TRANSPORTATION ENGINEERING & SURVEYING · SYLLABUS TRANSPORTATION ENGINEERING Highway Planning :...

TRANSPORTATION

ENGINEERING &

SURVEYING

For CIVIL ENGINEERING

SYLLABUS TRANSPORTATION ENGINEERING

Highway Planning : Geometric design of highways, Testing and specifications of paving materials, Design of flexible and rigid pavements. Traffic Engineering : Traffic characteristics, Theory of traffic flow, Intersection design, Traffic signs and signal design, Highway capacity.

SURVEYING Importance of surveying, principles and classifications, mapping concepts, coordinate system, map projections Measurements of distance and directions, leveling, Theodolite traversing, plane table surveying, errors and adjustments, curves

ANALYSIS OF GATE PAPERS TRANSPORTATION ENGINEERING SURVEYING

Exam Year 1 Mark Ques.

2 Mark Ques. Total

1 Mark Ques.

2 Mark Ques. Total

2003 2 5 12 - - -

2004 3 5 13 - - -

2005 4 5 14 - - -

2006 3 6 15 - 5 10

2007 3 6 15 - 5 10

2008 4 4 12 1 5 11

2009 2 3 8 1 2 5

2010 3 3 9 1 1 3

2011 3 3 9 1 1 3

2012 - - - 1 1 3

2013 3 3 9 1 2 5

2014 Set-1 2 4 10 1 2 5

2014 Set-2 2 5 12 1 2 5

2015 Set-1 2 3 8 2 2 6

2015 Set-2 2 3 8 2 2 6

2016 Set-1 2 2 6 3 1 5

2016 Set-2 2 2 6 3 1 5

2017 4 2 8 1 2 5

TRANSPORTATION ENGINEERING & SURVEYING

Topics Page No

1. GEOMETRIC DESIGN OF HIGHWAYS

1.1 Introduction 01 1.2 Camber or Cross Fall 02 1.3 Width of Carriage Way 04 1.4 Traffic Separators of Median 05 1.5 Sight Distance 05 1.6 Stopping Sight Distance 06 1.7 Horizontal Alignment 08 1.8 Analysis of Superelevation 09 1.9 Guidelines on Superelevation 10 1.10 Extra Widening 11 1.11 Horizontal Transition Curve 12 1.12 Vertical Alignment 12 1.13 Grade Compensation 14 1.14 Valley Curve 15

2. TRAFFIC ENGINEERING

2.1 Traffic Characteristics 17 2.2 Vehicular Characteristics 17 2.3 Braking Characteristics 17 2.4 Traffic Studies 18 2.5 Traffic Volume Study 18 2.6 Presentation of Traffic Volume Data 19 2.7 Speed Studies 20 2.8 Speed and Delay Study 21 2.9 Capacity and Level of Service 15

3. INTRODUCTION TO HIGHWAY

3.1 Development of Highway 29 3.2 Early Development of Highway Planning in India

Jaykar committee 30 3.3 Indian Roads Congress 30 3.4 The Nagpur Plan (1943 - 63) 30

CONTENTS (TRANSPORTATION ENGINEERING)

3.5 The Bombay Plan (1961 - 81) 31 3.6 The Lucknow Plan (1981 - 2001) 32 3.7 Road Patterns 33

4. TRAFFIC SIGNS AND SIGNAL DESIGN

4.1 Traffic Signs 36 4.2 TrafficControl Devices 37 4.3 Traffic Signals 38 4.4 Various Signal Design Method 39 4.5 Webster Method 40 4.6 IRC Method 40

5. INTERSECTION DESIGN

5.1 Types of Intersection 41 5.2 Traffic Rotaries 43 5.3 Advantage and Disadvantage of Rotary 43 5.4 Resign Elements 43

6. HIGHWAY OR PAVING MATERIALS

6.1 Pavement Materials: SOIL 48 6.2 Pavement Materials: Aggregates 51 6.3 Desirable Properties 51 6.4 Aggregate Tests 52 6.5 Bitumen 56 6.6 Testing of Bitumen 57 6.7 Selection of Appropriate Grade of Bitumen 59 6.8 Mix Design Methods 61

7. DESIGN OF PAVEMENT

7.1 Method of Pavement Design 63 7.2 Group Index Method 63 7.3 California Bearing Ratio Method 63 7.4 Triaxial Method 65 7.5 Design of Rigid Pavement 66 7.6 Temperature Stresses 67 7.7 Frictional Stress Less 68 7.8 Dowel Bar (Design) 70

8. GATE QUESTIONS 81

9. ASSIGNMENT QUESTIONS 105

Topics Page No

1. FUNDAMENTALS OF SURVEYING

1.1 Introduction 123 1.2 Plane & Geodetic Surveying 123 1.3 Classification of Surveying based on Purpose 124 1.4 Classification of Survey based on Instruments used 124 1.5 Principles of Surveying 126 1.6 Scale of a Map 126 1.7 Error due to wrong measuring scale 127 1.8 Use of Verniers in Scales 127

2. DIRECTION & DISTANCE MEASUREMENTS

2.1 Introduction 129 2.2 Taps 129 2.3 Accessories for Chaining 130 2.4 Ranging or Ranging Out 131 2.5 Errors in Chaining 131 2.6 Error & Corrections 132 2.7 Tape Corrections 133 2.8 Measurements of Direction Compass Surveying 135 2.9 Compass Traverse 136 2.10 Measurement of Angles 136 2.11 Types of Bearings 137 2.12 Designation of Bearings 138 2.13 Reduced Bearing 139 2.14 Fore Bearing and Back Bearing 139 2.15 Calculation of Included Angles from Bearings 139 2.16 Surveyor’s Compass 140 2.17 Prismatic Compass 141 2.18 Magnetic Declination 142 2.19 Variation in Declination 142

3. THEODOLITE

3.1 Introduction 143 3.2 Classification 143 3.3 Main parts of Vernier Theodolite 143 3.4 Essentials of the Transit Theodlites 144 3.5 Basic Definitions 144 3.6 Temporary Adjustments of a Theodolite 146

CONTENTS (SURVEYING ENGINEERING)

3.7 Measurement of Horizontal Angles 147

4. TRAVERSING

4.1 Introduction 149 4.2 Method of Traversing 149 4.3 Angular Measurements 150 4.4 Consecutive & Independent Co-ordinate 151 4.5 Error of Closure 151 4.6 Relative Error of Closure 152 4.7 Adjustment of Traverse 152 4.8 Gale’s Traverse Table 153 4.9 Omitted Measurements 157

5. LEVELLING

5.1 Introduction 155 5.2 Bench Marks (B.M.) 155 5.3 Different Methods of Leveling 156

6. CONTOURING

6.1 Introduction 160 6.2 Use of Contours 160 6.3 Definition of Contour 160 6.4 Contour Interval 160 6.5 Characteristics of Contour Lines 161 6.6 Typical Land Features and their Contour Forms Slopes 162 6.7 Valley Line and Ridge Line 162

7. TACHEOMETRY

7.1 Introduction 164 7.2 Tacheometer 164 7.3 Stadia Rod 164 7.4 Methods of Tacheometry 164 7.5 Distance and Elevation Formula for Inclined Sights 165 7.6 Advantages and Disadvantages of the Movable-hair Method 166 7.7 Tangential Method of Tacheometry 166

8. PLANE TABLE

8.1 Introduction 168 8.2 Accessories used in Plane Table Surveying 168 8.3 Setting up the Plane Table 170 8.4 Methods of Plane Table Orientation 170 8.5 Methods of Plane Table Surveying 171

9. GATE QUESTIONS 173

10. ASSIGNMENT QUESTIONS 184

TRANSPORTATION ENGINEERING

1.1 INTRODUCTION

A highway has many visible dimensionsboth in the horizontal plane and in thevertical plane. The art of design of thevisible dimensions is known asGeometric Design.

Proper geometric design will help in thereduction of accidents and theirseverity. Therefore, the objective ofgeometric design is the provideoptimum efficiency in traffic operationand maximum safety at reasonable cost.

Highway geometric design coverselements such as design vehicledimensions, user characteristics,terrain, highway classification, designspeed, horizontal curves, verticalcurves, gradient, sight distances, cross-sectional features, junctions,interchange etc.

