# Structural Analysis.pdf

In Engineering Ebooks » Civil & Architectural Engineering »
Tags: Beam, IIT, Multistory Frame, Statically Indeterminate Structures, Structural Analysis, Training Material, Truss » 86 Comments » August 7, 2008

Another Civil Engineering Course Material from IIT Kharagpur, cover structural analysis, in seven modules/ 40 lessons. All materials are in portable document format, enjoy these civil engineering materials for free!

Contents:

**Module 1 Energy Methods in Structural Analysis****Lesson 1 General Introduction**, objectives: Differentiate between various structural forms such as beams, plane truss, space truss, plane frame, space frame, arches, cables, plates and shells ~ State and use conditions of static equilibrium ~ Calculate the degree of static and kinematic indeterminacy of a given structure such as beams, truss and frames ~ Differentiate between stable and unstable structure ~ Define flexibility and stiffness coefficients ~ Write force-displacement relations for simple structure –contents– [ Classification of Structures ~ Equations of Static Equilibrium ~ Static Indeterminacy ~ Kinematic Indeterminacy ~ Kinematically Unstable Structure ~ Compatibility Equations ~ Force-Displacement Relationship ]**Lesson 2 Principle of Superposition, Strain Energy**, objectives: State and use principle of superposition ~ Explain strain energy concept ~ Differentiate between elastic and inelastic strain energy and state units of strain energy ~ Derive an expression for strain energy stored in one-dimensional structure under axial load ~ Derive an expression for elastic strain energy stored in a beam in bending ~ Derive an expression for elastic strain energy stored in a beam in shear ~ Derive an expression for elastic strain energy stored in a circular shaft under torsion –contents– [ Principle of Superposition ~ Strain Energy ~ Strain energy due to torsion ]**Lesson 3 Castigliano’s Theorems**, objectives: State and prove first theorem of Castigliano ~ Calculate deflections along the direction of applied load of a statically determinate structure at the point of application of load ~ Calculate deflections of a statically determinate structure in any direction at a point where the load is not acting by fictious (imaginary) load method ~ State and prove Castigliano’s second theorem –contents– [ Castigliano's First Theorem ~ Castigliano's Second Theorem ]**Lesson 4 Theorem of Least Work**, objectives: State and prove theorem of Least Work ~ Analyse statically indeterminate structure ~ State and prove Maxwell-Betti’s Reciprocal theorem –contents– [ Theorem of Least Work ~ Maxwell-Betti Reciprocal theorem ]**Lesson 5 Virtual Work**, objectives: Define Virtual Work ~ Differentiate between external and internal virtual work ~ Sate principle of virtual displacement and principle of virtual forces ~ Drive an expression of calculating deflections of structure using unit load method ~ Calculate deflections of a statically determinate structure using unit load method ~ State unit displacement method ~ Calculate stiffness coefficients using unit-displacement method –contents– [ Principle of Virtual Work ~ Principle of Virtual Displacement ~ Principle of Virtual Forces ~ Unit Load Method ~ Unit Displacement Method ]**Lesson 6 Engesser’s Theorem and Truss Deflections by Virtual Work Principles**, objectives: State and prove Crotti-Engesser theorem ~ Derive simple expressions for calculating deflections in trusses subjected to mechanical loading using unit-load method ~ Derive equations for calculating deflections in trusses subjected to temperature loads ~ Compute deflections in trusses using unit-load method due to fabrication errors –contents– [ Crotti-Engesser Theorem ~ Unit Load Method as applied to Trusses ~ Fabrication Errors and Camber ~ Procedure for calculating truss deflection ]

