CE 404 Lecture 5,4(Vertical Alighnment)
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Transcript of CE 404 Lecture 5,4(Vertical Alighnment)
LECTURE #4,5
Transi t ion curve
vert ica l a l ignment
2016CE 404. Highway Engineering
1
HIGHWAY ENGINEERING
(CE 404)
بسم هللا الرحمن الرحيم
By
ALGHRAFY
Transition curve
2016CE 404. Highway Engineering
2
Transition curve is provided to change the horizontal alignment from straight to circular curve gradually and has a radius which decreases from infinity at the straight end (tangent point) to the desired radius of the circular curve at the other end (curve point)
ALGHRAFY
Transition curve
2016CE 404. Highway Engineering
3
point of intersection (PI)
tangent to spiral (TS)
spiral to curve (SC)
curve to spiral (CS)
spiral to tangent (ST)
point of curvature (PC)
point of tangency (PT)
The length of the spiral (LS)
shift distance or throw distance (T)
tangent distance (TS)
the long chord (LCS) of the spiral
LT and ST long tangent and the short tangent of the spiral.
spiral point of intersection (SPI).
ALGHRAFY
Transition curve
2016CE 404. Highway Engineering
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Transition curve is not necessary when :
o In low speed environments where drivers regulate their travel speed from their judgment of the apparent curvature of the road ahead.
o On Large radii curves R > 900𝑚
o On small radii curves in low speed environments where pavement widening to accommodate the tracking widths required by heavy vehicles is necessary.
ALGHRAFY
Transition curve objectives
2016CE 404. Highway Engineering
5
o To introduce gradually the centrifugal force between the tangent point and the beginning of the circular curve, avoiding sudden jerk on the vehicle. This increases the comfort of passengers.
o To enable the driver turn the steering gradually for his own comfort and security,
o To provide gradual introduction of super elevation, . And
o To provide gradual introduction of extra widening
ALGHRAFY
Transition curve
2016CE 404. Highway Engineering
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o Spiral or clothoid,o Cubic parabola, ando Lemniscate.
Type of transition curve
Case-1:Rate of change of centrifugal acceleration
Length of transition curve
𝐿𝑆 =0.0215𝑉3
𝐶 × 𝑅
𝐶 =80
75 + 𝑉
0.5 < C < 0.8 IR0.3 < C < 0.9 AASHTO0.3 < C < 0.9 BC
Where, Ls= length of transition curve in ‘m’ C= allowable rate of change of centrifugal accleration, m/ sec² R= Radius of the circular cu rve in ‘m’ V= speed kmph
ALGHRAFY
Transition curve
2016CE 404. Highway Engineering
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case-2:Rate of introduction of super-elevation
𝑳𝑺 =𝒆 ×𝒘 × 𝒏𝟏 × 𝒃𝒘
𝑮𝒎𝒂𝒙
ALGHRAFY
Transition curve
2016CE 404. Highway Engineering
8
case-3:Minimum Spiral Curve Constant
𝑳𝑺 =𝑨𝒎𝒊𝒏𝟐
𝑹
By empirical formulacase-4:
𝑳𝑺 =𝟐. 𝟕𝑽𝟐
𝑹For plane and rolling terrain:
For mountainous and steep terrain: 𝑳𝑺 =𝑽𝟐
𝑹
The design length of transition curve(Ls) will be the highest value of case-1,2,3 and 4
ALGHRAFY
Transition curve
2016CE 404. Highway Engineering
9
ALGHRAFY
Transition curve
2016CE 404. Highway Engineering
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∆𝑪=𝐷 × 𝐿𝐶30.5
General Spiral Equations
∆𝑺=𝐷 × 𝐿𝑆61
∆= ∆𝑪 + 2∆𝑆
𝐿 = 𝐿𝐶 + 2𝐿𝑆
𝑇𝑆 = 𝑄 + 𝑅 + 𝑇 𝑡𝑎𝑛∆
2
𝐸𝑆 =(𝑅 + 𝑇)
𝑐𝑜𝑠∆2
− 𝑅
𝑇 =𝐿𝑆2
24𝑅
∆𝑺=𝐿𝑆2𝑅
𝐿𝐶 = 𝑹(∆ − 2∆𝑆)
ALGHRAFY
Vertical Alignment
2016CE 404. Highway Engineering
16
The vertical alignment is the elevation or profile of the centerline of the road.Consists of straight sections of the highway known as grades, or tangentsconnected by vertical curves.The design of vertical alignment involves selection of suitable grades for the tangent sections and the design of the vertical curves.Topography of the area which the road traverses has a significant impact on the design of the vertical alignment.
