(c) Total length of the curve Total length of curve =Total length (3) (d) Apex distance E
Q4.Explain the length of transition curve?A4) Length of transition curve:- Method of arbitrary gradient:-e = total super elevation provided at the junction of transition curve with the circular curveL = ne Where the rate of superelevation is ∆ in n
(b) Method of Time rate:- the time rate of superelevation
Method of the rate of change of radial acceleration Rate of change of radial accelerationt is the time attained by radial acceleration (a)a = Q5.What is cant?A5) It is defined as the raising of the outer end of a road or outer rail over the inner one.h = super elevation = ew = weight of the vehicleP = centrifugal force g = acceleration due to gravityR = radius of the curveG = gauge distance between railsu = speed of the vehicleB = width of pavement = Angle of superelevation h = super elevation = ew = weight of vehicleP = centrifugal force g = acceleration due to gravityR = radius of curveG = gauge distance between railsu = speed of vehicleB = width of pavement = Angle of super elevation
Centrifugal ratioQ6.Explain setting out of cubic parabola?A6) Setting out of Cubic Parabola
Φ1 = DL min = θL/60 degree x = l ( 1 – Φ2/10) = l (1 – l4/40R2L2) ...................................(5) y = l3/6RL ( 1 – Φ2/14) = l3/6RL ( 1 – l4/ 14 (2RL)2) .............(6) X = L ( 1 - Φ12/10) = L ( 1 – L2/40 R2) = L ( 1 – 33/ 5R) ..........(7) Y = L2/ 6R ( 1 – L2/ 56 R2) |
Q8.Explain setting out of lemniscates?A8) Setting out of Bernoulli‟s Lemniscate
∝s = Polar deflection angle OU bisect the ∆TUT’ at vertex V Hence TU & T’V are tangent of curve Make CA1 parallel to tangent TV intersecting OU at A1 Draw CC2& A1A2 normal tangent TV Φs = Total deflection angle at junction C ∠CTV = ∝s ∠CC1V= Φs TV = TC2 + C2A2 + A2V (tangent length = TV) Length of chord, TC = B = ∝s = Φ/3 TC2 = B cos ∝s ∠TUo = (180° - ∆)/2 = 90° - ∆/2 In ∆AC1V1, ext ∠OAC = ∠AGV + ∠GVA = Φs + (90° - ∆/2) ∠AOC = 90° - ∠AOC = 90° - [Φs + (90° - ∆/2)] β = ∆/2 - Φs From ∆OCA1⇒ C0/CA1 = sin (90° - ∆/2)/sin (∆/2 - Φs) CA1 = R sin (A/2- Φs)/cos (∆/2) = R sec (∆/2) [ sin (∆/2) cos Φs - cos (∆/2) sin Φs] CA1 = C2A2 = R [ tan (∆/2) cos Φs – sin Φs] A2 V = A1A2 Cot (90° - ∆/2) = CC2 Cot (90° - ∆/2) = B sin ∝s tan (∆/2) Adding all equation TU = TC2 + C2A2 + A2V TU = B cos ∝s + R [ tan (∆/2) cos Φs – sin Φs ] + B sin ∝s tan ∝s |