Syllabus
Unit 1
Introduction to theory of elasticity: Stresses and strains at a point, equilibrium equations, boundary conditions, stress and strain transformations, principal stresses and strains, Mohr’s circle, bi-axial and tri-axial stresses, constitutive relations, plane stress and plane strain conditions, stress and displacement formulations, strain compatibility relation, governing equations, Airy’s stress function, analysis of thin and thick walled pressure vessels.
Unit 2
Buckling of columns: Euler’s formula, effective length, load versus deflection plot, load eccentricity, imperfections, South- well plot; Theories of Failure: Maximum principle stress theory, maximum principle strain theory, maximum strain energy theory, maximum shear stress (Tresca) theory, and maximum distortion (von-Mises) theory. Application of failures theories in the design of structural members like bar, beam, column, shaft and pressure vessels.
Unit 3
Introduction to vibration, undamped vibration, natural frequency, damped vibration, viscous damped system, under, over and critically damped system, logarithmic decrement, Coulomb damping, response to initial condition, response to simple harmonic motion, rotating unbalance, base excitation, whirling of shafts, vibration measuring instruments, response to periodic motion
Objectives and Outcomes
Course Objectives
To make students understand and appreciate the importance of theory of elasticity, concept of principal stress and strains. And also, to make the students understand the importance of column bucking and theories of failure in design of structural elements.
Course Outcomes
CO1: Understand stress and strain transformation on different plane for combined loading.
CO2: Obtain critical loads for columns with different end conditions.
CO3: Apply the theories of failure in designing the structures.
CO4: Derive equation of motion for systems under translational and rotational motions.
CO-PO Mapping
PO/PSO |
PO1 |
PO2 |
PO3 |
PO4 |
PO5 |
PO6 |
PO7 |
PO8 |
PO9 |
PO10 |
PO11 |
PO12 |
PSO1 |
PSO2 |
PSO3 |
CO |
CO1 |
3 |
3 |
2 |
2 |
– |
– |
– |
– |
– |
– |
– |
3 |
3 |
2 |
– |
CO2 |
3 |
3 |
2 |
2 |
– |
– |
– |
– |
– |
– |
– |
3 |
3 |
2 |
– |
CO3 |
3 |
3 |
2 |
2 |
– |
– |
– |
– |
– |
– |
– |
3 |
3 |
2 |
– |
CO4 |
3 |
3 |
2 |
2 |
– |
– |
– |
– |
– |
– |
– |
3 |
3 |
2 |
– |
Text Books / References
Text Book(s)
James M Gere, Barry J. Goodno “Mechanics of Materials”, 9th Edition, Cengage Learning, USA, 2017.
- T. Thomson, “Theory of vibrations with applications,” Pearson, 1997.
Reference(s)
R.C. Hibbeler “Mechanics of Materials”,11th Edition, Pearson Prentice Hall, New Jersey, USA, 2022.
James M Gere, Stephen P. Timoshenko ” Mechanics of Materials”, 2nd Edition,CBS Publishers, New Delhi, 1986.
- T. Sun, “Mechanics of Aircraft Structures”, 3rd Edition, John Wiley & Sons, New York, 2021.