ALGHRAFY
Vertical Alignment
2016CE 404. Highway Engineering
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ALGHRAFY
Vertical Alignment
2016CE 404. Highway Engineering
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Vertical Alignment
Geometric Elements of Vertical Curves
Vertical Grades
Passing Lanes
Sight Distance
ALGHRAFY
Vertical Alignment
2016CE 404. Highway Engineering
19
The design of the vertical alignment is influenced by
o consideration of terrain (Topography) ,
o Type of roads
o Vehicle Operational Characteristics
o Design speed
o cost, and
o safety.
ALGHRAFY
Vertical Alignment
2016CE 404. Highway Engineering
20
Highway engineers generally separate the characteristics of variations in typography according to the terrain:
Level terrain: highway sight distances, as governed by both horizontal and vertical restrictions, are usually long or can be made without construction difficulty.Rolling terrain: natural slopes consistently rise above or fall below the road grade, and occasional steep slopes offer some restriction to normal alignment.Mountainous terrain: longitudinal and transverse changes in the elevation of the ground are usually abrupt, and benching and side hill excavation are frequently needed.
Consideration of terrain, Type of roads, and Design speed
Vertical Alignment
2016CE 404. Highway Engineering
21
Passenger cars: Grades as steep as 4% to 5% generally do not affect speed of most vehicles (may affect some compact/subcompact vehicles)Trucks: Effects on speed much more important
Vehicle Operational Characteristics
The term “critical length of grade” is used to indicate the maximum length of a specified ascending gradient upon which a loaded truck can operate without an unreasonable reduction in speed (commonly 10 mph [15 km/h])
ALGHRAFY
Vertical Grades
2016CE 404. Highway Engineering
22
Maximum Grades
o Maximum grades have been established, based on operating characteristics of design vehicle.
o Max grade vary from 5% for DS of 70 mi/h to 12% for DS of 30 mi/h.o See Table for recommended values of max grades.o Max grades in the Table should not be used frequently, particularly when grades
are long and traffic include high % of trucks.o on low volume rural highways, maximum grades may be increase by 2% When :o grade length (< 500 ft) and o roads are one-way in the downgrade direction,
ALGHRAFY
Vertical Grades
2016CE 404. Highway Engineering
23
Maximum Grades
ALGHRAFY
Vertical Grades
2016CE 404. Highway Engineering
24
ALGHRAFY
Vertical Grades
2016CE 404. Highway Engineering
25
Minimum Grades
o Minimum grades depend on the drainage condition of the highway.o 0% grades may be used on uncurbed pavements with adequate cross-slopes to
laterally drain the surface water.o When pavements are curbed, longitudinal flow should be provided to facilitate
the longitudinal flow of surface water.o Min of (0.5%).
Grade Change Without Vertical Curves
Designing a sag or crest vertical point of intersection without a vertical curve is generally acceptable where the grade difference (A) is:o 1.0 percent or less for design speeds equal to or less than 45 mph [70 km/h]o 0.5 percent or less for design speeds greater than 45 mph [70 km/h].
