surveying ii manual 10 11

8/13/2019 Surveying II Manual 10 11

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THE THEODOLITE

AIM: To study the parts of the theodolite.

DEFINITION:It is an intricate instrument used mainly for accurate measurement of horizontal and vertical angles

up to 20,10,and 1 depending upon the least count of the instrument.

TYPES OF THEODOLITE

1) Based on rotation of telescope.2 TypesTransit theodolite and Non-transit theodolite.

2) Based on vernier.2 TypesVernier theodolite and Micrometer theodolite.

PARTS OF THEODOLITE

a) Trivet:It is a plate having a central threaded hole for fixing the theodolite on the tripod stand.It is also called base plate. 3 foot screws have screwed to this plate by means of ball & socket

arrangements.

b) Foot screws:

It is meant for leveling the instrument. The lower is fixed to the trivet & upper part is threaded

passing through tribrach plate.

c) Tribrach plate:

It is a triangular plate carrying 3 foot screws.

d) Leveling head:

Trivet, tribrach & foot screw constitute the leveling head.

e) Spindle or Axis:There are 2 spindles or axis i.e. inner & outer axis, the inner is solid & conical & outer is hollow.

The 2 spindle are co-axial.

f) Lower plate:

It is attached to the outer axis & is also known as scale plate. The size of theodolite is designed by

diameter of the lower plate.

g) Upper plate:

The upper plate contains vernier scale A & B, it is attached to inner axis.

h) Plate bubble:

It is provided on the upper surface of the vernier plate. It is used to identify whether the instrument is

leveled or not.


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i) Standard or AFrame:

2 frames are provided on the upper plate to support the telescope, vertical circle & vernier scale.

j) Telescope:

It is provided between the standard frames, it can be rotated about horizontal axis in

Vertical plane & is also provided with a focusing screw, clamping screw & tangent screw.

k) Vertical circle or vertical angle:

It is rigidly fixed to the telescope & moves with it.

l) Index bar or T-Frame:

It is provided on standard in front of vertical circle which carries 2 verniers i.e., C&D.The vertical edge of the index bar is provided with a dip screw at the lower end which

is used to bring the altitude bubble to the centre.

m) Compass:It is mounted on vernier scale between standards.


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Exp. No: MEASUREMENT OF HORIZONTAL ANGLE

AIM:To measure the horizontal angles by repetition method

APPARATUS:Theodolite with tripod, ranging rod.

PROCEDURE:The method of repetition is used to measure a horizontal angle to a finer degree of accuracy

than that obtainable with the least count of the vernier.

To measure the angle PQR

1. Set the instrument at Q & level it. With the help of upper clamp & tangent screws, set 00

reading

on vernier A. Note the reading of vernier B.2. Loose the lower clamp & direct the telescope towards the point P, clamp the lower clamp &

bisect point P accurately by lower tangent screw.

3. Unclamp the upper clamp & turn the instrument clockwise about the inner axis towards R.Clamp the upper clamp & bisect R accurately with the upper tangent screw. Note the reading ofverniers A&B to get the approximate value of the angle PQR.

4. Unclamp the lower clamp screw & turn the telescope clockwise direction & bisect P again.Bisect P accurately by using the lower tangent screw. It should be noted that the vernier readingswill not be changed in this operation, since the upper plate is clamped to the lower.

5. Unclamp the upper clamping screw & turn the telescope clockwise & sight R. Bisect Raccurately by upper tangent screw.

6. Repeat the process until the angle is repeated the required number of times.The average of horizontal angle with face left will be equal to final reading divided by 3.

7. Change face and make 3 more repetition as described above. Find the average angle with faceright, by dividing the final reading by 3.

8. The average horizontal angle is then obtained by taking the average of the 2 angles obtained withface left & face right.

Any numbers of repetitions may be made. However, 3 repetitions with the telescope normal& 3 with the telescope inverted are quite sufficient for anything except very precise work.

RESULT:

Average of horizontal angle by repetition method =


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Instru

mentat

Sightedto

Face Left Face RightAverageHorizontal Angles

Ver A Ver B Mean

Horizontal

Angles Ver A Ver B Mean

Horizontal

Angles

o

o

o

o

o

o

o

A

B

C

D

E


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Exp. No: MEASUREMENT OF HORIZONTAL ANGLE

AIM:Measurements of horizontal angles by direction method or reiteration method

APPARATUS:Theodolite with tripod, ranging rod, arrow.

