Bridge geometry - Computational Analysis and Design of Bridge Structures - page 554

be obtained by a simple calculation procedures. Section 18.3.4, for instance,
provides principles and steps to calculate a spiral segment.
Vertical curves are compound curves too but contain only straight lines
and parabola. Figure 18.5 shows an example of vertical curves. Unlike
plane curves, connections in vertical curves are simple. When grade tran-
sition is needed, parabola is always used to connect one straight line to
another one. As slopes or tangents in the vertical curve of both connecting
grades are known, only external distance is needed to define a parabola fil-
leting two straight lines. The parabola used in vertical curves can be called
as vertical parabola. Similarly for spirals used in a plane curve, in which the
change of curvature is proportional to the curve length, the grade change
of a vertical parabola is proportional to curve horizontal length. Curve
tangents at connecting points, as shown in Figure 18.5, are continuous.
Having the earlier definitions on both plane and vertical curves, the
mainline of a bridge, or the roadway centerline, can be described separately.
When defining the vertical part, the horizontal ordinate is the unfolded
curve length of the corresponding plane curve, that is, the stations of road-
way centerline; the vertical ordinate is the elevations (Figure 18.5). The
following list provides examples of definitions of bridge mainline curves:
Plane curves. (1) A straight line with a length of 61 m (200′); (2) a spiral
with a length of 152 m (500′) connecting the straight line to the next arc
segment with a radius of 244 m (800′), curve goes clockwise; (3) an arc seg-
ment with a length of 122 m (400′) and a radius of 244 m (800′); (4) another
spiral segment with a length of 152 m (500′) connecting the arc to the next
straight line; (5) a straight line with a length of 122 m (400′); (6) a spiral with
a length of 122 m (400′) connecting the line and next arc segment with a
radius of 274 m (900′), curve goes counterclockwise; and (7) last arc segment
with a length of 152 m (500′) and a radius of 274 m (900′); starting tangent
is 120° to latitude axis and location is (0 longitude, 0 latitude).
Vertical curves. (1) Control point at station 0: altitude = 0; (2) control
point at station 274 m (900′): altitude = +20′ (6.1 m), parabola fillet with
an external distance of 1.2 m (4′); (3) control point at station 610 m (2000′):
altitude = −15′ (4.6 m), parabola fillet with an external distance of 0.3 m
(1′); (4) control point at station 762 m (2500′): altitude = −15′ (4.6 m),
parabola fillet with an external distance of 0.5 m (1.5′); and (5) last control
point at station of 884 m (2900′): altitude = 0.
18.3.2 roadway transverse curve model
Transverse curve model defines the roadway transverse slopes, crowns,
superelevations, and superwidening. As shown in Figure 18.6, the trans-
verse curve at a roadway cross section can be defined by (1) left width, the
horizontal distance from the mainline to road edge on the left; (2) right
width, the horizontal distance from the mainline to road edge on the right;