1.1.1 FACTORS CONTROLLING 1.1.2 GEOMETRIC DESIGN

Geometric design is influenced by a number of factors such as: (a) Road user characteristics (b) Vehicle characteristics (c) Safety requirements (d) Environmental considerations (e) Economy in construction, maintenance

and operation of vehicles (f) Topography (g) Functional classification of roads (h) Traffic volume and composition (i) Design speed

Safety, environmental needs and economy are built into various elements of design. The remaining factors have been discussed as given below.

1.1.2 ROAD USER CHARACTERISTIC

A driver takes a certain amount of timeto respond to a particular trafficsituation. This can be called as reactiontime.

The action of applying break on seeing avehicle or obstruction on the road is notan instantaneous phenomenon. But it isa time-consuming phenomenon basedon the psychological process involved.

We can call these processes asperception, intellection, emotion andvolition (PIEV)

Perception Time is the time requiredfor transmission of the sensationsreceived through eyes, ears and body tothe brain and the spinal chord by thenervous system. After perceptionintellection occurs, that is the formationof new thoughts and ideas. Recalling oldmemories of similar occasion.

Linked with these two stages isemotion, based on the situation, likefear or anger. This has vital influence onthe final message or decision sent bythe brain to the muscle. This actual actof talking a decision to produce action isdone through volition time.

The total time required for PIEV, that is,from the instant the object comes in theline of sight of the driver to the instanthe arrives at a decision, say, to slowdown or to overtake under normalcircumstance is called reaction time.

This could vary from 0.5 second forsimple situations to 3 to 4 seconds forcomplex situation. The reaction time isaffected by the condition of the driver-fatigue, disease, alcohol consumptionetc., his habits, skill, judgment andenvironmental conditions like climate,season, weather, time of duty, altitudeand light.

Driver characteristics that influencesafety are vision and hearing.

1 GEOMETRIC DESIGN OF HIGHWAYS

© Copyright Reserved by Inspiring Creativity & Endeavour Gate Institute. No part of this material should be copied or reproduced without permission. 1

Pedestrian characteristics that influence the design of pedestrian facilities are speed and space occupied. A speed of 1.2 m/sec is commonly taken for design (AASHTO).

1.1.2 TOPOGRAPHY The topography of the land, through which the road passes, also known as the terrain, controls the geometric design. The following terrain types are identified as controls for design in India:

S.No. Terrain Percentage

cross-slope of country

1 Plain 0 to 10 2 Rolling 10 to 25 3 Mountainous 25 to 60 4 Steep Greater than 60

If cross slope is large, increase in radius of curvature of road will lead to increase in construction cost. Hence, design speed is reduced so that radius of curve reduces leading in reduction in cost of construction.

1.1.5 DESIGN SPEED The maximum speed at which vehicles

can continuously travel safety under favorable conditions is known as design speed.

It may also be thought of as the maximum approximate speed that will be adopted by most drivers. Choice of design speed has to be made carefully, so as to match the terrain condition and also to be acceptable to most road users.

It is the basic parameter which determines all other geometric design feature.

1.1.6 CROSS SECTIONAL ELEMENTS The features of the cross-section of the

pavement influences the life of the

pavement as well as the riding comfort and safety. Of these, pavement surface characteristic affect both of these.

Camber, kerbs, and geometry of various cross-sectional elements are important aspects to be considered in this regards.

1.1.7 PAVEMENT SURFACE CHARACTERISTICS For safe and comfortable driving, four aspects of the pavement surface are important: (a) The friction between the wheels and the

pavement surface. (b) Smoothness of the road surface. (c) The light reflection characteristics of

the top pavement surface and (d) Drainage of water.

1.1.8 FRICTION Friction between the wheel and the pavement surface is a crucial factor in the design of horizontal curves and thus the safe operating speed. Further, it also affect the acceleration and deceleration ability of vehicles. Lack of adequate friction can cause skidding or slipping of vehicles. Skidding happens when the path

travelled along the road surface is more than the circumferential movement of the wheels due to friction.

Slip occurs when the wheel revolves more than the corresponding longitudinal movement along the road.

1.1.9 VARIOUS FACTOR THAT EFFECT FRICTION ARE Type of the pavement (like bituminous,

concrete, or gravel), Condition of the pavement (dry or wet,

hot or cold, etc), Condition of the tyre (new or old), and Speed and load of the vehicle.

The frictional force that develops between the wheel and the pavement is the load acting multiplied by a factor called the coefficient of friction and

© Copyright Reserved by Inspiring Creativity & Endeavour Gate Institute. No part of this material should be copied or reproduced without permission.

Geometric Design Of Highways

2

denoted as f. The choice of the value of f is a very complicated issue since it depends on many variables. IRC suggests the coefficient of longitudinal friction as 0.5-0.4 depending on the speed; coefficient of lateral friction as 0.15. The former is useful in sight distance calculation and the letter in horizontal curve design.

1.1.10 UNEVENNESS Unevenness affect the vehicle operating

cost, speed, riding comfort, safety, fuel consumption and wear and tear of tyres.

Unevenness Index is a measure of unevenness which is the cumulative measure of vertical undulation of the pavement surface recorded per unit horizontal length of the road.

An unevenness index value less than 1500 mm/km is considered as good, a value less than 2500 mm/km is satisfactory up to speed of 100 kmph and values greater than 3200 mm/km is considered as uncomfortable even for 55 kmph.

Pavement surface condition is measured by Bump Indicator in terms of unevenness index.

1.1.11 LIGHT REFLECTION White roads have good visibility at

right, but cause glare during day time. Black road has no glare during day, but

has poor visibility at night when the surface is wet.

Concrete roads has better visibility and less glare.

1.1.12 DRAINAGE The pavement surface should be absolutely impermeable to prevent seepage of water into the pavement layers. Further, both the geometry and texture of pavement surface should help in draining out the water from the surface in less time.

1.2 CAMBER OR CROSSFALL Camber or Cant is the cross slope provided to raise middle of the road surface in the transverse direction to drain off rain water from road surface. The objective of providing camber area: Surface protection especially for gravel

and bituminous road Sub-grade protection by proper drainage

Quick drying of pavement which in turn increases safety Too steep slope is undesirable because (a) It will erode the surface. (b) Due to too steep slope, transverse

tilt of vehicles causes uncomfortable side thrust and a drag on the steering of automobiles. Also the thrust on the wheels along the pavement edges is more causing unequal wear of the tyres as well as road surface.

(c) Discomfort causing throw of vehicle when crossing the crown during overtaking operations.

(d) Problems of toppling over of a highly laden bullock carts and trucks.

(e) Tendency of most of the vehicles to travel along the centre line.

1.2.1 SHAPE OF CROSS SLOPE The common types of camber are parabolic, straight, or combination of them



3

Parabolic or elliptic shape is given so that the profile is flat at the middle and steeper towards the edges, which is preferred by fast moving vehicles as they have to frequently cross the crown line during overtaking operation on a two lane highway.

When very flat cross slope is provided as in cement concrete pavements, straight line shape of camber may be provided.

The cross slope for shoulder should be 0.5% steeper than the cross slope of adjoining pavement, subject to a minimum of 3.0%.

1.2.2 PROVIDING CAMBER IN THE FIELD For providing the desired amount and shape of camber, templates or camber boards are preferred with the specified camber. Camber is measured in 1 in n or 1% (Eg., 1 in 50 or 20%) and the value depends on the type of pavement surface. The values suggested by IRC for various categories of pavement is given in table below :

IRC Values for camber Surface type Heavy

rain Light rain

Concrete/Bituminous 2% 1.7% Gravel/WBM 3% 2.5%

Earthen 4% 3.0% 1.2.3 CROSSFALL FOR SHOULDERS The crossfall for each shoulder should

be at least 0.5 per steeper than the slope of the pavement subject to a minimum of 3 percent.

On superelevated sections, shoulders should normally have the same crossfall as the pavement.

Example 1 In a district road where the rainfall is heavy major district road of WBM pavement, 3.8

m wide and a state highway of bituminous concrete pavement, 7.0 m wide are to be constructed. What should be the height of crown with respect to the edges in these two cases. Solution For WBM Road As the rainfall is heavy, provide a camber of 1 in 33.

From Figure

1 h

tanθ3.833

2

∴Rise of camber with respect to edges

3.8 1h 0.058m n50

2 33

Rise of crown with respect to the Edges For Bituminous Concrete Road, Provide a cross fall of 1

h 1tanθ h

7 50

2

13.5 0.07m

50

1.3 WIDTH OF CARRAIGE WAY Width of the carriage way or the width

of the pavement depends on the width of the traffic lane and number of lanes.

