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Homework 4
February , 2021
CE 392 Introduction to Highway Engineering
Chapter 3 Mannering and Washburn (Due Friday 8
th
)
Problems
Select Answers
3-6
Sta Highpoint = 113+36
Elev Highpoint 245.45ft
3-8
3-9
y= 1201.86 ft
3-13
8.9 ft
3-16
3-21
3-24
Homework 4
February , 2021
3.6
A vertical curve is designed for 55 mi/h and has an initial grade of +2.5% and a final grade of −1.0%. The
PVT
is at station 114 + 50. It is known that a point
on the curve at station 112 + 35 is at elevation 245 ft. What is the stationing and elevation of the
PVC
? What is the stationing and elevation of the high point on the curve?
GIVEN: K = 114 (@ 55 mi/h), G
1 =2.5, G
2 = -1.0, A= 3.5, PVT = 114+50
Point Station = 112+35, elev
point = 245’
Calculate Curve Length
L = K*A = 399’
Calculate PVC
PVC = PVT-L = 115+51
x:= point-PVC = 184’
Calculate offset of point above curve
Y
point
:= (A/200*L)*x
2 = 1.485’
x*(G
1
/100) – Y
point = 3.115’
from offset of point calculate elevation of PVC
elev
PVC
:= elev
point -3.115 = 241.885’
Calculate location of high point
x
h
:= KG
1 = 285’
Y
h
:= (A/200*L)*x
h
2
= 3.562’
Calculate station of high point
elev
hp
:= elev
PVC + Y
h = 245.45’
STA
hp
= PVC+x
h = 113+36
Homework 4
February , 2021
3.8
An equal-tangent crest vertical curve has a 50-mi/h design speed. The initial grade is
+3%. The high point is at station
33 + 40.76
and the
PVT
is at station
37 + 24.66
. What is the elevation difference between the high point and the
PVT
?
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Related Questions
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Q6. Given horizontal curve has two-lanes with lower-than-average coefficient of side
friction (0.1) and no superelevation. The lane width is 4-meter. The curve has a radius
of 500 meter and a design speed of 80 km/hr check the safety of this curve. How can
you show this?
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Determine variables requested below for a horizontal curve with the following
characteristics.
Length of curve 1255', Radius 1200', sta of PC 12+00 superelevation rotated
about the roadway centerline, 3 lane roadway, 14ft lane width, entire road
section normal crown=2%, road design speed=60 mph, max
superelevation=8%
8) The station of the NC is:
O 8+12.5
8+90
8+92.5
O 11+22.5
O 12+00
arrow_forward
Question 5
Calculate the horizontal sight line offset (ft) for a curve with a radius of 600 ft and a design speed of 40 mph.
Response Feedback:
850-R [1-co(28.655)]
HSO
R
arrow_forward
3. An engineering mistake has resulted in the need to connect an already constructed tunnel and
bridge with a vertical curve. The profile of the tunnel and the bridge is given in the figure below.
Devise a vertical alignment to connect the tunnel bridge if the highest common design speed is
20mph for the sag and 10 for crest (equal tangents).
STATION 4+00 PVT
BRIDGE DECK
E LEVATION
126.67 FT
TUNNEL FLOOR
E LEVATION
100FT.
STATION 0+00 PVC
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The deflection angles of two intermediate points A and B of a highway curve are given below. The chord distance between points A and B is CAB while the long chord is C. Comput
elements of the curve and find the stationing of the beginning and end of the simple curve.
**No space before and after the plus sign for stationing.
Station
A
B
CAB
с
Sta of P.I.
Deflection Angles
7° 30'
14° 31'
Chord distance (m)
39
151.500
70+500
Elements of the given circular curve
Radius (m)
Intersection Angle (degree-decimal)
Tangent Distance
Length of Curve (m)
Degree of Curve (degree-decimal)
Sta of P.C.
Sta of P.T.
arrow_forward
The ordinates of a 4-hour unit hydrograph for a particular basn
ordinates of the s-curve and therefrom the ordinates of 6-hiour ut
4-hr UGO (cumec) Time (hr)
3.
below Deterrmine the
Time (hr)
4-hr UGO ( E
110
70
12
25
14
100
16
160
18
20
8.
190
20
22
10
170
24
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Assignment 3 : Horizontal Curve Design
Question 1
A transition curve is required to connect two intersecting straights whose
deflection angle (0) is DD° dd’ dd" by a circular curve of radius XXX metre. The
though chainage of the intersection point (IP) is YYYY metre and pegs required
on the centre line of the road curve at exact 20 metre multiples of through
chainage. Bearing from T, to IP and coordinates at IP given as BB° bb’ bb"
and (Northing, Easting), respectively. While proposed design speed and
acceleration rate (a) are (SS)km/h and (AA) ms³, respectively. As a site
engineer you are required to prepare and verify the setting out data for the
proposed transition road curve design using tangential and chord distance
based on proposed design parameters given by project consultant.
