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# Civl Engr Measurements Lab CIVL 1101

University of Memphis

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This 16 page Class Notes was uploaded by Dana Yundt on Friday October 23, 2015. The Class Notes belongs to CIVL 1101 at University of Memphis taught by Charles Camp in Fall. Since its upload, it has received 33 views. For similar materials see /class/228416/civl-1101-university-of-memphis in Civil Engineering at University of Memphis.

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Date Created: 10/23/15

CIVL 1101 Mechanics of Materials 110 Engineering STrucTures and MaTerials l Mechanics of materials is a branch of applied mechanics ThaT deals wiTh The behavior of solid bodies subjecTed To various Types of loading I A Thorough undersTanding of mechanical behavior is essenTial for The safe design of all sTrucTures I Mechanics of maferas is a basic subjecT in many engineering fiel s Mechanics of MaTerial Earfiauakes I Early in The morning on Tuesday AugusT 17 1999 a deadly magniTude 74 earThquake sTruck along The AnaTolian faulT in The norThwesTern region of Turkey Mechanics of MaTerial Earfiquakes Mechanics of MaTerial Space ShuTTle Columbia i i A 1 The Space Shuttle Columbiadisaster occurred on February 1 2003 iiilieritlie duri g Space Shuttle Columbia disintegrated over Texas r22nTry into t e Eartli39s atmosp ere Mechanics of MaTerial Space ShuTTle Columbia Th2 lossof Columbia was a resulT of damage susTa ned during launch when a piece of foam insulation the size o asmall briefcase broke omtie space sliuttle 2xT2rnal Tlie debris sTruckThe lea iiig edge ofThe le t iii iig damaging the sliuttles tliermal protection system Mechanics of MaTerial I 35W Mississippi River bridge Tlie I35W Mississippi kiver bridge catastropliically failed during the evening rush hour on AugusT 1 2007 collaps rig to the river and ivrzrbanks beneatli CIVL 1101 Mechanics of Materials 210 Mechanics of Material I 35W Mississippi River bridge s 1 7 A in V V The Law Mississippi Rlver bridge catastrophlcally falled dur ng the evenan rush hour onAugust 12007 Collapsing to the river and rlverbanks beneath Mechanics of Material I 35W Mississippi River bridge TheIeaaw Mississippi Rlver brldge catastrophlcally falled during the evenan rush hour on August 1 2007 collaps ng to the river and rlverbanks beneath Mechanics of Material Collapse of Can Tho Bridge On September 2 2007 090 meter sectlon of an approach ramp which was over 30 meters above the ground collapsed e posslble due to 7 0 ns weaken the foundatlon Engineering Structures and Materials I The historical development of mechanics of materials is a fascinating blend of both theory and experiment Leonardo da Vinci 14521519 as a i o m a i E o e L o e 3 wires bars and beams Engineering Structures and Materials I Leonhard Euler 17071783 I Developed the mathematical theory of columns and calculated the theoretical critical load of a column in 1744 l 7 before an ex erimental evidence existed to show the significance of his results Engineering Structures and Materials I Numerical problems require that you work with specific IIIIts of measurements I The two acce ted standards o easure ent are the International System of IIIts SI and the ll 5 Customary System W565 I As you know signi cant digits are very important in engineering I In our work in this section three S39 III39 innquot 139 its provides enough accuracy CIVL 1101 Mechanics of Materials 310 STr39ess and STr39ain I The fundamenTal concest of sTress and sTrai n can be illusTraTed by considering a prismaTic bar ThaT is loaded by axial forces PaT The en s I A prismatic baris a sTraighT sTrucTural member having consTanT cross secTion ThroughouT iTs lengTh I In This illusTraTion The axial forces produce a uniform sTreTching o The bar hence The bar is said To be in feltsall STr39ess and STr39ain STr39ess I The Tensile load PacTs aT The boTTom end of The bar I AT The Top of The bar are forces represenTing The acTion of The removed parT of The bar I The inTensiTy oT Torce ThaT is The Torce per uniT area is called The 5 HESS commonly denoTed by The Greek leTTer cs STr39ess I The axial force is equal To The inTensiTy cTimes The cross secTional area A of The bar P 039 A I When The bar is sTreTched by The force F The resulTing sTresses are tells7e stresses I If The force Pcause The bar To be compressed we obTain compressive sses