Mechanics of materials

936 Pages·1997·102.01 MB·English

by  James M. Gere

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Conversions Between U.S. Customary Units and SI Units
Timesconversionfactor
Customaryunit EqualsSIunit
Accurate Practical
1
Acceleration(linear)
footpersecondsquared ft/s^ 0.3048* 0.305 meterpersecondsquared ra/s-
inchpersecondsquared in./s2 0.0254* 0.0254 meterpersecondsquared m/s^
Area
squarefoot ft^ 0.09290304* 0.0929 squaremeter m^
• squareinch in.2 645.16* 645 squaremillimeter mm^
Density(mass)
(Specificmass)
slugpercubicfoot slug/ft3 515.379 515 kilogrampercubicmeter kg/m'
Density(weight)
(Specificweight)
poundpercubic foot lb/ft' 157.087 157 newionpercubicmeter N/m'
poundpercubicinch lb/in.' 271.447 271 kilonewtonpercubic
meter kN/m-'
Energy;work
foot-pound ft-lb 1.35582 1.36 joule J
kiiouatt-hour kWh 3.6* 3.6 megajoule MJ
Britishthermalunit Btu 1055.06 1055 joule J
Force
pound lb 4.44822 4.45 newton N
kip(lOOOpounds) k 4.44822 4.45 kilonewton kN
Forceperunitlength
(Intensityofforce)
poundperfool lb/ft 14.5939 14.6 newtonpermeter N/m
poundperinch lb/in. 175.127 175 newtonpermeter N/m
kipperfoot k/ft 14.5939 14.6 kilonewtonpermeter kN/m
kipperinch k/in. 175.127 175 kilonewtonpermeter kN/m
Length
foot ft 0.3048* 0.305 meter m
inch in. 25.4* 25.4 millimeter mm
mile mi 1.609344* 1.61 kilometer km
Mass
slug 14.5939 14.6 kilogram kg
Momentofaforce;torque
Nm
pound-foot lb-ft 1.35582 1.36 newtonmeter
Nm
pound-inch Ib-in. 0.112985 0.113 newtonmeter
kip-foot k-ft 1.35582 1.36 kilonewtonmeter kNm
kip-inch k-in. 0.112985 0.113 kilonewtonmeter kNm
1
Conversions Between U.S. Customary Units and SI Units uouiinued)
Timesconversionfactor
Customaryunit EqualsSIunit
Accurate Practical
Momentofinertia(area)
inchtofourthpower in.^ 416.231 416.000 millimetertofourth
power mm""
inchtofourthpower in.^ 0.416231 X 10-^ 0.416 X 10-* metertofourthpower m^
Momentofinertia(mass)
slugfootsquared slug-ft- 1.35582 1.36 kilogrammetersquared kgm-
Power
W
foot-poundpersecond ft-lb/s 1.35582 1.36 watt
w
foot-poundperminute ft-lb/min 0.0225970 0.0226 watt
horsepower
w
(550ft-lb/s) hp 745.701 746 watt
Pressure:stress
poundpersquarefoot psf 47.8803 47.9 pascal(N/m-) Pa
poundpersquareinch psi 6894.76 6890 pascal Pa
kippersquarefoot ksf 47.8803 47.9 kilopascal kPa
kippersquareinch ksi 6.89476 6.89 megapascal MPa
Sectionmodulus
inchtothirdpower in.' 16,387.1 16.400 millimetertothird
power mm'
inchtothirdpower in.3 16.3871 X 10-<' 16.4 X lO" metertothirdpower m'
Velocity(linear)
footpersecond ft/s 0.3048* 0.305 meterpersecond m/s
inchpersecond in./s 0.0254* 0.0254 meterpersecond m/s
mileperhour mph 0.44704* 0.447 meterpersecond m/s
mileperhour mph 1.609344* 1.61 kilometerperhour km/h
Volume
cubicfoot ft^ 0.0283168 0.0283 cubicmeter m^
cubicinch in? 16.3871 X I0-* 16.4 X 10-" cubicmeter m^
cubicinch in? 16.3871 16.4 cubiccentimeter(cc) cm'
gallon(231 in.^) gal. 3.78541 3.79 liter L
gallon(231 in.^) gal. 0.00378541 0.00379 cubicmeter m-^
*Anasteriskdenotesanexactconversionfactor
Note:ToconvertfromSIunitstoUSCSunits,dividebytheconversionfactor
Temperature Conversion Formulas
/( C) = ^[TC^) - 32] = 7-(K) - 273.15
T(K) = "tITCF) - 32] + 273.15 = 7-(°C) + 273.15
n'F) = ^TrC) + 32 = -|r(K) - 459.67
Digitized by the Internet Archive
2011
in
http://www.archive.org/details/mechanicsofmaterOOgere
FOURTH EDITION
MECHANICS
OF MATERIALS
JAMES M. GERE
Professor Emeritus, Stanford University
STEPHEN TIMOSHENKO
P. (i878-i972)
Late Professor, Stanford University
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Includpe.sindexes.cm. 11560MexicoD.F..Mexico
ISBN0-534-93429-3(he). ISBN0-534-95102-3 InternationalThomsonPublishingJapan
I.Strengthofmaterials. I.Timoshenko,StephenP.,1878- HirakawachoKyowaBuilding.31
1972.
2-2-1Hirakawacho
II.Title. Chiyoda-ku,Tokyo102
TA405.G44 1997
Japan
624.I7I-dc20 CIP
ThomasNelsonAustralia
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FreeCopyEditionISBN0-534-95102-3 53227Bonn,Germany
CONTENTS
Preface ix
Symbols xiii
GreekAlphabet XVI
TENSION, COMPRESSION, AND SHEAR
1
1.1 Introductionto MechanicsofMaterials 1
1.2 Normal Stress andStrain 3
