Surveying Vol 1 PDF

Downloaded From : www.EasyEngineering.net Downloaded From : www.EasyEngineering.net ww w.E asy En g ine...

Downloaded From : www.EasyEngineering.net Downloaded From : www.EasyEngineering.net ww w.E asy En g ine eri n g.n et **Note : Other Websites/ Blogs Owners we requested you, Please do not Copy (or) Republish this Material. This copy is NOT FOR SALE. **Disclimers : EasyEngineering does not own this book/materials, neither created nor scanned. we provide the links which is already available on the internet. For any quarries, Disclaimer are requested to kindly contact us. We assured you we will do our best. We DO NOT SUPPORT PIRACY, this copy was provided for students who are financially troubled but deserving to learn. Thank You and God Bless! Downloaded From : www.EasyEngineering.net Downloaded From : www.EasyEngineering.net  Downloaded From : www.EasyEngineering.net Downloaded From : www.EasyEngineering.net paras- tawneja.blospo w t.in w. By Ea Dr. B.C. PUNM IA Formerly, Professor and Head, Deptt. of Civil Engineeri ng, & syE (VOLUME I) Dean, Faculty of Engineeri ng M.B.M. Engineeri ng College, Jodhpur ng Er. ASHOK KUMAR JAIN Dr. ARUN KUMAR JAIN Director, Assistant Professor Arihant Consultan ts, M.B.M. Engineer ing College, ine Jodhpur Jodhpur eri n SIXTEENTH EDITIO N g.n (Thoro ughly Revise d and Enlarg ed) LAXMI PUBLICATIONS (P) LTD et BANGALORE e CHENNAI e COCHIN e GUWAHATI e HYDERABAD JALANDHAR e KOLKAT A e LUCKNOW e MUMBAI e RANCHI e NEW DELHI INDIA e USA GHANA e KENYA......_ Downloaded From : www.EasyEngineering.net Downloaded From : www.EasyEngineering.net Downloaded From : www.EasyEngineering.net Downloaded From : www.EasyEngineering.net SURVEYING-I © 1965, 1984, 2005 B.C. PUNMIA rI © 1994, 2005 ASHOK KUMAR JAIN, ARUN KUMAR JAIN ; \ Copyright © by Authors. All rights reserved including those of translation into other languages. In accordance with the Copyri ght ww (Amend ment) Act, 2012, no part of this publica tion may be reproduced, stored in a retrieval system, or transm itted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise. Any such actor scanning, uploading, and or electro nic sharing of any part of this book withou t the permission of the publish er unlawfu l piracy and theft of the copyrig ht holder' s constitu tes intellec tual propert y. If you would like to use materia book (other than for l from the review purpose s), prior written permiss ion must be obtaine d from the publishers. w.E Printed and bound in India Typeset at : Arihant Consultants, Jodhpur. First Edition: 1965, Second Edition : 1966, Third Edition : 1972, Fourth Edition : 1976, Fifth Edition : 1978 Sixth Edition : 1980, Seventh Edition : 1981, Eighth Edition : 1983, Ninth Edition : 1985, Tenth Edition : 1987 Eleventh Edition : 1988, Twelfth Edition : 1990, Reprint : 1991, 1992, 1993, Thirteenth Edition : 1994 asy Reprint : 1995, 1996, Fourteenth Edition : 1997, Reprint : 1998, 1999, 2000, Fifteenth Edition : 2002 Reprint : 2003, 2004, Sixteen th Edition: 2005, Reprint : 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014 E5U-0603·495-5URVEYING I (E)-PUN Price: ~ 495.0 0 Limits of