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 Leelard- charoen 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 skill- ful 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 man- aged 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 pro- vided 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
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
Symbols A area At.Aw area of flange;area of web a,b,c dimensions,distances C centroid,compressive force,constant of integration distance from neutral axis to outer surface of a beam D diameter d diameter,dimension,distance E modulus of elasticity ErE 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) fr torsional flexibility of a bar G modulus of elasticity in shear 8 acceleration of gravity H height,distance,horizontal force or reaction,horsepower h height,dimensions moment of inertia (or second moment)of a plane area Le lyI moments of inertia with respect to x,y,and z axes Ll moments of inertia with respect tox and y axes(rotated axes) product of inertia with respect to xy axes la product of inertia with respect tox axes (rotated axes) Ip polar moment of inertia 11,2 principal moments of inertia torsion constant K stress-concentration factor,bulk modulus of elasticity,effective length factor for a column spring constant,stiffness,symbol for VP/EI X
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
xvi SYMBOLS KT torsional stiffness of a bar < length,distance LE effective length of a column In,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 factor of safety,integer,revolutions per minute (rpm) 0 origin of coordinates 0" center of curvature P force,concentrated load,power P altow allowable load (or working load) critical load for a column Pp plastic load for a structure Pr P 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 4 intensity of distributed load(force per unit distance) R reaction,radius r radius,radius of gyration (r=VIA S section modulus of the cross section of a beam,shear center distance,distance along a curve T tensile force,twisting couple or torque,temperature Tp:Ty plastic torque;yield torque thickness,time,intensity of torque (torque per unit distance) te lw thickness of flange;thickness of web strain energy strain-energy density (strain energy per unit volume) ur,u modulus of resistance;modulus of toughness V shear force,volume,vertical force or reaction deflection of a beam,velocity v',v",etc. dvldx,d2vldx2,etc. W force,weight,work load per unit of area (force per unit area) x,y,2 rectangular axes (origin at point O) xe ye Zc rectangular axes (origin at centroid C) x,y,Z coordinates 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
SYMBOLS xvii Z plastic modulus of the cross section of a beam angle,coefficient of thermal expansion,nondimensional ratio B angle,nondimensional ratio,spring constant,stiffness BR rotational stiffness of a spring 2 shear strain,weight density (weight per unit volume) Yy Yy Yax shear strains in xy,yz,and zr planes Yxy shear strain with respect toxy axes(rotated axes) Ye shear strain for inclined axes c deflection of a beam,displacement,elongation of a bar or spring AT temperature differential p,y plastic displacement;yield displacement normal strain ee normal strains in x,y,and z directions ∈x151 normal strains in x and y directions (rotated axes) E8 normal strain for inclined axes e1,e2,e3 principal normal strains lateral strain in uniaxial stress ET thermal strain Ey yield strain 8 angle,angle of rotation of beam axis,rate of twist of a bar in torsion (angle of twist per unit length) angle to a principal plane or to a principal axis angle to a plane of maximum shear stress K curvature (K=1/p) 入 distance,curvature shortening Poisson's ratio radius,radius of curvature (p 1/K),radial distance in polar coordinates,mass density (mass per unit volume) normal stress 0y2 normal stresses on planes perpendicular to x,y,and z axes Ox oy normal stresses on planes perpendicular to xy axes (rotated axes) ca normal stress on an inclined plane 0102,03 principal normal stresses Callow allowable stress(or working stress) Oex critical stress for a column (r=PrA) opl proportional-limit stress d residual stress OT thermal stress oU,Oy ultimate stress;yield stress
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
xviii SYMBOLS T shear stress To Tye Ta shear stresses on planes perpendicular to the x,y,and z axes and acting parallel to the y,z,and x axes x shear stress on a plane perpendicular to the x axis and acting parallel to the y axis (rotated axes) Te shear stress on an inclined plane Tallow allowable stress (or working stress)in shear TU Ty ultimate stress in shear;yield stress in shear 中 angle,angle of twist of a bar in torsion 中 angle,angle of rotation angular velocity,angular frequency (=2mf) *A star attached to a section number indicates a specialized or advanced topic. One or more stars attached to a problem number indicate an increasing level of difficulty in the solution. Greek Alphabet A Alpha Nu B B Beta Z Xi T y Gamma 0 0 Omicron △ 6 Delta Π 不 Pi E Epsilon P P Rho Z g Zeta 0 Sigma H 7 Eta T 入 Tau 0 8 Theta Y N Upsilon Iota Φ 中 Phi K Kappa X X Chi Lambda 亚 业 Psi M u Mu 2 w Omega
xviii SYMBOLS t shear stress txy, tyz, tzx shear stresses on planes perpendicular to the x, y, and z axes and acting parallel to the y, z, and x axes tx1y1 shear stress on a plane perpendicular to the x1 axis and acting parallel to the y1 axis (rotated axes) tu shear stress on an inclined plane tallow allowable stress (or working stress) in shear tU, tY ultimate stress in shear; yield stress in shear f angle, angle of twist of a bar in torsion c angle, angle of rotation v angular velocity, angular frequency (v 2pf ) Greek Alphabet a Alpha n Nu b Beta j Xi g Gamma o Omicron d Delta p Pi e Epsilon r Rho z Zeta s Sigma h Eta t Tau u Theta y Upsilon i Iota f Phi k Kappa x Chi l Lambda c Psi ! m Mu " v Omega ★A star attached to a section number indicates a specialized or advanced topic. One or more stars attached to a problem number indicate an increasing level of difficulty in the solution.