Width of a traffic-lane depends on the width of the vehicle and the clearance.

The maximum permissible width of a vehicle is 2.44 and the desirable side clearance for single lane traffic is 0.68 m. The required minimum lane width is 3.75 m for a single lane road & for double lane, however, the side clearance required is about 0.53 m, on either side on 1.06 m in the centre. Therefore a two lane road requires minimum of 3.5 m for each lane. The desirable carriage way which



4

recommended by IRC is given in table below.

1.4 TRAFFIC SEPARATORS OF MEDIAN The main function of traffic separator is to prevent head-on collision between vehicles moving in opposite directions on adjacent lanes The separator may also help to i) Channelize traffic into streams at

intersections ii) Shadow the crossing and turning traffic iii) Segregate slow traffic and to protect

pedestrians. The traffic separators used may be

in the form of pavement markings, physical dividers of area separators.

Area separators used may be medians, dividing island or parkway strips, dividing the two directions of traffic flow.

1.4.1 RIGHT OF WAY Right of way (ROW) or land width is the

width of land acquired for the road, along its alignment.

It should be adequate to accommodate all the cross-sectional elements of the highways and may reasonably provide for further development.

In order to prevent overcrowding and pressure, sufficient space for future road improvement, it is advisable to lay down restrictions on building activity along the roads. Thus, building line represents a line on either side of the road, between which and the road no building activity is permitted at all.

In addition, it will be desirable to exercise control on the nature of building activity for a further distance beyond the building line upto what are known as control lines.

1.5 SIGHT DISTANCE

1.5.1 OVERVIEW The safe and efficient operation of

vehicles on the road depends very much on the visibility of the road ahead of the driver.

Thus, the geometric design of the road should be done such that any obstruction on the road length could be visible to the driver from some distance ahead. This distance is said to be the sight distance.

1.5.2 TYPES OF SIGHT DISTANCE Sight distance available from a point is

the actual distance the road surface, over which a driver from a specified height above the carriage way has visibility or moving objects.

The sight distance situations that are considered for design are :

i) Stopping sight distance (SSD) or the absolute minimum sight distance

ii) Intermediate sight distance (ISD) is defined as twice SSD

iii) Overtaking sight distance (OSD) for safe overtaking operation

iv) Head light sight distance is the distance visible to a driver during night driving under the illumination of head lights.

V) Safe sight distance to enter into an intersection.

The computation of sight distance depends on : (i) Reaction time of driver

Reaction time of a driver is the time taken from the instant the object is visible to the driver to the instant when the brakes are applied. The total reaction time may be split up into four components based on PIEV theory. IRV suggests a total reaction time of 2.5 sec. 2.5 sec. is actually the 90th percentile reaction time.

(ii) Speed of the Vehicle Higher the speed, more time will be required to stop the vehicle. Hence it is evident that, as the speed



5

increases, sight distance also increases.

(iii) Efficiency of Brakes The efficiency of the brakes depends upon the age of the vehicle, vehicle characteristics etc. If the brake efficiency is 100%, the vehicle will stop the moment the brakes are applied. But practically, it is not possible to achieve 100% brake efficiency. Therefore, the sight distance required will be more, when the efficiency of brakes are less. Also for safe geometric design, we assume that the vehicles have only 50% brake efficiency. 1. Frictional Resistance between

the tyre and the roadWhen the frictional resistance is more, the vehicle stop immediately. Thus sight required will be less. No separate provision for brake efficiency is provided while computing the sight distance. This is taken into account along with the factor of longitudinal friction. IRC has specified the value of longitudinal fraction in between 0.35 to 0.4.

IV) Gradient of the road While climbing up a gradient, the vehicle can stop immediately. Therefore, sight distance required is less. While descending a gradient, gravity also comes into action and more time will be required to stop the vehicle. Sight distance required will more in this case.

1.6 STOPPING SIGHT DISTANCE Stopping sight distance (SSD) is the

minimum sight distance available on a highway at any spot having sufficient length to enable the driver to stop a vehicle travelling at design, safety without collision with any other obstruction.

The stopping sight distance is the sum of lag distance and the braking distance.

Lag distance is the distance the vehicle travelled during the reaction time t and is given by vt, where v is the velocity in m/sec2.

Braking distance is the distance travelled by the vehicle during braking operation.

For a level road this is obtained by equating the work done in stopping the vehicle and the kinetic energy of the vehicle.

If F is the maximum frictional force developed and the braking distance is l, then work done against friction in stopping the vehicle is Fl = fWl where W is the total weight of the vehicle. The kinetic energy at the design speed is

2 2 221 1 Wv Wv v

mv ;fwl l2 2 g 2g 2gf

Therefore, the SSD = lag distance + braking distance and given by

2vSSD vt

2gf

Where v is the design speed in m/sec2, t is the reaction time in sec, g is the acceleration due to gravity and f is the coefficient of friction. The coefficient of friction f is given below for variation design speed Coefficient of longitudinal friction

Speed, ,kmph

<30 40 50 60 >80

F 0.40 0.38 0.37 0.36 0.35

When there is an ascending gradient of say +n%, the component of gravity adds to braking action and hence braking distance is decreased. The component of gravity acting parallel to the surface which adds to the braking force is equal to Wsinθ≈tanθ ≈ Wn/100.

Case I: When vehicle is moving up the grade.



6

Equating kinetic energy and work done. 2Wn Wv

fw l100 2g

2vl

n2g f

100

Case II: When vehicle is moving down the grade.

2vSSD vt

2g f 0.01n

Therefore the general equation is given by equation

2vSSD vt

2g f 0.01n

Effect for grade should not be considered for undivided highway for two way traffic but must be considered for divided highway.

On roads with restricted width or single lane road when two-way movement of traffic is permitted, the minimum stopping sight distance should be equal to TWICE the minimum stopping distance to enable both vehicle coming from opposite directions.

SSD on vertical curves should be the length which a driver from a height of 1.2 m have visibility of an obstruction of height 0.15 m.

When the stopping sight distance for

the design speed is not available on any section of a road, the speed should be restricted by a warning sign and a suitable speed-limit regulation sign. Design speed

Safe stopping sight distance for design, m

20 20 25 25 30 30 40 45 50 60 60 80 65 90 80 120 100 180

1.6.1 OVERTAKING SIGHT DISTANCE (OSD) The minimum distance open the vision of the driver of a vehicle intending to overtake slow vehicle a head with safety against the traffic of opposite direction is known as minimum overtaking sight distance.

A = over taking vehicle travelling at design speed B = Slow vehicle on a two-lane road with two way traffic C = Third vehicle come from the opposite direction The overtaking manoeuvre is split into three parts d1, d2, d3. d1 is the distance travelled by overtaking vehicle a during the reaction time + sec of the driver from position A1 to A2. d2 is the distance travelled by vehicle A from A2 to A3 during T sec d3 is the distance travelled by on-coming vehicle C from C1 to C2.



7

OSD = d1 + d2 + d3m for two way traffic. OSD = d1 + d2m one way traffic

1 b bd v t v t 2S vt

vb = Speed of slow moving vehicle m/sec. v = Speed of overtaking vehicle m/sec. S = Spacing of vehicles m A = acceleration m/sec2. If vb is not given than vb = (v - 4.5)m/sec

1.6.2 SIGHT DISTANCE AT INTERSECTIONS

At intersection where two or more roads meet, visibility should be provided for the drivers approaching the intersection from either sides. Driver should be able to perceive a hazard and stop the vehicle if required. Stopping sight distance for each road can be computer from the design speed. The sight distance should be provided such that the drivers on either side should be able to see each other. This is illustrated in the figure below.

1.7 HORIZONTAL ALIGNMENT

1.7.1 OVERVIEW Horizontal alignment is one of the most important features influencing the efficiency and safety of a highway. A poor design will result in lower speeds and resultant in highway performance in terms of safety and comfort. In addition, it may increase the cost of vehicle operations and lower the highway capacity. The horizontal alignment design elements include radius of circular curve, design of superelevation, extra widening at horizontal curves, design of transition curve, and set back distance. 1.7.2 DESIGN SPEED

The design speed is the single most important factor in the design of horizontal alignment. The design speed depends on the type of the road, type of terrain. Indian road congress (IRC) has classified the terrains into four categories, namely plain, rolling mountains, and steep based on the cross slope. The recommended design speed for various terrains and type of roads are given in table below.