ALGHRAFY
Vertical Curve
2016CE 404. Highway Engineering
26
Used to provide gradual change from one tangent grade to another so that vehicle may run smoothly as they traverse the highway.o Classes or types
Change in grade: A = G1 – G2
where G is expressed as % (positive /, negative \)
G2
G1
G2
G1
G2
G1
G2
G1
Crest vertical curves, A is positiveSag vertical curves, A is negative
G1
G2
G2
G2
G2
G1G1
G1
ALGHRAFY
Vertical Curve
2016CE 404. Highway Engineering
27
Properties of Vertical Curves
For a vertical curve, the general form of the parabolic equation is;
y = ax2 + bx + c
Y
X
From an equal tangent parabola, it can be written as;
y = ax2
adx
dy2
2
2
But The rate of change of slope can also be written as;
L
GG
dx
dy 21
2
2
L
GGa
2
21
The rate of change of slope
L
Aa
2
2
2x
L
Ay
2
2
4L
xey
842
2 ALL
L
Ae
2
22
8x
L
ey
ALGHRAFY
Design Of Vertical Curve
2016CE 404. Highway Engineering
28
Elevation and station
Crest vertical curves
H1= HPVC + g1 x - (A)x2 / 2L
H2= HPVT + g2 x - (A)x2 / 2L
ALGHRAFY
Design Of Vertical Curve
2016CE 404. Highway Engineering
29Elevation on Vertical Curve
Sag vertical curves
H1= HPVC - g1 x + (A)x2 / 2L
H2= HPVT - g2 x + (A)x2 / 2L
ALGHRAFY
Design Of Vertical Curve
2016CE 404. Highway Engineering
30
The elevation and location of the high or low point
crest vertical curves
ALGHRAFY
Design Of Vertical Curve
2016CE 404. Highway Engineering
31
Elevation on Vertical Curve
Sag vertical curves
ALGHRAFY
Design Of Vertical Curve
2016CE 404. Highway Engineering
32Length of Crest (summit) Vertical Curves
G1G2
PVI
PVTPVC
h2h1
L
SSD
221
2
22100 hh
SSDAL
A
hhSSDL
2
212002
For SSD < L For SSD > L
Line of Sight
ALGHRAFY
Design Of Vertical Curve
2016CE 404. Highway Engineering
33Length of Crest (summit) Vertical Curves
Assumptions for design h1 = driver’s eye height = 1.07 m.
h2 = tail light height = 0.61 m.
Simplified Equations
658
2SSDA
L A
SSDL658
2
For SSD < L For SSD > L
SSD= d1+d2
d1 = 0.278 x v x t
ALGHRAFY
Design Of Vertical Curve
2016CE 404. Highway Engineering
34Length of Crest (summit) Vertical Curves
658
2SSDA
L
For SSD < L
KAL
658
2SSDK
ALGHRAFY
Design Of Vertical Curve
2016CE 404. Highway Engineering
35
Length of Crest (summit) Vertical Curves
ALGHRAFY
Design Of Vertical Curve
2016CE 404. Highway Engineering
36
Length of Crest (summit) Vertical Curves
passing sight distance
864
2PSDA
L
A
PSDL864
2
For PSD < L
For PSD > L
ALGHRAFY
Design Of Vertical Curve
2016CE 404. Highway Engineering
37Length of Sag Vertical Curves
The selection of the minimum length of a sag vertical curve is controlled by (1) comfort while driving on the curve, (2) general appearance of the curve, and (3) SSD provided by the headlight,
(1) comfort while driving on the curve,
(2) general appearance of the curve
395
2AvL
Minimum Length based on Comfort Criterion.
Minimum length for the general appearance criterion
AL 5.30
ALGHRAFY
Design Of Vertical Curve
2016CE 404. Highway Engineering
38
G1 G2
PVI
PVTPVC
h2=0h1
L
Light Beam Distance (SSD)
tan200 1
2
Sh
SSDAL
A
SSDhSSDL
tan2002 1
For SSD < L For SSD > L
headlight beam (diverging from LOS by β degrees)
Length of Sag Vertical Curves
ALGHRAFY
Design Of Vertical Curve
2016CE 404. Highway Engineering
39
Assumptions for design h1 = headlight height = 0.61 m.
β = 1 degree
Simplified Equations
SSD
SSDAL
5.3120
2
A
SSDSSDL
5.31202
For SSD < L For SSD > L
ALGHRAFY
Design Of Vertical Curve
2016CE 404. Highway Engineering
40Length of Sag Vertical Curves
For SSD < L
KAL
SSD
SSDAL
5.3120
2
SSD
SSDK
5.3120
2
ALGHRAFY
Design Of Vertical Curve
2016CE 404. Highway Engineering
41
Length of Sag Vertical Curves
Design Of Vertical Curve
2016CE 404. Highway Engineering
42
Length of Sag Vertical Curves Undercrossing
ALGHRAFY
Design Of Vertical Curve
2016CE 404. Highway Engineering
43
Length of Sag Vertical Curves Undercrossing
ALGHRAFYALGHRAFY
Design Of Vertical Curve
2016CE 404. Highway Engineering
44
Length of Sag Vertical Curves Undercrossing
ALGHRAFY
Thank You
2016CE 404. Highway Engineering
58
ALGHRAFY