Saturday, August 24, 2013

Super-elevation at horizontal curves


Super-elevation: It is the inward transverse slope provided throughout the length of the horizontal curves to counteract the centrifugal force and therefore to check the tendency of the vehicle to over turn or skid.
Outer edge of the pavement is raised with respect to the inner edge of the pavement, the ratio of the height raised to the width of the pavement is called super-elevation.

Superelevation on the horizontal curves
e = E/B = tan(angle w.r.t. horizontal)

Or E = e.B

e+f = v^2/ g.R
Here, e = rate of super-elevation
          f= design value of the lateral friction co-efficient = 0.15
        v = speed of vehicle in m/sec.
        R= Radius of the horizontal curve, m
  If velocity is in Kmph, then
  e+f = V^2/(127.R)

Methods of Providing Super-elevation:
Superelevation is provided at a gradual rate along the length of the transition curve. It  is done by changing crowned camber  a single cross slope before the start of the circular curve.  Full superelevation is attained at the end of transition curve or at the start of the circular curve.

Attainment of the Superelevation may be completed in following steps:
(i) Elimination of the crown of the cambered section.
(ii) Rotation of the pavement to attain a full super-elevation.

Second step can be completed in three ways,  (a) by rotating the pavement with respect to inner edge,  (b) by rotating the pavement with respect to the center of the pavement or  (c) by rotating the pavement with respect to the outer edge of the pavement.

Superelevation is introduced by rise in the outer edge of the pavement at a rate not exceeding 1 in 150 in plain and rolling terrain and 1 in 60 on mountainous and steep terrain as per the recommendations of the IRC(Indian Roads Congress).

Designing Superelevation:
The design procedure for providing the superelevation follows the following Four steps:

(1) Friction is neglected and super-elevation is designed for 75% of the design speed value,
     e = (0.75. v)^2/ (gR)   where v is in m/sec
 or e = (0.75. V)^2/ (127R)   where v is in Kmph/sec

(2) If e < 0.07 then value so obtained is provided
If e>0.07, then provide the maximum super-elevation equal to 0.07 and proceed with steps 3 and 4.

(3) Check the co-efficient of friction developed for the maximum value of e equal to 0.07 for the full design speed v.

   f= v^2/(g.R) - 0.07
if  f< 0.15, then e = 0.07 is safe for the design speed. If not, calculate the restricted speed as follows

(4) 0.07 + 0.15 = Va^2/ (g.R)
         Where, Va = allowable safe speed.

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