Liability/Disclaimer of Warran ty: The publisher respect to the accuracy or comple teness of the content advice, strategies, and activities contained herein may En and the author make no represe ntation or warranties with s of this work and specifically disclaim all warranties. not be suitable for every situation. In performing activitie The s TO MY FAT HER g adult supervision must be sought. Likewise, commo n sense and care are essential to the conduc t of any and all activitie whethe r described in this book or otherwise. Neither the s, publisher nor the author shall be liable or assume s any ine responsibility for any injuries or damages arising herefro m. The fact that an organization or Website if referred this work as a citation and/or a potential source of further to in information does not mean that the author or the publish endorse s the information the organization or Website may er provide or recomm endatio ns it may make. Further, readers must be aware that the Interne t Websites listed in this work may have change d or disappe ared betwee n when work was written and when it is read. this eri All trademarks, logos or any other mark such.as Vibgyor, USP, Amanda, Golden Bells, Firewall Media, Mercury, Trinity, laxmi appearing in this work are tradem arks and intellec tual propert y owned by or licensed to Laxmi Publications, subsidiaries or affiliates. Notwithstanding this disclaimer, its all other names and marks mentio ned in this work are trade names, trademark's or service marks of their respect the n ive owners. ,- g.n 10 Bangal ore 080-26 75 69 30 044-24 34 47 26 0484-2 37 70 04, 405 13 03 ~ ~ Hydera bad.,E ro Jalandhar 0361-2 54 36 69, 25138 81 040-27 55 53 83, 27 55 53 93 0181·2 22 12 72 033-22 27 43 84 et PUBliSHED IN INDIA BY 0522-2 20 99 16 ~ LAXMI PUBLICATIONS (P) LTD 022-24 91541 5, 24 92 78 69 0651-2 20 44 64 113, GOLDEN HOUSE, OARYAGANJ, NEW DElHI-11 Telepho ne: 91-11·4353 2500, 4353 2501 0002, INDIA - Fax; 91-11-2325 2572, 4353 2528 C-856 2/014/ 04 www.laxrnipublications.corn [email protected] Downloaded From : www.EasyEngineering.net Printed at: Reoro lnrlirl 1trl Mnmh;~i Downloaded From : www.EasyEngineering.net Downloaded From : www.EasyEngineering.net Downloaded From : www.EasyEngineering.net I I Preface ,.' ww This volwne is one of the two which offer a comprehensive course in those of theory and practice of Plane and Geodetic surveying that are most commonl y used parts by w.E Degree. civil engineers. and are required by the students taking examination in surveying for in thirteen chapters the more common surveying Diploma and A.M.I.E. The first volume covers operations. , Each topic introduced is thoroughly describOd, the theory is rigorously developed asy DUIJ?ber of numerical examples are included to illustrate its application. General and. a ~rge s~atemn of important principles and methods are almost invariably given by practical to illustrations. A large number of problems are available at the end of each chapter, stage~ illustrate theory and practice and to enable the student to test his reading at differem En of his srudies. Apan from illustrations of old and conventional