,/
,rn
'-'/
fhe
Ocess
,
?hpr
rurd
l
'to
;
Ith
ffil
j*fi,,:f*:r*#ffiff,::rii
l
)
t'2
-""*"" *1I;;Tiil'ifl""l'ffi,IlTi*31:.;,tr"Hr.d
,r'
where
?r ;:::""",::T,ll:*.,u " ^,,*
".,." "-i#tlii;i*r*t'i'ffie
,,,',11.':,
2,14.2
uor.,o^,,
Th. distrr^-- ."uor, for sro;
-sre*". rill._.*easured
poinr,.
r,o.i.orffi#. ,,.^^
r;::*"
#::"#:
.
it .nu", ', r1e dishn":T'-il'J'#''r?i
il'*r',
"oo..poraioe,;:X.ff,;1nffiffi;:
,
The srope
correcrion,
D = {}l-;2
?' :::1
=; -
t-
i .r,
!L.
n1'"
:i-it -!l,rt'"
,; ;ii,i\;J,,:,,, _
=
wftere
z
= dirrerenc
,---1
!"_
-
Fig. 224
-5
2.2<
,
;:"0',';;,.0..
"?r,l.l",ilrn"el';fi"c
;1*:;x*;{i;ffi1
"ruerrerrns)
,"
ff***fi*;#n***r"**
l,
c
52
Surueying
co=P-ur!9
t
where Po = standard pull
P - pull applied during measurement
A = areaof cross-section of the tape (in cm2)
E = modulus of elasticity of taPe
= 2.1 x lOs N/mm2 for steel
= 1.54 x 10s N/mm2 for invar
I = measured length (in m)
if the applied pull is more than the standard pull,
pull
is less than the standard pull'
and negative, if the applied
Tension correction is positive,
2.14.4 Correction for TemPerafure
Thetapelengthchangesduetochangesinthetemperaturewhiletakingthe
needs to be made
measurements. The teriperature correction C, which, therefore,
is given by:
Ct=q(T^-TOL
where
7* = mean temperature during measurement
Io = temperature of standardisation
a = coefficient of thermal expansion of material
= 0.0000035/oC for steel
= 0.0000001221"C fot invat
L = measured length (in m)
Thecorrectionispositive,ifthetemperatureduringmeasurementismorethan
measurement is
the standard temperature, and negative, if the temperature during
less than the temperature at which the tape was standardized'
2.14.5
Sag Correction
when the tape is stretched between two points, it takes the form of catenary
more and the
(assumed to be a parabola). consequently, the measured length is
given
by:
is
Cru
correction is applied. The sag correction
c*--@:!J =y*
24P' 24P'
IftherearezequalSpanspertapelength,thecorrectionpertaPelengthisgiven
by
co=nry#
24P'
24P'=vrl^:t:t'
(wt)zt tft
=-*,= -----;-24n"F
24n'P
Horizonht,
where
&asa,sient
ra,
= weigh,t of
tape per metre length
- --"r
_the
W = total weight
of the tape
p = pull applied (in
N)
,r_ = *u length
of tape suspended betvveen
= Iength ir m" op" = n/1 (in
Sag correction is always
negative.
m)
two supports
2.74.6 Reduction to Mean
Sea Level
The length of a line measured
at an altitud e of h
metres above mean *"1,I"r."l
Gt.
always
more as compared to- the
on
the
mean sea level (m.s.l.)
surfaJe. ft ,"lJrrirv
,r
reducing distances to
.o"'o.i"y*
II
il
-rl
;.rfi
length;;;.J
"
# ii:ry:-lii:HiH
i_ *;;; ;;l-,
ui"'-to
The correction denoted
O,
R
:li:
I
c*=ftr
1
R
there is the radius of the earth.
The correction is always
subtractive.
2.14.7 Combining
In actual practice,
J
Fig.2.25
Corrections
the above correction, based
-ri"rting,
on the length recorded,
are combined bv addition.
"f nut rtri"try
,n"r1o be combined
ii:l
"*"rr,
:l,i::HffiTilil:'ta*'""h1Ji{'JJ;:'il;x?jt1,:l::i,,rrer.,owingUnit sag correction c
=
Unit slope correction D
=
Unit temperature correction
=
c
Tlue length = Z
Recorded length _ /-,
Then
L=Ii (t + a) (t + b)(t + c)
;HHILj,.:#f ;ilff
,T#,Il";ff ;,:i;J:,-ffi
Zl{"u?"***o
L=Ll(l+a+b+c)
[*#:l
"
the correctio,
;t;
{:":r'"i,1"t,1,*,n
recorded,and combined
2.74.8 Normal Tension
The pull or tension whic.tr,
when applied to a tape
suspended in the air,
the correction due to pull
equarises
and ,",
,ffir#j,
no.rnut rension.
54
Surveying
For one tape length,
q=P=p
and
Since,
c*=
r
Yl
24P2
Cp = C.u
(P-Po)l _Wzl
-
--AE
,4?
The value of P may be calculated by trial and error'
!::rd:.::..:.'.a,..,i::.i.:::.. A line was measured with a steel tape which was exactly 30 m
$&6n''pte
at a temperature o{ 2o'c and a pull of 10 kg. The measured
"'o
pull applied
length was 1650 m. The temperature during measurement was 3O'C and the
kg. Find the true length of the line, if the cross-sectional area of the^tape was
ofLxpansion of the material of the tape per'C is 3'5 x 10and modulus of elasticity ol the material of tape is 2'1 x 10o kg/cm''
*"J ts
0.025 cmZ. The coefficient
Solution Correction to be applied are: (1) correction for temperature and (2)
correction for pull.
(1) Correction for temPerature:
'' =i!':;?',:'-
20)
1650
= 0.05775 m (+ve)
(2) Correction for pull:
c,=9;{l r
(ls - 10)
x 2.1x
0.025
1650
106
= 0.157101 m (+ve)
True length of the line = 1650 + 0.O5775 + 0.157101
=
1650.2'l'4831 m'
The downhill end ol a 30 m tape is held 90 cm too low' What is
the horizontal distance measured?