Terrain classification Terrain Classification

Cross Slope (%)

Plain 0-10 Rolling 10-25 Mountainous 25-60 Steep >60

Design Speed in km/hr as per IRC (rulling and minimum)

1.7.3 HORIZONTAL CURVE The presence of horizontal curve imparts centrifugal force which is a reactive force acting outward on a vehicle negotiating it. Centrifugal force depends on speed and radius of the horizontal curve and is counteracted to a certain extent by transverse friction between the tyre and pavement surface.

On a curved road, this force tends to

cause the vehicle to overrun or to side outward from the centre of road curvature. For proper design of the curve, and understanding of the forces acting on a vehicle taking a horizontal



8

curve is necessary. Various forces acting on the vehicle are illustrated in the figure below. These are the centrifugal force (P) acting outward, weight of the vehicle (W) acting downward and the reaction of the ground on the wheels (RA and RB). The centrifugal force and the weight is assumed to be from the centre of gravity which is at h units above the ground. Let the wheel base be assumed to be units. The centrifugal force P is given by

2WvP

gR ....(i)

where W is the weight of the vehicle, v is the speed of the vehicle, g is the acceleration due to gravity and R is the radius of the curve.

The centrifugal ratio or the impact

factor P

W is given by:

2P v

W gR ….(ii)

The centrifugal force has two effects.: A tendency to overturn the vehicle about the outer wheels and a tendency for transverse skidding. Taking moments of the force with respect to the outer wheel the vehicle is just about to overturn (under this condition, reactor at inner wheel will be zero).

b P bPh W or

2 W 2H

At the equilibrium, overturning is possible when

2v b

gR 2H

And for safety the following condition must satisfy

WbPh

2

P b

W 2h

2 2v b b vor

gR 2H 2H gR

(for no overturning) …………(iii)

The second tendency of the vehicle is for transverse skidding. i.e., when the centrifugal force P is greater than the maximum possible transverse skid resistance due to friction between the pavement surface and tyre. The maximum skid resistance (F) is given by: F = FA + FB = f(RA + RB) = fW where FA and FB is the frictional force at tyre A and B, RA and RB is the reaction at tyre A and B, f is the lateral coefficient of friction and W is the weight of the vehicle. This is counteracted by the centrifugal force (P), and equating:

PP fW or f

W

At equilibrium, when skidding takes place [from equation (ii)]

2P vf

W gR

and for safety the following condition must satisfy: P fW P

fW

2vf

gR

2vf

gR

(for no skidding) …(iv) Equation (iii) and (iv) gives the stable condition for design. If equation (iii) is violated, the vehicle will overturn at the horizontal curve and if equation (iv) is violated, the vehicle will skid at the horizontal curve. For no sliding & no overturning P b

fW 2h

1.8 ANALYSIS OF SUPERELEVATION Super-elevation or cant or banking is

the transverse slope provide at



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Topics Page No

1. HIGHWAY GEOMETRIC DESIGN & PLANNING 82

2. TRAFFIC ENGINEERING 88

3. HIGHWAY MATERIALS 94

4. PAVEMENT DESIGN 99

5. HIGHWAY MAINTAINANCE 104

GATE QUESTIONS

81

Q.1 Width of carriage way for a single lane is recommended to be a) 7.5 m b) 7.0 mc) 3.75 m d) 5.5 m

[GATE-2000]

Q.2 Stopping sight distance is the minimum distance available on a highway which is the a) distance of sufficient length to stop the

vehicle without collision.b) distance visible to a driver

during night driving.c) height of the object above the road

surface.d) distance equal to the height of the

driver’s eye above the road surface. [GATE-2000]

Q.3 The ruling minimum radius of horizontal highway curve of a national highway in plain terrain for a ruling design speed of 100 km/hour with e = 0.07 and f = 0.15 is close to a) 250 m b) 360 mc) 36 m d) 300 m

[GATE-2000]

Q.4 Design rate of super elevation for horizontal highway curve of radius 450 m for a mixed traffic condition, having a speed of 125 km/hour is a) 1.0 b) 0.05c) 0.07 d) 0.154

[GATE-2000]

Q.5 The design value of lateral friction coefficient on highway is a) 1.5 b) 0.50c) 0.35 d) 0.15

[GATE-2001]

Q.6 A car is moving at a speed of 72 kmph on a road having 2% upward gradient. If the reaction time of the driver is 1.5 seconds, assuming that f = 0.15, calculate the distance moved by the vehicle before the car stops finally a) 24 m b) 150mc) 1056 m d) 324 m

[GATE-2002]

Q.7 The start and grid pattern of road network as adopted in

a) Nagpur road planb) Lucknow road plan

c) Bombay pland) Delhi road plan

[GATE-2004]

Q.8 The co-efficient of friction in the longitudinal direction of a highway is estimated as 0.396. The braking distance for a car moving at a speed of 65km/hr is a) 87 m b) 45 mc) 42 m d) 40 m

[GATE-2004]

Q.9 For a road with camber of 3% and the design speed of 80 km/hr, the minimum radius of the curve beyond which NO super elevation is needed is a) 1680 m b) 948 mc) 406 m d) 280 m

[GATE-2004]

Q.10 A road is having a horizontal curve of 400 m radius on which a super elevation of 0.07 is provided. The coefficient at lateral friction mobilized on the curve when a vehicle is travelling at 100 kmph is a) 0.007 b) 0.13c) 0.15 d) 0.4

[GATE-2005]

1 HIGHWAY GEOMETRIC DESIGN & PLANNING


Q.1 (c) Single lane road width is 3.75m.

Q.2 (a) Stopping sight distance is the distance ahead of driver to avoid collision.

Q.3 (b) Design speed, = 100 ×0.28 = 28 m/s Radius of curve , R = ?

e + f = 2

gR

0.07 + 0.15 =

228

9.8R

R = 363 m 360 m

Q.4 (d) Radius of curve, R = 450m Design speed = 125 kmph = 34.7 m/s

e =

20.75

gR

e =

20.75 34.7

9.81 450

= 0.154

Q.5 (d) As per 1RC coefficient of lateral friction is 0.15.

Q.6 (b)

SSD = 2

tN

2g f100

= 0.278 ×72 × 1.5 + 2(0.278 72)

219.62 0.15

100

= 30 + 120 = 150m

Q.7 (a)

Q.8 (c) f = 0.396 Breaking distance

2

bS2gf

= 2(65 5 /18)

2 9.81 0.396

41.95 42bS m m

Q.9 (b) C = 3% 9 = 80×5/18 = 22.22mps Camber acts like super elevation

e + f = 2(0.759)

gR

use f = 0

0.03 = 2

0.75 22.22

9.81 R

R = 948 m

Q.10 (b)

e + f = 2( )v

gR

0.07 + f =

20.278 100

9.81 400

f = 0.13

Q.11 (d) Length of summit curve depends upon: a) SSD for single lane two way

highwayb) OSD for two lane two way

highway

Q.12 (b) PMGSY is completed in the year of 2007

Q.13 (b)

EXPLANATIONS


Q.1 The length of national highways as per 3rd 20 year (Lucknow) road plan is given by a) area of the country/75b) area of the country/50c) area of the country/40d) area of the country/25

Q.2 In 1927, Jayakar committee was set up to examine and report on road development in india, based on which certain institutions were subsequently set up. Which of the following were the direct outcome of Jayakar committee recommendations. 1. Indian Road Congress2. Central Road Fund3. CRRI4. National Highway Acta) 1, 2 and 3 b) 2, 3 and 4c) 1, 3 and 4 d) all the above

Q.3 Consider: 1. Creation of Central Road Fund2. National Highway Act3. Formation of Indian Road

Congress4. Creation of Highway Research

BoardThe correct chronological order of these events is a) 4, 3, 2, 1 b) 2, 1, 3, 4c) 1, 3, 2, 4 d) 2, 3, 1, 4

Q.4 The semiofficial body set up for controlling and standardization of roads and bridges in India is a) Highway researchb) National Highways Act Committeec) Central Road Fundd) Indian Road congress

Q.5 Nagpur road plan has recommended the use of road pattern type of

a) star and pattern type ofb) star and block patternc) star and grid patternd) star and hexagonal pattern

Q.6 Select the correct statement. a) Nagpur road plan formulae take

into account the towns with verylarge population

b) Nagpur road plan has a targetroad length of 32 km per 100square km

c) Second 20 year plan hasprovided 1600 km of expressways out of the proposedNational highway

d) Second 20 year plan alloweddeduction length of railway trackin the area while calculating thelength of roads

