738 Civil Booster (Civil Ki Goli Publication 9255624029)
19
RAILWAY ENGINEERING
1. Basic of Railway and Rail Joints
2. Sleepers and Track Fasteners
3. Ballast and Track Alignment
4. Track Stresses and Creep
5. Geometric Design of the track
6. Points and Crossings
7. Railway Station and Station Yard
8. Signalling and control Systems
9. Traction and Tractive Resistance

739
Railway Engineering
BasicofRailway&
RailJoints 1
 George Stephenson (father of railway) of England succeeded in running
the first train on 27th September 1825 between Stockton and Darlington
with steam engine.
 In the world India Railways are next only to Russian Railways under a
single management.
 Tejas train is first Private train of India (2019).
 First train (four coaches and one steam engine) were run in India on
16th April 1853 between Boribunder (Mumbai) and Thane.
Rail: These act as a continuous girders carrying axle loads made up of
high carbon steel which convert moving wheel loads of train into point
load, which then acts on sleepers.
Requirement of Rails:
(a) Rails are tested by falling weight test/tup test.
(b) Maximum wear of head allowed is 10 mm
(c) Rails are manufactured by open hearth or duplex process.
(d) Minimum tensile strength needed 72 kg/m2
.
Properties Flat Footed Ralls Bull Headed Rails or
Double Headed rails
2. Strength and Stiffness
1. Laying and Relaying
4. Maintenance cost
3. Initial cost
Fitting is simpler. So, these
can be easily laid or relaid.
These have more strength
& stiffness for same weight.
Fastenings are lesser and
cheaper. So initial cost is
less.
It has less maintenance cost.
These have lesser stiffness &
strength for same weight.
Laying or relaying is difficult.
Fastening are more and
costly. So initial cost is high.
It requires heavy maintenance
cost.

740 Civil Booster (Civil Ki Goli Publication 9255624029)
Special Points:
1. Double Headed rails were used in the beginning.
2. Flat footed rails also known as Vignole’s rails and these rails are
designed by weight of rail per unit length. These are most commonly
used in India.
3. 52 kg rail (52 kg/m F.F) is suitable upto 130 kmph & 60 kg rail is
suitable upto speed of 160 kmph.
4. Flat footed rails is commonly used in India.
Length of Rail: Rails of larger length are always preferred because
they will have less no. of joints. Rail length of 12.8m for BG tracks & rail
length of 11.89 m for MG track are used in Indian railways.
Special Point:
wt. of Rail
wt. of Iocomotive 510


When wear of head exceeds 5% of total weight, then rail must be replaced.
Permanent way (Railway Track)
 The combination of rails, fitted on sleepers and resting on ballast &
subgrade is called railway track or permanent way.
 It is Semi-elastic in nature due to packing of ballast cushion.
Width of formation
Ballast base
2:1
1.5:1 Ballast Cushion
Ballast
Gauge
Sleeper
Ballast shoulder
Major Defects of Rail
Corrugated/Roaring Rails
Minute depression
on the Surface of rails
Created where brakes
applied or train start
Buckling of rail
Occur due to
temperature
(specially summer)
when there is
insufficient gap
b/w two end joints.
Kinks in rail
(occur due to loose
packing of joints and
uneven wear)
Hogged rail
Created due to
impact action
of wheel at the
end of rail, had
get bend.

741
Railway Engineering
Gauges in Railway Track: It's the clear distance between inner faces/
running faces of two track rails.
Broad Gauge = 1.676m
Narrow Gauge = 0.762m
Meter Gauge = 1.0 m
Light gauge (Feather track) = 0.610 m
Standard gauge = 1.435m (Delhi metro) (In generally UK and USA)
Coning of wheels: Wheels of the train are made at a slope of 1:20.
Which is known as conning of wheels. It reduces the wear & Tear of wheel
flanges & also prevent the wheels from slipping.
Adzing of sleepers: Also called tilting of rails. For effective use of coning
of wheels, the rails are also laid at the slope of 1 in 20 on the sleepers.
1
20 Sleeper
Rail
Wheel
Axis
1:20
20
Adzing of sleeper
Rail Joints: Are needed to hold together the adjoining ends of the rail.
They are the weakest part of the track. It's strength is 50% of strength of
rail.
Types of Rail joints
Supported Welded
Suspended Compromise
Bridge Expansion
Rail ends
rests on a
single
sleeper, called
joint sleeper
Rail ends
are projected
beyond
sleepers, called
shoulder sleeper
Projected
rail ends
are
connected
by a flat
or corrugated
plate
Two different
rail sections
are joined by
fish plates.
Gap is
provided
for thermal
expansion
Most
perfect &
strongest type
of Joints.
Welded Rails: Rails are welded to provide sufficient restrain at the
ends of rail & better degree of fixity of rail to the sleeper.
Special Point:
Breathing length: minimum length of rail required to be welded at the
end of track, so the portion of rail between welded rail does not undergo
any thermal expansion or contraction.

742 Civil Booster (Civil Ki Goli Publication 9255624029)
Sleepersand
TrackFasteners 2
Sleepers (Rail road lines) are the members which support the rail & are laid
transverse to it. They act as elastic medium for providing longitudinal and
lateral stability to the track & distributed load from rail to ballast.
 Classification of sleepers on material basis -
(a) Wooden (timber) sleeper
(b) Concrete sleeper - (i) Reinforced concrete, (ii) Prestressed concrete
(c) Metal sleeper - (i) Cast iron sleeper, (ii) Steel sleeper
 Wooden sleepers are best sleepers but they have life of 12–15 years.
 Sal & Teak wood are most commonly used for sleepers.Box heart or
Ekka wood must be used for the construction of sleepers. Creosting &
Burnettising are done to incease life of wodden sleepers.
 Serviceable portion of the spiked wooden sleepers is cut & used with tie
bars in station yards is known as check sleepers.
 Check sleepers are not used on a track having running traffic.
 Steel Trough sleepers maintain the two tracks at the same level.
 Central Standard Trail no. 9 (CST-9) sleeper was standrised by Track
Standard Committee. It can be used upto a speed of 130 kmph & most
widely used in Indian Railways.
 C.I. Sleeper’s life is about 35–50 years.Their overall cost & cost of
Maintenance is low as compared to Wooden sleepers but scrap value is
high while their Initial cost is high.
 C.I sleepers are used more than steel sleepers as they are less prone to
corrosion.
 C.I sleepers can be used with every type of ballast but are not suitable
for track circuiting.
 Steel sleepers are light in weight, require less no. of fasteners but get
easily rusted/ corroded.
 Concrete sleepers have high track modulus, therefore used for developing
high speed tracks due to best absorbing capacity of shock.But they have
very poor scrap value.

743
Railway Engineering
 In prestress concrete sleepers, Generally M55 and M60 are used &
there are suitable for Track circuiting.But heavy damages occurs due to
derailment of trains.
Special point - Track circuiting is used to find out the location of a train on
track & also to find spacimg between two traains on the same track.
Composite Sleeper Index (C.S.I): It is used to measure the mechanical
strength of timber. Minimum CSI for track sleeper (783), crossing sleeper
(1352), bridge sleeper (1455).
S + 10 H
CSI =
20
S = strength Index H = Hardness Index (Measured at 12% moisture
content)
Track fasterners:
(a) Fish plates: Thse are used for connecting one rail to the next rail.
Also use to resist heavy transverse shear. Minimum 4 fish bolt are
required to connect 2 fish plate.The buckling occurs if fish plates
are bolted so tightly that rails are not allowed to slip/expansion.
(b) Spike: It is used to hold rail on wooden sleepers. Dog spikes are
used for wooden sleepers with flat footed rails.
(c) Chair: It support bull headed rails on sleepers. Slide chairs are used
to hold stock Rail & tongue rail.
(d) Keys: It fix rails to chairs on metal sleepers. Morgan key ( 18 cm
long & tapered 1:32 ) is most commonly used for CI chairs & steel
sleepers.
(e) Bolts: Dog/Hook bolt is used where sleepers rest directly on steel
girder.Fish bolts are used to resist heavy tranverse shear.
(f) Bearing plate: It is used below F.F rails to distibute load over
wooden sleeper.These are not used in concrete sleepers & metal
sleepers. Saddle plates are used to strengthen the steel
sleepers.These are rectangular plates of either MS or CI. They do
not required adzing of sleepers,
Sleeper density: No. of sleepers per rail length It is N + x
where N = rail lengh (13 for BG)
x = varies b/w 3 to 7
For BG sleeper density is N + 5 (18 sleepers/rail)
Squaring of Sleeper: Adjusting ballast under the sleepers to space them
parallel to each other. It is a maintenance process. It is done by Crow bar.

