college of engineering and technology · the telescope can be revolved through a complete...

VIDYAA VIKAS COLLEGE OF ENGINEERING AND TECHNOLOGY

TIRUCHENGODE-637 214 (Affiliated to Anna University-Chennai)

LABORATORY MANUAL

SUBJECT CODE: CE 6413

SUBJECT NAME: SURVEY PRACTICAL - II

YEAR : II

SEMESTER : IV

Prepared by

M.SOUNDAR RAJAN ASSISTANT PROFESSOR

DEPARTMENT OF CIVIL ENGINEERING

SURVEY PRACTICAL – II

SYLLABUS

OBJECTIVE

At the end of the course the students will posses knowledge about survey field

techniques.

1. Study of theodolite.

2. Measurement of horizontal angles by reiteration, repetition and vertical

angles.

3. Theodolite survey traverse.

4. Height and distances – Triangulation – Single Plane Method.

5. Tachometry – Tangential system – Stadia system – Subtense bar system.

6. Setting out works – Foundation Marking – Simple curve right/ left handed –

Transition curve. 7. Field observation for Calculation of azimuth.

8. Field work of Total Station.

Total Hours: 60

GENERAL INSTRUCTIONS

1. All the students are instructed to wear protective uniform, shoes

and cap before entering into the laboratory.

2. Before starting the exercise, students should have a clear idea

about the principles of that exercise.

3. All the students are advised to come with completed record and

corrected field book of previous experiments, defaulters will not

be allowed to do their experiment.

4. Don’t operate any instrument without getting concerned staff

member’s prior permission.

5. All the instruments are costly. Hence handle them carefully, to

avoid fine for any breakage.

6. Utmost care must be taken to avert any possible injury while on

laboratory work. Incase, anything occur immediately report to the

staff members.

7. One student from each batch should put his/her signature during

receiving the instrument in instrument issue register.

8. Don’t adjust the permanent adjustment screws of theodolite and

levelling instrument to avoid the collection of fine amount

equivalent to the servicing charge of the particular instrument.

CONTENTS

Ex.No.

Date NAME OF THE EXERCISES PAGE

NO.

THEODOLITE SURVEYING

01 Study of theodolite.

02 Determination of horizontal angles by repetition method.

03 Determination of horizontal angles by reiteration method

04 Determine the vertical angle to the given objects.

TRIGONOMETRICAL LEVELLING

05 Determine the elevation of the objects by Single Plane

Method.

06 Determine the elevation of the objects by Double Plane

Method.

TACHEOMETRIC SURVEYING

07 Determination of tacheometric constant by stadia method.

08 Determination of gradient of a line by stadia method.

09 Determination of gradient of a line by Tangential

Tacheometry.

10 Determination of Area by Tangential Tacheometry

11 Determination of gradient of the line joining staff station

and the target by Subtense Bar method

SETTING OUT WORKS

12 Setting out of the foundation for a building.

13 Setting out simple circular curve by long chord method.

ASTRONOMICAL SURVEY

14 Azimuth by the Ex-meridian observation on the sun

TOTAL STATION

15 Field work using Total station

Exercise No .1 Date:

STUDY OF THEODOLITE

DESCRIPTION:-

The theodolite is the precise instrument designed for the measurement of horizontal angle and

vertical angle and has a wide applicability in surveying such as laying of horizontal angle,

locating points on line, prolonging survey lines, establishing grades, determining difference in

elevation, setting out curves etc.

PARTS OF A TRANSIT THEODOLITE:-

The telescope can be revolved through a complete revolution about its horizontal axis in a vertical plane. A. Levelling head:

1. A Levelling head consists of two parallel triangular plates known as tribrach plates.

2. The upper tribrach has three arms each carrying a Levelling screw.

3. The main functions of the Levelling head is,

(a) To support the main part of the instruments.

(b) To attach the theodolite to the tripod.

(c) To provide a mean for leveling the theodolite.

B. Telescope:

1. It is mounted on a spindle known as horizontal axis or trunnion axis

C. Vertical circle:

1. It is a circular arc attached to the trunnion axis.

2. By means of vertical clamp screw and tangent screw the telescope can be accurately set at

any desired position in vertical plane.

3. The graduation in each quadrant is numbered from 0 to 90 in opposite directions.

D. Index Frame:

1. At the two extremities, two Vernier are fitted to read the vertical axis.

2. When the telescope is moved in a vertical plane, the Vertical circle moves relative to the

Vernier with the help of which reading can be taken.

3. A long sensitive bubble tube is placed on the top of the index frame.

E. Standards (or) A – Frame: 1. This stands upon the Vernier plate to support the horizontal axis.

F. Two Spindles:

1. The two axes have a common axis, which forms the vertical axis of the instruments.

G. Lower plate:

1. It carries a horizontal circle graduated from 0 to 360 in a clockwise direction as silvered,

beveled edge.

