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VERTICAL CURVES - 14070_248
Figure 11-16.Algebraic differences of grades. - 14070_250

Engineering Aid 1 - Advanced Structural engineering guide book
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parabola  is  used  primarily  because  its  shape  provides a transition and, also, lends itself to the computational methods  described  in  the  next  section  of  this  chapter. Designing  a  vertical  curve  consists  principally  of deciding   on   the   proper   length   of   the   curve.   As indicated in figure 11-13, the length of a vertical curve is the horizontal distance from the beginning to the end of the curve; the length of the curve is NOT the distance  along  the  parabola  itself.  The  longer  a  curve is, the more gradual the transition will be from one grade  to  the  next;  the  shorter  the  curve,  the  more abrupt  the  change.  The  change  must  be  gradual enough  to  provide  the  required  sight  distance  (fig. 11- 14). The sight distance requirement will depend on the  speed  for  which  the  road  is  designed;  whether passing  or  nonpassing  distance  is  required;  and  other assumptions,  such  as  one’s  reaction  time,  braking time,  stopping  distance,  height  of  one’s  eyes,  and height of objects. A typical eye level used for designs is 4.5 feet or, more recently, 3.75 feet; typical object heights are 4 inches to 1.5 feet. For a sag curve, the sight distance will usually not be significant during daylight;  but  the  nighttime  sight  distance  must  be considered  when  the  reach  of  headlights  may  be limited by the abruptness of the curve. ELEMENTS OF VERTICAL CURVES Figure  11-15  shows  the  elements  of  a  vertical curve. The meaning of the symbols and the units of measurement  usually  assigned  to  them  follow: PVC Point of vertical curvature; the place where the curve  begins. PVI PVT POVC POVT gI g2 Figure 11-15.—Elements of a vertical curve. Point of vertical intersection; where the grade tangents  intersect. Point of vertical tangency; where the curve ends. Point on vertical curve; applies to any point on the  parabola. Point on vertical tangent; applies to any point on  either  tangent. Grade of the tangent on which the  PVC  is located; measured in percent of slope. Grade  of  the  tangent  on  which  the  PVT  is located; measured in percent of slope. Figure 11-14.—Sight distance. 11-13







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