744 Civil Booster (Civil Ki Goli Publication 9255624029)
Ballastand
TrackAlignment 3
Ballast: It is high Quality crushed stone with desired specifications placed
immediately beneath the sleepers
Function of Ballast
1. It held the sleepers in position & prevent longitudinal and Lateral
movements due to Dynamic loads.
2. It give some elasticity to track and provides Good drainage.
3. Good Ballast should absorb minimum water.
Special Points:
 Size of Ballast varies from (1.9 – 5.1) cm. For wooden sleeper (5.1cm),
Steel sleeper (3.8cm) & at switches & crossings (2.54cm).
 Quantity of Ballast is more on curves with super elevation.
 In India, this width is kept in between 38 to 43 cm from end of sleepers.
 The ballast above packing which surrounds the sleeper, is loosely filled
called Boxing.
 The process of ramming the ballast under the sleeper is called packing.
 The loose ballast between the two adjacent sleepers is known as Ballast
crib.
Types of ballast
(a) Broken stone: Best material as ballast, has maximumstability.Igneous
Rock such as Granite, Quartzite make good ballast material.
(b) Sand: It provides good drainage & silent track.
(c) Gravel or River pebble or shingle: They are smooth & round, so
poorpackingand interlocking.Gravel ballastgives betterperformance
in soft formation.
(d) Ashes or Clinders: They have excellent drainage property, Excellent
ballast material for station yards & but it is corrosive in nature.
(e) Brick ballast : It is fairly good for drainage.

745
Railway Engineering
Depth of ballast-Section
Minimum depth of Ballast layer = Dmin
min
S W
D
2


S
W
S – W
S – W
2
45º
Width of ballast: On straight track it is sleepers length + 2 × 300 mm at
top which work out to be 3.35 m for BG. The side slope is 1.5 horizontal to
1 vertical.
Survey works for alignemnt of track.
(a) Traffic survey
(b) Reconnaissance survey
(c) Preliminary survey
(d) Detailed or location survey

746 Civil Booster (Civil Ki Goli Publication 9255624029)
TrackStressesand
Creep 4
Track Modulus (m)
 Track Modulus is Index for stiffness resistance to deformation of
permanent way.
 Load per unit length of the rail required to produce unit deformation or
depression in the track.
 For calculation of Track modulus, Initial load is 4 tones for BG track &
3 tones for MG Track.
Special Point: Elasto – plastic theroy is used to define track modulus
Stresses on the rail: Torsional stresses are developed due to eccentric
vertical loads but maximum shear stress below the contact surface of rail &
diesel locomotive is 36.25 kg/mm2
Creep of the rail: It is the longitudinal movement of rail wrt sleepers in
a track and its value varies from 0-16 cm.
Theories of creep
Wave Action theory Drag theory
Percursion theory
Vertical reverse curve Due to horizontal
component of the
resultant impact
force at the rail end
Drag of driving wheel
of locomotive have
opposite effect wrt.
direction of creep.
Wave motion is set up
by moving loads of wheel
Measurement of Creep
 Maximum permitted creep on BG track is 150 mm
 Creep should be measured at an Interval of about 3 month.
 No creep should be permitted on points & crossings.
Prevention of creep:
(i) Using steel sleepers
(ii) Pulling back rails to original position
(iii) By providing sufficient crib ballast & anchors

747
Railway Engineering
Factors affecting creep of the rail:
(i) Alignment of track: Observed greater on curves than tangent railway
track.
(ii) More creep in the direction of heaviest traffic.
(iii) Type of rails: Old rails have more creep than new rails.
(iv) Grade of track: More creep in downward steep gradients.
Crushed head:
 Crushed heads are those which have either sagged or flattened.
Crushed head
 Besides the defect of manufacture, crushed head are due to
(a) Weak supports at the rail ends. This weak end support may be due
to loose fish bolts.
(b) Flat spots on wheels which are developed due to skidding of wheels.
(c) Slipping of wheels.
Split heads:
 In it, cracks occur in the middle of the head or pieces are split from
the side to the end of the head.
Split head `
Horizontal fissure
 It occurs due to cavity formed during manufacturing or shrinkage of
metal when the metal is not closely welded together.
Horizontal fissures:
 These are developed in the rail head.
 They are more in the form of a fracture & develop gradually.

748 Civil Booster (Civil Ki Goli Publication 9255624029)
GeometricDesignof
thetrack 5
 Generally, the maximum Gradient allowed is known as Ruling Gradient
& It is the gradient allowed so that engine can haul the load with its
maximumcapacity. In hilly region (1:100 - 1:150) & plain region (1:150 -
1:250) .
 In pusher gradient, a pusher or helper engine is used. For B.G. Track of
Western Ghats pusher gradient is of 1:37. Generally used in hilly areas.
 In India, the minimum gradient provided on the station yards to drain out
off water is 1:400 to 1:1000.
 Momentum gradient is steeper than ruling gradient & comes only after a
falling gradient.
Grade compensation: Due to curvature on the grade, the gradients on
the curves are to be reduced to reduce the resistance in motion of train.
% per degree of curve
BG 0.04/
70
R
 
 
 
MG 0.03/
52.5
R
 
 
 
NG 0.02/
35
R
 
 
 

749
Railway Engineering
Safe speed of train as per Martin’s Formula
For low speed (<100 kmph) (>100 kmph)
For High speed
Transition curve Non-trasition curve
80% of speed
on transition curve.
on BG & MG on NG
max
V 4.35 R 67
  max
V 3.6 R 6.1
 
max
V 4.58 R (BG)

Degree of Curve:
1720
For 30m chain
R
1150
For 20m chain
R
As per Indian Railways.
Maximum degree of curve Minimum radius
BG 10º 175 m
MG 16º 109m
NG 40º 44m
Super elevation or cant
tan  =
2
G R
e v
g

2
G
127R
v
e 
V in kmph, R in m, G  Gauge (in m)

mg cos 
A B

C e
P
D
MV cos
2

R
MV
2
R
mg sin 

750 Civil Booster (Civil Ki Goli Publication 9255624029)
 The maximumvalue of superelevation is (1/10)th to (1/12)th of the Gauge.
 When the loads, pressure on both rail is equal. Then, the cant provided is
known as Equilibrium cant.
 Negative superelevation - When the main line lies on a curve & has
a turnout of contrary flexure leading to a branch line, then the
superelevation necessary for the average speed of trains running over
the main line curve cannot be provided. In such cases, the branch line
curve has a –ve superelevation & so speed on both tracks must be
restricted, particularly on the branch line.
Branch Line
Main Line
Negative Superelevation
Equilibrium speed
When sanction speed > 50 kmph When sanction speed < 50 kmph
max
3
V
V 4
safe speed by martin
equ lesser


 


max
equ
V
V lesser
safe speed by martin

 

N V
Weighted average speed =
N
i i
i


Ni
Number of train’s having speed Vi
Maximum limit of super elevation
Equilibrium Speed