2. By means of clamp screw and tangent screw this can be fixed at any desired position.

H. Upper plate:

1. It also carries clamp and tangent screw to accurately with the lower plate.

2. On clamping the upper clamp and unclamped lower clamp, the instrument can rotates on its

outer axis without any relative motion between the two plates.

3. If the lower clamp is clamped and upper clamp unclamped, the upper plate and the instrument

can rotate on the inner axis with a relative motion between the Vernier and the scale.

4. For using any tangent screw, its corresponding clamp screw, its corresponding clamp screw

must be tightened.

I. Level tubes:

1. This upper plate carries two level tubes placed at right angles to each other in which one is

kept parallel to the trunnion axis.

2. Theses can be centered with the help of foot screws.

J. Plumb Bob:

1. This is suspended from the hook fitted to the bottom of the inner axis to canter the

instruments exactly over the station mark.

TEMPORARY ADJUSTMENTS:

A. Setting over the station:

1. Centre the instruments over the station marked by a plumb bob.

2. Level approximately with the help of tripod leg.

B. Levelling Up:

1. Do these using three-foot screws similar to that of Levelling instrument.

C. Elimination of Parallax:

1. By focusing the eyepiece for distinct vision of the cross hairs.

2. By focusing the objective to bring the image of the object in the plane of cross hairs.

IMPORTANT TERMS:-

1. Vertical Axis:- The axis about which the theodolite may be rotated in a horizontal plane.

2. Horizontal Axis:- The axis about which the telescope along with the vertical circle of a

theodolite may be rotated in a vertical plane.

3. Axis of telescope:- The axis about which the telescope may be rotated is called axis of

telescope.

4. Axis of the level tube:- The straight line that is tangential to longitudinal curve of the level at

its centre is called axis of the level tube.

5. Centering:- The process of setting up theodolite exactly over the groundwork station is

called known as centering.

6. Transiting:- The process of turning the telescope in vertical plane through 180 about its

horizontal axis is called transiting.

7. Swing:- A continuous motion of the telescope about the vertical axis in horizontal plane is

called swing the swing may be either in face left or right.

8. Face left observation:- The observation of angles when the vertical circle is on the left side

of scope.

9. Face right observation:- The observations of angles when the vertical circle is on the right

of the telescope.

10. Changing the face:- The operation of changing the face of telescope from right to left and

vice-versa.

11. A set:- A set of horizontal observations of any angle consists of two horizontal measures one

on the left face and other on the right face.

12. Telescope normal:- A telescope is said to be normal when its vertical circles is to its left and

bubble of the telescope is up.

13. Telescope inverted:- A telescope is said to be inverted or reversed when its vertical circle is

to its right and the bubble of the telescope is down.


DETERMINATION OF HORIZONTAL ANGLE (REPETITION METHOD)

Aim :-

To determine the included angle between two object stations P and Q by using repetition method.

Instruments Required:-

Theodolite, Tripod.

Procedure :-

1. Set the instrument at “O” approximately at the middle of the given objects to avoid too obtuse

and too acute angles.

2. Do all initial adjustments and keep the vertical circle at left hand side.

3. Set 0 at Vernier A with the help of upper clamp and tangent screws.

4. Loosen the lower clamp screw and direct the telescope towards the objects P.

5. Tighten the lower clamp and bisect point P accurately by lower tangent screw.

6. Unclamp the upper clamp screw and turn the telescope clockwise towards “Q”

7. Clamp the upper screw and bisect “S” accurately by upper tangent screw.

8. Note the reading of verniers A and B to get the angle of POQ.

9. Loosen the lower clamp screw. Turn the telescope to sight “P” again and bisect accurately by

lower tangent screw.

10. Repeat steps 5 to 9 until the angle is repeated to the required number of repetitions.(usually 3)

11. Change the face to right, and set the Vernier A to 180 to eliminate graduation error in

horizontal circle and note the readings similarity as above.

Calculation:-

To find the horizontal included angle divide the total angle by the number of repatriations.

Result: -

Average Horizontal angles of POQ, QOR, ROS, SOP

S P

O

Q

R

Det

erm

inat

ion

Of H

oriz

onta

l Ang

le –

Rep

etiti

on M

etho

d.

Face

: R

ight

Swin

g : l

eft

A

vg.

Hor

izon

tal

A

ngle

’

o

Hor

izon

tal

Ang

le

’

o

No. of rep. M

ean

’

o

B

’

o

A

’

o

Face

: Le

ft

sw

ing

: Rig

ht

Hor

izon

tal

Ang

le

’

o

No. of rep.

