xillPREFACEand mathematicianswhocreated thesubjectof mechanicsof materials.Aseparatename index makes iteasyto look upanyofthesehistorical figures.AppendixesReference material appears in the appendixes at the back of the book. Muchofthematerial isintheformoftablespropertiesofplaneareas,propertiesof structural-steel shapes,properties of structural lumber,deflections andslopes of beams, and properties of materials (Appendixes D through H,respectively).In contrast, Appendixes A and B are descriptive-the former gives adetailed description of theSI and USCS systems ofunits,and the latterpresents the methodology for solving problems in mechanics. Includedin the latterare topics such as dimensional consistency and significantdigits. Lastly, as a handy time-saver, Appendix C provides a listing ofcommonlyusedmathematicalformulas.S.P.Timoshenko(1878-1972)andJ.M.Gere(1925-2008)Many readers of this book will recognize the name of Stephen P.Timoshenko-probablythemostfamous name inthefieldofappliedmechanics.Timoshenko is generally recognized as theworld's most out-standingpioneerin appliedmechanics.He contributed manynewideasand concepts and becamefamousforbothhis scholarship and histeach-ing.Through his numerous textbooks he made a profound change in theteachingof mechanics notonlyinthiscountrybut wherevermechanics istaught.Timoshenko was bothteacher andmentor toJamesGereandprovided the motivation for the first edition of this text, authored byJames M.Gere and published in 1972; the second and each subsequentedition of this book werewrittenby JamesGereoverthecourseof hislong and distinguished tenure as author,educator, and researcher atStanford University.James Gere started as a doctoral student at Stanfordin1952and retired fromStanford asaprofessorin1988havingauthoredthis and eight other wellknown and respected text books on mechanics,and structural and earthquake engineering.He remained active atStanfordas ProfessorEmeritus untilhis death in Januaryof2008.Abrief biography of Timoshenko appears in thefirstreference attheback of the book, and also in an August 2007 STRUCTURE maga-zine article entitled "Stephen P Timoshenko: Father of EngineeringMechanics in the U.S."byRichard G.Weingardt, P.E.This articlepro-vides an excellent historical perspective on this and the many otherengineering mechanics textbooks written by each of these authors.AcknowledgmentsTo acknowledge everyone who contributed to this book in some manner isclearlyimpossible,butIoweamajordebttomyformer Stanford teachers,especially my mentor and friend, and lead author, James M.Gere.I amalso indebted to the manyteachers of mechanics and reviewers of thebook who have helped to shape this textbook in its various editions over
PREFACE xiii and mathematicians who created the subject of mechanics of materials. A separate name index makes it easy to look up any of these historical figures. Appendixes Reference material appears in the appendixes at the back of the book. Much of the material is in the form of tables—properties of plane areas, properties of structural-steel shapes, properties of structural lumber, deflections and slopes of beams, and properties of materials (Appendixes D through H, respectively). In contrast, Appendixes A and B are descriptive—the former gives a detailed description of the SI and USCS systems of units, and the latter presents the methodology for solving problems in mechanics. Included in the latter are topics such as dimensional consistency and significant digits. Lastly, as a handy time–saver, Appendix C provides a listing of commonly used mathematical formulas. S.P. Timoshenko (1878–1972) and J.M. Gere (1925–2008) Many readers of this book will recognize the name of Stephen P. Timoshenko—probably the most famous name in the field of applied mechanics. Timoshenko is generally recognized as the world’s most outstanding pioneer in applied mechanics. He contributed many new ideas and concepts and became famous for both his scholarship and his teaching. Through his numerous textbooks he made a profound change in the teaching of mechanics not only in this country but wherever mechanics is taught. Timoshenko was both teacher and mentor to James Gere and provided the motivation for the first edition of this text, authored by James M. Gere and published in 1972; the second and each subsequent edition of this book were written by James Gere over the course of his long and distinguished tenure as author, educator, and researcher at Stanford University. James Gere started as a doctoral student at Stanford in 1952 and retired from Stanford as a professor in 1988 having authored this and eight other well known and respected text books on mechanics, and structural and earthquake engineering. He remained active at Stanford as Professor Emeritus until his death in January of 2008. A brief biography of Timoshenko appears in the first reference at the back of the book, and also in an August 2007 STRUCTURE magazine article entitled “Stephen P. Timoshenko: Father of Engineering Mechanics in the U.S.” by Richard G. Weingardt, P.E. This article provides an excellent historical perspective on this and the many other engineering mechanics textbooks written by each of these authors. Acknowledgments To acknowledge everyone who contributed to this book in some manner is clearly impossible, but I owe a major debt to my former Stanford teachers, especially my mentor and friend, and lead author, James M. Gere. I am also indebted to the many teachers of mechanics and reviewers of the book who have helped to shape this textbook in its various editions over