751
Railway Engineering
Track Speed< 120 kmph > 120 kmph
BG 16.5cm 18.5 cm
MG 10 cm
NG 7.6 cm
 Cant deficiency - It is the difference between the equilibrium cant
necessary for the maximum permissible speed on a curve & the actual
cant provided (on the basis of average speed of trains).
 Cant deficiency is limited due to -
(a) Extra pressure & lateral force on outer rail.
(b) Higher cant deficiency gives more discomfort to passengers.
 The allowable cant deficiency for BG is 75mm, for MG 50mm & for
NG 40mm.
 Cant Excess - It occurs when a rail travels round a curve at a speed
less than the equilibrium speed. It is the difference of actual cant &
theoretical cant required for such lower speed. The maximum cant
excess for BG is 75mm & for MG is 65mm.
Types of Transition Curve
 Transition curve is introduced in between the circular portion of track &
straight track at both ends.
 Cubic parabola ( also called Froud’s curve ) is used as transition curve &
Transition curve are early set out by offset method.
(a) Spiral curve is used in Highways
(b) Bernoulli’s Lemniscate satisfy the requirement of Transition curve
upto deflection angle of 30.
Transition Curve:
(a) Equation of deflection of cubic parabola
3
6RL
x
y 
(b) Deflection angle  =
1 1
tan tan
3
  

 
 
(c) Spiral angle  =
2
1
tan
2RL
x
  
 
 
(d) Shift s =
2
L
24 R
Length of transition curve

752 Civil Booster (Civil Ki Goli Publication 9255624029)
From 1st method -
L = max
max
7.2
max 0.073 V
0.073D V
e
e





,
where e = S.E in cm, Vmax
in kmph, D = cant deficiency in cm
From 2nd method - Maximum of following
(i) Railway board formula
L = 4.4 R
where L, R (in m)
(ii) Rate of change of super elevation
L = 3.6e
(iii) Change of radial acceleration
L =
3
3.28V
, V m/sec
R

Maximum speed based on length of transition curve
Speed < 100 kmph Speed > 100 kmph
max
V L
134
e
 max
V L
198
e

= (134 L/D) = (198 L/D)
(L in m, e in mm)
Gauge widening on curves
2
13(B + L)
W
R

e cm
B – Rigid wheel base in meters, (For BG = 6 m, For MG = 4.88m)
R – Radius of curve (in m)
2
L 0.02 D
h h
 
L = Lap of flange (in m ), D = Diameter of wheel
h = Depth of wheel flange below rails , Wc
= Widening of gauge
 Due to rigidity of wheel when the outer wheel of rear axle does not
follow the same path as by front axle, there is always a gap with the
outer rail. So, curve gague is a bit wide need but should not be more than
required.

753
Railway Engineering
Points and
Crossing 6
 Track circuiting is done in order to find out the location of a train on
track. It also tells the spacing between two trains on the same track.
 Turnout: It is the combination of points & crossing which enables a
back either a branch line or siding to take off from main track.
 Points crossings are weak kinks in the track where vehicles are suceptible
to derailment.
 High mangaese steel are used to make material (Steel) for points &
crossing.
 Check Rails are provided on the opposite side of the crossing for guiding
one wheel of the vehicle & thus to check the tendency of other wheel to
climb over the crossing.
 On the curves, check rails parallel to Inner rail can be Introduced to
control wear.
 Check-rails are used if the degrees of curves is more than 8º for BG and
more than 14° for MG.
 The correct sequence for a train when it passes a Turn out from the
facing direction is Toe of switch, Tongue rail, Lead rail & crossing.
 A tongue rail is tapered having toe at one end & heel at the other end.
 The position of the straight alignment against which the tongue rail fits is
known as stock Rail.
 Crow bars are used to raise sleeper to a desired height & also use in
replacement of track.
 Claw bar to remove dog spikes out of sleepers.
 Rail Tongue to lift & carry rails.
 Wire claw to clean & spread the Ballast.
 Wing rails help in channelising the wheels in their proper routes.
 Guard rails are extra rails provided over bridges to prevent damage.
 Treadle bar is used for Interlocking points & signals.

754 Civil Booster (Civil Ki Goli Publication 9255624029)
Over all length
Stretcher bar
End
of
stock
rail
Facing
direction
Throw of
switch
e
B
D
F
L
Bend in check
rail
Theoretical nose
of crossing (T.N.C.)
Check rail
Inner curve
lead rail
Actual nose of
crossing (A.N.C.)
Flore
Wing
rail
a
C
Check rail
Wing rail O
H
Throat
P
Lead rail
Inner straight lead rain E
C CD
Outer curve
Outer straight lead rail A AB – Stock rail
tongue
rail
I
TURN OUT DIAGRAM
Special Points:
 Lock bar is provided so that point may not be operated while train is on
it.
 Maximum axle load in India are 28.56 tonnes for BG & 17.34 tonnes
for MG.
 Realignment of straight Track is done by using crow bar &Track liners.
Turn out consists of
(a) 2 points or switches
(b) (1 pair) of stock rails
(c) An acute angle crossing/ V crossing.
(d) A pair of check rails
(e) 4 lead rails
Important Points of Switch:
(i) Flange way clearance: It is the distance between adjacent faces of
tongue rail & stock rail at the heel of switch.
(ii) Flange way depth: It is vertical distance b/w top of rail to heel block.
(iii) Heel divergence: It is the distance between running faces of stock
rail & tongue rail at the heel of switch.

755
Railway Engineering
Heel divergence
Flange way
clearance
Flange way
depth
Heel Block
Tongue rail
Stock rail
(iv) Throw of switch: It is the maximum distance by which toe of tongue
rail moves sideways. For BG (9.5 cm) & MG/ NG (8.9 cm)
(v) Switch angle: It is the angle between running faces of stock rail &
tongue rail when tongue rail touches the stock rail.
Heel divergence
Length of tongue rail
 
Tongue rail length

Heel
divergence
Crossing angle:
The spread at the leg of crossing
No. of crossing (N) =
The length of corssing T.NC.
T.N.C. Theoretical Nose of Crossing
/2
N
1/2
1/ 2
sin
2 N

 

 
 
/2
N
1 1
2cot (2N )

 

1
N
N = cot
Used in Indian
Railway

Methods to calculate crossing angle ‘N’
Cole’s method
(right angle triangle method)
Isosceles triangle
method
Centre line method

756 Civil Booster (Civil Ki Goli Publication 9255624029)
Design of Turnout:
(a) Curve lead: It is the distance measured along stock rail between
TNC and toe of switch
Curve lead = lead + switch lead
(b) Lead: It is the distance between TNC and heel of switch measured
along stock rail
(c) Switch lead: It is the distance between heel of the switch and toe of
the switch. It is measured on stock rail.
Diamond crossing: When curved track or straight traks of the same or
different gauges cross each other at an angle less than 90°, a diamond
shape is formed.Therefore, this crossing is known as diamond crossing.
Diamond crossing at Nagpur is a double diamond railway crossing.
Elbow


The salient features of diamond crossing are:
(a) It consists of 2 acute angle crossings , 2 obtuse angle crossings
& 4 check rails.
(b) Indian Standards specify the limit of flattest diamond to be 1 in 10
for BG tracks & 1 in 8.5 for other tracks.
(c) The length of the gap between two noses of an obtuse crossing
increases as the acute angle of crossing decreases.
(d) Diamond crossings should be avoided as far as possible on curves
because they necessitate restriction on speed.

757
Railway Engineering
Railway Station
and Station Yard 7
 Minimum length of passenger platform is 180 m for all gauges.
 Sidings provides temporary storage for wagons.
 Dyanamometer car is helpful in collecting the Information about the
Railway Track Condition.
 Turn Table has arrangement for Turning the direction of the engine of
locomotive.
Sidings: When a branch line from main line or a loop line terminates at
a dead end with a buffer stop or sand hump.
Station yard: It is a system of track laid for receiving, storing, sorting &
dispatching of new vehicles etc.
Types of station yard - (a) Passenger, (b) Locomotive,
(c) Goods, (d) Marshalling
Passenger yard: It includes the passenger platforms & a number of
tracks where idle trains can be accommodated, examined & cleaned.
Goods yard: It include the platform useful for loading& unloadinggoods.
Marshalling yard: It is considered as "the heart that pumps the flow of
commence along the track & main function of marshalling yard are reception,
sorting & (departure) reforming into desiganation wise of goods trains. It
may be flat yard, hump yard or gravitational yard.
 Flat yard is used when limited land is available on plains.
 Nowdays practise is to use Hump yards because shunting operations
are done more quickly than flat/Gravitational yards.
Locomotive yard: These are the yards where locomotives are housed
& where all the facilities like coaling, watering, repairing cleaning oiling are
provided for servicing of the Locomotives.
Special points - Drop pit is used to remove the wheels of an engine.
 Turn table is used for changing the direction of locomotive such as
triangle.
 Scotch blocks is used to separate all the sidings & shunting lines from
through running lines.