STr39ess I The sTress acTing perpendicular To The cuT surface iT is referred To as a nonna I39ess I The equaTion c PA will give The average IlaWill s Iess STr39ess I Sign convention for normal sTresses is for Tensile sTresses an for compressive sTresses I Because The normal sTress c is obTained by dividing The axial force by The crosssecTional area iT has units of me per unit of area P P CIVL 1101 Mechanics of Materials 410 STress I In SI units Force is expressed in newTons N and area in square meTers m2 A Nm2 is a pascals Pa I In 0565 units STress is cusTomarily expressed in pounds per square inch psi or kips per square inch ksl 7000 pascals To make 1 psi Normal STrain I The change in lengTh is oenoTeo by The Lrreek leTTer 6 delTa Normal STrain I An axially loaded bar undergoes a change in lengTh becoming longer when in Tension and shorTer when in compression I The concepT of elongaTion per uniT lengTh or strain denoTed b The Greek leTTer s epsilon and given by L 12 equaTion Q1 0 Normal STrain I If The bar is in Tension The sTrain is called a femlie sfrain I If The bar is in compression The sTrain is called a compressive sfrain I Tensile sTrain is Taken as posiTive and compressive sTrain as negaTive Normal STrain I The sTrain s is called a normal strain because iT is associaTed wiTh normal sTresses I Because normal sTrain s is The raTio of Two lengThs iT is a dimensionless quantify ThaT is iT has no uniTs Example I Consider a sTeel bar having lengTh L of 2 0 m When loaded in Tension The bar mighT elongaTe by an amounT 6 equal To 14 mm 14 xlu 3m 20m 6 g L I The resulTing sTaTe of sTress and sTrain is called uniaxia stress and srnain CIVL 1101 Mechanics of Materials 510 Example Example I A prlsmallc bar WlM aclr cular crass SBCllOYl ls 100 kN culawmmm suszclzd lo a lal lensllz force The measured elongallon ls 5 15 mm Calculalz M2 lensllz slr2ss and slralrl M We 07 a 5 m blameler 2 25 Drum 2 Miller craxxrxecllan 100 W I Assumlng M2 agtltlal force acl al M2 c2m2r of M2 2nd Q 22222 mm M22 M2 slr zss ls 35m blameler2 mm P lookN N I The PZSUlllYlg slal2 of slr2ss and Slr alYl ls call2d U 7 m 2037183Z7W 204M Minxcl sirlss and sirai 1000 mm 1 m Example Group Problem 1 Ummmmmm I If M2 allawabl2 slr2ss al fallur2 for M2 mal2rlal ls 100 kN 35 000 pSl and M2 appll2d load on M2 bar ls p 20 000 lbs whal ls M2 lelllem ar2a r2qulr2 la pr2v2rll fallur2gt 35m blameler2 mm P P 20000b IThzslralVlls a gt A 6 15 A a 35000psl mm 1m Tmm 00004286 Group Problem 2 S l39ressS l39rain Diagrams If we bar falls 039 slrams 9mm lhan015 and W l Th2 mecharllcal properllzs of malzrlals are dzlzrmlnzd orlgmal lenglh 0 We bar ls L ls 10 feel whal ls W by l2sls performed on small spzclmzns of M2 malzrlal maxlmum allowable deformallorl before fallurz I In ard2r Mal l2sl r2sulls 9 a 1 g 5 2 5 5L 01500 fear 2 applylng loads W2 been slandardlzzd 2 t 5mm wgnnlxmnm 222m mm m 7mm w mammal 222m ngAmmmasmm lt m Namm 52m 22 5mm was CIVL 1101 Tension TesT Mechanics of Materials 610 I The axial sTress o in The TesT specimen is calculaTed by dividing The load Pby The crosssecTional area A I A more exacT value of The axial sTress known as The fme sfress can be calculaTed by using The acTual area of The bar il o l 39 T 39 39 5 mm I STrain in The bar is found from The measured elongaTion 8 beTween The gage marks by dividing 8 by The gage engTh L I If The acTual disTance is used in calculaTing The sTrain we obTain The fme drain or nafura sfral39n do 05 in I LLO 2 inAl Compression TesT I Compression TesTs of meTals are cusTomarily made on small specimens in The shape of cubes or circular cylinders ConcreTe is TesTed n compression on every imporTanT consTrucTion projecT To ensure ThaT The required sTrengThs have been obTained The sTandard ASTM concreTe TesT specimen is 6 in n diameTer 12 in long and 28 days old The age of concreTe is imporTanT because concreTe gains sTrengTh as H cures Developing a STressSTrain Diagram I AfTer performing a Tension or compression TesT and deTermining The sTress and sTrain aT various magniTudes of The load we can ploT a diagram of sTress versus sTrain STresssTrain diagrams were originaTed by Jacob Ber7011M 16541705 and J l Ponceef 1788 1867 STressSTrain for STeel The firsT maTerial we will discuss is sfmcfura sfee A sTresssTrain diagram for a Typical sTrucTural sTeel in Tension is shown 6 FracTure UlTimaTe STress quot5 Yield STress r ElasTic PlasTic STrain Necking 8 Hardening CIVL 1101 Mechanics