xivPREFACEthe years. With each new edition, their advice has resulted in significantimprovementsinbothcontentandpedagogy.I wishtoalso acknowledgemyStructural Engineering and Mechanicscolleagues at Georgia Institute of Technology:James Craig,ReggieDesRoches,Mulalo Doyoyo,Bruce Ellingwood,Leroy Emkin,RamiHaj-Ali,Larry Jacobs,Larry Kahn,Kim Kurtis,RobertoLeon, YangWang,Don White, Kenneth (Mac) Will,Arash Yavari, and Abdul Zureick.I am especiallygrateful to Jim Craig,Rami Haj-Ali,Larry Jacobs,LarryKahn, Roberto Leon, Don White, Mac Will and Abdul Zureick, all ofwhom provided valuableadvice on various aspects of therevisionsandadditions leading to the seventh edition. It is a privilege to work with allof theseeducators andtolearnfromtheminalmostdailyinteractionsanddiscussions about structural engineering and mechanics in the context ofresearch and higher education.Two of my graduate research assistants, Mr.Kanoknart Leelard-charoen and Ms.Jee-Eun Hur,provided invaluable assistance inevaluating and solving many of the new and revised problems.Theircareful attention todetail was an important contribution to the currentedition.The editing and production aspects of the book were always in skill-ful and experienced hands,thanks to thetalented and knowledgeablepersonnel of Cengage Learning (formerly Thomson Learning).Theirgoal wasthe sameasmineto producethebest possible seventheditionofthistext,never compromisingonany aspectofthebook.The people with whom I have had personal contact at CengageLearning are Christopher Carson,Director, Global Engineering ProgramCengageLearning,who,along with Jim Gere,helped to involvemeandthen guide me through the project; Hilda Gowans, Senior DevelopmentalEditor,Cengage Learning,Engineering,who was always available toprovide information and encouragement; Nicola Winstanley who man-aged all aspects ofnewphoto selection; Andrew Adams,who created thecovers; Peter Papayanakis, who created the interior book design; andLaurenBetsos,GlobalMarketing Services Coordinator,who developedpromotional material in support of the text. I would like to especiallyacknowledgetheworkof RoseKernan of RPKEditorial Services,whoedited the manuscript and laid out the pages.To each of these individualsI express my heartfelt thanks not only for a job well done but also forthe friendly and considerate way in which it was handled.I am deeply appreciative of the patience and encouragement pro-vided bymyfamily,especiallymy wife,Lana,throughoutthisproject.Finally,I am honored and extremelypleased to beinvolved in thisendeavor,at the invitation ofmymentor and friend of thirty eight years,Jim Gere,which extends this textbook toward thefortyyearmark.Itooam committed to the continued excellence of thistext and welcomeallcomments and suggestions.Please feel free to provide me with yourcritical inputatbgoodno@ce.gatech.edu.BARRYJ.GOODNOAtlanta, Georgia
xiv PREFACE the years. With each new edition, their advice has resulted in significant improvements in both content and pedagogy. I wish to also acknowledge my Structural Engineering and Mechanics colleagues at Georgia Institute of Technology: James Craig, Reggie DesRoches, Mulalo Doyoyo, Bruce Ellingwood, Leroy Emkin, Rami Haj-Ali, Larry Jacobs, Larry Kahn, Kim Kurtis, Roberto Leon, Yang Wang, Don White, Kenneth (Mac) Will, Arash Yavari, and Abdul Zureick. I am especially grateful to Jim Craig, Rami Haj-Ali, Larry Jacobs, Larry Kahn, Roberto Leon, Don White, Mac Will and Abdul Zureick, all of whom provided valuable advice on various aspects of the revisions and additions leading to the seventh edition. It is a privilege to work with all of these educators and to learn from them in almost daily interactions and discussions about structural engineering and mechanics in the context of research and higher education. Two of my graduate research assistants, Mr. Kanoknart Leelardcharoen and Ms. Jee-Eun Hur, provided invaluable assistance in evaluating and solving many of the new and revised problems. Their careful attention to detail was an important contribution to the current edition. The editing and production aspects of the book were always in skillful and experienced hands, thanks to the talented and knowledgeable personnel of Cengage Learning (formerly Thomson Learning). Their goal was the same as mine—to produce the best possible seventh edition of this text, never