758 Civil Booster (Civil Ki Goli Publication 9255624029)
Signallingand
controlSystems 8
Absolute block system or space interval system is extensively used in India.
Classification of Signals - Based upon
(a) Operational characteristics - Detonating, hand & fixed signals.
(b) Functional characteristics- Shunting (disc or ground) , warner,
coloured light & semaphore (stop) signals.
(c) Locational characteristics - Reception signals like as home & outer
signal, Departure signal like as starter & advance starter signals.
(d) Special characteristics -Callingon, routing, point indicator &repeater
( co-acting ) signals.
(i) Detonating signals are used in foggy & cloudy weather. These are
placed on rails which explode with when train passes over them.
(ii) Warner signal: A semaphore signal at entrance is combined with a
warner system.It is painted with yellow, not red.
(iii) Stop/semaphore signal: If arm is horizontal, then it indicates stop or
danger indication. If arm is inclined at 45- 60 degree, it is said to be
off position meaning to proceed.
(iv) Shunting signals are used in station yards in shunting operation.
(v) Home Signal (Due to its location at the Door of station it is called as
Home signal) has bracketed arms which which line is to be used.
(vi) Repeater or co-acting signal’s are provided where driver’s vision is
obstructed. A duplicate arm of smaller size is placed at a suitable
position on the same post.
(vii) Calling on signals are very much useful with repair work.
(viii) Routing signals are provided where no of lines exist at a station
taking off different locations from main line.
(ix) Fixed signals are generally a semaphore type, fixed at a place.
(x) The starter signals mark the limit upto which trains stopping at a
station come to a stand or halt.
Special Points: Outer signal is placed minimum to 0.54km & 0.40km
away from station yard on BG and MG tracks respectively.
 Detonator must be placed on the rails atleast 400-500mahead of signals.
 The height of the centre of arm of semaphore signal is kept 7.5m above
the ground.

759
Railway Engineering
Traction and
Tractive Resistance 9
Tractive effort: Pull applied by engine on driving wheel
Hauling Capacity: Maximum value of frictional force due to driving
wheels
Hauling Capacity (H.C.) = W= wn
 
 = friction coefficient
n = no. of pair of driving wheels
w = weight on driving axle, W = total weight on driving wheels
Total resistance
Due to speed
Due to wind resistance Due to track profile Due to starting &
acceleration
Gradient
Curvature
Resistance due to train resistance
RT
= 0.0016 w + 0.00008 wv + 0.0000006 wv2
+ w tan  (due to
gradient) + 0.0004 DW (due to curve)
V = Speed of trains in kmph, w = wt. of train in tonnes

w sin 
Special Points:
 For moving train
Tractive Resistance > Hauling capacity > Total resistance
 For solving Numerical problems, we take. Tractive effort = Hauling
capacity = Total resistance

 Sudden expension:
2
1 2
(v v )
h
2g


l
 Entry Loss:
2
entry
v
h 0.5
2g
 , Exist of Pipe:
2
exit
v
h
2g

 Sudden Contraction:
 2
c 2
contraction
v v
h
2g


 Bending of the Pipe:
2
fitting
v
h k.
2g
 , k = constant,
T-Bend, k = 1.8, 90º-Bend, k = 1.2, 45º-Bend, k = 0.4
ENVIRONMENTAL ENGINEERING
 Variation of Demand
Max. daily Consump. = 1.8 × Annual avg. daily consump.
Maximum Weekly Consumption = 1.48 ×Avg. weekly
Maximum Monthly Consumption = 1.28 × Avg. monthly.
 Population Forecasting Mehtod
Arithmetic Increase Method: Pn
= o
P nx
 (For old cities)
Geometric Increases Method: Pn
=
n
o
r
P 1
100
 

 
 
(For new cities)
Incremental Increase Method: Pn
= o
n(n 1)
P nx y
2

 
 Physical characteristics
Turbidity: (limit 1-5 NTU) Baylis, Jackson, Nephelometer
Colour: Tintometer (limit 5-15 TCU), Taste & odour: T.O.N = 1 ( |
3)
Temperature: 10ºC desirable ( |
 25ºC)
Total solid = Dissolved solids + Suspended solids
(Gravimetric Method)
 Chemical Characteristics
Total solids & suspended solids: Limit 500-2000 ppm
PH = – log H+
(6.6 to 8.5) Methyl Orange & Phenolphthalein
Total Hardness: 2 50
[Ca ]
20

 + 2 50
[Mg ]
12
  
 
 
(EDTA using EBT)
Carbonate Hardness: min of total hardness or alkalinity
Chloride: limit – 120mg/L (Water), 250 mg/L (Sewage)
Nitrogen Content: Limits: Free ammonia |
 0.15mg/
L, Organic Nitrogen |
 0.3 mg/l, nitrite should be
zero, nitrate |
 45 mg/l
Measurement (i) Free Ammonia-by simple boiling of
water. (ii) Organic Ammonia – By adding Kmno4
,
(i+ii) are known as kjeldahl Nitrogen Nitrite and
Nitrate by - colour Matching Method.
 Chemical: (Mn = 0.05 mg/L) (Iron – 0.3 mg/L),
(Fluride : 1.0 –1.5 mg/L) (Sulphate : 250 mg/L) (Cya-
nides = 0.2mg/L) (Arsenic : 0.01 ppm)
 Screening: Velocity |
 0.8 to 1m/sec
Based on stokes law. Setting velocity: S
Q
V
.L


 Design Criteria: Over flow rate =
Q
BH
, 500–750 lit/
hr/m2
for plain sedimentation, Depth = 03 to 4.5m
Width B  10 m
 Coagulants
1. Use of Alum
2. Use of copperas: (FeSo4
,7H2
O)
3. Use of chlorinated copperas (Fe2
(So4
)3
+FeCl3
),
4. Use sodium Aluminate (Na2
Al2
O4
)
Comparision of slow sand and Rapid Gravity Filters.
Slow sand filter Rapid sand filter
Cu = 3—5 Cu = 1.2–1.6
D10 = (0.2–0.3) mm D10 = (0.35–0.55) mm
Frequency of cleaning = (1–3) Cleaned through Back washing
months
Design period = 10 year n = 1.22 Q
Use for smaller plants in village Rate of filtration (3000-6000)
Design on max. daily demand. l/m2
/hr
Rate of filtration (100-200) l/m2
/hr Operational Troubles–
is very low as compared to (a) Air Binding
R.S.F., but efficiency is High (b) Mud ball formations
(c) Cracking of filter
1. Minor Methods.
(i) Boiling, (ii) Treatment with excess lime, (iii) Treat-
ment with ozone (KMNO4
), (iv) Treatment with silver
Process.
2. Major Method Chlorination (Disinfection with Cl2
)
 pH 5
2 2
Cl H O HOCl HCl

