Surveying

586 Pages·1987·27.856 MB·English

by  Venancio I. Besavilla, Jr.

an Surveying, Higher Surveying, Mine Surveying, Hydrographic
urv ylng, Topographic Surveying, Astronomy, Simple Curves, Compound Curves,
plral Curves, Reversed Curves, Parabolic Curves, Sight Distance, Earthworks,
ass Diagram, Highway Engineering, Transportation Engineering, Traffic Engineering.
for CIVIL and DETI~
.>
LieeQSure Exam
Copyn~;t1987
Venancio I. Besavilla, Jr.
(BSCE,MSME, AS,F.(PICE)
CivilEngineer -CIT(2nd Place) -August, 1969
. GeodeticEngineer-CIT(7th Place) -July, 1966
FormerInstructor: Cebu InstituteofTechnology
FormerInstructor: Universityofthe Visayas
FormerChairman: CE Dept. UniversityoftheVisayas
Dean: CollegeofEngineering andArchitecture, Universityofthe Visayas
Awardee: AsanOutstanding Educatorfrom thePhil.
Veterans LegiononMay 1984
Awardee: AsOutstandingAlumnusinthe FieldofEducation
from CITAlumniAssociation, Inc., Marcil 1990
Awardee: AsOutstanding Engineering Educatorfrom the
CITHigh SchoolAlumniAssociation, December1991
Member: Geo-InstituteoftheAmericanSocietyofCivilEngineers(ASCE)
Member: StructuralEngineeringInstitute(ASCE)
Member: AmericanConcrete Institute(ACI)
(MembershipNo. 104553)
Member: AmericanSocietyofCivilEngineers(ASCE)
(MembershipNo. 346960)
Member: PICEDelegationtotheASCE(Minneapolis, Minnesota, USA) (Oct. 1997)
HeadPICEDelegationto VFCEA, Hanoi, Vietnam (April2009)
HeadPICEDelegationtoJSCE, FokukaJapan (September2009)
HeadPICEDelegationtoASCE.~ KansasCity, USA(October2009)
Director: PICENationalBoard(1997-2008)
Director: PICECebu Chapter1991-2008
~lcePresident: PICECebu Chapter2006, 2008
President: PICECebu Chapter2009
VicePresident: PICENationalBoard2009
President: PICENationalBoard2009
Chairman InternationalCommittee(PICE)Busan,Korea (February2010)
President: CebuInstituteofTechnologyAlumniAssociation(20OJ-uptothepresent)
ISBN971-8510-11-7
Availableat:
BISAVlllA
Engineering ReviewCenter
CEBU DAVAO CAGAYANDEORO MANILA
2ndFloor,Pilar-Bldg. 4thFloor, 3rdFloor, 2ndFloor,Concepcion
Cor.OsmenaBlvd. PorrasBldg. EcologyBankBldg. VillaromanBldg.,P.Campa
&SanciangkoSts. MagallanesSt., TianoBros.St. St.,SampalocMelroManila
CebuCity DavaoCity CagayanDeoroCity Tel.[phone]
Tel.No.[phone] Tel.No.[phone] Tel.[phone](Samsung)
BAGUIO TACLOBAN GENERALSANTOS
LujeanChaletBldg. Door11.-303,F.Mendoza RD.RiveraBldg.
LourdesGrotto CommercialComplex ConstarLodge,PioneerAve.
DominicanRoad 141 Sto.NinoStreet GeneralSantosCity
No.68SanRoqueSI.BaguioCity TaclobanCity Tel.No.[phone]
Tel.Nos.[phone] Tel.No.[phone]
SURVEYING
for
CIVIL and GEODETIC
Licensure Exam
Copyright1984byVenancioI.Besavilla,Jr. AllRights
Reserved. No part of this publication may be
reproduced,storedinaretrievalsystem,ortransmitted,
inany form or by any means, electronic, mechanical,
photocopying,recording,orotherwise,withouttheprior
writtenpermissionofthepublisher.
