**Structural Analysis – Tenth Edition in SI UnitsR. C. HibbelerSI Conversion byKai Beng YapWith Additional SI Contributions byFarid AbedCONTENTSInternal Loadings Developedin Structural Members. Internal Loadings at a Specified Point. Shear and Moment Functions. Shear and Moment Diagrams for aBeam. Shear and Moment Diagrams for aFrame. Moment Diagrams Constructed by theMethod of SuperpositionPreliminary ProblemsFundamental ProblemsProblemsProject ProblemsChapter ReviewTypes of Structuresand Loads. Introduction. Classification of Structures. Loads. Structural DesignProblemsChapter Review**

**Analysis of StaticallyDeterminate Structures. Idealized Structure. Load Path. Principle of Superposition. Equations of Equilibrium. Determinacy and Stability. Application of the Equationsof EquilibriumFundamental ProblemsProblemsProject ProblemChapter ReviewAnalysis of StaticallyDeterminate Trusses. Common Types of Trusses. Classification of Coplanar Trusses. The Method of Joints. Zero-Force Members. The Method of Sections. Compound Trusses. Complex Trusses. Space TrussesFundamental ProblemsProblemsProject ProblemChapter ReviewCables and Arches. Cables. Cable Subjected to ConcentratedLoads. Cable Subjected to a Uniform DistributedLoad. Cable Subjected to Its Own Weight. Arches. Three-Hinged ArchProblemsChapter ReviewDeflections UsingEnergy Methods. External Work and Strain Energy. Principle of Work and Energy. Principle of Virtual Work. Method of Virtual Work: Trusses. Castigliano’s Theorem. Castigliano’s Theorem for Trusses. Method of Virtual Work: Beamsand Frames. Virtual Strain Energy Caused by Axial Load,Shear, Torsion, and Temperature. Castigliano’s Theorem for Beams andFramesFundamental ProblemsProblemsChapter ReviewDeflections. Deflection Diagrams and the ElasticCurve. Elastic-Beam Theory. The Double Integration Method. Moment-Area Theorems. Conjugate-Beam MethodPreliminary ProblemsFundamental ProblemsProblemsChapter ReviewInfluence Lines for StaticallyDeterminate Structures. Influence Lines. Influence Lines for Beams. Qualitative Influence Lines. Influence Lines for Floor Girders. Influence Lines for Trusses. Maximum Influence at a Point due to aSeries of Concentrated Loads. Absolute Maximum Shear andMomentFundamental ProblemsProblemsProject ProblemsChapter ReviewAnalysis of StaticallyIndeterminate Structuresby the Force Method. Statically Indeterminate Structures. Force Method of Analysis: GeneralProcedure. Maxwell’s Theorem of ReciprocalDisplacements. Force Method of Analysis: Beams. Force Method of Analysis: Frames. Force Method of Analysis: Trusses. Composite Structures. Symmetric Structures. Influence Lines for Statically IndeterminateBeams. Qualitative Influence Lines for FramesFundamental ProblemsProblemsChapter Review**

**contents contentsDisplacement Method ofAnalysis: Slope-DeflectionEquations. Displacement Method of Analysis: GeneralProcedures. Slope-Deflection Equations. Analysis of Beams. Analysis of Frames: No Sidesway. Analysis of Frames: SideswayProblemsProject ProblemChapter ReviewBeams and FramesHaving NonprismaticMembers. Introduction. Loading Properties of NonprismaticMembers. Moment Distribution for Structures HavingNonprismatic Members. Slope-Deflection Equations forNonprismatic MembersProblemsChapter ReviewTruss Analysis Using theStiffness Method. Fundamentals of the StiffnessMethod. Member Stiffness Matrix. Displacement and Force TransformationMatrices. Member Global Stiffness Matrix. Truss Stiffness Matrix. Application of the Stiffness Method forTruss Analysis. Nodal Coordinates. Trusses Having Thermal Changes andFabrication Errors. Space-Truss AnalysisProblemsChapter Review**

**Approximate Analysis ofStatically IndeterminateStructures. Use of Approximate Methods. Trusses. Vertical Loads on Building Frames. Portal Frames and Trusses. Lateral Loads on Building Frames: PortalMethod. Lateral Loads on Building Frames:Cantilever MethodProblemsChapter ReviewDisplacement Methodof Analysis: MomentDistribution. General Principles and Definitions. Moment Distribution for Beams. Stiffness-Factor Modifications. Moment Distribution for Frames:No Sidesway. Moment Distribution for Frames:SideswayProblemsChapter ReviewBeam Analysis Using theStiffness Method. Preliminary Remarks. Beam-Member Stiffness Matrix. Beam-Structure Stiffness Matrix. Application of the Stiffness Method forBeam AnalysisProblemsAppendixA Matrix Algebra for Structural AnalysisPreliminary and Fundamental ProblemSolutionsAnswers to Selected ProblemsIndexPlane Frame Analysis Usingthe Stiffness Method. Frame-Member Stiffness Matrix. Displacement and Force TransformationMatrices. Frame-Member Global StiffnessMatrix. Application of the Stiffness Method forFrame AnalysisProblemscontentsStructural Modeling andComputer Analysis. General Structural Modeling. Modeling a Structure and itsMembers. General Application of a StructuralAnalysis Computer ProgramComputer ProblemsProject ProblemsIndexAbsolute maximum shear and moment,– ,Acceleration response spectrum,Adjoint matrix,Allowable-stress design (ASD) methods,American Association of State andHighway Transportation Officials(AASHTO),American Concrete Institute (ACI),American Forest and Paper Association(AFPA),American Institute of Steel Construction(AISC),American Railroad Engineers Association(AREMA),American Society of Civil Engineers(ASCE),Angular displacements (a),– ,Angular flexibility coefficient,Antisymmetric loads,Approximate analysis, –assumptions for, – ,– ,building frames, – ,–cantilever method for,lateral loads,models used for,portal frames,portal method for,trusses,vertical loads,Arches,compressive