Solution
Correction for sloPe = hzlzL
= Q.il2Tz
x
= 0.0135 m
Hence, the horizontal distance = 30
-
0.0135
=29.9865 m
30)
Horizontal
;'200Nft
,L:
lJ'^? Il,iT:,;;i:ii,"Jf3"ilT:":
rei,,,eishiJil;;EtTH",L,ff
Solution
tape ends.
correction for sag
Horizontal distance
=
Ss
^leasurement
:ro" unoer a purr ol
f [i"":?,lI:,#lg
w'lr=
z+F
x 1oo)/(24
=
!(30),
= 0.09375 m
x
eoo)z)
= 100 _ 0.09375
= 99.90A5 m.
2.75
rr6u.
ur rerr of the chain
boundaries.
Ii
as.shown
in Fig. 2.26 areca,ed
"rfu.rr..^li
tvpes
types of offsers:
offc.ro.
/1r p".p"nii"ui#'"ill"1lt;#6
n- '
are,
frl
offsets.
(z) oblique offsets.
Th". ur" t*o
Perpendicular offset
B
FU.
2.75.7 perpendicular
When the Iareral
me:
rine, rhe
2.26
Offsets
Offsets
"'r;;;#::W:';:";r:::i::r,ri::::rs
2.75.2 Ohligue
are ar right angres
to rhe chajn
Offsets
When the lateral
meas
rine, the
or perpendicutar
offsets and ro
ffi;'#.J;:3':;;:;"W:.iil:"* nor at right angres ro the chain
are used ro .n.It
tt" ,""r.*,
i;;#il ;hese
:ners of buildings
-:^r...16r t,ure
more
accurately'
Limiting Length of
offset
_2'1s.8
The offset should
not
wiil be *o;;;;":r be loo long. otherw,r.l r.l" error produced
by rong offsets
ur' ,."r.u"y a"s*a]r,plPer' The limiting length depenil;;;;r;'factors,
such
,r,rr'";;i;"'#
#ii"""J.:fj:':s,
Effict of emor d.ue
rras oeen"lala'irr,lr'0"
t
maximum
".."' inl"yi,,g
Let p
bt
!:"",r"n
l?r PD
on, ln",i'i,,.T;
ffiT,,.Tffi
"1,
*, dire*ion
Xiil:T,,.j5.7
fi
Surueying
/ and
paper
a is the error rnade in laying
the offset
will be CP, in.t"ua';;7;'i":"
r"'"'j:::
of CP
i'a."rr,g ,i;
;lr"#"d
of ptoning is
I
cm = ,t,,lno
ground' This, whea plotted
Gie' 2'27)'.T,tri' ,r,. priri ilJiirpr*"a on
uy
bv PrP, perpendicula.
,r;J;il;
,o _lsina
".t
of
accuracy
in plorring
ll]imir
0.025 cm
fu$"
rclrr
rhe scate
=
= o'025
or
l=O.O25Scoseca
the limiting length of
-^Therefore,
offset
is.0.025 S cosecafbr
an error of
ainlayingthe offset and
the disptace_
poinr
.;;;;
perpendicutar
I_nr^ol
Irne Prp, on paper
will be
PrPz
-
Cpt
-
_
n
/_"T:,r"
Fig.2.27 Error in direction
of
B
offset
Cp, = 1- / cpl a
Combined effect of
in direction and length Let p
be a point from
;;;',;;; ;; rn. in"urur"J rrrr,r..
.r rhe ofr.set
dir""ri"r;;';'ii$.\.rr.,.il;;;",iil
or the orfset and
o""o.u"r,,
'"tr" "r orr"u;rg u" r cm = s ,,. ir,", rhe roral
:r::r
where an orfset pc
is raid..on
cP, is / and the error in
;:;:i:"ff|t
pp,p, _ 96.
due to angular
erto\- Prp, = / sin a
and it ufroriO Jo
equal to displacement
drle to the linear
error, prp - l/r
Assuming angle
The_ displacement
4P
Fr
tI'
PPr=1Qppr=tEF,p,
t/r
also
a,so
lt^jyi,
of
0.025 cm, then
tilttrl
or
paper n
:r;,:1",:::
accuracy
in ptorting is
(1/S) = g.s25
t=(0.025/.,!T)rS
also .,1/ sin a/S 0.025
=
or
lPt
/,,
/r
|
/,
I l','
ta/'
t-.-/
= "E(ttr)
=",lil sin a
Corresponding displacernent
on
l- --ti,/
t=e.025/o)Scoseca
r..ig ?28
_/_
c
I
I
I
i
1
rine
,--fi,ain
n- --- -B
Error in directiort anct length
af
offset
2.15.4 Taking
Horizontal
lleasurement
Offsets
t, ".f a point where rhe offset is ro be
ok:n
2.29). Ther"ua", iorll"
end of^(Fre
the rape at the point p
Iow_er swings off
the tape in an"rd;;;;l:
arc with p
shown in Fig.-izi.-it"
3,1[ lentre,-as oj
3:::T11n_'Tging tape on trre crrain
dicutar from p. a,
way is also called swing
offset.
Sl
;";";
Tape
\
riJ
flffi:t:.::':,,^",r,Jr""i"i:i";:l#: - - V. - L _ .,,*[__chain
"n"ii"ill;Tff";
2.15.5 Establishing perpendicular
The most common
:_+s
c
*",r,"i:.ffi:J
m
rine
"______7
z.2g
mg.
Taking offsets
to a Chain Une
fi:Ti:dffiH:"Lffffi:1il ff
is the point from which
Ji":;,lffi # Jl;
a p".'p"ra"i"ri#,1'r"
o" erected. erruurli'u
the chain AB at 3 rinks,
poinr E on
from
i. ff;
i:jl[
Hil:;liP
"T,fl[
cP is the
desired
ti"'o'
,rrr?""ri'i"i,n
ti"',],.,, "trin.rint,
I'in 4 chain rink rrori i andr u, ,t"
with c
,d::fiil;".inrersecting
At-rg.
