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publisher's prior permission. Violators will be prosecuted.
PRINTED BY: Stefan Dominicus <[email protected]>. Printing is for personal, private use only. No part of this book may be reproduced or transmitted without
publisher's prior permission. Violators will be prosecuted.
Conversion Factors
U.S. Customary Units to SI Units
To convert from To Multiply by
(Acceleration)
footlsecond2( ftlsec2) meter/second2( m/s2) 3.048 X 10 1*
inch/second2( in./sec2) meter/second2( m!s2) 2.54 X 10·2*
(Area)
foto 2( ft2) meter2(m2) 9.2903 X 10-2
inch2 (in.2) meter2(m2) 6.4516 X 10-4*
(Density)
pound mass/inch3 Obmlin.3) kilogram/meter3( kg/m3) 2.7680 X 104
pound mass/foot" (lbm/ft3) kilogram/meter( lqVm3) 1.6018 X 10
(Force)
kip (1000 lb) newton (N) 4.4482 X 1o:'
pound force (lb) newton (N) 4.4482
(Length)
foot (ft) meter(m) 3.048 X 10 1*
inch (in.) meter(m) 2.54 X 10-2*
mile (mi),( U.S. statute) meter(m) 1.6093 X 1o:'
mile (mi),( international nautical) meter (m) 1.852 X 103*
(Mass)
pound mass Obm) kilogram (kg) 4.5359 X 10 1
slug( lb-sec2/ft} kilogram( kg) 1.4594 X 10
ton (2000 Ibm) kilogram {kg) 9.0718 X 10Z
(Moment of force)
pound-foot( lb-ft) newton-meter( N •m) 1.3558
pound-inch Ob-in.) newton-meter( N ·m ) 0.1129 8
(Moment of inertia, area)
inch4 41.623 X 10-8
(Moment of inertia, mass)
pound-foot·second2( lb-ft-sec2) 1.3558
(Momentum, linear)
pound-second( lb-sec) kilogram-meter/second( kg-m/s) 4.4482
(Momentum, angular)
pound-foot-second Ob-ft-sec) newton-meter-second( kg·m%) 1.3558
<Power)
foot-pound/minute (ft-lblmin) watt( W) 2.2597 X 10-2
horsepOwer (550 ft-lblscc) watt (W) 7.4570 X lOZ
(Pressure, stress)
atmosphere( stdX14.7lb/in.2) newton/meter <N/m2 or Pa) 1.0133 X lOS
pound/foot2( lblft2) newton/meter( N/m2 or Pa) 4.7880 X 10
pound/inch2 Oblin.2 or psi) newton/meter <N/m2 or Pa) 6.8948 X lo:'
(Spring constant)
pound/inch( lblin.) newton/meter( N/m) 1.7513 X 102
(Velocity)
fot/o second (ftlsec) meter/second( m/s) 3.048 X 10-1*
knot (nautical mi!hr) meter/second( m/s) 5.1444 X 10 1
mile/hour( milhr) meter/second( mls) 4.4704 X 10-1*
mile/hour( milhr) kilometer/hour (km/h) 1.6093
(Volume)
foot3( ft3) meterS (m3) 2.8317 X 10-2
inch3 (in.8) meter(m3) 1.6387 X 10-5
(Work, Energy)
British thermal unit( BTU) joule (J) 1.0551 X 1o:'
foot-pound force (ft-lb) joule (J) 1.3558
kilowatt-hour (kw-h) joule (J) 3.60 X 106*
*Exact value
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Sl Units Used in Mechanics
Quantity Unit SI Symbol
(Base Units)
Length meter* m
Mass kilogram kg
Time second s
(Deriued Units)
Acceleration,l inear meter/second2 m/s2
Acceleration,a ngular radian/second2 rad/s2
Area meter2 m2
Density kilogram!meteil kg/ms
Force newton N ("' kg·mls2)
Frequency hertz Hz(= lis)
Impulse,l inear newton-second N·s
Impulse,a ngular newton-meter-second N·m·s
Moment of force newton-meter N·m
Moment of inertia,a rea meter4 m4
Moment of inertia, mass kilogram-meter2 kg·m2
Momentum,l inear kilogram-meter/second kg·m/s ("" N·s)
Momentum, angular kilogram-meter2tsecond kg·m2/s (= N·m·s)
Power watt W( "" J/s"" N·m/s)
Pressure, stress pascal Pa(= N/m2)
Productofinertia,area meter4 m4
Productofinertia,mass kilogram-meter2 kg·m2
Spring constant newton/meter N/m
Velocity, linear meter/second m/s
Velocity, angular radian/second rad/s
Volume meter3 ms
Work, energy joule J(= N·m)
(Supplementary and Other Acceptable Units)
Distance( navigation) nautical mile (= 1.852km)
Mass ton (metric) t( = 1000 kg)
Plane angle degrees (decimal) 0
Plane angle radian
Speed knot (1.852 km!h)
Time day d
Time hour h
Time minute min
*Also spelled metre.
