IIT Madras Course , Prof. Devdas Menon

### Lecture 1: Review of Basic Structural Analysis 1

##### Lecture Details :

Advanced Structural Analysis by Prof. Devdas Menon , Department of Civil Engineering, IIT Madras. For more details on NPTEL visit http://nptel.iitm.ac.in

##### Course Description :

Review of basic concepts in structural analysis:structure (structural elements, joints and supports, stability, rigidity and static indeterminacy, kinematic indeterminacy);loads (direct actions, indirect loading);response (equilibrium, compatibility, force-displacement relations);levels of analysis; analysis of statically determinate structures (trusses, beams, frames);applications of principle of virtual work and displacement-based and force-based energy principles; deriving stiffness and flexibility coefficients - Review of analysis of indeterminate structures - Force methods:Statically indeterminate structures (method of consistent deformations; theorem of least work) - Displacement Methods:Kinematically indeterminate structures (slope-deflection method; moment distribution method) - Matrix concepts and Matrix analysis of structures:Matrix; vector; basic matrix operations; rank; solution of linear simultaneous equations; eigenvalues and eigenvectors;Introduction; coordinate systems; displacement and force transformation matrices;Contra-gradient principle; element and structure stiffness matrices - Element and structure flexibility matrices; equivalent joint loads; stiffness and flexibility approaches - Matrix analysis of structures with axial elements - Introduction:Axial stiffness and flexibility; stiffness matrices for an axial element (two dof), plane truss element (four dof) and space truss element (six dof) - One-dimensional axial structures:Analysis by conventional stiffness method (two dof per element) and reduced element stiffness method (single dof); Analysis by flexibility method - Plane trusses:Analysis by conventional stiffness method (four dof per element) and reduced element stiffness method (single dof); Analysis by flexibility method - Space trusses:Analysis by conventional stiffness method (six dof per element) and reduced element stiffness method (single dof) - Matrix analysis of beams and grids - Conventional stiffness method for beams:Beam element stiffness (four dof); generation of stiffness matrix for continuous beam; dealing with internal hinges, hinged and guided-fixed end supports; accounting for shear deformations - Reduced stiffness method for beams:Beam element stiffness (two dof); dealing with moment releases, hinged and guided-fixed end supports - Flexibility method for fixed and continuous beams:Force transformation matrix; element flexibility matrix; solution procedure (including support movements);

Stiffness method for grids:Introduction; torsional stiffness of grid element and advantage of torsion release; analysis by conventional stiffness method using grid element with six dof; analysis by reduced stiffness method (three dof per element) - Matrix analysis of plane and space frames - Conventional stiffness method for plane frames:Element stiffness (six dof); generation of structure stiffness matrix and solution procedure; dealing with internal hinges and various end conditions - Reduced stiffness method for plane frames:Element stiffness (three dof); ignoring axial deformations; dealing with moment releases, hinged and guided-fixed end supports - Flexibility method for plane frames:Force transformation matrix; element flexibility matrix; solution procedure (including support movements); Ignoring axial deformations - Stiffness method for space frames:Introduction; element stiffness matrix of space frame element with 12 dof and 6 dof; coordinate transformations; analysis by reduced stiffness method (six dof per element); - Analysis of elastic instability and second-order effects - Effects of axial force on flexural stiffness:Review of buckling of ideal columns; flexural behaviour and stiffness measures for beam-columns - braced and unbraced, under axial compression - Solution by slope deflection method:Slope deflection equations for prismatic beam columns using stability functions; modifications for pinned and guided-fixed-end conditions; fixed-end moments in beam-columns - Solution by matrix method:Stiffness matrix for prismatic beam-column element; estimation of critical elastic buckling loads; second-order analysis;

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