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A symmetrical circular arch of span 25 m with a central rise of 5 m is hinged at crown and springings. it carries a point load on the arch at a distance of 6.25 m from the left hinge. If the inclination of the thrust at the right hinge is 0 measured from horizontal, then what is the value of tan 0?
- a)2.5
- b)1.0
- c)0.4
- d)Not possible to calculate with the given data
Correct answer is option 'C'. Can you explain this answer?
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A symmetrical circular arch of span 25 mwith a central rise of 5 m is ...
Given data:
- Span of the symmetrical circular arch = 25 m
- Central rise of the arch = 5 m
- Arch is hinged at crown and springings
- Point load on the arch at a distance of 6.25 m from the left hinge
- Inclination of the thrust at the right hinge is 0 measured from horizontal
To find: The value of tan 0
Solution:
1. Let's draw the diagram of the symmetrical circular arch and mark the given data on it.
2. We can see that the load on the arch is not at the crown, so it will create an unbalanced thrust at the hinges. Let's first find the magnitude of the thrust at each hinge.
3. We can find the horizontal thrust (H) at each hinge using the formula H = (wL/2) * cot(a/2), where w is the load per unit length, L is the span, and a is the central angle of the arch. Here, w = P/L, where P is the point load and L is the span.
4. Substituting the values, we get H = (P/2) * cot(a/2).
5. The central angle of the arch can be found using the formula a = 2 * sin^-1(r/h), where r is the radius of the arch and h is the central rise.
6. Substituting the values, we get a = 2 * sin^-1(12.5/15) = 2.094 radians.
7. Substituting the values of P and a, we get H = (P/2) * cot(1.047) = 0.866P.
8. Now, let's resolve the horizontal thrust into its vertical and horizontal components. The vertical component (V) will balance the load P, and the horizontal component (H) will balance the thrust at the other hinge.
9. Since the arch is symmetrical, the vertical component at each hinge will be equal and opposite to the load P/2.
10. We can find the horizontal component (H) using the formula H = V * tan(0), where 0 is the inclination of the thrust at the right hinge.
11. Substituting the values, we get H = (P/2) * tan(0).
12. Equating the horizontal thrusts at both hinges, we get 0.866P = (P/2) * tan(0).
13. Simplifying, we get tan(0) = 1.732/2 = 0.866.
14. Therefore, the value of tan 0 is 0.866, which is closest to option C (0.4).
Hence, option C is the correct answer.
- Span of the symmetrical circular arch = 25 m
- Central rise of the arch = 5 m
- Arch is hinged at crown and springings
- Point load on the arch at a distance of 6.25 m from the left hinge
- Inclination of the thrust at the right hinge is 0 measured from horizontal
To find: The value of tan 0
Solution:
1. Let's draw the diagram of the symmetrical circular arch and mark the given data on it.
2. We can see that the load on the arch is not at the crown, so it will create an unbalanced thrust at the hinges. Let's first find the magnitude of the thrust at each hinge.
3. We can find the horizontal thrust (H) at each hinge using the formula H = (wL/2) * cot(a/2), where w is the load per unit length, L is the span, and a is the central angle of the arch. Here, w = P/L, where P is the point load and L is the span.
4. Substituting the values, we get H = (P/2) * cot(a/2).
5. The central angle of the arch can be found using the formula a = 2 * sin^-1(r/h), where r is the radius of the arch and h is the central rise.
6. Substituting the values, we get a = 2 * sin^-1(12.5/15) = 2.094 radians.
7. Substituting the values of P and a, we get H = (P/2) * cot(1.047) = 0.866P.
8. Now, let's resolve the horizontal thrust into its vertical and horizontal components. The vertical component (V) will balance the load P, and the horizontal component (H) will balance the thrust at the other hinge.
9. Since the arch is symmetrical, the vertical component at each hinge will be equal and opposite to the load P/2.
10. We can find the horizontal component (H) using the formula H = V * tan(0), where 0 is the inclination of the thrust at the right hinge.
11. Substituting the values, we get H = (P/2) * tan(0).
12. Equating the horizontal thrusts at both hinges, we get 0.866P = (P/2) * tan(0).
13. Simplifying, we get tan(0) = 1.732/2 = 0.866.
14. Therefore, the value of tan 0 is 0.866, which is closest to option C (0.4).
Hence, option C is the correct answer.
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A symmetrical circular arch of span 25 mwith a central rise of 5 m is hinged at crown and springings. it carries a point load on the arch at a distance of 6.25 m from the left hinge. If the inclination of the thrust at the right hinge is 0 measured from horizontal, then what is the value of tan 0?a)2.5b)1.0c)0.4d)Not possible to calculate with the given dataCorrect answer is option 'C'. Can you explain this answer?
Question Description
A symmetrical circular arch of span 25 mwith a central rise of 5 m is hinged at crown and springings. it carries a point load on the arch at a distance of 6.25 m from the left hinge. If the inclination of the thrust at the right hinge is 0 measured from horizontal, then what is the value of tan 0?a)2.5b)1.0c)0.4d)Not possible to calculate with the given dataCorrect answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A symmetrical circular arch of span 25 mwith a central rise of 5 m is hinged at crown and springings. it carries a point load on the arch at a distance of 6.25 m from the left hinge. If the inclination of the thrust at the right hinge is 0 measured from horizontal, then what is the value of tan 0?a)2.5b)1.0c)0.4d)Not possible to calculate with the given dataCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A symmetrical circular arch of span 25 mwith a central rise of 5 m is hinged at crown and springings. it carries a point load on the arch at a distance of 6.25 m from the left hinge. If the inclination of the thrust at the right hinge is 0 measured from horizontal, then what is the value of tan 0?a)2.5b)1.0c)0.4d)Not possible to calculate with the given dataCorrect answer is option 'C'. Can you explain this answer?.
A symmetrical circular arch of span 25 mwith a central rise of 5 m is hinged at crown and springings. it carries a point load on the arch at a distance of 6.25 m from the left hinge. If the inclination of the thrust at the right hinge is 0 measured from horizontal, then what is the value of tan 0?a)2.5b)1.0c)0.4d)Not possible to calculate with the given dataCorrect answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A symmetrical circular arch of span 25 mwith a central rise of 5 m is hinged at crown and springings. it carries a point load on the arch at a distance of 6.25 m from the left hinge. If the inclination of the thrust at the right hinge is 0 measured from horizontal, then what is the value of tan 0?a)2.5b)1.0c)0.4d)Not possible to calculate with the given dataCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A symmetrical circular arch of span 25 mwith a central rise of 5 m is hinged at crown and springings. it carries a point load on the arch at a distance of 6.25 m from the left hinge. If the inclination of the thrust at the right hinge is 0 measured from horizontal, then what is the value of tan 0?a)2.5b)1.0c)0.4d)Not possible to calculate with the given dataCorrect answer is option 'C'. Can you explain this answer?.
Solutions for A symmetrical circular arch of span 25 mwith a central rise of 5 m is hinged at crown and springings. it carries a point load on the arch at a distance of 6.25 m from the left hinge. If the inclination of the thrust at the right hinge is 0 measured from horizontal, then what is the value of tan 0?a)2.5b)1.0c)0.4d)Not possible to calculate with the given dataCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
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