Introduction to Transportation Engineering Alignment Design Vertical Alignment

1. Introduction to Transportation EngineeringAlignment DesignVertical Alignment Instructor Dr. Norman Garrick Hamed Ahangari May 2014

2. Basic Elements • Horizontal Alignment • Vertical Design • Cross Section

3. Horizontal Alignment Vertical Alignment Crest Curve G2 G3 G1 Sag Curve

4. Design of Vertical Curves

5. Parabolic Curve BVC G1 G2 EVC PI L/2 L/2 L Change in grade: A = G2 - G1G is expressed as % Rate of change of curvature: K = L / |A| Rate of change of grade: r = (g2 - g1) / L Equation for determining the elevation at any point on the curve y = y0 + g1x + 1/2 rx2 where, y0 = elevation at the BVCg = grade expressed as a ratio x= horizontal distance from BVC r = rate of change of grade (ratio)

6. El. 200 B 190 180 170 160 150 140 130 A ` El. 100 120 110

7. Alignment Standard related to Design Speed Site Engineering by Steven Storm

8. El. 200 B 190 180 170 160 150 140 130 A ` El. 100 120 110

9. 11+50 11+00 El. 200 B 190 8+00 7+00 9+00 6+00 10+00 180 5+00 4+00 170 3+00 160 2+00 150 1+00 140 130 A 0+00 ` 120 110

10. Longitude Profile Elevation 200 B (1150,200) 180 160 140 120 100 A (0,100) Distance 100 200 300 400 500 600 700 800 900 1000 1100

11. Elevation 200 B (1150,200) 180 G3=9.3% h=40’,d=430’ 160 G2=6.25% h=20’,d=320’ 140 G1=10% 120 h=40’,d=400’ 100 A (0,100) Distance 100 200 300 400 500 600 700 800 900 1000 1100

12. Elevation 200 B (1150,200) 180 G3=9.3% 160 G2=6.25% 140 G1=10% 120 100 A (0,100) Distance 100 200 300 400 500 600 700 800 900 1000 1100

14. Vertical alignment • Step 1: First provide the longitude profile of the road which contain earth elevations. • Step 2: Based on the maximum allowable slope and topographic condition, determine vertical tangents. • Step 3: Calculate the parabolic vertical curve specifications.

15. Example We want to design a road which connect point A and B • Design Speed is 30 mph • Provide vertical alignment for this road

16. ` B A