superelevation

Superelevation

Superelevation is the transverse slope to counteract the centrifugal force and reduce the tendency of the vehicle to overturn or Skid.

 e=\left(\frac{NL}{ML}\right)

 e= \tan \theta \approx \sin \theta = \left(\frac{e}{b}\right)

where,
B= Pavement width
E= Relative elevation of the outer edge.

Calculation of superelevation :

Force acting on a vehicle moving on circular curve radius R .with speed V m/sec

  1. Centrifugal force P acts horizontally outward through C.G
  2. The weight of the vehicle acts vertically through C.G
  3. The frictional force acts inward to the center of the curve

For Equilibrium

 P \cos\theta = W\sin\theta +f(W\cos\theta + P\sin\theta)

 P [\cos\theta- f\sin\theta] = W\sin\theta +f.W\cos\theta

 \frac{P}{W} = \frac{\tan\theta +f}{1-\tan\theta} = e+f

 e+f=\frac{P}{W}= \frac{v^{2}}{gr} Where\: v \:is\: in \:m/sec

 e+f= \frac{V^{2}}{127R} Where\: V \:is \:in \:kmph.

R= Radius in m
e= Rate of superelevation= tan$\theta$
f= Design value of lateral friction=0.15

Super elevation design:

Step-1: The super elevation for 75% of design speed (Vkmph) is calculated ignoring the friction.

 e=0.75 \frac{V^{2}}{127R} = 225R

Step-2: If the calculated value of “e” is less than 7% (0.07), the value so obtained is provided and if the value exceeds the 0.07 then provide the maximum super elevation i.e. 0.07 and proceed with steps iii & iv.

Step-3 : Then check the coefficient of friction f for maximum value of e=0.07 at the full value of design speed.  f= \frac{V^{2}}{127R} - 0.07

If f<0.15 the value of e=0.07 is safe else restrict the speed as given in next step.

Step-4 : Find the allowable speed V (kmph) at the Curve by  e+f= 0.07+0.15= \frac{V^{2}}{127R}

 V_{a} = \sqrt{27.94\:R} (kmph)

  • If the allowable speed Va is higher than the design speed V then the design is adequate and provide =0.07 & f = 0.15.
  • If the Va<V, then the sped is limited to Va kmph and appropriate warning sign & speed limits signs are installed.
  • Maximum super elevation IRC recommends emax=0.07(7%) for plain and rolling terrain Minimum super elevation IRC recommends emin=Camber from drainage considerations
  • Attainment of superelevation: The full S.E is attained by the end of the transition curve or at the beginning of the circular curve.

There are two methods of rotating after eliminating camber.

A. Rotation about Centre line:

 Depressing \:the \:inner \:edge\: by\: \frac{e}{2} and\: raising \:the\: outer \:edge by\: \frac{e}{2}

B. Rotation of pavement about the inner edge: Outer edge of the pavement is raised by e

Ruling minimum radius of horizontal curve :  R_{Rruling} =\left(\frac{ V^{2}}{127(e+f)}\right)

, where V= ruling design speed (kmph)

Ruling minimum radius

For N.H. & S.H.360 m
For M.D.R230 m
For O.D.R155 m
For V.R90 m

Superelevation

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