**Module 2 Analysis of Statically Indeterminate Structures by the Matrix Force Method****Lesson 7 The Force Method of Analysis: An Introduction**, objectives: Able to analyse statically indeterminate structure of degree one ~ Able to solve the problem by either treating reaction or moment as redundant ~ Able to draw shear force and bending moment diagram for statically indeterminate beams ~ Able to state advantages and limitations of force method of analysis –contents– [ Simple Example ]**Lesson 8 The Force Method of Analysis: Beams**, objectives: Solve statically indeterminate beams of degree more than one ~ To solve the problem in matrix notation ~ To compute reactions at all the supports ~ To compute internal resisting bending moment at any section of the continuous beam –contents– [ Formalization of Procedure ]**Lesson 9 The Force Method of Analysis: Beams (Continued)**, objectives: Calculate additional stresses developed in statically indeterminate structures due to support settlements ~ Analyse continuous beams which are supported on yielding supports ~ Sketch the deflected shape of the member ~ Draw banding moment and shear force diagrams for indeterminate beams undergoing support settlements –contents– [ Support Displacements ~ Temperature Stresses ]**Lesson 10 The Force Method of Analysis: Trusses**, objectives: Calculate degree of statical indeterminacy of a planar truss ~ Analyse the indeterminate planar truss for external loads ~ Analyse the planar truss for temperature loads ~ Analyse the planar truss for camber and lack of fit of a member –contents– [ Examples ]**Lesson 11 The Force Method of Analysis: Frames**, objectives: Analyse the statically indeterminate plane frame by force method ~ Analyse the statically indeterminate plane frames undergoing support settlements ~ Calculate the static deflections of a primary structure (released frame) under external loads ~ Write compatibility equations of displacements for the plane deformations ~ Compute reaction components of the indeterminate frame ~ Draw shear force and bending moment diagrams for the frame ~ Draw qualitative elastic curve of the frame –contents– [ Support settlements ]**Lesson 12 Three-Moment Equations-I**, objectives: Derive three-moment equations for a continuous beam with unyielding supports ~ Write compatibility equations of a continuous beam in terms of three moments ~ Compute reactions in statically indeterminate beams using three-moment equations ~ Analyse continuous beams having different moments of inertia in different spans using three-moment equations –contents– [ Three-moment equation ~ Alternate derivation ]**Lesson 13 The Three-Moment Equations-Ii**, objectives: Derive three-moment equations for a continuous beam with yielding supports ~ Write compatibility equations of a continuous beam in terms of three moments ~ Compute reactions in statically indeterminate beams using three-moment equations ~ Analyse continuous beams having different moments of inertia in different spans and undergoing support settlements using three-moment equations –contents– [ Derivation of Three-Moment Equation ]

**Module 3 Analysis of Statically Indeterminate Structures by the Displacement Method****Lesson 14 The Slope-Deflection Method: An Introduction**, objectives: Calculate kinematic degrees of freedom of continuous beam ~ Derive slope-deflection equations for the case beam with unyielding supports ~ Differentiate between force method and displacement method of analyses ~ State advantages of displacement method of analysis as compared to force method of analysis ~ Analyse continuous beam using slope-deflection method –contents– [ Degrees of freedom ~ Slope-Deflection Equations ~ Application of Slope-Deflection Equations to Statically Indeterminate Beams. ]**Lesson 15 The Slope-Deflection Method: Beams (Continued)**, objectives: Derive slope-deflection equations for the case beam with yielding supports ~ Estimate the reactions induced in the beam due to support settlements ~ Analyse the beam undergoing support settlements and subjected to external loads ~ Write joint equilibrium equations in terms of moments ~ Relate moments to joint rotations and support settlements –contents– [ Summary ]**Lesson 16 The Slope-Deflection Method: Frames Without Sidesway**, objectives: State whether plane frames are restrained against sidesway or not ~ Able to analyse plane frames restrained against sidesway by slope-deflection equations ~ Draw bending moment and shear force diagrams for the plane frame ~ Sketch the deflected shape of the plane frame –contents– [ Introduction ]**Lesson 17 The Slope-Deflection Method: Frames with Sidesway**, objectives: Derive slope-deflection equations for the frames undergoing sidesway ~ Analyse plane frames undergoing sidesway ~ Draw shear force and bending moment diagrams ~ Sketch deflected shape of the plane frame not restrained against sidesway –contents– [ Introduction ]**Lesson 18 The Moment-Distribution Method: Introduction**, objectives: Calculate stiffness factors and distribution factors for various members in a continuous beam ~ Define unbalanced moment at a rigid joint ~ Compute distribution moment and carry-over moment ~ Derive expressions for distribution moment, carry-over moments ~ Analyse continuous beam by the moment-distribution method –contents– [ Basic Concepts ]**Lesson 19 The Moment-Distribution Method: Statically Indeterminate Beams With Support Settlements**, objectives: Solve continuous beam with support settlements by the moment-distribution method ~ Compute reactions at the supports ~ Draw bending moment and shear force diagrams ~ Draw the deflected shape of the continuous beam –contents– [ Summary ]**Lesson 20 Moment-Distribution Method: Frames without Sidesway**, objectives: Solve plane frame restrained against sidesway by the moment-distribution method ~ Compute reactions at the supports ~ Draw bending moment and shear force diagrams ~ Draw the deflected shape of the plane frame –contents– [ Summary ]**Lesson 21 The Moment-Distribution Method: Frames with Sidesway**, objectives: Extend moment-distribution method for frames undergoing sidesway ~ Draw free-body diagrams of plane frame ~ Analyse plane frames undergoing sidesway by the moment-distribution method ~ Draw shear force and bending moment diagrams ~ Sketch deflected shape of the plane frame not restrained against sidesway –contents– [ Procedure ]**Lesson 22 The Multistory Frames with Sidesway**, objectives: Identify the number of independent rotational degrees of freedom of a rigid frame ~ Write appropriate number of equilibrium equations to solve rigid frame having more than one rotational degree of freedom ~ Draw free-body diagram of multistory frames ~ Analyse multistory frames with sidesway by the slope-deflection method ~ Analyse multistory frames with sidesway by the moment-distribution method –contents– [ Slope-deflection method ~ Moment-distribution method ]