forces and,– ,fixed,funicular,parabolic shape of,structural systems of,three-hinged,tied,two-hinged,uniform distributed loads and,,Atmospheric corrosion,Automatic model assembly for computeranalysis,Axial force, –deflection and,external loading,external work and,frame displacements and, –strain energy and,truss member displacement and,,virtual strain energy and,Ball-and-socket connections, –Baltimore truss, –Bay,Beam columns,Beams, – ,– ,– ,– ,– ,absolute maximum shear and momentof,angular displacements (u),– ,antisymmetric loadings of,axial loads on,bending moment variations along(functions), –bending moments, – ,– ,cantilevered, –carry-over factor (COF),–Castigliano’s theorem for,code numbers for, –concentrated forces on, –concentrated series of loads on,– ,concrete,conjugate-beam method for,– ,deflection diagrams for, –deflections, – ,– ,displacement methods for, – ,–distributed loads along, –distribution factor (DF), –double integration method for,– ,elastic-beam theory for, –elastic curve for, –energy methods for displacement of,– ,fixed-connected,fixed-end moments (FEM), – ,, – ,–fixed support,flanges,force method for, –framing plans using, –free,girders,global (structure) coordinate systemfor,haunched,hinged,idealized structure members, – ,– ,inflection point,influence lines for, – ,– ,intermediate loadings on,internal bending moment (M),– ,internal loadings, –joint connections, –kinematic indeterminacy of,laminated,linear displacements (∆),linear elastic response and, –live loads and, – ,–maximum influence at a point,– ,member (local) coordinate systemfor,member stiffness (k),member stiffness factor (K),member stiffness matrix (k), –modeling of, –moment-area theorems for,– ,moment diagrams for, – ,–moment distribution for, – ,–moments at points, – ,– ,Müller-Breslau principle for, – ,,node displacements,nonprismatic members, –overhang,pin-supported,,Portland Cement Association data for,–principle of work and energy appliedto,procedures for analysis of,,,reactions at points, –reinforcing rods in,relationships between loading, shear,and moment in, –relative joint translation of,roller guides for, –roller or rocker supported,rotational displacement of, – ,– ,shear and moment diagrams for,–IndexBeams (continued)shear force (V) and, – ,– ,shear force variations along(functions), –sign conventions for,,simply supported, –sliding device in,slope-deflection equations for,– ,statically determinate, – ,– ,statically equivalent loads, –statically indeterminate, – ,– ,stiffness factor (K), – ,–stiffness matrix (K) for, –stiffness method for, –strain energy in,structural elements of,structure stiffness matrix (K),superposition, method of for design of,–support connections, – ,– ,symmetric, –symmetric loadings of,tapered,temperature effects on, –torsion effects on,uniform loads on, –unit displacement,virtual displacement, –virtual strain energy and, –virtual work, method of for,web,Bending, – ,. See also Deflectionapproximate analysis,beams,building frames,curvature (r), radius of, –deflection diagrams and, – ,–double integration method for,– ,elastic-beam theory and, –elastic curve for,inflection point, –moment-area theorems for,– ,portal frames and trusses, –portal method for,strain energy and,Bending moment (M), – ,, – ,– ,– , . See alsoInternal bending momentsabsolute maximum,beams, – ,– ,concentrated loads and, – ,– ,deflections and,determination of,elastic-beam theory, –elastic curve and, –frame-member stiffness matrix for,–functions,influence lines for,internal loads and,maximum influence at a point,– ,method of sections for,Muller-Breslau principle for, –procedures for analysis of,relationships with loading and shear,–sign convention for,stiffness matrix and, –structural members,variations along beams, –Bent (columns),Boundary conditions for double integrationmethod,Bowstring truss, –Bracing,Bridges, – .See also Portal frames; Trussesbracing,cantilevered, –deck,floor beams,highway,impact factor,influence lines for, –joint loadings, –live loads, –load transmission in,primary member,railroad,secondary member,static determinacy of, –stringers,trusses, –Building and design codes,Building frames, – .See also Framesapproximate analysis of, – ,– ,cantilever method for,– ,exact analysis for,lateral loads,portal method for,vertical loads,Building loads, –design wind pressure for, –influence area,minimum for occupancy, –racking,reduction of for floors, –wind load effects, –By inspection process,Cables,concentrated loads and,flexibility of,inextensible property,parabolic shape of,structural systems of,support connections,uniform distributed loads and,– ,weight of,Camber,Cantilever method of analysis,– ,Cantilevered beams,– ,Cantilevered bridge analysis, –Carry-over factor (COF), –Castigliano’s theorem (second), – ,– ,beams,deflection analysis using, – ,– ,external work and, –force displacement (∆) and, –frames,linear elastic response and, –procedures for analysis using,strain energy and, –trusses,Catenary curve,Center of curvature (O’),Code numbers, –Collars,Column matrix,Columns,floor systems,modeling of,structural members as,Compatibility equations, – ,– ,degree of indeterminacy and,determinacy from, –force method using,statically indeterminate analysisrequirements,structural stability and,Complex truss, –classification as,method of substitute members for,– ,procedure for analysis of, –stability of,superposition of loadings,Composite structures, force analysis of,–Compound truss,analysis of,classification as,stability of,Compression members,Compressive force (C), – ,– ,arches,trusses, – IndexComputer analysis, –automatic assembly,building