Selected Rules for Writing Metric Quantities
Sl Unit Prefixes 1. (a) Use prefixes to keep numerical values generally between 0.1 and 1000.
(b) Use of the prefixes hecto, deka, deci, and centi should generally be avoided
Multiplication Factor Prefix Symbol
1 000 000 000 000 = 1012 tera T except for certain areas or volumes where the numbers would be awkward
1 000 000 000 = 109 giga G otherwise.
1 000 000 = 106 mega M (c) Use prefixes only in the numerator of unit combinations. The one exception
1000 = 103 kilo k is the base unit kilogram. (Example: write kN/m not N/mm; J/kg not mJ/g)
100 = 102 hecto h (d) Avoid double prefixes. (Example: write GN not kMN)
10 ""10 deka da 2. Unit designations
00.0.11 ="' 1100--21 cdeecnit i cd ((ab)) AUvsoei ad damotb fiogru mouusl tdipoluibcalet isonol iodfu usn. (iEts:ra. <Examplme: pwler:i twe rNite/m N2 n · mot nNo/tm/ Nmm))
0.0000 .0000000 . 000000111 === 111000 --639 nmmaiincllroio nm,., 3. (Nc)u mEbexpor ngreonutsp irengfe r to entire unit.( Example: mm2 means (mm)2)
0.000 000 000 001 = 10-12 pic o p Use a space rather than a comma to separate numbers in groups of three,
counting from the decimal point in both directions. (Example: 4 607 321.048 72)
Space may be omitted for numbers of four digits. (Example: 4296 or 0.0476)
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ENGIN EERING MECHANICS
VOLUME 1
Sl VE RSION
EIG HTH EDITION
J.L. MERIAM
L.G. KRAIGE
Virginia Polytechnic Institute
and State University
J.N. BOLTON
Bluefield State College
WILEY
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On thec over:TheAuditorio deT•eAndearinMf aert in"i sl ocatiedn S antaC ruz deTeneritfheeca, p itaolf
theC anarIys landSsp,a inI.tw as designedb ya rchiteScatn tiagCoa latraVvaal lasn dw aso penedi n2 003.
Copyright© 2016, 2013 John Wiley & Sons Singapore Pte. Ltd.
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fOREWORD
This series of textbooks was begun in 1951 by the late Dr. James L. Meriam. At that
time, the books represented a revolutionary transformation in undergraduate mechanics
education. They became the definitive textbooks for the decades that followed as well as
models for other engineering mechanics texts that have subsequently appeared. Published
under slightly different titles prior to the 1978 First Editions, this textbook series has
always been characterized by logical organization, clear and rigorous presentation of the
theory, instructive sample problems, and a rich collection of real-life problems, all with a
high standard of illustration. In addition to the U.S. versions, the books have appeared in
SI versions and have been translated into many foreign languages. These textboko s collec
tively represent an international standard for undergraduate texts in mechanics.
