c 1 highway design
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MINISTRY OF SCIENCE AND TECHNOLOGY
DEPARTMENT OF TECHNICAL AND VOCATIONAL EDUCATION
DEPARTMENT OF CIVIL ENGINEERING
CE 3017-HIGHWAY AND TRAFFIC ENGINEERING
(SAMPLE QUESTINS AND SOLUTIONS)
SEMESTER I
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SAMPLE QUESTIONS
CHAPTER 2
HIGHWAY PLANING
1. (a)What is the object of highway planning? Write down the planning requirements.(b) Explain the items which would be included in the Road Inventory2. Explain the methods of counting vehicle volume.3. Explain the Origin and Destination Survey.
CHAPTER 3
HIGHWAY LOCATION
4. Explain the highway plans and highway specifications.CHAPTER 4
DESIGN CONTROL AND CRITERIA FOR HIGHWAY DESIGN
5. Define the following terms:a) Flow or Capacity
b) Concentration or Densityc) Average Annual Daily Traffic (AADT)d) Average Daily Traffice) Peak Hour Trafficf) 10th, 20th, 30th highest hourly volume
6. Write down the short notes on the followinga) Traffic projection factor
b) Design Volumec) Design Hourly volume
7. Write down the short notes on the followinga) Theoretical or maximum Capacity
b) Mean journey speed and mean running speedc) Spot speedd) Time mean speed and space mean speed
8.(a) An OD survey carried out to determine the current traffic on a section of a highway
revealed an ADT of 5000 vehicles in the year 1960. It is proposed to improve the
highway to cater for the needs of traffic in 1980. From a travel forecast of the area, the
Normal traffic growth is found to be 52% of 1960 traffic. Generated traffic on the basis ofpervious experience in the area estimated to be 22%. Information revealed that an
increase of 2000 vehicles trips per day is expected by 1980 due to development traffic
calculate the ADT in 1980 Local studies show that the ratio of DHV to ADT both two
ways is 15% and are one way volume in the predominant direction is 60% of two way
DHV. Calculate DHV in 1980.
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(b) The OD survey curried out to determine current traffic on a section of four-lane two-
way. Data obtained from OD survey are as follows:
No. of days Volume/ 16 hours day in 1996
1 4180
2 4270
3 43004 4470
5 4870
6 5050
7 5240
It is proposed to improve the highway to cater for the nee of traffic in 2017. From
travel forecast of the area, the NTG is 45% of 1995, the GTG is 25%. Information reveals
that there is an increase of 2000 vehs trip/day due to the development traffic. Calculate
the DHV for predominant direction in 2017. The thirtieth hour factor is 18% and volume
in the predominant direction is 70% of two-way DHV.
9. (a) TRRL MethodMON TUE WED THU FRI SAT SUN AVG
JAN 418 421 417 429 439 392 394 409
FEB 430 442 450 450 465 416 391 434
MAR 440 447 455 457 478 443 424 449
APR 456 464 476 489 501 467 452 472
MAY 471 487 493 506 527 492 506 497
JUNE 488 505 515 520 530 521 486 509
JULY 508 524 542 545 587 582 562 550
AUG 530 531 551 547 572 558 521 544SEPT 508 513 518 527 552 546 539 529
OCT 468 479 478 491 509 470 428 474
NOV 446 459 468 472 490 434 402 453
DEC 454 464 468 473 488 436 462 463
AVG 468 478 485 492 515 470 456
On a rural road, traffic volume over 16 hours were recorded,
Wednesday 7th march, 1974 5850 vehs:
Thursday 8th march, 1974 5700 vehs:
Friday 9th march, 1974 5950 vehs:
What would be the predicted traffic on an average weekday in August 1990, assuming
an annual growth rate of 5%.
(b) Data for traffic spot speeds were detained by Enoscope over a base line of 200 feet.
Stop- watch time t (sec) 2.6 2.8 3.0 3.4 3.6
Number of vehicles 11 27 62 52 34
Determine (a) Time mean speed
(b) Space mean speed.
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10. Spot speed data from collecting at a short distance of roadway are given below. Analysesare made by graphical method. Determent the design speed, maximum speed limit,
minimum speed limit and then theoretical (or) maximum capacity of this roadway.
No of
vehicles
Spot Speed (mph) No of vehicles Spot Speed (mph)
2 53 19 45.2
3 51.5 20 43.0
3 49 22 40.1
5 48 21 35.5
8 47.6 20 34.3
8 46.4 18 32.7
11 45.6 16 30.0
12 45 9 26.2
14 49.2 8 23.1
15 48 5 20.917 461 2 18.2
CHAPTER 5
HIGHWAY GEOMETRIC DESIGN
11.(a) Write down the assumption for analyzing of Passing Sight Distance.(b) Drive the formula for determining passing sight distance for a two lane highway.
12.Define the Stopping Sight or Non-passing Sight Distance. How to calculate the stoppingsight distance for a highway?
13.(a) What are the design controls for horizontal alignment design?(b) What are the design controls for vertical alignment design?14.Derive the formula for calculating the rate of super elevation on the horizontal curve.15.Explain the method of providing super-elevation by revolving the road surface about the
crown-line of the road in second stage with neat sketches.
16.Explain the method of providing super-elevation by revolving the road surface about theinner edge of the road in second stage with neat sketches.
17.Explain the types of vertical curves with neat sketch.18.Derive the formula for determination of highest point on summit curve.19.Drive the formula for determination of lowest point on valley curve.20.(a) Calculate the stopping sight distance for a road for which the design speed is 30 mph.
The coefficient of fiction between the road surface and tires may be taken as 0.4 and thereaction time of the driver may be assumed as 3 seconds. The road way is level.
(b) Calculate the passing sight distance for a road for which the design speed is 30
mph. The rate of acceleration of the first moving vehicle may be taken as 2.5 mph/sec
and the different in speeds between the overtaking and the overtaken vehicles as 10
mph.
21.(a) Calculate the stopping sight distance for a road for which the design speed is 30 mph.the coefficient of friction between the road surface and tires may be taken as 0.4 and the
reaction time of the driver may be assumed as 3 seconds. The road way is level and the
brake efficiency is 40%.
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f
VdascedisBrakingtheGiven
30tan 2
where, d = breaking distance in feet
v = speed of vehicle in m.p.h.
f = coefficient of friction
(b)Calculate the non-passing sight distance required on a highway with a design speed of60 mph, assume f = 0.42. Also assume reasonable values for other items involve in
calculation.
22. (a) Determine the minimum non-passing sight distance that should be provided for avehicle coming down a 6% gradient. Give the following data.
Design speed V = 35 mph
sV
driveroftimeaction sec35
140Re
Coefficient of friction between type road surface = 0.5
(b)Cuts of a two lane highway have a back slope of 1:2 (1 horizontal: 2 vertical) andthe grade line is level. Calculate the distance required between the centre of the roadand the toe of the cut slope to satisfy the horizontal sight distance on a circular
curve of radius of 1910 feet. The eye is assumed to be 4.5 ft above the road surfaceand the object is also 4.5 ft high. Assume
Design speed of the road = 40 mphReaction time of driver = 2 seconds.
The coefficient of friction of the road = 0.6 with the safety factor of 2.0Horizontal and curve length are the same.
23. (a) A jeep catching up a slow moving truck a two lane highway on which the designspeed is 40 mph. the jeep is traveling at the design speed and the distance between thejeep and truck is 120 feet. The driver of the jeep saw the slow moving truck suddenlybrakes to a stop. Jeep driver is so alert that his reaction time is 2.5 sec. is the braking
distance of the truck is 120 feet. Will the jeep be able to stop in time without colliding thetruck? Use coefficient of friction of 0.6. Assume the road is level.