Examptc
2.9
;ffiil# ji ;
the previous
,n"rir".onsrrucred.
;*Chaintine
2.80
B
Establishing perpenclicular
to a chain line
An offset is laid 4"
out
rhl";rx:
fr
*imu{*{i#I;ir,;,
(i) tn rhe direction
(ii) ln the
f:9,to the tochain line'
-.._ directon
snEU,vr perpendicular
the chain
Solution
line.
(i) Displacement of
the point on ground
parallel to chain line
=/sina
=8sin4o
The scale of plan is
6 m to
-"
I
= 0.558 cm
cm
Displacement of the
point on plan
=
/ stn a
=EIq = o'oe3 cm
;m* d{;
58
Surueying
(ii) Displacement of the point on ground perpendicular
to the chain rine
=/(l_cosa)
=8(l_cos4o)
= 0.01948 cm
Displacement of the point on plan
/(1
=
-
c.os
a)
s
o'019+8
6
= 0.003 cm
,',"fr,ry4
raid
;g,1,;j,,r1i{,11,..
3. our rrom irs u,"
Solution
I
or
Find.tl.re lim.iting length of an offser so that
the disptacement of
rhe orrset was
? ?'f.
i,lJ"lii:ff,i:tSJ#"1,#',,"Jff::
"''
sin alS = 0.025
l=O.O25Scosec3o
= 0.025 x 10 x cosec
= 4.78 m
-..gt
.
sources or error
3o
Fing the.maximum length of an otfset so that the
displacement
oo". n:l
i:'*#,ffi
:["31"t:3,I:;l"i#'"ll5,
*,,,:Liiil
fl?f,
of 1 in 30 and the scale used is i cm 25 m.
=
solution The dispracement of point on the ground from both
sources of error
=ar
r
_30..
=Et ^^
The scale of plotting is 25 m = 1 cm
The displacemenr of point on paper
rhen
or
*"
-
;g+
"^
= 0.025
l=13.259m.
Hence, the maximum length of offset should be 13.25g
m.
r.,
]ff"iTj:"tiT:'J: g3s",[J:,"j,"jl,Ti:1f:i:"""J::,"Lil
which the offset shourd be measured so that the
maximum displacement of point on
paper from both the sources of error be the
same.
Solution
or
Of
I
I
sin
a=!
sin 5" = llr
r=COSSCS"
=
11.47
Hence, the offset must be measured with an accuracy
of about
r in
rr.47 m.
Hoizontal Measurement 59
r
;::t,r.
2.76
The chain survey work is recorded in a book known as field book. It is of
200 mm x 120 mm size. The pages of the field book can have either a red line
or two blue lines 12.5 - 15 mm apart ruled down the middle of each page. The
field work is commenced at the bottom of the page and worked upwards as shown
in Fig. 2.31. Following details are recorded in the field book on the commencement of a chain line.
Fig.2.31
1. Name or number of the chain line.
2. Name or number of the station.
3. The symbol denoting the station mark.
4. The direction of other survey lines at the stations.
5. The initial chainage (generally zero) enclosed in the symbol.
?/aA
To facilitate reference, no line is commenced on the same page that contains
a finish of
another Iine.
Booking the Data
In recording measurements as they are being taken in the field, the notekeeper
should ensure that every measurement that should be recorded is taken
and
that every measurement taken is recorded. Every linear measurement should
be
recorded in such a way that the last digit will indicate the degree
of precision
with which the measurement was made. The following points shiuld be observed
while booking the data.
N
Surveying
1. Chainage is written in the central colurnn.
2. chaiuage of the stations may be enclosed in a circle or ellipse.
3. Objects are sketched along the sides of the chain line.
4. Offsets are written close to the object.
5. Chainage of corners of the object are also eiltered.
6. when features like road, fence, lake, etc. cross the chain line, the chainage
of intersection is entered and the direction of the feature is sketched.
7. oblique offsets are written along with dimension line in the direction of
the offset.
2.17
The measurement of distances consists of chaining and making offsets. During
measurements, it is practically impossible to set out all the chain
lines in a
straightforward method because of a variety of obstructions to chaini'g
and
ranging in the field. The difficulties can be overcome by running perpendicular
and parallel lines or by running a few additional lines and measiring
angles by
some instrument. The scope of the chapter limits the solution of
the problems
involving only the essential equipments used in chain surveying. To find
the best
and rapid solution, the surveyor should have a good knowledge- of geometric
and
trigonometric principles.
The obstacies may be <tivided into trvo classes. Those which do not
obstruct
the ranging (view) like ponds, river:s and falr in the category of obstacres
to tneasurement. The others are those which we cannot see across, i.e. both
the chaining
and ranging are obstructed, e.g. houses, stacks, etc., and are known
as obstacle.t
to alignment only a few solutions have been discussed here and many more
can
be developed by the surveyor himself, depending upon the fielct conditions
and
method resorted to.
2.17.1
Obstacles to Measurement
First method (F;g. 2"32) Let ABCD be a chain line
obstructed by a pond. The problem consists in finding
out the distance BC. Two ofTsets BE a:nd CF of equal
length are made at B and C and chaining is done along
EF. The work is then continued from point C.
Seconrl method (Fig"
Z.SS) Let DAB be a chain
line obstructed by a river. Lay
offAC of any convenient
length, perpendicular to the requirecl distance,4g and lay
off DC perpendicular to BC. Then, AB = ,qdUO.
Third method (Fig. Z.S4) Let AB be a chain line
obstrucred by a river. Assume a point 1 anywhere in line
with the required distance AB. Take a point Il in such a
way that HJ = HI and HK = I1B. Establish t in the iine
AH and at the same time in the line JI( produced. Then
Di
cr-----i
i:'-....-l-\--_\\
l
rF
I
-
;
\\.\\\
\)11lt
/
.,t/,4/
;Z)t/t/
:1
Bl -----.-)E
I
AI
Fig.2.32
KL = AB.