safety and, –data results,global (structure) coordinates for,–load data input, –local (member) coordinates for,–member data input,modeling considerations, –node data input,node identification for, –preliminary steps,program operation for, –programs for,scaled drawing(s) for,structural modeling for, –structure members and materials for,–support data input,Concentrated force (F), –Concentrated loads, – ,– ,absolute maximum moment and shearfrom,beams,cables,influence lines and,live building loads, –maximum at a point, –moment and,series of,shear and,Concrete,beams,frames,reinforced,reinforcing rods,Concurrent forces, –Conjugate-beam method,beam deflection analysis,equilibrium equations for, –procedure for analysis using,supports for, –theorems for,zero displacement of,Connections, see Joint connections; SupportconnectionsConservation of energy principle,– ,Constrained degrees of freedom,Constraints, structural stability and,Continuity conditions for double integrationmethod,Coordinates, – ,–beams,computer analysis need for, –global (structure) system, – ,, –member (local) system, – ,, –model data input, –nodal, –scaled drawing(s) with,stiffness method use of, –support reactions and, –transformation matrices and, –trusses, –Coplanar truss, –complex,compound,determinacy of,simple,stability of,Cord of a cable,Cord rotation (c),Couple moments, –Cross-diagonal bracing,Curvature (r), radius of, –Curve reactions, influence lines and,–Data input, – . See also ComputeranalysisDead loads,densities for,design standards,load factors for modeling,Deck,Deflections, – .See also Displacementsaxial force,beams, – ,– ,bending,Castigliano’s theorem (second) for,– ,conjugate-beam method for,– ,conservation of energy principle,– ,curvature, –diagrams,double integration method for,– ,elastic-beam theory for, –elastic curve for, –energy methods for, –external work and, –flexural rigidity (M>EI),force displacement (∆), – ,– ,frames,inflection point,influence lines for,internal bending moment (M) and,– ,linear elastic response and,– ,moment-area theorems for,– ,Müller-Breslau principle for,– ,procedures for analysis of,,radius of curvature, –reinforcing rods for prevention of,roller guides for, –rotational (displacement), – ,, –shear force (V) and, –strain energy and,– ,supports and, –trusses, –virtual, –virtual work, method of, – ,– ,Degree of indeterminacy,Degrees of freedom,beams,constrained,displacement method and,kinematic indeterminacy and,,node displacement and,stiffness method and,trusses,unconstrained,Design codes,Determinacy, – ,– ,cantilever bridge determination,–comparison of structures, –compatibility equations for, –degree of indeterminacy,degrees of freedom and,equilibrium equations for, – ,,free-body diagrams for, –kinematic indeterminacy,structural determination of,trusses,Determinants of matrices, –Diagonal matrix,Displacement method, – ,– , . See also Stiffnessmethodbeam analysis, –carry-over factor (CO),–degrees of freedom for,equilibrium equations for, –fixed-end moments (FEM), – ,, –force method compared to,frame analysis, –moment distribution for, –nodes,nonprismatic member analysis,–procedure for, –procedures for analysis using,relative joint translation,sidesway effects and, –slope-deflection equations for,–statically indeterminate structures,– , IndexDisplacement method (continued)stiffness factor (K), – ,– ,symmetric beam analysis, – ,–Displacement transformation (T) matrix,– ,Displacements, – ,– ,– , . See alsoDeflections; Rotationangular (a or u),beams, – ,–Castigliano’s theorem (second) for,– ,code numbers for, –compatibility equations for,deflection per unit force,degrees of freedom,energy methods for deflections,–equilibrium equations for,external work and, –flexibility coefficients, – ,–force (∆), –force-displacement requirements,force method for analysis of, –frames, – ,–internal bending moment (magnitude),, –joints, –linear (∆),load-displacement relationships,– ,matrices for, –Maxwell’s theorem of reciprocal,– ,methods of analysis for, –moment distribution for, –nodal,plane-frame analysis, –rotational (u), – ,– ,sidesway, –slope-deflection equations for, – ,–statically determinate structures, – ,–statically indeterminate structures,– ,– ,stiffness factor (K), – ,– ,stiffness matrix for, – ,– ,stiffness method for analysis of,– ,strain energy and, – ,–trusses, – ,–unconstrained,unit,unknowns for,virtual work method for analysis of,– ,–Distributed loads, –beams, –cables,uniform, –Distribution factor (DF),Double integration method,beam deflection analysis,boundary conditions for,continuity conditions for,elastic curve for, –internal bending moments and,–procedures for analysis using,sign convention for,Earthquake loads, –Elastic-beam theory, –Elastic curve, –center of curvature (O’),deflection diagram representation of,– ,deflections and,double integration method for,– ,elastic-beam theory and, –flexural rigidity (EI),inflection point,internal moments and, – ,– ,moment-area theorems for,– ,radius of curvature (r), –slope and, –Elastic strain energy, . See also StrainenergyElements of a matrix,End spans, pin-supported,Energy methods, –beam analysis, – ,– ,Castigliano’s theorem (second),– ,conservation of energy principle,– ,displacements (deflections), –external work,force displacements (∆), – ,– ,–frame analysis,internal bending (virtual) moment of,–linear elastic response and,– ,moment displacements, – ,– ,procedures for analysis using,,rotational displacements (u), – ,, –strain energy and,– ,truss analysis, – ,–virtual displacements,method of,virtual forces, method of,virtual strain energy and, –virtual work, method