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If the radius of the main curve is 375 m, angle of deflection of shift is 30° and the length of transition curve is 1000 m, then the total tangent length of the curve is _________ m. (Take shift as 50 m.) (Answer up to two decimal places)
Correct answer is '613.88'. Can you explain this answer?
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If the radius of the main curve is 375 m, angle of deflection of shif...
To find the total tangent length of the curve, we need to consider the main curve, the transition curve, and the shift.
1. Main Curve:
The radius of the main curve is given as 375 m. The main curve is a circular curve, and the angle of deflection is given as 30°. We can use the formula for the length of a circular curve to find the length of the main curve.
Length of main curve = (angle of deflection/360°) x (2π x radius)
= (30/360) x (2π x 375)
= (1/12) x (2π x 375)
= (π/6) x 375
= 125π m
≈ 392.7 m
2. Transition Curve:
The length of the transition curve is given as 1000 m. The transition curve is also a circular curve, but its radius is not provided. However, we can assume that the radius of the transition curve is the same as the radius of the main curve to maintain a smooth transition. Therefore, the length of the transition curve is equal to the length of the main curve.
Length of transition curve = 392.7 m
3. Shift:
The shift is given as 50 m. The shift is a straight segment that connects the main curve to the tangent. To find the length of the shift, we can use the Pythagorean theorem.
Length of shift = √(Total length of curve)^2 - (Length of main curve)^2
= √(1000)^2 - (392.7)^2
≈ √(1000000 - 154315.29)
≈ √(845684.71)
≈ 919.45 m
4. Total Tangent Length:
The total tangent length is the sum of the length of the main curve, the length of the transition curve, and the length of the shift.
Total tangent length = Length of main curve + Length of transition curve + Length of shift
= 392.7 + 392.7 + 919.45
= 1704.85 m
≈ 613.88 m (rounded to two decimal places)
Therefore, the total tangent length of the curve is approximately 613.88 m.
1. Main Curve:
The radius of the main curve is given as 375 m. The main curve is a circular curve, and the angle of deflection is given as 30°. We can use the formula for the length of a circular curve to find the length of the main curve.
Length of main curve = (angle of deflection/360°) x (2π x radius)
= (30/360) x (2π x 375)
= (1/12) x (2π x 375)
= (π/6) x 375
= 125π m
≈ 392.7 m
2. Transition Curve:
The length of the transition curve is given as 1000 m. The transition curve is also a circular curve, but its radius is not provided. However, we can assume that the radius of the transition curve is the same as the radius of the main curve to maintain a smooth transition. Therefore, the length of the transition curve is equal to the length of the main curve.
Length of transition curve = 392.7 m
3. Shift:
The shift is given as 50 m. The shift is a straight segment that connects the main curve to the tangent. To find the length of the shift, we can use the Pythagorean theorem.
Length of shift = √(Total length of curve)^2 - (Length of main curve)^2
= √(1000)^2 - (392.7)^2
≈ √(1000000 - 154315.29)
≈ √(845684.71)
≈ 919.45 m
4. Total Tangent Length:
The total tangent length is the sum of the length of the main curve, the length of the transition curve, and the length of the shift.
Total tangent length = Length of main curve + Length of transition curve + Length of shift
= 392.7 + 392.7 + 919.45
= 1704.85 m
≈ 613.88 m (rounded to two decimal places)
Therefore, the total tangent length of the curve is approximately 613.88 m.
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Community Answer
If the radius of the main curve is 375 m, angle of deflection of shif...
Given: R = 375 m, S = 50 m, θ = 300 and L = 1000 m
Total tangent length of the curve is
= 613.88m
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If the radius of the main curve is 375 m, angle of deflection of shift is 30° and the length of transition curve is 1000 m, then the total tangent length of the curve is _________ m. (Take shift as 50 m.) (Answer up to two decimal places)Correct answer is '613.88'. Can you explain this answer?
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If the radius of the main curve is 375 m, angle of deflection of shift is 30° and the length of transition curve is 1000 m, then the total tangent length of the curve is _________ m. (Take shift as 50 m.) (Answer up to two decimal places)Correct answer is '613.88'. Can you explain this answer?, a detailed solution for If the radius of the main curve is 375 m, angle of deflection of shift is 30° and the length of transition curve is 1000 m, then the total tangent length of the curve is _________ m. (Take shift as 50 m.) (Answer up to two decimal places)Correct answer is '613.88'. Can you explain this answer? has been provided alongside types of If the radius of the main curve is 375 m, angle of deflection of shift is 30° and the length of transition curve is 1000 m, then the total tangent length of the curve is _________ m. (Take shift as 50 m.) (Answer up to two decimal places)Correct answer is '613.88'. Can you explain this answer? theory, EduRev gives you an
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