PROCEDURE:

The method known as direction method or Reiteration method or Method of series is suitable forthe measurement of the angles of a group having a common vertex point. Several angles are

measured and finally the horizon is closed.

To measure angles AOB, BOC, COD, DOA by reiteration method.

1. Set the instrument over O & level it. Set the vernier to zero & bisect point A accurately.2. Release the upper clamping screw & turn the telescope clockwise, bisect the station B using the

upper tangent screw. Read the verniers. The mean of the vernier readings will give the angles AOB.3. Similarly bisect successively C, D, thus closing the circle. Read both the verniers at each bisection.

Since the graduated circle remains in a fixed position through out the entire process, each included

angle is obtained by taking the difference between two consecutive readings.

4. On final sight to A, the reading of the vernier should be the same as the original setting. If not, notethe reading & find the error due to slips etc.& if the error is small, Distribute it equally to all angles.

If large, repeat the process and take a fresh set of reading.

5. Repeat steps 2 & 4 with the other face.RESULT:

Average horizontal angle by reiteration method =


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C

B

A

DO

Instrument

at

Sightedto

Face Left Face RightAverageHorizontal Angles

Ver A Ver B MeanHorizontalAngles

Ver A Ver B MeanHorizontalAngles

o

o

o

o

o

o

o

A

B

C

D

E


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Exp No: MEASUREMENT OF VERTICAL ANGLES

AIM:To find the vertical angles using theodolite.

APPARATUS:Theodolite with tripod, arrows

PROCEDURE:

1. Level the instrument with reference to the plate level, as already explained.2. Keep the altitude level parallel to any 2 foot screws & bring the bubble central. Rotate the

telescope through 90 degree till the altitude bubble is on the third screw. Bring the bubble to

the centre with third foot screw. Repeat the procedure till the bubble is in central in both thepositions. If the bubble is in adjustment it will remain central for all pointings of the telescope.

3. Loose the vertical circle, clamp & rotate the telescope in vertical plane to sight the object, usevertical circle, tangent screw for accurate bisection.

4. Read both verniers (ie, C & D) of vertical circle and take the mean of two vertical angles andsame observations may be made for other face.

RESULT:

Measurement of vertical angle is ..


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-

+

B

A

Instrumentat

Sightedto

Face Left Face RightAverageVerticalAngles

Ver C Ver D MeanVerticalAngles

Ver C Ver D MeanVerticalAngles

o

o

o

o

o

o

o

A

B


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Exp. No: TACHEOMETRIC SURVEYING

AIM:

To determine the tacheometric constants using horizontal and inclined line of sight.

APPARATUS:Theodolite fitted with stadia hairs, leveling staff, arrows, chain or tape, ranging rods.

THEORY:

Tacheometry is a branch of surveying in which horizontal & vertical distances are determined by

taking angular observation with an instrument known as tacheometer.The method is very rapid & convenient. The accuracy of the tacheometry is less compared to

chaining, but it is best adopted in steep or broken ground or in water, where chaining is difficult.

PROCEDURE:

To determine the tacheometric constants K & C.

1 Measure a line about 60m long on fairly leveled ground and drive pegs at interval of 20m.2 Keep the staff on the pegs and observe the corresponding staff interval with Line of Sight

horizontal.

3 Knowing the value of D & s for different points, a number of simultaneous equation are formedby substituting values D in the formula D = Ks + C.

4 Solution of successive pairs of equation will give values of K & C.

To find the distance and elevation of the point when Line of Sight is horizontal.1 Hold the staff on given point and take the staff reading corresponding to top, middle and bottom

cross hairs and staff intercepts calculated.

2 Values of K, C and s are substituted in distance formula, D = Ks + C and distance of that pointfrom instrument is objected.

3 If staff reading on BM is known elevation of point is also calculated as shown in calculation.

To find the distance and elevation of the point when Line of Sight is inclined.

1 Hold the staff on elevated point on ground and observe the staff reading corresponding to all the3 hairs and staff intercepts is observed.

2 The values of K, C and s are substituted in distance formula, D = K.s. Cos2 + C. Cos andthen the distance is obtained.

3 The staff reading is taken on BM and by calculating vertical intercept v the elevation of pointis calculated.

RESULT:

1 Tacheometric Constantsi). Multiplying constant K=ii).Additive constant C =

2 Distance and elevation of the point when Line of sight is horizontali). Distance =ii).Elevation =

3 Distance and elevation of the point when Line of sight is inclinedi). Distance =


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ii).Elevation =OBSERVATION:

To determine the tacheometric constants K & C.