instruments, emphasis has been placed g good deal on new or improved instruments both for ordinary as well as precise work. A ine ts with a thorough discussion of the geometrical of space has been given to instrumental adjustmen principles in each case. Metric system of units has been used throughout the text, and, wherever possible, eri since the the various formulae used in texc have been derived in metric units. However, the engineerin g cha~ge\ over to metric system has still nor been fully implemented in all i;~ JUr conntiy, a fe·,~- examples in F.P.S. system, hdxe ~!so beer: gi\'C!": ;~:Jtir n I should lik.e to express my thanks to M/s. Vickers Instruments Ltd. (successors their catalogues or providing special photograp hs. g.n M/s. Cooke, Troughton & Simm's), M/s. Wild Heerbrugg Ltd., M/s Hilger & and M/s. W.F. Stanley & Co. Ltd. for permitting me to use certain illustratio My thanks are also due to various Watci Ltd ns from Universiti to.. es et bodies of professional institution for pennitting me to reproduce some of and exami~g the questions from their examination papers. lnspite of every care taken to check. the numerical work. some errors may remain. and I shall be obliged for any intimation of theses readers may discover. B.C. PUNMIA JODHPUR 1st July, 1965 Downloaded From : www.EasyEngineering.net Downloaded From : www.EasyEngineering.net Downloaded From : www.EasyEngineering.net Downloaded From : www.EasyEngineering.net Jl( PREFACE TO THE THIRD EDITION PREFACE TO THE NINTH EDITION In this edition, the subject-matter has been revised thoroughly and the chapters have In the Ninth Edition. the subject-matter has been revised and updated. ww been rearranged. Two new chapters on "Simple Circular Curves' and 'Trigonometrical Levelling (plane)" have been added. Latest Indian Standards on 'Scales', 'Chains' and 'Levelling Staff JODHPUR B.C. PUNMIA have been included. A two-colour plate on the folding type 4 m Levelling Staff, conforming 1st Nov., 1984 to IS 1779 : 1%1 has been given. In order to make the book more useful to the ~tudens w.E appearing at A.M.l.E. Examination in Elementary Surveying, questions from the examination PREFACE TO THE TENTH EDITION papers of Section A. from May 1962 to Nov. 1970 have been given Appendix 2. Account has been taken throughout of the suggestions offered by the many users of the book, and In the Tenth Edition, the book has been completely rewritten, and all the diagrams grateful acknowledgement is made to them. Futther suggestions will be greatly appreciated. have been redrawn. Many new articles and diagrams/illustrations have been added. New asy instruments, such as precise levels. precise theodolites, precise plane table equipment, automatic levels. new types of compasses and clinometers etc. have been introduced. Two chapters JODHPUR B.C. PUNMIA on 'Setting Out Works' and 'Special Instruments' bav~ been added at the end of the 1st Feb.. 1972 book. Knowledge about special instruments, such as site square , transit-level, Brunton's En universal pocket transit, mountain compass-transit, autom.nic le~s, etc. will be very much useful to the field engineers. Account