of Materials 710 STressSTrain Diagram STressSTrain for STeel I MaTerials ThaT undergo large sTrains before failure are classified as duc e I DucTile maTerials include mild sTeel aluminum and some of iTs alloys copper magnesium lead molybdenum nickel brass bronze nylon Teflon and many oThers G A 2 quotJ a 0 05 0 10 l 0 20 0 25 STressSTrain for Aluminum STressSTrain for Rubber STeel Aluminum smu ks 0 05 0 10 0 15 0 20 0 25 Slrain Ha d Rubbe 2 I sun R bber 1 Slrai n smu m BriTTle MaTerials Compression TesT I MaTerials ThaT fail in Tension aT relaTively low values of sTrain are classified as brrre maTerials I Examples are concrete sTone casT iron glass ceramic maTerials and many common meTallic alloys I Ordinary glassis G a nearly i eal briTTle maTerial g E Slrai n s I STress sTrain diagrams for compressall have differenT shapes from Those for Tension I DucTile meTals such as sTeel aluminum and copper have proporTional limiTs in compression very close To Those in Tens39on CIVL 1101 Compression TesT I However when yielding begins The behavior differenT Consider compression of coppe is quiTe Slraln PlasTiciTy Mechanics of Materials 810 ElasTiciTy I The sTress sTrain diagrams described in The preceding secTion illusTraTe The be avior of various maTer39 l s They are loadedsTaTically in Tension or compression I Now leT us consider whaT happens when The load is slowly removed and The maTerial is uIIaaded c i luadlng I Now leT us suppose ThaT we load This same maTerial To a much higher level I If the loading is Too greaT a residual 51min or pendull strain remains in tlie rnaterial I The corresponding residual elongaTion of the bar is calle The r The material is said To be 39 Luadlng i i i U luadlng Resldual Elasilc Siraln Recovery Creep I DevelopmenT of addiTional sTrains over long periods of Time and are said To creep Time RelaxaTion TighT cable Linear ElasTiciTy I When a maTerial reTurns To iTs original dimensions afTer unloading iT is called eanC I When a maTerial behaves elasTically and also exhibiTs a linear relaTionship beTween sTress and sTrain iT is said To be linearly eas 39c CIVL 1101 Mechanics of Materials 910 Linear ElasTic iTy I The linear relaTionship beTween sTress and sTrain for a bar in simple Tension or compression can be expressed by The equaTion 039 58 where E is a consTanT known as The modulus of eas 39cify uniTs are eiTher psi or Pa Hooke39s Law I The equaTion 039 E s commonly known as Hooke39s law I For The famous English scienTisT koberT Hooke 16351703 I Hooke was The ir39sT erson To nvesTi aTe The elasT39 4 io propert es of materials and he tested such diverse materials as metal wood stone bones and sinews He measured The stretching of long wires supporting weights and observed that the elongations ulwa s bear th same proportions one to the other that the weights do that make themquot Hooke39s Law I The modulus of elasTiciTy Ehas relaTively large values for maTerials ThaT are very sTiff such as sTrucTural eTals I Steel has a modulus of 30000 ksi or 200 GPu I Alum num Eequuls approximately 10600ksi or 70 GPu I Wood is 1600 ksi or 11 Spa I The modulus of elasTiciTy is ofTen called Youug39s modulus a er anoTher English scienTisT Thomas Young 1773 1829 Linear ElasTiciTy I If The maTer39ial in The bar is considered linearelasTic and The Tensile sTress is 25000 si and The Tensile sTran is 0005 when is The modulus of elasTiciTy of The maTer39ia 058 3 E2 s 7 25000 psi 7 0005 7 E Linear ElasTic iTy I If you subsTiTuTe The formulas for sTress and sTrain inTo Hooke39s Law you ge Group Problem 3 I DeTermine The crosssecTional area of a 100fooT sTeel cable supporTing a 25 000 lbs Tensile force while noT exceed The an allowable Tensile sTress of 40 000 psi or aximum elongaTion of 01H Assume The modulus of elasTiciTy of sTeel is E 29 000 000 psi P P 039 3 A A 039 757 25000b 7 1 a 40000psi CIVL 1101 Surveying Introduction 18 InTroducTion To MeasuremenTs Why do we need me03uremenTs InTroducTion To MeasuremenTs I Some of The earliesT surviving measuring devices include gold scales recovered in presenTday Greece from The Tombs of Mycenaean kings InTroducTion To MeasuremenTs I The Tombs of EgypTian pharaohs The pyramids were consTrucTed by builders using no more Than simple rulers The pyramids are regular symmeTric and aligned wiTh The EarTh39s axis InTroducTion To MeasuremenTs I Babylon EgypT and The ciTy sTaTes of Greece all had sTandards for commercial measuring devices