ISBN971·8510·11.7 •
~, ~;:,_;_~_,m.,
• ..
PuntaPrincesa,CebuCity. Tel.[phone]
"~ I~ I~~ ~ ~"I~I~XTS ~
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@ X~'''~~"''{i:'t'¥m"", 0%l'0fu~!;·*kW ~" ~W<fm_~""""it" 0« W::~ill.Th,. ~~"
DESCRIPTION OF TOPICS PAGE NO.
1. Tape Correction ------------------------------ S- 1 - S- 12
2. Errors and Mistakes -------------------------- S- 13 - S- 129
3. LeveIing------------------------.- -,--------------S- 30 - S- 54
4. Compass SUNeying ------------------------- S- 55 - S- 66
5. Errors in Transit Work -------------------------- S~ 67 - S- 83
6. Triangulation-----------------:------------------ S- 84 - S-108
7. Spherical Excess ------------~------------------ S-108 - S-111
8. Areq of Closed Traverse -----------------"- S-112 - S-130
9. Missing Data------------------------------------ S-130 - S-144
10. Subdivision -------------------------------------- S-144 - S-172
11. Straightening of Irregular Boundaries -- S-172 - S-175
12. Areas of Irregular Boundaries ------------ S-176 - S-178
13. Plane Table ------------------------------------- S-179 - S-182
14. Topographic SUNey ------------------------- S-183 - S-187
15. Route SUNeying ------------------------------- S-188
16. Stadia SUNeying ------------------------------ S-189 ,. S-194
17. Hydrographic SUNeying -----"-------------- S-195 - S-208
18. Three Point Problem ------------------------- S-209 - S-213 .
19. Mine SUNeying------------------------------.- S-214 - S-222
20. Practical Astronomy ------------------------- S-223 - S-251
21. Simple CUNes ---------------------------------- S-252 - S-292
22. Compound CUNes --------------------------. S-292 - S-318
23. Reversed CUNes - '--------.----------------- S-318 - S-333
24. Parabolic CUNes ----------------------------- S-333 ~ S-361
25. Sight Distance ---------------------------------- S-361 - S-376
26. Head Lamp Sight Distance ---------------- S-376 - S-386
27. Sight Distance --------------------------------- S-387 - S-388
28. Reversed Vertical Parabolic CUNe ---- S-389 - S-390
29. Spiral CuNe----"-------------------------------- S-391 - S-404
30. Earthworks--------------------------------------- S-405 - S-430
31. Transportation Engineering -------.-------- S-431 - S-523
32. Miscellaneous --------------------------------- S-524 - S-542
5-1
TAPECORRECTION
I-~~-~~----' --~~-
i
2. PullCorrection:
(TobeaddedorsUbtracted)
1. Tapenotstandardlength
2. Imperfectalinementoftape
3. Tapenothorizontal
4. Tapenotstretchstraight
P2=actualpulldUringmeasurement
5. Imperfectionofobservation
P1 =appliedpullwhenthelengthof
6. Variationsintemperature
7. Variationsintension tapeisL1
A=Cross-sectionalareaoftape
E=Modulusofelasticityoftape
I~~------------'-~-
3. SagCorrection:
I (Tobesubtractedonly)
1. Addingordroppingafulltapelength.
2. Adding aem., usuallyin measuringthe
fractional partoftapelengthattheend
oftheline.
3. Recording numbers incorrectly, w=weightoftapeinpit.orkg.m.
example78isreadas87. L=unsupportedlengthoftape
4. Readingwrongmetermark. p=actualpUllortensionapplied
4. Slope Correction:
(Tobesubtractedonly)
1. Temperature Correction: (To be
addedorsubtracted)
H=S-C
s
H=horizontaldistanceorcorrected
distance
S=inclineddistance
K=000000645ft.perdegreeF. h=differenceinelevationattheendof
K=0.0000116m.perdegreeC. thetape
=
T1 temp.whenthelengthoftapeisL1
T2=temp.dUringmeasurement
5-2
TAPECORRECTION
5. SeaLevelCOffection:
1.~
Reductionfactor=
1. The3:4:5Method:
To erectaperpendicular to the line
AB,fromagivenpointCapointaonline
B=horizontaldistanceGorrectedfor on
AB is assumed to be the
temperature,sagandpUll.
