surveying new document recognized

8/17/2019 surveying New Document Recognized

1/53

78

Surveying

CIVIL ENGINEERING

bjective Q uest ions

^

1. Match L is t- I with L is t- II and select the correct answer using the codes given below the lists

List-I

List-II

A. Ver tical cliff

1.

Contour lines of different elevations unite to form one line

B. Steep slope

2.

Contour lines of different elevations cross one another

C. Hill

3.

Contour lines are closely spaced

D. verhanging cliff

4.

Closed contour lines with higher values inside

Codes:

A

B

C

D

(a) 4

3

1 .

2

(b) 1 3 4

2

(c) 1

2 4 3

(d) 4

2 1 3

2. A ssertio n (A): A series of closed contours indicate either a valley or a hill without any outlet,

when their elevations, respectively, increase or decrease towards the centre.

Reason (R): Contour lines of different elevations can unite to form one line only at a vertical

cliff.

f these statements:

(a) both A and R are true and R is the correct explanation of A

(b) both A and R are true but R is not a correct explanation of A

(c) A is true but R is false

(d) A is false but R is true

3. W hat is the angle of intersection of a contour and a ridge line?

(a) 30° (b) 0°

(c) 180° (d) 90°

4. Consider the following statements about the cha racteris tics of contours:

1. Closed contour lines with higher values inside show a lake.

2. Contour is an imaginary line joining points of equal elevations.

3. Closely spaced contours indicate steep slope.

4. Contour lines can cross each other in case an overhanging cliff

Which of these statements are correct?

(a) 2, 3 and 4 (b) 1 and 2 only

(c) 1 and 4 (d) 1, 2 and 3

.E.S M AS TE R

m$Mu(e fa EnQ^eer*

lES/GATE/PSUs

ffice: F-

126

. Ratwarm Sarai. New Delhi • 110

016

. .pin

Website: www.iesmasier.org E-mail: ies_mastereya

Phone: 011-11 01310 6 78 38 81 3106. 9711853908^


2/53

GI RI G

Cont

r v p i c a l L a n d F e a t u r e s a n d

curing

A slop

the r Cont

* *t«

475

or steei

our Forms

lopes;

Avery steep slope is termed as

A

f

h scrap is known as era

scarp

(a ) A gent le s lope

(b) A steep slope

(c) A hill

:au.

High-lying F o rm s

These are characterised v elevatprl o

g 'V elevated grounds, for example hill, hillock and plate,

Hills are elevated ground usuallv witv, Q

in shape and increasing the contour values''inwards* '' ^ C°Unt°UrS of hllls are it circular

Low-lying F o rm s

The most common among the low-lying forms are ravines, valleys, etc.

Rav ne

Ravine is a through like depression of the earth's surface, elongated in one direction with the

ottom inclined towards one side.

A ravine can e imagined as a depression washed out in the ground y flowing water.

Valley

A valley is a road ravine with a gental sloping ottom.

The countours of a valley are in a shape of V.

If the ground is low as compared to the surrounding land and the sides slope generally, it i

called as a depression.

The contours are quite few and far apait. , ■'

If the valley floor is very narrow and has steep sides on a level terrain, it is called as

gorge

and in mountains as

canyons.

Due to the steepness of sides, the contours aie cio

is


3/53

r iVIL ENGINEERING

Plane Table

69

List-I

A. Traversing

B. Resection

C. Intersection

D. Radiation

Codes:

List-II

1. Rays are drawn to locate the station on which the table is set-up

2. At least two rays are drawn from two different stations to the

details to be located

3. Rays are drawn in the direction of details through the station

point on which the table is set-up

4. Rays are drawn on the map by setting up the table over each of

the stations towards the subsequent station

A

B

C

D

(a) 4

3

2

1

(b) 2

1

4

3

(c) 4

1

2

3

(d) 2 3 4 1

The process of determining the location of the station (on the map) occupied by the plane table

is called as

(a) intersection (b) three-point problem

(c) traversing (d) resection

8. Which one of the following surveys employs alidade?

(a) Contour survey (b) Archeological survey

(c) Plane table survey (d) Reconnaissance survey

Pick out the correct statement .

(a) U-frame is used for orienting the plane table

(b) The drawing sheet used in plotting a plane table survey needs no special care in fixing on the

board.

(c) An alidade is also called a sight rule.

(d) A simple alidade and Indian pattern clinometer serve the same purpose.

. If the plotted position of an instrum ent station is not known, the most accurate or ientation

of the plane table can be achieved by

(a) a trough compass

(b) backsighting

(c) observations of two well-defined points

(d) observations of three well-defined points

The most rapid method of orientatation by the three-point method of plane tabling is the

(a) tracing paper method (b) graphical method

(c) trial-and-error method (d) both (a) and (b)

2 It is necessary to go to one of the plotted stations in the method of resection

(a) by trough compass (b) by a back ray

(c) by both (a) and (b) (d) by three points

i

□ L

.E.S M A S TER

insstme for Engineers

lES/GATE/PSUs

ffic e: F 126. Katwaria Sarai. New Delhi - 110 016

Website : www.iesmaster.org E-mail: ies_mastcr


4/53

4 6 6

Surveying

IVIL ENGINEERING

iii.

iv. >

v.

vi.

vii.

H the plane ta le is not properly oriented at each station,

If the plane ta le is not properly clamped after orientation

sights and the error will occur.

the plot o tained will e inaccurate,

the plane ta le will rotate etween

If the o ject is not sighted accurately and isected propeily, the en o i

If the alidade is not properly pivoted on the point, the lays diawn

Th is error is cumulative if the survey is extended from a small p a it to a g p

The error will occur if the tripod is not planted firmly into the giound.

3. E r r o r d u e t o I n a c c u r a t e C e n t rin g

If the plane ta le is not exactly centred over the station, an error will occur. The magnitude

of the erro r can e determined as elow.

Show s the case when the plane ta le is not centred, and the plotted position p of the station

P is not exactly over the station P. Let A and B sighted after pivoting the lalidade on p. The

plotted angle etween A and B is ApB, ut the actual angle in the field is AP B. The angulai

erro r y caused y inaccu rate centring is equal to the difference etween the angles APB and

ApB.

Angular error in centering = Z APB - Z ApB = a + (3

Let Pc & Pd are perpendicular to the line Ap & Bp.

Pc

sin a - ^p-

a = sin

Pc

AP

a —

sin P =

Pc

AP

Pd

BP

P sin

' P d '

, BP ,

P

Pd

BP

Angular error in centring, y = a +

P

Y

nsMute for Engineers

s /g a t e /p s u s .

oarcl l . I GVV D e lh i • 1 1 U U U >

Webs te: www. esmaster.org. E-ma l: es_master?yahoo.

Phone. 011-41013406, 7838813406.

9711853908


5/53

IVIL ENGINEERING

Example 4,

Measurement of Area & olume

445

Determ ine th e are a of the traverse ABC DEF of the below figure by the departure

atitude method.

ar>d the total

REFERENCE

STATI N

m

— •-+.

I *Xr>

m

■200 m -J*—i00m—*|

T ota l la titu d es o f the Doint^ ft e n n » .

below points B. C. D. E and F with respect to the refer

ence point A are a

Point B

Point C,

Point D.

Point E.

Point F.

L', = 0 - 100 = -1 0 0 m

L\,= -100 + 0 = -100 m

LV, = -100 + 100 = 0

L’, = 0 + 100 = 100 m

L ’5 = + 100 + 0 = 100m

The a lgebraic sum o f the departures of the two lines meeting at the stations B C D E and F are

as below ’ ’ u r are

Point B. 100 + 200 = 300 m

Poin t C. 200 + 100 = 300 m

Point D. 100 - 100 = 0.0

Point E, -1 0 0 - 200 = -300

Point F, - 200 - 100 = - 300

2A = - 100 x 300 - x

3

+ 0 + 100 x (-300) + 100 x (-300)

2A = - 120000 m2

or A = 600 00 m2 (Negative sign is neglected)

latitudes and departures of the lines of a closed traverse are given below. Calculate the

The

area o f the traverse


6/53


7/53

IVIL ENGINEERING

Mining Dial

• The mining dial is a simple form of theodolite with a built-in compass. It is mai y

mine surveying.

• * It consists of a large magnetic compass fitted with either a telescope plain s’g

vertical arc.

Brunton’s Compass

* Brunton’s compass or Brunton’s pocket transit is an instrument with is a combin

compass and a clinometer.

Pantagraph

A pantagraph is not a surveying instrument. This is an instrument used in the office to

enlarge or to reduce a plan already drawn.

Eidograph

An eidograph is an improved version of the ordinary pantagraph. It is used for the same

purpose as a pantagraph.

Sounding Sextant

A sounding sextant is similar to a nautical sextant. However, the index glass of a sounding

sextant is generally much larger as compared to that of a nautical sextant. The sounding

sextant is generally used in hydrographic surveying. As the small boats used in hydrographic

surveying may be rocking when the object is sighted, the sounding sextant is more useful than

a nautical sextant.