(b) A deer is running across the level road and a driver did his best to avoid hitting this
deer by attempting to stop his car. However, during the braking, his car slided from the
concrete pavement to the gravel shoulder but finally came to a halt safely. If the travelingspeed of this car is 100 kph and coefficient of friction on the concrete pavement is 0.252,
then what should be the coefficient of friction on the gravel shoulder?Assuming that the lengths of skid marks on concrete pavement and gravel shoulder
are 100m. and 50m., respectively. Reaction time is 0.5 sec.
24.Sketch the longitudinal profile and show the stationing of key points along the roadway.Assume that the side friction is neglected and the super elevation is obtained by revolvingthe road surface about the center line or crown. The following data are given:
Design speed V = 40 mph Degree of Curve D = 8 Width of the pavement =b = 24 Amount of normal crown = c = 3
The road is passes through the open flat country, maximum super-elevation runoffis 1:150
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Normal crown ends at station 20+0025.Degree of curve = 8
Design speed V = 40 mph Width of the pavement b = 24 Amount of normal crown c = 3
15
1,supmax max eelevationerofrateimumAllowable
Allowable maximum super- elevation runoff 1: x = 1:200Normal crown ends at sta: 20+00. Sketch the longitudinal profile. Assume f is
neglected and full super elevation is obtained by revolving about the centre line or
crown.
CHAPTER 2 (from semester II)
DRAINAGE AND EROSION CONTROL
DRAINAGE AND DRAINAGE STRUCTURES
26.(a) Describe the requirements of the good road drainages system.(b) Describe the causes of change in moisture content.
27.Describe the major causes of erosion and controlling method for a highway engineer.28.Describe the side ditches, curbs and gutters for surface drainage.29.Describe the intercepting drains, pipe drains, inlets, catch basins and manholes for surface
drainage.
CHAPTER 8 (from semester II)ROADSIDE DESIGN
30. Draw the guardrails and median barriers for roadside design.
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SOLUTIONS
1. (a)What is the object of highway planning? Write down the planningrequirements.
(b) Explain the items which would be included in the Road Inventory
Solution:
(a ) Object of Highway Planning
The object of highway planning is to provide a highway system which would give
maximum transportation facilities a minimum cost. For this purpose, a well defined
programme to collect data and analyze the existing conditions is most essential
Planning Requirements
Highway planning would include.
(1)Collection and tabulation of the formation about the existing transportationfacilities in the area.
(2)Determination of the general inter-relation of all branches of the transportationsystem and their effect on each other.(3)Determination of the adequacy or otherwise of the existing facilities as per
present needs and the improvements and extension of these facilities for
anticipated future needs for a certain period.
(4)Finding out the methods for financing these projects and the periods overwhich the construction can be spread.
(5)Estimating of the cost of construction and maintenance.(b)Items which would be included in the Road Inventory are:
(1)Clear demarcation of different states in the country from roadway point ofview.
(2)Man-made and natural features adjacent to the road. e.g. buildings, landlines,fence-lines, monuments, bench marks, water courses etc.
(3)Description of the geometrics of highway such as roadway width, right of waywidth, sight distance, curve dial, gradients and road camber etc.
(4)Information about the structural components of the pavement, surface type andthe pavement design, its cross section and soil characteristics.
(5)Roadway condition, i.e. conditions of surfaces, drainage and riding qualitiesetc.
(6)Detail information about the type of drainage, structures, their location,number of spans, lateral clearance, distance between roadway surface and
stream bed, width of the structures, vertical clearance, load-capacity, condition
of structures, adequacy of waterway and the approach alignment.(7)Railroad crossings, their names, number of rail tracks, gradients of thehighway at approaches, angle of crossings, property of sight distance,
curvature if any, near it.
(8)Land-use, agricultural and other potential periodicity.(9)Classification of the highway and its service to community.(10) Traffic volume, speeds and accident experience on the road.(11) Maintenance cost of the highway etc.
2. Explain the methods of counting vehicle volume.
Volume of traffic using a section of road can be measured by counting vehicles
passing a fixed point in both directions.
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Manual methods
In this method, the passing of a vehicle is recorded by an enumerator a specially
prepared form or on a series of hand tallies, the vehicles being simultaneously classified
into a number of predetermined groups. For many purposes, it is usual to convert the
actual numbers of vehicles into equivalent passenger car unit (p. c. u); these values beingdetermined by the relative effects of different types of vehicles on traffic flow. Since the
effect of a bus or heavy commercial vehicle in a traffic stream varies according to the
precise road and traffic conditions, it is not possible to give general value to suit all
purposes.
On account of the labor involved in the conducting of a manual count, the period of
counting has generally to be limited to a few days. Observations are usually made over
the 16 hr-period from can 6am to 10pm and should preferably continue over several
consecutive days.
Since traffic flow varies from month to month throughout the year, the volume count
should be taken at the busiest time of the year.
Automatic Methods
The passing of vehicle can be recorded automatically by special equipment used in
conjunction with some form of vehicle detector. The type most commonly used is a
pneumatic detector, which consists of a length of thick walled rubber tubing about in
internal diameter fastened down to the surface of the road perpendicular to the direction
of the traffic. The passage of a vehicle axle over the tube transmits a pressure pulse
through the tube which operates an electrical contact on a diaphragm switch, so actuating
a counter which is arranged to register every other pulse in order to correspond to one
count per vehicle.
Automatic methods of counting have the advantage that little attendant labor is required,
particularly with the more elaborate type of counters, and therefore measurements can be
made for long periods. Such counters are thus ideally suited for the continuous
measurement of seasonal and annual trends at the selected sites.
The chief advantage is that these counters are not able to give a classification break down
and therefore the results must generally be supplemented by a sample manual count.
Other disadvantages are that errors can be incurred with multi-axle vehicles and also with
light vehicles such as pedal cycles which may fail to register when using pneumatic
detector tubes.
3. Explain the Origin and Destination survey.
Solution
Origin and Destination Survey
An O.D Survey is necessary where it is anticipated that traffic will be drawn from a
number of existing routes onto a new or improved road. By means of this type of survey it is
possible to estimate the number of drivers traveling on each of the existing routes who will
choose to use the new road in future.
The O.D survey obtains, in addition to straight forward count of vehicles on each
road, further information concerning the place of origin and destination of each journey and
the location of any intended intermediate stops within the survey area.
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Survey Stations must be established on all the main roads entering and leaving the
area concerned, so forming a cordon or screen line. Sites for these stations should be on
straight, level sections of road with good visibility.
There are a number of basic method by which the required information may be
obtained, namely
(1)By roadside interview.(2)By the use of prepaid postcards(3)By attaching colored tags or stickers to vehicles(4)By observing vehicle registration numbers(5)By selective interview at home or at the place of employment
1) By roadside interviewIn this method vehicles are stopped and the drivers are questioned as to the origin
destination of the journey and the location of proposed intermediate stops.
The sampling technique may be carried out on either a numeral or a time basis, but in all
cases the system should be prearranged and used consistently. One method is to stop
every nth vehicle, whilst another is to stop all vehicles arriving within certain fixed time
limits. Both methods have the disadvantage that queues may form during times of heavyflows and a third method which involves stopping the next vehicle arriving after the
completion of successive interview may be preferred. In all cases, at least two people are
required, one to carry out the interviews and one to count and direct traffic, and after it
may prove advisable to use more than one interviewer.
(2) By the use of Prepaid Postcards
This system is to hand each driver a business reply-type prepaid postcard. Questions
asked by the interviewer are tabulated and the driver is requested to answer these and also
supply the additional information concerning the type of vehicle and number of passengers
before returning the card by post to the survey headquarters
(3) By attaching colored tags or stickers to vehicles
At the incoming survey station, a tag of distinctive color is stuck on the wide screen
of each vehicle entering the survey area, a different color and shape being used at each point.
