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HD19CE: Applied Mechanics
E-1 Theory of Plates and Shells
Plates : Cylindrical bending of plates, Pure bending of plates. Plate Equation, Rectangular plates - Navier's and Levy's solution, Axi-symmetrically loaded circular plates, Plates on elastic foundation, Anisotropic plates.
Shells : Classification of shells, Membrane theory of shells of revolution and cylindrical shells, Bending theory of axi-symmetrically loaded shells of revolution and cylindrical shells.
Introduction, Historical background, Applications. Fibres and matrix types and properties. Classification of composites. Particulate, Flaked Fibrous, Whisker and Hybrid composites. Forms of fibre reinforcement. Comparison of composites with R.C.C. and metals. Behaviour of uni-directional, crossply, angleply and other composites-strength and stiffness. Anisotropy, orthotropy etc. and generalized Hooke's law. Performance and behaviour of lamina and laminates. Beams, column etc. of sandwich composites and conventional composites. Short fibre composites. Manufacturing techniques, ingredients and equipment joints. Performance of composites under adverse conditions. Resin treated concrete. Wear and abrasion resistant composite. Liquid crystal polymers. Optical, electrical, absorption, conductivity and other properties.
E-3 Experimental Stress Analysis
Behaviour of light, Polarized light, Plane polariscope. Wave plates, Conditioning of light by a series combination of a linear. Polarizer and a wave plate. Arrangement of Optical elements in Polariscope, Construction Details of Diffused Light and Lense Type Polariscope.
Theory of Photoelasticity. The stress optic law in two dimensions at normal incidence. Effects of a stress model in a plane Polariscope, Effect of Stressed model in a circular Polariscope (Dark field and light field arrangement).
Criteria for selection of model materials, Properties of commonly employed photoelastic materials, Conclusions pertaining to material selection.
Introduction, Isochromatic fringe patterns, Isoclinic fringe pattern, Compensation techniques, Separation techniques, Scaling model to prototype stresses. Locking in, Model Deformations, Materials for three dimensional Photoelasticity, Slicing the model and interpretation of the resulting fringe patterns. Effective Stresses.
Birefringent coatings, sensitivity of briefringent coating. Reinforcing effects of birefringent coating. Introduction, Coating stresses, Failure theories, Brittle coating Crack patterns produced by Refrigeration techniques and releasing the load crack detection and types of brittle coating.
Basic characteristics of strain gauge, Types of strain gauge, Factors producing strain sensitivity in metallic alloys, Gauge construction, Temperature compensation, Factors influencing Gauge selection, Gauge sensitivities and gauge factor corrections for transient strain effect.
E-4 Matrix Methods in Vibrations
Vibrations, Introduction
Multidegree of freedom systems. 3 D freedom systems. Solution by iteration, Orthoganality, Jumping technique for calculating stiffness and mass matrix for axially loaded members.
Vibration of beams : Mode shapes of beams during vibrations, Load displacement relationship for beam elements, Vibration of beams with distributed mass. Distributed load on beams with uniformly distributed harmonic force. Consideration of damping force on a beam. Vibration analysis of systems with inclined members. Planar systems, Structures with stiff or welded joints. Computer Programme for the solution of multidegree of freedom vibration systems.
E-5 Analysis of Skeletal Structures
Matrix methods in Skeletal structural analysis : Stiffness method.
Nonlinear Structural Analysis : Matrix displacement analysis for large deflections. Geometrical stiffness. Stability analysis of simple truss, Columns using displacement method.
Vibrations of Elastic Systems : Principle of virtual work in dynamics of elastic systems. Equations of motion and equilibrium. Equivalent masses in matrix. analysis, condensed mass matrix. Lumped mass representation, Vibration analysis based on stiffness, orthogonality relations, Damped Structural systems.
Beam Column : Beam-column with concentrated load. distributed lateral load and end moments, Effect of Axial load on bending stiffness, slope deflection equation, Failure of beam column and interaction equations. Beams on Elastic Foundations : Infinite beam subjected to concentrated loads and distributed load segment. Semi-infinite beam subjected to loads at it ends and near its end, shock waves.
E-6 Advanced Strength of Materials
Stresses and strains in three dimensions. Theories of failure. Beams on elastic foundations. Infinite, semi-infinite and finite beams. Bending of curved beam in the plane of loading-carne hooks. chain-links. Bending of a curved beam out of its initial plane. Saint Venant's equations and equations of equilibrium. Bending of circular beams subjected to symmetric loading. Bending of circular arc Bow girder.
Shear centre of cross section of a beam. Bending axis, shear flow, shear centres for various sections composed of thin members torsion of non-circular members. St. Venant's theory, Torsional stresses in elliptical shaft. Approximate solution for rectangular section. Membrane Analogy, Torsion of hollow sections. Torsional stresses in thin walled open and closed sections. Plastic yielding of circular shafts.
Bending of thin plates. Assumptions of theory. Governing differential equation for deflection of plates, Boundary conditions, solutions for rectangular plates. Navier's and levy's solutions.
References 1. Advanced Mechanics of Materials. - A.P. Boresi and O.M. sidebottom. 2. Mechanics of Materials Vol. II. - J.E. Hearn.