perpendicularandapinissetata. With
B'=sealeveldistance
sidesamultipleof3,4and5m.suchas
h=averagealtitudeorobservation
24.32 and 40 m., aright triangle abc is
R=Radius.ofcurvature
constructed as follows: Apin is set on
lineABatb,32m. froma. Thezeroend
6. Normal Tension:
of(he tape is fixed with apin at a, and
Itis the tension which isapplied to
the100m. endatb. Thezeroendofthe
a t.ape supported over two supports
tapeisfixed with apin ata,andthe 100
which balances the cofrec!ion due to
m. endatb. Thehead chainmanmoves
pullandduetosag. Theapplicationof
to cand holds the 24m. and the 60 m.
thetensileforceincreasesthelength of
marks ofthe tape in onehand,with the
thetapewhereasthesagdecreasesits
tapebetweenthesemarkslaidoutsoas
length, the normal tension neutralizes
toavoidkinking. Hethen setsapinatc.
bothcorrections, thereforenocorrection
Therearchairman movesfromatobas
isnecessary.
necessary to check the position of the
tapeatthesepoints as cisestablished.
He then sightsalong aeto C' beside C,
usuallyCtothea(::'ismeasu"red,andthe
footaoftheperpendicularaC'is moved
alongthelineABbyan equalamount, to
P=applied'normaltension
thepointa'. Ifthetrialperpendicularae'
P1 =tensionatwhichthetapeis
fails to include the point Cby several
standardized
feet, the process is repeated for a', the
W=totalweightoftape
new point, otherwise the location of a'
A=cross-sectionalareaoftape
maybeassumedascorrect.
E=modulusofelasticityoftape
2. The ChordBisectionMethod:
To erect aperpendicularto the line
AB;from agiven pointC, theposition of
theperpendicularisestir,lated, andapin
IS set at d on this estimated
a) Addcorrectionwhenmeasuringdistances perpendicular, somewhat less than one
b) Subtract correction when laying out tape lengthfrom the lineAB. With das
distances centerand the length oftape as radius,
the head chainman describethe arc ED
of a circle, setting pins at the
intersections band cof the arcwith the
lineAB. Therearchainman stationedat
A or Bdetermines the location of the
o
a) Subtract correction when measuring intersectionsbandconline. Thepointa
distances isestablishedmidwaybetween bandc.
b) Add correctionwhenlayingoutdistances
S-3
TAPECORRECTION
ThelineadisprolongedtoC'besidesC, 2. ParaJle/lines:
andthepointaismovedifnecessaryas
describedforthe3:4:5method. A'i..· ·· ~B'
crc'
: y! A0-'"---- 1----"""'8
i *f,
i i '~~~~,
A.---.o-o-~-...."B If the necessary distance from the
a'a b
lineASisshort, perpendicularAA'=BB'
3:4:5Method
areerectedbyeitherusing3:4:5method
ofthe chord bi-section method to clear
the obstacle. The line A'B' is then
chained,anditslengthistakenasthatof
AB.
ChordBisectionMethod 3. SimilarTriang/es:
C
~.<:~:>~~'"
•
A / ..
Let Cbe apointfrom Aand Bare
visible. AC and BCaremeasured. CD
1. Swingoffsets: and CE bears to CB: that is CD/CA =
CEICB. Itwillgenerallybeconvenientto
makethis asimple ratio such as 1/2of
1/3. The triangles ACB and DCE are
similar. DE is measured and AS is
computed.
