I SEMESTER
MECHANICS OF DEFORMABLE BODIES
Subject Code : 10 CCS-11IA Marks : 50
No. of Lecture Hrs/Week : 04Exam Hrs : 03
Total No. of Lecture Hrs : 52 Exam Marks : 100
Introduction: Definition of stress and strain at a point, components of stress and strain at a point, strain displacement relations in cartesian co-ordinates, constitutive relations, equilibrium equations, compatibility equations and boundary conditions in 2-D and 3-D cases, plane stress, plane strain – Definition.
Two-dimensional problems in Rectangular Coordinates : Airy’s stress function approach to 2-D problems of elasticity. Solution by Polynominals – End Effects, Saint – Venant’s Principle – solution of some simple beam problems, including working out of displacement components.
Two - dimensional problems in Polar coordinates:General equation in Polar coordinates – Strain and displacement relations, equilibrium equations - Stress distribution symmetrical about an axis – Pure bending of curved bars – Displacements for symmetrical stress distributions – Rotating disks – Bending of a curved bar by a force at the end – The effect of a small circular hole on stress distribution in a large plate subjected to uni-axial tension and pure shear. Other instances of stress concentration.
Analysis of Stress and Strain in Three Dimensions : Introduction – Principal stresses –Determination of the principal stresses and principal planes.– Stress invariants – Determination of the maximum shearing stress- Octohedral stress components, Principal strains – strain invariants.
Torsion : Torsion of straight bars of Elliptic Cross section – St.Venants semi inverse method and Prandtl’s function Approachd – Membrane analogy – Torsion of a bar of narrow rectangular cross section Torsion of thin walled open cross sections – Torsion of thin walled tubes.
REFERENCES:
1. Timoshenko and Goodier, Theory of elasticity, McGraw Hill Book Company, III
Edition, 1983.
2. Fung.Y.C, Foundations of Solid Mechanics, Prentice-Hall.
3. Valliappan.S, Continuum Mechanics fundamentals, Oxford and IBH.
4. Srinath.L.S., Advanced Mechanics of Solids, Tata McGraw-Hill Publishing Co ltd.,
New Delhi
COMPUTATIONAL STRUCTURAL MECHANICS
Subject Code : 10 CCS-12IA Marks : 50
No. of Lecture Hrs/Week : 04Exam Hrs : 03
Total No. of Lecture Hrs : 52 Exam Marks : 100
Brief history of Structural Mechanics, Structural Systems, Degrees of Static and Kinematic indeterminacies, geometrical and Material Non Linearities, Concepts of Stiffness and Flexibility. Energy concepts in Structural Mechanics, strain energy – Axial, Flexural & Shear - Real work and Complementary work – Principle of virtual displacement for a rigid body and a deformable body – Principles minimum potential energy, and minimum complementary energy. Maxwell Betti theorem.
Relationship between element and system – transformation of information from system forces to element forces using equilibrium equations, transformation of information from system displacement to element displacement, contra gradient law, element stiffness and flexibility matrices, (bar, beam and grid elements), generation of system stiffness matrix using uncoupled element stiffness matrices. Analysis of statically indeterminate structures (i) Truss, (ii) Continuous beam and (iii) Simple frames by stiffness method (element approach)
Direct stiffness method local and global coordinate system – Direct assembly of element stiffness matrices – Analysis of indeterminate structures (i) Truss, (ii) Continuous beam & (iii) Simple frames (iv) Frames subjected to loads perpendicular to plane of the frame.
Storage techniques – Half band, skyline storage. Equation solvers – Gauss elimination, Gauss – Siedel , Cholesky methods, - Flow charts & Algorithms.
REFERENCES:
1. Rajasekaran.S, “Computational Structural Mechanics”, PHI, New Delhi 2001
2. Reddy.C.S, “Basic Structural Analysis,” TMH, New Delhi 2001
3. Beaufait.F.W. et al., Computer Methods of Structural Analysis, Prentice Hall, 1970.
4. Weaver.W and Gere.J.H., Matrix Analysis of Framed Structures, Van Nastran,
1980.
