Important point for the method of curve setting

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Bernadette Blankenship
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1 Important point for the method of curve setting Assumption:- 1) The length of chord is assumed to be equial to that of arc. 2) The difference between the arc and chord is negligible. Peg Interval :- 1) Peg are normally fixed at equal interval on curve as along the straight. 2) The interval between the peg is normally 20m to 30m.

2 Chord Length:- 1) The unit chord length for flat curve is 30m o 20m 2) The unit chord length for sharp curve is 10m or less than 10m. 3) The chord length is limited to ( 1/20 th ) of the radius of the the curve

3 Designation of curve by Radius & Degree of curve A curve is Designated By The Degree of curve Radius of curve

4 1)The Degree of Curve :- The angle a unit chord of 30m length subtended at the centre by standard chord 30m is called degree of curve. Where D is the degree of curve this common method to designated the degree of the curve & more advantageous setting out of the curve. For Example If the unit chord ( 30m chord ) subtended on angle of 1 0 then it is called one degree Curve when the angle is 2 0 then it is called two degree curve. DCE,BE(Civill),ME(Geotechnical Engg),AMIEI

5 2) Radius of curve :- A curve is also designated in term of its radius such as,80m curve,100m,200 curve etc. or 2 chain curve,4 chain curve, 5 chain curve,etc.

6 The relation between degree of curve & its radius

7 Let R be the radius of the curve in meter D be the degree of curve. Relation between the degree of curve and its radius is given by R = ½ length of standard chord sin D/2 for the chord 30m long = R = 1719/ D (1 0 = 1719 ) for the chord 20m long = R = 1145/ D (1 0 = )

8 Method of setting out of curve Method Linear method Instrumental method

9 linear Method 1) By ordinates or offset from Long chord. 2) By successive bisection of arc. 3) By offset from tangent. i) Radial method. ii) Perpendicular method. 4) By offset from chord produced. DCE,BE(Civill),ME(Geotechnical Engg),AMIEI Mr.R.S.Sonawane

10 Instrumental Method or angular Method 1) Rankine Method of tangential angle. 2) Two theodolite Method. 3) Tacheometric Method. DCE,BE(Civill),ME(Geotechnical Engg),AMIEI

11 1) By ordinates or offset from Long chord.

12 1) Let AB and BC be the tangent to the curve at the two tangent point T1 & T2 resp. 2) Length of the chord ( L ) = T1T2. 3) Offset at mid point of chord T1 T2 = DE = O0. 4) The offset at distance x from D = PQ =Ox Dp = x 5) Radius of the curve ( R ) = OE = OT1 = OT2.

13 Derivation :- let QQ1 be parallel to the long chord T1T2 And join OQ so as to intersect the long chord T1T2 at point P as shown in fig. In OT1D let DE =O0 OT1 =R and T1D = L/2 OD = OE DE = R- O0 ( OE = R and DE = Oo ) DCE,BE(Civill),ME(Geotechnical Engg),AMIEI

14 By Pythagoras ( OT1) 2 = ( T1D) 2 +( OD ) 2 R 2 = ( L/2 ) 2 + ( R Oo ) 2 Reaarranging above Eqn. ( R Oo ) 2 = R 2 - ( L/2 ) 2 Square root ( R Oo ) = R 2 - ( L/2 ) 2 (Oo ) = R R 2 - ( L/2 ) 2 I If L & R Or L and O0 are known then remaining terms can be found out equation Mr.R.S.Sonawane

15 In OQQ1 Use Pythagoras theorem. ( OQ ) 2 = ( QQ1) 2 + ( OQ1) 2 But ( OQ1) = OD + DQ1 =OD + Ox = ( R Oo) + Ox but( OD= R-Oo ) ( OQ1) = x & OQ = R R 2 = x 2 + [( R Oo) + Ox ] 2 [ox + ( R Oo) ] 2 = R 2 - x 2 ox + ( R Oo) = R 2 - x 2 Ox = R 2 - x 2 - ( R Oo) II Equation II is the exact formula for Ox

16 Procedure of setting out of curve Split up the long chord into even number of equal part. Set out the offset which are calculated from Ox = R 2 - x 2 - ( R Oo) & obtain the required points on the curve,note that the curve is symmetrical along DE, hence the offset for the right half of the curve will be the same as that on the left half.

