Solved problems · 12 problems
Curve staking
Horizontal and vertical curves solved from plan data and taken all the way to the stakes: stations, deflection angles, chords, offsets and grade elevations.
- Stake a simple circular curve by deflection angles from the PCA 1150.00 ft radius curve with a 28°42′00″ central angle is solved for every element, stationed through the PI, and taken to a full deflection-angle and chord table for staking from the PC.
- Recover a curve radius from a measured long chord and middle ordinateAn existing curve with no plan record is measured with a tape: the long chord between two identifiable points and the middle ordinate at its center. Radius and central angle follow in closed form.
- Fit a horizontal curve to a required external distanceAn obstruction near the PI forces the curve to stay at least 65.00 ft out from the intersection point. The minimum radius is solved from the external distance, rounded to a design value, and stationed.
- Degree of curve on plan data: arc definition against chord definitionA plan labels a curve D = 3°30′00″ with Δ = 24°15′00″ but does not say which definition of degree of curve applies. Both radii are computed and the two sets of elements compared.
- Curve stationing and the PT equals PC plus L trapA 900 ft radius curve is stationed from its PI, with the 29.63 ft of chainage lost at the corner made explicit and every full station on the curve tabulated.
- Stake a circular curve by tangent offsets and by chord offsetsA 700 ft radius curve is laid out with a tape alone: first by rectangular offsets from the back tangent, then by successive offsets from the prolonged chord, with the approximate and exact formulas compared.
- Radial staking of curve points by coordinates from a control stationCurve stations are converted to coordinates through the PC and the back tangent, then inversed to a control point to give the angle and distance a total station needs for radial layout.
- Compound curve: tangent distances and stationing from the main PITwo arcs of different radius meet at a point of compound curvature. The vertex triangle gives the two tangent distances back to the main PI, and the alignment is stationed through both arcs.
- Equal-tangent crest vertical curve: grade elevations and the high pointA 600 ft crest curve joining a +3.20 percent grade to a −2.40 percent grade is reduced to a grade sheet at full stations, with the high point located and the K value reported.
- Sag vertical curve: low point, overhead clearance and the drainage checkA 500 ft sag curve is reduced to a grade sheet, the low point is located for drainage, clearance under an overhead structure is verified, and the flat zone around the low point is measured against a 100 ft criterion.
- Vertical curve length fitted to a fixed elevation at a fixed stationA sag curve must pass through an existing manhole rim at a set station and elevation. The required length comes out of a quadratic with two roots, only one of which puts the point on the curve.
- Superelevation runoff and tangent runout layout for a highway curveA 6 percent superelevation transition is laid out around a 1000 ft radius curve: runoff and runout lengths from the relative gradient, the five key stations, and edge-of-pavement elevations for the stakes.
Other categories
All problems- Traverse adjustmentClosed traverses computed from field notes: angular closure, azimuths, latitudes and departures, misclosure and precision, compass-rule adjustment, final coordinates.
- Area & partitioningAreas by coordinates and by DMD, curved boundaries, and the partition problems that split a parcel to a required area by a line of given direction or through a given point.
- Error propagationRandom error carried through sums, series, products and functions; weights and weighted means; the precision a procedure can actually deliver.
- Levelling loopsDifferential and trigonometric levelling reduced from notes, loop closure against a tolerance, and distribution of the misclosure.
- Boundary retracementGeneric retracement computations: proportionate measurement, aliquot subdivision of a section, and reconciling record and measured dimensions.