Islamic University of Gaza Civil Engineering Department Surveying
- Slides: 22
Islamic University of Gaza Civil Engineering Department Surveying II ECIV 2332 By Belal Almassri
Chapter 9 Route Surveying – Part 5 Transition Curve Layout Using Theodolite. - Preliminary work and calculations. - Setting out the curves. - The whole procedure. - Example 9. 4. -
Transition Curve Layout Using Theodolite: �In order to lay out a combination of circular curve and transition curve, the following procedure is used: 1. Preliminary work and calculations. - Transition Curve. - Circular Curve. 2. Setting out the curve. - Left transition curve. - Right transition curve. - Circular curve. - Common tangent between transition and circular curves.
Transition Curve Equations �Length of transition curve (L): - Past experience or uniform rate or equation a: Rate of change of radial acceleration in m/sec^3 (0. 3 – 0. 5). - R: Circular curve radius. - V: Design speed in m/sec. -
�Transition curve shift (S): - The amount of distance that the circular curve is shifted inward to be adopted with the transition curve. L: Length of transition curve. - R: Circular curve radius. -
�The total length of the tangent Ts or PT line: - The total length from the point of the intersection PI to the start point of the transition T can be computed through the following formula: L: Length of transition curve. - S: Shift of transition curve. - R: Radius of circular curve. - Δ: Central Angle. -
�Chainage of TS ( T ) and SC ( T 1): Chainage of T = Chainage of PI - P T Chainage of T 1 = Chainage of T + L �Lengths of partial chords for the left transition curves: - C ≤ R/40 - C 1 to be as computed in circular curves. - C 2 = L – (C 1+ n. C), n: intermediate chords.
�Deflection angles of the transition curve: - Angle of T 1 (the spiral angle): - Deflection angle of transition curve: - CHECK!. . . Sum of di =
Underground. . .
�The 1. 2. 3. 4. - Whole Calculations Procedure: Find R and Δ of the circular curve. Find L, S and PT of the transition curve. Find Chainage of T , T 1, T 2 and T 3. Find the Partial chords and the deflection angles for the following: Right transition curve. Circular Curve. Left Transition Curve.
Example 9. 4
Vertical Curves �Def: A parabolic curve that is applied to make a smooth and safe transition between two grades on a roadway or a highway. VPC: Vertical Point of Curvature VPI: Vertical Point of Intersection VPT: Vertical Point of Tangency. VPC G 1, G 2: Tangent grades in percent A: Algebraic difference in grades L: Length of vertical curve VP I VPT
There are two kinds of vertical curve: �Summet. Vertical Curves: Type I and Type II. �Sag Vertical Curves : Type III and Type IV.
�Information needed for vertical curves design: 1. Gradients g 1 and g 2. 2. Chainage and elevation of VPI. 3. Length of the curve L. �Sight Distance: The length of the roadway visible to driver. 1. Stopping sight distance. (S. S. D) 2. Passing sight distance. (P. S. D)
�Stopping Sight Distance (SSD) is the viewable distance required for a driver to see so that he or she can make a complete stop in the event of an unforeseen hazard.
V: Velocity in m/s t: Perception and reaction time (2. 5 sec) f: coefficient of friction for roads i: gradient (Up is +ve, Down is –ve) g: gravity (9. 81 m/s^2)
�Passing Sight Distance (PSD) is the clear distance that the driver must view in order to be able safely pass the car in front of him. (PSD=2. SSD)
Vertical Curve Calculations �Location of Max/Min elevation on the curve: �Elevation of any point on the curve:
�Chainage VPT: and elevation of VPC and
�Length of Vertical Curve: Method 1: K: Rate of curvature. (By Tables) A: Difference of gradients. Method 2: depends on the sight distance, gradient difference: Equations (9. 46, 9. 47, 9. 48, 9. 50) from the text book.
Example 9. 7
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