has been taken throug~ of the suggestions offered PREFACE TO THE FOURTH EDITION by the many users of the book, and grateful acknowledgement is made to them. Further g In this edition, the subjec1-matter has been revised and updated. An appendix on suggestions will be greatly appreciated. ine 'Measurement of Distance by Electronic Methods' has been added. JODHPUR B.C. PUNMIA JODHPUR lOth July, 1987 A.K. JAIN B.C. PUNMIA 15-10-1973 PREFACE TO THE FIFTH EDmON eri PREFACE TO THE TWELFTH EDITION In the Twelfth Edition, the subject-matter has been revised and updated. In the Fifth Edition. the suhiect-matter ha!< on SI units bas been added. JODHPUR ~n thnrnnQ:hly rP:vic:.,-1 An Apenrli'~ B.C. PUNMJA n JOlJHPUR 30th March, 1990 g.n PREFACE TO THE THIRTEENTH.EDITION B.C. PUNMIA A.K. JAIN et 25-4-1978 In the Thirteenth Edition of the book, the subject mauer has been thoroughly revised PREFACE TO THE SIXTH EDmON and updated. Many new articles and solved examples have ·been added. The entire book bas been typeset using laser printer. The authors are thankful to Shri Moo! singb Galtlot In the Sixth Edition of the book, the subject-matter bas been thoroughly revised and for the fine laser typesetting done by him. updated. JODHPUR B.C. PUNMIA JODHPUR B.C. PUNMIA 2nd Jan., 1980 15th Aug. 1994 ASHOK K. JAJN ARUN K. JAIN Downloaded From : www.EasyEngineering.net Downloaded From : www.EasyEngineering.net fl! Downloaded From : www.EasyEngineering.net - I:! Downloaded From : www.EasyEngineering.net i SI X !! Contents PREFACE TO TilE SIXTEENTH EDITION In !he Sixteenth Edition, !he subject matter has been thoroughly revised, updated and CHAYI'ER I FUNDAMENTAL DEFINITIONS AND CONCEPTS rearranged. In each chapter, many new articles have been added. ·Three new Chapters have I 1.1. SURV~YING : OBJECT been added at !he end of !he book : Chapter 22 on 'Tacheomelric Surveying'. Chapter ww 1.2. PRIMARY DIVISIONS OF SURVEY I 13 on 'Electronic Theodolites' and Chapter 24 on 'Electro-magnetic Disrance Measurement 1.3. CLASSIFiCATION 3 (EDM)'. All !he diagrams have been redrawn using computer graphics and !he book has 1.4. PRINCIPLES OF SURVEYING 4 been computer type-set in bigger fonnat keeping in pace with the modern trend. Account 1.5. UNITS OF MEASUREMENTS s 1.6. PLANS AND 8 w.E has been taken throughout of !he suggestions offered by many users of !he book and grateful MAPS 1.7. SCALES.8 acknowledgement is made to !hem. The authors are thankful to Shri M.S. Gahlot for !he 1.8. PLAIN SCALE 10 fine Laser type setting done by him. The Authors are also thankful Shri R.K. Gupta. II 1.9. DIAGONAL SCALE Managing Director Laxmi Publications. for laking keen interest in publication of !he book 1.10. THE VERNIER 12 and bringing it out nicely and quickly. 1.11. MICROMETER 18 asy MICROSCOPES 1.12 SCALE OF CHORDS 19 Jodhpur 1.13 ERROR DUE TO USE OF WRONG SCALE 20 B.C. PUNMIA Mabaveer Jayanti 1.14. SHRUNK SCALE 21 ASHOK K. JAIN 1.15. 