**Module 4 Analysis of Statically Indeterminate Structures by the Direct Stiffness Method****Lesson 23 The Direct Stiffness Method: An Introduction**, objectives: Differentiate between the direct stiffness method and the displacement method ~ Formulate flexibility matrix of member ~ Define stiffness matrix ~ Construct stiffness matrix of a member ~ Analyse simple structures by the direct stiffness matrix –contents– [ A simple example with one degree of freedom ~ Two degrees of freedom structure ]**Lesson 24 The Direct Stiffness Method: Truss Analysis**, objectives: Derive member stiffness matrix of a truss member ~ Define local and global co-ordinate system ~ Transform displacements from local co-ordinate system to global co-ordinate system ~ Transform forces from local to global co-ordinate system ~ Transform member stiffness matrix from local to global co-ordinate system ~ Assemble member stiffness matrices to obtain the global stiffness matrix ~ Analyse plane truss by the direct stiffness matrix –contents– [ Local and Global Co-ordinate System ~ Member Stiffness Matrix ~ Transformation from Local to Global Co-ordinate System ~ Analysis of plane truss. ]**Lesson 25 The Direct Stiffness Method: Truss Analysis (Continued)**, objectives: Transform member stiffness matrix from local to global co-ordinate system ~ Assemble member stiffness matrices to obtain the global stiffness matrix ~ Analyse plane truss by the direct stiffness matrix ~ Analyse plane truss supported on inclined roller supports ~ ~ Summary ]**Lesson 26 The Direct Stiffness Method: Temperature Changes and Fabrication Errors in Truss Analysis**, objectives: Compute stresses developed in the truss members due to temperature changes ~ Compute stresses developed in truss members due to fabrication members ~ Compute reactions in plane truss due to temperature changes and fabrication errors –contents– [ Temperature Effects and Fabrication Errors ]**Lesson 27 The Direct Stiffness Method: Beams**, objectives: Derive member stiffness matrix of a beam element ~ Assemble member stiffness matrices to obtain the global stiffness matrix for a beam ~ Write down global load vector for the beam problem ~ Write the global load-displacement relation for the beam –contents– [ Beam Stiffness Matrix ~ Beam (global) Stiffness Matrix ~ Formation of load vector ~ Solution of equilibrium equations ]**Lesson 28 The Direct Stiffness Method: Beams (Continued)**, objectives: Derive member stiffness matrix of a beam element ~ Assemble member stiffness matrices to obtain the global stiffness matrix for a beam ~ Write the global load-displacement relation for the beam ~ Impose boundary conditions on the load-displacement relation of the beam ~ Analyse continuous beams by the direct stiffness method –contents– [ Summary ]**Lesson 29 The Direct Stiffness Method: Beams (Continued)**, objectives: Compute moments developed in the continuous beam due to support settlements ~ Compute moments developed in statically indeterminate beams due to temperature changes ~ Analyse continuous beam subjected to temperature changes and support settlements –contents– [ Support settlements ~ Effect of temperature change ]**Lesson 30 The Direct Stiffness Method: Plane Frames**, objectives: Derive plane frame member stiffness matrix in local co-ordinate system ~ Transform plane frame member stiffness matrix from local to global co-ordinate system ~ Assemble member stiffness matrices to obtain the global stiffness matrix of the plane frame ~ Write the global load-displacement relation for the plane frame ~ Impose boundary conditions on the load-displacement relation ~ Analyse plane frames by the direct stiffness matrix method –contents– [ Member Stiffness Matrix ~ Transformation from local to global co-ordinate system ]