The innovations and contributions of Dr. Meriam (1917-2000) to the field of engineer
ing mechanics cannot be overstated. He was one of the premier engineering educators of
the second half of the twentieth century. Dr. Meriam earned the B.E., M.Eng., and Ph.D.
degrees from Yale University. He had early industrial experience with Pratt and Whitney
Aircraft and the General Electric Company. During the Second World War he served in the
U.S. Coast Guard. He was a member of the faculty of the University of California-Berkeley,
Dean of Engineering at Duke University, a faculty member at the California Polytechnic
State University, and visiting professor at the University of California-Santa Barbara,
finally retiring in 1990. Professor Meriam always placed great emphasis on teaching, and
this trait was recognized by his students wherever he taught. He was the recipient of sev
eral teaching awards, including the Benjamin Garver Lamme Award, which is the highest
annual national award of the American Society of Engineering Education (ASEE).
Dr. L. Glenn Kraige, coauthor of the Engineering Mechanics series since the early
1980s, has also made significant contributions to mechanics education. Dr. Kraige earned
his B.S., M.S., and Ph.D. degrees at the University of Virginia, principally in aerospace
engineering, and he is Professor Emeritus of Engineering Science and Mechanics at
Vrrginia Polytechnic Institute and State University. During the mid-1970s, I had the singular
pleasure of chairing Professor Kraige's graduate committee and take particular pride in
the fact that he was the first of my fifty Ph.D. graduates. Professor Kraige was invited by
Professor Meriam to team with him, thereby ensuring that the Meriam legacy of textbook
authorship excellence would be carried forward to future generations of engineers.
In addition to his widely recognized research and publications in the field of spacecraft
dynamics, Professor Kraige has devoted his attention to the teaching of mechanics at both
introductory and advanced levels. His outstanding teaching has been widely recognized
and has earned him teaching awards at the departmental, college, university, state, re
gional, and national levels. These awards include the Outstanding Educator Award from
the State Council of Higher Education for the Commonwealth of Virginia. In 1996, the
v
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vi Foreword
Mechanics Division of ASEE bestowed upon him the Archie Higdon Distinguished Educator
Award. The Carnegie Foundation for the Advancement of Teaching and the Council for Advance
ment and Support of Education awarded him the distinction ofVirginia Professor of the Year for
1997. In his teaching, Professor Kraige stresses the development of analytical capabilities along
with the strengthening of physical insight and engineering judgment. Since the early 1980s, he
has worked on personal-computer software designed to enhance the teaching/learning process
in statics, dynamics, strength of materials, and higher-level areas of dynamics and vibrations.
Welcomed as a new coauthor for this edition is Dr. Jeffrey N. Bolton, Assistant Professor of
Mechanical Engineering Technology at Bluefield State College. Dr. Bolton earned his B.S., M.S.,
and Ph.D. in Engineering Mechanics from Virginia Polytechnic Institute and State University.
His research interests include automatic balancing of six-degree-of-freedom elastically-mounted
rotors. He has a wealth of teaching experience, including at Virginia Tech, where he was the
2010 recipient of the Sporn Teaching Award for Engineering Subjects, which is primarily chosen
by students. In 2014, Professor Bolton received the Outstanding Faculty Award from Bluefield
State College. He has the unusual ability to set high levels of rigor and achievement in the
classroom while establishing a high degree of rapport with his students. In addition to main
taining time-tested traditions for future generations of students, Dr. Bolton will bring effective
application of technology to this textbook series.
The Eighth Edition of Engineering Mechanics continues the same high standards set by
previous editions and adds new features of help and interest to students. It contains a vast col
lection of interesting and instructive problems. The faculty and students privileged to teach or
study from the Meriam/Kraige/Bolton Engineering Mechanics series will benefit from several
decades of investment by three highly accomplished educators. Following the pattern of the pre
vious editions, this textbook stresses the application of theory to actual engineering situations,
and at this important task it remains the best.
John L. Junkins
Distinguished Professor of Aerospace Engineering
Holder of the Royce E. Wisebaker '39 Chair in Engineering Innovation
Texas A&M University
College Station, Texas
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PREFACE
Engineermiencgh aniicsbs o tah foundatainodna frameworfko rm osto ft heb ranches
ofe ngineerMianngy. o ft het opicisns ucha reaass civimle,c hanicaaelr,o spaacned,
agriculteunrgailn eerainndgo ,fc ourseen gineermiencgh aniictss ealr�e b aseudp ont he
subjecotfss t atiacnsdd ynamicEsv.e ni na disciplineas eslueccht reincgailn eerpirnagc,
titionienrt sh,ec oursoefc onsidertihneeg l ectrciocmaplo nenotsf a robotidce vicoera
manufacturpirnogc esmsa,y findt hemselvfierss th avintgo d ealw itht hem echanics
involved.
