# Theory of Elasticity

-stress and strain stress -constitutive equations.

Theory of Plasticity y y

-Yielding Criteria, -Von mises criterion and Tresca criterion. - Plastic analysis and limit design methods for structural systems( beams, frames and plates)

1-ELASTICITY yp -Introduction for different types of nonlinear behavior -Tensors symbolic -Unidirectional stress and strain Unidirectional -3D components of stress and strain - Equilibrium equations - Invariants of stresses tensor -Principal stresses - Deviatoric and hydrostatic stress tensors

-Strain tensor -Compatibility equations -Constitutive law -Plane elasticity-Plane stresses and plane strains. 2-PLASTICITY - Definition of plastic state and plastic materials – Yi lding stress Yielding tr -Uni axial nonlinear curve of stress strain –Ideal stress strain curve

- Plastic analysis of indeterminate structural truss members -3-D plasticity- Yield criteria-Maximum shear stress criterion(Tresca) -Distortion Energy Criterion(Von mises) -Octahedral shear stress and second invariant of devatoric stress tensor, as relations with yielding criterion q y y -Equivalent yield stress and yield strain. - Geometrical representation ,Von mises cylindrical yield surface, and hexahedral i ld f h h d l yield surface of T f Tresca criterionit i

-Yield locus in 2-D space -Plastic stress strain law Plastic -Modified stiffness matrix for plastic increments p BEAM ELEMENTS -Plastic bending of beams -Elastic b di moment and plastic or yielding bending moment El ti bending t d l ti i ldi b di t -Shape factor p -Moment and curvature relationships in elsto plastic state - Residual stresses.

-Plastic hinges -Length and depth of plastic region Length -Elastic and plastic deflections in indeterminate beams -Representing moments deflection curves Representing moments-deflection -Calculating the residual deflections-The variation of stiffness and deflections according to the degree The of ends fixation –The effect of...

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