5. Karde Stuncer.H, Elementary Matrix Analysis of Structures, McGraw-Hill 1974.
6. Jain.A.K. Advanced Structural Analysis with Computer Application Nemchand and
Brothers, Roorkee, India
7. Rubinstein M.F, Matrix Computer Methods of Structural Analysis Prentice-Hall.
8. Krishnamoorthy.C.S. Finite Element theory and programming TMH, India.
9. Bathe.K.J, Finite element procedures in Engineering Analysis. PHI. New Delhi
COMPUTATIONAL STRUCTURAL DYNAMICS
Subject Code : 10 CCS-13IA Marks : 50
No. of Lecture Hrs/Week : 04Exam Hrs : 03
Total No. of Lecture Hrs : 52 Exam Marks : 100
Single Degree of Freedom System- degrees of freedom, undamped system, springs in parallel, in series. Newton’s laws of motion, free body diagrams. D’Alembert’s principle, solution of the differential equation of motion, frequency and period, amplitude of motion. Damped Single degree of freedom system – viscous damping, equation of motion, critically damped system, overdamped system, underdamped system, logarithmic decrement. Response of single degree of freedom system to harmonic loading – undamped harmonic excitation, damped harmonic excitation, evaluation of damping at resonance, bandwidth method (Half power) to evaluate damping, response to support motion, force transmitted to the foundation, seismic instruments.
Response to General Dynamic Loading – Impulsive loading and Duhamel’s integral, numerical evaluation of Duhamel’s integral, undamped system, numerical evaluation of Duhamel’s integral, damped system. Fourier analysis and response in frequency domain – Fourier analysis, Fourier co-efficients for piece-wise liner functions, exponential form of Fourier series, discrete Fourier analysis, fast fourier transform.
Generalised Co-ordinates and Rayleigh’s method – principle of virtual work, generalised single degree of freedom system (rigid body and distributed elasticity), Raylegh’s method. Hamilton’s principle.
Multistory Shear Building. Free vibration – natural frequencies and normal modes. Forced motion – modal superposition method – response of a shear building to base motion. Damped motion of shear building – equations of motions – uncoupled damped equation – conditions for uncoupling. Damping.
Discretiszation of Continuous Systems : Longitudinal Vibration of a uniform rod. Transverse vibration of a pretensioned cable. Free transverse vibration of uniform beams – Rotary inertia and shear effects – The effect of axial loading. Orthogonality of normal modes. Undamped forced vibration of beams by mode superposition.
Dynamic Analysis of Beams – stiffness matrix, mass matrix (lumped and consistent); equations of motion for the discretiesed beam in matrix form and its solutions.
REFERENCE:
- Mario Paz, “structural dynamics, Theory and computation”, 2nd Edition, CBS Publisher and Distributors, New Delhi.
- Clough, Ray W and Penzien.J, “Dynamics of Structures”, 2nd Edition, McGraw-Hill, New Delhi.
- Mukhopadyaya, “Vibration, Dynamics and structural problems,” Oxford IBH Publishers New Delhi.
COMPUTER AIDED OPTIMUM DESIGN OF STRUCTURES
Subject Code : 10 CCS-14IA Marks : 50
No. of Lecture Hrs/Week : 04Exam Hrs : 03
Total No. of Lecture Hrs : 52 Exam Marks : 100
Introduction: Engineering applications, Statement of optimization problem, Classification of optimization problems, Optimization techniques.
Classical Optimization Techniques: Single variable optimization, Multivariable optimization with no constrains, with equality constraints - Lagrange multiplier -method, constrained variation method - and with inequality constraints Kuhn Tucker conditions.
Linear Programming: Standard form of Linear programming problem, simplex method, revised simplex Method.