22 SURVEYING - CHARACI'ER OF WORK En lsi July, 2005 ARUN K. JAIN CIIAYI'ER 2 ACCURACY AND ERRORS 2.1. GENERAL '1:1 2.2. SOURCES OF ERRORS '1:1 g 2.3. KINDS OF ERRORS 28 29 ine 2.4. TIIEORY OF PROBABILITY ACCURACY IN SURVEYING ERROR 3() 2..5. PERMISSmLE 2.6. ERRORS IN COMPUI'ED RESULTS 31 CHAPTER 3 LINEAR MEASUREMENTS eri 3.1. DIFFERENT METHODS 37 3.2. DIRECT MEASUREMENTS 37 3.3. INSTRUMENTS FOR CHAINING 38 n RA..'IJG!t-;G OL-; S0RVEY U.NJ;.s 46 3.5. CIWNING 49 g.n 3.6. MEASUREMENT OF LENGfH WITH TilE HELP OF A TAPE so 3.7. ERROR DUE TO INCORRECI' CHAJN. so 3.8. CHAINING ON UNEVEN OR SLOPING GROUND S4 3.9. ERRORS IN CHAlNING S7 et 3.10. TAPE CORRECTIONS 60 3.11. DEGREE OF ACCURACY IN CHAINING 70 70 ~ PRECISE UNEAR MEASUREMENTS 4 CHAIN SURVEYING 4.1. CHAIN TRIANGULATION 8S 4.2. SURVEY STATIONS ss 4.3. SURVEY LINES 8S "'.___ I Downloaded From : www.EasyEngineering.net Downloaded From : www.EasyEngineering.net Downloaded From : www.EasyEngineering.net Downloaded From : www.EasyEngineering.net XIII xn G 8.3. CASE I ' BEARING. OR LENGTH, OR BEARIN 181 _;{4 LOCATING GROUND FEATURES : OFFSETS 87 92 AND LENGTH OF ONE SIDE OMIITED G OF ANOTF.HR SIDE OMmE D 182 4.5. FIELD BOOK 8.4. CASE D : LENGTH OF ONE SIDE AND BEARIN 182 94 ED CASE m ' LENGTHS OF TWO SIDES OMIIT ww 4.6. FIELD WORK 8.l. 182 S 9S OMmE D 4.7. INSTRUMENTS FOR SEITING OUT RIGJIT ANGLE 8.6. CASE IV : BEARING OF TWO SIDES 183 98 SIDES ARE NOT ADJACENT 4.8. BASIC PROBLEMS IN CHAINING 8.7. CASE II, m, IV : WHEN THE AFFECTED 100 ~. OBSTACLES IN CHAINING 4.10. CROSS STAFF SURVEY lOS ~R 9 LEVELLING 19l DEANIDONS w.E 106 9.1. -196 PLO'ITING A CHAIN SURVEY / 4.11. 5 THE COMPASS _fl METHODS OF LEVELLING 197 VCH APTE R 9.3. LEVELLING INSTRUMENTS 201 109 5.1. INTRODUCfiON 9.4. LEVELLING STAFF 204 110 5.2. BEAIUNGS AND ANGLES 9.5. THE SURVEYING TELESCOPE 211 116 mE 'I'HEORY OF MAGNETIC COMPASS TEMPORARY ADJUSTMENTS OF' A LEVEL 7 asy 5.3. 9.6. 213 118 ING) 5.4. THE PRISMATIC COMPASS THEORY OF D!RECT LEVELLING (SPIRIT LEVEL 21l 120 5.5. THE SURVEYOR'S COMPASS 9.8. DIFFERENTIAL LEVELLING 216 124 S.6. WILD 83 PRECISION COMPASS 9.9. HAND SIGNALS DURING OBSERVATIONS 216 !25 5.1. MAGNETIC DECUNATION '-)kf'( BOOKING AND REDUCING LEVELS 222 En 127 5.8. LOCAL ATTRACTION 9.11. BALANCING BACKSIGIITS AND FORESimiTS 226 133 SURVEY CURVATURE AND REFRAcriON /~R ERRORS IN COMPASS ~ 230 6 THE THEODOLITE 9.13. RECIPROCAL LEVELLING 233 g 137 NJNG) 6.1. GENERAL 9.14. PROALE LEVELLING (LONGITUDINAL SECfiO 23"? THEODOLITE 137 THE ESSENTIALS OF THE TRANSIT 9.15. CROSS-SECTIONING 238 ine 6.2. 141 6.3. DEFINITIONS AND TERMS 9.16. LEVELLING PROBLEMS 240 142 6.4. TEMPORARY ADJUSTMENTS 9.17. ERRORS IN LEVELLING 243 S GENERAL PROCEDURE 144 MEASUREMENT OF HORlZONTAL ANGLE 9.18. DEGREE OF PRECISION 244 j 6.l. MEASUREMENT OF VERTICAL ANGLE S ISO THE LEVEL TUBE eri { 6.6. 9.19. 244 Ill 6.7. MISCELLANEOUS OPERATIONS WITH THEOD OLITE 9.20. SENSITIVENESS OF BUBBLE TIJBE 2"48 RElATIONS ISS 6.8. FUNDAMENTAL LINES AND DESIRED 9.21. BAROMETRIC LEVELLING 2l2 WORK ll6 SOURCES OF ERROR IN TI!EOD OLITE HYPSOMETRY ~ 6.9. n CHAPTER 7 TRAVERSE SURVEYING 10 CONTOURING 257 g.n , !!'l'TP0!"