At'/
Tofindthe distanceASbythesWing
offset method, the head chainman
attachedthe endofthetapetooneend .~i.tl'"iI
ofthelineasatBanddescribesan arc
with center S and radius 100 m. The
rearchainman stationedatAlinesinthe rll~anteTperature<()t~5·9·,.a@us$djl)l)f
endiofthetapewithsomedistantobject stan9a~l~ngth.1lt20·QunderaP4IIAf§~g,
as 0 and directs the setting of pins a1 Cr9$csezliQnClI"are<l.of,l~pe.,is •••Q.Q~~q;pm;,.
pointsaandbwheretheendofthetape CQefficfe!1t()ltheyrMex:e~n$iM>I~
crossed line AO. A point Cmidway Q.009011~WC,.M~dtllu$ ••ofela$tic~Y.(jf,tllP~ls,
between ablies on the perpendicular 2x1mkg1Crl12. ' , ",
CB. ApinissetatC,andthedistances
BCand CAaremeasuredtoobtain the G) [)eterllline.the•••errot•••of.the.,tapedu#.to
necessarydataforcomputingthelength
changeintempera1ure. ,. ' ",' '. '
ofAS,
® DetElfrninelheerrprduetotension, ••'.','
® Oetenninethecorreetedlengthoftheline.
8-4
TAPECORRECTION
Solution: @ Truelengthoftheline:
G) Temp. correction: Correctedhor.distance=673.92+0.1348
=
Ct KL(T-Ts) Correctedhor.distance=674.055m.
C,=0.0000116(2395.25}(35-20)
Ct=+0.4168m.
@ Tensioncorrection:
(P-Ps)L
Cp=---xE
c -
(4-5)(2395.25) .A·••$Q.·.rIl·••••m~EH•••[email protected] ••·and
p- 0.03(2)106 sj~ppporteq1:ttrougholJttts •••wbole•.•lergth.·.~nd
Cp=•0.0399m. ·1QlJJldJ9b{l;.Q.O()~Q5nl. ••long~r~t·an.•pb~ery~d
t~mp~rliIW~(ff~1.~·C~Qd~pulh~flON~~,
@ Correctedlength: Thl$taReW<1l.SlJ$edlomea~ure ••a••liqe••v.'hjCh
L=2395.25+0.4168-0.0399 Wfl$f~~'nd••f~b$.••66Z.702.%••at••an•••~v~mge
L=2395.6269m. ·~~Beralljr~•••8f••24·B·9.@ingJh~•••s~me·••pull,
Y$e.·C()~fflci$nt.pf.e~Bansion.·pf.0.()Ooo116·m·
pl:ifgegreeCE!ntigiage~< .
(j)..¢oIl1IM~lhesl!lnd?~.terilp·•••••••••··
~·••··G9IllP~~me.t()!al••telTlp>Wq'El(;tiOn-
® CQmPlJf~the.{icllTE!CflenglhJ:iflh~·IiI1~;·
[email protected]!l$f@hd.
l$bep:Q<l42m:IQO)?n~>tf1~nJhe$t<1ln~~rd
Solution:
.lE!gg1:tt~t~r:[email protected]£!rnP~r~fw~6fR~~Q·{:l[l9
••~~~t~~~~~iri~r~~~~~aW~~~e~td· CD Standardtemperature:
Cr=K(Tz-Ts)L
••19~~7~.~4.m···long.M.~n.(l~S7!Ye<J.·~~mp:.Of
.~~~[t·:~~~~~lIfs°6;~.~~~j~··idi~ji:~~I .•• +0.00205=0.0000116(31.8-Ts)(50)
o.f 31.8-Ts=3.53
qj\P~I~!QElme$!Md~Jem@@tt!rEf; . Ts=28.27'C (standardtemp.)
··~.··~~{~I~~m:I'~I'~ihe.lioe
..
@ Totalcorrection:
Solution: Cr=K(T2-Ts)L
G) Standardtemperature: Cr=0.0000116(24.6-28.27)(50)
Cr=K(TZ-T1)L1
Cr=;_0.00213 (tooshort)
+0.0042=0..0000116(58-T1}(50)
· 0.00213(662.702)
+0.0042=0.03364-0.00058 T1 7iataIcorrectIOn= 50
T1 =50.76'C(standardtemp.)