I
t
I
i
I
Hoizontal Measurement
Fis. 2.33
2.17.2
6l
Fig. 2.34
Otrstacles to Nignment
Let DE be a chain line obstructed by a
house.
First mcthod (Fig. z.ss) Assume a point c arbitrarily.
Make EC =
DC = CA. Then AB = DE.
cB
and.
second, method, (Fig. 2.s6) Estabrish a point F
at equal distances from D and
E at any convenient distance. Make F/1 rG. Th"n D:E (HG
=
x DF)/HF.
=
,
/fih'
il'lllV
v/ *,-
t..,
\,
E
H'r---7'G
,'
\
)'(0
AF
Fig.2..35
,/
\,,
,\/
"/
Fig.2.ts6
A chain line ABC crosses a river at 90. as shown in
Fig.2.S7.
B an!_C are two points located at the near anO tar
Oants,
respectively. AB = 57.79 m, BD
=100 m and LABD 90". The *11olu
magnetic
bearing (w.c.B.) of c and A taken al D are 30" and =
120., respectir"rv. "ii"r"
rino the width
of the river.
ExawpLe
- Z..tS
,
Solution
V/.C.B. of C at
D = 30o
WC.B. of AatD=!2Oo
ZADC=120-30o=90"
62
SurueYing
Fig.2'37
Consider triangles BCD arrd BDA
ZCBD=ZABD=90"
IBCD = ZBDA, arrd Z-BDC = IBAD
triangles'
Hence, triangles BCD and BDA ate similar
BC _BD
ED_AN
or
=%- =W
BC
Hence, width of river
Frunpl,e 2.74 .,
ing the obstacle. Th"
=
=
ti3.22 m
173'22 m'
in Fig' 2'38'
A big pond obstructs the chain line ab as shown circumvent,"""rred on the lett of the line ab for
; il; li*u,
am. was measured on
b;;il';i'i *ut sor .m' Similarly' them'lineb and
/ are in the same
1'100 m' Points
the right of the line uO *"not" length was
are 502 m and 548 m, respectively. Find
bm
oland
ri"r"
straight line. Lengths
"r'in"
the distance ab.
Solution Consider tr\angle alm
Let
5O2m b
548m
llma = a
(am)z+(lm)2-@lt
cos d=
Z(am)(lm)
'(1100)2 + (1050)2
=ffi
-
(901;2
= 0.6497
Fig.2.3B
In triangle abm
(ab)z
or
=
(bm)z + (a*)2
-
2 (am) (bm) cos a
x 548 x 0'6497
= (548)2 + (1100)2 - 2 x 1100
ab = 852-b6 m-
i..$,|#r,,
1t:t::l tiejef
Horizontal Measurement 63
cros3ing. a
lver at risht
ansres cur
ts
banks
;1;ffiffi;;ffiJ'":"fl*:i"1"
following operation was *:yr'i
l'n i t, i" ##Yff # ;tif?[
carried out.
A 60 m long line BE was
paraltel ro the river.
Line CE was extended
D and mid-noinr F nr
p:=Tp
^"::::T::ghty rffi;.li,i,ji,T;,!lj.;i"-a'""ff,,i""1
FG EF. Line
lTll-T*i^,:"":_r^r-:L_"$ll;d"I
DG
was
extenoeJt"
.=
.riii"
vey line ABC at H. GH and HB
"r"
were;";;;;
and found to be 40 m and g0
Find the width of the river.
,, ,""p;;;;il"
Solution
Given
BE =gQ m, BH = 80 m and
HG =40 m
GD=39=60m
HD=HG+GD
=40+60=100m
'
Consider similar triangles CHD
and CBE
CBICH =BE|HD
or CBI(CB + BII) = BE\(HG + GD)
i.e. CBI(CB + 80) = 6Ot(40 + 60) _
0.6
CB =0.6 (CB + 80)
CB (l - 0.6) = g6 1 6.6
CB=39x0.6/0.4
=4910.4
=
Fig.2.39
120 m
obstacre, a 200 m rons
_6- ;ll""HT;_"":iTll'::1:,r:l an
;
"::, :i#1"" ::',::i l^?* :il;i ^ t, "i'J',I"#; il::!
f, ?"?;:if,,e":y*"11";:f1^u^olg,:'li:,i"""'J"1iil:tri?"f,?""?f
"
ff
jff ff the obstiucted
X;:'ffi
Also
determine
:1""?:,"?;,^*^",Fi;#;ffi#;;,#.'j:lllffi
length.
Solution Refer to Fig. 2.40.
"'ffi 'f,Tfl
.lI1,?,;L'$:.L:,I
iff
From ABCD,
CD =
gg
sec 60"
x sec 60"
=400m
= 200
From A,BCE, CE BC sec 45o
=
= 200 x sec 45o
and
Fig.2.40
= 292.94 m
BC = BC tan
200
x
45o
tan 45.
= 200 m.
lir][fi;rri;l;:n s:
fifuh[lf{ffi!:::
CE,
set our i{
at ifii!
angleJ irr io;
;;
are
""JiirJ;,i,
64
Suruaying
respectively. Determine the lengrths cD and cE so
that.o and E may be on
- the prolon_
gation of A8. lf the chainage ot a is 1OO
m; find the chainage ot O.
Solution
From ABCD (Fig.2.4l)
cD =*3€06
=#s.
= 173.205 m
From ABCE
ce=#" =#0. = 195'81 m
BP=lCDz-BC|z
= [(t73.20r2 _ $50)2)yz
=86.602 m
Chainage of D=chainage of B+BD
= 100 + 86.602
= 186.602 m.
i:t;
:ai,.:.1:i:::'*;1::,rr...ii:.Tiii:rl,r!t.Irfi!i.i
ii:'dl!*
Fig.2.47
A- river is flowing from west to east. For determining
rha:n,^.