!U':'T!0!'J' 161 10.1. UE.i>it:RA.i.. '-" 161 7.2. CHAIN TRAVERSING 10.2. CONTOUR INTERVAL 2S9 METIIOD 162 7.3. CHAIN AND COMPASS TRAVERSING FREE OR LOOSE NEEDLE 10.3. CHARAcrERISTICS OF CONTOURS 260 162 7.4. TRAVERSING BY FAST NEEDLE METHOD 10.4. METHODS OF LOCATING CONTOURS 264 et 164 7.5. TRAVERSING BY DIRECT OBSERVATION OF ANGLES IO.S. INTERPOLATION OF COtiTOURS 266 AND TAPE 16l 7.6. LOCATING DETAILS WITH TRANS IT 10.6. CONTOUR GRADIENT 267 167 MAPS 7.7. CHECKS IN CLOSED TRAVERSE _/ 10~7. USES OF CONTOUR 168 7.8. PLOTIING A TRAVERSE SURVEY \.QHAPTER 11 PLANE TABLE-SURVEYING 271 169 7.9. CONSECUTlVE CO-ORDINATES LATmJDE AND DEPARTURE GENERAL ACCESSORIES 171 11.1. 273 7.10. CLOSING ERROR 11.2. WORKING OPERATIONS 27S 172 7.11. BALANCING TilE TRAVERSE 11.3. PRECISE PLANE TABLE EQUIPMENT 27l 177 DEGREE OF ACCURACY IN TRAVERSING METHODS (SYSTEMS) OF PLANE TAD LING i 7.12. 276 CHAPTER 8 OMITIED MEASUREMENTS. INTERSECTION (GRAPHIC TRIANGULATION) m AND DEPARTURE 179 8.1. CONSECUTIVE CO-ORDINATES : LATITUDE 6 TRAVERSING 278 ISO 8.2. OMITfED MEASUREMENTS. RESECITON Downloaded From : www.EasyEngineering.net Downloaded From : www.EasyEngineering.net  ~ Downloaded ', From : www.EasyEngineering.net Downloaded From : www.EasyEngineering.net ~' 11.8. THE THREE-POINT PROBLEM:-. ""' "' 279 CHAPI'ER 16 PERMANENT ADJUSTMENTS OF LEVELS 11.9 TWO POINT PROBLEM 285 16.1. INTRODUCriON 365 11.10. ERRORS IN PLANE TABLING 287 16.2. ADUSTMENTS OF DUMPY LEVEL 365 ~ 11.11. ADVANTAGES AND DISADVANTAGES OF PLANE TABLING 289 372 16.3. ADJUSTMENT OF TILTING U:VEL r/CIIAPI'E R 12 CALCULATION OF AREA 16.4. ADJUSTMENTS OF WYE LEVEL 373 ww 12.1. GENERAL 291 CHAPI'ER 17 PRECISE LEVELLING 12.2. GENERAL METHODS OF DETERMINING AREAS 292 17.1. INTRODUCfiON 377 12.3. AREAS COMPIJTED BY SUB-OMSION IJ'IITO TRIANGLES 292 17.2. THE PRECISE LEVEL 377 ~ vz.5. AREAS FROM OFFSETS TO A BASE LINE : OFFSETS AT REGULAR INTERVALS OFFSETS AT IRREGUlAR INTERVALS 292 17.3. WILD N-3 PRECISION LEVEL 378 w.E 2'11 17.4. THE COOKE S-550 PRECISE LEVEL 378 ~ AREA BY DOUBLE MERIDIAN DISTANCES 298 17.S. ENGINEER'S PRECISE LEVEL (FENNEL) 319 12.7. AREA BY CO-ORDINATES 302 17.6. FENNEL'S FINE PRECISION LEVEL 319 12.8. AREA COMPUTED FROM MAP MEASUREMENTS 304 17.7. PRECISE LEVELLING STAFF 380 _/ -~9. AREA BY PLANIMETER 305 17.8. FIELD PROCEDURE FOR PRECISE LEVELLING 380._,.£HAYfER 13 asy MEASUREMENT OF VOLUME 17.9. FlEW NOTES 381 13.1 GENERAL 17.10. DAILY ADJUSTMENTS OF PRECISE LEVEL 382 315 ~ MEASUREMENT FROM CROSS-SECTIONS 315 CHAPI'ER 18 PERMANENT ADJUSTMENTS OF THEODOLITE $ THE PRISMOIDAL FORMULA ~THE 319 18.1. GENERAL 385 En TRAPEZOIDAL FORMULA (AVERAGE END AREA METHOD) 321 18.2. ADJUSTMENT OF PlATE LEVEL 386.\....J¥5. THE PRISMOIDAL CORRECTION 322 18.3. ADJUSTMENT OF LINE OF SIGHT 386 13.6. THE CURVATURE CORRECTION 322 18.4..JYI'/ VOLUME FROM SPOT LEVELS 327 18.5. ADJUSTMENT OF THE HORIZONTAL AXIS ADJUSTMENT OF ALTITUDE LEVEL AND VERTICAL INDEX FRAME 388 g 388 __!) Then, EIn sure that irs entire length lies along the line. The leader then pushes the arrow... (3.2) into the or A=A' (LL' )' ground, opposite the zero. The pin is usually inclined from vertical about 20 or 30 degrees, i starting at right angles to the line so that it slides under the rape. with irs centre L' L+M.. M.. opposite Allernatively, -=-=1+- the graduation point on the rape. L L L gin 3. The follower then releases his end of the rape and