Observers at the outgoing survey stations note the color designation for each vehicle leaving
the survey area, and, if desired, other observers at selected points within the area may be used
to help trace the routes followed by the vehicles.
(4) By observation vehicle registration number
The methods mentioned above all suffer from the disadvantage that vehicles have to
be stopped to some extent. An alternative method in which the registration numbers of
vehicle passing the survey station are noted avoids these disadvantages.
To work effectively in heavy flows, two observers are required; one reading the
registration numbers of passing vehicles and the other nothing them down. Alternatively asingle observer can record the information into a portable type recorder.
(5) By selective interview at home or at the place of employment
In this method, a random sample of population is interviewed either at home or at the
place of employment to obtain information concerning details of all journeys made by the
person of family concerned on a particular day or days.
4. Explain the highway plans and highway specifications.Solution
Highway plans
In general, the plans contain the engineering drawings of the project whereasthe specifications present the written instructions.
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After the final location for a given project has been completed, including the
field soils investigation the data are forwarded to the design office. There a complete
scheme for the road is worked out by the specialist in the fields of geometric design,
drainage, structures, soils and pavements. All the dimensional features and many
other details of each final design are recorded on a series of drawings commonly
refers to as plans. Figure shows one sheet of plans for a typical two lane ruralhighway. Other sheets of plans show roadway cross-sections fitting every situation in
the entire project. Figure is typical. Also included will be sheets of drawings for all
structures and roadway appurtenance. A partial list of subjects covered by the
standard would include pipe culverts, concrete box culverts, guard rails and parapets,
curbs and gutters and curb returns, sidewalks, drainage inlet and outlet structures of
numerous types, manholes, riprap and other devices used for bank protection, fences,
and right of way and other permanent survey markers.
Highway specifications
Specifications can result in the use of improper materials and poor
workmanship. On the other hand, specifications are too exacting results in higher cost.Specifications contain the written instructions highway projects and outline carefully
and detail the procedures and the methods to be followed for each operation. Often
they are divided into two parts: standard specifications and special provisions. The
standard specifications apply to every project constructed by the agency and treat
subjects that occur repeatedly in the agencys work. The special provisions cover
subjects peculiar to the projects and in question and include additions or modifications
to the standard specifications. The special provisions issued by some highway
agencies include copies of all the documents required for securing competitive bids
and for the contract. This is helpful to both contractor and construction engineer.
5. Define the following terms:a) Flow or Capacityb) Concentration or Densityc) Average Annual Daily Traffic (AADT)d) Average Daily Traffice) Peak Hour Trafficf) 10th, 20th, 30th highest hourly volume
Solution
a) Flow or Capacity
The number of vehicles passing a point in a unit time.b) Concentration or Density
The number of vehicle traveling over a unit length of highway at a specified
instant in time.
c) AADT. (Average Annual Daily Traffic)
The total yearly volume divided by the number of days in the year.
d) ADT (Average Daily Traffic)
The total volume during a given period divided by the number of days in that
period.
No. of days Traffic VolumeDay 1 x1
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Day 2 x2
Day n xn
AADT =n
xn
n =365-366
ADT =n
xn n= 7, 14
e) Peak Hour Traffic
The highest number of vehicles found to be passing over a section of a lane or
a roadway during 60 minutes.
f) Tenth, Twentieth, Thirtieth etc. Highest Annual hourly Volume
The hourly volume on a given roadway that is exceeded by 9, 19, 29 etc,
respectively hourly volume during a designated year.
6. Write down the short notes on the following
a) Traffic projection factorb) Design Volumec) Design Hourly volumed) Theoretical or maximum CapacitySolution
a) Traffic projection factorThe future needs of traffic over a period of 20-25 years, which is taken as the
normal life of a highway, it is essential to know the development of traffic and its
ultimate value at the end of the design period. The design period is usually taken as 20
years.
It is not possible to project traffic to some future year exactly but a reason ably
accurate value can be arrived at by considering the following elements
Current traffic, made up of
(i) Existing traffic: and(ii) Diverted traffic.
Increase in traffic due to
(iii) Normal Traffic growth:(iv)
Generated Traffic growth.(v) Development traffic growth
Traffic Projection Factor
0.1
100
(%)%%1
100
,%1
DTGGTGNTGTPF
trafficcurrenttorespectwithDTGandGTGNTGoftheofsum
b) Design VolumeTraffic studies on highway both in rural and urban areas have shown that the
traffic volume varies considerably in volume throughout the day and even a greater
fluctuation in hourly volumes is indicated during a year. So it is essential to determine
which of the hourly volumes should be used for design since such a situation arises,
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only once a year and the rest of the period during the year, such a situation does not
arise. At the same time the hourly volume used for design should not be exceeded
very often during the year. It has been established that where only motor traffic is
involved, the design should be based upon the 30th Highest Hourly Volume (30 HV)
s y 29 hourly volumes in a year.
for highway catering for motor traffic only should
30th Hour factor (k)
both taken t
esearch lab method
ection (or) in both direction for two lane or three-lane during a
al (or) Maximum Capacity (Qmax) can be expressed by headway-lationship.
o that this volume of traffic is exceeded onl
c) Design Hourly volume,DHVDesign hourly volume to be takenbe the 30th highest hourly volume.
The DHV may be repressed as a percentage of ADT (or)
wo ways. DHV for future needs can be estimated by
(a) Traffic projection factor method and(b) Transport and Road r
d) Theoretical or maximum CapacityThe maximum number of vehicles which has passing over a given section of a lane or
roadway in one dir
given time period.
The theoreticspeed re
2053.004.120 VVmax
5280VQ
here acity in veh/hr
V = speed in mph
ey speed and mean running speed
c) Time mean speed and space mean speedd and mean running speed
from traffic control measures and congestion being
time.
Mean r
rsown the vehicle without actually stopping it will still be included .]
b) Spo
or new facilities. Spot speeds are
. Hence the
o measure
ll vehicles. Vehicles should be selected at random from the traffic stream.
w Qmax = Maximum Cap
7. Write down the short notes on the following
a) Mean journb) Spot speed
Solution
a) Mean journey spee
Mean journey speed
It is derived from measurement of journey time between two points a known
distance apart, delays arising
included in the journey
unning speed
It is reduced by a moving observer in the same manner as the mean journey
speed, except that all the periods of time when the vehicle is actually stationary are
deducted from the total journey time. Delays caused by congestion and other factowhich the slow d
t speed
It refers to the speed of vehicle at one particular instant of time at a specified
location. Spot speed has a variety of uses. They can be used as evidence regarding the
effect of particular traffic flow construction such as intersection and bridges. They can
be used for geometric design purpose or improved
also used in determining enforceable speed limits.
Spot speed measurement should be conducted so as to reduce a minimum
influence of the observer and his equipment upon the values obtained
observer and equipment should be located as in conspicuous as possible.
It can be measured directly by various methods and is not possible t
a
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c) Time mean speeds and space mean speedTime M
rithmetic mean of speed of vehicles passing a point during a given
ithmetic mean of speed of vehicles on a given length of road at an
stant
erages speed or space mean speed Vs is given by:
ean Speed
It is an a
interval of time.
Space Mean SpeedIt is the ar
in in time.
The difference between the two can be illustrated by considering a set of
vehicles spaced a uniformed distance apart along an infinite length of road and all
moving at the same speed V1 together with a second set of vehicles superimposed in
the first and also speed uniformly, but moving at a constant speed V2 in speed
measurements are made on all vehicles within the fixed length L of road at a
particular instant of time, then the av
.... nms
where, there are m vehicle
....21 VmV
V
s moving at speed V1 and n vehicles at speed V2 within this
oving at speed V2. Therefore, the average speed or time mean
eed VT is given by:
length at any given time.