StaffStation

DistanceStaff Reading

Staff InterceptTop Middle Bottom

Distance Formula

D = Ks + C


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Exp. No. : ELEVATION OF OBJECT WHEN BASE IS ACCESSIBLE

AIM:To determine the elevation of an object using single plane method when base is accessible.

APPARATUS:Ranging rods, arrows, theodolite, tripod, tape & leveling staff.

PROCEDURE:

1) Level the instrument with reference to the plate level.2) Keep the altitude level parallel to any 2 foot screws & bring the bubble centre. Rotate the

telescope through 90 degree till the altitude bubble is on 3rd

foot screw. Repeat the procedure tillthe bubble remains in centre in both the position. If the bubble is in adjustment it will remain

centre at all the points of telescope.

3) Losing the vertical circle clamp, sight the B.M & the staff reading is noted. (Make the vernierreading C & D =0 & clamp).

4) Rotate the telescope to the object whose vertical distance has to be determined. Use tangent

screw for accurate bisection.5) Read both the vernier C & D of the vertical circle.6) The mean of 2 gives vertical angle. Similar observation has to be made with other face. The

average of 2 will give the required vertical angle.

7) Measure the distance between instrument station & object. Calculate the RL of the point.

RESULT:

1. The elevation of the object =

2. The height of the object =


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OBSERVATION:

Sightedto

Face Left Face RightAverage

Vertical AngleVer C Ver D Mean Ver C Ver D Mean

o

o

o

o

o

A

CALCULATION:

Horizontal distance of object from instrument D=Vertical angle to top of object, =

Staff reading on B.M, s =

Staff reading at base of object, s1=

In figure,

tan =

h = D tan=

R.L of A= R.L of B.M +s + h =

Height of object = s1+h =


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Exp. No. : ELEVATION OF OBJECT WHEN BASE IS INACCESSIBLE

AIM:To determine the elevation of an object using single plane method when base is inaccessible.

APPARATUS:

Ranging rods, arrows, theodolite, tripod, tape & leveling staff.

PROCEDURE:1) Set up a Theodolite at P and level it accurately with respect to altitude bubble.2) Direct the telescope towards Q and bisect it accurately. Clamp both the plates & read the vertical

angle 1.3) Transit the telescope so that the line of sight is reversed. Mark the second instrument station R

on the ground. Measure the distance RP accurately.

4) Repeat the step 2 for both face observation and the mean value of 1 is obtained.5) With the vertical vernier set to zero reading and altitude bubble to the centre, take the reading on

the staff kept near benchmark.

6) Shift the instrument at R. Set up instrument and then measure vertical angle2for both the faceobservation.

7) With the vertical vernier set to zero reading and altitude bubble centre of its run. Take thereading on the staff kept near benchmark.

8) Values entered in tabular column and elevation of object is calculated.

RESULT:Case 1: when s2> s1

1. Horizontal distance between instrument station and tower =

2. Elevation of tower =

Case 1: when s1> s2

1. Horizontal distance between instrument station and tower =

2. Elevation of tower =


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OBSERVATION:

Case (i) s2> s1

Instrumentat Face Left Face Right

AverageVertical Angle

Ver C Ver D Mean Ver C Ver D Mean

o

o

o

o

o

P

R

CALCULATION:

Staff intercept when instrument at A, s1=

Staff intercept when instrument at B, s2=

Staff intercept s= s2-s1

D =

=


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=

h1= D tan1

R.L of Q= R.L of B.M +s1+ h1

Case (ii) s1> s2




o

o

o

o

o

P

R


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Q

P

b

R

AB

h

BM

S

D

Staff intercept when instrument at A, s1=

Staff intercept when instrument at B, s2=

Staff intercept s= s1-s2

D =

Case (ii) s1= s2

=

=

h1= D tan1

R.L of Q= R.L of B.M +s1+ h1


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Exp. No: DOUBLE PLANE METHOD

AIM:

To determine the distance and difference in elevation between two inaccessible point usingdouble plane method.

APPARATUS:Theodolite with tripod, arrows, ranging rods, tape & leveling staff.