**Module 5 Cables and Arches****Lesson 31 Cables**, objectives: Differentiate between rigid and deformable structures ~ Define funicular structure ~ State the type stress in a cable ~ Analyse cables subjected to uniformly distributed load ~ Analyse cables subjected to concentrated loads –contents– [ Cable subjected to Concentrated Loads ~ Cable subjected to uniform load. ]**Lesson 32 Three-Hinged Arch**, objectives: Define an arch ~ Identify three-hinged, two-hinged and hingeless arches ~ State advantages of arch construction ~ Analyse three-hinged arch ~ Evaluate horizontal thrust in three-hinged arch –contents– [ Type of arches ~ Analysis of three-hinged arch ]**Lesson 33 Two-Hinged Arch**, objectives: Compute horizontal reaction in two-hinged arch by the method of least work ~ Write strain energy stored in two-hinged arch during deformation ~ Analyse two-hinged arch for external loading ~ Compute reactions developed in two hinged arch due to temperature loading –contents– [ Analysis of two-hinged arch ]**Lesson 34 Symmetrical Hingeless Arch**, objectives: Analyse hingeless arch by the method of least work ~ Analyse the fixed-fixed arch by the elastic-centre method ~ Compute reactions and stresses in hingeless arch due to temperature change –contents– [ Analysis of Symmetrical Hingeless Arch ~ Temperature stresses ~ Elastic centre method ]

**Module 6 Approximate Methods for Indeterminate Structural Analysis****Lesson 35 Indeterminate Trusses and Industrial Frames**, objectives: Make suitable approximations so that an indeterminate structure is reduced to a determinate structure ~ Analyse indeterminate trusses by approximate methods ~ Analyse industrial frames and portals by approximate methods –contents– [ Indeterminate Trusses: Parallel-chord trusses with two diagonals in each panel ~ Industrial frames and portals ]**Lesson 36 Building Frames**, objectives: Analyse building frames by approximate methods for vertical loads ~ Analyse building frames by the cantilever method for horizontal loads ~ Analyse building frame by the portal method for horizontal loads –contents– [ Analysis of Building Frames to Vertical Loads ~ Analysis of Building Frames to lateral (horizontal) Loads ]

**Module 7 Influence Lines****Lesson 37 Moving Load and Its Effects on Structural Members**, objectives: Understand the moving load effect in simpler term ~ Study various definitions of influence line ~ Introduce to simple procedures for construction of influence lines –contents– [ Definitions of influence line ~ Construction of Influence Lines ~ Numerical Examples ~ Influence line for beam having point load and uniformly distributed load acting at the same time ]**Lesson 38 Influence Lines for Beams**, objectives: How to draw qualitative influence lines? ~ Understand the behaviour of the beam under rolling loads ~ Construction of influence line when the beam is loaded with uniformly distributed load having shorter or longer length than the span of the beam –contents– [ Muller Breslau Principle for Qualitative Influence Lines ~ Maximum shear in beam supporting UDLs ~ Maximum bending moment at sections in beams supporting UDLs ~ Closing Remarks ]**Lesson 39 Influence Lines for Beams (Contd.)**, objectives: Construction of influence line for maximum shear at sections in a beam supporting two concentrated loads ~ Construction of influence line for maximum moment at sections in a beam supporting two concentrated loads ~ Construction of influence line for maximum end shear in a beam supporting a series of moving concentrated loads ~ Construction of influence line for maximum shear at a section in a beam supporting a series of moving concentrated loads ~ Construction of influence line for maximum moment at a section in a beam supporting a series of moving concentrated loads ~ Construction of influence line for absolute maximum moment in s beam supporting a series of moving concentrated loads ~ Understanding about the envelopes of maximum influence line values –contents– [ Maximum shear at sections in a beam supporting two concentrated loads ~ Maximum moment at sections in a beam supporting two concentrated loads ~ Maximum end shear in a beam supporting a series of moving concentrated loads ~ Maximum shear at a section in a beam supporting a series of moving concentrated loads ~ Maximum Moment at a section in a beam supporting a series of moving concentrated loads ~ Absolute maximum moment in s beam supporting a series of moving concentrated loads ~ Envelopes of maximum influence line values ]**Lesson 40 Influence Lines for Simple Trusses**, objectives: Understand the bridge truss floor system and load transfer mechanism ~ Draw the influence line for the truss reactions ~ Draw the influence line for the truss member forces –contents– [ Bridge Truss Floor System ~ Influence lines for truss support reaction ~ Influence lines for truss member forces ]

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### Comments

**86 Responses to “Structural Analysis.pdf”**

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