Department of Civil Engineering
SUB-Highway Engg.
TOPIC NAME-Parts Of Vertical Curve
Semester-4th
BY
ER. Ankit Joshi
(Asst Hod. CIVIL Engineering Department)
AY:2021-2022
Parts of a Vertical curve
Summit Curve
Length of summit curve for stopping sight distance
1- When the length of the curve is greater than the sight distance ( L > SSD )
Where,
L = Length of summit curve
S = Stopping sight distance
N = Deviation angle = n1 + n2
H = height of eye level = 1.2 m
h = height of subject above the
pavement surface = 0.15m
By substituting the value of H and
H, the above equation can be written as
Length of summit curve for stopping sight distance
2- When the length of the curve is less than the sight distance ( L < SSD )
By substituting the value of H and
H, the above equation can be written as
S = 180
H = 12
H = 8
N = 14/300
Length of summit curve for OSD & ISD
When L > S
When L < S
A vertical summit curve is to be designed when two grades +1/50 & - 1/80 meet on a highway. The SSD & OSD required are 180 m & 640 m respectively. But due to site conditions the length Of vertical curve is restricted to 500m if possible. Calculate the length of summit curve needed To fulfil the requirements of SSD & OSD .
Given data,
SSD = 180 m, OSD = 640 m, n1 = 1 in 50, n2 = 1 in 80
maximum length of summit curve= 500 m
Check for SSD,
Condition 1 – When L > SSD
L = 239.6 m or 240 m
Hence it satisfy the condition so
Length of Vertical curve considering SSD = 240m
Check for OSD condition :-
Condition 1 – L < OSD
L = 984.6 m
As it fails to satisfy the condition, we must check for condition 2
When L > S
L = 439 m
It satisfy the condition of OSD so
Length of curve in case of OSD = 439 m
Valley Curve or Sag Curve
Length can be calculated by following two methods :-
Here,
L = Length of valley curve
N = Deviation angle = -n1 – ( +n2 ) = - (n1+n2)
Condition – 2
Length of valley curve for head light sight distance
A valley curve is formed by a descending grade of 1 in 25 meeting an ascending grade of 1 in 30. Design the length of valley curve to fulfil comfort condition & head light condition requirements for Design speed of 80 Kmph. Assume C = 0.6 m / cubic second
Given data,
V = 80 Kmph
n1 = 1 in 25 & n2 = 1 in 30
Find deviation angle N = -(n1+n2)
V in m/ sec = 22.2 m/s
For comfort condition :-
L = 73.1 m
For Head light sight distance :-
Find SSD by assuming t = 2.5 s,
f =0.35 for speed 80 Kmph
SSD = 127.3 m
L = 199.5 m