E

E.S MASTER

nsfttiie for Engineer*

lES/GATE/PSUs

ffice: F-126. Katwaria Snrni New Delhi •110 010

Website: www.iesmaster.org. E-mail: [email protected]

T hone: 011-11013406. 783881:1106. 971185:1908


8/53

CIVIL ENGINEERING

Minor Instrument

81

There are two types of sextants :

(1) Nautical sextant, and

(2) Box sextant.

Naut ica l sex tan t

It has two glasses called Index glass and Horizon glass. If the angle of inclination between

Index glass and Horizon glass is angle 0 then angle between two sides objects in the ground

will be 20.

Used of Nautical Sextant

1. The nautical se xta nt m easures angle in the plane of the two objects and the telescope. It is

unlike a theodolite (or a compass) which measures the angle in a hoiizontal plane. Therefore,

the nautical sextant is a more versatile instrument.

2. An angle can be measured while the observer is on a ship 01 a boat.

3. It is specially useful for navigation and astronom ical puiposes.

4. The angle measured between the two objects at d ifferen t elevation s can be reduced to the

horizontal angle, if required.

Box Sextant

The box sextant is a small, pocket instrument used for measuring angles. It consists of a box about 75 mm.

in diameter and 40 mm deep.

Uses o f a Box Se xtan t

1. The box sexta nt is generally used for m easu ring angles in cha in surveying, if required.

2. The box sex tan t can be used like an optical square for se ttin g the perp endicu lar in chain

surveying if the vernier is set at 90°.

3. It can be used for locating inaccessib le points in chain su rvey ing by intersection.

4. It can be used for locating details by rad iation method in trav ers e surveying.

5. It can also ’be used for checking ap prox ima tely the a ng les measu red by means of other

instruments.

6. The box sexta nt is extremely useful in reco nn aissa nce .

Advantages of a Box extan t

1. It is a very compact and handy instru m en t.

2. It can be used in any position.

3. It can be used even in a moving boat or a ship .

4. It is a pocket instrum ent, and can be easily c arr ied from one place to the other.

5. It is quite inexpensive.

Site Square

The site square is an instrument used to set out two lines at right angles to each othei.

l. .S M A ST R

nsStute for Engineers

E /GATE/P Us

ffic e: F* 126. Katwaria Sara i. New Delhi -1 10 01G

Website: www.iesmaster.org. E-mail: ies_master? vahno n> in

Phone: 01111 0131 0(5. 783881 010(3. 971 185:1908


9/53

Minor Instr ment

Hand Level

• A hand level is a small levelling instrument which is held in hand while levelling.

• It is used for approximate determination of elevations in reconnaissance, preliminary surveying,

for locating contours on the ground, and for taking short cross-sections in profile levelling.

A ney Level

• An A ney level is an improved version of the hand level. It can e used as a hand le\el for

levelling, and as a clinometer for measuring slopes. It is a quite light and compact instrument.

• The vertical scale is extended type

Indian Pattern Clinometer

• The Indian Pattern Clinometer, also called the tangent clinometer, is a simple instrument used

for determining the difference of elevations of the two points y measuring the inclination of

the line of sight.

• It is specially useful for plane ta ling.

Ceylon Ghat Tracer

• The C'eylon ghat tracer is a simple instrument used for measuring the slopes.

• It is specially useful for setting out a grade contour on a given gradient in the preliminary

survey of a road in a hilly area.

Sextant

A sextant is an instrument used for measurement of the horizontal and vertical angles.

The distinguishing feature of a sextant is the arrangement of . . ” , ..

i . • . . . . rr . i . , , s utm oi two mirrors which ena les the

o server to sight two different o jects simultaneously.


10/53

g i r i g

Contouring

9

9.

AJtonetry may be depicted moat accurately by

» haChU,'e3 W relief .hading

* Unt,ng » contour line.

\latch L is t-I with L is t- Ii and selppt tk,

j ^ g n I ec ans wer using the codes given below the lists:

a

Equally spaced contour lines L ist -II

B- Contours are alwa ys perp end icular to « 8l°Pe

C Contours

increase

in elevation from

*

AA]

inside to

outside ‘ ‘ e

4. A depression

5. Uniform slope

7.

Codes:

A

B

C

(a) 1

2

4

(b) 1

3

4

(c) 5

3

2

(d) 5

1

4

Contour inte

rval on

a map s

(a) vertical distance of contour lines above the datum plane

(b) vertical distance between two successie contour lines

(c) slope distance between two successive contour lines

(d) horizontal distance between two successive contour lines

Which of the following characteristic features may be used while plotting a contour plan?

1. Two con tour lines having the sam e elevation cannot unite and continue as one line.

2. Contour lines close toge ther indicate a gentle slope.

3. Contour lines cros s a valley line at righ t angles.

Select the correct answer using the codes given below.

(a) 1, 2 and 3 (b) 1 and 2

(c) 2 and 3 (d) 1 and 3

A ss er tio n (A): Exc ept in the case of an over-hanging cliff, two contour lines cannot merge

or intersect at a point on the map.

Reason (R): Intersection of two contour lines means one point on the surface of the earth will

have two different elevations. This is not possible.

6- (d)

7.

(b)

8

)

9.

(d)

u

I. .S M A ST R

institute for ngineers

lES/GATE/PSUs

ffi ce ’ F-126 , Katwaria Sarai. New Delhi •110 016

Website www.ie8master.org, E mail: ies.maste^yahoo.co m

Phone: 01 M I m K. 7838»i:M0(i. 1853908


11/53

ENGINEERING

high land, hav in g fla t narrow top with 7----------------

on the other side is called as

e s c r a p m e n t

?

^

°n ° " e side and gentle (dip) s,ope

The contou rs will e clo ser towa rd* 1

s^cepjudeanci far apart towards the gentle side.

( j ) Esc r a p m e n t

Cl

Cliff are the stee p ro ck fac es along the sea coa st and may e vertical where the contour lines

concide with each other, an o v e r h a n g i n g c l i where the contour lines intersect each other.


12/53

76

CIVIL ENGINEERING

(d) /I depression.

m i i

i

- f '

m

(e) A gorge or canyon

Valley Line and Ridge Line

• The slopes of ravine intersect along a line referred as the axis of the ravine, the line o

discharge, or a valley line in case of a valley.

• Counter part of a ravine is a ridge—a convex form of terrain gradually declining in one

direction.

• Two ravines are generally separated by a more or less pronounced ridge.

• The line along which the slopes intersect is referred as the axis o/ridge, thewatershed or

watershed line.

The watershed line is generally wavy.

avine represented by contours

Scraps

indicated

b/ teeth

If ttvtnt*

Metres

1050

1000

950

900

850

800

i 4 - s h t i p a i W i e y

add e

• The lowest points on the watershed are known as passes.

• Pass is narrow low land passing through high mountains on either sides.

• Sometimes this narrow low land is cut back by the streams. This steep-sided depression is

called as a C L. When this depression is broad and low, it is known as saddle.

• A part of the land in form of tongue, which cuts out from a hilly area is called as spur.

» The contours are similar to that of a valley, with a difference that here the counter values

decrease towards the vee.

ffice: P-126 Katwarii Sarai New Delhi • 6

Website: www iesmaster.org. E mail, irs_ master*'yahoocoin

1hone P IP 410134061 78388 m tlf i 97 11S539HS

| t- S MAS TE R

insatuUfa Er>«iocr5

IFS/GATE/PSUS


13/53

7

Surveying

CIVIL ENGINEERING

Characteristics of Contour Lines

1- All the points of a contour line have the same eleva tion . I he eleva tions o t e con tou rs are

shown either y ins ertin g the figure in a reak in the respective contoui pi intec c ose to

the con tour. When no value is represented, it indicates a flat te n ain. A zeio m etei contoui

cave penetrating a hillside.

3. A con tour line is a closed curve. They may close eith er on the m ap or ou tside the map. it

depends on the topography.

4. Eq ually spaced contour represent a uniform slope and contours tha t are well ap art represents-

a gentle slope.

5. A se t of close conto urs with higher figures inside and lower figures outs ide indic ate a hillock,

whereas in case of depressions & lakes, etc., the lower figures are inside and the higher figures

are outside.

6. A w a t e r h e d or r idge l ine (line joining the highest points of a series of hills) and the thalweg

or

val ley l ine

(line joing the lowest points of a valley) cross the contours at right angles.

7. Irre gu lar contours represent an uneven ground surface.

8. The direction of the steepest slope is along the sho rtest distance etween th e contours.

At a point the d irection of the steep est slope on a contour is. th ere for e, at rig h ang les to the


14/53

GI RI G

Con ouring

473

■JT ra lly th' contours m e not risib le on the

grounds excepts in the case of shoreline*.

• The vir tual dis tan t< between consecutive contours Je term< I i contour interval

• It desirable to hu\e a con sta nt contou r inter val throughout the map

• In special cases, a variable contour interval may also he provided.

