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Unsymmetrical  Vertical  Curves - 14071_256
USING A PROFILE WORK SHEET - 14071_258

Engineering Aid 2 - Intermediate Structural engineering guide book
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Figure  11-20.—Table  of  computations  of  elevations  on  an  unsymmetrical  vertical  curve. In this example, then, the middle vertical offset at the PVI is calculated in the following manner: e = [(4 x 2)/2(4 + 2)] x [(+6) - (–4)] = 6.67 feet. Second,  you  are  cautioned  that  the  check  on  your computations  by  the  use  of  second  difference  does NOT work out the same way for unsymmetrical curves as for a symmetrical curve. The second difference will not check for the differences that span the PVI. The reason is that an unsymmetrical curve is really two parabolas,  one  on  each  side  of  the  PVI,  having  a common   POVC  opposite  the   PVI;  however,   the second difference will check out back, and ahead, of the first station on each side of the  PVI. Third, the turning point is not necessarily above or  below  the  tangent  with  the  lesser  slope.  The horizontal location is found by the use of one of two formulas as follows: from the PVC or from the PVT The procedure is to estimate on which side of the  PVI the turning point is located and then use the proper formula to find its location. If the formula indicates that the turning point is on the opposite side of the  PVI, you must use the other formula to determine the correct location; for example, you estimate that the turning point is between the PVC and PVI for the curve in figure 11-19. Solving the formula: xt= (l1)2(g1)/2e xt= [(4)2(4)]/(2 x 6.67) = 4.80, or Station 42 + 80. However, Station 42 + 80 is between the PVI and PVT; therefore,  use  the  formula: xt= (l2)2(g2)//2e xt= [(2)2(6)]/(2 x 6.67) = 1.80, or station 42 + 20. Station 42 + 20 is the correct location of the turning point. The elevation of the POVT, the amount of the offset, and the elevation on the curve is determined as previously  explained. CHECKING THE COMPUTATION BY PLOTTING Always  check  your  work  by  plotting  the  grade tangents and the curve in profile on an exaggerated 11-19







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