 
  ,  pH 8
HOCl H OCl
  

 
 pH 7 –
HOCl H OCl
 


  ,  3 2 2
NH HOCl Cl H O
   
NH3
+ HOCl is called combined chlorine.
Chlorine forms: Free chlorine, Hypochlorites (Swim-
ming Pool), Chloramines, Chlorine dioxide
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
C
D
III
II
Formation of free chlorine and
Presence of chloro-organic
compounds not destroyed
Free and com
bined
residual
Free
residual
Destruction of chloramines
and chloro organic comp
Formation of chloro-organic
compounds and chloramines
Break
point Combined residual
Chlorine Added (p.p.m)
Combined residual
Destruction of
chlorine by
reducing compound
I
0.5
0.4
0.3
0.2
0.1
0
Chlorine
residual
(p.p.m)
Treatment With Water
1. Treatment with Copper Sulphate (CuSO4
.H2
O)
 Added to open reservoir and lakes to kill algae
or to check the growth.
2. Treatment with KMNO4
 Acts as oxidizing agent to remove to taste, odour
and colour and to kill bacteria.
3. Aerations
 For increasing Di-oxygen to remove CO2
, upto
some extent removal of Fe and Mn.
4. Fluoridation
 Necessary if F < 1mg/L. Add Naf or Na2
SiF6
or H2
SiF6
to keep fluorine content between 1 to 1.5 mg/L
(1) De-Fluoridation. (if F > 1.5 mg/L) In India, Treat-
ment is done by Nalgonda Technique (Use Alum for
reducing flurides)
5. Removal of Radioactive Substances By coagulation & filtration.
6. Desalination (i) By evaporation and distillation
(ii) Electrodialysis (iii) Reverse Osmosis.
 Hydraulic design of sewers: V = 2/ 3 1/ 2
1
R S
n
 Oxgen Demand:
t
dL
dt
= D
k t
KL, L L 10
t 0

   ,
BODt
= D
k t
0 t 0
L L L 1 10
 
  
  ,
[BOD5
= 0.684L0
],
DTº
K = KD20
[1.047]T-20
Bar
Screen
Grit
chamber
Oil and Grease Trap
(Skimming Tank)
Biological Unit SST
Disinfection
SST
Sludge
PST studge
 Note: On principle plane shear stress will always 0.
 Radius of Mohr’s Circle (max
):
max min
max.
R
2
  
  
 Normal stress at Location of (max
) (max
-max shear
stress):
1 2
n
2
  
 
 Volumetric Strain of Rectangular:
 
x y z
v
V
(1 2 )
V E
 
    

 
    
 
 
 Volumetric Strain of Cylindrical: v e D
2
    
 Volumetric Strain of Spherical: v D
3
  
 Relationship Between Elastic Constant:
E
G
2(1 )

 ,
E
K
3(1 2 )

  ,
k 2G
6k 2G
 
 
 ,
9kG
E
3k G


Number of independent Elastic Constant:
Homogenous & Isotropic = 2, Anisotropic = 21,
Orthotropic = 9
 Axial Elongation of the Prismatic Bar:
PL
L=
AE
 ,
2PL
L=
AE
 (for Instantaneous loading)
 Deflection In Non-Prismtic Bars:
1. Stepped Bar:
1 1 2 2
1 1 2 2
PL P L
L=
A E A E
     
  kt
p c 0 c
f f f f e
   ,
fp
= Infiltration capacity at any time t,
f0
= initial infiltration,
fc
= Final steady state infiltration.
IRRIGATION
Methods of Irrigation
Free flooding, Border flooding, Check flooding, Basin
flooding, Furrow Irrigation, sprinkler Irrigation, Drip
Irrigation.
 Sodium Absorption Ratio:
Na
S.A.R
Ca Mg
2

 


 Depth of water stored in root zone: d
w C 0
w
d.
d (F M )

 

 Relation b/w duty and Delta:
.
(meter)
D
 
  ,
B = Base period in days, D = Duty in hectare/cumec
 Irrigation Efficiency
(a) Water conveyance Efficiency:
f
c
r
W
n 100
W
  ,
wf
= water delivered to the farm, wr
= water supplied
(b)Water appliacation Efficiency (na
):
s
a
f
W
n 100
W
 
Below the farm root-zone f s f f
W W R D
   ,
WS
= Water stored in the root zone,
Wf
= Water delivered to the farm,
Rf
= Surface run off, Df
= deep percolation
(c) Water use efficiency (nu
):
u
u
d
w
n 100
w
  ,
wu
= water used beneficialy,
wd
= water delivered.
(d)Water Storage Efeiciency (ns
):
s
s
n
w
n 100
w
  ,
ws
= water needed in the root zone prior to Irrigation,
wn
= (field capacity–Available moisture)
(e) Water Distribution Efficiency (nd
):
d
Y
n 100 1
d
 
 
 
 
, Y = average numerical deviation in
depth of water average depth stored during Irrigation (d).
 Consumption Irrigation Requirements (CIR): u e
CIR C R
 
Field Irrigation Requirement (FIR): a
NIR
FIR
n

Gross Irrigation Requirement: c
FIR
GIR
n

NIR CIR LR PSR NWR
    , (GIR > FIR > NIR > CIR)
 Kennedy’s theory: 0.64
o
V 0.55.my

 Kutter’s/ chezy’s Formula:
0.00155 1
23
S n
V RS
0.00155 n
1 23
S R
 
 
 
 

 
 
 
 
 
 
 
 Lacey’s Theory:
1/ 6
2
Qf
V
140
 
  
 
, mm
f 1.76 d


2
5 V
R
2 f
 
  
 
 
5/3
1/6
f
S
3340 Q
 Q
A
v

wetted perimeter P 4.75 Q
 scour depth
1/3
2
1.35
q
f
 
 
 
 

Difference B/W Lacey & Kennedy Theory
Kennedy Lacey
1. Trapezoidal channel 1. Semi elliptical channel
2. Applicable for alluvial 2. Applicable for alluvial channels
channels as well as for rivers.
3. Silt is kept in suspension 3. Silt is kept in suspension
due to eddies generated due to eddies generated both
from bottom. from side slope and the bottom
i.e. through out the parameter.
4. No eq. for bed slope 4. Gave eq. to calculate bed slope
5. Recommended Kutter eq. 5. Gave his own velocity equation
to find velocity
6. Trial & error procedure 6. Diret procedure
 By Rate of introduction of super elevation:
 
S e
L e.N. w w (Rotation about inner edge)
 
 
e
S
e.N. w w
L (Rotation wrt centre line)
2


 Empirial Formula:
2
S
2.7v
L (Plain & Rolling)
R
 ,
2
S
v
L (Hilly area)
R

 Length of Summit Curve:
4.4
L 2S
N
  (L<SSD)
2
NS
L
4.4
 (L> SSD)
 Length of Valley Curve:
1/ 2
3
S
Nv
L 2
C
 
  
 
 
(Comfort criteria)
 L > SSD:
2 2
1
NS NS
L
(2h 2Stan ) (1.5 0.035S)
 
   (h1
= 0.75,  = 1°)
 L< SSD:
1
(2h 2S.tan )
L 2S
N
 
 
 Basic Capacity of Single lane, Vehicle Per hours: v
= speed kmph, T(Sec/km) =
3600
v
,
f j
max
v k
q
4
 ,
Where,
vf
= Free mean speed, (Maximum speed at zero density.),
kj
= jam density, (Maximum density at zero speed), Maximum
flow qmax
occurs when the speed is f
V
2
and density is kj
/2.
Number of potential conflicts: Both roads are two way
= 24, Both road one way = 6, One road is two way,
other one way = 11
1 2
weaving
e p
280w 1 1
e e
w 3
Q , W 3.5
w 2
1
  
 
   
  
  
 

 
 
l
Types of interchange:Trumpet,
Diamond, Full Cloverleaf,
Partial Cloverleaf
 
 
 
 
Floating Car Method: For Speed and delay study.
 Aggregate crushing value:
2
1
w
100
w

 Coefficient of Hardness:
Loss of wt. in gm
20
3
 
 Rigidity factor:
Contact Pressure
R.F
Tyre Pressure

 California Resistance Value: 1/5
k.(T.I)(90 R)
t
C


 Elastic Modulus:  is maximum vertical deflection of
the flexible plate, s
p.a
F

  , Rigid circular plate is
used instead of flexible S
5P.a
F

  , a = radius of plate,
p = pressure at deflection, Es
= young’s modulus of
pavement material.
 California Bearing Ratio M/D:
1/ 2
1.75P A
t
CBR
 
 
 

 
,
t = Pavement thickness in Cm, P = wheel load in kg,
CBR = California Bearing Ratio (%), A = Contact Area
in cm2
 CBR TEST:
Load or pressure Substained
at2.5 or 5.0 mm Penetration
CBR
Load or pressure Substained
by standard aggregate at
corresponding pressure level.