• A variable contour interval i> as far as pc»’ *ible avoided since it gives a false impression of the

relative steepness of the ground in different parts of the map.

•

Generally

contour intervals are taken to m

• The smaller the contour interv ii the

m o r e

preci*el> the terrain relief is predicted on the plan

• The contour interval depends upon the following factors.

(

) Scale of the map Purpose of the map

lull Nature of the Country (tv) Time

■p (v) Funds

L Scale o f th e M ap: If scale is small, the coutour interval is kept large so that there is no

overcrowding of the contours. n the other hand, if the scale of the map is large* the contour

: interval can be kept sm all.

Purpose o f M ap: The con tour interval selected should be small so that the map serves the

intended purpose, but at the same time it should not be too small otherwise the cost of the work

would be too much The contour in terval should be kept small when the plan is required for

the detailed design

* Nature o f G ro u nd : For a flat ground, the contour interval is small, but for a steep slope the

contour interv al is large. If the ground is broken, the contour interval is kept large so that the

contours do not come too close to each other.

*

Time: Contour

interval is kept large when time is less

4

Funds: Contour interva a kept artie when fund- un

lew

(Mir# 134 k#nn in« V # N b I10 0U

il


15/53

C

h p e r

Conto r ing

Introduction

The re a tiv e position of points in it p ane are represented by a map The v a ue of the n a p t*

even more if the re ief (variation in the e evation of earth * surface) i$ a so inc uded a ong with

their re ative position*.

There are two

method

by which the conformation of the ground may he presented on a map

( ) By de ineatin g the surface s ope* b\ shading intended to given an im pression of re ative re ief

The re ative e evation* of the point* are not indicated in thi* case.

ib) By p otting the contour ines (imaginary ine parsing through points Prop er and precise ocation of engineering work* -uch an road* can a * etc

i >

In ocation of w ater supp y water distribution and to so ve the prob ems of steam

pollution

te In planning and designing of dam* reservoirs aq uedu ct* transm ission ines etc

idi In se ection of Mte« for new ind ustria p ants

te) Determining the intervisibihty of station* J

(0

Determining

the profi e of the

country

a ong any direction.

ig) To

estimate

the quan tity of cuttin g fi ing, and the capacity of rese rvo ir*

Definition of Contour

1T ” ? * d' f,ntd " * " ,ln' point* of . I m o w t *

A contour l.nc m ., . 1 * e defined . . the m ter«c.u.n of . U „ , *urftK.. , „ h >f

earth.

Contour line* on a plan illustrate the topography of the ground '

When the contours are drawn underwater, they are termed -

or

baihyme r ic u n e*

M contours.


16/53

R ason


17/53

70

CIVIL ENGINEERING

The major source of error is small-scale mapping by plane table is due

(a) inaccurate centring (b) long sight

(c) shrinkage of drawing sheet (d) few observations

Which one of the following errors is more severe in plane-table surveying.

(a) Defective sighting

(b) Defective orientation

(c) Movement of board between sights

(d) Non-horizontality of board when points sighted are at large differences of theii elevation

15. A sse rt io n (A): The solution of a three-point problem in plan e-tab le surveying is aided by

Lehmann’s rules.

Reason (R): The application of Lehmann’s rules reduces the triangle of error and is a

controlled trial-and-error technique.

16. Consider the following statem ents:

A ssert io n (A): In plane table photogrammetry. the area s to be mapped are tak en from either

end of a base line.

Reason (R): The position of the detail point with reference to the base line is obtained by

intersection of rays drawn to it from each end of the base.

f these statements

(a) both A and R are true and R is the correct explanation of A

0)) both A and R are true but R is not a correct explanation of A

(c) A is true but R is false

(d) A is false but R is true

17. In a plane table survey, the plane table station position was to be fixed with resp ect to three

reference points. It was found that one of the reference points was not visible due to some

obstruction. It was, therefore decided to make use of the other two points only. Which one of

the following statements is true regarding the determination of station position?

(a) The work can be done faster

(b) Two settings of the plane table will be needed but the work will be accurate

(c) nly one setting of the table is needed, however the work will be less accurate

(d) The work will be less accurate and time consuming

The fix of a plane table from three known points is good if

(a) the middle station is the nearest

(b) the middle station is farther than the other two stations

(c) eith er of the extreme stations is the nearest

(d) the middle station is close to the great circle

19. A ss e rt io n (A): If the plane table station P lies on the great u i

stations A. B and C, then the position of point y can be determined b ^ h e tl X -p o :

problem. • J

j

•i ■»1


18/53

68

Surveying

CIVIL ENGINEERING

b j e c ti v e Q u e s t io n s

It is required to produce a small-scale map of an area in magnetic zone by directly plotting

and check ing the work in the field inself. Which one of the following su rveys w ill ie most

appropriate for purpose?

(a) Chain (b) Theodolite

(c) Plane Table (d) Compass

For locating an inaccessible point with the help of only a Plane table, one should use

(a) traversing (b) resection

(c) radiation (d) intersection

The method of plane tabling commonly used for establishing the instrument station is the

method of

(a) radiation (b) intersection

(c) resection (d) traversing

ytT' Match L is t- I (Statemen t) with L is t-I I (Situation) and select the correct answ er using the

codes given below the lists:

A.

List-I

Accurate centering in plane table surveying

i.

List-II

Inaccessible points

B.

is necessary for

Exact orientation is more important, than 2. pen country with good intervisib ility

C.

accurate centering for

The intersection method of plane table 3.

Large scale maps

D.

surveying is particularly employed for

Plane table survey is useful for 4. Small scale maps

Codes:

5. Hilly regions

A

B C

D

(a) 3

4

1

2

(b) 4 3 2 5

(c) 5

4

3

1

(d) 3

1

4

2

j The method of orienting a plane table with two inaccessible points is known as

(a) intersection (b) resection

(c) back sighting (d) two-point problem

X M atch L 18* '1 (Methods.) Wlth L is t-H (Procedures) and select the correct answer using the

codes given below the lists:

E.S MASTER

nstitute for Engineers

lES/GATE/PSUs


19/53

CIVIL ENGINEERING

Plan Tabl

6

- sin

Pc

AP

+ sin

-i

Pd

BP

The above figure s how s the c or re ct position of points A & B as a' & b', therefore the error

potting is a'a & b’b.

We know that

, Pc

a'a = pa sin a = pa x a = pa x

bb' - pb x sin P = pb x p = pb x

AP

Pd

BP

If R.F (r) =

1

n x 100

pa = AP x r

pb= BP x x

Le t Pc = Pd = e mtr.

Pc

[i.e. scale is 1 cm = n meter]

.

aa = pa

AP

= AP x r x

AP

= er

Pd e

bb' = pb x — = E p x r x — = er

It is observed that displacements of the points from their correct positions is re.

If the limit of precision is 0.25, for insignificant effect in plotting,

i.e. re < 0.00 02 5 •

e <

For r =

0.00025

r

1

100

0.00025

Similarly for =

1 100

1

(i.e. 1 cm = lm )

= 0.025 m = 25 mm.

1000

e = 250 mm

Hence it is observed that centering error is quite important when the scale is large.

Example 1.

In setting up the plane table at a station P, the corresponding plotted point p was no

accurately centred over P. If the displacement of P was 20 cm in a direction at right angle

to the ray, determine the displacement of the point from its true position on the plan if

(a) r =

5000

Sol. We know that,

aa' = r x e.

In this case, e = 20 cm = 200 mm

1

(b) * -

50 0

(c)

50

1

(a) aa ' = 200 x = 0.0 4 mm (b) a a ' = 2 0 0 x = 0.4 mm (c)

aa

5000

500

' = 200 x — = 4.0 mm

50

■

.S M AST R


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20/53

lV IL ENGINEERING

Plane Table

465

Remove the tracing paper and move it

through the plotted points a. and c 6 Plan Untl1 the tllree rays simultaneously pass

Fix the point p on the plan with Q ,,

ta le. ' n°pdle point to o tain the position of p on the plane

Pivot the alidade on p, with erltm

isected. The plane ta le is now oriented.^’ ^ ^ ^ Pla" e Until the 8tati°n A

Strength of Fix in Three-Point Pro lem

The following points should e considered while selecting a plane ta le station.

. \Vhen the plane ta le station P is inside the great circle, the station should e selected near

t etc n lmc o f gii at ti langle. When p is at the orthocentre of the great circle ABC, the

strength ot tix is a maximum.

2. Avoid the plane ta le station near the circumference of the great circle, as its position is

indeterminate.

3. When the plane ta le station P is outside the great circle, select the station near the middle

known station.

4. If one angle is small or when the station P is in line with the two known station, the larger

the angle to the third known station, the etter is the fix. But the angle should not e larger

than 90°, and the two known stations on the line should not e near to each other.

5. If the point P is within the great triangle, and the middle station is much nearer to p then

the other two stations, the fix is good.