of, – ,– ,virtual work, principle of, – ,,work and energy, principle of,Envelope for maximum influence linevalues,Equilibrium, – ,, – ,– ,carry-over factor (CO) for,compatibility equations and,conjugate beam method using,–determinacy and, – ,,displacement method using, –displacements and,distribution factor (DF) for,equations of,fixed-end moments (FEM) and,–force analysis method equations, – ,,free-body diagrams and, –joints,moment distribution and,– ,procedure for analysis using,reactions determined using, –requirements for,stability and,statically determinate structures,– ,statically indeterminate analysisrequirements,statically indeterminate structures,,– ,structural stability and, –trusses,Exact analysis,External loading,External stability,External work,Castigliano’s theorem and, –conservation of energy principle,,deflection (rotational displacement)and,force and, –moment of,principle of work and energy,strain energy and, IndexFabrication errors, –Fan truss,Finite elements,Fink trusses, –Fixed arch,Fixed-end moments (FEM), – ,– ,–beams, – ,–equilibrium and, –frames, –haunch properties, –moment distribution and, – ,– ,nonprismatic members, – ,–relative joint translation ofbeams,slope-deflection equations and,– ,Fixed-support connections, – ,,conjugate beams,deflection and,idealized structures,portal frames and trusses,zero displacement from,Flanges,Flexibility coefficients, –angular,force method of analysis using,– ,linear elastic materials, –Maxwell’s theorem of reciprocaldisplacements and, –Flexibility of cables,Flexural rigidity (EI),Floor beams,Floors,beams,columns,concentrated live loads for, –framing plans for, –girders,idealized structures,influence lines for,joists,load transmission,one-way (slab) system,panel points,panel shear,reduction of live loads for, –span ratio,tributary loadings, –two-way (slab) system,uniform live loads for, –Force, – ,– ,– ,– , . See alsoLoadsarches subjected to, –axial,bending member stiffness methodand,Castigliano’s theorem for, – ,– ,compressive (C), – ,– ,concentrated,concurrent, –displacements (∆), – ,– ,energy methods of analysis and,– ,equilibrium of,external work (P) as,idealized structures,influence lines for reactions,by inspection,internal loadings,line of action,magnitude of,method of joints for,method of sections for, – ,– ,normal (N),principle of work and energy for,procedures for analysis of,– ,resultant force coefficients,resultant (F) reactions, –rotational displacement (u) from,– ,shear (V),strain energy and,structural member, – ,,support connections, –tensile (T), –truss members, – ,–unknown, determination of, – ,– ,virtual work and, – ,–x, y, z components,zero-force members, –Force-displacement equations, staticallyindeterminate analysisrequirements,Force method, –angular flexibility coefficient,antisymmetric loads,beam analysis, – ,–compatibility of displacements for,– ,composite structures, –deflection per unit force,displacement method compared to,equilibrium equations for, – ,,flexibility coefficients, – ,–force-displacement requirements,– ,frame analysis, –free-body diagrams for, –influence lines,Maxwell’s theorem of reciprocaldisplacements for, – ,– ,procedure for,procedure for analysis using,statically determinate structures, –statically indeterminate structures,–superposition for, –symmetric structures,truss analysis, –unit load and, –Force transformation (Q) matrix,– ,Frames, – ,– ,– , .See also Nonprismatic members;Plane framesapproximate analysis of, – ,–axial loads on,bending,building, –cantilever method for,Castigliano’s theorem for,deflection diagram for,deflections of,displacement method for, – ,–fixed-end moments (FEM), –fixed supported,force method for, –inflection point, – ,– ,influence lines for, –internal bending moment of, – ,–internal loads in, –joint displacement, –lateral loads on,linear elastic response and, –moment distribution for, –multistory, –pin supported,portal method for,portals,procedures for analysis of,–reinforced concrete,restrained to prevent sidesway,– ,rotational displacement (u) of,– ,shear and moment diagrams for,–shear force and,sidesway of, –sign convention for internal loads,,slope-deflection equations for, – IndexFrames (continued)statically determinate,statically indeterminate, – ,– ,stiffness factor (K) for, –structural systems as,supports and,tables for integration of,temperature effects on, –torsion effects on,vertical loads on,virtual strain energy and, –virtual work, method of for,– ,Framing plans, –floor systems, –idealized structures, –line drawings for,one-way (slab) system,span ratio,tributary loadings, –two-way (slab) system,Free-body diagrams, –equilibrium equations and, –force analysis using, –importance of,method of sections for,procedure for analysis using,statically determinate structures, –Funicular arch,Girders, –framing plans using,idealized structure members,influence lines for,modeling of, –panel points,panel shear,panels, –structural loads and,support connections,Global (structure) coordinate system,– ,Global stiffness matrix,Gusset plate,Handbook of Frame Constants,Haunched beams,Haunches, – . See also NonprismaticmembersHighway bridge loads, . See also BridgesHinge connections,Howe trusses, –Hurricanes, effects of wind loads from,Hydrostatic pressure (loads),Idealized structures,beams,floor systems, –framing plans, –girders,joint connections for, –line drawings for, –models of, –support connections for,tributary loadings of,Identity matrix,Impact factor (loads),Inextensible property of cables,Inflection point, – ,– ,Influence area,Influence lines,absolute maximum shear and moment,– ,beams, – ,– ,bending