Suppose that instead of measuring the speed of all vehicles within the fixed
length L, measurements are made on all vehicles passing a fixed point during a time
interval t. There will be mt V1/L vehicles in this time moving at speed V1 and nt V2/ L
vehicles in this time m
sp
...
...
21
22
21
21
21
1
nVmV
nVmV
L
ntV
L
mtV
L
ntV
L
mtV
VVT
8. (a) An OD survey carried out to determine the current traffic on a section of a
highway revealed an ADT of 5000 vehicles in the year 1960. It is proposed to
improve the highway to cater for the needs of traffic in 1980. From a travel forecast
of the area, the Normal traffic growth is found to be 52% of 1960 traffic. Generated
traffic on the basis of pervious experience in the area estimated to be 22%.
Information revealed that an increase of 2000 vehicles trips per day is expected by
1980 due to development traffic calculate the ADT in 1980 Local studies show thatthe ratio of DHV to ADT both two ways is 15% and are one way volume in the
redominant direction is 60% of two way DHV. Calculate DHV in 1980.
section of
four-lane t s:
No. of
p
(b) The OD survey curried out to determine current traffic on a
wo-way. Data obtained from OD survey are as follow
days Volume/ 16 hours day in 1996
1 4180
2 4270
3 4300
4 4470
5 48706 5050
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7 5240
ur factor is 18% and volume in the predominant direction is 70% of two-
way DHV.
olution
(a)
Generated traffic growth = 22%
It is proposed to improve the highway to cater for the nee of traffic in 2017.
From travel forecast of the area, the NTG is 45% of 1995, the GTG is 25%.
Information reveals that there is an increase of 2000 vehs trip/day due to the
development traffic. Calculate the DHV for predominant direction in 2017. Thethirtieth ho
S
Normal traffic growth = 52%
%401005000
2000 xtraffictDevelopmen
Sum of the traffic growth = 52+22+40 =114
14.2100
1 114
100
%%%1)(
DTGGTGNTGTPFfactorprojectonTraffic
ence ture A T (198
irections
= ADT (1980) x 30th hour factor (k)
H fu D 0) = TFP x ADT (1960)= 2.14 x 5000 = 10700 vehicles
Two-way DHV in 1980 provided the traffic is equal in both d
hourpervehilcesx 1605
100
10700 15
DHV in 1980 in the predominant direction
hrvehsx /:963100
1605 60
r say the design may be carried out for 1000 vehicles per hour
(b)
o
7
524050504870447043004270418
1995
n
XADTADT ncurrent
= 4626 vehs/16 hrs
DTG = 2000veh trip/day
NTG = 45%, GTG = 25%
1004626
2000x
= 43.23%
X 2017 in the predominant direction = 0. 7 x DHV2017 in both direction
k = 18%
% in predominant dir. = %
DHV2017 in the predominant direction = ?
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1323.2100
23.4325451
100
%%%1)(
DTGGTGNTGTPFfactorprojectonTraffic
ADTfuture = TPF x ADTcurrent= 2.1323 x4626veh/16hr day
DHV2017 in both direction = kxADT2017
=0.8x9864= 1776= 1224veh/hr
9. (a) TRRL Method
MON TUE WED THU FRI SAT SUN AVG
JAN 418 421 417 429 439 392 394 409
FEB 430 442 450 450 465 416 391 434
MAR 440 447 455 457 478 443 424 449
APR 456 464 476 489 501 467 452 472
MAY 471 487 493 506 527 492 506 497JUNE 488 505 515 520 530 521 486 509
JULY 508 524 542 545 587 582 562 550
AUG 530 531 551 547 572 558 521 544
SEPT 508 513 518 527 552 546 539 529
OCT 468 479 478 491 509 470 428 474
NOV 446 459 468 472 490 434 402 453
DEC 454 464 468 473 488 436 462 463
AVG 468 478 485 492 515 470 456
On a rural road, traffic volume over 16 hours were recorded,
Wednesday 7th
march, 1974 5850 vehs:
Thursday 8th
march, 1974 5700 vehs:
Friday 9th
march, 1974 5950 vehs:
What would be the predicted traffic on an average weekday in August 1990,
assuming an annual growth rate of 5%.
(b) Data for traffic spot speeds were detained by Enoscope over a base line of 200 feet.
Stop- watch time t (sec) 2.6 2.8 3.0 3.4 3.6
Number of vehicles 11 27 62 52 34
Determine (a) Time mean speed(b) Space mean speed.
(a) Solution
1974 1974 1990
March August August
Available) (Required)
Best estimation of average weekdays traffic in March 1947 is
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dayhrvehiclesx
ADTyADT
dayhrvehiclex
isAugustintrafficweekdayofaverageestimationBest
dayhrvehiclesxx
xx
n
16/953,14685010
51
1
16/6850449
5445654
1974
16/5654478
449
5950457
4495700
455
4495850
3
1
16
19741990
(b) Solution
Time t (sec) no. of veh. V (ft/sec) mV12
mV1
2.6 11 76.92 65083.55 846.12
2.8 27 1.42 137722.04 1928.34
3.0 62 66.67 275583.11 4133.54
3.4 52 58.82 179909.20 3058.64
3.6 34 55.55 104917.28 1888.7
Total 186 763215.18 11855.34
(a)
Time mean speed, VT
...
...
21
2
2
2
1
21
211
nVmV
nVmV
L
ntV
L
mtV
L
ntV
L
mtVV
VT
mphft 79.43sec/38.6434.11855
18.763215
(b)
Space mean speed, Vs
mphftnm
VmVVs 36.43sec/74.63
186
34.11855
....
....21
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10. Spot speed data from collecting at a short distance of roadway are given below.
Analyses are made by graphical method. Determent the design speed, maximum speed
limit, minimum speed limit and then theoretical (or) maximum capacity of this
roadway.
No ofvehicles
Spot Speed (mph) No of vehicles Spot Speed (mph)
2 53 19 45.2
3 51.5 20 43.0
3 49 22 40.1
5 48 21 35.5
8 47.6 20 34.3
8 46.4 18 32.7
11 45.6 16 30.0
12 45 9 26.2
14 49.2 8 23.115 48 5 20.9
17 461 2 18.2
Solution
Speed Class Interval
hourpervehilcesn
RCI 49.3
258log322.31
2.1853
log322.31
Speed class
(mph)
Avg:
speed
(mph)
No of vehs: frequency Commutative
frequency
15-18.9 17 2 0.78 0.78
19-22.9 21 5 1.94 2.75
23-26.9 25 17 6.59 9.31
27-30.9 29 16 6.20 15.51
31-34.9 33 38 14.73 30.24
35-38.9 37 21 8.14 38.38
39-42.9 41 22 8.53 46.91
43-46.9 45 87 33.72 80.6347-50.9 49 45 17.44 98.07
51-54.9 53 5 1.94 100.0
total 258
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Minimum speed limit = 15 percentile speed = 30.5 mph
Medium speed limit = 50 percentile speed = 44 mph
- to determine the maximum capacity
hrveh
xx
x
VxV
VQ
/1323
8.47053.08.4704.120
8.475280
053.004.120
528022max
11.(a) Write down the assumption for analyzing of Passing Sight Distance.(b) Drive the formula for determining passing sight distance for a two lane
highway.
Solution (a)
Assumptions;
(1)Speed of overtaken vehicles is considered as uniform along the road and equal to (V-m) mph.