&.r^ -^:-rOf
^, the fiVef, tWO pgints
A and B afe SeleCted
100 m. eginr
::ll.:1"1j:l_0p11?."9.18:
{is
on the northern bank are observed to
fhe width
On the S'Uthefn
west wards.
rhe bearinss ar a tree c
be 40. ano sao",-iesp";tir"ry
Calculate the width of the river.
;i;," A
Solution In A,ABC (Fig.2.a2)
ICAB=90o-40o=50o
ICBA = 340'- 270" =70o
ZACB = tB}"
-
(ICAB + Z.CBA)
= l80o _ (50. + 70.)
By sine rule
-
60.
#fu=#=#fu
AC
='l4ii!Jq:
srn 60" =
and
BC =
loo x
0.e396
0.966
44ii4,iq - 76.60
srn 60" 0.966
= 88.455 m
Width of the river = AC sin 50o
=
108.50 sin 50o
= 83.116 m
width of the river = BC sin 70o
= 88.455 x sin
= 83.116 m.
Width of the river = 83.116 m.
F---loom___+j
Fis.2.42
108.50 m
70o
and B.
Hotizantal filtaeurement
6
2.1 Explain how a chain is tested and adjusted in the field.
2.2 Bnefly describe the process of chaining.
2.3 Describe the various methods of chaining on a slope along with their
advantages and disadvantages.
2.4 Describe the following with sketches:
(i) Line ranger (ii) Optical square
(iii) Prism square(iv) Clinometer
2.5 Differentiate betwean the following terms:
(i) Base line and check line
(ii) Main station and tie station
(iii)
Chainage and offset
(iv) Cumulative and compensating
errors
2.6 Explain the following terms: normal tension, hypotenusal allowance,
cumulative error, and ranging.
Explain the various sources and nature of errors in chain survey.
2.8 Describe the various tape corrections with sketches.
2.9 The area of a plan of an old map plotted to a scale of 10 m to 1 cm measures 100.2 cm2 as measured by a planimeter. The plan is found to have
shrunk so that line originally l0 cm long now measures 9i cm. Further,
the 20 m chain used was 8 em too short. Find the true area of survey.
2i
fAn*
105.6438 acresl
2.10 An area actually measures 0.8094 hectares. How much will it measure
in m2 by a 30.48 m chain which was 20.32 cm too short at the start and
60.96 cm too long at the end of the survey?
lAns.7987.L5 mzl
2.ll The area of a piece of a land which had been surveyed with a chain
was calculated to be 9562 m2. Of this, 8935 m2 was the total area of the
triangles and 627 m2 was the area included between chain lines and the
boundary. The 30 m chain used was found 0.05 m too long, and the 30
m tape used for measuring offsets was found 0.03 m too short from their
nominal lengths. Calculate the correct area of the land.
[Ans. 9590.5 m2]
2.12 A line was measured with a 30 m long steel tape, standardized at 15oC,
with a pull of 100 N. Find the correction per tape length, if the temperature
at the time of measurement was 20'C and the pull exerted was 160 N.
Weight of I cm3 of steel
= 0.0786 N
Weight of tape
213
=8N
Modulus of elasticity
= 2.lO x 105 N/mm2
Coefficient of expansion of tape/oC = 7.1 x l}a
[Ans. 0.49 mm]
The distance between two points P and Q measured along a slope is
250 m. Find the horizontal distance between P and Q, if
(a) the angle of slope is 10",
(b) the slope is I in 4.5, and
66
Surueying
(c) the difference in elevation is 35 m.
fAns. 246.20 m.244.04 m.247.53 m]
2.14 Calculate up to five decimar praces, the sag correction for a r00
m tape
weighing 13.0 N. It is used under a pul of 90 N and in four equal
spans
of 25 m each.
[Azs. 0.00543i m]
2.15 To what precision would you measure the offsets, if the plan of the
survey
is to be plorted to a scale of (i) 1 cm = 1m and (ii) 1 cm 10 m.
=
/
[Ans.2.5 cm, 25 cm]
'
rzed under no pull at
15'c. The tape has cross-sectional area of 3.75 mm2.
one-half of the line is measured at temperature of 20oC and the other
half at 26oC and the tape is stretched with apul of 22kg,find the corrected total length, given that the coefficient of expansion is tz x 10{ per
oC
weight of 1 cm3 of steel = 7.7504 g and E 2.ll x t06 tgl"-r. '
If
=
[Ans. 2000.384 m]
2.17 a-steeltape is 30 m rong between the end graduations at a temperature of
15"c when it is laid horizontally on the ground. Its sectional area equals
0.065 cm2, total weighr is 15.g N and the coefficient of expansion
being
11.5 x 10-6 per oC. The tape is stretched on two supports
30 m apart
and is also supported in the middle, the three supports being at
the same
level. calculate the actual length between tt e ena graduatiJns under
the
following conditions: temperature = 25"C, pulr on tL" tup" 100 N,
and
=
E = 2.It x 105 N/mm2.
fAns. 29.991 m]
2.18 A base line measured with a steel tape gives an approximate length
of
1000 m. Compute the correct length of the base line at mean
sea lever
when the pull at the standardization equals 15 kg.,The applied pull
is
23 kg.^The cross-sectionar area of tape is 0.0645 cm2 and z 2.ri x
106
=
kg/cm2. Temperatures e and To aie 35.C and 15.C, respectively.
The
difference in level of the two ends of base line is 2 m. Radius of
earth, R
= 6400 km. Elevation of base line above mean sea level = 1000 m.
2.t9
, uiSr'#if
:l::#
Thethree bays of a base line were measured o,
as 30.084, 29-973 and 25.233 m, under respective pults of z7 and
5 kg,
temperatures of 12, 13o and 17'C and differences of level of supports
of
0.3' 0.7 and 0.7 m. If the tape was standardized on the flat at a temperature
of l5'c under a pull of 4.5 kg, what are the lengths of the bays? 30 m of
tape is exactly 1 kg with steel at g300 kg/m2. The coefficient of expansion
is 0.000011 per oc and the modulus of elasticity E=2.L x rOs i.i/mm2.
