HIGHWAY ENGINEERING(Part 4)
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EXTRAWIDENING
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EXTRAWIDENING
Additional width of a carriageway that is required on horizontal curve is referred as extrawidening. The rear wheels follow the inner path on the curve as compared with the front wheels. This phenomena is called off tracking.
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| Extrawidening |
- The reason to provide extrawidening are-
(ii) To avoid over tracking due to rigidity of wheelbase.
(iii) To increase the visibility of curves.
(iv) To encounter psychological tendency while over tracking operation.
Extrawidening split up into two parts-
(i) Mechanical widening(Wm)- It is provided due to the rigidity of wheel base, when a vehicle travels on a horizontal curve, only front wheel can be controlled and the rear wheels does not follow the same path as front wheel.
- Mechanical widening(Wm) = nl^2/2R ( If a road has n lanes, R= Radius of curve, l = length of the wheel base)
- Psychological widening(Wps) = V/ 9.5√R ( where v = speed of the vehicle kmph)
= (nl^2/ 2R + V/ 9.5√R) m.
- Grade compensation at curves on hill roads-
Compensated gradient = Gradient - Grade compensation.
CURVES
Transition Curves-
When a vehicle traveling on a straight road enters into a horizontal curve instantaneously, it will cause discomfort to the driver.It is required to provide a transition curve to avoid this.
Transition Curves
The objectives of providing a transition curves are-
(i) To gradually introduce the centrifugal force between straight amd circular curves.
(ii) To avoid the certain jerk.
(iii) To gradually introduce superelevation and extra widening.
(iv) To enable the driver turn the steerinng gradually for comfort and security.
(v) To improve aesthetic appearence.
Vertical Curve-
Vertical curves are provided at the intersections of different grades to smoothen the vertical profile.
The vertical curves used in highway are two types-
1. Summit Curve-
A summit curve is a vertical curve with convexity upward or concavity downward .This occur when an ascending gradient intersects a descending gradient or when a ascending gradient meets another ascending gradient or an ascending gradient meets a horizontal or when a descending gradient gradient meets an another descending gradient.
Length of the summit curve
- Case 1-
When length of the curve exceeds the required sight distance i.e, L> S.
Here, L is the length of the curve and S is the sight distance.
Then length of the summit curve is given as,
L = NS^2/2( √H + √h)
Where H is the height of eye of driver from road surface and h is the height of object above pavement surface.
For SSD, H= 1.2 m , h = 0.15 m
L = (NS^2/ 4.4) m
For ISD/OSD, H = 1.2 m, h = 1.2 m.
L = (NS^2/ 9.6) m.
- Case 2-
When, L< S.
Then length of the summit curve is given as,
L = 2S - 2( √H + √h)^2/N
For SSD, L = 2S - (4.4/N ) m
For ISD/OSD, L = 2S - ( 9.6/N) m
2. Valley Curve or Sag Curve-
A valley curve is a vertical curve with concavity upward or convexity downward.
This formed when a descending gradient intersects an ascending gradient or when a descending gradient meets another descending gradient or when a descending gradient joint a horizontal path or when a ascending gradient meets an ascending gradient.
- Length of the Valley Curve-
(i) Based on comfort condition-
Length of the valley curve, Ls = 2√(NV^3/C)
(ii) Based on Headlight Sight Distance-
- Case 1
Let h is the height of the headlight above the road surface and S is the headlight sight distance.
The length of the valley curve , if beam angle is α is given by
Lv = NS^2/(2h + 2Stanα) m.
If, h = 0.75 m , α = 1
Lv = NS^2/(1.5 + 0.035S) m
- Case 2
The length of the valley curve, Lv = 2S - (2h + 2Stanα)/N m
Lv = 2S - ( 1.5 + 0.035s)/N m
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