Tiêu đề 118 Horizontal Curves.pdf ✅

MSTC 118: Horizontal Curves 1. Stationing Distances along routes are marked with stationing values. It consists of two numbers separated by a plus (+) sign. The stationing shows the distance along the route from a reference location. In the Philippines, the reference location is Rizal Park in Manila. In metric units, stationing consists of the number of kilometers from the reference and the number of meters exceeding that kilometer. For example, a stationing of 10+110 says that that place is 10 kilometers from Rizal Park, and then another 110 meters after that. The total distance to be used in calculations is 10110 meters. In English units, stationing consists of the number of hundred feet from the reference, and the number of feet exceeding that hundred mile. For example, a stationing of 11+19 says that the place is 11 hundred miles (or 1100 feet), and then another 19 feet after that. The total distance to be used in calculations is 1119 feet. Note that stationing should always be measured along the route. If a stationed place is outside the route, then it should be first traced to the beginning of that segment before adding new distances. 2. Components of Simple Curves A horizontal curve is placed where there are changes in the horizontal alignment of the road. It is a circular arc that has the intersecting roads as its tangents. The curve starts at the point of curvature (PC) and ends at the point of tangency (PT). The point of intersection (PI) is where the original roads intersect without the curve. Idealizing this figure,

In English units, 100 = RD ( π 180°) D = 5729. 578 R In terms of the degree, R = 1145. 916 D (metric units) R = 5729. 578 D (English units) The chord basis states that the degree of the curve is the central angle that subtends a 20 m (or 100 ft, note that this is not equivalent) chord. In metric units, 20 = 2R sin D 2 D = 2Arcsin 10 R In English units, 100 = 2R sin D 2 D = 2Arcsin 50 R In terms of the degree, R = 10 sin D 2 (metric units) R = 50 sin D 2 (SI units) If the basis of the degree is not specified, the convention is to use the arc basis. 2.3. Length of Curve Since a horizontal curve is just a circular arc, its length can also be found that way. L = RI ( π 180° )
2.4. Tangent Distance From triangle OVA (by symmetry, OVB is the same) in the idealized figure, tan I 2 = T R T = Rtan I 2 2.5. Chord From triangle OAB in the idealized figure, let point X be the point of intersection of AB and OV. The length from PC to PT (or in other words, AB) is called the long chord of the curve. By symmetry, AX = BX = C/2. In triangle OAX, sin I 2 = C 2 R C = 2Rsin I 2