 Tri Axial Method:
3
y
2 S
P
S P
3p. y E
T d
2 E
 
   

 
 
  
 
 
     
 
 
1/3
1 2
2 1
t E
t E
 
  
 
 
 Design of Rigid Pavement:
p P
k
0.125
 

 Radius of Relative Stifiness:  
1/ 4
3
2
Eh
I
12K 1
 
 


 
 
,
2 2
b 1.6a h 0.675h
   when (a < 1.724 h)
t 2
3P
S
h
 (Glodbeck’s formula)
N =
n
365A [(1 r) 1]
r
 
× FD
Bankelman Beam Deflection Method
Overlay Thickness: h0 = c
10
a
D
550 log
D
Test Purpose
CBR test For classifying & evaluating soil subgrade & base
course materials for flexible pavements
Crushing test Strength of Aggregates
Abrasion test Hardness of Aggregate
Impact test Toughness of Aggregate
Soundness test Durability of Aggregate
Shape test Gives idea of workability & stability of mix
Bitumen Adhesion test Gives stripping value of Aggregates
Softening point test It is done by Ring & ball apparatus to ensure safety
of Bitumen
Float test for viscosity of Bitumen.
RAILWAY ENGINEERING
CSI =
S + 10H
20
, Sleeper density = M + x,
Dmin =
S – W
2
, e =
2
GV
127R
Length of transition curve
I approach II approach
Maximum of the following
Chart for Most Economical Sections
 GEDMETRICAL  RECTANGULAR  TRIANGULAR  TRAPEZOIDAL
PARAMETERS
 DIAGRAM
B
y
1V:MH
1
B
my
IV:mH
my
y
 Condition for most Economical 
B
y
2
 m = 1,  = 45º

60º Hor.
2y 1
B m
3 3 30º Vert.
 
 
 
 Area A = B.y = 2y.y 
2
A my
  A (B my) y
  

2
A 2y
 
2
A y
    2
2y 1
A y y 3 y
3 3
 
  
 
 
 Perimeter P 4y
 p 2 2y
  P 2 3y

 Hydraullic Radius  R y/ 2
 
y
R
2 2
 
y
R
2

(R = A/P)
 Top width (T)  T 2y
  T 2y
 
4y
T
3

 Hydraullic Depth  D y
  D y/ 2
 
3
D y
4

A
D
T
 

 
 
Cambium Layer
Inner Bark
Pith
Heart Wood
Outer Bark
Medullary Rays
Sap Wood
Gelogical
Igneous Sedimentary Metamorphic
Stratified Unstratified foliated
Chemical
Agrillaceous Silicious Calcareous
Physical
ROCK Classification
Rock Types Chemically Physically Geologically
Granite Siliceous Unstratified Igneous
Quartzite Siliceous foliated/Stratified Metamorphic
Marble Calcarious Stratified Metamorphic
Limestone Calcarious Stratified Sedimentary
Sandstone Siliceous Stratified Sedimentary
Slate Argillacous Stratified Metamorphic
Laterite Argillacous Stratified Sedimentary.
Tools for Quarrying stones
Jumper, Dipper, Crow bar, Tamping bar
Test Purpose
Smith test for presence of soluble matter
Brard’s test for frost resistance
Acid test To check weather resistance
Hardness test Mohr scale
Window Width =
1
[Width of room Height of Room]
8

• The sill of a window should be located about (70 –
80) cm above floor level of the room.
• Generally Height of a Door should not be less than
(1.8 – 2) m
• Commonly Width height relation used in India:
(i) Width = (0.4 – 0.6) Height
(ii) Height = (Width + 1.2) m
• Doors of residential Buildings:
(a) External Door – (1 × 2) to (1.1 × 2) m
(b)Internal Door – (0.9 × 2) to (1 × 2) m
(c) Doors for bathrooms and Water closets:
– (0.7 × 2) to (0.8 × 2) m
• Public Buildings (School, Hospital, library)
(a) (1.2 × 2) m (b) (1.2 × 2.1) m (c) 1.2 × 2.25) m
Designation of Door = Length × Type of Door × Height
8 DS 20 – A door opening Having width (8 × 100 mm) ×
Height (20 × 100 mm) with S (Single SHutter) D (Door)
Types of Window
1. fixed 2. Pivoted 3. Sliding 4. Bay 5. Corner 6. Cable (7)
Dormer (8) Skylights (9) Louvered (10) Lantern (11) Gable
Stairs
• No of steps are not more than 12 and not less than
3 in a flight.
• Angle of Inclination (Pitch) – (25° – 40).
• Head room must not be less than 2.05 m.
• Minimum width of stairs in residential building –
85 cm and in commercial building is 1 m.
s
Type of Structure Degree of Indeterminacy D
2D (plane) frames (3m+r)-3j
3D frames (6m + r)-6j
2D (plane) (m+r)-2j
pin-jointed truss
3D truss (m+r)-3j
Slope Deflection Equations
AB A B
FAB
2EI 3
M M 2 (Continuous Beam)

 
     
 
 
l l
AB
BA BA B
M 3EI
M M
2 L L
é ù
d
ê ú
= - + q -
ê ú
ë û (one end is pin supported)
Important Points
y shear plane ( )

y
x x
Principle
plane ( )

( )
n, max

( )
n,0

n
min max
SLOPE & DEFLECTION
B
M
L
P
B
B
A
A
= 0 B
=
M.L
EI
B
=
2
PL
2EI
B
=
3
WL
24EI
A
= 0 B
=
2
ML
2EI
A
=
3
PL
3EI
B
=
4
WL
30EI
w/m
B
A B
M M c
A B
L/2 L/2
B
=
3
WL
6EI
A
= B
=
ML
2EI
A
= B
=
ML
24EI
B
=
4
WL
8EI
max @1/2
=
2
ML
8EI
c
=
ML
12EI
c
A L/2 L/2 B
w/m
A B
C
w/m
A B
A
= B
=
2
PL
16EI
A
= B
=
3
WL
24EI
A
= B
=
3
5 WL
192 EI

C
=
3
PL
48EI
C
=
4
5 WL
384 EI
 
 

 
 
 
2L/3
L
max
B
M
A L/2 L/2
P
A B
C
w/m
B
=
ML
4EI
A
= B
= C
=  A
= B
= C
= 0
Max
@
2L
3
from A.
2
ML
27EI
C
=
3
PL
192EI
C
@ l/2
4
WL
384EI
a
P
b B
c

c
L
M
A B
W
B
A
l/2 l/2
MBA
MAB
C
=
2
Pa
2EI
’  Total
B
 =
3
Pa
3EI
+
2
Pa b
2EI
(C
= B
) B
=
ML
3EI
MAB
=
2
11
w
192

l
B
= C
+ 1
, 1
= b.
2
Pa
2EI
A
=
ML
6EI
= B
/2 MBA
=
2
5
w
192
l
B
=
3 2
Pa Pa
b.
3EI 2EI
 max
@
L
3
from A,max
=
2
ML
9 3 EI
2. Circular Tapering Bar: 1 2
4PL
L=
D D


 Defection of Composit Bar: 1 2
1 1 2 2
PL
L = L
A E A E
   

 Deflection due to Self Weight of Bar:
1. Prismatic Bar:
2
WL L
2AE 2E

   ,
2. Conical Bar:
2
WL L
2AE 6E

  
 Thermal Expansion: = ET, = LT
Coefficient of Thermal expansion (Aluminium >
Brass > Copper > Steel)
2
cr 2
EA
P (Euler's Theory)


 
c
R 2
A
P (Rankine's Formula)
1 .