Q.7 The shape of the camber, best suited for cement concrete pavements, is a) Straight lineb) Parabolicc) Ellipticald) Combination of straight and

parabolic

Q.8 For water bound macadam roads in localities of heavy rainfall, the recommended Value of camber is a) 1 in 30 b) 1 in 33c) 1 in 48 d) 1 in 60

Q.9 When the path travelled along the road surface is more than the circumferential Movement of the wheels due to rotation, then it results in a) slipping b) skiddingc) turning d) revolving

Q.10 Coefficient of friction is less when the pavement surface is

ASSIGNMENT QUESTIONS


a) rough b) dry

c) smooth and dry d) smooth and wet Q.11 Compared to a level surface, on a

descending gradient the stopping sight distance is

a) less b) more c) same d) dependent on the speed Q.12 The desirable length of overtaking

zone as per IRC recommendation is equal to a) overtaking sight distance b) two times the overtaking sight

distance c) three times the overtaking sight

distance d) five times the overtaking sight

distance Q.13 If the stopping distance is 60 metres,

then the minimum stopping sight distance for two lane, two way traffic is

a) 30 m b) 60 m c) 120 m d) 180 m Q.14 The ruling design speed on a

National Highway in plain terrain as per IRC recommendation is

a) 60 kmph b) 80 kmph c) 100 kmph d) 120 kmph Q.15 The equilibrium super elevation required to

counteract the centrifugal force fully is given by

a) 2V

27.5R b)

2V

75R

c)

20.75V

127R d)

2V

127R

Q.16 The attainment of super elevation by

rotation of pavement about the inner edge the pavement

a) is preferable in steep terrain b) results in balancing the earthwork c) avoids the drainage problem in

flat terrain d) does not change the vertical

alignment of road

Q.17 The mechanical extra widening required for 10.5 m wide pavement on a horizontal curve of radius R metre is given by

a) 2

2R

l b)

22

2R

l

c) 2

R

l d)

23

2R

l

Q.18 The maximum design gradient for vertical profile of a road is

a) ruling gradient b) limiting gradient c) exceptional gradient d) minimum gradient

Q.19 The maximum width of a vehicle as recommended by IRC is

a) 1.85 m b) 2.44 m c) 3.81 m d) 4.72 m

Q.20 Transition curve is provided in horizontal alignment a) to increase the radius of

curvature b) to facilitate the application of

super elevation c) to counteract the centrifugal

force developed d) to prevent vehicles from

skidding late rally

Q.21 The off-tracking of a vehicle having a wheel base of 6.0 m and negotiating a curved path of mean radius 25 m is

a) 0.82 m b) 0.72 m c) 0.65 m d) 1.44 m Q.22 The important factor considered in

the design of submit curves on highways is


Assignment Questions

106

Q. 1 i) Length of National Highways (NH) = Area of the country/50

ii) Length of State Highways (SH)= Area of the state/25= 62.5 number of towns in thestate – area of the state/50

iii) Length of the major DistrictRoads (MDR)= Area of the state/12.5= 90 number of towns in thestate

iv) Total length of all categories ofroads in a district i.e.NH + SH + MDR + ODR + VR= Area of District 0.82

Q. 2 (a)

Q. 3 (c)

Q. 4 (d)

Q. 5 (c)

Q. 6 (c)

Q. 7 The camber is given a parabolic, elliptic or straight line shape in the cross-section. Parabolic or elliptic shape is given so that the profile is flat at the middle and steeper towards the edges, which is preferred by fast moving vehicles. When very flat cross slope is provided as in cement concrete pavements, straight line shape of camber may be provided.

Q. 8 (b)

Q. 9 Skid occurs when vehicles slide without revolving i.e., when the path travelled along the road surface is more than the circumferential movements of the wheels due to

their rotation. Slip occurs when a wheel revolves more than the corresponding longitudinal movement along the roads.

Q. 10 The coefficient of friction reduces considerably when the pavement surface is smooth or wet. The coefficient or friction also decreases slightly with increase in temperature, tyre pressure and load. But on wet pavements new tyres with good treads give higher friction factors than worn out tyres.

Q. 11 When there is a descending gradient the components of gravity is subtracted from the braking distance and hence the stopping sight distance is more.

Q. 12 The minimum length of overtaking zone should be three times the safe overtaking distance i.e., 3(d1 + d2) for one-way roads and 3(d1 + d2 + d3) for two-way roads. It is desirable that the length of overtaking zone is kept five times the overtaking Sight distance.

Q. 13 The minimum stopping sight distance should be equal to the stopping distance in one-way traffic lanes and also in two-way traffic roads when there are two or more traffic lanes.

Q. 14 (c)

Q. 15 As we know, 2V

e fgR

e = rate of superelevation f = lateral friction coefficient = 0.15 V = speed of vehicle, m/s

EXPLANATIONS


R = radius or horizontal curve, m g = acceleration due to gravity = 9.8 m/s2 If speed of vehicle is represented as V kmph then

2 2(0.278V) V

e f9.8R 127R

If f = 0, the equilibrium super elevation required to counteract the centrifugal force fully will be given by

2Ve

127R

Q. 16 The method of rotating about inner

edge is preferable in flat terrain in high rain fall area, when the road is not taken on embarkment, in order to avoid the drainage problem.

Q. 17 Mechanical widening 2nl

2R

Where, n = no. of lanes For 10.5 m wide pavement n = 3

2

m

3lW

2R

Q. 18 Ruling gradient is the maximum

gradient within, which the designer attempts to design the vertical profile of a road.

Q. 19 (b) Q. 20 (b)

Q. 21 Off-tracking 2 26

2 2 25

l

R

= 0.72 m Q. 22 When a fast moving vehicle travels

along a submit curve, the centrifugal force will act upwards, against gravity and hence a part of the pressure on the tyres and spring of the vehicle suspensions in relieved. So there is no problem of discomfort

to passengers on submit curves, particularly because the deviation angles on roads are quite small. The only problem is designing submit curves is to provide adequate sight distance or the abQ.ute minimum sight distance should invariably be provided at all sections of the road system and so also on submit curves.

Q. 23 Circular submit curve is ideal as the

sight distance available throughout the length of circular curve is constant.

Q. 24 (b)

Q. 25 (b)

Q. 26 (c)

Q. 27 1 1 1

50 30

N

30 50

50 30

1

75N

Q. 28 (a)

Q. 29 (d)

Q. 30 (b)

Q. 31 (b)

Q. 32 (b)

Q. 33 If the pavement is kept horizontal across the alignment, the pressure on the outer wheels will be higher due to the centrifugal force acting outwards and hence the reaction RB at the outer wheel would be higher. When the limiting equilibrium condition for overturning occurs the pressure at the inner wheels



116

SURVEYING

122

1.1 INTRODUCTION

Surveying may be defined as themethod of making measurements of therelative of the relative positions of,natural & man – made features n earth’ssurface and the presentation of thisinformation either graphically ornumerically.

The commonest methods ofpresentation are by means of a Plan orMap.

Both Plans and Maps are the graphicalrepresentations of the features on ahorizontal plane.

Plan is a large scale representationwhereas Map is a small scalerepresentation.

Height information can be added eitheras spot heights, which are individualheights of points, or as contours whichgive a less detailed but better visualrepresentation of the area.

1.2 PLANE & GEODETIC SURVEYING

Surveying is divided primarily intoGeodetic surveying & Planesurveying.

In Geodetic surveying, large areas ofearth’s surface are involved and thecurvature of earth is taken intoaccount.

In Plane surveying, relatively smallareas are under consideration, and it isassumed that the earth’s surface is flat.

In Plane surveying, measurementsplotted will represent the projection onthe horizontal plane of the actual fieldmeasurements.

For example, AB is plotted as AB’

A horizontal plane is normal to thedirection of gravity (as defined by a

plumb bob at that point).

However, such a plane will infact betangential to the earth’s surface atthat point.Thus, if a large area is considered, thediscrepancy will become apparentbetween the area of the horizontalplane and the actual curved area of theearth’s surface.

In the above figure if actual area is ABC,the projected area will become A’B’C’.Note: That Arc AC will be projected asChord A’C’ represented by dotted line. IfArc AB = 18.5 km then Chord A’B’ willbe 1.52 cm shorter than Arc AB.

Length AB, BC & CA in Geodeticsurveying are determined usingspherical trigonometry, whereaslengths A’B’, B’C’ & C’A’ are determinedin plane surveying using planetrigonometry.