moments (M) and, – ,– ,concentrated forces (F),concentrated loads,connection devices used for, –construction of,curve reactions and, –deflection and, –envelope of maximum values,floor girders,force reactions and,force systems,frames, –live or moving loads and,maximum at a point, –Maxwell’s theorem of reciprocaldisplacements and, –moment (M) distribution and, – ,– ,moments at a point, –Müller-Breslau principle for, – ,,procedures for analysis of,qualitative, –reactions at points, –series of concentrated loads and,– ,shear (V) and, – ,– ,statically determinate structures,–statically indeterminate structures,– ,trusses,uniform loads,unit load for,Internal bending moments (M), – ,– ,– ,beams, – ,– ,Castigliano’s theorem and,– ,conjugate-beam method for, –deflection diagrams of,deflections and, –double integration method and,– ,elastic-beam theory for, –elastic curve and, – ,– ,frames, – ,–M/EI diagrams,moment-area theorems and,– ,shear force (V) and, –sign convention for,strain energy and,virtual work and, –Internal end moments, slope-deflectionequations for, –Internal loads, –beams,bending moment (M),frames, –method of sections for,moment diagrams for,normal force (N) and,procedures for analysis of,shear and moment diagrams for,– ,shear and moment functions of,– ,shear force (V) and,sign convention for,specific points, at,superposition, method of for,– ,Internal stability,Inverse of a matrix, –Joint connections, – ,, .See also Method of Jointsapproximate analysis for,beams,carry-over factor (CO),deflection and,distribution factor (DF),– ,equilibrium of, –fixed,fixed-end moments (FEM),– ,frames,gusset plate,idealized structures, –moment distribution method for,–nonprismatic members,pinned,procedure for analysis of,relative joint translation,statically determinate structures,,statically indeterminate structures,–trusses, –Joint displacement, – ,–Castigliano’s theorem for, –displacement method for, –frames, –multistory frames, – Indexsidesway and, –slope-deflection equations for, –statically determinate structures,–statically indeterminate structures,–Joint loadings, trusses,Joint reactions, procedure for analysis of,Joint stiffness factor,Joists,K-truss, –Kinematic indeterminacy,Knee braces,Laminated beams,Laplace expansion,Lateral loads,bending from,building frames,cantilever method,portal method,tipping from,Line drawings,Line of action,Linear displacements (∆),Linear elastic response, – ,– ,Castigliano’s theorem and, –deflections and, – ,–flexibility coefficient for, –internal bending moment and,shear effects and,strain energy and, – ,–torsion effects and,Live loads, –absolute maximum shear and momentcaused by,beams, –bridges, –buildings, –concentrated,earthquake, –floor girders,frames, –impact factor,influence area,influence lines for, –load factors for modeling,maximum at a point,minimum, –procedure for analysis of,reduction of, –series of concentrated,snow, –structures and,trusses,uniform, –wind,Load and resistance design factor(LRFD),Load-displacement relationships, – ,– ,beams, –bending moments,combined axial, bending, and shear,–force method for, –intermediate loadings,member stiffness matrix and, – ,– ,member stiffness method for, –plane frames, –rotation and,shear forces,trusses, –Load path,Loads, – ,– ,, – ,– ,– , . See also Force;Influence linesabsolute maximum shear and momentcaused by,antisymmetric,arches,assumption analysis for, –axial,beams, – ,– ,– ,bridges, –building and design codes for,buildings, –cable structures,carry-over factor (CO) for, –concentrated, – ,– ,data input for computer analysis,–dead,design pressure, –distributed,earthquake, –external,fixed-end moments (FEM) for,–floor girders,force method and,frames, –haunches, –highway bridges,hydrostatic,idealized structures,impact,influence lines and, – ,– ,intermediate,internal, –lateral,live, – ,– ,load factors for modeling,moment diagrams for, –Muller-Breslau principle for, –natural, –nonprismatic members, – ,– ,Portland Cement Association data for,–railroad bridges,series of,shear and moment diagrams for,–snow, –soil pressure,statically equivalent, –stiffness factor (K) for, – ,–stiffness method and,structural members, in, –structural modeling considerations,–structures and,symmetric,tributary,truss joints,trusses, – ,– ,uniform, – ,–unit,vertical,virtual work and,wind,Magnitude,Material properties for structuralmodeling,Matrices, – ,– , . See alsoStiffness matrixaddition and subtraction of,adjoint,algebra for structural analysis use of,–beams, –column,determinants of, –diagonal,displacement transformation (T),– ,elements,equality of,force transformation (Q),– ,identity,inverse of, –member stiffness (k), – ,,multiplication of, –node identification for,order of,partitioning, –plane frames, –row,scalars multiplication with,square, IndexMatrices (continued)structural analysis use of, –structure stiffness (K), – ,, –symmetric,transformation, –transposed, –trusses, –unit,Maxwell’s theorem of reciprocaldisplacements, – ,– ,M/EI diagrams,Member (local) coordinate system,,Member data input, –Member identification, see NodesMember-relative stiffness factor,Member stiffness factor,Member stiffness influence coefficients,–Member stiffness matrix, see Stiffness matrixMethod of joints,equilibrium conditions for,planar truss analysis,procedures for analysis using,space truss analysis,unknown force determination for,– ,Method of least work, see Castigliano’stheoremMethod of sections, – ,– ,free-body diagrams for,internal loads determined from,– ,planar truss analysis,procedures of analysis using,,space truss analysis,unknown force determination for,– ,Method