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- 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 ]