[Ans. 30.057 m, 29.94O m and 25.194 m)
2.20 A steel tape was exactly 30 m long at 1g"c when supported throughout
it,s
length under a pull of 8 kg. A line was measured with a tape
under a pull
of 12 kg and found to be 1602 m. The mean temperature o*ing measurement was 26'C. Assuming the tape was supported at every 30 m,
carcurate
of
the line, given cross-sectional
oi
the
tape
.l:ngtr= 0.04
cm'. weight of 1 cubic cm is 0-0077 kg, coefficient of thermar expansion,
{z = 0.000012 C, E = 2.1 x Lff
fAns. t6OZ.22 ml
*"rT:
*u
kglcmz.
Hoizontal Measurement 67
2.21 A line measured with a steer tape which was exactry 30 m
at a temperature of 20'c and a pull of 10 kg. The measured length was
1650 m.
The
temperature during measurement was 30oc and a pull applied
was 15 kg.
Find the true length of the line, if the cross sectional area of the
tape was
0.025 cmz. The coefficient of thermal expansion of the material
of the
tape per "c is 3.5 x 106 and the modulus of elasticity of the
material of
tape is 2.1 x 106 kglcm2.
[Ans. 27.776g m)
2'22 A steel tape of 30 m nominal length was suspended between two
supports to measure the rength of a line. The measured length
on a slope bf
4o 25' is 29.8605 m. The mean temperature during the ireasurement
was
15oc and the pull applied was r20 N. If the standard rength
of the rape
is 30.008 m at 27"c at the standard pull of 50 N, calcuhG the
corrected
horizontal length- Take the weight of tape 0.16 N/m" it's cross
=
sectional
area = 2.75 mm2, coefficient o1tfr".rrrut expansion
1.2
x
10-;;;;;;
=
and E = Z.O5 x 106 N/mm2.
[Ans. 29.]7002 ml
2.23 The slope distance between two stations A and B of elevations 1572.25
m
and 4260.46 m, corrected for meteororogical conditions is 33449.215
m.
Determine sea level distance, R = 6370 km.
fAns. 33332.7g9 m)
2.1 In chain surveying, field work is limited to
(a) linear measurements only
(b) angular measurements only
(c) both linear and angular measurements
(d) none of the above
2.2 The accuracy of measurement in chain surveying,
(a) length of the offset
(b) scale of the plotting
(c) importance of the features
(d) general layout of the chain lines
2.3 Chain survey
2.4
,<
2.6
does not depend upon
is well adopted for
(a) small surveys in open ground
(b) small surveys with ups and downs
(c) large area with simple details
(d) large area with crowded details
In a metric chain, number of links per metre can be
(a) 2
(b) s
(c) 8
(d)
Cross-staff is used for
(a) setting out right angles
(c) both (a) and (b)
10
(b) measuring horizontal angles
(d) measuring the bearing oi lin",
In chain surveying, perpendiculars to the chain line are set oui
ty
(a) a theodolite
@) a prismatic compass
(c) a clinometer
(d) an optical ,qru."
68
Surueying
2.7 Ranging is defined
as
(a) measuring the distance f,rom
starting point
(b) establishing intermediate points
on a chain line
(c) the distance between end points
(d) a point on chain line
2.8 Chainage in chain survey means
(a) the distance between end
stations
(b) the perpendicular distance of
the object from
(c) the distance of the object along
the chain rine
the chain line from the zero end
of
the chain
(d) any disrance measured by chain
in field
2.9 Main stations in chain survey are
the points
(a) lying in the area enclosed
by survey lines
(b) connected by main sorrey lines
(c) on main survey lines to cover
the rocal details
(d) on main survey lines to check
the accuracy of the survey work
2.10 Oblique offsets are used to
(a) locate broken boundaries
(b) locate boundary lines of property
(c) check the accuracy of tne plottea
work in chain survey
(d) plot the chainage
2'll which of the following methods results
horizontal distance on rough grounds:
(a)
(c)
chaining
in higher accuracy for measuring
@) raping
tacheometr
z'rz wn**""rr.rlrorizonrar am*""(1],i,io:[]nt,
h,ls, it is berter
measure the distance
by
to
(a) stepping down slope
(c) both of the-above
@) stepping up slope
(dj suspending tape in air
2.13 The maximum tolerances in
aZOrn
30 m chain are
(a) t2 mm tg *"ra
(b)
t:
mm +5 mm
(c) t5 .n- *,
(d) t8 mm +5 mm
pickrp
2il
rh";";;;Tatementls).
(i) A metric chain is 30 m long
(ii) A metric chain is 20 m lon!
(a) (i) is correct
(b) Gi) is correct
(c) both (i) and (ii) are corecr
uotr, are wrong
2'15 Prolongation of a chain rine across iaj
anobstruction in cha-in survey is done
(a) making angular observations
(b) drawing perpendiculars with
a chain
(c) solution of triangle
(d) ail of the above
(e) onty (a) and (b)
Hotizontal Measuremenf 69
2.16 while measuring a line between two stations A and B intervened by
raised ground,
(a) the vision gets obstructed
(b) the chaining gets obsrructed
(c) vision and chaining both get obstructed
(d) none of the above
a
2.17 A well-conditioned triangle should not have angles more than
(a) 30'
2.18 Offsets are
(b)
120.
(c) 45'
(d) 60"
(a) short measurements from the chain line
(b) ties or check lines which are perpendicular to the chain line
(c) chain lines which go out of alignment
(d) both (a) and (b)
2.19 The correction to be applied to each 30 m chain length along slope is
,/
Yo
(a) 30 (1 (c) 30 (1 -
sec
cos
a) m
a) m
(b) 30 (sec a- 1) m
(d) 30 (cos a _ l) m
A-tape of length / and weight w N/m is suspended at its end with a pull
of P newtons. The required sag correction is
1a) twztzupz 1a1 Pw3tz+r, @) p*ztz4pz
2.21 Compensating or accidental errors are proportional to
(d) lw2t24p
(u) L,,,
(b) L1t3
(d) uL
@) L
2.22 Check lines (proof lines) in chain surveying are essentially required
(a) to plot the chain line
(b) to plot the offsets
(c) to indicate the correctness of the survey work
(d) to increase the efficiency of the surveyor
2.23 Perpendicularity of an offset may be judged by eye if the length of
the
offset is less than
(a)5m
(b)10m
(c)15m
(d)20m
2.24 which of the following instruments is generally used for base line
measurement?