Mea

n

’

o

B

’

o

A

’

o

Sight to

Inst.At

O


DETERMINATION OF HORIZONTAL ANGLE (REITERATION METHOD)

Aim:-

To determine the included angle between the given objects (A, B, C and D) by reiteration

method.


Theodolite, Tripod, Ranging rods.

Procedure: -

1. Set the instrument over “O” which should be at the center of the arrangement of the given

objects.

2. Do all the initial adjustments and keep the vertical circle to left.

3. Set Vernier A to 00’0” , bisect the ground point “A” and turn the telescope to bisect object B

by loosening the upper clamp screw and upper tangent screw.

4. Read t\both Vernier. The mean of the Vernier readings will give the angle AOB

5. In the same way bisect the other objects in clockwise direction and note down the readings.

6. Since the graduated circle remains in a fixed position throughout the entire process, each

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

7. On final sight to A the reading of the Vernier should be the same as the original settings. If

not, note the reading and find the error due to slips ect., If the error is small, distribute it

equally to all angles, if large, repeat the procedure and a fresh set of readings.

8. Do the same procedure with the other face in anticlockwise direction.

A

B

E O

C

D

Results :-

The Horizontal Angle between the given points by

REITERATION method is

Det

erm

inat

ion

Of H

oriz

onta

l Ang

le –

Rei

tera

tion

Met

hod.

Face

: R

ight

Sw

ing

: lef

t

Avg

.

Inc

lude

d

A

ngle

’

o

Incl

uded

Ang

le

’

o

Mea

n

’

o

B

’

o

A

’

o

Face

: Le

ft

Sw

ing

: R

ight

Incl

uded

Ang

le

’

o

Mea

n

’

o

B

’

o

A

’

o

Sigh

t

to A

B

C

D

E A

Inst.

At

O


DETERMINATION OF VERTICAL ANGLE

Aim :-

To determine the vertical angle to the given objects.

Instruments Required: -

Theodolite, Tripod.

Procedure: -

1. Set up the instrument at any convenient place to cover all the given points.

2. Level the instrument with reference to the altitude bubble by using foot screws as in the case

of horizontal bubble Levelling.

3. Set the zero of the vertical Vernier exactly in coincidence with the zero of the vertical scale.

4. Loosen the vertical plane until the focused object is bisected use tangent screw for accurate

bisection.

5. Read both the verniers C and D of vertical circle.

6. Denote the depression angle with negative sign.

7. Similarly bisect all other objects and find out the readings accurately.

8. Change the face and follow the steps 4 to 6 above.

Results :-

The Vertical angle is = ……………. C

A B

Det

erm

inat

ion

of v

ertic

al a

ngle

:-

Face

: Rig

ht

Avg

.

Ver

tical

Ang

le o

f

Face

s

“

’

o

Ver

tical

Ang

le “

’

o

Mea

n

“

’

o

D

“

’ o

C

“

’

o

Face

: Lef

t

Ver

tical

Ang

le “

’

o

Mea

n

“

’

o

D

“

’

o

C

“

’

o

Sight to

Instrument at


DETERMINE THE ELEVATION OF THE OBJECT BY SINGLE PLANE METHOD

Aim: -

To find out the Reduced Level (R.L.) of inaccessible elevated point by Trigonometrical

Levelling.

Instruments required: -

Theodolite, Levelling staff, Ranging rod, Tape.

Given data: -

Elevation of B.M. = 100.000 m

General:-

(a) Trigonometry is the process of determining the differences of elevation of the stations from

observed vertical angles and known horizontal distance either measured directly or computed

trigonometrically.

(b) Instruments stations and the elevated object are in the same plane.

Procedure: -

1. Set up the theodolite at A, level it carefully and observe the angle of elevation 1.

2. Set the vertical vernier to zero, and take a reading on a staff held vertically on a BM.

Let it be S1

3. Transit the telescope, so that the line of sight is reversed.

4. Mark a point B in the line of sight at a convenient distance d, Measure it accurately,

5. Shift the theodolite to the point B, Centre it and level it. Observe the angle of elevation 2.

6. Set the vertical vernier to zero and take again a B.M., reading as S2.

C

h2

h1

a2 a1

B S2 S1 A d D B.M. Instrument axis at B is higher than A. h1 = D tan 1

h2 = ( D + d ) tan 2

S = S2 – S1

S = h1 – h2

h1 – h2 = D tan 1 – ( D + d ) tan 2

S = D (tan 1 – tan 2) – d tan 2

then,

S + d tan 1 D = tan 1 – tan 2 R.L. of C = R.L. of B.M. + S1 + h1

A is higher than B. then,

d tan 2 – S D = tan 1 – tan 2 R.L. of C = R.L. of B.M. + S1 + h1 Result: Reduced Level of the given inaccessible elevated point=

Det

erm

inat

ion

of v

ertic

al a

ngle

:-

Face

: Rig

ht

Avg

.

