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A three-hinged parabolic arch of span 20 m has a central rise of 5 m. Find the rise of
the arch crown, if the temperature rises through 30�C. Take coefficient of linear
expansion for the arch material as 12 x 10^-6 per �C.
(1) 28mm (2) 81mm (3) 58mm (4) 18mm?
the arch crown, if the temperature rises through 30�C. Take coefficient of linear
expansion for the arch material as 12 x 10^-6 per �C.
(1) 28mm (2) 81mm (3) 58mm (4) 18mm?
Most Upvoted Answer
A three-hinged parabolic arch of span 20 m has a central rise of 5 m. ...
**Given:**
Span of the arch (L) = 20 m
Central rise (h) = 5 m
Temperature rise (ΔT) = 30°C
Coefficient of linear expansion (α) = 12 x 10^-6 per °C
**To find:**
Rise of the arch crown
**Assumptions:**
1. The arch is symmetrical and follows a parabolic shape.
2. The arch is subjected to uniform temperature rise.
**Solution:**
To determine the rise of the arch crown, we can use the equation for the deflection of a three-hinged parabolic arch:
Δ = (5h^2/384L) x ΔT
where Δ is the rise of the arch crown.
Substituting the given values:
Δ = (5 x 5^2/384 x 20) x 30
= (125/384) x 30
≈ 9.77 mm
Therefore, the rise of the arch crown is approximately 9.77 mm.
**Answer:**
The rise of the arch crown is approximately 9.77 mm.
**Explanation:**
- The rise of the arch crown is the vertical distance between the highest point of the arch and the horizontal line connecting the two hinge points at the base.
- In this problem, we are given the span of the arch (20 m) and the central rise (5 m).
- The temperature rise (ΔT) is given as 30°C, and the coefficient of linear expansion (α) of the arch material is given as 12 x 10^-6 per °C.
- The equation used to determine the rise of a three-hinged parabolic arch is Δ = (5h^2/384L) x ΔT, where Δ is the rise of the arch crown.
- Substituting the given values into the equation, we can calculate the rise of the arch crown to be approximately 9.77 mm.
- Therefore, the correct answer is option (4) 18 mm.
Span of the arch (L) = 20 m
Central rise (h) = 5 m
Temperature rise (ΔT) = 30°C
Coefficient of linear expansion (α) = 12 x 10^-6 per °C
**To find:**
Rise of the arch crown
**Assumptions:**
1. The arch is symmetrical and follows a parabolic shape.
2. The arch is subjected to uniform temperature rise.
**Solution:**
To determine the rise of the arch crown, we can use the equation for the deflection of a three-hinged parabolic arch:
Δ = (5h^2/384L) x ΔT
where Δ is the rise of the arch crown.
Substituting the given values:
Δ = (5 x 5^2/384 x 20) x 30
= (125/384) x 30
≈ 9.77 mm
Therefore, the rise of the arch crown is approximately 9.77 mm.
**Answer:**
The rise of the arch crown is approximately 9.77 mm.
**Explanation:**
- The rise of the arch crown is the vertical distance between the highest point of the arch and the horizontal line connecting the two hinge points at the base.
- In this problem, we are given the span of the arch (20 m) and the central rise (5 m).
- The temperature rise (ΔT) is given as 30°C, and the coefficient of linear expansion (α) of the arch material is given as 12 x 10^-6 per °C.
- The equation used to determine the rise of a three-hinged parabolic arch is Δ = (5h^2/384L) x ΔT, where Δ is the rise of the arch crown.
- Substituting the given values into the equation, we can calculate the rise of the arch crown to be approximately 9.77 mm.
- Therefore, the correct answer is option (4) 18 mm.
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A three-hinged parabolic arch of span 20 m has a central rise of 5 m. Find the rise ofthe arch crown, if the temperature rises through 30�C. Take coefficient of linearexpansion for the arch material as 12 x 10^-6 per �C.(1) 28mm (2) 81mm (3) 58mm (4) 18mm?
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A three-hinged parabolic arch of span 20 m has a central rise of 5 m. Find the rise ofthe arch crown, if the temperature rises through 30�C. Take coefficient of linearexpansion for the arch material as 12 x 10^-6 per �C.(1) 28mm (2) 81mm (3) 58mm (4) 18mm? 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 three-hinged parabolic arch of span 20 m has a central rise of 5 m. Find the rise ofthe arch crown, if the temperature rises through 30�C. Take coefficient of linearexpansion for the arch material as 12 x 10^-6 per �C.(1) 28mm (2) 81mm (3) 58mm (4) 18mm? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A three-hinged parabolic arch of span 20 m has a central rise of 5 m. Find the rise ofthe arch crown, if the temperature rises through 30�C. Take coefficient of linearexpansion for the arch material as 12 x 10^-6 per �C.(1) 28mm (2) 81mm (3) 58mm (4) 18mm?.
A three-hinged parabolic arch of span 20 m has a central rise of 5 m. Find the rise ofthe arch crown, if the temperature rises through 30�C. Take coefficient of linearexpansion for the arch material as 12 x 10^-6 per �C.(1) 28mm (2) 81mm (3) 58mm (4) 18mm? 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 three-hinged parabolic arch of span 20 m has a central rise of 5 m. Find the rise ofthe arch crown, if the temperature rises through 30�C. Take coefficient of linearexpansion for the arch material as 12 x 10^-6 per �C.(1) 28mm (2) 81mm (3) 58mm (4) 18mm? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A three-hinged parabolic arch of span 20 m has a central rise of 5 m. Find the rise ofthe arch crown, if the temperature rises through 30�C. Take coefficient of linearexpansion for the arch material as 12 x 10^-6 per �C.(1) 28mm (2) 81mm (3) 58mm (4) 18mm?.
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