1
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Two tangents intersect at station 26+050. A compound curve laid on their tangents has the following data:
1=31°, 12=36°, D1=3°, D2-5°
1. Compute the stationing of the PC. [Select]
2. Compute the stationing of the PT Select )
26 + O50
P.I. V
T1
P.C.
OP.T.
R1
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A 500-ft curve, grades of g₁ = +2.00% and g2 = -2.50%, VPI at station 96+80, and
elevation 845.260 ft, stakeout at full stations.
Part A
Determine the elevation at the high point of the curve.
Express your answer in feet to six significant figures.
Elev =
Submit
Part B
AΣo↓ vec
Request Answer
Determine the station at the high point of the curve.
O 97+12.77
O 96+13.33
O 96+52.22
O 97+96.66
?
ft
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[Situation 1] A simple curve connects two
tangent roads AB and BC with bearings
N88°40'E and S61º40'E, respectively. If the
chainage (or stationing) of the point of
intersection of the two tangents is 4+331.42
and the radius of the curve is 300 m,
determine the following:
i. Versine, V
ii. Long Chord, C
iii. Length of the curve, LC
8:45 PM /
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(auall b L) Microsoft Word
ASSIGNMENTS 2 133
جد هوز أيجد هوز
T| |师 年,ヨ
wai
تأگید دقیق
V úlgic
blosi
I2 1 3 1 4
51·6
9. 1
10 1
11. 1
12.I 13.I 14 1 15 1 16 1
QI. For a compound normal curve, given the following
data, Draw a neat compound curve
a) The total interior angle = 142° 25' 43",
b) Radius of Curve 1 =716.197 feet
c) Length of Curve 2 = 1568. 572 feet
d) Degree of Curve 2, D2°= 5° [Not Mentioned
whether arc or chord definition]
e) Station of Point of Common Curvature =25+49.080
Find the Radius of Curve 2 R2, Interior angle of curve2
A2, Interior angle of curvel A1, D1°, Length of curve
1 L
DELL
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The highway engineer of a certain road construction decided to use a
radius of 100 m. in laying out a simple curve having an angle of intersection
of 36-20'. The stationing of the vertex is 30 + 375.20 after verifying the
actual conditions of the proposed route, it was found out that the P.T.
should be moved out in a parallel tangent having a perpendicular distance
of 10 meters with the angle of intersection remaining the same while the
curve shall have the same P.C.
1. Compute the new tangent distance.
2. Compute the new radius of curve.
3. Compute the stationing of new P.T.
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NEED ASAP! THANK YOU
A straight railroad AL intersects the curve highway route BC as shown in the figure. Distances on he route are measured along the arc using the data specified.
(USING STATION C)
-Compute angle COP
-Compute the length of curve (Lcu) in meter, from point C to point P in meters.
-Determine station C.
-Find the stationing at the point of intersection “P” of the railroad and the highway curve
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% PY . I. . *
o Home Work No.3...
Home Work No. 2
An engineer has been decided to connect a tunnel with floor
elevation (100.00m) and station (0.00) with bridge elevation
(112.50 m) and station (0+450). He suggested vertical curves
with equal tangents. Sketch the Figure. Is the crest vertical curve
safe to provide sight distance for design speed (70 km/hr.)? Use
t=2.5 sec.
Bridge levation =112 5
Bridge Station od450m
Tunel elevation J00m
Tunnel station a00
II
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if the TS is 23+20.25 what is the station the
tangent runout begins ?
Given a four lane roadway with a 50 mph travel speed, thatis entering a spiral curve and han a design max superelevaton of 4 0% he TS 23-20 25 what is the saton the langent
nunout begins?
(enter the h sation with sign, example, enter as 15-35 75)
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Practical part:
Q1). It is required to connect two intersecting straights whose deflection angle is
39°18'30" by a circular curve of radius 600m. Pegs are required on the centerline of the
curve at exact multiples of 25m of through chain. Calculate the data necessary to set out
the curve by the tangential angles method and draw the horizontal curve.
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Using the information given,
compute the deflection angles (in degrees only not deg-min-sec) for the first three full stations of the simple highway curve. Express
answers into two decimal places and do not type the unit.
PI = 0+762.27
1 = 10 degrees
D = 1 degree
Station Notation Format 9+999.99
1st Sta
2nd Sta
3rd Sta
Deflection Angle
Deflection Angle
Deflection Angle
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A +4.5 percent grade on rural freeway intersects with a -3.5
percent grade at chainage 67 +500 at an elevation 75.000.