compromising on any aspect of the book. The people with whom I have had personal contact at Cengage Learning are Christopher Carson, Director, Global Engineering Program, Cengage Learning, who, along with Jim Gere, helped to involve me and then guide me through the project; Hilda Gowans, Senior Developmental Editor, Cengage Learning, Engineering, who was always available to provide information and encouragement; Nicola Winstanley who managed all aspects of new photo selection; Andrew Adams, who created the covers; Peter Papayanakis, who created the interior book design; and Lauren Betsos, Global Marketing Services Coordinator, who developed promotional material in support of the text. I would like to especially acknowledge the work of Rose Kernan of RPK Editorial Services, who edited the manuscript and laid out the pages. To each of these individuals I express my heartfelt thanks not only for a job well done but also for the friendly and considerate way in which it was handled. I am deeply appreciative of the patience and encouragement provided by my family, especially my wife, Lana, throughout this project. Finally, I am honored and extremely pleased to be involved in this endeavor, at the invitation of my mentor and friend of thirty eight years, Jim Gere, which extends this textbook toward the forty year mark. I too am committed to the continued excellence of this text and welcome all comments and suggestions. Please feel free to provide me with your critical input at bgoodno@ce.gatech.edu. BARRY J. GOODNO Atlanta, Georgia
SymbolsAareaAp,Awarea of flange; area of weba,b,cdimensions,distancesccentroid,compressiveforce,constantofintegrationcdistancefromneutralaxistooutersurfaceofabeamDdiameterddiameter,dimension,distanceEmodulus of elasticityE, E,reduced modulus of elasticity; tangent modulus of elasticityeccentricity,dimension, distance, unit volume change (dilatation)Fforcefshearflow,shapefactorforplasticbending,flexibility,frequency(Hz)JTtorsional flexibility of a barGmodulus ofelasticity in shear8acceleration of gravityHheight,distance,horizontal force or reaction,horsepowerhheight,dimensions1momentof inertia (or secondmoment)ofaplaneareaI ly.Imoments of inertia withrespect to x,y,and zaxesI lyimoments of inertia withrespecttox,and y,axes (rotated axes)iyproductof inertia with respect toxy axesIxyproduct of inertia with respect to xyi axes (rotated axes)ppolarmoment of inertia11,12principal moments of inertiaJtorsionconstantKstress-concentrationfactor,bulk modulus ofelasticity,effectivelengthfactorforacolumnKspring constant, stiffness,symbolforVP/EIXV
Symbols A area Af , Aw area of flange; area of web a, b, c dimensions, distances C centroid, compressive force, constant of integration c distance from neutral axis to outer surface of a beam D diameter d diameter, dimension, distance E modulus of elasticity Er, Et reduced modulus of elasticity; tangent modulus of elasticity e eccentricity, dimension, distance, unit volume change (dilatation) F force f shear flow, shape factor for plastic bending, flexibility, frequency (Hz) f T torsional flexibility of a bar G modulus of elasticity in shear g acceleration of gravity H height, distance, horizontal force or reaction, horsepower h height, dimensions I moment of inertia (or second moment) of a plane area Ix , Iy , Iz moments of inertia with respect to x, y, and z axes Ix1, Iy1 moments of inertia with respect to x1 and y1 axes (rotated axes) Ixy product of inertia with respect to xy axes Ix1y1 product of inertia with respect to x1y1 axes (rotated axes) IP polar moment of inertia I1, I2 principal moments of inertia J torsion constant K stress-concentration factor, bulk modulus of elasticity, effective length factor for a column k spring constant, stiffness, symbol for P/EI xv
xviSYMBOLSkTtorsional stiffness of a barLlength, distanceLEeffective lengthofa columnIn, lognatural logarithm (basee);commonlogarithm(base10)Mbendingmoment,couple,massMp,Myplasticmomentforabeam;yield momentforabeammmoment per unit length, mass per unit lengthNaxialforcenfactor ofsafety,integer,revolutionsperminute(rpm)0originof coordinatesocenter of curvaturePforce,concentratedload,powerPallowallowableload (orworkingload)Percritical loadforacolumnPpplastic load for a structureP,P,reduced-modulus load for a column;tangent-modulus loadfora columnPyyield load for a structureppressure (force per unit area)Qforce,concentrated load,firstmoment of aplaneareaqintensity of distributed load (force per unit distance)Rreaction,radiusrradius, radius of gyration (r =VIA)ssection modulus ofthe cross section ofa beam,shear centersdistance,distance alonga curveTtensileforce,twisting coupleortorque,temperatureTp,Typlastic torque; yield torquetthickness, time, intensity of torque (torque per unit distance)pwthickness offlange;thickness of webUstrain energyustrain-energy density (strain energy per unit volume)ur, ufmodulus of resistance; modulus of toughnessvshearforce,volume,verticalforceorreactionVdeflectionof abeam,velocityv',v",etc.dv/dx, d-v/dx2, etc.Wforce, weight, workwloadperunitof area(forceperunitarea)rectangular axes (origin at pointO)x,y,zrectangular axes (origin at centroid C)XeyeZcX,Jcoordinates of centroid