Ver

tical

Ang

le o

f

Face

s

’

o

Ver

tical

Ang

le

’

o M

ean

’

o

D

’

o

C

’

o

Face

: Lef

t

Ver

tical

Ang

le

’

o

Mea

n

’

o

D

’

o

C

’

o

Sight to

Instrument at


DETERMINE THE ELEVATION OF THE OBJECT BY DOUBLE PLANE METHOD

Aim :-

To find out the R.L. of the inaccessible elevated point by Trigonometrical Levelling with

instrument at double vertical plane.


Theodolite, Levelling staff, Ranging rod, Tape.

Given Data:-

R.L. of the B.M. = 100. 000m.

General: -

Instrument stations and the elevated objects are in different planes.

Procedure: -

1. Let the given point is “B”

2. Set up the theodolite station A, centre it carefully and fix the ranging rod at C of known

distance “d”

3. Measure horizontal angles BAC, Let it be 1, in angles BAC should be individually equal to

30 to 75.

4. Sight ‘B’ the top of the object and observe the angle of elevation 1 ensuring that altitude

bubble is center of its run.

5. Setting the vertical vernier to zero take a reading on a staff held vertically on a benchmark.

Let the reading be S1.

6. Shift the theodolite the station C at a known distance ‘d’ and centre it over the mark and

observe that the horizontal angle BCA. Let it be 2.

7. Sight ‘B’ the top of the object and observe the angle of elevation 2, ensuring that the altitude

bubble is central of its run.

8. Setting up the vertical vernier to zero takes a reading on a staff on the same benchmark. Let it

be S2.

9. Measure the horizontal distance ‘d’ between stations A and C.

Calculation:-

B

A C

Applying SIN rule to triangle ABC we can find AC & BC.

Sin A D

Sin B d

D be the distance between B and C

Angle ABC = 180° (θ1+θ2)

then,

Sin A D = x d Sin B

H.I. = D tan α1

Reduced Level of B = R.L. of B.M. + S1 + H1

Result:-

Reduced Level of the given inaccessible elevated point =

C h2 B h1 s2 d C s1 A BM

Det

erm

inat

ion

of g

radi

ent o

f lin

e:

Fac

e: L

eft

Sw

ing

: Rig

ht

Stad

ia R

eadi

ng

Bottom

Fac

e: R

ight

Sw

ing

: Lef

t

Middle

Top

Hor

izon

tal A

ngle

Mea

n

’

o B

’

o

A

’

o

Ver

tical

Ang

le

Mea

n

’

o

D

’

o

C

’

o

Sight to

B B

Inst. at

A C


TACHEOMETRIC CONSTANT – STADIA METHOD

Aim :-

To determine the additive and multiplication constant of Tacheometer by Stadia Tacheometry.


Tacheometer with stand, Levelling Staff, Ranging rods, tape.

General :-

An ordinary transit theodolite fitted with stadia hair is known as Tacheometer. This method

completely eliminated the use of tape or chain and is vary rapid and convenient.

Procedure: -

1. Setup the instrument at A.

2. Measure a line AB, 120metres long on a fairly level ground and fix arrows at 30m intervals.

3. Note down the stadia hair readings (top, middle, bottom) by placing the staff over the arrow

stations (PQRS).

4. Keep the vertical circle to read zero during observations.

5. Calculate the other staff intercepts in the manner.

Calculation:-

Stadia intercept:

S = Difference of top and bottom hair readings.

Let S1 is the staff intercept corresponding to distance D1 and S2 corresponding to D2.

By using tacheometric equation.

D= f/i S + ( f + d ), since vertical angle is zero.

Where, f/i = Multiplying constant denoted by K

and, ( f + d ) = additive constant denoted by C

then, D = KS + C

Now we have,

D1 = KS1 + C

D2 = KS2 + C

Solving the above two equations to get the values for K and C.

Similarly find out the values for K and C, by other set of readings.

The average values of the K and C will be the tacheometric Constants.

Tabulation:- (Tacheometric constant)

Inst. at Staff station Horizontal

Distance

Stadia hair readings Stadia

intercept Top Middle Bottom

A P 30m

Q 60m

R 90m

S 120m

Result: -

Tacheometric Multiplying constant K =

Tacheometric additive constant C =

Staff

Instrument

A 30m 60m 90m


DETERMINATION OF THE GRADIENT OF THE LINE BY STADIA METHOD

Aim :-

To determine the gradient of the line joining two staff stations (A and B) by stadia method.


Tacheometer, Levelling Staff.