Errors in Plane ta le Surveying

1. Ins trum en tal E rro r

i. The error will occur if the top surface of the plane ta le is not perfectly plane.

ii. If the fiducial edge of the alidade is not straight, the lines drawn would not e straight and

in error will occur.

hi. If the fittings of the ta le and the tripod are loose, the plane ta le will not remain sta le

iv. If the magnetic compass is sluggish, there will e an error in orientation done with the

magnetic compass.

v.

vi.

If the sight vanes are not perpendicular to the ase of the alidade,

sighting.

there would e an error in

If the level tu e is defective, the plane ta le will not e horizontal when the u le is central.

The plot o tained will e inaccurate.

vii. If the drawing paper is not of good quality, it will e affected y the weather conditions. It may

expand or contract. The plot o tained will not e conect.

2. Erro r of M anipulation and ighting

i. If the plane ta le is not properly levelled and made horizontal, the r i g h t . v a n e s e inclined

to the vertical. There would e an error and the pomts located will not conect.

ii. If the plane ta le is not accurately centred, the error will occur. The error is more important

in large scale plotting

E S M A S TER

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21/53

6

CIVIL ENGINEERING

3.

4.

5

.

.

7.

If the point P lies on the great circle passing through the « t a t i^ e ^ a y s w ^ U n t e r s e T t

of the point p cannot he determined y three-point pro lem,

at one point, irrespective of the the orientation of the plane ta le, oi exa I

If it is suspected that the point

is

on the great circle, change the

orientation

a second trial. I f three rays again meet at the same point, the point ie- on

And if it is confirmed that the station P is on the great circle, replace o k of the

A, B and C with another point D such that the point p does not fall on t u new

If the point P is outside the great circle passing through A, B and C, the point d o * d y

the intersection of the two rays drawn to the nearest points and the point P me

side of the ray to the most distant point. For example p,

If the point P lies outside the great triangle ut inside the great circle, the ray to the middle

point lies etween p and the point e o tained from the intersection of the i ays to t

k

ot ei two

(extreme) points. For example p,.

If the point P lies on or near one side (say, AC) of the great triangle, the point p will lit etween

the two parallel rays drawn to points A and C, and it will e on the same side of each of the

rays. For example pv

If the point P lies on or near the prolongation of one line (say, AC) the point p lies outside the

parallel rays and on the same side of all the rays. For example p(>

8. If A, B and 0 are on one .straight line, the great triangle gets converted into a straigh t line

and the great circle will have a c as its arc, and an infinite radius. A ray drawn to the middle

point is etween the point p and the point f o tained from the intersection of th e rays to other

(extreme) point.

M echa nica Method for Three-Point Prob em

The three-point pro lem can e solved y a mechanical method

using a tracing paper.

1. Set up the plane ta le at station P w'hose location is required

and orient it approximately using a compass or y eye-

2.

3.

4.

and orient it appi

judgement

Stretch a sheet of tracing paper over the plan and fasten it on

the plan.

Select any convenient point p, on the tracing paper to represent

the station p.

Pivot the alidade on p, and sight the station A and draw a

ray. Similarly sight the stations B and C and draw the rays.

I P S m a s re?

\

(a) Trac ng Paper

a \

/ c

P

Plan

( )

Fnsit Je Eng'neere

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22/53

C V L ENG NEER NG

Basic ru les

Rule 1

The point p is on the same side of all the three resection lines a 'a? b'b and c'c.

When the surveyor faces such a problem the corresponding to stations A, B and C, the point

P *ies e*ther t0 t,le r*Sht of all resection lines or to the left of all resection lines. In above, the

point p lies to the left of all the lines.

Rule 2. I

he distance of p from a resection line is proportional to the length of that line. Hence.

pi p2 p3

pa pb pc

Now keep the alidade along p'a and rotate the plane table to sight the station A. Clamp the

plane table. This orientation of the plane table is more accurate than the first trial.

8. Now pivot the alidade at b, sight B and draw a ray. In a same way alidade at c. sight C. and

draw a ray.

9. Determine the intersections of the three rays drawn. These rays will form a smaller triangle

of error than the previous one.

10. Now select a point p'\ satisfying the two rules, and repeat above steps.

The above procedure is repeated till the triangle of error reduces to a point p.

In this way, the location of station P is fixed on the plane table.

Supplementary Lehmann’s Rules

1. If the plane table station P is outside the

great triangle ABC the triangle of error will

also be outside the great triangle abc formed

by joining the plotted points a, b and c.

As per basic rule 1, the point p lies on the

same side of all rays, therefore, the point p

shall be outside the triangle of error. For

example p,.

2. If the plane table station is inside the great

triangle ABC, the triangle of error will also

be inside the great triangle abc. As per basic

rule 1, the point p shall be inside the triangle

of error. For example p2.

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23/53

62

Surveying

CIVIL ENGINEERING

N o t e :

For better results the point P should be chosen quite far o f the point C.

Resection After rientation by Three Pointŝ

The three-point problem consists in locating the position of a plane table station on the drawing

sheet by means of observation of three well-defined points, whose positions are already been

plotted on plan.

Let A, B, and C, be the three well defined points and let their plotted positions be

a.

b

and c.

It is required to fix ground station

P

on plan as

p.

Three point problem can be solved by several methods.

1. Graphical method 2. Tr ial and Error method

3. Mechanical method 4. An alytica l method

5. Geometrical - construction method.

Jv G ra p h ic a M e th od

• There are several graphical methods to solve the three-point problem.

V But the most simple and the best one is the Bessel s solution by the inscribed quadrilateral.

• This is based on the geometric principle that in any inscribed quadrilateral, the angle made

between one of the sides and one of the diagonals is equal to the angle made between the

opposite side and the other diagonal.

Tria -and-Error Method or Lehm ann’s M ethod

• Th is method is very comrp^nly nspd in fipJH measurements

as it gives very accurate^r&snits^

• The position of a plane table is estimated by judgement. Let

it be p\

• The alidade is kept against p a and the table is oriented.

• Now, pivot the alidade on point b and sightB. Draw a back

ray. Pivot the alidade against point

e

and sight C. Draw a

back ray. If the orientation of plane table is correct, the

three rays will intersect at one point p, otherwise a triangle

or error is formed.

• This triangle is reduced to a point by trial and error.

Lehmann’s Rule

There are two basic rules and few supplemantary rules. Although the basic rules are sufficient

for determining the position of point P but the supplementary rules also facilitate in the quick

solution.

f .E.S MASTER

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24/53

riV L ENG NEER NG

Pl ne T ble

1

, in this case the two point problem is used to nl ‘

whose position s are alread y plotted on p|an P ° 3 Statlon C by sighting: to sta tio ns A & B

procedure

1. Choose a suitable station D near ,

two obtuse. 6 angles CAD and CBD are neith er two acute nor

Set up the plane table at station D C W nt t, ui

or alterna tively, by eye-judgm ent Surb

th t

l'* ° approximately usin g a magnetic compass

Clamp the plane table Ch ^ lmG

° b

15 made aPProximately parallel to AB.

. Pivot the alida de on o and eigh t sta tion A. Draw a ray through

“ n ^ 6 “ d S- h ‘ B »• intersecting the ray

I t t ionD i t'appVeo x^ ataePPr05dmate P0Siti° ' ’ ° f “ “ «I0’“ d P° ' " ‘ *>— orientation a.

Now transfer the point d, to the ground using a plumbing fork.

3' n r ' M hV l i ade pi™ t ed fa t

*>•

“ Sht the station . Draw a ray

d , ,

to represent the distance

DC . Maik the position of

}

by approx, estimation.

4. Now, sh ilt the pla ne ta ble to station C and cen tre it such that the point c, is above C.

rient the pla ne tab le by ba cksig htin g on D. Thus the orientation at C is the same as it was

at D.

5. Now, pi\ot the alidade at point a and sight sta tion A. Draw a ray ., to intersect the ray

at point

.,.

Hence,

^

represents the approximate position of the station

.

because the orientation is still

approximate.

Pivot the alidade at point

.2

and sight station B. Draw a ray c2fe, through

.,.

In general, the

ray 2b2 will not pass through the correct positionb. because the orientation is approximate.

This point fa, gives the approximate position of station B with respect to the orientation made

at D.

As the length

b

is the true representation of distance AB, the error in the orientation is equal

to the angle fa, ab between the lines

b

and crfa,.

To eliminate this error in the orientation, place the alidade along ab,. Fix a ranging rod at a

point P (a random point) at some distance from the plane table and in line with ab,.

Place the alidade along line ab and turn

the plane until the ranging rod at P is

bisected. Clamp the plane table in this

direction.

Now the orientation of the plane table is

correct and the line ab is exactly parallel

to AB.

9. Now to find the tru e position point of

the station C, pivot the alidade on a and

sight A. Draw a ray

i

through

.

Sim ilarly pivot the alidade on fa and sight

B. Draw a ray

b

through fa. The

intersection of the rays and

b

gives

the true position of c.

.E .S MASTER

6

.

8

.

