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A parabolic arch, symmetrical; with hinges at centre and ends, carries a point load P at a distance x from left support. The arch has a span of 20 m and rise of 5 m. What is the value of 'x' if the left hinge reaction is inclined with a slope of two vertical to one horizontal?
- a)8 m
- b)5 m
- c)4 m
- d)2.5 m
Correct answer is option 'C'. Can you explain this answer?
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A parabolic arch, symmetrical; with hinges at centre and ends, carries...
Given data:
Span of arch = 20 m
Rise of arch = 5 m
Load carried by arch = P
Distance of load from left support = x
Slope of left hinge reaction = 2 vertical to 1 horizontal
To find: Value of x
Solution:
1. Let's assume the arch to be a parabola with its vertex at the origin and the x-axis along the span of the arch.
2. The equation of the parabola is given by: y = a*x^2, where a is a constant.
3. At the ends of the arch (x = -10 m and x = 10 m), the height of the arch is zero. Hence, we have two equations:
0 = a*(-10)^2 ----(1)
0 = a*(10)^2 ----(2)
4. From equations (1) and (2), we get a = 1/10.
5. The equation of the parabolic arch is thus given by: y = (1/10)*x^2.
6. Let R1 and R2 be the reactions at the left and right hinges respectively, and H be the horizontal component of the left hinge reaction. Let V be the vertical component of the left hinge reaction.
7. By resolving forces horizontally and vertically, we get:
H = P*(5-x)/10 ----(3)
V = P/2 ----(4)
R2 = P - R1 ----(5)
8. By using the condition that the slope of the left hinge reaction is 2 vertical to 1 horizontal, we get:
V/H = 2/1
=> 2H = V
=> 2H = P/2
=> H = P/4
9. Substituting the value of H from equation (8) in equation (3), we get:
P*(5-x)/10 = P/4
=> 5-x = 2.5
=> x = 2.5 m
Therefore, the value of x is 2.5 m. Hence, option (c) is the correct answer.
Span of arch = 20 m
Rise of arch = 5 m
Load carried by arch = P
Distance of load from left support = x
Slope of left hinge reaction = 2 vertical to 1 horizontal
To find: Value of x
Solution:
1. Let's assume the arch to be a parabola with its vertex at the origin and the x-axis along the span of the arch.
2. The equation of the parabola is given by: y = a*x^2, where a is a constant.
3. At the ends of the arch (x = -10 m and x = 10 m), the height of the arch is zero. Hence, we have two equations:
0 = a*(-10)^2 ----(1)
0 = a*(10)^2 ----(2)
4. From equations (1) and (2), we get a = 1/10.
5. The equation of the parabolic arch is thus given by: y = (1/10)*x^2.
6. Let R1 and R2 be the reactions at the left and right hinges respectively, and H be the horizontal component of the left hinge reaction. Let V be the vertical component of the left hinge reaction.
7. By resolving forces horizontally and vertically, we get:
H = P*(5-x)/10 ----(3)
V = P/2 ----(4)
R2 = P - R1 ----(5)
8. By using the condition that the slope of the left hinge reaction is 2 vertical to 1 horizontal, we get:
V/H = 2/1
=> 2H = V
=> 2H = P/2
=> H = P/4
9. Substituting the value of H from equation (8) in equation (3), we get:
P*(5-x)/10 = P/4
=> 5-x = 2.5
=> x = 2.5 m
Therefore, the value of x is 2.5 m. Hence, option (c) is the correct answer.
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A parabolic arch, symmetrical; with hinges at centre and ends, carries a point load P at a distance xfrom left support. The arch has a span of 20 m and rise of 5 m. What is the value of xif the left hinge reaction is inclined with a slope of two vertical to one horizontal?a)8 m b)5 mc)4 md)2.5 mCorrect answer is option 'C'. Can you explain this answer?
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A parabolic arch, symmetrical; with hinges at centre and ends, carries a point load P at a distance xfrom left support. The arch has a span of 20 m and rise of 5 m. What is the value of xif the left hinge reaction is inclined with a slope of two vertical to one horizontal?a)8 m b)5 mc)4 md)2.5 mCorrect answer is option 'C'. 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 parabolic arch, symmetrical; with hinges at centre and ends, carries a point load P at a distance xfrom left support. The arch has a span of 20 m and rise of 5 m. What is the value of xif the left hinge reaction is inclined with a slope of two vertical to one horizontal?a)8 m b)5 mc)4 md)2.5 mCorrect answer is option 'C'. 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 parabolic arch, symmetrical; with hinges at centre and ends, carries a point load P at a distance xfrom left support. The arch has a span of 20 m and rise of 5 m. What is the value of xif the left hinge reaction is inclined with a slope of two vertical to one horizontal?a)8 m b)5 mc)4 md)2.5 mCorrect answer is option 'C'. Can you explain this answer?.
A parabolic arch, symmetrical; with hinges at centre and ends, carries a point load P at a distance xfrom left support. The arch has a span of 20 m and rise of 5 m. What is the value of xif the left hinge reaction is inclined with a slope of two vertical to one horizontal?a)8 m b)5 mc)4 md)2.5 mCorrect answer is option 'C'. 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 parabolic arch, symmetrical; with hinges at centre and ends, carries a point load P at a distance xfrom left support. The arch has a span of 20 m and rise of 5 m. What is the value of xif the left hinge reaction is inclined with a slope of two vertical to one horizontal?a)8 m b)5 mc)4 md)2.5 mCorrect answer is option 'C'. 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 parabolic arch, symmetrical; with hinges at centre and ends, carries a point load P at a distance xfrom left support. The arch has a span of 20 m and rise of 5 m. What is the value of xif the left hinge reaction is inclined with a slope of two vertical to one horizontal?a)8 m b)5 mc)4 md)2.5 mCorrect answer is option 'C'. Can you explain this answer?.
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