PROCEDURE:

1) Let P and R be the two instrument station & Q is the object. Set the instrument at P and level it

accurately with respect to the altitude bubble. Measure the angle of elevation 1.2) Sight the point R with reading on horizontal scale as zero and measure the angle 1at P.3) Take back sight s1on the staff held at benchmark when line of sight is horizontal.

4) Shift the instrument to R and measure 2and 2.5) The readings are tabulated and distance and elevation can be obtained as shown.

RESULT:1. Distance between P and Q= 2. Elevation of top of station Q=..3. Distance between Q and R= 4. Elevation of top of station R=..


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OBSERVATION:

CALCULATION:

In lePQR,

Apply sine rule,

=

=

Tabulation for Horizontal angle:

Instrumentat Face Left Face Right Average

HorizontalAngleVer A Ver B Mean Ver A Ver B Mean

o

o

o

o

o

P

R


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Tabulation for Horizontal angle:




o

o

o

o

o

P

R


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Exp. No:

SETTING OF CURVE BY PERPENDICULAR OFFSETS FROM LONG CHORD

AIM:To set out a simple curve by perpendicular offsets from long chord.

APPARATUS:Ranging rods, cross- staff, tape, chain & arrows.

PROBLEM:Give length of long chord 80m and Mid-ordinate 4m interval along long chord is 10m.

PROCEDURE:

1. Set T1and T2at distance of 80m on level ground and divide T1and T2and locate mid point.2. Measure 10m distance on either side of mid point along long chord and locate points.

3. Calculate the Radius using the formula,

O0=22 (L/2)-R-R

4. Calculate the ordinates of remaining points using the formula,

Ox=)O(Rx-R 0

22

5. Knowing the value of the perpendicular offsets (ordinate) from each of offset points on groundby using cross staff at various points. i.e O10, O20, O30etc are located at a distance of 10, 20,

30.etc. from mid point of long chord.

6. Join ends of all these perpendicular offsets to get smooth simple curve.

RESULT:

Hence a simple curve set on the ground and observed


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OBSERVATION:

Distance from mid oflong chord in m

Perpendicular Offset inm


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Exp. No: CHORD PRODUCED

AIM:Set out a simple curve by the method of deflection distance (offset from chords produced).

APPARATUS:Ranging rods, cross- staff, tape, chain & arrows.

PROBLEM:

Two tangents intersect at chainage=1000m, the deflection angle 500. Set out a curve of 100m

radius to connect the tangents by the method of deflection distance. Take peg interval of 20m

PROCEDURE:

1) Locate the tangent point T1 and obtain its chainage as per the calculation. Calculate the length of

first subchord(C)

2) With zero at T1spread the chain along first tangent point A1on its such that T1A1= C= length of

first subchord.

3) With T1 as center, T1A1 as radius. Swing the chain such that arc A1.A=O1, O1=R2

C 2

1 Fix the point

A on the curve.

4) Now stretch the chain along T1A & pull it straight in the direction point B2such that zero of

chain at A and distance 22 ABCC

5) With zero of chain center at A and AB2 as radius, swing the chain to point B. Such that B2B=

O2= Length of second offset of point B on the curve.

O2 =R2

)C(CC 212 .

6) Now stretch a chain along AB and repeat the step 4 and 5 till tangency T2 is reached

RESULT:Hence setting of simple curve by successive bisection of chords can be done.


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OBSERVATION:

CALCULATION:

Tangent Length , T= R tan

Length of curve, L=

Given chainage of point of intersection=

Chainage at T1= Chainage of P.I- Tangent Length

Chainage at T2= Chainage at T1+ Length of curve


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No. of intermediate chords=

Total No. of chords=

Length of 1stsub chord, C1=

C2= C3= C4= C5

C6=

Formula Length of offset

O1=R2

c2

O2 =R2

C)(cC .

O3= O4= O5=R

C2

O6=

.

Where c = First Subchord

C = Intermediate Chords

c= Last Subchord


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Exp. No: RANKINES DEFLECTION ANGLES MEHOD

AIM:To set out simple curve by using Rankines deflection angles method.

APPARATUS:Theodolite, Ranging rods, arrows, tape, etc.

PROCEDURE:1) Set the theodolite at the point T1with both the plates clamped to zero, direct the theodolite to

bisect the point of intersection (V). The line of sight is thus in the direction of the rare tangent.

2) Release the verniers plate. Set the angle 1on the vernier. The line of sight is thus directed alongT1A.

3) With the zero end of the tape pointed at T1 and arrow held at distance T1A=C1along it. Rotatethe tape around T1, till arrow is bisected by the cross-hair. Then the first point A is fixed.

