# L5 - Poisson's Ratio For a slender bar subjected to axial...

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Poisson’s Ratio • For a slender bar subjected to axial loading: 0 = = = z y x x E σσ σ ε • Elongation in the x-direction -> contractions in other directions. • material is isotropic and homogeneous 0 = z y • Poisson’s ratio is defined as x z x y ν = = = strain axial strain lateral

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Multi-axial loading E x z y νσ εε = = E x x σ ε= E y y ε = E z z E y z x = = E z y x = =
Generalized Hooke’s Law •I f 1) strain is linearly related to stress 2) deformations are small E E E E E E E E E z y x z z y x y z y x x σ νσ ε + = + = + = • Use superposition:

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• For element subjected to uniform hydrostatic pressure, ( ) () 31 2 bulk modulus p ep Ek E k ν =− == • Subjected to uniform pressure, dilatation must be negative, therefore 2 1 0 <
Shearing Strain shear strain is quantified in terms of the change in angle between the sides: •Reduction of the angle between two sides-> + shear stress

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## This note was uploaded on 04/20/2008 for the course ENGR 2530 taught by Professor Lindaschadlerfeist during the Spring '08 term at Rensselaer Polytechnic Institute.

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L5 - Poisson's Ratio For a slender bar subjected to axial...

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