(2)Passing is accomplished by accelerating during the entire period.(3)A passing (overtaking) vehicle is forced to travel at the same speed as the overtaken
vehicle before overtaking.
(4)The opposite vehicle appears at the instant where the overtaking maneuver begins andit travels at the design speed V mph.
(5)The driver of the passing vehicle requires a short period of perception time to takeover the situation.
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For two lane highways, passing sight distance represents the sum of these distances.
Passing right distance D = d1 + d2 + d3
Where d1 = Distance traveled by the vehicle A from its position A1 during the perception
time to taken by the driver of A to decide whether or not he should be taken over
the slow moving vehicle B.
d2 = Distance traveled by the vehicle A from its position A1 to its position at A2
during the actual overtaking time t
d3 = Distance traveled by the vehicle C from its position C1 to its position at C2during the time in which the overtaking operation is completed (i.e. overtaking time t)
Let, V = design speed for the road in mph.
M = difference in speeds of the fast moving vehicle A and the slow moving vehicle
B in mph.
v, m = the corresponding values of V and m respectively in ft/sec.
a = Rate of acceleration during the overtaking maneuver in mph/sec, during the time interval
of t seconds.
a = the corresponding rate of acceleration, in ft/sec2
t = time interval in seconds to complete the actual overtaking operation.
S = Average speed of vehicles in the positions when they are closet just before and just after
the overtaking operation; and is usually called the headway
to = the perception time during which the driver of vehicle A gauges the situation, watches
the opposing traffic, gets the signal from the vehicle moving ahead and decides to
overtake.
It has been observed that the value of S so calculated is in excess of the actual
spacing between vehicles in such a case. In general,
- S in ft = Speed of vehicle B in mph + length of the vehicle in ft
S = (V-m) + 20 feet
- The perception time t0 is assumed as 2 seconds since most of the drivers can
visualize the whole situation within this period. The distance d1, d2, d3 may then be calculated
as under.Distance d1: Distance d1 = 1.47 x (V m)x t0 in feet
= 1.47 (V-m) x 2 in feet
OR d1 = 2.94 (V-m) feet
d2 = 2s + the distance covered by the slow moving vehicle in time t
OR d2 = 2s + 1.47 (V-m) x t in feet
The distance d2 can also be calculated by another method, is by considering the
distance traveled by vehicle A with an initial speed of (V m) and an acceleration a in time
t all taken in the same system of units.
Assuming, for the time being, the speed in feet/sec distance in feet and time in
seconds,
This distance covered by the vehicle A is given by
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feetintxVddceDis
mphinaandondintwherea
St
mphintakenisrateonacceleratiifNow
a
St
staor
stmvtatmv
equaitonfromstxmvdalso
tatxmvd
47.1;tan
sec/''sec'',,73.2
sec/.
'
4
22
1
2)(2
1)(
)9(:2
2
1
33
2
2
2
2
2
The passing sight distance D = d1 + d2+ d3 for two lane highways.
12.Define the Stopping Sight or Non-passing Sight Distance. How to calculate thestopping sight distance for a highway?
Solution
Analysis of stopping sight distance
Reaction time and Breaking time.
(a) Reaction time
The time elapsed between the instant when the danger was first realized up to the
instant just before starting applying the brakes.The reaction time depends upon the physical and mental ability and alertness of the
driver. If can be divided into two parts.
(1)Perception time and(2)Foot reaction time
(1)Perception timeThe time that further elapses between the moment that the danger was first realized
and the moment the message is conveyed to the foot of the driver to take action.
(2) Foot reaction time
The time that further elapses between the moments that the foot is removed
from the accelerator and place on the brake paddle is known as foot reaction time.
Then,Reaction time = Perception time + Foot Reaction time
(b) Reaction Distance
The distance traveled by the vehicle during the reaction time is called the
Reaction Distance.
If V is the speed in mph and t, the reaction time in seconds, then the distance
covered during. The reaction time called the Reaction distance is given by
feettxVtxVx 47.160
88
Braking Distance
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The distance which the vehicle covers from the time of application of brake while
moving of the design speed to the time when it comes to a stop is called the Braking
Distance.
It can be determined by two methods.
1st
method - From considerations of the coefficient of friction of the vehicles tires againstthe road surface.
2nd method - From considerations of the efficiency of the vehicle.
1st method - The Breaking distance may be calculated as under.
Let D = Breaking distance in feet after application of brakes
f = Coefficient of friction between the tires and the road surface
v = Speed of the vehicle at the time the brakes are applied (in ft/sec)
W = Weight of the vehicle in lbs.
g = Acceleration due to gravity (32.2 ft/sec2)
Then, on a level surface, the force along the surface = W x f
Work done by the vehicle in the distance D before stoppingunder this force = W x f x D
Work done = the difference in the kinetic energy
2
2v
g
W
Equation (1) and (2)
systemfpsin
fg
vD
v
g
WDfW
2
2
2
2
If the speed of the vehicle has to be taken in m.p.h
i.e. V = mph, then the formula (3) becomes
gradeonGf
VD
roadlevelonf
VD
gf
VD
)(30
30
2
47.1
2
2
Take + ve sign for uphill
- ve sign for do untilWhere D is in feet and V in m.p.h
2nd Method
Let D = Braking distance in feet
= Efficiency of vehicle brakes in percent
v = Speed of the vehicle at the time the brakes are applied (in ft/sec2)
-g = Deceleration rate due to gravity (32.2 ft/sec2)
Assumed with 100% efficient brakesThe vehicle moves from a speed of v ft/ sec to a stop in distance D feet.
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Also deceleration produced by brakes with an efficiency of
Then the bodies in motion
2sec100
ftg
V2 U2 = 2as
Where, V = final speed
a = rate of acceleration
s = distance covered
100/30
100/247.1
)5(;..
100/2
10020
2
2
:
2
22
VDor
gVD
becomesequhpmVif
g
vD
Dxgn
V
n
Where D is in feet and V is in m.p.h.
13.(a) What are the design controls for horizontal alignment design?(b) What are the design controls for vertical alignment design?
Solution
Design Controls for Horizontal Alignment
(1)Alignment should be as directional as possible.(2)Use of maximum radii of curvatures should be made for the prescribed design speed
since that leads to uniform speeds and greater safety.
(3)Surprise elements e.g. sharp curvature after easy alignment, should not be introducedand consistency of design maintained as far as possible.
(4)On high and long embankments, only that curves should be used and to safeguardagainst any emergency, properly designed guard-rails should be provided.
(5)Reverse curves which introduce abrupt reversal in the direction of motion of thevehicle should be avoided.
(6)Horizontal and vertical alignment should be properly coordinated in order to give auniformly of design for safe operation.
(7)Curve approaches to the bridges should be avoided.(8)Sites for rail-road crossings must be carefully selected and curved approaches to such
crossings avoided.
Design control for the vertical alignment design
g) Short lengths of steep grades and numerous breaks should be avoided.Instead, it is perfectible to have a grade line with gradual changes
consistent with the topographic features of the area by making use of
standards laid down for gradients in a manner that gives the feeling of a
continuous line
h) Sudden, hidden and unexpected dips are undesirable since they presenthazardous situations.
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i) Two vertical curves in the same direction separated by a short section ofa tangent grade should be generally avoided.
j) Where the length of a grade line is sufficiently great, it is preferable toprovide steeper grades of the bottom of an up grade and go on making it
milder till the top is reached, instead of making it a uniform sustained
gradek) Separate lanes should be provided for slow moving traffic when the
length of the road along any particular grade exceeds the initial length
conveniently negotiable by slow traffic
l) Where the highways meet at grade and they run at steep to moderategradients, it is better to reduce the gradient near and at the crossing to
decrease the chances of accidents.
