Advanced Structural Analysis

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3 STUDENTS

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;

Course Curriculum

Review of Basic Structural Analysis 1 Details 52:22
Review of Basic Structural Analysis 2 Details 51:4
Review of Basic Structural Analysis 3 Details 56:37
Review of Basic Structural Analysis 4 Details 51:55
Review of Basic Structural Analysis 5 Details 50:19
Review of Basic Structural Analysis 6 Details 49:18
Review of Basic Structural Analysis 7 Details 53:6
Review of Basic Structural Analysis 8 Details 51:8
Review of Basic Structural Analysis 9 Details 59:38
Review of Basic Structural Analysis 10 Details 50:50
Review of Basic Structural Analysis 11 Details 51:22
Review of Basic Structural Analysis 12 Details 52:3
Review of Basic Structural Analysis 13 Details 46:26
Review of Basic Structural Analysis 14 Details 51:55
Review of Basic Structural Analysis 15 Details 1:46
Review of Basic Structural Analysis 16 Details 47:19
Basic Matrix Concepts 1 Details 52:49
Basic Matrix Concepts 2 Details 52:42
Basic Matrix Concepts 3 Details 1:1:35
Basic Matrix Concepts 4 Details 50:26
Basic Matrix Concepts 5 Details 53:50
Matrix Analysis of Structures with Axial Elements Details 50:59
Matrix Analysis of Structures with Axial Elements 1 Details 48:56
Matrix Analysis of Structures with Axial Elements 2 Details 58:53
Matrix Analysis of Structures with Axial Elements 3 Details 43:27
Matrix Analysis of Structures with Axial Elements 4 Details 57:32
Matrix Analysis of Beams and Grids 1 Details 48:16
Matrix Analysis of Beams and Grids 2 Details 47:33
Matrix Analysis of Beams and Grids 3 Details 46:43
Matrix Analysis of Beams and Grids 4 Details 49:20
Matrix Analysis of Beams and Grids 5 Details 47:28
Matrix Analysis of Beams and Grids 6 Details 45:53
Matrix Analysis of Plane and Space Frames 1 Details 49:41
Matrix Analysis of Plane and Space Frames 2 Details 42:44
Matrix Analysis of Plane and Space Frames 3 Details 47:6
Matrix Analysis of Plane and Space Frames 4 Details 45:19
Matrix Analysis of Plane and Space Frames 5 Details 48:12
Analysis of elastic instability and second-order effects 1 Details 1:24
Analysis of elastic instability and second-order effects 2 Details 45:45
Analysis of elastic instability and second-order effects 3 Details 45:15
Life beyond Structures & Analysis Details 57:57

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