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Published byMaurice Gibson Modified over 9 years ago
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Horizontal Curves Circular Curves Transition Spirals
Degree of Curvature Terminology Calculations Staking Transition Spirals
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Circular Curves I – Intersection angle Portion of a circle R - Radius
Defines rate of change I R
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Degree of Curvature D defines Radius Chord Method Arc Method
R = 50/sin(D/2) Arc Method (360/D)=100/(2R) R = /D D used to describe curves
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Terminology PC: Point of Curvature PC = PI – T PT: Point of Tangency
PI = Point of Intersection T = Tangent PT: Point of Tangency PT = PC + L L = Length
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Curve Calculations L = 100I/D T = R·tan(I/2) L.C. = 2R·sin(I/2)
E = R(1/cos(I/2)-1) M = R(1-cos(I/2))
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Curve Calc’s - Example Given: D = 2°30’
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Curve Calc’s - Example Given: D = 2°30’
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Curve Design Select D based on: Determine stationing for PC and PT
Highway design limitations Minimum values for E or M Determine stationing for PC and PT R = /D T = R tan(I/2) PC = PI –T L = 100(I/D) PT = PC + L
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Curve Design Example Given: I = 74°30’ PI at Sta 256+32.00
Design requires D < 5° E must be > 315’
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Curve Staking Deflection Angles Transit at PC, sight PI
Turn angle to sight on Pt along curve Angle enclosed = Length from PC to Pt = l Chord from PC to point = c
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Curve Staking Example
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Curve Staking If chaining along the curve, each station has the same c: With the total station, find and c, use stake-out
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Computer Example
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Moving Up on the Curve Say you can’t see past Sta 177+00.
Move transit to that Sta, sight back on PC. Plunge scope, turn 7 34’ 24” to sight on a tangent line. Turn 115’ to sight on Sta
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