Thust,h ee ngineering mescehqauneinciscs e c rititcoat lh ee ngineering curriculum.
Noto nliys t hisse quenncee edeidn i tselbfu,tco urseisn e ngineermiencgh aniaclss soe rve
tos oliditfyhe s tudenutn'dse rstandoifno gt heirm portasnutb jecitnsc,l udianpgp lied
mathematipchsy,s icasn,dg raphiIcnsa .d dititohne,s ceo ursseesr vaes e xcellseenttt ings
inw hictho s trengtphreonb lem-soalbviilnigt ies.
PHILOSOPHY
Thep rimaryp urposoeft hes tudoyf e ngineermiencgh aniicstos develtohpe c apacity
to preditchtee ffectosff orcaen dm otiownh ilcea rryinogu tt hec reatidvees igfunn ctions
ofe ngineerTihnigsc. a pacirteyq uirmeosr et hana merek nowledogfet hep hysicaanld
mathematipcrailn cipolfme esc hanicasl;sr oe quiriesdt hea bilittoyv isualpihzyes ical
configuratiinot nesr mosf r eamla teriaalcst,u aclo nstraianntdts h,e p ractilciamli tations
whicgho vertnh eb ehavioofmr a chineasn ds tructuOrneeso .f t hep rimaroyb jectiivnae s
mechaniccosu rsiest oh elpt hes tudednetv eltohpi asb ilittovy i sualwihziec,ih s s ov ital
top roblefmo rmulation. tIhnecd oenesdt,r ucotfia o mne aningfumla thematimcoadle li s
oftena more important extphearnii tessno cleu tion. Mapxriomgurme isssm adew hen
thep rinciplaensdt heilri mitatareio nlse arnteodg ethweirt hitnh eco ntexotf e ngineering
application.
Theries a frequentte ndenicnyt hep resentaotfim oenc hanitcous s ep roblemmasi nly
as a vehictloei llusttrhaetoer rya thetrh ant od eveltohpe orfyo rt hep urposeo fs olving
problemWsh.e nt hefi rsvti ewi sa llowteodp redominaptreo,b letmesn dt ob ecomoev erly
idealiazneddu nrelatteoed n gineerwiintght her esutlhta tth ee xercibseec omedsu ll,a ca
demica,n du ninteresTthiinsag p.p roacdhe privtehse s tudenotfv aluabelxep erieinnc e
formulatpirnogb leamns dt huso fd iscovertihneng e edf ora ndm eaninogf t heroy.T he
seconvdi ewp rovidbeysf art hes trongmeort ivfeo rl earnitnhge orya ndl eadtos ab etter
balanbceet weetnh eorayn da pplicatTihoecn r.u ciraollp el ayebdyi nteraensdtp urposien
providitnhegs trongpoesssti blmeo tivfeo lre arnincga nnobte o veremphasized.
Furthermoraes,m echaniecsd ucatowres s,h oulsdt restsh eu nderstandtihnagta ,t
bestt,h eorcya no nlayp proximtahteer eawlo rlodf m echanircast hetrh ant hev iewt hat
vii
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viii Preface
ther eawlo rladp proximattehset heoryT.h isd ifferenicnpe h ilosoipshi yn deebda siacn d
distinguitshheeeng sin eering ofm echanifrcosm thesc ience ofm echanics.
