HW3 due today Feedback form online Midterms distributed HW4 available tomorrow No class Wednesday CEE 320

Transcription

1 Course Logistics HW3 due today Feedback form online Midterms distributed HW4 available tomorrow No class Wednesday Midterm, 11/5

2 Geometric Design Anne Goodchild

3 Introduction PhpKA

4 Outline 1. Concepts. Vertical Alignment a. Fundamentals b. Crest Vertical Curves c. Sag Vertical Curves d. Examples 3. Horizontal Alignment a. Fundamentals b. Superelevation 4. Other Stuff

5 Draw a roadway Street view Arial view Side view

6 Identify a point on that roadway Address (relative system) Milepost system Linear referencing system Grid system Longitude and latitude Altitude

7 Highway Alignment Simplify from x-y plane to a linear reference system (distance along that roadway) Assume travel is along some horizontal plane, not the surface of the earth Elevation from this horizontal plane

8 Concepts Alignment is a 3D problem broken down into two D problems Horizontal Alignment (arial or plan view) Vertical Alignment (side or profile view) Piilani Highway on Maui

9 Concepts Stationing is a measurement system for the design problem Along horizontal alignment One station is 100 feet along the horizontal plane 1+00 = 1,00 ft. The point of origin or reference is at station 0+00

10 Stationing Linear Reference System Horizontal Alignment Vertical Alignment

11 Stationing Linear Reference System Horizontal Alignment Vertical Alignment 100 feet >100 feet

12 Questions How are mileposts or mile markers different from stations? Could two distinct pieces of roadway have the same station? Why stationing?

13 Kawazu-Nanadaru Loop Bridge

14 Alignment Main concern is the transition between two constant slopes Vertical alignment this means transition between two grades Horizontal alignment this means transition between two directions

15 Existing tools Autodesk AutoCAD Civil 3D x?siteid=1311&id=

16 Vertical Alignment

17 Vertical Alignment Objective: Determine elevation to ensure Proper drainage Acceptable level of safety Can a driver see far enough ahead to stop? Do the driver s light illuminate the roadway far enough ahead to stop? Can the vehicle be controlled during the transition under typical conditions?

18 Vertical Alignment Sag Vertical Curve G 1 G G 1 G Crest Vertical Curve G is roadway grade in ft/ft. G=0.05 is a 5% grade.

19 Vertical Curve Fundamentals Assume parabolic function Constant rate of change of slope y = ax + bx + y is the roadway elevation x stations (or feet) from the beginning of the curve c

20 Vertical Curve Fundamentals PVC G PVI 1 δ G L/ PVT L=curve length on horizontal x y = ax + bx + c Choose Either: G 1, G in decimal form, L in feet G 1, G in percent, L in stations

21 Vertical Curve Fundamentals PVC G PVI 1 δ G L/ PVT L=curve length on horizontal x PVC and PVT may have some elevation difference Rate of change of grade is constant, not grade itself Maximum height of the curve is not necessarily at L/

22 y = ax + bx + c At the PVC : x = 0

23 y = ax + bx + c dy = dx At the PVC : x = 0

24 Choose Either: G 1, G in decimal form, L in feet G 1, G in percent, L in stations Relationships 1, p, d Y G G1 G G1 Anywhere: = a = a = dx L L PVC PVI G 1 δ G G PVT L/ x L

25 Example A 400 ft. equal tangent crest vertical curve has a PVC station of at 59 ft. elevation. The initial grade is.0 percent and the final grade is -4.5 percent. Determine the elevation and stationing of PVT, and the high point of the curve. PVI PVT PVC: STA EL 59 ft.

26 PVI PVT PVC: STA EL 59 ft. Determine the elevation and stationing of PVT, and the high point of the curve.

27 PVI PVT PVC: STA EL 59 ft.

28 PVI PVT PVC: STA EL 59 ft.

29 Other Properties G 1, G in percent L in feet G 1 PVC PVT G A = G 1 G PVI A is the absolute value in grade differences, if grades are -3% and +4%, value is 7

30 Rate of change of slope different from slope Slope of curve at highpoint is 0 Slope of curve changes, but at a constant rate

31 Other Properties G 1, G in percent Linfeet Y versus y G 1 x PVC PVT Y Y m G A = G 1 G PVI Y f Y = A 00L x AL AL Y m = Y f =

32 Go back to the parabola y = ax + bx + c

33 Other Properties K-Value (defines vertical curvature) The number of horizontal feet needed for a 1% change in slope K = L A high / low pt. x = K G 1 G is in percent, x is in feet G is in decimal, x is in stations

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35 Vertical Curve Fundamentals Parabolic function Constant rate of change of slope Implies equal curve tangents y = ax + bx + c y is the roadway elevation x stations (or feet) from the beginning of the curve

36 Vertical Curve Fundamentals PVC G PVI 1 δ G L/ PVT L=curve length on horizontal x PVC and PVT may have some elevation difference Rate of change of grade is constant, not grade itself Maximum height of the curve is not necessarily at L/

