Symmetrical Vertical Curves

Figure 11-16.Algebraic differences of grades. - 14071_252

Figure 11-18.Table of computations of elevations on a symmetrical vertical curve. - 14071_254

Engineering Aid 2 - Intermediate Structural engineering guide book
Page Navigation
236

x y The Horizontal distance from the PVC to any POVC or POVTback of the PVI, or the distance from the PVT to any POVC or POVT ahead of the PW, measured in feet. Vertical distance (offset) from any POVT to the corresponding POVC, measured in feet; which is the fundamental relationship of the parabola that permits convenient calculation of the vertical offsets. vertical curve computation takes place after the grades have been set and the curve designed. Therefore, at the beginning of the detailed computa- tions, the following are known: g₁, g₂, l₁, l₂, L, and the elevation of the PVI. The general procedure is to compute the elevations of certain POVTs and then to use the foregoing formulas to compute G, then e, and then the Ys that correspond to the selected POVTs. When the y is added or subtracted from the elevation of the POVT, the result is the elevation of the POVC. The POVC is the finished elevation on the road, which is the end result being sought. In figure 11-15, the y is subtracted from the elevation of the POVT to get the elevation of the curve; but in the case of a sag curve, the y is added to the POVT elevation to obtain the POVC elevation. The computation of G requires careful attention to the signs of g₁and g₂. Vertical curves are used at changes of grade other than at the top or bottom of a hill; for example, an uphill grade that intersects an even steeper uphill grade will be eased by a vertical curve. The six possible combinations of plus and minus grades, together with sample computations of G, are shown in figure 11-16. Note that the algebraic sign for G indicates whether to add or subtract y from a POVT. The selection of the points at which to compute the y and the elevations of the POVT and POVC is generally based on the stationing. The horizontal alignment of a road is often staked out on 50-foot or 100-foot stations. Customarily, the elevations are computed at these same points so that both horizontal and vertical information for construction will be pro- vided at the same point. The PVC, PVI, and PVT are usually set at full stations or half stations. In urban work, elevations are sometimes computed and staked every 25 feet on vertical curves. The same, or even closer, intervals may be used on complex ramps and interchanges. The application of the foregoing funda- mentals will be presented in the next two sections under symmetrical and unsymmetrical curves. Symmetrical Vertical Curves A symmetrical vertical curve is one in which the horizontal distance from the PVI to the PVC is equal to the horizontal distance from the PW to the PVT. In other words, l₁equals l₂. The solution of a typical problem dealing with a symmetrical vertical curve will be presented step by step. Assume that you know the following data: g₁ = +97% g₂= –7% L = 400.00´, or 4 stations The station of the PVI = 30 + 00 The elevation of the PVI = 239.12 feet The problem is to compute the grade elevation of the curve to the nearest hundredth of a foot at each 50-foot station. Figure 11-17 shows the vertical curve to be solved. Figure 11-17.—Symmetrical vertical curve. 11-15

Privacy Statement
Press Release
Contact