Syllabus

Module I: [4 hrs]
Pure Bending of Plates: Slope & curvature of slightly bent plates, Relations between bending moments and curvature in pure bending of plates, Strain energy in Pure bending of plates.

Module II: [6 hrs]
Symmetrical bending of Circular plates: Differential equation for symmetrical bending of laterally loaded circular plates, uniformly loaded clamped and simply supported circular plates, Circular plates with circular hole at center, circular plate concentrically loaded. Design of simply supported and clamped Circular plates as per IS Codes of practice using the stresses calculated as above.
Module III: [8 hrs]
Small deflections of laterally loaded plates: Differential equation of the deflection surface, Boundary conditions, Simply supported rectangular plates under sinusoidal load, Navier solution for simply supported rectangular plates, Further applications of the Navier solution, Alternate solution for simply supported and uniformly loaded rectangular plates, Concentrated load on simply supported rectangular plates. Design of simply supported and clamped rectangular plates as per IS Codes of practice using the stresses calculated as above.
Module IV: [6 hrs]
Shells: Classification of shell structures, importance of membrane theory of shells,
Membrane theory of shells in the form of a surface of revolution and loaded un-symmetrically with respect to their axes, spherical dome, conical shells and cylindrical shells. Design of spherical dome, conical shells and cylindrical shells as per IS Codes of practice using the stresses calculated as above.
Module V: [6 hrs]
General bending theory of cylindrical shells: Circular cylindrical shell loaded symmetrically with respect to its axis, particular cases of symmetrical deformations of circular cylindrical shells, cylindrical tanks of uniform wall thickness. Design of cylindrical shells as per IS Codes of practice using the stresses calculated as above.
Module VI: [6 hrs]

Membrane theory of doubly curved translation shells using vector approach, Analysis of Elliptic paraboloid, hyperbolic paraboloid and conoids using membrane theory subjected to varieties of loading conditions. Design of elliptic paraboloid, hyperbolic paraboloid and conoids as per IS Codes of practice using the stresses calculated as above.

Students will be able to study the behaviour of pure bending of plates.

Students will be able to do analysis and design of circular plates for various load cases and boundary conditions

Students will be able to analysis and design of rectangular and square plates for various load and boundary conditions

Students will be able to analysis and design of single and doubly curved shellsincluding cylindrical , spherical shells, like elliptic paraboloid, hyperbolic paraboloid and conoids

CO1. Understand the behaviour of pure bending of plates.
CO2. Determination of stress and design of circular plates
CO3. Calculation of stress and design of rectangular plates
CO4. Determination of stresses and design of singly curved cylindrical and conical shells

CO5. Calculation of stresses and design of various doubly curved shells.

S. P. Timoshenko and Woinowsky-Kriegar, Theory of plates and shells, Mc Graw Hill International, New Delhi , .

G. S. Ramaswamy, Design and construction of concrete shells Roofs, CBS Publishers, Delhi , .

D. P. Billington, Thin shell concrete structures, Mc Graw Hill international, New York , .

W. T. Marshall, Design of cylindrical shell roofs, E& FN SPON, London , .

Modal analysis of woven fiber composite plates with different boundary conditions, International Journal of Structural Stability and DynamicsVolume 15, Issue 116 January 2015

Experimental and numerical studies on free vibration of laminated composite shallow shells in hygrothermal environment, Composite StructuresVolume 127, Pages 165 - 174September 01, 2015