Bridge geometry - Computational Analysis and Design of Bridge Structures - page 555

(3) left and right slopes; and (4) external distance of the crown. Although
most roadway crowns are parabolic, an arc crown can be simply included
in this definition by using a signed value of the external distance. For exam-
ple, a negative external distance indicates a parabolic crown and an arc
crown if otherwise.
Considering the vertical curve model that contains only parabolic fillets,
a generic parabolic/arc vertical curve model can be shared among vertical
and transverse curves. When this model is applied to vertical curves, only
parabolic fillets are applicable.
The local coordinates system, which is used to describe transverse
curve at any cross section, is important in roadway surface calculations.
Figure 18.6 shows the transverse curve coordinate system, whose origin is
aligned with roadway mainline. From the definitions of plane and vertical
curves of mainline, once geometric parameters (e.g., longitude, latitude,
altitude, and tangent of the plane curve) of a given point on the mainline
are known, any point on the roadway surface along a cross section will be
known. For design purposes, these separated representations of roadway
cross sections are practical and accurate enough. For the purpose of digi-
tal visualization, triangular surface meshes can be easily established, given
two consecutive roadway cross sections.
18.3.3 transitions of transverse curves
As discussed in the previous sections, transverse curves may vary in curve
segments as superelevation and superwidening are required. Key transverse
curves can be explicitly specified at certain known locations along curve
segments. Transverse curve properties of cross sections in between consec-
utive key locations, such as widths, slopes, and external distances, can be
interpolated by linear, circular, or parabolic methods. When linear method
is used to interpolate a geometry property, only two key cross sections are
required. When the circular or parabolic method is used, three consecu-
tive key cross sections are required. The following list provides examples
of transverse curve transition definitions: (1) cross section at station 30 m
(100′) is symmetric with a total width of 9.1 m (30′), a slope of 1.5% and
a parabolic crown with an external distance of 15 mm (3/5″); (2) cross
section at station 61 m (200′) has a 1.5 m (5′) superwidening on the right
side, superelevation on the left side causes the slopes to +1% and −2.5% on
the right side, crown maintains the same; (3) cross section at station 122 m
(400′) remains the same as that at 61 m (200′); and (4) cross section at sta-
tion 600′ changes back to that at station 30 m (100′) (Figure 18.7).
As a generic example, Figure 18.8 shows the plane view of transverse
curve transitions. Dot lines are roadway edges; radial lines are cross sec-
tions of interested. Figure 18.9 shows the perspective view of mainline and
interested cross sections.