For Survey up to 195.5 km2 in area, thisdiscrepancy is not serious and thereforeplane surveying will be adequate.However precautions are requiredwhen connecting such survey to controlpoints established and co – ordinate bygeodetic surveys.

1 FUNDAMENTALS OF SURVEYING


Plane surveys are done for engineering projects such as factories, bridges, dams, location & construction of canals, highways, railways etc.

Geodetic surveying is done for fixing widely spaced control point, which may afterwards be used necessary control points for fixing minor control points for plane survey.

Geodetic survey is carried out by Department of National Survey of India. Note: Control points are points of known co – ordinates. It is used as a reference for taking other measurements during surveying.

1.3 CLASSIFICATION OF SURVEYING BASED ON PURPOSE

Based on the purpose the surveys can be classified as under. 1. Topographical Survey

It is a survey conducted to obtain data and to make a map indicating inequalities of land surface by measuring elevations and locating the natural and artificial features of the earth, e.g. rivers, woods, hills, etc. There scales ranges from 1 : 25000 to 1 : 1000000.

2. Engineering Survey These are survey work required before,

during and after any engineering works. Before any work is started, large-scale

topographical maps or plans are required as a basis for design.

It is especially used for the design and construction of new routes, e.g. roads and railways.

It is also used to calculate the areas and volumes of land and data for setting out curves for route alignment. Typical scales are as follows :

Building work Site plans, Civil engineering works :

Town surveys, Highway surveys :

3. Cadastral Survey These are undertaken to produce plans of property boundaries for legal purposes. These are also known as public land survey. Scales are 1 : 1000 to 1 : 5000.

4. Hydrographic Survey These surveys are conducted on or near

the water body, such as lakes, rivers, bays, harbours. Marine surveys are special type of hydrographic surveys, covers a broader area near sea for offshore structures, navigations, tides, etc.

The hydrographic survey consists of locating shore lines, water flow estimation, and determination of the shape of area under the water surface, determination of channel depth, location of locks, sand bars, buoys, etc.

5. Astronomic Survey These surveys are conducted for

determinations of latitudes, azimuths, local time, etc. at various places on the earth by observing heavenly bodies (the sun or stars).

6. Geological Survey These surveys are conducted to obtain

information about different strata of the earth’s surface for the purpose geological studies. Geological maps are prepared depicting the details of the strata.

1.4 CLASSIFICATION OF SURVEY BASED ON INSTRUMENTS USED Based on the instruments used, the surveys can be classified as under : 1. Chain Surveying

It is the simplest type of surveying in which only linear measurements are taken either with a chain or a tape.


Fundamentals Of Surveying

124

Note: Angular measurements are not taken in chain surveying.

2. Compass Surveying In compass surveying, horizontal angles are measured with the help of a magnetic compass, in addition to these linear measurements taken with chain or tape.

Although a magnetic compass is not a precise angle- measuring instrument, hence the compass survey is not very accurate. However, it is more accurate than a chain survey.

3. Leveling In this type of survey a leveling

instrument is used for determination of relative elevations (levels) of various points in the vertical plane.

4. Plane Table Surveys In this type of survey, a map (or plan) is prepared in the field while viewing the terrain after determining the directions of various lines and measuring the linear distances with a chain or a tape.

The accuracy of the plane table survey is low. Its main advantage is that measurements and plotting are done simultaneously in the field.

5. Theodolite Surveys It’s this type of survey horizontal and

vertical angles are measured with the help of theodolite. A theodolite is a very precise instrument used for measuring horizontal and vertical angles.

The theodolite surveys can be broadly classified into two types: (i) Traverse survey (ii) Triangulation survey

In traverse survey, the various stations form a polygon. The horizontal angles are measured with the help of a theodolite, whereas the linear measurements are made with a tape.

In triangulation survey, the lines form a system of triangles. The base line is measured accurately and the lengths of

all other lines are computed from the measured angles.

Triangulation is used for establishing control points over extensive areas. Note: Theodolite surveys are quite accurate.

6. Tachometric Surveys In this type of survey a special type of

theodolite called as Tachometer is used, which is fitted with a stadia diaphragm having two horizontal cross hairs in addition t the central horizontal hair.

In tachometric surveying, horizontal angles, horizontal distances and vertical distances (elevation) are measured with tachometer.

Although tachometric surveys are not very accurate in plane areas, but these are extremely convenient and gives better result than the theodolite surveys in rough terrain.

7. Photogrammetric Surveys Photogrammetry is the science of taking

measurements with the help of photographs.

Photogrammetry surveys are generally used for Topographic mapping of large areas.

These are extremely useful for obtaining Topographical details of areas which are difficult to access.

Photographs are generally taken from an aeroplane. However, for certain areas where suitable sites exist, photographs can be taken from ground-based cameras.

8. EDM Surveys Trilateration is a type of triangulation in

which all the three sides of each triangle are measured accurately with the help EDM instruments.

Then angles are computed indirectly form the known sides of the triangles.

Hence all the sides and angles are determined.



125

1.5 PRINCIPLES OF SURVEYING

There are two basic principles of surveying. 1. Work from whole to part. 2. Locate a point by at least two

measurements.

1. Work from Whole to Part The main idea of working from whole to

part is to localize the errors and prevent their accumulation.

The survey area is covered with the simplest possible frame-work of high-quality measurements. If the rest of the survey work is carried out within this area, the possible accumulation of error can be contained.

If we work from part to whole, the errors accumulate and expand to a greater magnitude in the process of expansion of survey.

2. Locate a Point by at Least Two Measurements

Two control points A & B (any two important features) are selected in the area and the distance between them is measured accurately. Line AB is called baseline.

If A and B be the two control points, whose positions are already known on the plan, the position of C can be plotted by any of the following methods.

1.6 SCALE OF A MAP

Scale of a map or plane represents the ratio of a line on the map (or plan) to the length of the same line on ground.

A scale may be represented numerically by Engineer’s scale or Representative Fraction.

The Engineer’s scale is represented by a statement, e.g. 1 cm = 40 m.

When a scale is represented as a fraction, it is called as Representative Fraction. Engineer’s scale 1 cm = 40 m

Representative Fraction (R.F) = 1

4000

Note:1

1000 scale is larger scale than

1

10000 scale

Scale can also be graphically represented by drawing a line on map and marking the ground distance directly on it.

The graphical scales have the

advantages over the numerical scales that the distances on the maps can be determined by actual scaling even when the map has shrunk. In the case of shrinking of map, the graphical scale also changes with the map, and, therefore, the ratio is unaffected.

If x mm on map = 100m on ground, then

length of line AB will be 400m. If now the map shrinks such that 100m

is represented by y mm on map, then again the distance A’B’ measured on



126

map, with the help of scale on map, will be 400 m. This is the advantage of graphical scale

Shrunk scale =y

100×1000

Original scale =x

100×1000

yS

= =x

hrunk length Shrunk scale

Original length Original scale

The ratio of shrunk length to the actualis known as Shrinkage Ratio (SR), orShrinkage Factor (SF)Thus,Shrinkage ratio (SR) or (SF) =

Shrunk length Shrunk scale Shrunk RF

Original length Original scale Original RF

Correct distance on map in terms of original scale = measured distance on map

SF

Correct area on map in terms of original scale

=

2

measured area on map using planimeter

SF

1.7 ERROR DUE TO WRONG MEASURING SCALE

If a wrong measuring scale is used to measure the length of a already drawn line on the plan, the measured length will not be correct. For example, if a plan has been drawn to a scale of 1 : 200, and the length is measured with a scale of R.F. of 1 : 250,

Hence, correct length = (1 250)

(1 200) ×250

Correct length = RF of the wrong scale

measured lengthRF of the correct length

As the area is the product of two distances, hence Correct area =

2

RF of the wrong scalemeasured area

RF of the correct length

Example 1 A surveyor measured the distance between two points marked on the plan drawn to a scale of 1 cm = 1 m (R.F. = 1:100) and found it to be 50 m. Later he detected that he used a wrong scale of 1 cm = 50 m (RF = 1:50) for the measurement. Determine the correct length. What would be the correct area if the measured area is 60 m2? Solution Correct length =

RF of the wrong scalemeasured length

RF of the correct length

1/ 5050 100m

1/100

Correct area =2

21/ 5060 240m

1/100

1.8 USE OF VERNIERS IN SCALES

A vernier is a device for measuringaccurately the fractional part of thesmallest division on a graduated scalei.e. , main scale. Thus the readings aretaken closer than the smallest readingon the graduated scale.