Given R.L. of Bench Mark = 100.000m

Procedure: -

1. Set up the instrument at P approximately between the given objects A & B and do the initial

adjustments.

2. If the given points A & B are ground points, the line of sight is horizontal line of sight, so no

need of taking vertical angle, the vertical Vernier reading should be set to 0, take horizontal

angle between A & B, and stadia hair readings at A and B.

3. If the given points A & B are an elevation points or depression points means, the line of sight

is inclined line of sight. For that measure the vertical angle as well as the corresponding

horizontal angle and also the stadia hair readings.

4. Take horizontal angles, vertical angles, and stadia readings in both the faces and swings.

5. Hold the staff on given Bench Mark, take Bench Mark staff readings.

6. Then by calculation find the gradient between the given points.

Calculation:

Case: I

When the observed vertical angle D is of an angle of elevation

V = The vertical distance from the instruments axis to the point

S = central cross-hair reading taken at A.

ho = B.M. Staff reading

V = D tan

D = KS Cos2 + C Cos

R.L. of H.I. = Elevation of B.M. + Back sight (h0)

R.L. of A = R.L. of H.I. + V – h

Case: II

When the observed vertical angle is an angle of depression.

R.L. of A = R.L. of H.I. – V – h

Case: III

When the observed vertical angle is zero.

R.L. of A = R.L. of H.I. – h

D2 = D12 + D2

2 – 2D1D2 cos

S h V A

S h0 D

BM

S V S h A

Staff Instrument h S A

A B D1 S Ø

P

Result :- The gradient of the line joining A and B =

Det

erm

inat

ion

of g

radi

ent o

f lin

e:

Face

: Lef

t

Sw

ing

: Rig

ht

Stad

ia R

eadi

ng

Bottom

Face

: Rig

ht

Sw

ing

: Lef

t

Middle

Top

Hor

izon

tal A

ngle

Mea

n

’

o B

’

o

A

’

o

Ver

tical

Ang

le

Mea

n

’

o

D

’

o

C

’

o

Sight to

A B A B

Inst. at P P


GRADIENT OF THE LINE BY TANGENTIAL METHOD

Aim :-

To determine the gradient of the line joining the given staff stations A and B by tangential

method.


Theodolite, Ranging rods, leveling staff.

Given data: -

Elevation of B.M. = 100.000m

Target Distance = 1.000m

Description:

In the tangential method, two targets are fixed on the given object at some interval. The interval

distance between two target is consider as staff intercept. The vertical angle are taken for the two

targets.

Procedure: -

1. Set up the instrument at P approximately between the given objects A, B and do the initial

adjustments.

2. Fix the two targets at the ranging rod at some fixed constant interval, say 1m, denote the

interval distance as “S”

3. Direct the telescope towards objects A and find the vertical angles 1, 2 by bisecting the

ranging rod at two targets having a distance of 1m, and also take the staff reading “r” at A.

4. Take the horizontal angle APB

5. Place the ranging rod at point B and repeat the step 3

6. Hold the staff on B.M. and take the staff reading.

7. By calculation find the gradient of any two points.

Case – I

When both the observed angles are angles of elevation.

B.M. = 100.000m

S = 1m = Target distance

1 & 2 = Vertical angle to upper and lower targets respectively.

h0 = B.M. staff reading

D1 = Horizontal distance between P and A = S / (tan 1 – tan 2)

D2 = Horizontal distance between P and B = S / (tan 1 – tan 2)

D2 = D12 + D2

2 – 2D1D2 cos

V = D tan 2

R.L. of H.I. = R.L. of B.M. + h0

R.L. of A = R.L. of H.I. + V1 - r

S V h1 A P h0 D

B.M.

Case – II

When the observed angles are angles of depression.

D1 = S / (tan 1 – tan 2)

D2 = D12 + D2

2 – 2D1D2 cos

V = D tan 2

R.L. of A = R.L. of H.I. – V – r

S V S h A D

Case – III

When one of the observed angle is an angle of elevation and the other angle of depression.

D = S / (tan 1 + tan 2)

D2 = D12 + D2

2 – 2D1D2 cos

V = D tan 2

R.L. of A = R.L. of H.I. – V – r

Gradient: - R.L. of A – R.L. of B

The gradient between the points “A” and “B” = Horizontal distance between them

Result :- The gradient of the line joining A and B =

S V S h A D

D A B D1 D2 Ø

P

V S Instrument h D

Det

erm

inat

ion

of g

radi

ent o

f lin

e:

Face

: Rig

ht

Sw

ing

: Rig

ht

Stad

ia R

eadi

ng

Top

Face

: Lef

t

Sw

ing

: Lef

t

Middle

Bottom

Hor

izon

tal A

ngle

Mea

n

“

’

o

B

“ ’

o

A

“

’

o

Ver

tical

Ang

le

Mea

n

“

’

o

D

“

’

o

C

“

’

o

Position of vane

Top

vane

Bot

tom

va

ne

Top

vane

Bot

tom

va

ne

Top

vane

Bot

tom

va

ne

Top

vane

Bot

tom

va

ne

Sight to

A B A B

Inst. at P P


DETERMINATION OF AREA BY TANGENTIAL METHOD

Aim :-

To determine the area enclosed by the given points with the help of theodolite and ranging rods.