REQUIRED

TURN


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25/53

460

Surveying

C V L ENG NEER NG

Kin 's lire drawn from these stations to the station to he plotted.

I hi intersection of the rays from these two stations gives the position of th. station to l„

plotted on the drawing sheet.

Sometimes, this method is also called as

graphical triangululion.

• 1his method is most commonly used for plotting details. It is preferred when the distance

between the stations is too large, the stations are inaccessible, or the ground is undulating

l‘ °r example is of broken boundaries, which can be very conveniently plotted by this method

4. Resecti n

• This method of orientation is employed when the plane table occupies a position not yet plotted

on the drawing sheet.

• Resection can be defined as the process of locating the instrument station occupied by the plane

table by drawing rays from the stations whose positions are already plotted on the drawing

sheet.

• 1 he point representing the resection of two rays will he the station to he located provided the

orientation at the station to he plotted t> correct, which is seldom achieved.

• 1his problem can he solved by any of the methods such as resection after orientation by back

ray. by two points, or by three points

• This method is employed when surveyor feels that some important details can be plotted easily

by choosing any station other than the trinngulntinn stations.

The position of such a station is fixed on the drawing sheet by resection.

Resection After rientation by Back Ray

This method is very useful when one of the plotted stations is accessible from the station to

be plotted, problems.

Pr cedure

1. Let

a

&

b

be the plotted positions of the two ground

stations A & B and station C is to be plotted.

Set up the table at station A with point a being over

station A.

3 By keeping the alidade over 06, bisect the station B.

I Now as the table is oriented, bisect the station

C

and

draw a ray ac.

5 Shift the table at station C and place the alidade along

ca and rotate the table till it is oriented and clamp it.

6 With the alidade pivoted on b. sight the station B and

draw a back ray

be .

7. The point of intersection of

ac

and

be

gives the required position of station C on the plane table

R esection After rientation by Two Points

• The two-point problem consists of locating the position of a plane table station on the drawing

sheet by observation of two well defined points, whose positions have already been plotted on

plan.

E S MASTER

ifVSATE PSU»

fHcr r.|.̂ Kktwana Sam V» TVht H C*!#

WW »i» Wai(lfrof| ■ a.lero.fcu*'

j w mi iioimK > it iuk ■


26/53

r iV IL ENGINEERING

Plane Table

S„, the table on station B, place the alidade along the plotted line

„

and rotate the till until

the line o atg i bisects the station A. Clamp the board along this line of sight. The line

b

truly represents the line BA on the ground.

3. Resecti n

The method of resection will be discussed later in this chapter in details.

Methods of Plane Table Surveyin

a

u

The methods of surveying with a plane table are

^

Radiation,

• Traversing.

/

.# Intersection and

Resection.

1. Radiati n

In this method the instrument is setup at a station

and rays are drawn to various stations which are

to be plotted.

The distances are cut to a suitable scale after

actual measurements.

This method is suitable only when the area to be

surveyed is small and all the required stations to

be plotted are clearly visible and accessible from

the instrument station.

The scope of the method is increased when the

distances are measured with the help of a

tacheometer.

2: Traversing

• This method is similar to compass or theodolite traversing.

• The table is set at each of the stations in succession.

• A foresight is taken to the next station and required the distance is cut according to a suitably

chosen scale.

• This method is most suited when a narrow strip of terrain is to be surveyed, e.g. survey of

roads, railways, etc.

• This method can be used for traversing both the open as well as close traverses.

3. Intersecti n.

• In this method two stations are selected such that

all the other stations to be plotted are visible from

these.

• A line joining these two stations is called base

l ne.

The length of this base line is measured

very accurately.

—

/

x c

b

Base line

a b

8

B

.E.S MASTER

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27/53

3. Orientation

It is the operation of keeping the plane table parallel to the position it occupi

station.

In such a case all the lines plotted will be parallel to the corresponding lines g

If the position of board is different at successive stations, the relative positions p

details will not remain same as the relative positions of the details on t e groun

As a result, the plotted work of the previous stations cannot be connected to t he

successive stations.

During orientation the table is rotated and the plotted position of the insti ument stat’o also

disturbed and shifts relative to the ground stations.

Therefore operations of orientation and centring are therefore interrelated. iientation of plane

table can be close using a trough compass, back sighting or by resection

* * „

C V L ENG NEER NG

zHf:________________________________Surveying

Methods of Plane Table rientatio

1. By Trough Compass

A trough compass is placed on the top right side corner of the plane table in such a way that

the magnetic needle points exactly towards the N —S direction.

• Draw a line along the edge of the compass.

• Shift and set up the plane table on the next station. Place the trough compass along the N

S line.

• Rotate the table till the magnetic needle coincides with N—S line previously drawn.

Nota:

This method o orientation arid cannot be employed at stations where local attraction is

suspected.

2. By Back ighting

This is the most accurate method of orientation.

Traversing with a plane table

In this method plane table is set on a new station and the alidade is placed against the line

joining the new station with the preceding station and the table is rotated until the line of sight

bisects the previous station.

To achieve this, let the plane table is shifted from station A

plotted with the plane table at A.

to B and let the line ab has been

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28/53

g i r i g

Plane Ta le

The portion of the plane ----------------

7 r [he 7 7 oc' u' " ed »>■ • *. * » , M , h

* *« .

.

(C

------

x M i e ii i.

V e

of a plumbing fork is justified only if the plotting i* done at large

* *cal«? an*

»•

* " ,; Z e ° n t th ‘

B° “ rd * hOU,d b' •» t t .. Vertical A> l. of the

This can be achieved by placing a spirit level over the plane table

The Fu dic ial Ed ge of the Alidade should be a traigh t L

ne

This can e checked hv drawing a line along the ruling edge, reverse the ..lida.le and place it

against the end* of (he line.

Again draw a line which ahould coincide with the previous line

If the two line* do not coincide, the edge are corrected

3.

The Two

Vanes

should

he

Perpendicular

to

the Base

of

Alidade

Set (ho alidade on the co rner edge of a huilding or on a suspended plum o

Set the alidade vane* along any of the a ove two case.

The plum line and vane should coincide. If they do not coincide adjust the hinge* till tin* vane

coincides with the plum line.

E

P

k

tting up the Plane Ta l

Following operat ion* art* included in netting up of the Plane Ta le

Cen tering f-

lt in the operation o f ringin g th e plotted station point exactly over th«* ground station. A

plum ing fork in used for checking the centering

.fixuct cent ing i* im po tant fo la ge-scale mapping -----

-----------

--------------------------------------------------... tr in v of about 30 cm is permissible

or sma -sca e mapping, an error m e

>eve ing *

. .he operation of brtng.np the p ane tabie in a honron.a pian.

**ve the board with the he p of a spiritjeve

~ ~-v

E.S MASTER

NWi hi Emrsw

IE!

itof


29/53

IVIL ENGINEERING

Tripod

An open frame type light tripod is usually used in the simplest form of plane tables, levelling

o the board is achieved with the tripod legs and checking the horizontality of the board with

the help of two spirit levels fixed at right angles to each other in a block of wood.

Alidade

An alidade is a straight-edge ruler having some

sighting device, it is used for sighting the objects

and drawing the lines.

Plain Alidade it is a straight-edge ruler about 450

mm long, made of a metal or wood. ne of the

edges is bevelled and graduated. The alidade is

provided with a sight vane at each end. The sight

vanes have hinges at the lower end so that they

can be folded down on the ruler when not in use.

narrow slit and is used as an eye vane. The object

wire at its centre. The two sight vanes is open and

The two sight vanes provide a definite line a sight

The bevelled edge of the ruller is also known as the fiducial edge. The line of sight of the

alidade is in the same plane as that of the fiducial edge or in a plane parallel to it.

A ata:

N on a days Telescopic Alid ad e a e also much in use, in place o f pla ne A lid ad e. When the

po int s too high o low a e to be sigh ted

the accu acy and the ange a e conside ably

inc eased by p oviding a telescopic alidade.

4 . Tro u g h Co m p a s s

~ Generally it is 15 cm long and is provided to plot the

m agn etic m eridian (N - S direction) to- fac ilitate

orientation of the plane table in the magnetic meridian

At the extremities of the trough compass, there are

graduated scales with zero at the centre and marking upto 5° on either side of the zero line.

Longer sides of the trough compass are parallel and plane such that they can be used as a ruler

for drawing the line or for placing the compass such that it coincides with a line already drawn

on the drawing sheet.

5

/

5

0 - j

_______________ ^

0

5 '

° '

Trough com/>


30/53

Plane Table

455

Disadvantages

X

It is not suitable for, work in i ,•

' ’ , f c climate and in a densely wooded country

2. The absence of measurements (field 3 a unt iy-

to some different scale. ° ( S Causes ^convenience, if the survey is to be replotted

3

Plane table is heavy and ak

wa*A *■

• , t ■ c d t0 car.ry and the accessories are likely to be lost

k It does not glve very accurate results.

iyiL ENGINEERING

Accessories

used

in

Piane Table Surveying

s ®


31/53

Plan Tabl

Introductioi

The plane ta le is an instrument used for surveying y a graphiealjnethod in . r

work aqd plotting are done mmulLanequsly.