(a) Chain
(c) Steel tape
@) Metallic tape
(d) Invar tape
2.25 Invar tape is made of an alloy of
(a) copper and steel
(b) brass and nickel
(c) brass and steel
(d) steel and nickel
2.26 The length of a chain is measured from the
(a) centre of one handle to the centre of other handle
(b) outside of one handle to the outside of other handle
(c) outside of one handle to the inside of other handle
(d) inside of one handle to the inside of other handle
2.27 The angle of intersection of the two plain mirrors of the optical
is
(a) 30'
(b) 45.
(c) 60'
(d) 90'
square
7O
Surueying
2.28 which of the folrowing angres can be set out
with the help of French
cross-staff?
2.29
lt
(a) 45. only
(c) borh of the above
by
@) 90. only
(d) any angle
the length of a chain is found to be short on testing,
it can be adjusted
(a) straightening the links
(b) rgmoving one or more small circurar rings and by
placing bigger
rlngs
(c) closing the joints of the rings, if opened
(d) all of the above
2.30 lt the length of a chain is found to be too long
on testing, it can
adjusted by
(a) closing the opened joints of rings
(b) reshaping elongated links
(c) removing one or more circular rings
(d) replacing the worn out rings
(e) all of the above
2.31 The position of a point can be fixed accurately
by
(a) cross-staff
@) optical square
(c) clinometer
(d) perpendicular
be
offset
2.32 Figure 2.43 shows one of the brass tallies of a 30
m chain. The
distance of this tally from the nearest end of the
chain is
(a) 5m
(b) 10 m
(c) 15 m
(d) 20 m
2'33 which of the following is an obstacle to chaining but
not to
r^\
)"/
1)
ranging?
(a)
(c)
River
Building
@) Hiilock
2.34 A building is an obstacle to
Fig. 2.43
(d) None of the above
(a) chaining but not to ranging
(b) ranging but not ro chaining
(c) both chaining and ranging
(d) neither chaining nor ranging
2.35 which of the forowing is not used in measuring perpendicular
offsets?
(a) Line ranger
(b) Tape
(c) Optical square
(d) Cross-staff
2.36 During chaining arong a straight rine with a 20 mchain,
the leader of the
party has 4 arrows in his hand while the foilower
has 6. Distance of the
follower from the starting point is
(a) 4 chains (b) 6 chains (c) g chains (d)
lZ chains
2'37 The main difference between an optical square and
a prism square is
(a) the difference in the principle of working
(b) that an optical
square is more accurate than a prism square
Hoizontal Measurement 71
(c) that no adjustment is required in a prism square since the
angle
between the reflecting surfaces cannot be changed
(d) all of the above
2.38 The allowable length of an offset depends upon the
(a) degree of accuracy required
(b) method of setting out the perpendicular
(c) scale of plotting
(d) all of the above
and nature of ground
2.39 Normal tension is that pull which
(a) is used at the time of standardizing the tape
(b)
(c)
(d)
neutralizes the effect due to sag
makes the correction due to sag equal to zero
makes the correction due to pull equal to zero
2.40 The correction for sag is
(a) always additive
(b) always subtractive
(c) always zero
(d) sometimes additive
and sometimes subtractive
2.41 The permissible error in chaining for measurement with
a chain on rough
or hilly ground is
(a) 1 in 100
(b) 1 in 250
(c) I in 500
(d)
1
htzL
(O
zh2lL
2.42 Corrcction for slope is given by
61
nznr
g) htL
(c)
in
1000
2.43 The required slope correction for a length of 30 m, along a gradicnt of
1
in 20 is
(a) 3.75 cm
(b) 0.375 cm (c) 27.5 cm
(d) 2.75 cm
2.44 lf the length of a chain line along a slope of a is l, the required slope
correction is
(a) 2l
cot2
a/2 (b) 2l sinz al2 (c) I tanz al2 (d) I
2.45 Match the following
(I) Correction for standard length
cosz atT
(A) C" = LCll
(II)
Correction for
(IV)
(V)
Sag correction
=' ;{o t
(C) C, = u (T^ - T)L
@) q" = \f tl24 Pz
Reduction to m.s.l.
(E)Cn=LhlR
(VI)
Normal tension
trtr=:
tension
(III) Correction for temperature
where
(B)
Cp
.L =measured length,
O.2O4w,lAE
{P-Po
C = correction applied, and
/ = nominal length of tape
(a)
(b)
I-A, II-B, III-C, IV-D, V-E,
I-C, II_D, IIT_B, IV_A. V_F,
VI-F
VT_E
72
Surueying
(c) I-B, II-A, III-F,
(d) none of the above
IV-C, V-E, VI-D
2.46 For setting out an offset at an angle of 45' with a chain line, the instrument used is
(a) an optical square
(b) an open cross-staff
(c) a French cross-staff
(d) a prism square
2.47 A pair of slots at right angles to each other are provided in
(a) cross-staff (b) arrow
(c) ranging rod (d) offset rod
2.48 The limiting length of an offset does not depend upon
(a) accuracy of the work
(b) method of setting out perpendicular
(c) scale of plotring
(d) the number of features to be surveyed
2.49 Pick up the correct statement.
(a) The cost of making a horizontal measurement decreases with an
increase in the desired precision.
