JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

Course Objectives

To impart knowledge on the behavior of plates and to analyse the problems

pertaining to beams on elastic foundation.

Course Outcomes

The learner will be able to understand the behavior of plates for loadings and

boundary conditions.

UNIT - I

Cylindrical Bending: Different kind of plates – Assumptions – Derivation of differential equation for cylindrical bending of long rectangular plates - Analysis of uniformly loaded rectangular plates with edges simply supported and fixed subjected to uniform load. Pure Bending of Plates: Slope and curvature of slightly bent plates – Relations between moments and curvature - Particular cases of pure bending - Strain energy in pure bending –Energy methods like Ritz and Galerkin Methods to rectangular plates subjected to simple loadings.

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’s 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 : Symmetrical loading – Relations between slope, deflection, moments and curvature – Governing differential equation – Uniformly loaded plates with clamped and simply supported edges – Central hole – bending by moments and shearing forces uniformlydistributed. Orthotropic Plates: Introduction – Bending of anisotropic plates - Derivation of governing differential equation – Determination of Rigidities in various cases like R.C. slabs, corrugated sheet – Application to the theory of grid works.

UNIT - IV

Plates on Elastic Foundations: Governing differential equation – deflection of uniformly loaded simply supported rectangular plate – Navier and Levy type solutions – Large plate loaded at equidistant points by concentrated forces P.

UNIT - V

Buckling of Plates: Governing equation for Bending of plate under the combined action of in-plane loading and lateral loads – Buckling of rectangular plates by compressive forces acting in one and two directions in the middle plane of plate Finite Difference Methods: Introduction - Application to rectangular plates subjected to simple loading.

TEXT BOOK

• 1. Theory of Plates and Shells by Timoshenko, McGraw Hill Book Co., New York.

REFERENCES:

• 1. Theory and Analysis of Plates by P. Szilard, Prentice Hall.
• 2. Theory of Plates by K. Chandrasekhara, University Press.
• 3. Plate Analysis by N. K. Bairagi, Khanna Publishers. New Delhi.
• 4. Numerical Methods for Engineering Problems, N. Krishna Raju & K. U Muthu, Mac-Millan publishers M. Tech – I Year – II Sem. (Structural Engg.)