Course Details
Subject {L-T-P / C} : CE4205 : Advanced Mechanics of Solids { 3-0-0 / 3}
Subject Nature : Theory
Coordinator : Asha Patel
Syllabus
| Module 1 : |
Elementary Concept of Elasticity : Stress and strains in three dimensional bodies, stress and strain invariants, principal stress and principal strain, strain rosette, Mohr’s diagram, octahedral, hydrostatic, deviatoric stress/strain, strain displacement relations, stress strain relations, partial differential equations of equilibrium, compatibility conditions, boundary conditions, (8 hours) |
| Module 2 : |
Theory of Elasticity: Plane stress and Plane strain , Governing differential equations using displacement and Stress formulation. Airy Stress Function , polar co-ordinate, Thick walled cylinders, compound cylinders, shrink-fit. (8hours) |
| Module 3 : |
Energy methods and Failure Theories: Strain energy expression in three dimensions, strain energy due to axial load, bending and torsion, Castigliano’s theorems, Principle of virtual work, Unit load and unit couple method. Theories of Failure and its graphical representation for two-dimensional cases. (6 hours) |
| Module 4 : |
Advanced bending problems : Unsymmetrical bending: principal axes of section, slope of neutral axis, stresses and deflections in unsymmetrical bending. Shear Centre of thin wall beam section. (5 hours) |
| Module 5 : |
Curved beams: bending of beams of large initial curvature, stress distribution in beams with rectangular, circular and trapezoidal cross sections, location of neutral axis, stresses in crane hooks, rings and chain links. (4 hours) |
| Module 6 : |
Plastic Analysis :Inelastic moment, plastic hinge, plastic modulus, shape factor, redistribution of moments, collapse load, mechanisms, Upper and Lower bound theorems, Static and kinematic methods of plastic analysis, plastic analysis of continuous beam and portal frame, plastic moment diagrams. (6 hours)
|
| Module 7 : |
Special Topics : Repeated stresses in structural and machine components, fatigue in metals, endurance limit, concept of stress concentration, stress concentration factor and notch sensitivity. (2 hours) |
Course Objective
| 1 . |
To describe the generalised concepts of stress and strain in a solid spatial elastic body. |
| 2 . |
to present the energy methods for solving structural mechanics problem and failure theories for design. |
| 3 . |
to familiarize with the solution of advanced bending problems |
| 4 . |
to introduce the basic concepts of plastic analysis of indeterminant beams and portal frames |
| 5 . |
to introduce the basic concept of fatigue analysis, stress concentration, |
Course Outcome
| 1 . |
students will have a mature understanding of stress and strain and their relationship in an elastic spatial body. |
| 2 . |
students will be able to analyse a plane elastic problems. |
| 3 . |
students will be able to implement basic energy theorems and failure theories to analyze and design structural elements. |
| 4 . |
students will be able to analyze curved beam and understand the concept of unsymmetrical bending and shear center of various cross section . |
| 5 . |
students will be able to perform plastic analysis of beams and portal frames |
| 6 . |
students will be able to learn the effect of repetitive loads on elements |
Essential Reading
| 1 . |
L. S. Srinath, Advanced Mechanics of Solids, Tata-McGraw Hill Publishing Co. Ltd |
| 2 . |
A.C. Ugural, S.K. Fenster, Advanced Strength and Applied Elasticity, Pearson Education, 2003. |
Supplementary Reading
| 1 . |
A.P. Boresi, R.J. Schmidt, O.M. Sidebottom, Advanced Mechanics of Materials, John Wiley&Sons, 1993 |
| 2 . |
4. S. P. Timoshenko and J. N. Goodier, Theories of Elasticity, McGraw Hill Publisher |
Journal and Conferences
| 1 . |
non |