| |
Solution of Combined Vertical
Curve Problems
- Refer to Table 1. Locate the colored bar indicating
desired slope in the proper radius column.
- Project horizontally to either side of the table
and determine drop "D".
- Calculate "f" from Formula 1.
- Determine "e" from Table 2. Note that if "f" is not
shown in the table, it can be broken up. For example, if "f" = 14' -
6 3/8" add "e" values for "F" = 10' - 0 ", 4' - 0", 6" and 3/8".
- Locate "L" for proper slope and radius in Table 1.
- Calculate total length Le from Formula 2.
- Determine "g" and "A" as in steps 4 and 5.
- Calculate developed length of curve from Formula 3.
Note: Single bent rails are fabricated with a straight
tangent section "T" on each end.
Formulae
- Formula 1: f (Table 2) = DF -D (Table 1).
- Formula 2: Le = L (Table 1 ) = e (Table 2).
- Formula 3: Developed length of rail = 2A (Table 1)
+ g (Table 2)
|
Example
Problem |
|
Given: |
| Total Drop Df |
15' - 6" |
| Radius R |
8' - 0" |
| Angle of incline Θ |
30° |
|
Find |
| Total horizontal length
Le an Length of rail needed to fabricate vertical curve |
|
Solution |
- Drop D for 8' - 0" Radius 30° slope is 2'
1 3/4" (From Table 1)
- f = Df - D = 15'-6" - 2'-1 3/4" = 13'-4 1/4"
(Formula 1
- e = 17'-3 13/16" + 6 15/16" + 7/16 = 23'-1
916" (Table 2)
- L for 8'-0" Radius 30 slope is 8'-0"
(Table 1)
- Le = L + e = 8'-0" + 23'-1 9/16" = 31'-1
9/16"
- Arc A for 8'-0" Radius 30° Slope is 4'-2
1/4" (Table 1)
- g = 20'-0" + 6'-0" + 1/2" = 26'-8 1/2"
(Table 2)
- Length of rail = 2A + g + 8'-4 1/2" + 26'-8
1/2" = 35' - 1"
|
|