of substitute members,Method of virtual displacements,Method of virtual forces,Method of virtual work, see Virtual workModeling, see Structural modelingMoment-area theorems,beam deflection analysis,first theorem,M/EI diagrams, –procedures for analysis using,second theorem,Moment diagrams,beams, –cantilevered beams,frames, –overhang beams,procedure for construction of,simply supported beams,slope of,statically equivalent loads, –superposition, method of forconstruction of,Moment distribution, –antisymmetric loading,beams, –carry-over factor (CO),displacement method of analysis using,–distribution factor (DF),fixed-end moments (FEM),– ,frames, –joint connections and, –nonprismatic members, –pin-supported beams,principles of, –procedure for analysis using,relative joint translation,sidesway effects on, –sign convention for,statically indeterminate structures,–stiffness factor (K), – ,– ,symmetric beams, –symmetric loading,Moments (M), – ,, – ,– ,, – ,, – ,– .See also Bending moment;Fixed-end moments (FEM)absolute maximum,beam-member stiffness matrix,–beam points,bending, – ,– ,–Castigliano’s theorem and,concentrated loads and, –couple, –deflection and, – ,, –displacements and, – ,– ,energy methods of analysis, – ,, –external work and,fixed-end (FEM), – ,–frame-member stiffness matrix,–influence lines and, – ,– ,internal bending, – ,, –internal end, –internal loads as,maximum at a point, – ,– ,method of sections for,relationships with loading and shear,–resultant,sign convention for,slope-deflection equations, –stiffness method and, –strain energy and,superposition and, –virtual work and,work (magnitude),Müller-Breslau principle, – ,– ,deflection and,hinge or pin displacement,influence lines and, – ,– ,Maxwell’s theorem of reciprocaldisplacements and, –procedure for analysis using,qualitative influence lines and,– ,reactions at points from, –roller guide displacement, –sliding devices,statically determinate beams,– ,statically indeterminate beams,– ,virtual displacement and, –Multistory frame analysis, –Nodal coordinates, –Nodal loadings,Nodes, – ,–beams,computer analysis and, –coordinates for, –data input,degrees of freedom and,displacement method of analysis and,– ,global (structure) coordinate systemfor,identification of,local (member) coordinate systemfor,slope-deflection equations and,–stiffness method of analysis and,–structure stiffness matrix use of,support reactions and, –trusses, –Nonprismatic members, –beams, –carry-over factor (COF), –deflections, equations for,fixed-end moments (FEM), – ,, –haunches, –loading properties of,moment distribution for, –parabolic haunches,pin-supported,Portland Cement Association data for,– Indexrelative joint translation of,rotation of, –slope-deflection equations for, –stepped haunches,stiffness factor (K), –symmetric, –tapered haunches,Normal force (N),One-way (slab) system,Overhang beams,Panel points,Panel shear,Panels, –Parabolic haunches,Parabolic shapes,Parker truss, –Partial fixity of portal frames,Partitioning of a matrix, –Pin-supported connections, – ,,,beams,conjugate beams,deflection and,end spans,idealized structures,influence lines and,joints,moment distribution for,nonprismatic members,portal frames,slope-deflection equation for,stiffness factor (K) modificationsfor,truss joints,Planar trusses, – ,–bridges, –design assumptions for,determinacy of,member composition,method of joints for,method of sections for,procedures for analysis of,roofs, –stability of, –zero-force members, –Plane frames, – . See also Framesaxial force and, –bending moments and, –displacement transformation (T)matrix for,force transformation (Q) matrix for,–global stiffness matrix (k) for,load-displacement relationships,–member stiffness matrix (k) for,– ,procedures for analysis of, –shear force and, –stiffness method for, –structure stiffness matrix (K) for,–Plate girder, . See also GirdersPortal frames,approximate analysis of,fixed supported,partial fixity,pin supported,trusses used in, –Portal method of analysis,Pratt truss, –Pressure,design, –enclosed buildings, –hydrostatic,resultant force,signs,snow,soil,velocity,wind, –Primary member,Primary stress,Primary structure,Principle of work and energy,Program operation for computer analysis,–Purlins,Qualitative influence lines, . Seealso Müller-Breslau principleRacking effects of wind,Radius of curvature, –Railroad bridge loads, . See also BridgesReciprocal displacements, –Reciprocal rotation,Reinforced concrete frames,Reinforcing rods,Resultant force coefficients,Resultant force reactions,Rocker supports,Roller guides, –Roller supports, – ,,Roofs, – ,–bay,bent (columns),framing plan,idealized structure of, –purlins,snow loads on, –tributary loadings, –trusses, –wind loads on,Rotation, –building frames,cantilever method for,fixed-end moments for, –inflection points and,lateral loads and tipping from,nonprismatic members, –portal frame supports,Rotational displacements (u),– ,– ,beams,deflection and, – ,– ,external work and, –force (∆) and, – ,–frames, –Maxwell’s theorem of reciprocaldisplacements,member-stiffness matrix for,moments (magnitude) and,– ,statically determinate structures,– ,strain energy and, –support connection prevention of,,support reactions,thermal gradient acting on beams,–virtual energy strain and, –virtual work and, –Row matrix,Sag of a cable,Sawtooth truss, –Scissors truss, –Secondary member,Secondary stress,Shear and moment diagrams,beams, –distributed loads and, –frames, –internal loadings and, –procedure for construction of,relationships between loading,moments, and shear, –sign convention for,slope of,Shear force (V), – ,– ,– ,–absolute