Non-Linear Programming: One dimensional minimisation methods, Elimination and Interpolation methods, unconstrained Optimization Techniques, Direct Search methods, Descent Methods, Constrained Optimization Techniques, Direct methods. Indirect methods.
Stochastic Programming: for optimization of design of structural elements with random variables
Application Problems: Optimum design RC, PSC, Steel structural elements. Algorithms for optimum designs.
Genetic Algorithms : Introduction – fitness function including the effect of constraints cross over, mutation.
REFERENCES:
1.Rao.S.S - Optimization Theory and Applications, Wiley Eastern Limited,1978.
2. Fox.R.L. - Optimization Methods for Engineering Design, Addison Wesley, 1971.
3. Stark.R.M. Nicholls.R.L., Mathematical Foundations for Design, McGraw Hill
Book Company.
4. Narsingk Deo – System simulation with digital computer, Prentice – Hall of India
Pvt, Ltd. New Delhi – 1989.
COMPUTER BASED ADVANCED NUMERICAL METHODS
Subject Code : 10 CCS-151IA Marks : 50
No. of Lecture Hrs/Week : 04Exam Hrs : 03
Total No. of Lecture Hrs : 52 Exam Marks : 100
Linear System of Equations ( Direct Methods) : Introduction – Cramer’s Rule –Gaussian Elimination – Gauss – Jordan Method – Factorization method – Ill conditioned matrix – sealing of a matrix – How to solve AX = b on a Computer – Summary – Exercises
Iterative Methods for Solving Linear Equation : Introduction – Basic Ingredients – Stationary Methods : Jacobi Iteration – Computer Time Requirement for Jacobi Iteration – Gauss – Seidel Method – Relaxation Method – Condition of Convergence of Iterative Method – Summary - Exercises
Storage Schemes and Solution of Large System of Linear Equations : Introduction – Solution of Large sets of Equations – Band Form – Skyline storage – Solution of Band Matrix in Core – Band Solver for large number of equations – Cholesky (L), (U) Decomposition in skyline storage – Bandwidth Reduction – Frontal Solvers – Substructure Concept – Submatrix Equation Solver - Summary
Solution Techniques for Eigenvalue Problems : Introduction – Practical problems – Methods for solution of Eigenvalue problems – Methods of characteristic polynomial – Vector Iteration Techniques – Transformation Method – Transformation of the Generalized Eigenvalue Problem to a standard form – number of eigenvalues smaller than - Sturm sequence property – Approximate solution techniques – Polynominal iteration techniques – Solution strategy for eigen solution of large systems – comparison of various techniques – Summary - Exercises.
Numerical Integration : Introduction – Newton – Cotes Closed quadrature – Trapezoidal rule – Romberg – integration – Newton – cotes Open quadrature – Gaussian quadrature – Gauss – Laguerre quadrature – Gauss – Chebyshev quadrature – gauss – Hermite quadrature – Numerical integration using spline – Monte – Carlo method for numerical integration – How to choose a method for estimating a proper integral - Discontinuities and improper integrals = Multiple integration – integration by using mapping function – Summary Exercises
Solution of Ordinary First Order Differential Equations :Introduction – nth order differential equation – Physical problem – Taylor series – Euler method or first order Taylor series – modified Euler method – Picard method of successive approximation – Runge – Kutta methods – solution of simultaneous ordinary differential equations by R K Methods. Predictor / Corrector method – How to select numerical integration method – Summary Exercise.
