Question

Two straight rail lines intersect at point B, and are to be joined by a circular curve. The centreline of the rails must pass through point D which is a signalling switch. The bearing of the first line is 70° 00'00" and the bearing of the second line is 123° 00'00". Point D is located exactly 78° 28' 10" at a distance of 118.594 metres from the first tangent point. a) (6 marks) Calculate the exact radius for the centreline of the rails to pass through this point. Due to construction constraints it was later decided to use a radius of 400 metres. Use R=400 for all further calculations. b) (4 marks) Given the chainage of the intersection point (B) is 1000 calculate the chainages of the two tangent points. c) (5 marks) Calculate the bearing and distance from the intersection point (B) to the mid point of the curve. d) (5 marks) Calculate the bearing and distance from the second tangent point to set out a point at chainage 1100. 70'00'00" 123'00'00" 4 NOT TO SCALE Please put answers in the space provided on the next page

Answer 1

a) Exact radius 402.609m

b) Chainage of TP1 = 80057m, Chainage of TP2 1199.43

c) Bearing and distance from B to mid point of curve = 186'30' and 42.03m

d) Bearing and distance from TP2 to CH 1100 = 303' and 99.43m

Ans BIS?EC SCIENTIFICO A PO Bearing of First line = foto Bearing of second line = 123- 8= 123° 70°=53° SED=53° (a) D is a point on curve. S=AD cheed = 118.594m LOAD=78°28 10"-70° Si = 8°28° 10 Si=20 Rsin20i = 9 52- 8.82110' WS R = $x sinza 2 = 118.994 x sinexp*zoºlo' = 402.609m (6) Tengent Length = R tan s = 40oxtan 53 = 199.43m Chain age of intersection point (B) = 1000. chainage at point A= 1000- Tengeht Length = 1000 - 199.43 = 800.57m chainage at point c = 1000 + Tengent Length = 1000 + 199.43 = 1199.43 m

(C) . mid esdinete - Distane Distance between mid point of wow & intessution point (B) = R-R los a = 400 - 400XL 2 Distance - 42.03m Bearing Angle AA' = too Bearing CC = 123° LA, BC = 123° 70°=53° LA BC = 180-53° = 127° CABE = LEBC = 122° 67°80° Bearing of BE = 123°+63 30 = 186° 30°

99.uson D Chainge of point (= 1199.43m change of setting out point = 1100 Distances from point c=1199.43-1100 = 99. 4m Bearing = 180 + 123 = 303° Curl Enter
303' and 99.43m