maximum,beam deflections and,beam ends,beam points,beams, variations along, –concentrated series of loads and,–determination of,floor girders,frame-member stiffness matrix,– ,frames, effects on,functions,influence lines for, – ,,internal loads as,maximum influence at a point, – ,– IndexShear force (V) (continued)method of sections for,Muller-Breslau principle for, –panel,procedures for analysis of,relationships with loading andmoments, –resultants,sign convention for,stiffness method and, –structural members,virtual strain energy caused by,Shells,Short link, –Sidesway, –moment distribution for, –multistory frames, –restraining force for, –slope-deflection equations for, –Sign convention,,beam-member stiffness matrix,bending moments,,deflection and,double integration method,influence lines,internal bending moments,internal loads,moment distribution,shear and moment diagrams,shear forces,slope-deflection equations,Signs, design wind pressure for,Simple truss,Simply supported beam,Slabs, see FloorsSliding devices,Slope-deflection equations, – ,–angular displacements (u), –beam analysis using, –cord rotation (c),displacement method of analysis using,–fixed-end moments (FEM), – ,–frame analysis using, –general form of, –internal end moments for, –joint displacement and, –joint rotation and, –linear displacements (∆),member stiffness (k),nonprismatic members, –pin-supported end spans,procedure for analysis using,relative joint translation,sidesway and, –sign convention for,Slope of deflection diagrams, – ,– ,Snow loads, –Soil pressure (loads),Space truss, –design assumptions for,determinacy of,member composition,member stiffness matrix (k) for,–procedure for analysis of,stability of,stiffness method for, –supports and connections for, –x, y, z force components of,zero-force members in, –Span of a cable,Span ratio,Span stiffness (k),Spring constant (k),Square matrix,Stability of structures, – ,,classification of, –compatibility equations for,concurrent forces and, –equilibrium equations and, –external,improper constraints for,by inspection,internal,partial constraints for,reactions and,trusses,Statically determinate structures, – ,– ,analysis of, –beams, – ,– ,Castigliano’s theorem for, – ,– ,conjugate-beam method for,– ,deflections in, –determinacy of,double integration method for,– ,energy methods of analysis, –equilibrium requirements for,,floors,force analysis method of, –frames,idealized structures,influence lines for, –method of joints for,method of sections for,method of substitute members for,– ,procedures for analysis of,– ,,stability of,trusses, – ,– ,virtual work and, – ,–Statically equivalent loads, –Statically indeterminate structures, – ,, – ,– ,advantages and disadvantages of,–approximate analysis of, –beams, – ,– ,building frames, – ,–cantilever method of analysis,– ,compatibility requirements for,composite structures, –determinacy of,displacement (stiffness) method for,, –equilibrium requirements for,exact analysis,force-displacement requirementsfor,force (compatibility) method for,–frames, – ,–influence lines for,lateral loads,Maxwell’s theorem of reciprocaldisplacements for,model uses,moment distribution for, –nonprismatic members, –portal frames and trusses,portal method for,procedures for analysis of,,sidesway effects on, –slope-deflection equations for,–stiffness factor (K) for, – ,– ,symmetric structures,trusses, – ,– ,vertical loads,Stepped haunches,Stiffness factor (K), – ,– ,beams, –displacement method and, – ,– ,frames, –joint,member,member relative,modifications of, –moment distribution and, – ,– ,nonprismatic members, –pin-supported members,Portland Cement Association data for,–symmetric beams, –total, IndexStiffness matrix, – ,– ,–angular displacements and,beam member, –beam structure,code numbers for, –frame-member,global,linear displacements and,member (k), – ,– ,member global,member stiffness influence coefficients,– ,plane frame structure, –rotational displacement and,space trusses, –structure (K), – ,–truss member, –truss structure, –use of for stiffness method,Stiffness method, –applications of, –axial loads and, –beam analysis, –bending moments and, –code numbers for, –degrees of freedom,displacement transformation (T)matrix,displacements and, –fabrication errors and, –force transformation (Q) matrix,,global (structure) coordinate systemfor,intermediate loadings and,kinematic indeterminacy and,load-displacement relationships,– ,matrix analysis for, –member (local) coordinate system for,,member stiffness matrix (k) for, – ,– ,nodal coordinates for, –node identification for,plane frame analysis, –procedures for analysis using,–shear force and, –space truss analysis, –structural stiffness matrix (K) for,– ,structure stiffness equation for,–support reactions and, –temperature change effects and,–truss analysis, –unit displacement,Strain energy, – ,– ,axial force of,axial loads and,Castigliano’s theorem and, –conservation of energy principle,,deflection and,– ,elastic,external work and,internal bending moment of,linear elastic response and,–principle of work and energy,shear and,temperature changes and, –torsion and,virtual, –Strength design,Stresses in truss members,Stringers,Structural modeling, –beams, –building safety and design from,–columns,computer analysis using, –coordinates for, –data input, –general structure specifications,–girders, –idealized structures, –loading considerations, –material properties considerations,members for, –scaled drawing(s) for,support connections for,tie rods,Structural system,Structure, defined,Structure stiffness matrix, see StiffnessmatrixStructures, – ,– ,analysis