Boundary Value Problems Region Method ( Finite Difference Approach) :
Introduction – Classification – basic methods – Practical examples – Numerical solution – One dimension – two dimensions – Solution of Elliptic equation – Parabolic Equations (practical examples) Hyperbolic equations – Summary –Exercises
REFERENCE BOOKS :
- Gerald, G.F and Wheatley, P.O., “ Applied Numerical Analysis” 6 Ed. Pearson Education 1999
- Chapra S.C and Canale. R.P “ Numerical Methods for Engineers with Programming and Software Applications” 3 Ed. Tata McGraw Hill, New 1998
- Scaborough.J.B. “ Numerical Mathematical Analysis” Oxford IBH Publishers, New Delhi
- Salvadori.M, “ Numerical Methods” PHI, New Delhi
- Jain, Iyenger & Jain “ Numerical Methods for Scientific Engineering Computation” Wiley Eastern ltd.
- Saxena.H.C. “ Examples in Finite Difference & Numerical Analysis” S Chand & Co, New Delhi
COMPUTER AIDED ADVANCED DESIGN OF METAL STRUCTURES
Subject Code : 10 CCS-152IA Marks : 50
No. of Lecture Hrs/Week : 04Exam Hrs : 03
Total No. of Lecture Hrs : 52 Exam Marks : 100
Design of Industrial Structures : Design of trussed bent, Design principles of single storey rigid frames, open-web beams and open-web single storey frames.
Design of Storage Structures and Tall Structures : Design of Liquid Retaining Structures, Silos, Bunkers, Chimneys and transmission towers.
Design of Steel Bridges : Design principles of trussed bridges.
Design of Light Gauge Steel Sections : Design principles of members in compression, tension, bending and torsion.
Design of Aluminum Structures : Codes and Specifications, Design principles of tension members, welded tension members, compression members, beams, combined loading cases.
Design Principles of Structures with round tubular sections : Introduction, round tubular section, permissible stresses, compression members, Tension members, beams and roof trusses.
REFERENCES:
1. Ramachandra, design of Steel structures, Vol.I and Vol.II.
2. Duggal.S.K., design of Steel structures.
3. Vazirani & Ratwani, Steel structures, Vol. III.
4. Cyril Benson, Advanced Structural Design.
5. Gaylord.E.H and Gaylord.C.N., Structural Engineering Hand Book
6. Bresler, Boris and .Lin.T.Y., design of Steel Structures.
7. Lothers, Advanced Design in Steel.
8. IS:800 : Indian Standard Code of Practice for general construction in steel.
9. S.P.6 (1) : Hand Book for Structural Engineers. – Structural steel sections.
10.I.R.C. Codes and Railway Board Codes, pertaining to bridges.
11.IS : 6533. Code of practice for Design and Construction of steel chimneys.
12.IS 811. Cold Formed Light Gauge structural steel sections.
13.IS : 801. Code of practice for use of cold formed light gauge steel structural
members in general building construction.
14. SP : 6(5) : ISI Hand Book for Structural Engineers. Cold – Formed Light gauge
steel structures.
15. IS : 4923. Specifications for Hollow steel sections for Structural use.
16. IS : 1161. Specifications for Steel tubes in general building construction.
17. IS : 806. Code of Practice for use of steel tubes in general building construction.
COMPOSITE AND SMART – MATERIALS
Subject Code : 10 CCS-153IA Marks : 50
No. of Lecture Hrs/Week : 04Exam Hrs : 03
Total No. of Lecture Hrs : 52 Exam Marks : 100
Introduction to Composite materials, classifications and applications. of fibers, volume fraction and load distribution among constituents, minimum & critical volume fraction, compliance & stiffness matrices, coupling,
Anisotropic elasticity - unidirectional and anisotropic laminae, thermo-mechanical properties, micro- mechanical analysis, classical composite lamination theory,
Cross and angle–play laminates, symmetric, antisymmetric and general asymmetric laminates, mechanical coupling, laminate stacking,
Analysis of simple laminated structural elements ply-stress and strain, lamina failure theories - first fly failure, environmental effects, manufacturing of composites.