17 2) By successive bisection of arcs of chord

18 Joint the tangent T1,T2 and Bisect the long chord at O. Erect the perpendicular ON & make it equal to the versed sine of the curve Thus, NO = R ( 1 Cos Θ/2 ) = R - R 2 - ( L/2) join the T1N and T2N and bisect at O1 & O2 respectively at O1 and O2 set out perpendicular offset N1O1= N2 O2 = R ( 1 Cos Θ/4) to get the point O1 & O2 on the curve. By the successive bisection of these chords more point may be determine. Mr.R.S.Sonawane

19 3)By offset from tangent The curve can be set out by offset from the tangent.if the deflection angle and radius of curvature both are small. The offset from the tangent can be two types 1) Radial offsets 2) Perpendicular offsets.

20 1) Radial offsets Let, ox = Radial offset PN at any distance x along he tangent. T1 p = x From T1 P O, Use pythagorous (PO) 2 = T1O 2 + T1 P 2 Or (PN+NO) 2 = T1O 2 + T1 P 2 (Ox+R) 2 = R 2 + x 2 (Ox+R) = R 2 + x 2 Ox = R 2 + x 2 - R

21 2) Perpendicular offsets. Let, DN = Ox =offset perpendicular to the tangent T1D =x= Measured along the tangent,drawn NN1 parallel to the tangent. N1NO,use pythagorous N1O 2 = NO 2 + NN1 2 ( R Ox ) 2 = R 2 + x 2 ( R Ox ) = R 2 + x 2 Ox = R 2 + x 2 R

22 Procedure to set curve 1. The distance x1,x2,x3 etc are measured from the first tangent point T1 along the tangent. 2. The perpendicular offset calculate,are erected with the help of an optical square at the corresponding point. 3. When the distance x increase the offset becomes too large to set out accurately. 4. In such case,the central point position of the curve may be set out from a third tangent drawn through apex of the curve. 5. This method is useful only for small curve.

23 4) By offset from chord produced ( By deflection distance ) When the curve is long,this method is useful ( generally Highway) When the theodolite is not available Let, T1 L1 = T1L =initial sub-chord = C1, L,M,N. Point on the curve. LM = C2, MN = C3 etc T1x = rear tangent <L1T1L = δ = deflection angle of first chord. L1L = O1 = first offset. M2M = O2 = Second offset N2N = L1L = O1 = T1 L δ I

24 Now, Since T1x is the tangent to the circle at T1 angle T1 O L = 2 < L1T1L = 2 δ T1L = R2.δ δ = T1 L / 2R..II Substituting the value of the δ in Eq n in ---I We get Arc L1L = O1 = T1 L.(T1 L / 2R ) = T1 L 2 / 2R Taking arc T1 L =chord T1 L ( very nearly )

25 O1 = C1/2R..III O2 = C2/2R (C1+ C2)..VI O3 = C3/2R (C2+ C3)..V The last on the offset given On = Cn/2R (Cn+ Cn+1)..III

26 Procedure for setting out the curve 1) Locate find the out change point T1 T2. 2) Calculate the length of first sub-chord (c ) so that first peg is the fall station. 3) Measure the length T1 as with the help of chain is at T1 now T1 1 = C = length of the first sub-chord. 4) with T1 as centre and T1 1 as the radius,swing the chain such that the arc L1L = calculate offset O1. 5) Now fig.the point L on the curve. 6) With zero of the chain at,spread the chain along T1 L and pull.it straight towards M2 the distance M 2 = C

27 Length normal chord. 7) With zero of the chain at station L and M 2 as radious swinging the chain to point M. Such that M2M = O2 = length of second offset.fix point on the curve. 8) Spread the chain along MN & repeat the above step till the point of tangency ( T2 ) is reached.

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