of, –approximate analysis of, –arches,beams, –bracing struts,building and design codes for,cables for,classification of, –columns,compatibility equations for,design of,determinacy of,elements for, –equilibrium, equations of, – ,– ,flanges,floor systems,force analysis method, –frames, –free-body diagrams for, –girders,idealized,improper constraints for,influence lines for, –internal loadings in members, –load path, –loads and,partial constraints for,procedures for analysis of,slabs,stability of,statically determinate, – ,–statically indeterminate, – ,–superposition, principle of,support connections for,surface,systems, types of, –tie rods,tributary loadings,trusses, – ,– ,Struts,Subdivided trusses,Superposition, – ,– ,beams design and, –complex truss analysis,force method using, –moment diagrams constructed bymethod of,principle of,Support connections, – ,– ,,ball-and-socket, –beams, – ,– ,cable,collars,conjugate-beam, –data input for computer analysis,deflection and, –end spans,fixed,free,girders,hinge,idealized models,influence lines using, –joints, – ,– ,nodal coordinates for reactions,–nonprismatic members,partial fixity,pin, – ,,portal frames and trusses, IndexSupport connections (continued)rocker,roller,rotation and,short link, –sliding devices,slope-deflection equation for,slope and displacement determinationand,space trusses, –spring constant (k) for,stiffness factor (K) modifications for,stiffness method for, –translation and,trusses, –zero displacement from,Surface structures,Symmetric beams, –antisymmetric loading of,moment distribution of, – ,–nonprismatic members, –stiffness-factor (K) modifications for,– ,symmetric loading of,Symmetric matrix,Symmetric structures, force analysis of,– ,Tapered haunches (beams),Temperature effects, – ,–deformation from,stiffness method for, –trusses, –virtual strain energy and, –Tensile force (T), –Tension members,Tetrahedron, . See also Space trussThin plates,Three-hinged arch,Tie rods,Tied arch,Tornadoes, effects of wind loads from,Torsion effects on virtual strain energy,Transformation matrices, – . See alsoForce transformation (Q) matrixTranslation,joints, relative displacement and,nonprismatic members,support connection prevention of,Transposed matrix, –Tributary loadings,floors,framing plans for, –one-way (slab) system,roofs, –trapezoidal,triangular,two-way (slab) system,Trusses, – ,– ,– ,approximate analysis of, – ,– ,axial force members,bridge, –camber of,Castigliano’s theorem for,code numbers for,complex,compound,compression members,compressive (C) forces, – ,–coordinate systems for, – ,–coplanar, –cross-diagonal bracing,deflections of, – ,–degrees of freedom,design assumptions,determinacy of,displacement transformation (T)matrix for, –energy methods of analysis, – ,– ,external loading and,fabrication errors,–finite elements,force displacements (∆), – ,– ,force method of analysis, –force transformation (Q) matrix for,, –frames for,global (structure) coordinate systemfor, –gusset plate,influence lines for,joint connections,joint loadings,kinematic indeterminacy of,matrix analysis of, –member stiffness matrix (k) for,– ,method of joints for,method of sections for,method of substitute members for,– ,nodal coordinates, –node identification,pin connections,planar,portal frames and, –procedures for analysis of,– ,roof, –sign convention for,simple,space, –stability of,statically determinate, – ,, –statically indeterminate, – ,– ,stiffness method of analysis, –stresses in,structural systems as,structure stiffness equation for, –structure stiffness matrix (K) for,–subdivided,supports and connections for,–temperature effects on, –tensile (T) forces, – ,–tension members,unit displacement,unknown forces, determination of,– ,vertical loads, –virtual work method of analysis,– ,x, y, z force components of,zero-force members, –Two-hinged arch,Two-way (slab) system,Unconstrained degrees of freedom,Uniform loads, – ,–arches,beams, –cables,distributed,influence area,influence lines and, –live building loads, –parabolic shape from,Unit displacement,Unit load,deflection per unit force,force method using, –influence lines for reactions,,Unit matrix,Unknown forces, –equilibrium equations for,by inspection,method of joints, –method of sections, –support reactions, –Velocity pressure, wind loads,Vertical loads,building frames,truss cross-diagonal bracing, –Virtual displacement,Virtual forces, method of,Virtual strain energy, –axial loads,deformation effects from, –shear and,temperature effects, –torsion and, IndexVirtual work, – ,– ,beams, method of for,conservation of energy for,couple moments of,deflection and, – ,– ,external,force displacement (∆),frames, method of for,influence lines and, –internal bending moments and,–Maxwell’s theorem of reciprocaldisplacements using, –method of analysis,Müller-Breslau principle using,–principle of,procedures for analysis using,rotational displacement,– ,tables for integration of,trusses, method of for,– ,Warren trusses, –Web,Weight, cables subjected to,Wide-flange beams,Wind loads,buildings, effects on, –design wind pressure, –dynamic approach for,enclosed buildings, –hurricanes,modeling for,pressure, –racking effects of,resultant force coefficients,signs,static approach for, –tornadoes,velocity pressure,Work, – ,–conservation of energy and,deflection (rotational displacement)and, – ,–external,force and, –internal bending moments and,–magnitude, –principle of work and energy,rotational displacement and,– ,virtual, – ,–x, y, z force components,Zero displacement from supports,Zero-force members**

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