If the design speed of the freeway is 100 km/h, NB: obtain
the value of (K) from table
Automatic Zoom :
TABLE: 2
MINIMUM VALUES OF K FOR VERTICAL CURVES
DESIGN
CREST
SAG
SPEED
CURVES
CURVES
(km/h)
40
8
50
11
12
60
16
16
70
23
20
80
33
25
90
46
31
100
60
36
110
81
43
120
110
52
130
133
57
2. 5.1. Determine the chainages and elevations of the BVC,
EVC, and the highest point. (13) 5.2. If the road is staked at
50m interval Calculate the elevations of all full chainages
along the curve.
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12. For a 3-hr unit hydrograph, determine a 3-hr S-Curve?
18 24
Time (hours) 0
Q(cfs/inch) 0
6 12
30 100 40 0
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Determine the cant to be provided on a BG track of 3 ° curve if the speed of several trains is as follows
Number of vehicle
8
10
23
11
13
Speed (kmph)
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50
60
70
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Question
t Pow
t Edge
Calculate the length and radius for the following curve. The PC is at Sta 8+10. The PT is at Sta 10+50. The delta is 17d 32m 00s.
t Excel
t Word
t Word
t Pow
t Pow
t Wore
t Pow
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Problem
A horizontal curve with R=268m is part of a 2-lane highway, and the minimum
distance that a large billboard can be placed from the centerline of the inside lane of the
curve is 18m. Find the maximum_speed (in Km/hr) on the curve without reducing
required SSD? Assume t-2.5 Sec. and a=3.5.
CS Scanned with CamScanner
arrow_forward
H.M 6:
Use the following figure, to calculate the curve
elevation of full and main stations by using Analytic
method?
P.V.I
-3%
P.Y.T
P.V.C
36. Som
41 +60
=240m
十
arrow_forward
The highway engineer of a certain road
construction decided to use a radius of 100 m.
in laying out a simple curve having an angle of
intersection of 36'20', The stationing of the
vertex is 30 + 375.20 after verifying the actual
conditions of the proposed route, it was found
out that the P.T. should be moved out in a
parallel tangent having a perpendicular
distance of 10 meters with the angle of
intersection remaining the same while the
curve shall have the same P.C.
O Compute the new tangent distance.
@ Compute the new radius.of curve.
3 Compute the stationing of new P.T.
arrow_forward
A highway curve was designed to connect intersecting tangents intersecting at an angle
of 72°. The degree of curve is 4°30'.
What is the length of chord that connects the PC and the midpoint of curve?
a) 167.78m
b) 157.38m
c) 174.67m d)166.89m
What would be the difference in the length of curve if this will be applied for railway?
a) 0.12m
b) 0.08m
c) 1.45m
d) 2.56m
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Q3) The perpendicular
offset
distance from point A on a simple
curve to Q on the tangent line is
64m. If the distance from PC to Q on
the tangent is 260m, compute:
(a) the radius of the simple curve
(b) the length of curve from PC to A
P.C.
64
0.
260
R-64
20
68
P.T.
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Compute the passing sight distance available given a 440-ft curve, grades of ₁₂
Express your answer in feet to five significant figures.
|VG ΑΣΦ
S=
vec 4
A
I
?
ft
+2.00% and 9₂
-1.50%. VPI at station 96+80, and elevation 845.26 ft, stakeout at full stations. (Assume h₂
3.75 ft and h₂=4.75 ft.)
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Complete the table below.
Unit
Simple Curve
Intersection angle
Degree of Curve
Radius
1
2
22
25
Tangent Distance
m
|Long Chord
m
Length of Curve
m
Compound Curve Elements
ICommon Tangent
m
Length of Curve
Angle of Intersection
Sta of Tangent intersection
4+200
m
IStation of the start of the curve
USEFUL EQUATIONS
1145.916
D° =
C = 2Rsin
R
[D°
sin
10m
2.TR LC
360° 0°
2
R
=
T = Rtan
20 LC
E = R[sec(0/2)-1]
27-
M = R[1- cos(0 /2)]]
10m
sin(D° /2) LC
360°
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Quèstion 9
A 1800-kg truck travels at 85kph around a banked curve with a radius of 250 m. What should be the super-
elevation so that the tire friction is not needed to prevent the car from sliding?
O A. 0.114
Ов. 0.295
Ос.8.227
O D.0.382
O E. None of the above
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Question 11
A 12-degree simple curve i5 to l
between the tired and pavement
ened fon a maximum speed of 88 kph. The coefficient of friction
that is the reguired super-elevation in percent?
O A7.87
OB.8.11
OC 63.8
O0.23.8
OE None of the above
Question 11 of 50
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Determine the height h in meters of the 100m2 cross section at Station 1+180 if the base of the roadway is 12meters and having a 2 : 1 side slope.
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