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Horizontal Curves

Horizontal Curves. Circular Curves Degree of Curvature Terminology Calculations Staking Transition Spirals Calculations Staking. I. Circular Curves. Portion of a circle. I – Intersection angle. R - Radius Defines rate of change. R. Degree of Curvature. D defines Radius

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Horizontal Curves

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  1. Horizontal Curves • Circular Curves • Degree of Curvature • Terminology • Calculations • Staking • Transition Spirals • Calculations • Staking

  2. I Circular Curves • Portion of a circle • I – Intersection angle • R - Radius • Defines rate of change R

  3. Degree of Curvature • D defines Radius • Chord Method • R = 50/sin(D/2) • Arc Method • (360/D)=100/(2R) • R = 5729.578/D • D used to describe curves

  4. Terminology • PC: Point of Curvature • PC = PI – T • PI = Point of Intersection • T = Tangent • PT: Point of Tangency • PT = PC + L • L = Length

  5. 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))

  6. Curve Calc’s - Example • Given: D = 2°30’

  7. Curve Calc’s - Example • Given: D = 2°30’

  8. Curve Design • Select D based on: • Highway design limitations • Minimum values for E or M • Determine stationing for PC and PT • R = 5729.58/D • T = R tan(I/2) • PC = PI –T • L = 100(I/D) • PT = PC + L

  9. Curve Design Example • Given: • I = 74°30’ • PI at Sta 256+32.00 • Design requires D < 5° • E must be > 315’

  10. 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

  11. Curve Staking Example

  12. Curve Staking If chaining along the curve, each station has the same c: With the total station, find  and c, use stake-out

  13. Computer Example

  14. 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 115’ to sight on Sta 178+00.

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