The main feature of plane ta ling is that the topographic featuies to e mapped

view. Hence no chance of missing of any important detail.

It is suita le for small and medium scale-mapping (1: 10,000 toJj2^5Q ^0qp)^

here

the gi eat

accuracy is not required. It is also used for plotting the topogiap ica map.

Before commencing a plane ta le survey, the instrument stations aie fixed

to co\u

the entire

area.

These stations may e fixed y surveying a trigonometrical framework, esta lishing a network

of control points on a pattern to suit the scale at which plane ta ling is carried out.

The elevations of these points are determined with the help of Levelling.

A surveyor starts filling in details from any of these control points, one y one. and traverses

all the control points.

The finished maps so produced are known as topographic map .

This graphical method of producing topographic maps is known as cartographic urveying.

It should e noted that all the measurements made are plotted directly on the drawing sheet

instead of recording in the field ook.

The principle used in plane ta le surveying is that an unknown point of interest can e

esta lished y measuring its directions from known points.

Advantag s

simultaneously. Therefore there i, no risk of omittmg

The error and mistakes in plotting can e checked y drawing the check

lines

C3r Irregular o jects can also e plotted accurately as the lay of land is

in

view

It is most rapid and useful for filling in details.

No great skill is required.

6. It is less costly in comparision to theodolite survey.

7. It is very advantageous in areas, where compass survey is not mKoki

magnetic fields. * ‘ ehaMe e* area ^ t e d *


32/53

c,wn ENGINEERING

^ The method oi com puting ar ea s by subdividing a plot into triangles is suitable for

ja) work ot small na ture (b) work of big nature

(C road work (d) canal work

*5 3

& The method suitable for computing th* .

from a straig ht line is a ,ea when the boundary hnes departs considerablyrom a straight line is

(a) Mid-ordinate rule

(c) Trapezoidal rule

(b) Average ordinate ride

(d) Simpsons rule

9. The area of an irre gu lar nlnM„a

of a gUre can be accurately obtained with the help

(a) Pentagraph (b) paraUax bar

(C) Plamme‘er (d) any of the above

10. If is the number of sides and

L

the length

f

r , ,

gtn or the sides of a regular polygon, its area is

n .. 1ftn°

r2 .a 180c

(a) —L" cotJ —

n

n . n o 2 IS 0

0}) —L sec

4 n

(d)

n T2, 2180-

-I. tan

n . •>

■

180°

(c) —L" cosec"

4 n 4 n

11. Simpson s rule for calcu latin g area is applicable only when the ordinates are

(a) odd (b) even

(c) either (a) or (b) (d) hone

12. Volume of earth work can be calculated by

(b) Average ordinates

(d) Hund’s rule

(a) Mid-ordinates

(c) Prismoidal rule

^ bje ct ive Q uestions

Answers

1.

(b) 2. (c) 3. (c)

6.

(b)

7.

(b)

8. (c)

11.

(a)

12.

(c)

4. (c)

9. (c)

5. (a)

10. (a)

.E.S M AS TE R


33/53

452

IVIL ENGINEERING

2

3.

4.

5.

6

bjective Questions

1. Which one of the following methods estimates best the area of an irregular and cur ndarv.

(a) Trapezoidal method (b) Simpson’s method

(c) Average ordinate method (d) Mid-ordinate method

What is the volume of a 6 m deep tank having rectangular shaped top6 m 4 m a bottom

4 m x 2 m (computed through the use of prismoidal formula).

(a) 96 nr* (b) 94 m *

(c) 92 m* (d) 90 m*

Which one of the following methods of computing area assumes that the short lengths of the

boundary between the ordinates are parabolic arcs?

(a) Average ordinate rule (b) Middle ordinate rule

(c) Simpson’s rule (d) Trapezoidal rule

In the given formula formats, L is the length of the base line split into n equal segments

each of length *d\ (),, 0 . n. , are the ordinates at the sequential ends of the segments

and M,. M

0

Mu are the mid-ordinates of successive segments. Which of the following

pairs of rules and the formulae for computation of the area standing on the base line are

correctly matched?

. Mid-ordinate Rule

A =

, + g +... + n

n

x L

2. Average ordinate Rule A - —[M, + M2 f... + Mn|

n

( 0 i.._Qa±l'

2

+ ()., + .j +... + n

. Trapezoidal Rule ................A -d

Simpson’s Rule ................ A = |[( , + n+1) +

(0 ,

+ ,... + n) + 2(0 :i + 0

5

+... + n_,)]

Select the correct answer using the codes given below:

(a) and

2

(b) and 3

(c) 3 and 4 (d) 2 and 4

If the cross-section areas of an embankment at 30 m intervals are 20, 40, 60, 50 and 30 m

2

respectively, then the volume of the embankment on the basis of prismoidal rule, is

(a) 5300 m

3

(b) 8300 m

3

(c) 9300 m

3

(d) 9400 m

3

Excavation is to be made for a reservoir measuring 20 m long, 12 m wide at the bottom and

2 m deep. The side slopes aie to be 1. and the top to be flush with the ground which is level

in the vicinity. As per piismoidal formula, the volume of excavation will be

(b) 618.66 m3

(d) 633.66 m3

(a) 610.33 m

3

(c) 625.00 m:!

I S

T T

m a t e

Insltute for ngineers

IES/GATE/PSU

ffice: F-126, Katwaria Sarai, New Delhi - 0 0 6

Websjte: www.ieamaster.org. E-mail:

ies_master^yahoo.co.m

- hone: 011-41013t0(>, 7838813-t fi. 9711853908


34/53

ENGINEERING

Meas rement of Area & Vol me

= 9° + (45 6.67 -32 8.33 )

= 90 + 1 273

= 91.273 m

x(361 -328.33 )

P r i s m o i d a l Rule calculate the volume of a 5 m deep pit whose top and bottom dimens

rrespect vely 10 m x 20 m and 20 m x 40 m.

. in pr ismoidal Rule ordinates required should be even but here ordinates pio l

Sol. bm t^e average of the sides and then calculate the area.

even so

A = 10 x 20 = 200 m2

A, = 20 x 40 = 800 m

2

y__ A

t

+4Am

+ A ]

3

£^ [20 0 + 4x 45 0 + 800]

v _ £ ^

x

2800

v 3

V= 2333.33 nv

%


35/53

50

Surveying

CIVIL ENGINEERING

Example 11.

In a proposed reservoir, the areas containing within the

contours are:

Using the method of Prismoidal rule and End area formula,

calculate

(i) capacity of the reservoir when it is full at m level:

(ii) elevation of the water level when it is 60% full.

Ignore the volume below RL 65 m.

Sol.

V = 5

32 + 2

2

+ 26 + 24+18 + 15 + 13 + 7

V= 600ha - m

6

V= 3

+4(7 + 15 + 24) + 2(13 + 18) + ( — ]x5

V= 456.67 + 145 = 601.67 ha - m

Capacity of Reservoir when it is 60% full

601.67

V =

100

x 60 = 361.002 ha - m

Capacity of reservoir upto R.L of 95 m

= 3 ( ^ ~ ^ J +4*7 +5 + 2', , +2* 3 + 18)

= |(l4+18 4 + 62) = 456.67

Capacity of Reservoir upto R.L. of 90 m

Contour (in m)

Area (in ha)

32

95

26

90 24

85

18

80 ^

15

75

13

70

7

65

2

.E.S MAS TER

insttue la Ergtncera

S/GATE/PSUs

ffice: P-126.

Katwaria

Sarai, New Delhi •11 0 016

Website: www.iesnm

8

ier.org. E-mail ies_ma8terrtynhooc

Phone: 011-11013100. 7838813106. 9711853908


36/53

ENGINEERING

easurement

of Area & volume

9

ohoVfi the existing ground levels on a 15 m square grid for a plot of land which is to

figuV° .̂aled to a uniform formation level of .

. Calculate the volume of

earth require

H 8 i a l

Sol.

Num er of times a particular corner height is used in various squares is marked in the circles.

Ih , = 2.40 + 1.20 + 1.80 + 1.40 = 6.80

Eh., = 2.10 + 1.70 + 2.30 + 1.30 + 1.90 + 1.60 = 10.90

Sh;i =

Eh, = 1.50 + 2.70 = 4.20

V = — (Eh, +2Eh. + 3Eh, + 4Eh,)

4

(15x15)

(6.80 + 2x10.90 + + x .2 )


37/53

8

Surveying

CIVIL ENGINEERING

Example 8.

Figure shows the three cross-sections of an embankment at an intreval of 30.0 m. Calculate

the volume between the end sections by (a) Trapezoidal rule, and (b) Prismoidal formula.

fHlnv-H

SSCT10N1

—-

m

SEC T ON-2

A

Sol.