Introduction-smart materials, types of smart structures, actuators & sensors, embedded & surface mounted,
Piezoelectric materials, piezoelectric coefficients, phase transition, piezoelectric constitutive relation
Beam modeling with strain actuator, bending extension relation
REFERENCE:
1. Robart M Jones, “Mechanic of Composite Materials”, McGraw Hill Publishing Co.
2. Bhagwan D Agaraval, and Lawrence J Brutman, “Analysis and Performance of
Fiber Composites”, John Willy and Sons.
3. Lecture notes on “Smart Structures”, by Inderjith Chopra, Department of
Aerospace Engg., University of Maryland.
4. Crawley, E and de Luis, J., “Use of piezoelectric actuators as elements of
intelligent structures”, AIAA Journal, Vol. 25 No 10, Oct 1987, PP 1373-1385.
5. Crawley, E and Anderson, E., “Detailed models of Piezoceramic actuation of
beams”, Proc. of the 30th AIAA /ASME/ASCE/AHS/ASC- Structural dynamics and
material conference, AIAA Washington DC, April 1989.
II SEMESTER
COMPUTER AIDED STABILITY ANALYSIS OF STRUCTURES
Subject Code : 10 CCS-21IA Marks : 50
No. of Lecture Hrs/Week : 04Exam Hrs : 03
Total No. of Lecture Hrs : 52 Exam Marks : 100
Beam column- Differential equation. Beam column subjected to (i) lateral concentrated load, (ii) several concentrated loads, (iii) continuous lateral load. Application of trigonometric series. Euler’s formulation using fourth order differential equation for pinned-pinned, fixed-fixed, fixed-free and fixed-pinned columns.
Buckling of frames and continuous beams. Elastica. 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 non-conservative follower and pulsating forces.
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.
Expression for strain energy in plate bending with in plane 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- Buckling of a Rectangular Plate Simply Supported along Two opposite sides and uniformly compressed in the Direction Parallel to Those sides – Buckling of a Simply Supported Rectangular Plate under Combined Bending and Compression – Buckling of Rectangular Plates under the Action of Shearing Stresses – Other Cases of Buckling of Rectangular Plates.
REFERENCE:
- Stephen P. Timoshenko, James M. Gere, “Theory of Elastic Stability”, 2nd Edition, McGraw-Hill, New Delhi.
- Robert D Cook et al, “Concepts and Applications of Finite Element Analysis”, 3rd Edition, John Wiley and Sons, New York
- Rajashekaran.S, “Computational Structural Mechanics”, Prentice-Hall, India
- Ray W Clough and J Penzien, “Dynamics of Structures”, 2nd Edition, McGraw-Hill, New Delhi.
- Zeiglar.H,”Principles of Structural Stability”, Blaisdall Publications
COMPUTER AIDED ANALYSIS OF PLATES AND SHELLS
Subject Code : 10 CCS-22IA Marks : 50
No. of Lecture Hrs/Week : 04Exam Hrs : 03
Total No. of Lecture Hrs : 52 Exam Marks : 100
Bending of plates : Introduction -Slope and curvature of slightly bent plates – relations between bending moments and curvature in pure bending of plates – strain energy in pure bending – Differential equation for cylindrical bending of plates–Differential equation for symmetrical bending of laterally loaded circular plates – uniformly loaded circular plates with and without central cutouts, with two different boundary conditions (simply supported and clamped). Centrally loaded clamped circular plate - Circular plate on elastic foundation.
Laterally loaded rectangular plates – Differential equation of the deflection surface – boundary conditions. Simply supported (SSSS) rectangular plates subjected to harmonic loading. Navier’s solution for SSSS plate subjected to udl, patch udl, point load and hydrostatic pressure –Bending of rectangular simply supported plate subjected to a distributed moments at a pair of opposite edges.
Bending of rectangular plates subjected to udl (i) two opposite edges simply supported and the other two edges clamped, (ii) three edges simply supported and one edge built-in and (iii) all edges built-in. Bending of rectangular plates subjected to uniformly varying lateral load (i) all edges built-in and (ii) three edges simply supported and one edge built-in.