14.Derive the formula for calculating the rate of super elevation on the horizontalcurve.
SolutionMaximum allowable rate of super elevation
Super elevation may be defined as the raising of the outer edge of the road along a
curve in order to counteract the effect of centrifugal force, in combination with the friction
between the road surface and tires developed in the lateral direction.
Let the road curve be super elevated at the rate of one in e and let the inclination of
the plane of the surface to the horizontal be .
Then,
tan = e.
let W = Weight of the vehicle in lbs acting vertically downwards.
v = Speed of the vehicle in feet/sec at the curve.
R = Radius of curvature in feet.
f = Lateral coefficient of friction between the road surface and tires.
R = normal reaction of the road on the road surface
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The centrifugal force (C.E) acting in the outward direction ,2
gRWv
where g is the acceleration due to gravity in ft/ sec2
cossin2
WgR
WvNNRRactionThe
RL
Force of friction along the surface of the road acting down incline tending to partially
the effect of the C.F shall be equal to f R
cossin
2
gR
Wv
WRf
Substituting the value of R from equation (11) in equation (12) we have,
gRfv
fgR
v
e
gRfv
fgR
v
fgR
v
gR
fv
gR
vf
gR
fv
WgR
WvW
gR
Wv
2
2
2
2
22
22
22
1
1
tancos
sin
cossin1
sincoscossin
sincoscossin
Since, the value of f is very low, the factor fv2/gR in the denominator may be ignored for all
practical purposes
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gR
vfe
fgR
ve
2
2
This is the relation between the rate of super elevation, the coefficient of friction, the designspeed and the radius of the curve.
.)13(exp ratiolCentrifugacalledisequationingR
VensionThe
OR
R
V
gR
Vfe
2.32
47.1
47.1
2
2
feV
RORR
Vfe
1515
22
Where V = design speed in mph
If f is neglected and V is taken as 0.75 of the design speed, we have
R
VeelevationSuper
15
75.02
15.Explain the method of providing super-elevation by revolving the road surfaceabout the crown-line of the road in second stage with neat sketches.
Solution
Method of Providing Super-elevation
The super elevation at the curves is provided in two stages:
1st stage: Neutralizing the camber of the road gradually and bringing it to straight line
slope.
2nd stage: Increasing the slope of this line gradually till design super elevation is
attained
The 1st
stage involves the rotation of the outer slope of camber about a pivot point, thelevel of which is kept constant throughout the length till the camber is neutralized.
After the surface becomes a straight fall, full super elevation is gradually achieved by
any of the following two methods:
1st method- In the1st method, the surface of the road is rotated about the crown (pivot
point)
2nd method- In the second method, surface of the road is rotated about the inner edge
of the road.
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16.Explain the method of providing super-elevation by revolving the road surfaceabout the inner edge of the road in second stage with neat sketches.
Solution
Method of Providing Super-elevation
The super elevation at the curves is provided in two stages:
1st stage: Neutralizing the camber of the road gradually and bringing it to straight line
slope.
2nd stage: Increasing the slope of this line gradually till design super elevation is
attainedThe 1st stage involves the rotation of the outer slope of camber about a pivot point, the
level of which is kept constant throughout the length till the camber is neutralized.
After the surface becomes a straight fall, full super elevation is gradually achieved by
any of the following two methods:
1st method- In the1st method, the surface of the road is rotated about the crown (pivot
point)
2nd method- In the second method, surface of the road is rotated about the inner edge
of the road.
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17.Explain the types of vertical curves with neat sketch.Solution
Types of vertical curve
Summit curves andValley curves
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Summit curves
The major factor affecting the design of summit curves is the sight distance
across the summit since it is essential that an obstruction on the other side of the
summit whether stationery or in motion must be visible to the driver on this side of
summit and vice versa.
Summit curves are required to be introduced at the situations where,(1)A positive grade meets a negative grade(2)A positive grade meets another milder positive grade(3)A positive grade meets a level stretch(4)A negative grade meets a steeper negative grade
Valley curves
The problems of seeing across the road on both sides do not exist. Valleycurves are required to be introduced at the situation where
(1)A negative grade meets a positive grade(2)A negative grade meets a milder negative grade(3)A negative grade meets a level stretch(4)A positive grade meets a steeper positive grade
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18.Derive the formula for determination of highest point on summit curve.Solution
Highest Point or the Summit Point on the curve
Sometimes the highest point on the curve is required to be located
a. If the gradients on either side of the point of intersection are equal, the highest pointlies on the bisector of the angle between the two grades.
b. If the gradients on either sides of the point of intersection are unequal the highestpoint lies on the side of the flatter grade.
The calculations for location can be made as under.
Let Xh be the distance AD of the highest point C on the curve measure d along the x
axis from the start of the curve on the steeper grade and yh be its ordinate from the
first grade line and equal to QC.
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Let the distance CD is denoted by :z
Lggg
xOR
LG
gx
xL
Ggthen
G
LaPut
a
xgei
zerobeshoulddx
dzthencurvetheonhighesttheiscifNow
a
xxgZ
a
xxgQCQDZCD
equationstwoabovetheFrom
xgQDAlso
a
xyQCThen
h
h
h
h
h
h
h
h
h
h
h
h
.
.
0,,2
02
..
,
21
1
1
1
1
2
1
2
1
1
2
The distance xh is measured from the start of the curve on the side of the steeper grade
and the highest point lies on the side of flatter grade.
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19.Drive the formula for determination of lowest point on valley curve.Solution
Lowest point on the curve
Sometimes the lowest point on the curve is required to be located. It is essential in the
valley curves, since if any gutter-gratings are fixed at any other point, the water may collect
on the curve during the rainy season and damage the road. Its position may be located asunder.
(a).If gradients on either side of the points of intersection are equal, then the lowest pointlies on the bisector of the angle between two grades.
(b).If the gradients on either side of the point of intersection are unequal, then the lowestpoint lies on the side of the flatter grade. The calculations can be made as
Fig. 5.19 Determination of lowest point on valley curve
Let xL be the distance AD of the lowest point C on the curve measured along the x-axis from
the start of the curve on the steeper grade and yL be its ordinate from the 1st grade line equal t
QC in Figure,
Let the distance CD be denoted by z.
LxgQDAlso
b
xyQCThen
1
2
11
From the above two equations,
bxxgZ
b
xxgQCQDCD
LL
L
L
3
1
3
1
If C is the lowest point on the valley curve, then dz/x should be zero
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21
1
1
2
12
2
21
3
1
2
2
02,
.2
3
03
gg
gxor
L
G
gx
G
Lgx
xLGgThen
G
LbPut
b
xg
L
L
L
L
L
The distance xL is measured from the start of the curve on the side of the steeper grade
and the lowest point lies on the side of the flatter grade.
20.a) Calculate the stopping sight distance for a road for which the design speed is30 mph. The coefficient of fiction between the road surface and tires may be
taken as 0.4 and the reaction time of the driver may be assumed as 3 seconds.
The road way is level.
(b) Calculate the passing sight distance for a road for which the design speed is
30 mph. The rate of acceleration of the first moving vehicle may be taken as 2.5
mph/sec and the different in speeds between the overtaking and the overtaken
vehicles as 10 mph.
Solution
(a) Design speed V = 30 mph
Coefficient of friction f = 0.4
Reaction time t = 3 seconds
Then Reaction distance = 1.47 V t
= 1.47 x 30 x 3 = 132.30 ft
feetx
x
f
VceDisBraking 75
4.030
3030
30tan
2
Stopping Sight Distance = Reaction distance + Braking Distance
= 132.3 + 75 = 207.3 feet
which may be round of f to 200 ft.