Instruments Required :-

Theodolite, Ranging rods, Levelling staff.

Given data :-

Elevation of B.M. = 100.0000m

Target Distance = 1.000 m

Procedure: -

1. Set up the instrument at O approximately between the given objects A,B,C and do the initial

settings.

2. Fix the two targets at the ranging rod at some fixed constant interval, say 1m, denote the

interval distance as “S”

3. Set the Vernier A as 00’0”, Direct the telescope towards ranging rod at A and find the

vertical angles 1, 2 by bisecting the ranging rod at two targets having a distance of 1m, and

also take the staff reading “r” at A.

4. Direct the telescope towards objects B and find the vertical angles 1, 2 by bisecting the

ranging rod’s targets having a distance of 1m at B, take the staff reading “r” at B and also

take the horizontal angle AOB.

5. Direct the telescope towards objects C and find the vertical angles 1, 2 by bisecting the

ranging rod’s targets having a distance of 1m at C, take the staff reading “r” at C and also

take the horizontal angle BOC.

6. Now direct the telescope towards objects A and also take the horizontal angles COA.

7. Hold the staff on B.M. and take the staff reading.

8. By calculation find the area of the triangle.

a A B D1 D2 O c D3 c C

AREA CALCULATION:

Area of the triangle ABC = SQ. ROOT OF [S ( S – a ) ( S - b ) ( S - C)]

Where,

S = (a + b + c) / 2

a = Horizontal distance between A & B

b = Horizontal distance between B & C

c = Horizontal distance between C & A

D1 = Horizontal distance between O and A = S / (tan α1 – tan α2)

D2 = Horizontal distance between O and B = S / (tan α1 – tan α2)

D3 = Horizontal distance between O and C = S / (tan α1 – tan α2)

a2 = D12 + D2

2 – 2D1D2 cos θ1

b2 = D22 + D3

2 – 2D2D3 cos θ2

c2 = D32 + D1

2 – 2D3D1 cos θ3

Result :-

Area of the triangle ABC is ………..

Det

erm

inat

ion

of A

rea

of th

e tr

iang

le:-

Face

: Le

ft

S

win

g : R

ight

Hor

izon

tal A

ngle

Mea

n

“

’

o

B

“

’

o

A

“ ’

o

Ver

tical

Ang

le

Mea

n

“

’

o

D

“

’

o

C

“

’

o

Position of Vane

Top

vane

Bot

tom

van

e

Top

vane

Bot

tom

van

e

Top

vane

Bot

tom

van

e

Sight to

A B C

Inst. at

O


GRADIENT JOINING STAFF STATION AND TARGET OF SUBTENSE BAR

Aim: -

To determine the gradient of the joining the staff station at d left target of Subtense bar.


Theodolite, staff, arrow and subtence bar.

Given data:-

R.L. of the B.M. = 100.000m

Procedure: -

1. Set up the instrument at P, staff at A and the Subtense Bar at B.

2. Keeping the Vernier A as 00’0”, Note down the axial hair reading of the staff held vertical

over the staff station A.

3. Sight the apex of the left target of the Subtense bar and note down the horizontal angle

between the staff station and left target, and also the vertical angle by Sight the left target.

4. By Sight the other target and from the instrument station note down the horizontal angle

between the left and right target, and also the vertical angle.

5. Find out the benchmark staff readings.

s

Substence Bar

h1

Staff Station Instrument Station

2m

B Q C

A d1

D Ø1

Ø2

P

Calculation:-

d = KS+C

S1 is the axial hair reading of staff held vertically over A

V1 = d tan α1

RL of A = B.M. + B.M. staff reading + V1 + S1

From triangle PBQ,

S/2 sin θ1/2 = ------- d1

S/2 d1 = ----------- sin θ1/2 From triangle PAB, AB = d2 + d1

2 –2 d d1 cosθ2 V2 = d1 tan α2

RL of B = B.M. + B.M. staff reading + V2 + S2

R.L. of A – R.L. of B Gradient of AB = Horizontal Distance AB

Result :-

Gradient of line joining left target of Subtense bar and foot of the leveling staff =

Det

erm

inat

ion

of g

radi

ent o

f the

line

:

Face

: Lef

t

S

win

g : R

ight

Stad

ia R

eadi

ng

Top

Middle

Bottom H

oriz

onta

l Ang

le

Mea

n

“

’ o

B

“

’

o

A

“

’

o

Ver

tical

Ang

le

Mea

n

“

’

o

D

“

’

o

C

“

’

o

Sight to

A B C

Inst. at P


SET OUT THE FOUNDATION FOR A BUILDING BY USING CENTER LINE METHOD

Aim: -

To determine the setting out the foundation for a building, by using center line method.