The vernier consists of a small scale,called vernier scale, which moves alongthe graduated scale called the mainscale.

The vernier scale has an index mark(arrow) which represents the zero ofthe vernier scale.

The divisions of the vernier are madeeither slightly shorter or slightly longerthan that of the main scale.

The least count of the vernier is equal tothe difference in length of one divisionof the main scale and one division of thevernier scale.

1. Direct VernierThe direct vernier has divisions whichare slightly shorter than those ofthemain scale. Let us assume that ndivisions on the vernier scale are equalin length to



127

(n – 1) divisions on the main scale. Thus nv = (n-1)s

or n-1

v= sn

where v = length of one division on the vernier, and s = length of one division on the main scale. The least count (L.C) is, therefore, given by L.C. = s – v

or n-1

L.C.=s- sn

or s

L.C.=n

The least count (L.C) of the vernier is

thus equal to the value of the smallest division on the main scale (s) divided by the total number (n) of divisions on the vernier.

In the above fig(b), reading is taken as follows. = 5.3 (i.e. Reading on main scale before index mark) + 5 × least count

= 5.3 m + 5 × 0.1

10 = 5.35 m

2. Retrograde Vernier

A retrograde vernier has divisions which are slightly longer than those of the main scale. If n divisions of the

vernier scale are equal to (n+1) divisions on the main scale, nv = (n+1)s

or n+1

v= sn

Therefore, least count (L.C.) = v – s

= n+1

s-sn

or L.C.= s

n

As in the case of a direct vernier, the least count is equal to the smallest division on the main scale (s) divided by the number (n) of divisions on the vernier.

It may be noted that the readings in the case of a retrograde varnier increase in a direction opposite to that of the main scale, whereas in the case of a direct vernier both increase in the same direction.



128

Topics Page No

1. FUNDAMENTAL CONCEPT OF SURVEYING 174

2. THEODOLITES, COMPASS AND TRAVERSE SURVEYING 175

3. LEVELLING AND CONTOURING 179

4. TACHEOMETRIC, CURVE & HYDROGRAPHIC SURVEYING 182

5. REMOTE SENSING, GIS, GPS & PHOTOGRAMMETRY 183

GATE QUESTIONS

173

Q.1 The plan of a map was photo copied to a reduced size such that a line originally 100 mm, measures 90 mm. The original scale of the plan was 1:1000. The revised scale is a) 1:900 b) 1:1111c) 1:1121 d) 1:1221

[GATE – 2007]

Q.1 (b) Original length of a line, L = 100 mm Shrunk length, L1 = 90 mm

Shrinkage ratio = 1L 9

=L 10

Shrunk scale = original scale x Shrunk

Ratio = 1 9

1000 10

Q.2 The plan of a survey plotted to a scale of 10 m to 1 cm is reduced in such a way that a line originally 10cm long now measures 9 cm. the area of the reduced plan is measured as 81cm2. The actual area (m2) of the survey is a) 10000 b) 6561c) 1000 d) 656

[GATE-2008]

Q.2 (a)

Shrinkage ratio, SR = 9cm

10cm = 0.9

Reduced area = 81 cm2

Actual area = 2

81

(0.9) = 100 cm2

Actual area in the field = 100 x 10 = 10000 m2

1 2

(b) (a)

ANSWER KEY:

1 FUNDAMENTAL CONCEPT OF SURVEYING

EXPLANATIONS


Q.1 In the figure shown, the lengths PQ (WCB 30°) and QR (WCB 45°) respectively up to three places of decimal are

a) 273.205, 938.186b) 273.205, 551.815c) 551.815, 551.815d) 551.815, 938.186

[GATE-2006]

Q.2 The observed magnetic bearing of a line OE was found to be 185°. It was later discovered that station O had a local attraction of +1.5°. The true bearing of the line OE, considering declination of 3.5°E will be a) 180° b) 187°c) 190° d) 193°

[GATE-2006]

Q.3 The lengths and bearings of a closed traverse PQRSP are given below.

Line Length(m) Bearing (WCB)

PR 200 0° QR 1000 45° RS 907 180° SP ? ?

The missing length and bearing, respectively of the line SP are a) 207m and 270°b) 707m and 270°c) 707m and 180°d) 907m and 270°

[GATE-2008]

Q.4 Inquadrantal bearing system, bearing of a line varies from a) 0° to 360° b) 0° to 180°c) 0° to 90° d) 0° N to 90°

[GATE-2009]

Q.5 The magnetic bearing of a line AB is S 45°E and the declination is 5° West. The true bearing of the line AB is a) S 45°E b) S 40°Ec) S 50°E d) S 50°W

[GATE-2009]

Q.6 The magnetic bearing of a line AB was N 59° 30’ W in the year 1967, when the declination was 4° 10’ E. If the present declination is 3°W, the whole circle bearing of the line is a) 299° 20’ b) 307° 40’c) 293° 20’ d) 301° 40’

[GATE-2009]

Q.7 The local mean time at a place located in Longitude 90° 40’ E when the standard time is 6 hours and 30 minutes and the standard meridian is 82° 30’ E is? a) 5 hrs, 2 min and 40 secb) 5 hrs, 57 min and 20 secc) 6 hrs, 30 mind) 7 hrs02 min and 40 sec

[GATE-2010]

Q.8 The observations from a closed loop traverse around obstacle are

Segment

Observation from Station

Length(m)

Azimuth(clockwise from magnetic north)

PQ P Missing 33.7500° QR Q 300.00 86.3847° RS R 354.524 169.3819° ST S 450.000 243.9003° TP T 268.00 317.5000°

2 THEODOLITES, COMPASS & TRAVERSE SURVEYING


Q.1 (a) ∑L = 1000 – 100 = PQ cos 30 + QR cos 45 ∑D = 1000 – 200 = PQ sin 30 + QR sin 45 ⇒ 900 = PQ(0.866) +QR(0.707) ...(1)⇒800 = PQ(0.5) + QR(0.707) ...(2)Solving the above two equations PQ = 273.205 m QR = 938.186 m

Q.2 (b) Observed magnetic bearing of the line OE = 185 Local attraction = + 1.5°, Correction for local attraction = -1.5° Declination = 3.5°E True bearing = 185– 1.5 + 3.5 = 187°

Q.3 (b) ∑L = 200 cos 0° + 1000 cos 45 + 907 cos 180° + l cos θ = 0 lcos θ + 0.107 = 0 ∑D = 200 sin 0 + 1000 sin 45 + 907 sin 180 + l sin θ = 0 707.1 + l sin θ = 0

lsinθ

lcosθ =

707.1

0.107

θ = 270° L = 707 m

Q.4 (c) In quadrantal bearing system minimum angle is 0° and maximum angle is 90°

Q.5 (c) Magnetic bearing of a line = AB = S 45° E Declination = 5° W True bearing = S 45° E+5°= S 50° E

Q.6 (b) Magnetic bearing of a line = N59°30’W Declination in 1967 is 4°10’E Present declinations is 3°W

= N52°20’W Present quadrantal bearing = N59°30’W - 4°10’ -- ° = N52°20’W Present W.C.B = 307° 40°

Q.7 (d) Local meridian = 90° 40’E Standard meridian = 82° 30’E Standard time = 6 to 30 m Local meridian is a head of standard meridian by 8° 10’E For 360° → 24 hrs

For 8°10’→ 8

360

10' 24 = 0h 32m 40s

Local mean time is ahead by 0h 32m 40s ∴ Local mean time = 6 h 30 m + 0 h 32 m 40 sec = 7 hrs 2 mins 40 sec = 7 hrs 2 min 40 sec

Q.8 (b) In a closed traverse, ∑ latitudes = 0 & also ∑ Departures = 0 using, ∑ latitudes = 0 1 cos 33.75 + 300 cos 86.3847 + 354.524 cos 169.3819 + 450 cos 243.9003 + 268 cos 317.5 = 0 ∴ 1 = 396.79 m.