the two move forward where M.. = error in length of chain along the line. the leader dragging the rape. When the end of the rape reaches the I!.L arrow jusr Let placed, follower calls our "tape". He then picks up the end of rape and lines T=e the leader I eer (L )' in and the procedure is repeated as in srep 2. A= /} x A' =(I + e)' x A' 4. When the second arrow has been established by the leader. the follower picks up the first arrow, and both the persons move ahead as described in srep 3. The + e)2 = I + 2e + e' ~ procedure Bur (I I + 2e , if e is small is repeated until ten rape lengths have been measured. At this stage, the... (3.2 a) leader will be A= (I+ 2e)A' ing out of arrows. while the follower will h?.ve nine arrows. The leadc~ wili then call "arrows" or "ten". When the leader moves further after the rape length has been measured (iii) Correction to volume :. and Le~ = measured or computed volume J reaches the rape length ahead, the follower rakes our the tenth arrow, erects V' a ranging rod or a nail in irs place aod then transfers 10 arrows to the leader. The surveyor V = actual or rrue volwne..n e records.the transfer of arrows in the field bock. 5. At the end of the line, at B, the last measurement will generally be a panial Then, true volume = measured volume x( ~ j rape length from the last arrow set to the end point of the line. The leader holds the L' ".(3.3) V=V' [ L )' t end of the rape at B while the follower pulls the rape back rill it becomes taut or and then re~ds against the arrow. L' L+I!.L I!.L 3.7, ERROR DUE TO INCORRECT CHAIN A/Jernatively, -=-=1+- L L L If the length of the chain used in measuring length of the line is not equal I!.L to Let -=e the true length or the designated length, the measured length of the line will nor L be correct and suitable correction will have 10 be applied. If the chain is too long, the distance will be less. The error will, Jherefore, be negative and the correction measured.V=( ~ )' V' =(I +e)' V' is positive. Downloaded From : www.EasyEngineering.net I ·~ Downloaded From : www.EasyEngineering.net Downloaded From : www.EasyEngineering.net Downloaded From : www.EasyEngineering.net ~ SURVEYING 53 LlNP.AR MEASUREMEI'ITS (I + e) = I + e' + 3e' + 3e ~(I+ 3 But 3e), if e is small 4 Hence 11 = zc;-~ x 1400.= 1409.80 m V =(I + 3e)ll'... (3.3 a) Total length= I=!,+ I,= 1503.75 + 1409.80 = 2913.55 m. Example 3.1. The length qJ a line measured with a 20 metre chain was found 10 ww be 250 mmes. Calculate the true length of the line if the chain was 10 em too long. Example 3.4. A surveyor measured the distance· be/Ween two poims on the plan drawn Solution. to a. scaie of l em = 40 m and the result was 468 m. lAter, however, he discovered that he used a scale qJ 1 em = 20. m. Find the true distance between the two poims. Incorrect length of the chain = L' = 20 + _!Q_ = 20.1 m Solution. Distance between two points measured with a scale of I em to 20 m 100 w.E Measured length =I'= 250m 468 =-=234 20. em Hence true length of the line =I' (f) = 250 [~(/) = 251.25 metres. Actual scale of the plan is I em = 40 m True distance between the points = 23.4 x 40 = 936 m