1.3 Mechanical PropertiesofMaterials 9
1.4 Elasticity, Plasticity, andCreep 19
1.5 LinearElasticity, Hooke'sLaw,andPoisson'sRatio 22
1.6 ShearStressand Strain 27
1.7 Allowable StressesandAllowableLoads 37
1.8 DesignforAxialLoadsandDirect Shear 42
Problems Al
AXIALLY LOADED MEMBERS 65
2.1 Introduction 65
2.2 Changes inLengthofAxiallyLoadedMembers 66
2.3 ChangesinLengthofNonuniformBars 74
2.4 Statically IndeterminateStructures 80
2.5 Thermal Effects 91
2.6 Stresseson InclinedSections 99
2.7 StrainEnergy 110
*2.8 ImpactLoading 122
*2.9 RepeatedLoadingandFatigue 132
*2.10 StressConcentrations 134
*2.11 NonlinearBehavior 140
*2.12 ElastoplasticAnalysis 147
Problems 152
*Asterisksdenotespecializedandadvancedtopics III
71
IV CONTENTS
TORSION 187
3.1 Introduction 187
3.2 TorsionalDeformationsofaCircularBar 188
3.3 CircularBarsofLinearlyElasticMaterials 19
3.4 NonuniformTorsion 203
3.5 StressesandStrains in Pure Shear 209
3.6 RelationshipBetween Moduli ofElasticityEand G 216
3.7 TransmissionofPowerbyCircularShafts 21
3.8 StaticallyIndeterminateTorsional Members 222
3.9 Strain EnergyinTorsionandPure Shear 225
3.10 Thin-WalledTubes 232
*3.11 StressConcentrationsinTorsion 241
*3.12 NonlinearTorsionofCircularBars 243
Problems 248
SHEAR FORCES AND BENDING MOMENTS 267
4.1 Introduction 267
4.2 TypesofBeams, Loads,andReactions 267
4.3 ShearForcesandBendingMoments 272
4.4 RelationshipsBetweenLoads, ShearForces, and
BendingMoments 278
4.5 Shear-ForceandBending-MomentDiagrams 283
Problems 293
STRESSES IN BEAMS (BASICTOPICS) 303
5.1 Introduction 303
5.2 PureBendingandNonuniformBending 304
5.3 CurvatureofaBeam 304
5.4 Longitudinal StrainsinBeams 306
5.5 NormalStressesinBeams(LinearlyElasticMaterials) 310
5.6 DesignofBeamsforBending Stresses 321
5.7 NonprismaticBeams 328
5.8 ShearStresses in BeamsofRectangularCross Section 332
5.9 ShearStresses inBeamsofCircularCrossSection 341
5.10 ShearStressesintheWebsofBeamswithFlanges 342
5.11 Built-upBeamsandShearFlow 349
5.12 Beams withAxial Loads 353
*5.13 StressConcentrations in Bending 359
Problems 361
1
CONTENTS
STRESSES IN BEAMS (ADVANCEDTOPICS) 391
6.1 Introduction 391
6.2 Composite Beams 391
6.3 Transformed-SectionMethod 400
6.4 Doubly Symmetric Beams with InclinedLoads 405
6.5 BendingofUnsymmetric Beams 412
6.6 The Shear-CenterConcept 420
6.7 ShearStresses in BeamsofThin-WalledOpenCross
Sections 422
6.8 ShearCentersofThin-WalledOpen Sections 430
6.9 Elastoplastic Bending 438
6.10 NonlinearBending 446
Problems 455
ANALYSIS OF STRESS AND STRAIN 473
7.1 Introduction 473
7.2 PlaneStress 474
7.3 Principal StressesandMaximum ShearStresses 482
7.4 Mohr'sCircleforPlaneStress 492
7.5 Hooke'sLawforPlaneStress 507
7.6 Triaxial Stress 51
7.7 Plane Strain 516
Problems 531
APPLICATIONS OF PLANE STRESS (PRESSURE VESSELS,
BEAMS, AND COMBINED LOADINGS) 549
8.1 Introduction 549
8.2 Spherical PressureVessels 549
8.3 Cylindrical PressureVessels 556
8.4 MaximumStressesinBeams 563
8.5 CombinedLoadings 572
Problems 587
VI CONTENTS
DEFLECTIONS OF BEAMS 599
9.1 Introduction 599
9.2 Differential Equationsofthe DeflectionCurve 599
9.3 Deflectionsby Integrationofthe Bending-Moment
Equation 605
9.4 Deflectionsby Integrationofthe Shear-Forceand
Load Equations 615
9.5 MethodofSuperposition 620
9.6 Moment-AreaMethod 628
9.7 Nonprismatic Beams 637
9.8 Strain EnergyofBending 641
*9.9 Castigliano'sTheorem 646
*9.10 Deflections Producedby Impact 658
*9.11 TemperatureEffects 660
Problems 662
10
STATICALLY INDETERMINATE BEAMS 681
10.1 Introduction 681
10.2 TypesofStatically Indeterminate Beams 682
10.3 Analysisbythe Differential Equationsofthe Deflection
Curve 684
10.4 MethodofSuperposition 691
"10.5 Continuous Beams 701
*10.6 Temperature Effects 711
*10.7 LongitudinalDisplacementsattheEndsofaBeam 714
Problems 718
11
COLUMNS 731
11.1 Introduction 731
11.2 BucklingandStability 732
11.3 Columnswith PinnedEnds 735
11.4 ColumnswithOtherSupportConditions 746
11.5 Columns with Eccentric Axial Loads 757
11.6 TheSecant Formula forColumns 762
11.7 ElasticandInelasticColumn Behavior 767
11.8 Inelastic Buckling 769
11.9 Design Formulas forColumns 775
Problems 788