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a7_cee3604_2011_sol - CEE 3604 Introduction to...

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CEE 3604: Introduction to Transportation Engineering Fall 2011 Assignment 7: Geometric Design and Turning Maneuvers Partial Solutions Instructor: Trani Problem 1 a) Calculate the minimum length of a vertical curve designed for an Interstate Highway with a design speed of 70 mph. The design provides the transition between two grades: -1.95% and 2.45%. An interstate highway has divided lanes, hence the stopping distance criteria governs the design of the vertical curve. First determine if the curve is a crest of a sag. Following standard nomenclature used in the handout entitled “Highway Geometric Design” the transition from a negative slope to a positive slope is a sag curve (see page 6 of the handout). The formulas to estimate the length of the sag vertical curve are given on page 31 of the handout. The stopping sight distance for a “flat” highway designed for 70 mph according to AASHTO is 730 feet or 230 meters (rounded to nearest 10 meters). If we wanted to be conservative we could use the stopping distance considering the downgrade of -1.95%. However, the stopping distance is combines a downhill section and an uphill section. AASHTO guidelines assume h =0.6 meters and β =1 degree. Assume SSD L or S L . L = A SSD 2 200(0.6 + SSD tan(1 deg) L = 4.40 230 2 200(0.6 + 230tan(1 deg) L = 253 meters For design purposes we can round to the nearest 10 meter thus resulting in L = 260 meters . Since the condition SSD L or S L is true we use the calculated result for the length of the sag vertical curve. CEE 3604 A7 Trani Page 1 of 9
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Alternate method. Use the rate of vertical curve (K) provided in Table 7.7 on page 33 of the handout. The minimum value of K is 50 for a design speed of 120 km/hr (closest to 70 mph - upwards). L min = K min A = 50(4.4) = 220 meters L desirable = K max A = 73(4.4) = 321 meters Engineers have some decision making in the specification of the sag curve according to the AASHTO table 7.7. The First method provides a balance between the two solutions provided in the alternate method. b) Find the elevations of stations along the vertical curve if the VPC is station 2+412.00 (meters) and at an elevation of 102.10 meters above sea level. Create elevations and offsets every 10 meters. Plot the results obtained using Excel or Matlab.
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