Theory of Elasticity and Plasticity Handwritten Premium Lecture Notes, Prepared by Buvana. Syllabus is Based on Anna University , Post Graduate M.E. Structural Engineering R2013 Regulations

CONTENT:

Unit-1 (Pages: 36)

ELASTICITY

Unit-2 (Pages: 26)

ELASTIC SOLUTION

UNIT-3 (Pages: 22)

TORSION OF NON – CIRCULAR SECTION

UNIT-4 (Pages: 18)

ELASTIC FOUNDATION

UNIT-5 (Pages: 16)

THEORY OF PLASTICITY

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Unit-1

ELASTICITY

Types of stress

Bending equation

Strain

Longitudinal strain

Lateral strain

Poisson strain

Determinate structure

Indeterminate structure

Materials

Homogeneous

Isotropic

Analysis of stress and strain

3D equation of equilibrium

Problems

Analysis of strain

Principle stresses

Plane stress problem

Method of solution of elastic problem

First value boundary problem

Second boundary value problem

Mixed boundary value problem

Plane stress

Boundary condition in terms of stress

Unit-2

ELASTIC SOLUTION

Two dimensional problem in Cartesian co – ordinates

Airys stress function method

Complex potential method

Cauchy’s integral method

Fourier transfer method

Real potential method

Plane stress

Polynomials

To satisfies the equilibrium condition

To satisfies the boundary condition

Polynomial for three degree

Fourth degree of polynomial

Bending of a cantilever beam loaded at the end

UNIT-3

TORSION OF NON – CIRCULAR SECTION

St.venant’s principle

Stress distribution

Boundary condition

Torsion of the non linear section

Torsion of thin walled tube

Thin walled open section

UNIT-4

ELASTIC FOUNDATION

Winkler foundation

Governing equation for uniform straight beams on elastic foundation

Beam on elastic foundation

Concentrated moment

Uniformly distributed loads

Method of elastic line

Simply supported beam with point load and UDL

UNIT-5

THEORY OF PLASTICITY

Crystal grains

Mechanism of plastic deformation

Consecutive stages of deformation

Elastic deformation

Plastic deformation

Fracture

Inelastic deformation

Factors affecting plastic deformation

Strain hardenings

Strain relationship

Rigid materials

Perfectly linear elastic materials

Rigid, perfectly plastic

Rigid with strain hardening

Elastic , perfectly plastic

Elastoplastic with strain hardening

Visco elastic materials

Linear standard body

Theories of plastic flow

Maximum principle stress theory

Maximum principle strain theory

Strain energy theorydirection energy theory

Maximum shear stress theory

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