Course Details
Subject {L-T-P / C} : CE3204 : Advanced Structural Analysis { 3-0-0 / 3}
Subject Nature : Theory
Coordinator : Dr. Shyamal Guchhait
Syllabus
Prerequisites: Undergraduate level courses on structural analysis and Mathematics of Matrix analysis
Unit I: Review of basic concepts in structural analysis:
Definition of Structure Different structural elements Joints and support conditions rigidity, Loads vector, Displacement vector
Static indeterminacy, kinematic indeterminacy Example of trusses, beams, frames, stability, Equilibrium, compatibility, force-displacement relationship Example solution of Static Determinate Structures, Introduction to matrix method Difference with Finite element method and Finite Difference Method
Unit II: Review of Analysis of indeterminate structures:
Force Method: Statically indeterminate structures Example of method of consistent deformations theorem of least work Example problem
Displacement Method: Kinematically indeterminate structures Example of slope-deflection method moment distribution method
Unit III: Mathematical Back ground of Matrix Method:
Vector Matrix tensor rank of matrix Transpose of force Displacement Vector Basic matrix operations Difference between Matrix and Determinate Multiplication of Matrix, Inversion of Matrix Solution of linear equations
Properties of Stiffness matrix, Flexibility Matrix ill Condition matrix, Rigid body motion
Unit IV: Matrix analysis of Truss Structure:
Introduction of Truss, DOF, Plane truss considering 2DOF in each element (plane truss) element, Example for formation of global Stiffness matrix for plane truss implement of force (active and reactive) and Displacement boundary conditions and solution for Displacement and Reactions
Plane truss element with four DOF each element Transformation from local coordinate system to global coordinate system Formation of global matrix considering the connectivity Solution of Example problem, Space truss element (six DOF each element) Global matrix formation and solution, Reduced element stiffness method (single DOF) Analysis by flexibility method
Unit V: Matrix analysis of 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
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 10 flexibility matrix solution procedure (including support movements)
Unit VI: 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 deformation 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)
Unit VII: Unsymmetric Bending and shear centre
Principle moment of inertia, Stress in beam due to Unsymmetric bending, Shear Centre, Method of Locating shear center and another Advance topic if time permits
Unit VIII: Analysis if elastic instability and second-order effects:
Effects of axial force on flexural stiffness:
Review of buckling of ideal columns flexural behavior and stiffness 7 measures for beam-column-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
Unit IX: Virtual Work Principle and any other advance topic if time permits
Course Objectives
- This course will enable students to: <br />1. To develop a skills to idealize, formulate, and analyze determinate and <br />indeterminate structures (beams, trusses, and frames) using classical and matrix structural analysis methods.
- 2. To present modern methods to determine the force distribution and <br />deformed shapes of structures.
- 3. To develop skills in interpreting and predicting solutions from structural analysis.
- 4. To introduce computer-based applications for the analytical methods as <br />presented.
Course Outcomes
This course will enable students and prospective graduates to minimally <br />achieve the following educational outcomes: <br />(a) An ability to apply knowledge of mathematics, science, and engineering. <br />(e) An ability to identify, formulate, and solve engineering problems. <br />(k) An ability to use the techniques, skills, and modern engineering tools <br />necessary for engineering practice.
Essential Reading
- (1) Menon, Devdas, Advanced Structural Analysis,Narosa, (2) MATRIX ANALYSIS of FRAMED STRUCTURES, 3-rd Edition, by Weaver and Gere Publishe, Chapman & Hall, New York, New York, 1990, (3) Junarkar, S. B. and Shah, H. J. (1999). Mechanics of Structures – Vol. II, Charotar Publishing House, Anand
- (4) Kassimali, Aslam, Matrix Structural Analysis, Cengage Learning, 2012, (5) Armenakas, A. E. (1988). Classical Structural Analysis – A Modern Approach, McGraw-Hill Book Company, NY, ISBN 0-07-100120-4, (6) Hibbeler, R. C. (2002). Structural Analysis, Pearson Education (Singapore) Pte. Ltd., Delhi, ISBN 81-7808-750-2
Supplementary Reading
- (7) Przeminiecki, J.S, Theory of Matrix Structural Analysis, Dover Press , 1985
- (8) Dym, C.L.,, Structural Modeling and Analysis, Cambridge University Press , 2005