Lec-3(CE3209) Horizontal Curves.pptx

very good notes

1. 1 Horizontal Curves Lec M Rizwan Shahid Lec#03

2. 2 Key points of the previous lecture Survey drafting and computation Area calculation Volume calculation

3. 3 Objectives of the current lecture To learn about the Horizontal curve layout Types of curves Degree of curve Superelevation Horizontal curve stakeout/ layout methods

4. 4 Curves Curves are provided whenever a road, rail or other civil engineering projects changes its direction from right to left (vice versa) or changes its alignment from up to down ( vice versa ).

5. 5 Curve There are two types of curves provided primarily for the comfort and ease of the drivers in the road namely : Horizontal Curve Vertical Curve

6. 6 Curve Layout Horizontal Curves in Surveying Horizontal curves are provided to change the direction or alignment of a road. Horizontal Curve are circular curves or circular arcs . The sharpness of a curve increases as the radius is decrease which makes it risky and dangerous. The main design criterion of a horizontal curve is the provision of an adequate safe stopping sight distance.

7. 7 Curve Layout Types of Horizontal Curve : Simple Curve: A simple arc provided in the road to impose a curve between the two straight lines . Compound Curve: Combination of two simple curves combined together to curve in the same direction . Reverse Curve: A reverse curve (or "S" curve) is a section of the horizontal alignment of a highway or railroad route in which a curve to the left or right is followed immediately by a curve in the opposite direction.

8. 8 Curve Layout Transition or Spiral Curve: A curve that has a varying radius. Its provided with a simple curve and between the simple curves in a compound curve. A transition curve may be defined as a curve of varying radius of infinity at tangent point to a design circular curve radius provided in between the straight and circular path in order that the centrifugal force was gradual. This is also known as easement curve

9. 9 Curve Layout

10. 10 Curve Layout

11. 11 Curve Layout

12. 12 Curve Layout

13. 13 Curve Layout

14. 14 Degree of Curve Degree of curve or degree of curvature is a measure of curvature of a circular arc used in civil engineering for its easy use in layout surveying . We can determine the degree of any curve by first finding the circumference of a circle.

15. 15 Degree of Curve The rate of curvature of circular curve can be designated either by their radius or by their degree of curve. The degree of curvature is defined as the central angle to the ends of an arc or chord of agreed length.

16. 16 Degree of Curve by arc definition Degree of curvature is based on 100 units of arc length, the conversion between degree of curvature and radius is D/360 = 100/2πR, where D is degree and R is radius . Equation for degree of curve as arc definition R=5729.58/D

17. 17 Degree of Curve by Cord definition Degree of curvature is based on 100 units of cord length, the conversion between degree of curvature and radius is LC = 2R sin(D/2), where D is degree and r is radius . Equation for degree of curve as Cord definition R=50/sin(D/2)

18. 18 Degree of Curve

19. 19 Elements of Circular Curve

20. 20 Elements of the Circular Curve PC = Point of curvature . PT = Point of tangency PI = Point of intersection of the tangents . T = Length of tangent from PC to PI and from PI to PT . R = Radius of simple curve, or simply radius. L = Length of chord from PC to PT. Lc = Length of curve from PC to PT . m = Middle ordinate, the distance from midpoint of curve to midpoint of chord . Sub chord = chord distance between two adjacent full stations.

21. 21 Elements of the Circular Curve I = I ntersection /central angle. It is the angle of intersection of the tangents. The angle subtended by PC and PT at O is also equal to I, where O is the center of the circular curve. x = offset distance from tangent to the curve. Note: x is perpendicular to T. θ = offset angle subtended at PC between PI and any point in the curve D = Degree of curve. It is the central angle subtended by a length of curve equal to one station. In English system, one station is equal to 100 ft.

22. 22 Parts of the Circular Curve

23. 23 Parts of the Circular Curve

24. 24 Parts of the Circular Curve

25. 25 Parts of the Circular Curve

26. 26 Layout Circular Curve

27. 27 Layout of Circular Curve Methods of Setting out of single Circular curve • Linear Methods • Angular Methods . 1) Linear Methods • By offsets or ordinate from the long chord • By successive bisection of arcs or chords. •By offsets from the tangents. •By offsets from the chord produced.

28. 28 Layout of Circular Curve 2) Angular Method • Used when length of curve is large • More accurate than the linear methods • Theodolite and Total Station is used Deflection Angel/ Rankine method of tangential angles OR One theodolite method Two theodolite method Coordinates

29. 29 Curve Layout Q-1 Why we need to incorporate horizontal curve. Ans :- Horizontal curves are provided to change the direction or alignment of a road

30. 30 Curve Layout Q-2 What is degree of curve Ans :- The rate of curvature of circular curve can be designated either by their radius or by their degree of curve. The degree of curvature is defined as the central angle to the ends of an arc or chord of agreed length. This angle is also the change in forward direction as that portion of the curve is traveled . Degree of curve or degree of curvature is a measure of curvature of a circular arc used in civil engineering for its easy use in layout surveying.

31. 31 Curve Layout Q-3 Enlist the angular methods of curve layout Ans :- Rankine method of tangential angles OR One theodolite method Two theodolite method

32. 32 Topics covered in the lectures To learn about the Horizontal curve layout Types of curves Degree of curve Superelevation Layout of simple Curve and its method

33. 33