(b) A base line may be measured with a precision of 1 in 106
(c) Tie stations are generally located on the intersection of two main
survey lines
(d) Base line is a line lying at the base of the
area to be surveyed by
a chain
2.50 Pick up the correct statement(s).
(i) offset is the distance from the foot of an object to the chain line
(ii) Perpendicular offsets may have infinite length
(a) only (i) is correct
(b) only (ii) is correct
(c) both (i) and (ii) are correct (d) none of the above is correct
2.51 Pick up the correct statement.
(a) A revenue chain is 66 ft long.
(b) Gunter devised the invar tape.
(c) A tally is used to facilitate observation in an optical square.
(d) A brass ring is provided at every metre length in a metric chain.
2.52 While testing a chain, a tension of 80 N is applied at the ends of
(a) 20 m chain
(b) 30 m chain
(c) both (a) and
(b)
a
(d) Gunter,s chain
2.53 Pick up the correct statement.
(a) Invar is an alloy of sreel (36Vo) and fickel
(64Vo)
(b) A steel tape is soft and easily deforms as compared to invar tape.
(c) Metallic tape is made by weaving linen with brass wires.
(d) Steel tapes can be used comfortably in grounds with weeds and
vegetation.
2.54 Pick up the correct statement.
(a) A ranging rod is provided with a stout open ring recessed hook.
(b) An offset cannot be laid with a French cross-staff.
Horizontal Measurement 73
(c) Optical square and cross-staff are used for the same purpose.
(d) clinometer is used to measure the directions of survey lines in chain
survey.
2.55 Pick up the correct statement(s).
' (i) In the process of chaining, the leader inserts the arrows and the
follower picks them up.
(ii) A leader follows
the instructions of the follower.
a) only (i) is correct.
(b) only (ii) is correct.
(c) both (i) and (ii) are correct. (d) none of the above is correct.
Pick up the incorrect statement.
(a) It is easy to measure distance down the slopes.
(b) Incorrect plumbing, while measuring distances on slopes, is a cumulative error-
(c) Sag correction is a cumulative error.
(d) Incorrect holding of chain at arrow is a compensating
error.
2.57 Pick up the correct statement.
(a) Sag correction may be positive or negative.
(b) The limiting length of an offset is independent of the scale of
plotting.
(c) Error due to laying of the direction of offset is negligible.
(d) The slope correction is always subtractive.
2.58 Pick up the correct statement(s).
(i) The length of the offsets in a chain survey is always limited to
reduce error in plotted work.
(ii) Perpendicular offsets are used for filling in details.
(a) only (i) is correct.
(b) only (ii) is correct.
(c) both (i) and (ii) are correct. (d) none of the above is correcr.
2.59 Pick up the correct statement(s).
(i) Optical square is better than a prism square.
(ii) In both the optical and prism
squares, the principle
of operation is
same.
(a) only (i) is correct.
(b) only (ii) is correct.
(c) both (i) and (ii) are correct. (d) none of the above is correct.
2.60 which of the following is the most precise instrument for measuring
horizontal distances.
(a) Chain
(b)
Tape
(c) Tacheometer (d) Tellurometer
2.61 Two mirrors are used for offsetting in
(a) cross-staff
(c) miner's dial
(b) optical square
(d) prismitic compass
2.62 What is the angle between two plane mirrors of an optical
(a) 30"
(b)
60'
(c)
45"
2.63 The object of chain and cross-staff survey is to
1. locate the boundaries of an area.
2. plot the figure to a scale.
square?
(d) 90.
74
Surueying
3. find the area of the plot.
4. find the reduced levels of the
plot.
Which of the above statements is/are correct?
(d) 4 alone
(a) 1,2,3 and4 (b) 1,2, and 3 (c) 1 and 2
2.64 Which of the following instruments have both horizon glass and index
glass?
2. Line ranger
4. Pedometer
1. Optical square
3. Box sextant
Select the correct answer using the codes given below:
(a) 2,3, and 4 (b) 1, 3, and 4 (c) 1 and 3 only (d) 2 and 4 only
2.65 What is the slope correction for a length of 30.0 m along a gradient of
1
in 2O?
(d) 0.0375 cm
(c) 0.375 cm (c) 37.5 m
(a) 3.75 cm
2.66 A 30 m metric chain is found to be 10 cm too short throughout a measurement.
If
the distance measured is recorded as 300 m, what is the actual
distance?
(d) 310.0 m
(c) 299.0 m
(b) 301.0 m
(a) 300.1 m
2.67 A 20 m chain was found to be 10 cm too long after chaining a distance
' of 2000 m. If was found to be 18 cm too long at the end of the day's
work after chaining a total distance of 4000 m. What is the true distance
if the chain was correct before the commencement of the day's work?
(d) 4038 m
(C) 3981 m
(b) 4019 m
(a) 3962 m
to Objectiae-type Questions
2.3 (a)
2.2 (d)
2.t (a)
2.9 (b)
2.7 (b)
2.8 (c)
z.ts (d)
2.r3 (c)
2.14 (c)
Answers
(c)
2.2s (d)
2.31 (d)
2.37 (c)
2.43 (a)
249 (b)
2.55 (c)
2.61 (b)
2.19
2.67 (b)
2.20
2.26
2.32
2.38
2.44
2.50
2.s6
2.62
(a)
(b)
(a)
(d)
(b)
(a)
(b)
(c)
(a)
2.27 (b)
2.33 (a)
2.39 (b)
2.45 (a)
2.51 (d)
2.s7 (d)
2.63 (b)
2.21
2.4 (b)
2.10 (b)
2.t6 (a)
2.22 (c)
2.28 (c)
2.34 (c)
2.40 (b)
2.46 {c)
2.52 (c)
2.58 (c)
2.64 (a)
(a)
Z.rt (c)
2.t7 (b)
2.23 (c)
2.29 (a)
2.35 (a)
2.4t (b)
2.47 (d)
2.53 (c)
2.s9 (b)
2.6s (d)
2.5
2.6 (d)
2.t2
(a)
2.18 (d)
2.24 (d)
2.30 (e)
2.36 (b)
2.42 (a)
2.48 (d)
2.54 (c)
2.60 (d)
2.66 (c)