Solution
(b) Design Speed, V =30 mph
Difference in speed, m = 10 mph
Rate of acceleration, a =2.5 mph
V m = 30 10 = 20 mph
Assume the perception time, t0 = 2 seconds
d1= 1.47 (30 -10) x2 =58.8 feet
Spacing between the vehicles S = 20 + (V m )
=20 + 20 = 40 feet
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Time of overtake, t =5.2
73.2 S
=
5.2
4073.2 x=6.6 second
d2 =1.47 (V- m) x t + 2.5
=1.47 (30 10 ) x 6.6 + 2 x 40
=270 feet
d3 =1.47 x V x t =286 ft
Passing sight distance = d1 + d2 +d3
=58.8 + 270 + 286
=614.8 ft, say 600 feet
21. (a) Calculate the stopping sight distance for a road for which the design speed is 30
mph. the coefficient of friction between the road surface and tires may be taken as 0.4
and the reaction time of the driver may be assumed as 3 seconds. The road way is leveland the brake efficiency is 40%.
f
VdascedisBrakingtheGiven
30tan 2
where, d = breaking distance in feet
v = speed of vehicle in m.p.h.
f = coefficient of friction
(b) Calculate the non-passing sight distance required on a highway with a design speed
of 60 mph, assume f = 0.42. Also assume reasonable values for other items involve in
calculation.
Solution (a)
Design speed V = 30 mph
Coefficient of friction f = 0.4
Reaction time t = 3 seconds
Then Reaction distance = 1.47 Vt
= 1.47 x 30 x 3 = 132.30 ft
Feetx
x
f
VceDisBraking 75
4.030
3030
30tan
2
Stopping Sight Distance = Reaction distance + Braking Distance= 132.3 + 75 = 207.3 feet
which may be round of f to 200 ft.
Solution
Design speed V = 60 mph
Coefficient of friction f = 0.42
Reaction time t = 2 seconds
Road is level
Then Reaction distance = 1.47 Vt
= 1.47 x 60 x 2 = 176.4 ft
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feetx
x
f
VceDisBraking 71.285
42.030
6060
30tan
2
Stopping Sight Distance = Reaction distance + Braking Distance
= 176.4 + 285.71 = 462.11 feet
22. (a) Determine the minimum non-passing sight distance that should be provided for a
vehicle coming down a 6% gradient. Give the following data.
Design speed V = 35 mph
sV
driveroftimeaction sec35
140Re
Coefficient of friction between type road surface = 0.5
(b) Cuts of a two lane highway have a back slope of 1:2 (1 horizontal: 2 vertical) and the
grade line is level. Calculate the distance required between the centre of the road and the toe
of the cut slope to satisfy the horizontal sight distance on a circular curve of radius of 1910
feet. The eye is assumed to be 4.5 ft above the road surface and the object is also 4.5 ft high.
Assume- Design speed of the road = 40 mph
- Reaction time of driver = 2 seconds.
- The coefficient of friction of the road = 0.6 with the safety factor of 2.0
- Horizontal and curve length are the same.
Solution (a)
Design speed V = 35 mph
Coefficient of friction f = 0.5
Reaction time of driver =
V
35
140secs
=3535
140
= 2 secs
Gradient downhill G = 6 %
Reaction distance = 1.47Vt
=1.47x35x2 = 102.9 ft
The Braking distance =)(30
2
Gf
V
,using negative sign in the formula since the gradient is
downhill
= )06.05.0(30
352
=92.8 ft
Non-passing sight distance =102.9+92.8 = 195.7 ft adopt: 200feet
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Solution (b)
Radius of circular curve = 1910 ft
Design speed = 40mph
required horizontal sight distance on horizontal curve = SH = 2 2)(2)5( mRR
-However, safe stopping sight distance =SH =reaction distance +braking distance
=1.47vt +f
v
30
2x S.F
= 1.47 x 40 x 2.0 +6030
2)40(
xx2.0
=295.38 ft
-But, SH = 2 2)(2)5( MRR
-Taking square on both sides, SH2 = 4[(R-5)2 (R-m) 2]
SH2 =4[(1910-5)2-(1910-m) 2]
4
2SH
= (1905)2-(1910-m) 2
(910-m)2= (1905)2-4
)38.295( 2
1910- m = 1899.27~ 1900
m = 10 ft
Minimum distance required between the centre line of the road and the toe of the cutsiope is 7.75 feet.
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.
23.(a) A jeep is catching up a slow moving truck a two lane highway on which the
design speed is 40mph, the jeep is traveling at the design speed and the distancebetween the jeep and truck is 12 feet. The driver of the jeep saw the slow moving
truck suddenly brakes to a stop. Jeep driver is so alert that his reaction time is 2.5
sec. If the braking distance of the truck is 120 feet. Will the jeep be able to stop in
time without colliding the truck? Use coefficient of friction of 0.6. Assume the road is
level.
(b) A deer is running across the level road and a driver did his best to avoid hitting
this deer by attempting to stop his car. However, during the braking, his car slided
from the concrete pavement to the gravel shoulder but finally came to a halt safely.
If the traveling speed of this car is 100 kph and coefficient of friction on the concrete
pavement is 0.252, then what should be the coefficient of friction on the gravel
shoulder?Assuming that the lengths of skid marks on concrete pavement and gravel shoulder
are 100m. and 50m., respectively. Reaction time is 0.5sec.
Solution (a)
Stopping sight distance of the jeep = reaction distance+ braking distance
f
VV
3047.1
2
Design speed, V= 40 mph
Reaction time, t = 2.5 secCoefficient of friction, f = 0.6
ftx
xxcedissighStopping 2366.030
)40(5.24047.1tan
2
Available length between the jeep and truck = 120 +120 =240 ft> 236 ft
Therefore the jeep will be able to stop in time without colliding with the truck.
Solution (b)
Level road, G = 0 %
V = 100 kph
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Lengths of skid marks on concrete pavement = 100 m
Lengths of skid marks on gravel shoulder =50 m
t = 0.5 sec
f for the concrete pavement = 0.252
f for the gravel shoulder = ?
d =f
VV
254
2
2
2
1
100 =252.0254
1002
2
2
x
V
V2 = 60 kph
50 =f
VV
254
2
3
2
2
50 =xf254
060 22
f = 0.283
Therefore friction coeff: for the gravel shoulder, f = 0.283
24.Sketch the longitudinal profile and show the stationing of key points along the roadway.Assume that the side friction is neglected and the super elevation is obtained by
revolving the road surface about the center line or crown. The following data are given:
Design speed V = 40 mph Degree of Curve D = 8 Width of the pavement =b = 24 Amount of normal crown = c = 3 The road is passes through the open flat country, maximum super-elevation
runoff is 1:150
Normal crown ends at station 20+00Solution
Degree of curve, D = 8
Design speed, V = 40 mph
Width of pavement, b = 24 feet
Amount of normal crown, c = 3
ftxbxeelevaitonerofamountTotal
x
xe
RceelevaitonerofRate
DRccurvecirculartheofRadius
212124sup
12
1
25.71615
4075.0
15
75.0sup
25.7168
57305730
22
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In this problem, full super-elevation has to be reached at the start of the circular curve
Rc = Rc, Ls = Le
Finding out the length of the transition curve,
015
sup..
1501.2
1
sup
15025.7168/15
)40(15.3
8
15
4040
150
40
15040
160515.3
3
3
s
s
s
c
s
LUse
givenasrunoffelevationerallowableei
LESrunoffelevationerAvailable
ftx
L
VemphVSince
hourpervehilcesCR
VL
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25.Degree of curve = 8 Design speed, V = 40 mph Width of the pavement, b = 24 Amount of normal crown, c = 3
15
1
,supmax max
eelevationerofrateimumAllowable
Allowable maximum super- elevation runoff 1: x = 1:200Normal crown ends at sta: 20+00. Sketch the longitudinal profile. Assume f is
neglected and full super elevation is obtained by revolving about the centre line
or crown.
