizontal thrust isa)wRb)wR/2c)4wR/3πd)2wR/3πCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A three hinged semicircular arch of radius R carries a uniformly distributed load w per unit run over the whole span. The horizontal thrust isa)wRb)wR/2c)4wR/3πd)2wR/3πCorrect answer is option 'B'. Can you explain this answer?.
A three hinged semicircular arch of radius R carries a uniformly distributed load w per unit run over the whole span. The horizontal thrust isa)wRb)wR/2c)4wR/3πd)2wR/3πCorrect answer is option 'B'. Can you explain this answer? for GATE 2025 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A three hinged semicircular arch of radius R carries a uniformly distributed load w per unit run over the whole span. The horizontal thrust isa)wRb)wR/2c)4wR/3πd)2wR/3πCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A three hinged semicircular arch of radius R carries a uniformly distributed load w per unit run over the whole span. The horizontal thrust isa)wRb)wR/2c)4wR/3πd)2wR/3πCorrect answer is option 'B'. Can you explain this answer?.
Solutions for A three hinged semicircular arch of radius R carries a uniformly distributed load w per unit run over the whole span. The horizontal thrust isa)wRb)wR/2c)4wR/3πd)2wR/3πCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
Download more important topics, notes, lectures and mock test series for GATE Exam by signing up for free.
Here you can find the meaning of A three hinged semicircular arch of radius R carries a uniformly distributed load w per unit run over the whole span. The horizontal thrust isa)wRb)wR/2c)4wR/3πd)2wR/3πCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A three hinged semicircular arch of radius R carries a uniformly distributed load w per unit run over the whole span. The horizontal thrust isa)wRb)wR/2c)4wR/3πd)2wR/3πCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for A three hinged semicircular arch of radius R carries a uniformly distributed load w per unit run over the whole span. The horizontal thrust isa)wRb)wR/2c)4wR/3πd)2wR/3πCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of A three hinged semicircular arch of radius R carries a uniformly distributed load w per unit run over the whole span. The horizontal thrust isa)wRb)wR/2c)4wR/3πd)2wR/3πCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A three hinged semicircular arch of radius R carries a uniformly distributed load w per unit run over the whole span. The horizontal thrust isa)wRb)wR/2c)4wR/3πd)2wR/3πCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice GATE tests.
|
|
Explore Courses for GATE exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up
within 7 days!
within 7 days!
Takes less than 10 seconds to signup