Instruments Required :-

Theodolite, Pegs, Arrows, Measuring Tape or Chain, mason’s square, ball of string, lime powder.

Planning and organization:-

A small area is to be kept ready for setting out a simple rectangular building of size 6m x 3m.

The site has to be cleaned off any vegetation and made level. or given plan.

Given:-

A hall 6m x 3m internal dimension has to be constructed. The wall are 230mm thick. The width

of the foundation is 900mm. Set out the building, mark foundation trench.

Procedure :-

1. Study the plan of the building and note down the internal dimensions and also the width of

the foundation.

2. Prepare the centre line sketch of the building.

3. Remove the any vegetation in the construction site.

4. Setting out a straight line slightly greater than the length of the front wall. The frontage is to

be located with respected to other features is site plan such as road etc., this line will be the

centre line of the front wall.

5. Now mark the two ends of the front wall.

6. Drive two pegs a little away from the ends marked and tied a string accurately.

7. At two ends, set out perpendicular strings using masons square.

8. Strectched strings of the sidewalls and ties\ with pegs a little beyond the required.

9. Repeat the same for other aside walls.

10. Now, stretched strings through the points C and D indicates the ends of the centers lines of

the side wall give a rectangle bounded by strings. This rectangle indicates the centre line of

the building.

11. Measuring the four sides of the rectangular and check its accuracy as per the centre line

sketch prepared.

12. Check the angles of the corners.

13. Measure the diagonals and check for its accuracy.

14. If items 11,12,13 are satisfied the rectangle is marked.

15. Mark the width of foundation of wall on ground have the wide on either side of the centre

line marked and apply lime powder to indicate outline of the foundation trench.

RESULT: -

The foundation marking is done for the given layout.

MARK THE WIDTH OF THE FOUNDATION FOR THE GIVEN BUILDING

PLAN AND CHECK THE DIAGONAL LENGTH.

(USING CENTRE LINE METHOD)

(All dimensions are in mm)

N 230 115 ROOM 3300X 3000 ROOM 3300X 3000 ROOM 3300X 2770 900 700 PLAN FOUNDATION DETAILS FOUNDATION DETAILS

FOR MAIN WALL FOR PARTITION WALL


SETTING OUT SIMPLE CIRCULAR CURVE

BY ORDINATES FROM LONG CHORD

Aim :-

To set out the simple curves in between two center line of roads which are meet at one point by

long chord method.

Instruments required:-

Theodolite

Chain

Ranging rods

Arrows and hammer

Description:-

Curve is defined as an arc provided between intersecting straight to negotiate a change in

direction, the provision of a curve makes the change of direction not only easy and smooth, but

also safe and comfortable, the straight or the tangent are the lines connected by the curve and

they are tangential to the curve, the curvature is usually provided by simple curve.

Simple curve:

Simple curve is defined as a circular curve of single radius connecting two straight.

Back tangent:

The tangent AT1 previous to the curve is called as the back tangent. It also known as the forward

tangent or rear tangent.

Forward tangent:

The tangent BT2 following the curve is called as the forward tangent. It also known as the second

tangent.

Intersection and deflection angles:

The angle AVB between the tangent lines AV and BV is called the angle of intersection and

the angle V’VB by which forward tangent deflects from the rear tangent is called the deflection

angle of the curve.

Length of the curve:

The arc T1DT2 is called the length of the curve.

Long chord:

The line T1T2 joining two tangent points is called as the long chord.

Mid Ordinate:

The intercept DC on the line VO between the mid point of the long chord and the mid point of

the curve is known as mid ordinate or the versed sin of the curve.

Point of curvature: The point T from which the curve begins is called the point of curvature P.C.

Point of intersection:

The tangent lines AT1 and BT2 when produced, meet at point V which is called the vertex or

point of intersection P.I.

Point of tangency:

The point T2 where the curve ends is called point of tangency P.T.

Tangent distance:

The distance from the point of intersection to the tangent point i.e., VT1 or VT2 is called the

tangent distance or tangent length.

Tangent:

The straight line VA and BV which are connected by the curve are known as the tangents or

straight of the curve.

Principle:- The angle between the target and the chord is equal to the angle which that chord subtends in

opposite segment.

