GE 117 3B WF Problem Set 1

GE 117 1st Semester AY 15-16. Prepared by: Bien G. Carcellar III GE 117 3B WF Problem Set 1 (Horizontal Curves) Date given: September 02, 2015 (Wednesday) Due: September 18, 2015 (Friday) 10:00 AM Instructions: Answer the following questions on letter-sized (8.5”x11”) paper or A4 (8.27”x11.69”) preferably recycled (i.e. one side already used). Only one side of every sheet of paper shall be used to write your solutions to the problems. I.

Simple Curves (Choose 2 of 3 problems, 5 pts each) 1. Two tangents intersecting at V whose stationing is at 1+027.32 has the angle of intersection of 260 12’. It is to be connected with a 40 curve based on the arc basis. Without changing the directions of the two tangents, it is required to shorten the curve to 100m starting from the same PC. Find the stationing of the new point of tangency.

2. A circular curve has the following properties. External distance is 18 m angle of intersection of tangents is 380 30’. Stationing of vertex V (intersection of the tangents) is 10+252.32. A line MK intersects the forward tangent at M and the circular curve at K. Point M is 23.32 m from V and the angle VMK is 450 30’. Find the stationing of K.

3. In the figure shown, AB=103.20 m with A at station 10+158.93. The angle VAC is 150 21’ and angle VBC is 180 31’, where C is the point to which a simple curve is to be constructed tangent to the line AB. Determine the stationings of points C and PT.

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GE 117 1st Semester AY 15-16. Prepared by: Bien G. Carcellar III II.

Compound Curves (Choose 2 of 3 problems, 5 pts each) 1. In a compound curve, the line connecting the PI at point V and the PCC is an angle bisector. AV is 270 meters and BV=90 m. The stationing of A is 6+421 and that of B is 6+721. Point A is along the tangent passing through the PC while point B is along the tangent passing through the PT. The PCC is along line AB. Compute for the length of the radii for both curves.

2. In the figure shown, AV is the straight road and DF is a curved street. The radius of the curved street is 30 m. A circular curve of 8 m radius is to be introduced at H to round off the intersection. AM is 64.52 m. and FM is 58.64 m. The angle AMF is equal to 470 36’. The stationing of A is 12+320.30. Deflection angle of point K from F is 200 27’. Find the stationing of points G, E, and K. 3. Two tangents that intersect at an angle of 440 36’ are to be connected by a compound curve. The tangent at the beginning of the curve at the PC is 125.70m long and that at the PT is 155.6 m long. The degree of curve of the first curve on the PC is 40 using arc basis. Compute the radius and the central angle of the 2nd curve. III.

Reversed Curves (Choose 2 of 3 problems, 5 pts each) 1. The curve near the PC of a reversed curve has a radius of 200m. while the curve near the PT has a radius of 460 m. If the central angle of both curves is 12, find the perpendicular distance between the two parallel tangents. 2. The perpendicular distance between two parallel tangents of a reversed curve is 7.5m and the chord distance from the PC to the PT is equal to 65. Compute the central angle and the length common radius of the reversed curve. 2

GE 117 1st Semester AY 15-16. Prepared by: Bien G. Carcellar III 3. A reversed curve with diverging tangents is to pass through three lines to form a center line of a proposed road. The first line AB has a bearing of N 880 E and a distance of 120m. BC has a bearing of N 620 E and a distance of 340m., while that of CD has a bearing of S 400 E and a distance of 300m. PC has a stationing of 12+340. If the first tangent has a distance of only ¼ that of the common tangent measured from the point of intersection of the first curve, compute for the length of the radii of the 1st and 2nd curves, and the stationing of the PT. IV.

Spiral Curves (Choose 2 of 3 problems, 5 pts each) 1. The length of spiral curve is 80 m with a radius of 250 m at the central curve. Determine the length of throw and the offset distance from the tangent on the first quadrant point of the spiral. 2. The spiral angle at the SC of a spiral easement curve is equal to 11.46 degrees, with a radius of 200 m for the central curve. Compute the length of throw and the length of the long tangent of the spiral curve if the distance along the tangent from TS to SC is 79.29m 3. A spiral curve was laid out in a certain portion of the Manila-Cavite Coastal Road. It has a length of spiral of 80 m. and an angle of intersection of the two tangents of 40 degrees. If the degree of curve is 6 degrees, determine the length of throw, length of long and short tangent, and the length of the external distance.

Maximum points: 60/40 Sir B.G. Carcellar III “As the men started on their way to map out the land, Joshua instructed them, „Go and make a survey of the land and write a description of it..‟” (Joshua 18:8)

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