  
 In case of Pure Bending:
3
Z D



 In case of pure Torsion: max 3
p
T 16T
Z D
  

3
p
Z D



 Bending Equation:
b M E
y I R

 
 Pure Torsion Equation For Circular Shaft:
T G
J r L
 
 
 Combined Bending & Torsion:
2 2
max 3
16
M M T
D
 
   
 
 
 ,
2 2
max 3
16
M T
D
 
  
 
 

 Equivalent Moment:
2 2
eq
1
M M M T
2
 
  
 
 
 Equivalent Torque:
2 2
eq
T M T
 
 
 
 
Theory Given by Remark
Maximum Principle Rankine Suitable for
Stress or Brittle
Maximum Normal
stress
Maximum Principle St. Venant Can be applied for
Strain Brittle and Ductile
Maximum shear Guest and Suitable for Ductile
Stress Treseca
Maximum Strain Haigh and Ductile
Energy Beltrami
Maximum shear Vonmises and Ductile
Strain energy Hencky
 Shear Stress:
VAy
Ib
 
 Shear Stress In Rectangular Section:
2
2
3
6s d
q y
bd 4
 
 
 
 
 
(q = ),
 Hoop Strain: H
pD
(2 )
4tE
   
 Longitudinal Strain: L
pD
(1 2 )
4tE
   
 Thin Spherical Pressure Vessels: n L
pD
4t
   
or t z
pD
4t
   
 Euler’s Buckling Load:
min
2
eff .
EI
P




 End Condition of column:
End
condition
One end fixed
one end free
Both end
Hinged
Both end
Fixed
One end fixed
one end Hinged
L
(Theoretical)
eff 2L L L/2 L
2
L (As per
IS code.)
eff
2L L 0.65L 0.8L
 Shaft In series:
4. DS
< Dk
4.Dk
< Ds
Force Method/Flexibility Method/ Displacement Method/Stiffness
Compatibility Method Method/Equilibrium Method
5. (i) Virtual work/Unit load method (i) Slope deflection method
(ii) Method of consistent deformation (ii) Moment distribution method
(iii) Elastic centre method (iii) Minimum potential energy
method
(iv) Column analogy method
(v) Three moment theorem
(vi) Castigliano’s theorem of
minimum strain energy
(vii) Maxwell-Mohr equation.
HYDROLOGY
 Water Budget Equation. P R G E T S
     
Instruments used in measurement
Relative humidity Psychrometer
Humidity Hygrometer
Wind speed Anemometer
Rainfall depth Ombrometer
Transpiration Phytometer
Evapotranspiration Lysimeter
Evaporation Atmometer
Name Isopleth
Isobar Pressure
Isohyets Rainfall
Isonif Snowfall
Isotherm Temperature
Isopleths Evapotranspiration
Isohaline Salinity
Annual Rainfall
 The Coefficient of variation
Cv
=
100 standard deviation
mean

=
m-1
100
P

 Number of Stations
2
v
C
N
E
 
  
 
, 
 10%,
m 2
i
i
m 1
(P P)
m 1




 ,
HIGHWAY ENGINEERING
Roman Roads  Tresaguet Construction  Metcalf Construction 
Telford Construction  Macadam Construction
Nov. 1927  Jayakar Committee formed
Feb. 1928  Recommendations by Jayakar Committee
net 1 2 1
A A A k
   
1
1
1 2
3 A
k
3 A A


  
'
1 1
A ( t / 2 d )t
  
l  2 2
A ( t / 2) t
  
l 
net 1 2
A ( t)t
  
l l
S.SOROUT, 9255624029
FOLLOWING BOOKS
AVAILABLE BY
CIVIL Ki GOLI PUBLICATION:
1. CIVIL Ki GOLI
2. CIVIL BOOSTER
3. REASONING Ki GOLI
4. HARYANA Ki GOLI
5. SOLUTION OF CIVIL Ki GOLI
6. ELECTRICAL & MECHANICAL
ENGINEERING ROCKET CHART
7. CIVIL’S CAPSULE
Note: Circular section (a) For maximum discharge 2
= 302º22, d = 0.938 D, (b) For maximum velocity 2
= 257º27, d = 0.81 D
Type of flow Depth of Velocity of Froude Comments
flow flow No
Subcritical y > yc
v < vc
Fr
< 1 As streaming or transquil
flow
Critical y = yc
v = vc
Fr
= 1
Super Critical y < yc
v > vc
Fr
> 1 Shooting flow, rapid
flow, torrential flow
Dynamic eq. for G.V.F.: o f
2
3
dy S S
q
dx
1
gy
 
 

 

 

 
 
Hydraulic Jump Eq.
1.
2
1 2 1 2
2q
y y (y y )
g
  , 2. Energy Loss EL =
3
2 1
1 2
(y y )
4y y

3.  
2
2
1
1
y 1
1 8F 1
y 2
   , 4.
3 1 2 1 2
c
y y (y y )
y
2


Types of Jump Fr EL
/E1
Water surface
Undular 1-1.7  0 Undulating
Weak 1.7-2.5 5–18% Small rollers form
Oscillating 2.5-4.5 18–45% Water oscillates in random
manner
Steady 4.5-9 45–70% Roller and jump action
strong  9  70% Very rough and choppy
NS = 5/4
N P
(H) (for Turbine), NS = 3/ 4
m
N Q
(H ) (for Pump)
Laminar Transition Turbulent
Flow in pipe Re
< 2000 2000 < Re
< 4000 Re
> 4000
Flow between Re
< 1000 1000 < Re
< 2000 Re
> 2000
parallel plate
Flow in open channel Re
< 500 500 < Re
< 2000 Re
> 2000
Flow through soil Re
< 1 1 < Re
< 2 Re
> 2
BMC
Test of Cement
 FINENESS TEST  Sieve Method
 Air permeability Method
 (Nurse and Blaine’s method)
 Sedimentation mehtod
 (Wanger Turbidimeter Method)
 CONSISTENCY TEST  Vicat’s Apparatus.
 SETTINGTIME  Vicat’s Apparatus.
 SOUNDNESS TEST  Le-chatelier Method
 Auto clave test
 TENSILE STRENGTH  Briquette test
 HEAT OF HYDRATION  Calorimeter test
 SPECIFIC GRAVITYTEST  Le-chatelier’s Flask.
Test On Concrete
 WORKABILITY  Slump test
 Compacting factor Test
 Vee-bee consistometer method
 DIRECT TENSILE  Cylinder Splitting Test
STRENGTH OF
CONCRETE
 BOND B/W CONCRETE  Pull out Test
&STEEL
 COMPRESSIVE  Rebound hammer Test
STRENGTH
Open-channel Flow
Steady unsteady
Uniform
canal flow
Gradually
Varied
(GVF)
Rapidly
Varied
(RVF)
Spatially
Varied
(SVF)
Gradually
Varied
(GVUF)
Rapidly
Varied
(RVUF)
Spatially
Varied
(SVUF)
Backing up
of water due
to dam
Hydraulic
Jump
Flow
over
side weir
River flow in
alluvial reach
during rising
flood
A surge
moving
upstream
Surface runoff
due to
rainfall
   
 Chezy’s Formula: V C RS
 , Manning equation 2 / 3 1/ 2
0
1
V R S
n

Dimension of C = L1/2
T–1
, n = L–1/3
T1
, f = Dimensionless
Surveying Chain: Revenue chain (33 ft), Gunter’s chain
(66 ft), Engineer’s chain (100 ft), Metric chain
Equipments for Measurement Right Angles: Cross
staff, optical square, Prism square.
 Tap Corrections:
 Correction for Slope: CS
= 2 2
L L h
 
 Correction for alignment or bad ranging: Cal
=
2
h
2L
 Correction for Temperature: Ct
= (Tm
-To
)L
 Correction for pull or Tension: CP
=
 