Example 3.2. The length of a survey line was measured with a 20 m chain and was found to be equal to 1200 metres. As a check, the length was again measured with · Example 3.5. A 20 m chain used for a· survey was found to be 20.10 m at the asy I a 25 m chain and was found to be 1212 m. On comparing the 20 m chain with the test gauge, it was found to be 1 decimerre too long. Find the actual length- of the 25 m chain used. Solution. beginning and 20.30 m at the end of the worL The area of the plan drawn to a scale of l em = 8 m was measured with the help of a planimeter and was found to be 32.56 sq. em. Find the true area of the field. Solution. With 20 m chain : "(L' 1 En L' = 20 + 0.10 = 20.10 m ?O 10 1=1' -1=1200x=-.:_ =1206m=True length of line. 20 i.. L'= Average length of the cham= 20.10 + 20.30 · _ Area of plan= 32.56 sq. em = 20.20 m g L) ! 1 I Area of the ground= 32.56 (8) = 2083.84 sq. m =A' (say) With 25 m chain f)/' I ine I=[ True area= A = 'L')' l- '20201'1 x 2083.84 = 2125.73 sq. m. A'=(-·- "1206 = ( ~ or L 20 J. )1212 Alternatively, from Eq. 3.2 (a), eri L' _ 1206 X 25 = A=(l +2e)A'. 24"88 m. I 1212 where e= ll L = 20.20-20 _ 0.20 =O.OI Thus, the 25 m chain was 12 em too short. L 20 20 Example 3.3. A 20 m chain was found to be 10 em too long after chaining a ng A= (I + 2 x 0.01) x 2083.84 = 2125.52 m' distance of 1500 m. It was found to be 18 em too long at the end of day's work after chaining i:-~ diJ;.,.;l(; 1 l changes, stout posts are driven firntly in the ground. The setting out pany then places by two methods : g.n the measuring tripods in alignmentS in advance of the measurement which can be done (i) Measurement on Wheeler's method by Wheeler's base line apparatus. et length of a'~ (ir) Jaderin's method. ''" ·"' 24(10)1 33(1.886)' = 0.0309 - 0.0445 = - 0.0136 m (subtractive) When Po= 10 kg = P, sag correction is zero. J n Now, when y=k,x', for CA where the origin is at C in beth the cases. x=l1, y=a; and y =kzx', for CB g.n.. kl =.!!._ I( et Final correction and, When x=h. y=b; k, =.!'.. [,' (a) Total correction=- 0.0010 + 0.0018 + 0.0004 + 0.0250 m = + 0.0262 m. =- 0.0132 m Hence the equations are (b) Total correction=- 0.0010 + 0.0018 - 0.0004- 0.0136 (c) Total correction=- 0.0010 + 0.0018 + 0 + 0 = + 0.0008 m ax' y=- for CA and ' Y -_bx' for CB Example 3.14. (Sl units). It is desired to find the weight of the rape hy measuring 1.' [, its sag when suspended in CJllenary with both ends level. If the rape is 20 metre long !!l = 2ar for CA and !!l__ 2bx for CB and the sag amounts to 20.35 em aJ the mid-span under a tension of 100 N, what is d:t. 1.' d:t. - 1,' the weight of the tape ? Thus. the length of the curve. Downloaded From : www.EasyEngineering.net Downloaded From : www.EasyEngineering.net Downloaded From : www.EasyEngineering.net Downloaded From : www.EasyEngineering.net ~'- 81 80 SURVEYING UNBAR MEASUREMEN'!S s = S1 + s, = ~ 1 !I +( ~ J' )dx + tII +( Z~x J' l dx ·:~ OM of ,the tape, of lengths, such that the horizontal tension at 0 is H. aod the tension P at point T ; ' :...·a ' 1 T ~3 -a' II +b')] ww 2 M makes an angle IV with the ' ' ' = [ 11+1,+ 2(a' - =1+- [, - +b- 3 II I, )