Solution
Degree of curve, D = 8
Design speed, V = 40 mph
Width of pavement, b = 24 feet
Amount of normal crown, c = 3
)(
15
1
12
1
25.71615
4075.0
15
75.0sup
25.7168
57305730
22
allowablex
xe
Rc
VeelevaitonerofRate
DRccurvecirculartheofRadius
use max. allowable rate of super elevation =15
1
ft
x
xe
e
VR
e
900
15115
4075.0
15
75.022
In this problem, full super-elevation has to be reached before the start of the circular
curve
c
eCR
VL
315.3
8
15
4040
150
40
150
Vc
'1205.1199008
4015.315.3
33
xx
CRVLc
e
Full super elevation = e x b = ftx 6.12415
1
Super elevation runoff = )(120
1
150
1
120
8.02
1
allowableLe
SE
Use super elevation runoff =200
1
Revised Le=200x0.8=160ft
Finding out the length of spiral curve,Ls
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(a) From the properties of transition curve
LsRc= LeRe
'20125.716
900160
x
R
RLL
c
ee
s
(b) From the consideration of the rate of radial acceleration ,c
ftx
xx
CR
VL
c
s150
25.71615
84015.315.3 33
Use max. Ls = 201ft.
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26.(a) Describe the requirements of the good road drainages system.(b) Describe the causes of change in moisture content.
Solution
(a)Requirements of the good road drainages system
A good drainage system for highways would require:
(i) Sufficiently wide and deep side-ditches to carry away all water that accumulates therein,
to some drainage structure. Water level in these ditches should remain at all times below the
sub grade level.
(ii)Sufficiently wide end deep off-take and outlet ditches to carry the water that is brought tothem.
(iii) Adequate crown along the center-line of the road to drain off quickly the water that falls
on the road-surface without allowing it to percolate.
(iv) All springs and underground sources of water to be tapped and the water drained by sub-
surface drains.
(v) Where the topography is such that the water flows towards the roadway itself, It is
essential to construct intercepting drains parallel to the road but outside the road limit to
intercept water before it reaches the road.
(vi) All drainage structures should be adequately designed to drain off water immediately
without overflowing.
Solution
(b) Causes of Change in Moisture Content
Moisture content of subgrade soil changes due to a number of causes. They can be
enumerated as:
1. Seepage of water into the subgrade from higher ground adjacent to theroad.
2. Rise or fall in the level of the water table.3. Percolation of water into the subgrade through cracks on the road surface
of through previous road surfaces.4. Transfer of moisture to or from lower soil layers by suction.
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5. Transfer of moisture either to or from the soil in the verges as a result ofdifference in moisture content.
6. Transfer of water vapor through the soil.The net result of the change in the moisture contents of the subgrade soil is the
decrease in the stability and consequent settlement of the subgrade, which causes
either total of partial failure of the road structure.At situations where frequent changes in the moisture content of t he soil are
encountered, design of a suitable subsoil drainage system is necessary. For this
purpose, it is essential to know the soil types and thick-nesses of various layers, the
position of water table if it is close to the formation and the position of the seepage
zones.
27. Describe the major causes of erosion and controlling method for a highway
engineer.
Solution
Avery vital problem that confronts a highway engineer is that of erosionoccurring due to the running water. Soils of the type that lack cohesion are most
susceptible to the effects of flowing water. In case the velocity of flow is high, every
soil will get eroded and the problem of the controlling erosion will arise.
The major cause of erosion is the capacity of water to transport fine solid
material in suspension and to roll the bigger solid particles along with it. This capacity
increases with the increase in the velocity of flow. Thus, the solution to control
erosion lies in keeping the velocity of flow within safe limits.
Of special importance to a highway engineer is the problem or erosion of
drainage ditches, side slopes of cuts and fills of shoulders adjacent to the paved
portion of the roadway. Sometimes, the streams cut in on the right of way or even
cross the highway.
There are only two ways of controlling erosion namely the control of the
velocity of flow and the use of non- erodable materials. The first method is cheaper
than the second one, which is mostly employed for the urban roads.
Prevention of erosion of the side slopes in cuts and fills is achieved by
intercepting the water before it flows down these slopes. This will involve the
construction of intercepting drains, spillways and outlet- drain to drain the water into
a natural channel. Where the soil and rainfall characteristics are such that grass or
weeds can be grown to cover the side slopes every effort should be made to cover the
surface with such small plants. The roots of these plants will spread in the soil below
and will hold the particles together. The velocity of flow will also be reduced.To limited extent special types of drainage structures can be constructed to
minimize the stream erosion and thus aid in the control of erosion along a highway. A
drop- inlet type of culvert, for example, has proved very useful in place of an ordinary
culvert, for controlling erosion. The reservoir of still water preserves the slit of fine
material that settles down due to sedimentation and can be taken out from time to
time.
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28. Describe the side ditches, curbs and gutters for surface drainage.
Solution
Side Ditches for Surface Drainage
Side ditches are used along the roadway in cuts and on ground that is fairly level andsometimes adjacent to embankments to prevent road water from flowing over cultivated of
otherwise improved land. These ditches are usually V- shaped or trapezoidal. However, the
trapezoidal ditches have a greater capacity.
One essential requirement of kutcha ditch design is that the safe velocity of flow
should never be exceeded otherwise it may create erosion. And, it is essential to ensure that
the slope of the ditch in the longitudinal direction is sufficient to drain off water quickly,
otherwise it may lead to ineffective arrangement. Side ditches should also be lined if possible
financially.
Curbs and Gutters
Curbs and gutters are essential for the city streets to drain off the storm water quickly and
to maintain the cleanliness required. Usually a kerb and gutter combination is employed for
the purpose. Sometimes, separate kerb and gutters are employed for draining off water from
the city streets. The kerb and gutter combinations are fixed at the edge of the roadway and
gullies are placed at suitable intervals. The water from the gutter flows through the grating
into the gully and is drained off through an outlet pipe to a storm sewer, which takes the
water away to a natural water channel.
29.Describe the intercepting drains, pipe drains, inlets, catch basins and manholes forsurface drainage.
Solution
Intercepting Drains
Intercepting drains are used on natural slopes to prevent erosion of the cut slops in the
hilly areas. They are sometimes also used to relieve the side ditches of greater discharge than
the one for which they are designed. The water from the intercepting drain is carried down to
the side ditch at specified points along spillways.
Pipe Drains
Pipe drains or storm sewers are widely used for removing surface water and are
sometimes desirable for carrying the water along roadways when sufficient widths of right-
of-way are not available for suitable ditch construction. Vitrified clay sewer pipes and
concrete sewer pipes are the most suitable. Sewers properly designed and constructed in brick
masonry are also used for the purpose. In soils where settlement may occur, corrugated metal
pipe is used. All sections of corrugated metal pipe are connected with metallic bands.
Inlets, Catch Basins and Manholes
Inlets are the openings from gutters or ditches into pipe drains or culverts and are of
various types. Along a rural highway, it may simply be a V-shape or straight concrete
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headwall with or without a paved approach. Drop inlets are used where the water has to be
discharged into a drain or a culvert at a lower level.
Catch basins and manholes are usually of circular shape and are generally connected
to the drop inlets of pipe drains. They are spaced 500 to 1000 feet apart depending upon the
individual design requirement and are meant for inspection.
30. Draw the guardrails and median barriers for roadside design.
Solution
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BY
WYTU
ukmaye@gmail.com
01-685277/685266
09-5006311
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