Solutions Manual for Construction Surveying and Layout Third Edition Chapter 16 Prepared by Wesley G. Crawford
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1 Solutions Manual for Construction Surveying and Layout Third Edition Chapter 16 Prepared by Wesley G. Crawford
2 Chapter 16 - Horizontal Curves QUESTIONS AND PROBLEMS Problems 1-10: Calculate the missing curve parts in the following table. Curve Problem# I R Degree of Curve T L E M.O. LC º º º º º º º º º º Given +43, "I" angle = 7 29', Da = 9, compute tangent (T). length of arc (L) and compute the stationing of the PC and PT. Central Angle 7 29'00.0" Degree of Curve 9 00'00.0" Radius Arc Length Tangent Length P.C P.T Copyright Creative Construction Publishing - 2
3 14. Given , "I" angle = 33 54', and R = 800 feet, compute the deflection at every halfstation. Central Angle 33 54'00.0" Degree of Curve 7 09'43.1" Radius Arc Length Chord Length Tangent Length Offset P C ø00' º40' º28' º15' º03' º50' º38' º25' º12' º00' º47' P T º57' Given Da = 3.22 degrees, L = ', and PC = , find the remaining components of the curve. Central Angle 21 17'54"'00.0" Degree of Curve '00 Radius Arc Length Chord Length Tangent Length External MO P.I P.C P.T Copyright Creative Construction Publishing - 3
4 18. If a simple circular curve has a length of curve 410', and the degree of curvature (Da) is known to be , and the station of the PI is , what is the central angle of this curve? I = 86 06'00" 20. Two parallel highways 1000 meters apart are to be joined by a reverse curve made up of two circular curves of equal radius. These curves are to have a radius of 700 meters. Determine all parts of the curves. R = 700 Cos = = 73 23' 54" with I and R known, use curve formulas to solve for the remaining curve parts. See Table m Reverse Curve I = Cos = Adj/hyp = 400/1400 = 73 23'54" R = 700 T = L = LC = Given the following coordinates for a curve in a subdivision. PI=N , PC =N 1500, E 1500 PT = N , E RP = N , E Copyright Creative Construction Publishing - 4
5 a) Calculate the parts of the curve. I, R, Da, LC, L, T, PC & PT Station. Central Angle 45 00'00.0" Degree of Curve 15 49'18.5" Radius Arc Length Chord Length Tangent Length P.C P.T b) Calculate the layout data (Deflections and long chords for 50 foot stations) for this curve? Station Deflection Short Chord Centerline Long Chord Centerline P.T º30'00" º01'07" º03'47" º06'27" º09' º11'48" º14'28" P.C º00' c) The +40 foot offset layout data for the curve. Station Deflection S.C. Offset + 40 L.C. Offset + 40 P.T º30'00.0" º01'06.7" º03'47.1" º06'27.5" º09' º11'48.2" º14'28.6" P.C ' Copyright Creative Construction Publishing - 5
6 d) The 30 foot offset layout data for the curve. Station Deflection S.C. Offset -30 L.C. Offset - 30 P.T º30'00.0" º01'06.7" º03'47.1" º06'27.5" º09' º11'48.2" º14'28.6" P.C º00' e) What are the coordinates of the stations on the centerline of the curve? Station Centerline Direction from PC to Point Long Chord Distance from PC to Point North East P.T P.C N 1500 E 1500 Copyright Creative Construction Publishing - 6
7 f) What are the coordinates of the +40 Offset points on the curve? Station +40 North East P.T P.C g) What are the coordinates of the -30 Offset points on the curve? Station -30 North East P.T P.C Copyright Creative Construction Publishing - 7
8 24. The azimuth along the tangent from the PC of a curve to the PI is '. The coordinates of the PC are N , E If the curve has an I angle of 41 22', R = 475' and the station of the PI is Data Shown for a CURVE LEFT. a. Calculate the curve parts Da, LC, L, T, PC & PT Station. Central Angle 41 22'00" Degree of Curve 12 03'44" Radius Arc Length Chord Length Tangent PC PT b. Calculate the deflections, and long chords for 50' stations. Station Deflection Short Chord Long Chord PC ' '21" '17" '13" '09" '05" '01" '57" P.T '00.0" Copyright Creative Construction Publishing - 8
9 c. Calculate the coordinates of these curve points. Station Ctrline Direction from PC to Point Long Chord Distance from PC to Point North East PC To PI N , E P.T The layout data for curve #4 on the highway has been calculated and shown in the table below. Arriving at the PC of the curve, it is seen that the area hasn't been cleared yet and it will be impossible to establish the curve entirely from the PC. Layout will require "moving up on the curve" frequently. The PC was occupied and points and were located before obstacles were encountered. Station Arc Deflection Increment Total Deflection Short Chord Long Chord PT PC a) If the instrument is moved to 19+50, what angle will you set on the circle if you BS the PC? You would set the deflection of the point you are SIGHTING on which is '00" for the PC. b) If you are set at 19+50, what angle will you turn to set 20+00? You will continue your original notes and will turn to 20 32'37" c) If the instrument is moved to and and the BS is on 19+50, what will you set on the circle before turning to the deflection for 20+00? You will set the deflection of the point you are sighting on. The deflection for is 12 35' 37". That is what you would set on the instrument Copyright Creative Construction Publishing - 9
10 d) If you are at and you turn to a line that is tangent to the circle, what angle will you read on the circle? You will turn the deflection of to get a line that is tangent to the curve. The deflection for is 20 32'37". e) If you want a line radial to the curve at 20+00, what angle will you turn to on the circle? You would turn the deflection of point plus the 90. This would total '37". f) If a line radial to the curve is needed at station , what deflection angle and long chord will be needed to set that point, and what angle will be turned from a setup at that point to establish the radial line? Assuming you are set up at the PC. The deflection angle to will be 16 36'05" an the long chord will be The angle that would be turned at that point to establish a radial line would be 16 36'05" + 90 or '05". g) Finally you have a clear line of sight to the PT and prepare to shoot it in. What long chord will need to be measured from your setup at to the PT The chord distance would be h) What is the chord length for an arc of 100 feet on this curve? The chord for an arc of 100 feet is Copyright Creative Construction Publishing - 10
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