0
P P L
AE

 Correction for Sag: CS
=
2
2
L(wL)
24P

 Important Terms
 Bearing: Direction of a line with respect to fixed me-
ridian is called bearing.
 True Meridian/Bearing
 True meridian is a line joining True North pole,
True South Pole end and point of reference. It never
changes with time.
 Angle measured for any line w.r.t True Meridian is
called Ture bearing.
 Bearing Taken W.r.t magnetic meridian is called mag-
netic Bearing.
W E
S
N
A
M.M


E
O
Eastern Declination
W E
S
O
MM
TM
A

w

Western Declination
Magnetic Declination
 At any place horizontal angle b/w True Meridian and
Magnetic Meridian is called magnetic Declination.
For Eastern Declination:  = B + E
or T.B = M.B +E
For western Declination:  = B – w
or T.B = M.B – w
Note
(+) Sign is used for declination is to the east, sign (–)
is used if declination is to west
Fore bearing and Back Bearing: B.B = F.B  180º
Local Attraction: F.B – B.B  180º
Latitude and Departure
Projection of a line on N-S direction is called lati-
tude: L cos
  
l
Projectione of a line on E-W direction is called
deparature: D sin
 
l
Adjustment of closing Error.
 Sum of all internal Angles of a closed Traverse: (2n–
4)×90º where n = No. of sides.
 Sum of all deflection Angle = 360º
 Sum of latitude: L 0
 
 Sum of departure: D 0
 
 Closing error In the Traverse: 2 2
e = ( L) ( D)
  
 Bowditch’s Method (Compass Rule)
Permissible error in linear Measurment e 
Permissible error in angular measurement
1
e
.


 Correction to latitude: CL
= L
 



 Correction due to departure: CD
= D
 



 Transit Method: CL
= D
r r
L D
L , C D
L D
    
 Axis Method.
Correction of any length:
1
closing error
2
That length
Length of Axis

Direct levelling methods
Simple
levelling
Differential
levelling
check
levelling
Profile
levelling
Reciprocal
levelling
Fly
levelling
cross-section
levelling
Precise
levelling
 Sensitivity: Angle b/w the line of sights in radius
S
n
D R
   
 S
206265
R nD
 
 
 
 
l
D = Distance of the instrument from the staff
n = Number of divisions
l = length of one divison (2mm)
R = Radius of curvature
S = Staff intercept.
 Check in Height of Instrument Method
 BS–  FS =  Rise –  Fall = Last RL–First RL
 Curvature: CC
= –
2
d
2R
= –0.0785d2
. Refraction: Cr
=
2
1 d
7 2R
 
 
 
 
 Final Combination Correction:
C = Cc
– Cr
= –
2
6 d
7 2R
 
 
 
 
= –0.06735d2
• Distance of Visible Horizon
d = 3.85 h , d = in km and h = in meter.
 Reciprocal Levelling: The true difference Elevation:
H =  
a b a b
1
(h h ) (h ' h ')
2
  
 Determining Areas: Mid ordinate rule  (Area) = Av-
erage ordinate × Length of base,  = 1 2 n
O O .... O
L
n
  

 Average ordinate Rule: Area D = Average ordinate of
the base= 0 1 n
O O .... O
L,
n 1
  
 

 

 
L
D D
(n 1)
 

,
Member max
A member carrying compressive load 180
resulting from dead load and imposed load
A tension member in which reversal of
direct stress due to load other than 180
wind and seismic force
A member subj

ected to compressive
forces resulting from wind EQ force 250
provide deformation of such member
does not affect stress
Compression flange of Beam against 300
laterial torsional buckling.
A member normally act as a tie in 350
Roof Truss
Tension member other than Pre-tension 400
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Strength of plate between rivet holes in Tension =
at
× (p-d)x t
 Bearing strength of rivet = at
× d × t or = Pb
×d×t.
 Shear Strength of rivet =
2
vf
T d

 

(in single
shear),
2
vf
2 T d

  

in double shear), d = gross di-
ameter of rivet, d 6.01 t
 (unwins formula)
 Diameter: Grosss diameter = nominal diameter + 1.5
mm (if  25mm), Nominal diameter + 2mm (if >
25mm)
 Pitch: Should not exceed 16t or 200mm, which ever
is less in tension member, and 12t or 200mm, which
ever is less in Compression Members. Tacking riv-
ets should not exceed 32 t or 300 mm which ever is
less. Minimum pitch = 2.5d
 Force due to axial load on each rivet: Fa
=
W
n
 Force due to moment M on any rivet: Fm
= 2
M r
h


 Area along Section: Ant
=
2 2
1 2
1 2
S S
t b n d
4 g 4 g
  
   
 
  
 
  

 Net Effective Area:
l2
l1
 For pair of Angle Placed back to back connected by
only one lag of each angle.
net 1 2 2
A A A k
    ,
1
2
1 2
5 A
K
5 A A

 
 
The area of a web of Tee = Thickness of web × (depth
- thickness of flange)
Tacking rivet
Gusset plate
 Shape Factor: S =
p
y
M
M =
y p p
yz
a z z
a z

(Load factor = FOS × S)
Shape factor For different Shapes
Section Shape factor
1. Rectangular Section 1.5
2. Solid circular Section 1.7
3. Triangular Section 2.34
(vertex upward)
4. Hallow circular Section
3
4
1 k
1.7
1 k
 

 
 

 
5. a. Diamand Section Rhombus 2.00
b. Thin Hollow Rhombus 1.50
6. Thin Circular ring Solid 1.27
7. I section
a. About strong Axis 1.12
b. About weak Axis 1.55
8. T Section. 1.90 to 1.95
 Method of Analysis:
Plastic moment
condition
Equilibirim
condition
Mechanism
condition
(a) Lower bound theorem
(a) Upper bound theorem
 u
(P P )
 u
(P P )
Simply supported Beam
L/2 L/2
W
P
u
4M
W
L

Fixed Beam
L/2 L/2
W
P
c
8M
W
L

Eccentric Load
Fixed Beam:
b
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Books from CIVIL Ki GOLI Publication
1. Civil Booster: It is a Handbook which include 23 subject
of civil engineering . Civil Capsule and Civil
Engineering Rocket Chart are free with it.
2. Civil Capsule: It is a type of CIVIL Engineering
Pocket Dictionary. It can be used during travelling, office
time etc for quick revision.
3. CIVIL Engineering Rocket Chart: It is a 2 × 3 feet
wall chart of Civil Engineering Subjects. You can revise
whole Civil Engineering within 1-2 hour from it, which is
required during last time preparation of any exam.
4. CIVIL Ki GOLI :
This book has Qualitative questions
combination of previous years of IES, IAS, Gate, SSC-JE,
PSU’s, Various AE/JE Exams of states. This book has
Topic wise questions of each subject.
Each topic has divided into four levels:
(A) Level-1 (Basic Theory Questions)
(B) Level-2 (Theory Base Conceptual questions)
(C) Level-3 (Numerical Questions)
(D) Level-4 (Confusing Questions)
Note- Its solution is available in separate book named
Detailed solution of CIVIL Ki GOLI Book.

5. Reasoning Ki GOLI - This book contain (Total 94
papers) of reasoning topics only. It is design as per
Engineering exams pattern.
(a) Topic wise theory and Questions with detailed solutions
using short tricks.
(b) Previous 13 year papers of SSC JE with detailed
solution.
(c) RRB JE/SSE Previous year papers with detailed
solution.
(d) Previous year papers of Various AE/JE exams of various
States ( Up, Haryana, J&K, Delhi, Madhya Pradesh,
Punjab etc.) & PSU’s Papers like as FCI, DMRC, LMRC,
CIL etc. with solutions.
Note-
(1) Before purchasing any book of our publication, you must
check the BOOK content, which is available on CIVIL Ki
GOLI Facebook page/ Telegram Channel. You can also
download CIVIL Ki GOLI app for free CIVIL Engineering
qualitative material.
(2) We believe in quality of questions, not quantity.
(3) We believe in Error free content, So we have “Get One
Book Free On Each Data Error” .
(4) All books available on Amazon/Flipkart.
(5) For bulk order by coaching institute, you can contact to
Golden Book Depot, Delhi (Mob. 9811421791).