Overt hep asste verdaelc adesse,v eruanlf ortuntaetned enchiaevseoc curreidn e ngi
neeriendgu catiFoirns.te ,m phasoinst heg eometraincdp hysicmaela ninogfsp rerequisite
mathematiacpspe arst oh aved iminishSeedc.o ntdh,e rhea sb eena significraendtu ction
ande vene liminatoifio nns tructiingo rna phiwchsi,c hi nt hep aste nhancetdh ev isual
izatiaonnd r epresentaotfmi eocnh anipcrso blemTsh.i rd,a divna ncitnhgem athematical
leveolfo urt reatmeonftm echanitchse,r hea sb eena tendentoc ya llotwh en otational
manipulatoifvo enc toopre ratitoonm sa sko rr eplagceeo metrviics ualizaMteicohna.n iicss
inherenat sluyb ject wdheipcehn dosn g eometraincdp hysicpaelr ception,w eas nhdo uld
increaosuere fforttsod eveltohpi asb il.i ty
A specinaolt oen t heu seo fc omputeirsis n o rdeTrh.e e xperienocfef ormulatpirnogb
lemsw,h erree asoann dj udgmenatr ed evelopeidsv, a stmloyr ei mportafnotrt hes tudent
thani st hem anipulateixveer ciisne carroyuitnt gh es olutiFoonrt. h irse asoconm,p uter
usagmeu stb ec arefuclolnyt rolAltep dr.e sencto,n strucfrteien-gb oddiya gramasn df or
mulatignogv erning equatioanrseb estd onew ithp encialn dp ape.rO n theo thehra nd,
theraer ei nstanicenws h icht heso lution to theg overning equcaatnbesi to nbse c arried
outa ndd isplayuesdi ntgh ec omputeCr.o mputer-<>riepnrtoebdl esmhso ulbde g enuinien
thes ensteh at thiesar ceo nditoifod ne sigonrc riticatlobi etf yo und, rathe"rm atkhean
work" probilnew mhsi csho mep arametiesrv ariefdo rn oa pparerneta soont hetrh anto
forcea rtifiucsieao lft hec omput.eT rheset houghhtasv eb eenk epti nm indd urintgh e
desigonf th e computer-oripernotbelde misnt heE ightEhd itioTno. co nservaed equate
timef orp roblefmo rmulatiitoi nss, u ggesttehda t tshteu debneta ssignoendl ay limited
numbeorf t hec omputer-<>ripernotbelde ms.
As withp revioeudsi tiotnhsi,Es i ghtEhd itioofnE ngineering Mechanics isw ritten
witht hef oregoing phiilnosm oipnhdyI. t i si ntendperdi marifloyrt hefi rsetn gineering
coursienm echanigcesn,e ratlaluyg hitnt hes econdy eaorf s tud.Ey ngineering Mechanics
isw ritteinn a stylweh ichi sbo th concainsdefr iend.lT yhem ajore mphasiisso n basic
principalnedms e thodsr athetrh ano na multituodfse p eciacla seSst.r onegff orhta sb een
madet os howb otht hec ohesiveonfet shser elatifveelwfuy n damentiadle aasn dt heg reat
varieotfpy r oblems wthhiecshfe e wi deawsi lslo lve.
PEDAGOGICAfLE ATURES
Theb asisct ructoufrt eh itse txboocko nsisotfas n a rticwlhei crhi goroutsrleya tthse
particular subjeactht a nmdaf,to tlelro wbeydo neo rm oreS amplPer oblemfso,l lowbeyd
a grouopf P roblemTsh.e ries a ChapteRre vieawt t hee ndo fe achc haptwehri cshu mma
rizetsh em ainp ointisnt hacth apetrf,o llowbeyad ReviePwr oblesme t.
Problems
The8 9 SamplPer oblemasp peaorn s pecially cpoalgoerbsey dt hemselvTehse.s olu
tiontsot ypical sptraotbilcesam rse p resentiendd e taiIlna. d ditieoxnp,l anataonrdyc au
tionanryo te(sH elpfuHli ntsi)nb lutey paer en umber-ketyoet dh em ainp resentation.
Therea re1 060 homeworekx ercisoefws h,i chm oret han5 0 percenta ren ewt ot he
EightEhd itioTnh.ep roblesme tasr e diviidnetIdon troductory Problems andR epresen
tative Problems. Thef irssetc ticoonn sisotsfs impluen,c omplicaptreodb ledmess igntoe d
helspt udengtasi connfi dencew itht hen ewt opiwch,i lmeo sto ft hep robleimnst hes econd
sectiaorneo fa veragdei fficulatnyd l engtThh.e p robleamrse g eneraalrlrya ngiendo rder
ofi ncreasdiinffigc ulMtoy.r ed ifficuletx erciaspepse anre art hee ndo ft heR epresentative
Problems anda rem arked witthhet rianguslyamrbo l..,. . Computer-Oriented Problems,
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Preface ix
markewdi tahn a steraipspke,a trh roughtohuept r obleamnsda lsiona specisaelc tiaotn
thec oncluosfit ohneR e view Problems att hee ndo fe acchh aptTehre.a nswetor sa lplr ob
lems have beeni nap s rpoevciidaeld sectthieeo nnd o nfe attrhe ex tbook.