Q.9 (d) Fore bearing of DE – back bearing of DE = 180° Station D and E are free from local attraction CD – DC = 340° 30’- 161° 45’ = 178° 45’ Error at station ‘C’ = (-) 1°15’ Correction at station ‘C’ = (+) 1° 15’ Corrected bearing CB = 227° 30’ + 1° 15’= 228°45’ BC – CB = 45° 15’ - 228° 45’ = (-) 183° 30’ Error at station B = (-) 3° 30’ Correction at station B = +3°30’

EXPLANATIONS


Q.1 The sides of a rectangle are (120 ± 0.05) m and (180 ± 0.06) m. The probable error in the area will be a) ± 16.8 sq m b) ± 12.3 sq mc) ± 16.2 sq m d) ± 11.53 sq m

Q.2 If a quantity A has a weight of 3, then the weight of A/3 will be a) 28 b) 27c) 24 d) 21

Q.3 Theory of errors and adjustments deals with minimizing the effects of a) instrumental errorsb) mistakesc) systematic errorsd) personal and accidental errors

Q.4 A plot of land 60 m x 20 m is measured by a steel tape. If the standard error of length and width measurements is taken as ±1 cm, then the standard error of the area of the plot would be a) ±0.1414 m2 b) ±0.566 m2

c) ±0.632 m2 d) ±0.8484 m2

Q.5 Which one of the following closely represent the shape of the earth? a) Spheroidb) Ellipsoidc) Oblate spheroidd) Prolate spheroid

Q.6 The representative fraction 1/2500 means that the scale 1 cm is equal to a) 025 m b) 2.5 mc) 25 m d) 2.5 km

Q -7 A circle of radius 7 m has a standard error of 0.02 m on the radius. The standard error of its area is a) 0.04 m2 b) 0.14 m2

c) 0.28 m2 d) 0.88 m2

Q.8 Geodetic surveying is different from plane surveying because of a) the curvature of earthb) the large difference of elevations

between various pointsc) coverage of very large aread) undulations of very large area

Q.9 The difference between the most probable value of a quantity and its observer value is a) true errorb) weighted observationsc) conditional errord) residual error

Q.10 The error due to bad ranging is a) cumulative; positiveb) cumulative; negativec) compensatingd) cumulative; positive or negative

Q.11 Offsets are a) lateral measurements made with

respect to main survey linesb) perpendiculars erected from

chain linec) taken to avoid unnecessary

walking between stationsd) measurements which are not

made at right angles to the chainline

Q.12 The plan of a map was photo copied to a reduce size such that a fine originally 100 mm, measures 90 mm. The original scale is a) 1 : 900 b) 1 : 1111c) 1 : 1121 d) 1 : 1221

Q.13 The shrinkage factor of an old map is found to be 15/16 and the representative fraction for the map is a) 1/1600 b) 1/1500c) 1/1906.6 d) None of these

ASSIGNMENT QUESTIONS


Q.14 Which of the following instruments is generally used for base line measurement?

a) chain b) metallic tape c) steel tape d) invar tape Q.15 The correction for sage is

a) always additive b) always subtractive c) always zero d) sometime additive and

sometime subtractive

Q.16 A 30 m metric chain is found to be 0.1 m too short throughout the measurement. If the distance measured is recorded as 300 m, then the actual distance measured will be

a) 300.1 m b) 301.0 m c) 299.0 m d) 310.0 m Q.17 The length of a chain is measured from

a) centre of one handle to centre of other handle

b) outside of one handle to outside of other handle

c) outside of one handle to inside of other handle

d) inside of one handle to inside of other handle

Q.18 A surveyor measured the distance

between too point on the plain drawn to a scale of 1 cm = 40 m and the result was 468 m. Later he discovered that he used a scale of 1 cm = 20 m. What is the true distance between the two point?

a) 936 m b) 234 m c) 117m d) 702 m Q.19 The length of a line measured with a

20 meter chain was found to be 250 meters. What is the true length of line if the chain was 10 cm too long a) 251.25 m b) 248.75 m c) 250.1 m d) 249.9 m

Q.20 The required slope correction for a length of 60 m along a gradient of 1 in 20 is a) 7.5 m b) 75 cm

c) 0.75 cm d) 5.50 cm Q.21 A 30 m steel tape was standardized

at 20C and measurement of distance were taken at 15C. If the coefficients of linear expansion α of the material of the tape were 0.000112 per C, then error due to temperature per tape length would be

a) -0.0000560 m b) +0.0000560 m c) +0.0016800 m d) -0.0016800 m Q.22 A 100 m tape is suspended between

thee ends under a pull of 200 N. The weight of the tape is 30 N. The correction for sag and correct distance between the tape ends is

a) 0.056 m; 99.944 m b) 0.094 m; 99.906 m c) 0.094 m; 100.094 m d) 0.056 m; 100.056 m Q.23 A 20 m chain was found to be 10 cm

too long after chaining a distance of 2000 m. It was found to be 18 cm too long at the end of the day’s work after chaining a total distance of 4000 m. What is the true distance if the chain was correct before the commencement of the day’s work?

a) 3962 m b) 4019 m c) 3981 m d) 4038 m

Q.24 Normal tension is that pull which a) is used at the time of

standardizing the tape b) neutralizes the effect due to pull

and sag c) makes the correction due to sag

equal to zero d) makes the correction due to pull

equal to zero

Q.25 The length of a base line is measured on ground at an elevation



Q. 1 (d) Error of area is given by

2 2

A l b

dA dAe e e

dl db

dAb 180

dl

dA1 120

db

2 2

Ae 0.05 180 0.06 120

2 29 7.2

11.53 sq.m

Q. 2 (b) Weight of quantity A = 3, Then weight of quantity

= 3

A = 3 × 32 = 27

Q. 3 (d) Systematic or cumulative errors which occurs from well understood causes can be reduced by adopting suitable methods. It follows some definite mathematical or physical law and a correction can be determined and applied. Accidental errors are those which remain after mistakes & systematic errors have been eliminated and are caused by a combination of reasons beyond the ability of the observer to control. Personal errors arise from the limitations of the human senses such as sight, touch and hearing. Both accidental and personal error represent the limit of precision in the determination of a value. They obey the law of probability and therefore theory of errors and adjustments applies to them.

Q.4 (c) Standard error of area is given by

2 2

A l b

dA dAe e e

dl db

A = l × b

dA

b 20dl

And dA

l 60db

Now, el = eb = ± 1 cm = 0 = 0.01 m ∴ eA = ± 0.632 m2

Q. 5 (c) The actual shape of the earth is an oblate spheroid. It is an ellipsoid of revolution, flattened at the poles and bulging at the equator. The length of the polar axis is about 12, 113.168 km and that of equatorial axis is about 12,756.602 km. Thus polar axis is shorter than the equatorial axis by about 43.434 km.

Q. 6 (c) 1/2500 means 1 cm = 2500 cm 1 cm = 25 m

Q. 7 (d)

Are of circle A = 2πr

dA2 r

dr

Let standard error in radius be er

Standard error in area,

A r

dAe e

dr

= 0.02 × 2 × π × 7 = 0.88 m2

Q. 8 (a)

Q. 9 (d)

EXPLANATIONS


Q. 10 (a) Q. 11 (b) The distance measured right or left

of the chain line to locate details like boundaries, culverts etc. are called offsets. These are of two types: (i) Perpendicular offsets at right

angles to the chain line (ii)oblique offsets not at right angles

to the chain line Q. 12 (b)

Reduction factor = 90

0.9100

Revised scale = original scale × reduction factor

= 1 1

0.91000 1111

Q. 13 (c) Corrected scale= SF × RF

= 15 1 1

16 1600 1906.6

Q. 14 (d) Inver tapes are used for linear

measurement of very high degree precision such as base line measurements cloth or lines tap for rough and subsidiary measurements such as offset.

Q. 15 (b) Always negative

2

1 1

st 2

l wlC

24p

(Assuming parabola curve) l1 =length suspended (m) p = pull applied (kg or N) w = weight of tape per meter length wl= weight of tape suspended

between supports Q. 16 (c) Actual length of chain = 30 – 0.1 =

29.9 m

Actual distance =299

30300=299.0m

Q. 17 (b) Q. 18 (a) Distance between two points

measured with a scale of 1 cm to 20 cm

468

23.420

cm

Actual scale of the plan is 1 cm = 40 m

∴ True distance between points = 23.4 × 40 = 936 m Q.19 (a) The true length of line is given by

L'

l l 'L

20.1

25020

= 251.25 m

Q. 20 (a)

True length = 2 260 3 = 60.075 m

Correction = 0.075 cm = 7.5 m Q. 21 (a) α∆T = 0.00000112 (15 - 20) = -0.0000560 m Q. 22 (b)

Correction for sag = 2

2

W L

24p

=2

2

30 1000.094

24 200

m

Correct distance = 100 – 0.094 = 99.906 m Q. 23 (b)



195

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