List of SymbolsPuaConstant; distanceUltimate load (LRFD)A,B,C,...Forces; reactionsqShearing force per unit length; shearflowA,B, C,...PointsQA,aForceAreabQDistance; widthFirst moment ofareacTConstant; distance; radiusRadius; radius of gyrationcRCentroidForce; reactionCy, Ca,...RConstants ofintegrationRadius; modulus of ruptureCpsColumn stabilityfactorLengthsdDistance; diameter; depthElastic section modulusDtDiameterThickness; distance; tangentialeDistance; eccentricity, dilatationdeviationTETorqueModulus of elasticityTJFrequency;functionTemperatureFForceu,vRectangular coordinatesF.S.Factor of safetyuStrain-energy densityGUModulus of rigidity; shear modulusStrain energy; workhvDistance; heightVelocityHVForceShearingforceVH,J,KPointsVolume; shearI, I..wMoment ofinertiaWidth; distance; load per unit lengthProduct of inertiaw,wWeight, loadIxy ..JPolar moment of inertiaRectangular coordinates; distance;x,y,zkSpring constant; shapefactor; bulkdisplacements; deflectionsjzmodulus; constantCoordinates of centroidKZStress concentration factor;torsionalPlasticsectionmodulusα,β,Anglesspring constant~Length; spanαCoefficient ofthermal expansion;LLength; spaninfluencecoefficientLeYEffective lengthShearing strain; specific weightmMassLoad factor, dead load (LRFD)YDMCoupleLoad factor, live load (LRFD)YL8M, M....Bending momentDeformation; displacementMpEBending moment, dead load (LRFD)Normal strain6MLBending moment, live load (LRFD)Angle; slopeMu入Bending moment, ultimate load (LRFD)Direction cosinenVNumber; ratio of moduli of elasticity;Poisson'sratioRadius of curvature; distance; densitynormaldirectionppPressureaNormal stressPTForce; concentrated loadShearing stressPp$Dead load (LRFD)Angle; angle oftwist; resistance factorPLwLive load (LRFD)AngularvelocityXV
xv a Constant; distance A, B, C, . . . Forces; reactions A, B, C, . . . Points A, A Area b Distance; width c Constant; distance; radius C Centroid C1, C2, . . . Constants of integration CP Column stability factor d Distance; diameter; depth D Diameter e Distance; eccentricity; dilatation E Modulus of elasticity f Frequency; function F Force F.S. Factor of safety G Modulus of rigidity; shear modulus h Distance; height H Force H, J, K Points I, Ix, . . . Moment of inertia Ixy, . . . Product of inertia J Polar moment of inertia k Spring constant; shape factor; bulk modulus; constant K Stress concentration factor; torsional spring constant l Length; span L Length; span Le Effective length m Mass M Couple M, Mx, . . . Bending moment MD Bending moment, dead load (LRFD) ML Bending moment, live load (LRFD) MU Bending moment, ultimate load (LRFD) n Number; ratio of moduli of elasticity; normal direction p Pressure P Force; concentrated load PD Dead load (LRFD) PL Live load (LRFD) PU Ultimate load (LRFD) q Shearing force per unit length; shear flow Q Force Q First moment of area r Radius; radius of gyration R Force; reaction R Radius; modulus of rupture s Length S Elastic section modulus t Thickness; distance; tangential deviation T Torque T Temperature u, v Rectangular coordinates u Strain-energy density U Strain energy; work v Velocity V Shearing force V Volume; shear w Width; distance; load per unit length W, W Weight, load x, y, z Rectangular coordinates; distance; displacements; deflections x, y, z Coordinates of centroid Z Plastic section modulus a, b, g Angles a Coefficient of thermal expansion; influence coefficient g Shearing strain; specific weight gD Load factor, dead load (LRFD) gL Load factor, live load (LRFD) d Deformation; displacement e Normal strain u Angle; slope l Direction cosine n Poisson’s ratio r Radius of curvature; distance; density s Normal stress t Shearing stress f Angle; angle of twist; resistance factor v Angular velocity List of Symbols bee98233_FM_i-xvi_1.indd xv 11/15/13 10:21 AM
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SeventhEditionMechanics of Materials
Seventh Edition Mechanics of Materials bee98233_FM_i-xvi_1.indd 1 11/15/13 10:21 AM
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bee98233_ch01_002-053.indd 2 11/15/13 9:41 AM
1IntroductionConcept of StressStresses occurinall structures subjecttoloads.This chapterwill examine simplestatesofstressin elements,suchas inthetwo-forcemembers,bolts andpins usedinthestructureshown.ObjectivesReviewof statics neededto determineforcesinmembersofsimplestructures.Introduce concept of stress.Definedifferentstresstypes:axialnormal stress,shearingstressand bearing stress.Discuss engineer'stwoprincipaltasks,namely,theanalysisanddesignofstructuresandmachines.Developproblemsolvingapproach.Discuss the components of stress on different planes and underdifferent loading conditions.Discussthemanydesignconsiderationsthatanengineershouldreviewbeforepreparingadesign
1 Introduction— Concept of Stress Stresses occur in all structures subject to loads. This chapter will examine simple states of stress in elements, such as in the two-force members, bolts and pins used in the structure shown. Objectives • Review of statics needed to determine forces in members of simple structures. • Introduce concept of stress. • Define diff erent stress types: axial normal stress, shearing stress and bearing stress. • Discuss engineer’s two principal tasks, namely, the analysis and design of structures and machines. • Develop problem solving approach. • Discuss the components of stress on diff erent planes and under diff erent loading conditions. • Discuss the many design considerations that an engineer should review before preparing a design. bee98233_ch01_002-053.indd 3 11/15/13 9:41 AM