SIu nitasr eu setd hroughtohuebt o oke,x ceipnta limited noufmi bnetrr oductory
areaisnw hicUh. Su.n itasr em entionfeopdru rposoefcs o mpleteannedsc so ntrwaistth
SIu nits.
A notable foefta hteEu irgeh tEhd itiaosnw ,i tahl plr eviedoiutsi oinsst ,h ew ealth of
interesatnidin mgp ortant prwohbilcaehpm pslt yoe ngineedreisniggW nh.e thedri rectly
identiafises du cohr n otv,i rtuaallollfy t hep robledmesaw li tphr inciapnldep sr ocedures
inheriennt th ed esiagnnd a nalyosfie sn gineesrtirnugc taunrdem se chaniscyaslt ems.
Illustrations
Ino rdetrob rintgh eg reatpeossts idbelger eoefr ealiasnmd c lartiott yh ei llustra
tiontsh,it se xtbsoeorki ceosn tintuobee sp roducienfud l lc ol.oI rti si mporttaonn to tteh at
coliosru secdo nsistfeontrth leiy d entificoafcet ritoaniq nu antities:
• red fofro rcaensdm oments
• green fovre locaintday c celeraartrioowns
• orange dashes fosre lectterdlij ectoorfmi oevsi ng points
Subduedc oloarrseu sefdo rt hospea rtosfa ni llustrwahtiicoahnr en otc entrtaol
thep roblaetmh andW.h enevpeors sibmleec,h anisomros b jecwthsi ccho mmonhlayv ea
certacionl woirl ble p ortraiynet dh acto loArl.ol f t hefu ndamentealle menotftes c hnical
illustratiohna vwebh eiecnah n e ssentpiaarlot f t hiEsn gineering Mechanics serioefs
textboohkasv bee erne tainTehdea. u thowriss tho restthaect oen victthiaoatnh igsht an
darodf i llustriasct riiotnit coaa nlyw rittewno rki nt hefi elodfm echanics.
Special Features
We havree taitnheefd o llowhianlgl mafreka tuorfep sr eviedoiutsi ons:
• Allt heopryo rtiaornesc onstanrteleyx amiinneo dr detrom aximirzieg ocrl,a rity,
readabialnidlt ey,v oeflfr iendliness.
• KeyC oncepatrse awsi thtihnet heoprrye sentaatrieso pne ciamlalryk eadn dh igh
lighted.
• TheC haptReerv ieawrseh ighligahntdfe eda tuirteem izseudm maries.
• Approxima50t peelryc eonftth heo mewoprrko bleamrsne e wt ot hiEsi ghth Edition.
Alnle wp roblehmasv bee einn dependseonltvlieyndo rdetroe nsuarh ei gdhe groefe
accuracy.
• AlSla mplPer obleamrsep rintoensd p ecicaollloyr peadg efso qru icikd entification.
• Within-the-pchhoatpotgerraa prheps r ovidienod r detrop roviadded iticoonnanlec
tiotnoa ctusailt uatiinow nhsi csht athiacssp layaem da jorro le.
ORGANIZATION
InC hapter1, thefu ndamentcaoln ceptsn ecessafryo rt hes tudoyf m echanicsa re
established.
InC hapte2r, t hep roperotfif eosr cemso,m entsc,o uplaensdr, e sultaarnetsd eveloped
so thatth es tudemnaty p roceeddi recttolt yh ee quiliborfin uomn concurrfeonrtcs ey s
temsi nC haptSe wri thouuntn ecessbaerlialbyo rtihnerg e latitvreilvypi raolb loefmt he
equiliborfic uomn currfeonrtca ecst ionnga particle.