E-7 Plastic Analysis of Structures
Introduction, Historical review, plastic failure, plastic moment, capacity of a cross-section, shape factor, concept of load factor. Plastic hinge and collapse Mechanisms. Analysis of beams and frames. Semi Graphical method and Mechanism method. Plastic moment distribution for multi-storey and multi-bay frames. Analysis for deflections at collapse. Effect of axial force and shear.
References
1. Plastic Analysis - L.S. Beedle 2. Plastic Analysis - B.G. Neal 3. Plastic Analysis - Mogg.
E-8 Dynamic Analysis of Structures
Free and forced vibration of single degree and multi-degree freedom systems in direct load, bending, shear and torsion. Earthquake loading and structural idealisation for dynamic analysis. Vibrations of simple and continuous beam. Vibrations of portal and multistorey building frames. Use Lagrange's equation and its applications.
References
1. Dynamic Framed Structures - Rogers. 2. Dynamical Behaviour of Structures - Warburton. 3. Structural Design of Dynamic Loads - Morris.
E-9 Seismic Analysis of Structures
Type of Dynamic Loading : Static vs. dynamic analysis. Earthquake : Occurence and its elements Analysis of SDOF systems and MDOF systems Rayleigh's stodata's method of analysis
Seismic Response of Buildings (Structures)
Calculation of Time period, Base shear and distribution of forces etc. by using conventional approaches e.g. seimic coefficient method, response spectrum method. Effect of torsion on the building P-S effect. An introduction to Seimic analysis of special structures : Nuclear power plant, water tower, Dam, Chimney etc. An introduction to Dynamics of soil-structure interaction.
References
1. Theory of Vibration with Application : W.T. Thomson. 2. Dynamics of Structures : R.W. Clough & Pension. 3. Elements of Earthquake Engg. : A.R. Chandrasekharan and Jaikrishna. 4. Fundamentals of Earthquake Engineering : Newmarks and Rosenbleuter.
E-10 Theory of Elasticity and Plasticity
Fundamentals of Elasticity Theory : The requirements for a solution, solution procedures, the St. Venant's principle, Stress functions. Beams : Some exact solutions for the bending of beams. Beams of irregular cross-section, Curved beams. Plates : circular plates. Shells : Membrane theory of shells of revolution and cylindrical shells. Concentrated Loads and Stress Concentrations, Fracture Mechanics : Stress distributions due to cracks, & Fracture, Vibrational and Energy Methods. Numerical Methods. Plasticity : Yield surfaces, Prandtl - Reuse. Theory and Deformation Theory, Generalized stress-strain relations, Bending and torsion of prismatic bars, Axisymmetric problems. Metal forming processes.
Classification, description, types energy and momentum equation for prismatic and non prismatic channels. Uniform flow, critical flow, critical depth, specific energy. Gradually varried flow, dynamic equation, flow profiles, computation, analytical and graphical methods, transitions of subcritical and supercritical flow.
Spatially varied flow : Basic principles assumptions, dynamic equation, analysis of flow profile, methods of numerical interaction.
Rapidly varied flow : Characteristics of the flow, hydraulic jump in horizontal, and sloping channels, submerged hydraulic jump. Flow in channel of non-linear alignment and non-prismatic channel sections.
Books Recommended
1. Flow in Open Channel - Ven Te Chow. 2. Flow Through Open Channel - K.G. Ranga Raju. 3. Open Channel Flow - Henderson.
Theory of small amplitude periodic waves, Effect of slope of continental and nearshore shelf, Types of breakers, Refraction and mach stem effect, Coastline features littorial drift Break water and forces thereon, Mooring and mooring forces, Concepts of wave generation. Wave forces on structures.
Contenrs : River morphology, behaviour of river flow vis-vis-geophysical consideration and readjustment, mechanics of sediment transport, River Gauging, Socio-economic and Ecological study of river flows and their utilisation.
Unsteady flow in open channels, water hammer in pipes, Layout of hydropower systems, Civil works, Surge tanks, Design of penstocks and surge tanks and their hydraulic performance, Mass curves, Load curves, Peak percentage curves, Reservoir Capacity Design. Types of power supply Role of water power in multi-source power systems, Penstocks, Power channels, Accessories values, etc. Pondage and storage requirements. Types of plants Run-off river, storage, pumped, storage, tidal, diversion, valley dam, Fundamental Concepts of tidal basins and generation of tidal power, power houses, surface and underground, Turbines - Progressive changes from impulse to ractive radial flow to axial flow units.
Of Euler's Equations Navier-Stokes' equations, Integration, to Bernoulli's equation, Time dependent potential, Stokes theorem and Greens' theorem, Conformal transformation, Flow nets, Axisymmetric boundary layer flows, Helmhortz principle, vorticity and momentum transfer concepts on turbulence, spectra of turbulence, Turbulence measurements.
E-16 Analysis and Design of Hydraulic Structures
Analysis and Design of Hydraulic Structures, Brief description of various hydraulic structures Hydraulic Design of weir on permeable foundation, Hydraulic/Design of culverts, cross drainage works, River Training works, falls. Design considerations in non-linear channels. Hydraulic Design of earthen dams and rigid dams (gravity and arch dam).
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