MTech Structural Stability Analysis - Classical And Fe Approach syllabus for 2 Sem 2020 scheme 20CCS23

Module-2 Buckling of frames and continuous beams 8 hours

Buckling of frames and continuous beams.

Elastic Energy method: Approximate calculation of critical loads for a cantilever, Exact critical load for hinged-hinged column using energy approach. Buckling of bar on elastic foundation, Buckling of cantilever column under distributed loads. Determination of critical loads by successive approximation, Bars with varying cross section, Effect of shear force on critical load. Columns subjected to pulsating forces.

Module-3 Stability analysis by finite element approach 8 hours

Stability analysis by finite element approach:

Derivation of shape functions for a two noded Bernoulli-Euler beam element (lateral and translational DOF) –element stiffness and Element geometric stiffness matrices – Assembled stiffness and geometric stiffness matrices for a discretised column with different boundary conditions – Evaluation of critical loads for a discretised (two elements) column (both ends built-in). Algorithm to generate geometric stiffness matrix for four noded and eight noded isoparametric plate elements, Buckling of pin jointed frames (maximum of two active DOF)-symmetrical single bay Portal frame.

A d v e r t i s e m e n t
Module-4 Lateral buckling of beams 8 hours

Lateral buckling of beams:

Differential equation –pure bending – cantilever beam with tip load – simply supported beam of I section subjected to central concentrated load. Pure Torsion of thin – walled bars of open cross section. Non – uniform Torsion of thin – walled bars of open cross section

Module-5 Expression for strain energy in plate bending with in plate forces 8 hours

Expression for strain energy in plate bending with in plate forces (linear and non – linear):

Buckling of simply supported rectangular plate– uniaxial load and biaxial load. Buckling of uniformly compressed rectangular plate simply supported along two opposite sides perpendicular to the direction of compression and having various edge condition along the other two sides.

 

Course outcomes (CO):

On completion of this course, students will be able to:

1. Formulate differential equations for beam column elements with various combinations of loads and end conditions.

2. Analyse buckling of frames and continuous beams.

3. Carry out stability analysis of structures using Finite Element Method.

4. Analyse buckling of beams and torsion in beams.

5. Apply strain energy method for buckling of plates.

 

Question paper pattern:

  • The question paper will have ten questions, carrying equal marks.
  • There will be two full questions with a maximum four sub questions from each module.
  • Students shall answer five full questions selecting one full question from each module.

 

Reference Books:

1. Timoshenko, S.P. and Gere, J.M., Theory of Elastic Stability, 2nd Ed., McGraw Hill Book Co., New York, 1961.

2. Simitses, G.J. and Hodges, D.H., Fundamentals of Structural Stability, Butterworth & Heinemann, 2006.

3. Gambhir, M.L., Stability Analysis and Design of Structures, Springer, 2009.

4. Manicka Selvam, V.K., Elements of Matrix and Stability Analysis of Structures, 6ed., Khanna Publishers, New Delhi, 2004.

5. Srinath, L.S., Advanced Mechanics of Solids, 3ed., Tata McGraw-Hill Publishing Co. Ltd., New Delhi, 2017.

6. Rajashekaran. S, Computational Structural Mechanic s, Prentice-Hall, India, 2001.

7. Ray W Clough and J Penzien, Dynamics of Structures, 2 nd Edition, McGraw-Hill, New Delhi, 1968.

Categories

VTU Updates