Totalcorrection=0.02823m.
@ Totalcorrection:
Cr=K(T-T1)L1 @ Correctedlengthofline:
Cr=0.00(J01Q(68'50.76)(50) Correctedhorizontaldistance
Cr=0.01 (tapeistoolong)
b.;;; G1J =662.702-0.02823
T,otalcorrect·Ion=673.9250(0.01) ~D =662.67377m.
"" G .--
Totalcorrection=0.1348m. \...0
::co,OI ;:r~,"1'2.\
~
\-:1,t.\&llvDb -)
I')\
8-5
TAPE CORRECTION
@ Tota/error:
Tooshortby=30-29.992
Tooshortby=0.008m
-472.90(0.008)
7iot'aJerror- 30
Totalerror=0.126m. (tobesubtraded)
@ Truehorizontaldistance:
Correctedinclineddistance
=472.90•0.126
=472.774m
. e
h
Solution: Sin =472.774
CD Actuallength: h=472.774(0.03)
Cr=K(T2-T1)L1 h=14.183m
Cr=0.0000116(5·20)(30.005) . for (14.183f
Cr=·0.00522mm Correction slope=2(472.774)
(P2·P1)L1 Correctionforslope=0.213m
Cp- AE
Correctedhorizontaldistance
C - (75·5OX3O.005) =472.774·0.213
p- 3(200x103) =472.561m.
Cp=tQ.00125m
w2L3
CS=24P2
0.65x9.81 \'
w=.30":' .
C «(0.65x9.8115(30)3
t
S- . (3O)t(24)(75
Cs=-0.00904m
Totalcorrection=·0.00522+0.00125
·0.00904
-Tata/Cf)ffection=-0.009G4-
Totalcorrection=·0.00522+0.00125 ,
-0.00904 .(!)... (;q~PIJtEl~.~¢@Illeng{h9f.tcl~ ••4IJling
Totalcorrection=·0.013m mAA~~rerrEl9t. ••'> ••••••i •••••••••••••••••••••••••••••••>•••••••••••>./.
® Wl'!litlsttletfuEl·atilll' .••.'••'..•..•••••..'".<•••< .....••.
Actuallengthoftapeduringmeasurement @. ·Whab$lh$¢~&ln~rea.ln$q.m.<········<·······
=30.005·0.013
·=29.992m.
S-6
TAPECORRECTION
Solution: Solution:
CD Actuallength: CD Cross-sectionalarea:
Cr=K(T2-Tl)Ll A(1OOX100X7.86)=267
Cr=0.ססOO16(30-2OX30·002) 1000 .
Cr=0.00348m(toolong) A=0.034sq.m. W"f1:
1
Actuallengthoftapeduringmeasurement
=30.002+0.00348 ® Totalcorrection:
=30.00548m.
Cr=K(T2'Tl)L jt1
® Truearea: Cr=7x10-7(20•15X1,l:1J
Thereforethetapeis0.00548mtoolong Cr=0.00035m.
Forthe144.95mside:
= =
144.95(0.00548) 026 Pullcorrection:
7iotalerror 30 . m.
. (P2-P1)L
Truelength=144.95+0.026 Cp= AE
Truelength=144.976m
C -(16·10)(100)
Forthe113mside: p- 0.034(2)106
=113(0~)= Cp=0.009m
Totalerror 0.021
Correction=0.00035+0.009
Truelength=113+0.021 Correction=0.00935m
Truelength=113.021m
~~6
Truearea=(144.976X113.021) No. oftapelengths= =4.306
Truearea=16,385.33~
Totalcorrection=4.306(0.00935)
® Errorinarea: Totalcorrection=0.0403m
Erroneousarea=(144.95)(113)
Erroneousarea:::16,379.35m2 ® Truelengthofbaseline:
Errorinarea=16,385.33-16,379.35 Truelengthofbaseline=430.60+0.0403
Errorinarea=5.982~ Truelengthofbaseline=430.6403m
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