A, = 2.0 (11 + 2 x 2) = 30.0 m2

A

2

= 3.5 (11 + 2 x 3.5) = 63.0 m

2

A

3

= 5.0

(

+

2

x 5.0) = 105.0 m

2

Trapezoidal rule V = D

'A , + A

—+ A„ + A3 +...

\

V = 30

(30.0 + 105.0)

+ 63.0

= 3915m:i

Prismoidal formula

D

V = —[(A, + An) + 4(A3 + A., +...) + 2(A3 + A5 +...)]

o

= — [(30.0 + 105.0) + 4 63.0] = 3870m3

3

E.S MAS TER

nstitute for Engtieens

lES/GATE/PSUs

ffice: F-126, Katwaria Sarai. New Delhi -11 0 016

Website: www.iesniaster.org, E-mail: ies.master̂ yahoo co in

J-honc 01M1Q1340C. 7838813406. 9711853908 ___.


38/53

c v l e n g n e e r n g

easurement of Area & Volume

447


39/53

6

CIVIL ENGINEERING

Sol. Calculated using any one of the methods

Let the independent coordinates of A be (0, 0). The coordinates of other poii

as below.

Line Latitude

Departure

c t - n f in n T n r l A n p n d e n t C / o o rd i f ir tv y -

X

y

r\

AB

-157.2

+154.8

A(l)

0.0

o .u

. i r i

BC

210.5

52.5

B (

2

)

-157.2

+ 5 4 0

. r\ r* o

CD +175.4 -98.3

C(3)

+53.3

+20/. 3

| DA

-228.7

-109.0

' D(4) 1

+228.7 +109.0

n n

A(5)

0.0

u .u

( )

(

2

)

-157.2

+154.8 "

+207.3'

x 0

y * 0

We know that 13.1G a. 2A = IP - IQ

2A = [0 x 154.8 - 157.2 x 207.3 + 53.3 x 109.0 + 228.7 x 0.0]

- [0 x -157.2 + 154.8 x 53.3 + 207.3 x 228.7 + 109.0 x 0.0]

2A = - (32587.65 - 5809.7 + 8250.S4 + 47409.51]

= 41219.105 m-

Example 6 .

ad

e m o a riK m e iiL a m

».ide at the formation level. The centre line of the embankment

m above the ground surface. If the ground slope is

1

in

22

at angles to the centre line,

the side slopes are

2

:

1

, calculate the side widths and the area of cross-section by various

A road embankment is 11 m w

is 3 m

and

formulae.

Sol.

n

I- I~ '

B

n

GS

m

w-

w«

In above figure, - 5'5m’ m

= 22 , n = 2 and h = 3m.

m

.E.S MASTER

InsaueforEnQiccr

ES/CATE/PSU

ffice: F-126. Katwana Sarai. New Delhi * 110 016

Website: www.iesmaster org E-mail: [email protected].»

Phone: il-

11013406. 7838813406. 9711853908


40/53

Surveying

CIVIL ENGINEERING

Example 2 .

The following perpendicular offsets were taken from a chain line to an irregular boundary

Chainage 0

8

20

35

47

60m

ffsets

14.5

24.5

30.8 27.4 28.4

18.4m

Sol.

----- » *— —— i

determine the area between the chain line, the boundary and the end offsets.

Gi\en, dj

8

m, d

2

-

12

m, d

3

= 15m, d, =

12

m and d

5

= 13m.

Ai'ea = |(14.5 + 24.5) + ̂ (2 4 .5 + 30.8) + ̂ (3 0 .8 + 27.4)

2

2

^ (2 7 .4 + 28.4) + — (28.4 + 18.4)

2 2

= 156 + 331.8 + 436.5 + 334.S + 304.2 = 1563.3 m 2

Example 3.

Determine the area of the traverse shown in figure below using the meridian distance method.

] 00 m

45" * 1

Reference'

100m

Parallel

100 m

Sol.

100m

Meridian distances of the various lines are determined as below,

Line AB,

m

= 50 m

Line BC, m., = 50 + 50 + 50 = 150. m

Line CD, m3 = 150 + 50 - 50 = 150 m

Line DA, m = 150 - 50 - 50 = 50 m

Line

M.D.

(m)

Latitude


41/53

urveying

C V L ENG NE ERS

Example 2.

he following perpendicular offsets were taken from a chain line to an irregular ound

i—

ary.

Sol.

Civen, d, - 8m, d, - 12m, d:1= 15m. d, = 12m and d5 = 13m.

Area = §(14.5 + 24.5) + ̂ (24.5 + 30.8) + ̂ (3 0.8 + 27.4)

IS

+^(2 7.4 + 28.4) + ̂ -(28.4 + 18.4)

156 + 331.8 + 436.5 + 334.8 + 304.2 = 1563.3 m2

Example 3.


42/53

CIVIL ENGINEERING


443

Volume from Spot

• T his method of estimating the earthwork quantities is also known as the unit area method.

• In this method the area is divided into regular figures such as squares, rectangles or triangles

and the levels of corners the figures are measured before and after the construction.

• If the depth of the excavation are op 6 ,f c, and d v respectively, andA is the area of the figure

ob iy then the volume is given by

y =°\ + c/

4

A

Example 1.

The following perpendicular offsets were taken at 5 m intervals from a traverse line to an

irrregular boundary line 2.10; 3.15, 4.50; 3.60; 4.58; 7.85; 6.45; 4.65; 3.14 m.

Compute the area enclosed between the traverse line and the irregular boundary from the first

to the last offset. Use

(a) Average ordinate rule; (b) Trapezoidal rule (c) Simpson’s rule

Sol. (a) A

( , + + —+ ni)

n + 1

Given

L = 40m, n = 8.

- — 12 10 + 3 15 + 4.50 + 3.60 + 4.58 + 7.85 + 6.45 + 4.65 + 3.14]

A - y

(b)

= 177.87 m2

A = d

Qi + Qnq. + +o3+ + o n

2

= 5

2 , 1 0

+ 3.14 + 3 15 + 4 50 +

3

eo + 4.58 + 7.85 + 6.45 + 4.65

2

= 187.0 nv

Sim pson s r the number of offsets is odd, the Simpson’s rule can be applied,

(c) There are 9 onsets.

_ d [(2 l0 + 3.14) + 4(3.15 + 3.60 + 7.85 + 4.65) + 2(4.50 + 4.58 + 6.45)]

. 5rg 2 4 +7 7 . 0 0 + 31-06] = 188.83 m2.

A " 3

D e lh i- H 0 «

ffice: F-126. Katwaria . * jeg [email protected]

Website. ^83881-!^


43/53

Sur eying

C V L ENG NEER NG

Area in excavation

wh.

A =

2

w

A = 7

(n - s)

+nh

A = k2

(n -s)

Centre line in em ankment

w, =

- w

f + h \(

ns

hl =

r h Jl

n - s ,

ns (

A _ h

dl

=

n-si

,2n

Area in em ankment.

v

. _ w.hi _

A > " 2

-nh

(n -

)

End Area Formula

This is also called as trapezoidal formula.

V= A l A + A, + A, +... + A„_,

where A,. A,, A., A„ are the end consecutive areas and L is the distance etween them

Prismoidal Formula

This is also called as Simpson s rale for volumes.

V = —[(A, +A„) + 4( A, + A, +... A,,.,) + 2(A

2

+ A

5

+... + A„_2)]

3

No e :

•

It is n ecesary to have an o dd number o f cross sections to use this fo rm ula .

In case o f even number oj cross sections, the end strip is treated sep ara tely an d the volu

o f the remaining strips is detei mined by the prism oidal formu la a nd the volume of the l

strip is calculated either by the end area or Prismoidal rule.

In case if only Prismoidal rule is to be applied , the area half ivay between the section

interpolated by averaging the dimensions o f the end sections and not by averagin g the

areas.

_______________________

ffice: F

-126

Katwaha

Sarai New Delhi •

110016

ttebsiu- www ies muster org E-mail »e*_inaMerc* yaho

Phone il -1 101 3uw 7838Hl;U0ti U?11853908


44/53

C V L ENG NEER NG


4

sh,= (h - h ,) n -^

n| h - A

__ n

hl

s + n

n

hi -

s + n

2

n

h -

2n

From equation (

1

)

d =

d = ^ + -£il

h, =

2

n + s

n

' h - i )

2n )

n - s

, b

h + —

2n

• b sn

d, =

~ +

l n - s

b '

h + —

2n )

Substituting the values of d,, h, and h., in equation (

1

)

A =

b )

+ n2(bh + sh‘ )

( i r - s 2 )

3. Three-level ection

d = l h + £

d = (h+

5

j

b V ns

Kn + s )

f

n,s

vni - s

Area AB DE = Area ACF + Area FCD + Area FDE + Area FEB

=

-

—h. +hd + hd. + —h„

2

L

2

1

1

2

-

A = £ (h I +hs) + |(d + dI)


45/53

440

Surveying

C V L ENG NEER NG

Planim eter are used to ind out area o irregular shapes.

t is a mechanical integrator used for the measurement of areas of figures, plotted to a scale.