I By abouT 500 BC AThens had iTs own cenTral deposiTory of official weighTs and measures The Tholos InTroducTion To Surveying Early Hisfory of Surveying I IT is impossible To deTermine when surveying was firsT use I Renave not the ancient landmark which thy fathers have set DeuTeronomy 1914 I The word geometryis derived from The Greek meaning earth measurements Early Hisfory of Surveying I In EgypT surveyors were called rope sTreTchersquot because They used ropes To measure I Roman surveyors goT Their name gromaTici from The groma Wm hilgMurmlhsasu ennedugmmmxwmi CIVL 1101 Surveying Introduction 28 Introduction to Surveying Introduction to Surveying Types f lmy I ludsnnys aides type If surveys and Have been perfarmed since eariiest recarded I hwy ssmys iacatian er ab eats and measuring the reiief raugimess er r ree dimensianai variatians I suns iacatian er naturai and artificiai sbyeers aiang aprsyssea raute far a Highway miran canai pipe me pawer iine er ether uti wy Types of Slways I at u Ika slrns use ta iay cut streets pian sewer systems and prepare maps l ashnib sunys iaca ting structures and pravidmg required eieva tian paints during rreir ca structian I linkmbi sun spertaintaiakes streams and errer bodies er water Introduction to Surveying Introduction to Surveying Types of lmy Marin slrnys reiarea ta ryarsgrapme surveys burrrey are rrsugrrrs caver a breeder area I Mile slrnys reiative pasitians and eievatians er undergraund shafts geaiagicai farmatians etc I Fmsh1 irt0121 sun I Inkymum slrns prmgraprs generaiiy aeriai are used in canJunctian wwr iimited graund surveys Types r Sunday I 4sIm slrns pravide rre pasitians and dimensians errre reaures afti39ie praJect as rrey were actuaiiy canstructe allnlslrnys pravides verticai and Harixantai rerereree paints Introduction to Surveying Introduction to Measurements mu sunning I m I Typicaiiy we are accustamed ta quotum but m quotInsuring I Engineers are cancerned wwh distances eievatians vaiumes direction and weighrs I Fundamentai principie er measuring N ntsmnlll is um and lb Im win is unr haw CIVL 1101 Introduction to Measurements Accuracy and Precision l Accuracy degree of perfection obtained in a measurement I Precision the closeness of one measurement to Introduction to Measurements Accuracy and Precision Target 2 This target grouping is accurate Surveying Introduction 38 Introduction to Measurements Accuracy and Precision Target 1 This target grouping is precise Introduction to Measurements Accuracy and Precision Target 3 This target grouping is accurate and precise Introduction to Measurements Accuracy and Precision I Better precision does not necessarily mean better accuracy I In measuring distance precision is defined as error of measuremem precrsron I a ls39fance measured I Here are a couple of other web s r Introduction to Measurements Accuracy and Precision ites for additional info mation in accuracy and precision tntml m en Wm Bdlaor Wm Accuracv CIVL 1101 Surveying Introduction 48 In l39rod uc l39ion l39o Measurements In l39rod uc l39ion l39o Measurements Accuracy and Precision I For exampie it adistance at 4200 teet is measured and the error is estimated 007 feet then the precision is 07 feet 1 mm 4200 feet 6 000 I The ObJeCtive of surveying is to make measurements that are both precise and accurail Source of Errors I Personal Errors 7 no suryeyor has pertect senses at sight and touch I Instrument Errors 7 devices cannot be manutactured pertectiy wear and tear and compatibiiity With other components I Natural Errors 7 temperature Wind moisture magnetic variation etc In l39rod uc l39ion l39o Measurements In l39rod uc l39ion l39o Measurements Syste matic and Accidental Errors I Systematic or Cumulative Errors 7 typicaiiy stays constant in sign and magnitude I Accidental Compensating or Random Errors 7 the magnitude and direction at the error is beyond the controi of the surveyor Group Problem I How long is the hallway outside the classroom I How did you measure this distance what was your precision I what is your accuracy 7 I By the way I measured the hallway with a tape and determined it to be l99 20 feet In l39rod uc l39ion l39o Measurements In l39rod uc l39ion l39o Measurements Repeated Measurements of a Single Quantity I When asingie quantity is measured severa time t s random rrors tend to accumuiate in proportion to the square root of the number of measurements ETora i 5J5 Repeated Measurements