BANGALORE UNIVERSITY
SCHEME OF STUDY AND EXAMINATION FOR
M.E. DEGREE COURSE IN CIVIL ENGINEERING
MAJOR: EARTHQUAKE ENGINEERING
(2008-2009 ONWARDS)
DEPARTMENT OF CIVIL ENGINEERING

2K8EQ101 THEORY OF ELASTICITY AND PLASTICITY
Part – A
Introduction, theory of elasticity vs. ordinary mechanics, notation for forces and stresses, components of stresses and strains, concepts of homogeneity, anisotropy, isotropy, and orthotropy. Generalized Hook’s law, ideal stress-strain diagram for rigid elastic plastic and viscous materials. Plane stress and plane strain, strain Rosettes, Mohr’s circle of stress and strain, Differential equations of equilibrium, boundary conditions, compatibility equations, and stress functions.

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Two-dimensional problems in rectangular coordinates – displacements and
deformation – solution to problems using polynomials. St. Venant’s principle, determination of displacements. Bending of a cantilever loaded at the end and beam with uniform load, application of Fourier series.
Two-dimensional problems in polar coordinates – governing equations, stress distribution symmetric about an axis, pure bending of curved bars. Strain components in polar coordinates (displacement are excluded). Effect of Circular holes on stress distribution in plates. Concentrated force at a point and any vertical load of a straight boundary. Wedge problems given the stress function. Three-dimensional stress systems, stress and strain tensor, stress gradient, deviatoric stress strain and plane ( - plane), stress and strain invariant octahedral shear stresses and its planes.

Part – B
Plasticity: General concept, yield criteria, bending of prismatic beams, residual stresses.
References
1. Theory of Elasticity by Timoshenko. S.P & Goodier J.N, McGraw Hill
Publication.
2. Theory of Elasticity, by Sadhu Singh, Khanna Publication 1988
3. Advanced Mechanics of Materials, Krishnaraju & Gururaj
4. Applied Elasticity, Sitharam T.G. & Govindaraju L. Interline Publications, 2004
5. Theory of Plasticity by Sadhu Singh, Khanna Publication 1981
6. Theory of Plasticity, by Chakrabarthy J., McGraw Hill Publication, 1987.

2K8EQ102 THEORY OF VIBRATION
Introduction : Classification of Dynamic System Models, constraints, generalized coordinates and degrees of freedom, classification of vibrations, elementary parts of vibrating systems, discrete and continuous systems, vibration analysis, elements of vibratory systems, review of dynamics. Free Vibration of Single-Degree-of-Freedom Systems: Free vibration of undamped translational system, free vibration of undamped torsional system, Rayleigh’s Energy Method, stability of undamped linear system, free vibration with viscous damping, free vibration with Coulomb Damping, free vibration with Hysteric Damping. Harmonically Forced Vibrations of Single-Degree-of-Freedom Systems: Equations
of Motion, forced undamped vibration, interpretation of the solutions, resonance, beating phenomenon, forced vibration of damped systems, force transmission, quality factor and bandwidth, rotating unbalance, base excitation, resonance under Coulomb damping, resonance under Hysteresis damping .
General Forcing Conditions and Response: Periodic forcing functions, Fourier Series and harmonic analysis, harmonic functions, response under a periodic force of irregular
form, response under a general periodic force, transient vibration, Laplace Transform
Method.
Two-Degree-of-Freedom Systems: Equations of motion for a two-degree-of-freedom
systems, free vibration of undamped systems, torsional systems, coordinate coupling and
principal coordinates, damped free vibration, forced vibration of undamped systems,
forced vibration with damping, orthogonality of modes.
Multi-Degree-of-Freedom Systems: Equations of motion, stiffness influence
coefficients, flexibility influence coefficients, matrix formulation, inertia influence
coefficients, free vibration of multi-degree-of-freedom systems, free vibration of
undamped system, free vibration of damped system, forced vibration of Multi-Degreeof-
Freedom systems, modal analysis for undamped systems and systems with
proportional damping, numerical solutions.
Analytical Dynamics: Degrees of freedom, generalized coordinates, constraints,
principle of virtual work, D’Alembert’s principle, generalized force, Lagrange’s
Equation of motion, Rayleigh dissipation function, impulsive motion, integrals of
motion, variational principles, Hamilton’s principle.
Vibration of Continuous Systems: Transverse vibration of a string, longitudinal
vibration of rods, torsional vibration of shafts, transverse vibration of beams, vibration
of membranes, approximate methods.

Approximate Methods for Finding Natural Frequencies and Mode Shapes:
Dunkerley’s equation, Rayleigh Method, Rayleigh-Ritz Method, Holzer Method, Jacobi
Diagonalization Method, Cholesky Decomposition Method, iteration methods.
Dynamic Response by Numerical Integration Methods: Single degree of freedom
system, multi degree of freedom systems, explicit schemes, implicit schemes, case
study.

References
1. Mechanical Vibrations – 4th Edition by SS Rao, Pearon Education
2. Structural Dynamics – Theory & Computation by Mariopaz CBS Publishers
and distributors
3. Mechanicsl Vibrations by GK Grover – New Chand & Bros, Roorkee (UP)
4. Structural Dynamics – An Introduction to Computer Methods by Roy R. Craig,
Jr. – John Wiley & Sons
5. Vibration Analysis & Foundation Dynamics – Kameshwara Rao – Wheeler
Publishing
6. Vibrational Mechanics – Non Linear Dynamic effects, general approach,
applications – By Iliya I. Blekhman – Allied Publishers Pvt. Ltd.,
7. Fundamentals of Mechanicsl Vibrations – By S. Graham Kelly – McGraw Hill
International Editions Mechanical Engineering Series
8. Mechanical Vibrations – Theory & Applications – By Francis S. Ise, Ivan E.
Morse, Rolland T. Hinkle – 2nd Edition CBS Publishers & Distributors
9. Dynamics of Structures – by Anil K. Chopra – 2nd Edition, Theory &
Application to Earthquake Engineering-Prentice Hall of India, NewDelhi-2002.