xvi SYMBOLS kT torsional stiffness of a bar L length, distance LE effective length of a column ln, log natural logarithm (base e); common logarithm (base 10) M bending moment, couple, mass MP, MY plastic moment for a beam; yield moment for a beam m moment per unit length, mass per unit length N axial force n factor of safety, integer, revolutions per minute (rpm) O origin of coordinates O center of curvature P force, concentrated load, power Pallow allowable load (or working load) Pcr critical load for a column PP plastic load for a structure Pr, Pt reduced-modulus load for a column; tangent-modulus load for a column PY yield load for a structure p pressure (force per unit area) Q force, concentrated load, first moment of a plane area q intensity of distributed load (force per unit distance) R reaction, radius r radius, radius of gyration (r I/A ) S section modulus of the cross section of a beam, shear center s distance, distance along a curve T tensile force, twisting couple or torque, temperature TP, TY plastic torque; yield torque t thickness, time, intensity of torque (torque per unit distance) t f , t w thickness of flange; thickness of web U strain energy u strain-energy density (strain energy per unit volume) ur, ut modulus of resistance; modulus of toughness V shear force, volume, vertical force or reaction v deflection of a beam, velocity v, v , etc. dv/dx, d2v/dx2, etc. W force, weight, work w load per unit of area (force per unit area) x, y, z rectangular axes (origin at point O) xc, yc, zc rectangular axes (origin at centroid C) x, y , z coordinates of centroid
xviiSYMBOLSzplasticmodulus of the cross sectionof a beamαangle,coefficientofthermal expansion,nondimensionalratioβangle,nondimensionalratio,spring constant,stiffnessBRrotational stiffness of a springyshear strain, weight density (weight per unit volume)shear strains in xy, yz, and zx planesYxyeye,YzxYx1y1shear strain with respect to x,y,axes (rotated axes)shear strain for inclined axesYe8deflection of a beam,displacement, elongationofa baror springATtemperature differentialOpoyplasticdisplacement; yield displacementenormal strainnormal strains in x,y,and zdirectionsE,EyEnormal strains in x, and y,directions (rotated axes)Exp Sy1normal strainforinclined axesEeprincipal normal strainsE1,E2,E3elateral strain in uniaxial stressETthermal strainyield strainEy0angle, angle of rotation of beam axis,rate of twist of a bar in torsion(angle of twist per unit length)0angletoaprincipalplaneortoaprincipalaxis0.angletoaplaneofmaximum shear stressKcurvature (k=1/p)入distance, curvature shorteningVPoisson'sratiopradius,radiusofcurvature(p=1/k),radial distancein polarcoordinates, mass density (mass per unit volume)gnormal stressnormal stresses on planes perpendicular tox,y,and z axesOrCy,Cnormal stresses on planes perpendicular to x; axes (rotated axes)OxpCylnormalstressonan inclinedplanegeprincipal normal stressesO1,2,3allowable stress (or working stress)Callowcritical stressfora column(ocr=P.r/A)Cer°plproportional-limit stressresidual stressOfthermal stressGrultimate stress; yield stressQu,y
SYMBOLS xvii Z plastic modulus of the cross section of a beam a angle, coefficient of thermal expansion, nondimensional ratio b angle, nondimensional ratio, spring constant, stiffness bR rotational stiffness of a spring g shear strain, weight density (weight per unit volume) gxy, gyz, gzx shear strains in xy, yz, and zx planes gx1y1 shear strain with respect to x1y1 axes (rotated axes) gu shear strain for inclined axes d deflection of a beam, displacement, elongation of a bar or spring T temperature differential dP, dY plastic displacement; yield displacement e normal strain ex, ey, ez normal strains in x, y, and z directions ex1 , ey1 normal strains in x1 and y1 directions (rotated axes) eu normal strain for inclined axes e1, e2, e3 principal normal strains e lateral strain in uniaxial stress eT thermal strain eY yield strain u angle, angle of rotation of beam axis, rate of twist of a bar in torsion (angle of twist per unit length) up angle to a principal plane or to a principal axis us angle to a plane of maximum shear stress k curvature (k 1/r) l distance, curvature shortening n Poisson’s ratio r radius, radius of curvature (r 1/k), radial distance in polar coordinates, mass density (mass per unit volume) s normal stress sx, sy, sz normal stresses on planes perpendicular to x, y, and z axes sx1 , sy1 normal stresses on planes perpendicular to x1y1 axes (rotated axes) su normal stress on an inclined plane s1, s2, s3 principal normal stresses sallow allowable stress (or working stress) scr critical stress for a column (scr Pcr/A) spl proportional-limit stress sr residual stress sT thermal stress sU, sY ultimate stress; yield stress