M easurement o Volumes

• The computation of volumes of various quantities from the measurements done in the field is

required in p lann ing and design of many engineering works.

Volume of Earthw ork Selection of suitable alignm ent of road, canal and sewers. n estimation

of pavement materials.

Volume o f Regervoior — Design and p lann ing of reservoirs.

• 'Fhe dire ct computation of the volume from the measurement of length, w idth and depth is not

fesible for large engineering works.

• n such a case computation of the volume of ea rthwork is generally done after computing the

areas of var ious cross sections.

• Spot levels of the ground are taken to estimate the volume of the ea rthw ork .

• The es tima tion of the volume of water in a reservoir, the contour map is genera lly used.

M easuremen t o Area o Cross-section

For estim ation of the volume o f earthwork, cross-sections are taken at rig h t angles to a fixed

line (generally, the centre line) which runs longitudinally through the earthwork. Spacing of

the cross-sections w ill depend upon accuracy required and the character o f the ground.

Fo llow ing type of cross-section generally occur in field.

1. Level section

2. Two-level section

3. Sidehiil two-level section

4. Three level section

1 . L v l S c t i o n

A = (b + sh) h

2 . T w o - l v l S c t io n

Area ABEDC = Area ACF + Area CDF + Area DEF + Area FEB


46/53

CIVIL ENGINEERING

Measurement of Area & Volume

3

4

. Simpson’s ne Third Rule

• If the irregular boundaries are curved Simnenn'o „,i„ ■

r

. , . , ,

calculate the area of the grven tract. ' ' Ver the tra|,az0,dal ,rule “

. According to this rule the short length of boundaries between the two, adjacent ordinates

parabolic arch

is

Area of trapazoid ABDC = * 2d

2

2 *

Area of segment CIDHC = -x Area of Parallelogram CDP"E

3

( X -

j + o,

~2~

2 2

= -x(ABxHI) = "

= y [ > 0 , - ( 0 , + 0 3)]

Area f firs t tw divisi ns

A = ^ ^ x

2

d + y (

20

._,-(

0 1

+

0

3)]

A = ^ [30,+ 30 ,+4 0,-2 0 ,-20 ,]

A = | [0 ,+ 4 0 ,+ 0 3]

Similarly, area of next two divisions

A - ^(03+ 4 0 ,+ 0 5)

Area of last two divisions

d

x 2d

A= |(0„-2+ 40n-.+°n)

Adding up

i-eaA = - [(0 J + 40s +20i +404+... + 20n_3+40n1+0n]

Total area ^ ~

A

_ -[( , + n) + 4(0, +0,

+... +

0,,

,) + 2(Q,

+0. +... + 0,,-u)]

• lm;


47/53

38

CIVIL ENGINEERING

A = R-

ttot

360“

sin a

~2~

Area of a tract with approximate methods

1. M id-ordinate Ru e

• If offsets /i,,

hv hn

are measured at the mid-point of each division.

Area = average ordinate x length of base

_ l\+ ,h + —+ h„ ^

n

/i + /i

2

+ ...

+ h j

n

= (/?! + h2 + ... +hn) d

where n = number of divisions.

2. Average Ordinate Ru e

• II offsets p

0.r

...,

On

are measured at the end of each division and are spaced apart at equal

distances d.

Area = average ordinate x length of base

_ °1 +

0 2

+ - - +Q,. n. . L

n + \

_ + —+ On ncj ndl.0

n + l 77+1

3. T rapezoida Ru e

. The trapazoidal rule is more accurate than the mid-ordinate rule and average ordinate rule.

• The end ordinate are considered even though they are equal to 0

, + ., .

Area of first trapezoid =

— - —~d

O.}

+ o , ,

Area of second trapezoid = —̂ —- a

0

;,_i +on ,

Area of last trapezoid = 2 ”

By adding up

A = d

o, + o9 o 2

+

o 3

, , o„_, +

0„

2

2

2

A = d

+o , +o j + ... + o

„

/

I . L S M A S T E R

insNuie for Enomeere

lES/GATE/PSUi

c p: www.iesmaster org, E-mail. ies_mastei

Phone: 011-11013406, 78388KU06, 971185.W08

— ■ —


48/53

r lV l ENG NEER NG

Measurement of Area & Volume

437

(3) T ria n g le

A = a«« * half of the perpend,cular height.

Huight

Bam

(4) P a r a l l e l o g r a m

A = ase x perpen dicular height.

Height

/ i f l l

(5) Tra pez oid

A - h a lf of the sum o f pa ralle l sides x perpend icular height.

A

(6) Trapezium

(7) Re gu la r polygon

A = length of perimeter *

h a lf o f the perpendicular distance from the centre o f sides.

A n

one side.

l ique triangle

;re a. 6 and c are the atdea. and a = ^

. _J55l«o-ix2R“nt xRc“ I


49/53

13


Introduction

ne of the objective of many of the survey is to obtain quantities such as ai eas and volumes.

Measurement f Area

The method selected for computation of area depends upon the shape of the tract and the

accuracy desired. Foremost reasons for making land surveys is for the determination of aiea.

Prevalent methods of measurement of areas are:

1. By Field Measurements

2. By Plan Measurements

• If the plan is enclosed by straight lines, it can be divided into geometrical figures e.g.:-

Triangle. Rectangle. Square etc. The area of these figures can be determined by using appropriate

form ulas.

• But. if the boundaries are irregular, then approximate methods are being used.

ot* :

Plan imete r is used to determine area o irregular shape.

Computation of Area of Geometrical Figures

(1) Rectangle

H length H

width

i A ̂ length x width

(2) Square

«— length H

length

| A = length x length


50/53

lVIL ENGINEERING

Field stronomy

435

13. Which one of the following

(a) Astronomical survey 18 ' equired ,n observations of stars?

x » • i * (b) Cadastral survey

(c) Aerial survey

(d) Photogrammetric survey

14. If the equation of time is —13'28 tu u

hour Greenwich Mean Time ~ inen the Greenwich Apparent Time corresponding to zero

(a) 13’ 28.5" 3 day 1S

, (b) 46’ 31 5"

(c) 23h 46’ 31.5" of same dav

(d) 23h 46’ 31.5" of previous day

15. Consider the following statements:

Assertion (A): In a spheri

circumference of the great circle113ng e’ l*le 8um sides is always less than the

Reason (R): The sum of the tv

angles, but less than six right angles^ ^ ^

3

Spherical trian^le is greater than two right

f these statements

(a)

(b)

(c)

(d)

both A and R are true and R is the

both A and R are true but R is not

A is true but R is false

A is false but R is true

correct explanation of A

a correct explanation of A

16. At a given place of observation, the declination of a circumpolar star is

(a) greater than the latitude (b) equal to the latitude

(c) less than the co-latitude (d) greater than the co-latitude

17. The process of determining the location of the station (on the map) occupied by the plane table

is called as

(a) intersection (b) three-point problem

(c) traversing (d) resection

18. Which one of the following is the angular distance between the observer s meridian and the

vertical circle passing through a star measured along the celestial hoiizon?

(a) Right ascension (b) Azimuth

(c) Declination (d) Hour angle

Answers

ctive Questi ns

I. (c)

6. (b)

II. (b)

16. (d)

2.

(b)

3. (d)

7.

(d)

8. (c)

12. (a) 13. (a)

17.

(d)

18.

(b)

4. (b)

5.

(b)

9.

(a)

10.

(b)

14. (d)

15.

(b)

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CIVIL e n g n e e r n g

5.

How many sidereal days are there in a solar year/

(a) 365.2840 ' (b) 366.2422

(c) 360.2500 (d) 365.0000

6. Consider the follow ing statements:

A sidereal year can be defined as the time interval

1. between two successive transits of the sun through the meridan ol any of the fixed stars

2. between two successive vernal equinoxes

3. between two successive passages of the sun through perigee

Which of these statements is/are correct?

(a) 3 only (b) 1 and 2

(c) 2 and 3 (d) 1 only

7. The declination of a celestial body is the arc of the declination circle intercepted between that

body and the

(a) prime vertical through that body (b) azimuth of the body

(c) equinoxes of the Earth (d) equator of the Earth

8. The difference between the apparent solar time and mean solar time is know n as

(a) real time (b) average time

(c) equation of time (d) sidereal time

9. The standard time meridian in ndia is 82°30c E. f the standard time at any ins tan t is 20

hours 10 minutes, the local mean time for the place at a longitude of 20°E would he

(a) 4 h PM (b) 4 hlO m PM

(c) 1 h 20 m PM (d) 0 h 20 m PM

10. Which one of the following methods would give accurate results in d eterm inin g the direction

of the observer's meridian?

(a) Observation o f circumpolar stars on the same vertical

(b) Observation of circumpolar stars at culmination

(c) Extra-m erid ian observation of a circumpolar star

(d) Observation of the Sun at equal altitudes

11. Given that 6 denotes declination, 0 the latit

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