4) Set the second deflection angle 2 on the vernier so that, the line of sight is directed along T1A.5) With the zero end of the tape pinned at A and arrow head at a distance AB=C2 along it.6) Move the tape around Atill the arrow is bisected by cross-hair, thus fixing the point B.7) Repeat the procedure till the last T2is reached.

CHECK:The last point S0located must co inside with the point of tangency (T2). If the error is small, last few

pegs may be adjusted. If the error is more, the whole curve should be reset.

RESULT:The desired curve is set on the ground.


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OBSERVATION:

CALCULATION:

Radius of curve =

Deflection angle, =

Tangent Length , T= R tan

Length of curve, L=


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Given chainage of point of intersection (V) =

Chainage at T1= Chainage of P.I- Tangent Length

Chainage at T2= Chainage at T1+ Length of curve

No. of intermediate chords=

Length of 1stsub chord =

Length of last sub chord =

Points Chainage

in m

Chord

length in

m

Tangential angle,

n=

Formulae for

Deflection

angle

n=n-1+ n

Deflection

angle

Actual

theodolite

reading

T1

A

B

C

D

E

F

T2

CHECK:

1.The Final angle of VT1T2 =

2. Length of T1T2 = 2R sin


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Exp. No: TO SET OUT COMPOUND CURVE WITH ANGULAR METHODS WITH

USING THEODOLITE ONLY

AIM:To set a compound curve of radius RS=30m, RL=40m, 1=40

0, 2=50

0.

APPARATUS:

Theodolite, Ranging rods, arrows, tape, etc.

PROCEDURE:

1) Compound curve we can set using deflection angle method. Set the theodolite at T1with vernierA=0, directed along T1B.

2) Set the curve T1Das simple curve from radius RS.3) Shift the theodolite to PCC & orient the instrument make vernier A to read an angle(360- 1/2)

and bisect the station T1& clamp the bottom screw.4) Turn the telescope clockwise till the vernier from A reads 00. Now telescope is turned by 1/2

from the long chord T1D, that it is the line of sight is along DD1, which is common tangent to the

compound curve.5) Plunge the telescope. Now the line of sight is along DD2which is also common tangent for the

arc DT2. Set the second point of the curve using deflection angle method till we get point T2.

CHECK:The observation by measuring the angle T1T2should be equal to

2180

21 or

2180

RESULT:The desired curve is set on the ground.


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OBSERVATION AND CALCULATIONS:

Total deflection angle =1+2

Length of back tangent arc T1D = D1D = ts = Rstan

Length of tangent arc T2D = D2T2= D2D = tL = RLtan

Tangent distance corresponding to shorter radius Ts= ts+


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Tangent distance corresponding to Larger radius TL= tL+

Length of curve corresponding to shorter radius Ls=

Length of curve corresponding to larger radius LL=

Chainage at T1= Chainage of P.I- Ts

Chainage at T2= Chainage at T1+ Ls+ LL

Chainage at P.C.C= Chainage at T1+ Ls


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1stcurve

Points Chainage

in m

Chord

length inm

Tangential angle,

n=

Formulae for

Deflectionangle

n=n-1+ n

Deflection

angle

Actual

theodolitereading

T1

A

B

C

PCC

2nd

curve

Points Chainagein m

Chordlength in

m

Tangential angle,

n=

Formulae forDeflection

angle

n=n-1+ n

Deflectionangle

Actualtheodolite

reading

PCC

D

E

F

G

T2


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Exp. No: SETTING OUT CENTRE LINE OF COLUMN

AIM:

Set out centre of line for the column of building.

APPARATUS:

Prismatic compass, Ranging rods, arrows, tape, lime powder etc.

PROCEDURE:

1) Prismatic compass is set out at a column A and centre line A-A is fixed with respect to North bystretching string between arrow direction at ends.

2) The centre line 1-1 which is perpendicular to A-A. Setting out right angle by forming a triangle with

3-4-5 units along sides (3-4-5 by using tape)

3) The other centre line of the column are marked with reference to centre line A-A and 1-1 as per theplan measurements.

4) The column pits and other lines of the foundation trench of all the walls are set by measuring distance

from centerline on either side of equal to trench width.5) The column and trench pits are marked on the ground by lime powder.

RESULT:

The centre line of column of given plan is marked and observed on the field

surveying ii manual 10 11

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