CEE 3604 Transportation Geometric Design. Highways. Transportation Engineering (A.A. Trani)

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1 CEE 3604 Transportation Geometric Design Highways 1

2 History Roads have been developed in ancient cultures for trade and military reasons Silk Road km in length Appian Road - Rome to Brindisi (Italy) Source: Wikipedia 2

3 Types of Alignments Horizontal Vertical 3

4 The Concept of Station The position of a specific point on a highway is traditionally determined using the concept of stations A datum point on a highway alignment is specified. This initial point is designated station The positions of all other points on the highway are calculated by measuring the corresponding distances on a horizontal plane along the highway from the initial point For example, the point on a highway located m from the previously specified point, is designated station

5 Vertical Alignment Vertical alignment is composed of straight sections that are connected by vertical curves These straight sections are called grades or tangents Once a vertical alignment is designed, the elevations of all the points along the highway are established. Vertical curves are classified as "crest" or "sag" curves 5

6 Types of Vertical Alignments 6

7 Elements of a Vertical Curve Vertical Point of Curvature (VPC) Vertical Point of Intersection (VPI) Vertical Point of Tangency (PVT) Length of Curve (L) Grades (G1 and G2) 7

8 Vertical Alignment Profile grade tangents are connected by the parabolic curve. Mathematically, the basic definition of a parabola is: b = G 1 8

9 Vertical Curves The grades are expressed in [m/m]. Let the difference in grades be (A = G2 - G1) The difference in grades is positive for sag curves and negative for crest curves 9

10 Example 1 The length of a tangent vertical curve equals 300 [m]. The initial and the the ;inal grades are known to be 2.5% and respectively The grades intersect at the station and at an elevation of m 10

11 Example 1 (a) Determine the station and the elevation of the VPC and PVT points (b) Calculate the elevation of the point on the curve 100 meters from the VPC point (c) Determine the station and the elevation of the highest point on the curve 11

12 Example 1 - Solution 12

13 Example 1 - Solution 13

14 Example 1 - Solution 14

15 Example 1 - Solution 15

16 The Concept of Offset 16

17 Offset Equations 17

18 Stopping Sight Distance Considerations Ver%cal curve design requires considera%on of the average stopping sight distances Drivers should have a clear view of the road ahead to stop before and obstacle while driving on a ver%cal curve 18

19 Crest Vertical Curve Design 19

20 Crest Vertical Curve Design where: A = G 2 - G 1 20

21 Crest Vertical Curve Design 21

22 Crest Vertical Curve Design Do you remember how to calculate SSD? Please review notes 22

23 Crest Vertical Curve Design Rate of Vertical Curve Parameter (meters / %) 23

24 Example 2 For example 1, The highway designers are considering design speeds ranging from 100 [km/h] to 120 [km/h] Calculate corresponding minimum length of the vertical curve that satisfies the minimum stopping sight distance 24

25 Example 2 - Solution Rate of Vertical Curve Parameter K = 62 m/% from AASHTO Table

26 Example 2 - Solution AASHTO Table 26

27 Example 2 - Solution Note the large difference in the lengths of the curves required This has a significant effect on the cost of building the road (cuts and fills) 27

28 Passing Sight Distance Considerations 28

29 Passing Sight Distance Equations Do you remember how to calculate PSD? Please review notes 29

30 Sag Vertical Curves 30

31 Sag Vertical Curve Design 31

32 AASHTO Design Equations 32

33 AASHTO Design Standards 33

Horizontal and Vertical Curve Design

Horizontal and Vertical Curve Design CE 576 Highway Design and Traffic Safety Dr. Ahmed Abdel-Rahim Horizontal Alignment Horizontal curve is critical. Vehicle cornering capability is thus a key concern