Given data:-

Chainage of curve, angle of intersection ( ) and radius of curve ( R )

Procedure :-

1. First extent the center line of the cross roads i.e., extend the two straight, fix the point of

intersection V.

2. Measure the intersection angle with the help of theodolite. Then deflection angle is

calculated by = 180 -

3. Choose the suitable radius of curvature R.

4. Then fix the points, point of curve T on back tangent and point tangency T on forward

tangent by fixing the distance R tan /2

5. Then directly measure the distance between the two tangent points T1 and T2 to get the length

of the long chord (L)

6. To calculate the length of the long chord from the formula L = 2R sin /2

7. Then the length of the curve is equal to R /2

8. To get the change point T1, deduct the length of tangent distance of back tangent from the

chainage of intersection point V.

9. To get the chainage of point T2, add the length of curve to chainage of point T1.

10. Find the mid point of the long chord “C”. Then from this mid point of long chord, fix the mid

point of curve “D” , by fixing the mid ordinate length R – R2 – L2/4 towards the point V.

11. Fix the other points on the curve on either side of the mid ordinate by fixing the

corresponding length R2 – X2 – (R–O0) from the long chord. Where x is the distance of

corresponding ordinates from the mid ordinate. O0 is the length of the mid ordinate.

Calculation:-

Chainage at V =

Radius of curve ( R ) =

Deflection angle () =

Formula:-

Length of tangent = VT1 = BT2 = R tan /2

Length of Chord = T1T2 = L = 2R sin /2

Length of Curve = T1T2 = R/180

Chainage at T1 = Chainage at V – VT1

Chainage at T1 = Chainage at T1 + T1T2

Mid ordinate = R – R2 – L2/4

The ordinates are fixed on either side of mid ordinate, at x m interval, i.e., the distance between

the successive ordinate is equal to x m.

The length of the ordinate R2 – X2 – (R–O0)

V T1 T2 O3 O2 O1 O O1 O2 O3 R O

Result:-

The given simple curve is setout by the method of ordinates from long chord.


AZIMUTH BY THE EX-MERIDIAN OBSERVATION ON THE SUN

Aim :-

To find the angle between the observers meridian and the vertical circle through the body.


Theodolite, Ranging rods, Chain, Arrows and pegs.

General:-

The required altitude and the horizontal angle and those to the sun’s centre. Hence the hairs

should be set tangential to the two limbs simultaneously. The opposite limbs are then observed

by changing the face.

Procedure:-

1. Set the instrument over the station mark and level it accurately.

2. Clamp both the plate to zero and sight the reference mark.

3. Turn to the sun and observe altitude and horizontal angle with the sun in quadrant of the cross

wire system. The motion in the azimuth is slow and the vertical hair is kept in contact by the

upper slow motion screw, the sun being allowed to make the contact with the horizontal hair.

The time of observation is also noted.

4. Using the two tangent screws and quickly as possible bring the sun into quadrant 3 of the

cross wires and again read the horizontal and vertical angle observe also the chronometer

time.

5. Turn to the RM reverse the face and take another sight to RM.

6. Take two more observations of the sun preciously in the same way also in step (3) and (4)

above but this time with the sun in quadrants 2 and 4. Note the time of each observation.

7. Finally bisect the RM to see that the reading is zero.

Result: -

Azimuth of the given line = ----------------------------------

Det

erm

inat

ion

of a

zim

uth

angl

e obs

erva

tion:

-

Face

: Lef

t

Sw

ing:

Lef

t Tim

e

“

’

o

Alti

tude

doub

le “

’

o

Ver

tical

Ang

le

Mea

n

“

’

o

D

“

’ o

C

“

’

o

Hor

izon

tal A

ngle

Incl

uded

Ang

le

“

’

o

Mea

n

“

’

o

B

“

’

o

A

“

’

o

Sight to P Q S A P S

Inst. at P B


Field work using Total Station

Aim :-

To find distance and elevation for given station by total station.


Total Station

Prism

Prism range

USB Memory device or SD card

Plumb bob

Procedure:-

REM MEASUREMENT:

1. Set the target directly under or directly over the object and measure the target height with

tape measure etc.,.

2. After inputting the height accurately sight the target.

3. The measured distance data(s), vertical angle(ZA) and horizontal angle(har) are displayed

press(STOP) to stop the measurement.

4. In the second page of means mode screen press(menu) then select “REM”

5. Press (OBS).The REM Measurement is started and the height from the ground to the object is

displayed in “Ht”.

6. Press(STOP) to terminate the measurement operation. To re-observed the target sight then

press(OBS)

7. When (REC) is pressed, REM data is saved.

Result: -

(i) Thus the height of the given station is=

(ii)Distance of given prism station from the instrument station=

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