of a Single Quantity I If adistatice is measured 9 time and the estimated error in each meas ement is 0 05 feet what is the estimate of the totai error7 E7390m i 5J5 E osfr 7390 CIVL 1101 Surveying Introduction 58 Infr39od ucfion 1390 Measuremenfs Repeated Measurements of a Single Quantity I Surveyors iypicaHy measure a series of quantities distance angies eieuaiians etc I A circie is made up of 360 degrees or 360 A degree is made up of 60 minutes 31 60 A minute is made up of 60 secands 3139 Infr39od ucfion 1390 Measuremenfs Repeated Measurements of a Single Quantity I If an angie is measured ien time and ine esiimaied error in each measurement is 30 seconds what is the estimate of ihe iaiai error EM 3039R13 94quot Infr39od ucfion 1390 Measuremenfs A Series of Unrepeated Measurements I wnen aseries of measurements are made Wiin prababie errors at 52 E inen ine iaiai prababie error is E Tora Infr39od ucfion 1390 Measuremenfs A Series of Unrepeated Measurements I wnatistne praeaeie err Erml iJElZ 522 E2 ioognz oo1 2 40159 40429 Infr39od ucfion 1390 Measuremenfs Significant Figures I Measurements can be precise aniy ta tne degree tnat easuring instrument is precise I The n mber at significant figures tne number at digits yau are certain abaut pius ane tnat is estim I Far exampie teiis yautnatyau snauid 9a dawn Centrai Avenue 15 miies and turn iett unatsnauid yen da39 Infr39od ucfion 1390 Measuremenfs Significant Figures I Far exampie yau measure 342 H and 343 ff I Yen esfimafe The disahce as 3426 H I wnat is tne significance at reparting avaiue at 3426 ft CIVL 1101 Surveying Introduction 68 Introduction to Measurements Significant Figures I The answer obtained by solving a problem can107 be more accurate than the Information used I For example If you measure two loads of concrete as 23 5 cubic yards yd3 and 31 yd3 what is t e an estimate of the total amount of concrete Introduction to Measurements Significant Figures 3600620 7 significant figures 102 3 significant figures 000304 3 significant figures Introduction to Measurements Significant Figures I Zeroes between other significant figures are significant 2307 1007 4 significant figures 4 significant figures Introduction to Measurements Significant Figures I For numbers less than one zeroes immediately to the right of the decimal place are norsignificant 00007 003401 1 significant figures 4 significant figures Introduction to Measurements Significant Figures I Zeroes placed as the end of a decimal number are significant 0700 39030 3 significant figures 5 significant figures Introduction to Measurements Significant Figures I When a number ends with one or more zeros to the left of the decimal you must indicate the exact number of significant figures How man si nificant 420000 guresgy 9 CIVL 1101 Surveying Introduction 78 InTroducTion To MeasuremenTs Significant Figures I When a number ends wiTh one or more zeros To The lefT of The decimal you musT indicaTe The exacT number of significanT figures 432 105 4320 105 4 significanT figures 3 significanT figures InTroducT ion To MeasuremenTs Significant Figures Mathematical Operations I When Two numbers are mulTiplied or divided The answer should noT have more significanT figures Than Those in The facTor wiTh The leasT number o significanT figures 5 SW cam figures 3 Significam figures 5 Significam figures 4 Sigmf cam gures InTroducTion To MeasuremenTs Significant Figures Mathematical Operations I Typically you wanT To carry more decimal places in The your calculaTions and round of The final answer To correcT number of significanT figures 3 Sigmf cam aws 5 SW cam figures 325 x 46962 InTroducT ion To MeasuremenTs Significant Figures Mathematical Operations I In addiTion and subTracTion The final answer should correspond To The column full of significanT figures InTroducTion To MeasuremenTs Significant Figures Mathematical Operations I When The answer To a calculaTion conTains Too many significanT figures iT musT be rounded off I One way of rounding off involves mderesfhla hg The answer for five of These digiTs 0 1 2 3 and 4 and overes maTIy The answer for The oTher five 5 6 7 and 9 InTroducT ion To MeasuremenTs Significant Figures Mathematical Operations I This approach To rounding off is summarized as follows I If The digiT is smaller Than 5 drop This digiT and leave The remaining number unchanged Thus 1684 becomes 168

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