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What is the value of Bending Moment in KN-m at 3 m from the left support of a three-hinged parabolic arch of span 10 m and rise 4 m which carries a uniformly distributed load of 5 kN/m over the whole span ? Ans is 0 . Can anyone explain?
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What is the value of Bending Moment in KN-m at 3 m from the left suppo...
To determine the bending moment at a specific point on the three-hinged parabolic arch, we can follow these steps:
1. Determine the equation of the parabolic arch:
- The equation of a parabola can be written as: y = ax^2 + bx + c, where y is the vertical displacement and x is the horizontal displacement.
- Given the span of the arch is 10 m and the rise is 4 m, we can substitute the coordinates of the endpoints (0,0) and (10,4) into the equation to solve for a, b, and c.
2. Calculate the reactions at the supports:
- Since the arch is symmetric and carries a uniformly distributed load of 5 kN/m over the whole span, the reactions at the supports will be equal.
- The total load on the arch can be calculated as the product of the load intensity and the span: 5 kN/m * 10 m = 50 kN.
- The reactions at the supports will each be half of the total load: 50 kN / 2 = 25 kN.
3. Determine the equation for the bending moment:
- The bending moment at any point on the arch can be determined using the equation: M = wLx - wx^2/2, where M is the bending moment, w is the load intensity, L is the span, and x is the distance from the left support.
- Substituting the given values, we have M = 5 kN/m * 10 m * 3 m - 5 kN/m * (3 m)^2 / 2.
4. Calculate the bending moment:
- Simplifying the equation, we have M = 150 kN-m - 22.5 kN-m = 127.5 kN-m.
Therefore, the bending moment at 3 m from the left support of the three-hinged parabolic arch is 127.5 kN-m, not zero as stated in the given answer. It's important to double-check the calculations and equations to ensure accuracy.
1. Determine the equation of the parabolic arch:
- The equation of a parabola can be written as: y = ax^2 + bx + c, where y is the vertical displacement and x is the horizontal displacement.
- Given the span of the arch is 10 m and the rise is 4 m, we can substitute the coordinates of the endpoints (0,0) and (10,4) into the equation to solve for a, b, and c.
2. Calculate the reactions at the supports:
- Since the arch is symmetric and carries a uniformly distributed load of 5 kN/m over the whole span, the reactions at the supports will be equal.
- The total load on the arch can be calculated as the product of the load intensity and the span: 5 kN/m * 10 m = 50 kN.
- The reactions at the supports will each be half of the total load: 50 kN / 2 = 25 kN.
3. Determine the equation for the bending moment:
- The bending moment at any point on the arch can be determined using the equation: M = wLx - wx^2/2, where M is the bending moment, w is the load intensity, L is the span, and x is the distance from the left support.
- Substituting the given values, we have M = 5 kN/m * 10 m * 3 m - 5 kN/m * (3 m)^2 / 2.
4. Calculate the bending moment:
- Simplifying the equation, we have M = 150 kN-m - 22.5 kN-m = 127.5 kN-m.
Therefore, the bending moment at 3 m from the left support of the three-hinged parabolic arch is 127.5 kN-m, not zero as stated in the given answer. It's important to double-check the calculations and equations to ensure accuracy.
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What is the value of Bending Moment in KN-m at 3 m from the left support of a three-hinged parabolic arch of span 10 m and rise 4 m which carries a uniformly distributed load of 5 kN/m over the whole span ? Ans is 0 . Can anyone explain?
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What is the value of Bending Moment in KN-m at 3 m from the left support of a three-hinged parabolic arch of span 10 m and rise 4 m which carries a uniformly distributed load of 5 kN/m over the whole span ? Ans is 0 . Can anyone explain? 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 What is the value of Bending Moment in KN-m at 3 m from the left support of a three-hinged parabolic arch of span 10 m and rise 4 m which carries a uniformly distributed load of 5 kN/m over the whole span ? Ans is 0 . Can anyone explain? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the value of Bending Moment in KN-m at 3 m from the left support of a three-hinged parabolic arch of span 10 m and rise 4 m which carries a uniformly distributed load of 5 kN/m over the whole span ? Ans is 0 . Can anyone explain?.
What is the value of Bending Moment in KN-m at 3 m from the left support of a three-hinged parabolic arch of span 10 m and rise 4 m which carries a uniformly distributed load of 5 kN/m over the whole span ? Ans is 0 . Can anyone explain? 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 What is the value of Bending Moment in KN-m at 3 m from the left support of a three-hinged parabolic arch of span 10 m and rise 4 m which carries a uniformly distributed load of 5 kN/m over the whole span ? Ans is 0 . Can anyone explain? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the value of Bending Moment in KN-m at 3 m from the left support of a three-hinged parabolic arch of span 10 m and rise 4 m which carries a uniformly distributed load of 5 kN/m over the whole span ? Ans is 0 . Can anyone explain?.
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