37

38 PVC PVI PVT

39 Vertical Curve Fundamentals PVC G PVI 1 δ G L/ PVT L=curve length on horizontal x y = ax + bx + c Choose Either: G 1, G in decimal form, L in feet G 1, G in percent, L in stations

40 Other Properties G 1, G in percent L in feet G 1 x PVC PVT Y Y m G A = G 1 G PVI Y f Y = A 00L x AL AL Y m = Y f =

41 Other Properties K-Value (defines vertical curvature) The number of horizontal feet needed for a 1% change in slope K = L A high / low pt. x = K G Small K tighter curves, less L for same A, slower speeds Larger K gentler curves, more L for same A, higher speeds 1

42 Design Controls for Crest Vertical Curves from AASHTO s A Policy on Geometric Design of Highways and Streets 004

43 Stopping Sight Distance (SSD) Practical stopping distance plus distance travelled during driver perception/reaction time Distance travelled along the roadway Use this to determine necessary curve length V SSD = 1 + V a 1 g ± G g t r

44 Sight Distance (S) Horizontal distance between driver of height H 1 and a visible object of height H Want to design the roadway such that length of curve, L, allows a driver to observe an object with enough time to stop to avoid it (S=SSD).

45 Roadway Design Want to design the roadway such that length of curve, L, allows a driver to observe an object with enough time to stop to avoid it. Set SSD = S. Approximation works in our favor.

46 Crest Vertical Curves L For S < L For S > L A ( S ) = 00( H H ) ( ) 1 + ( H + ) 00 H 1 L = S A

47 Crest Vertical Curves Assumptions for design h 1 = driver s eye height = 3.5 ft. h = tail light height =.0 ft. Simplified Equations For S < L For S > L ( ) A S L = L ( S ) 158 = 158 A

48 Crest Vertical Curves Assume L > S and check Generally true Always safer K = S 158 If assumption does not hold K values cannot be used At low values of A it is possible to get a negative curve length

49 Sag Vertical Curves Light Beam Distance (S) G 1 headlight beam (diverging g from LOS by β degrees) G PVC PVT h 1 PVI h =0 Sight distance limited by headlights at night L

50 Sag Vertical Curves Light Beam Distance (S) G 1 headlight beam (diverging g from LOS by β degrees) G PVC PVT h 1 =H PVI h =0 For S < L L For S > L L A ( S ) ( H + ) = L = ( S ) 00 S tan β ( H + ( SSD ) tan β ) 00 + A

51 Sag Vertical Curves Assumptions for design H = headlight height =.0 ft. β = 1 degree Simplified Equations L For S < L For S > L ( ) A S = L = ( S ) ( S ) A ( S )

52 Sag Vertical Curves Assuming L > S K = S SS Again, set SSD=S

53 Design Controls for Sag Vertical Curves from AASHTO s A Policy on Geometric Design of Highways and Streets 004

54 Example 1 A car is traveling at 30 mph in the country at night on a wet road through a 150 ft. long sag vertical curve. The entering grade is -.4 percent and the exiting grade is 4.0 percent. A tree has fallen across the road at approximately the PVT. Assuming the driver cannot see the tree until it is lit by her headlights, ht is it reasonable to expect the driver to be able to stop before hitting the tree? 1 Assume S<L 1. Assume S<L A ( S ) L = ( S ). Solve for S. Roots ft and ft. Driver will see tree when it is 146 feet in front of her.

55 Sag Vertical Curve Required SSD V 1 SSD = + V1t r a g ± G g What do we use for grade? ft assumes 0 grade

56 Sag Vertical Curves Light Beam Distance (S) G 1 diverging from horizontal plane of vehicle by β degrees G PVC PVT h PVI 1 h =0 L Daytime sight distance unrestricted

57 Example A car is traveling at 30 mph in the country at night on a wet road through a 150 ft. long crest vertical curve. The entering grade is 3.0 percent and the exiting grade is -3.4 percent. A tree has fallen across the road at approximately the PVT. Is it reasonable to expect the driver to be able to stop before hitting the tree? 1. Assume S<L A ( S ). A=6.4 L = S=+/- 4.9 ft. But our curve only 150 ft. So assumption wrong.

58 Crest Vertical Curve L ( S ) = S = 43 ft SSD = ft 158 A V1 SSD = + V1t r a g ± G g Yes she will be able to stop in time.

59 Example 3 A roadway is being designed using a 45 mph design speed. One section of the roadway must go up and over a small hill with an entering grade of 3. percent and an exiting grade of -.0 percent. How long must the vertical curve be? Using Table 3., for 45 mph, K=61 L = KA = (61)(5.) = 317. ft.

60 Passing Sight Distance Only a concern on crest curves On sag curves Day: unobstructed view Night: headlights can be seen ( ) A S L = 00( H H ) ( ) 1 + ( H + ) 00 H 1 L H 1 =H =3.5 ft, let S=PSD = S A

61 Underpass Sight Distance

62 Underpass Sight Distance On sag curves: obstacle obstructs view Curve must be long enough to provide adequate sight distance (S=SSD) SSD) S<L S>L L m = ( S ) A H1 + H 800 H c L m = S H H c A H