JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

Pre-requisites

Theory of Elasticity, Structural Analysis

Course Objectives:

• 1. To understand the behaviour of Rectangular and circular Plates subjected to various loading
• 2. To understand the behaviour of various types of Shells subjected to various loading
• 3. To study the analysis procedures for plates and shells
• 4. To study the analysis of folded plates

Course Outcomes

After completion of the course, students should be able to

• 1. Use analytical methods for the solution of thin plates and shells
• 2. Use analytical methods for the solution of shells and folded plates
• 3. Apply the numerical techniques and tools for the complex problems in thin plates
• 4. Apply the numerical techniques and tools for the complex problems in shells

UNIT - I

Introduction: Space Curves, Surfaces, Shell Co-ordinates, Strain Displacement Relations, Assumptions in Shell Theory, Displacement Field Approximations, Stress Resultants, Equation of Equilibrium using Principle of Virtual Work, Boundary Conditions.

UNIT - II

Small Deflection Theory of Thin Rectangular Plates : Assumptions – Derivation of governing differential equation for thin plates – Boundary conditions – simply supported plate under sinusoidal load – Navier solution – Application to different cases – Levy’s solution for various boundary conditions subjected to different loadings like uniform and hydrostatic pressure.

UNIT - III

Circular Plates: Differential Equation for symmetrical bending of Laterally loaded circular Plates – Uniformly loaded circular plates –circular plate concentrically loaded – circular plate loaded at center

UNIT - IV

Shells – functional behaviour – examples – structural behaviour of shells classification of shells – Definitions – various methods of analysis of shells – merits and demerits of each method – 2D. Membrane equation. Equations of equilibrium: Derivation of stress resultants – cylindrical shells – Flugges simulations equations.

UNIT - V

Introduction to the shells of Double curvatures: Geometry, analysis and design of elliptic paraboloid, conoid and hyperbolic parabolic shapes, inverted umbrella type.

Axi- Symmetrical shells: General equation - Analysis and axi-symmetrical by membrane theory. Application to spherical shell and hyperboloid of revolution cooling towers.

REFERENCES:

• 1. Theory of Plates & Shells –Stephen, P. Timoshenko, S. Woinowsky-Krieger – Tata MC Graw Hill Edition
• 2. Analysis and design of concrete shell roofs By G. S. Ramaswami, CBS publications.
• 3. Design of concrete shell roofs By Billington – Tata MC Graw Hill, New York
• 4. Design of Shells and Folded Plates by P.C. Varghese, PHI Learning Pvt. Ltd M. Tech in COMPUTER AIDED STRUCTURAL ENGINEERING I YEAR I – SEMESTER