LECTURE 4 3 11 MECHANICS OF MATERIALS F03 INSTRUCTOR Professor Christine Ortiz OFFICE 13 4022 PHONE 452 3084 WWW http web mit edu cortiz www Review Lecture 3 Multiaxial Stress States Review Lectures 3 1 Definition of Elasticity when a material is deformed it recovers it s original shape and dimensions strain is recoverable linear vs nonlinear elasticity molecular origins 2 Poisson s Ratio y x z x 0 25 0 35 metals ceramics 0 5 volume conservation 0 auxetic volume exp ansion uniaxial loading y y x P z z x Lo 3 Shear Stress and Strain V shear stress V shear force A force parallel to Ao Ao Lo 2001 Brooks Cole a division of Thomson Learning Inc Thomson Learning is a trademark used herein under license shear strain shear displacement Lo initial length G G shear modulus Hooke s Law for Shear Generalized Multiaxial 3D Stress States y yy yz yx zy O zz z zx xy xz xx x Most solid materials are subjected are subjected to a combination of different shear and normal loads in 3D Consider a free body diagram FBD of an infinitesimally small cubic stress element where the sides are parallel to the x y z axes and the sides are length dx dy dz 3 distinct faces defined by their normals Normal Reaction Stresses and Sign Conventions y y yz yx zy O z z zx xy xz x x Conditions of Static Equilibrium Conditions of Static Equilibrium 2D and 3D Normal Reaction Stresses and Sign Conventions y y yz yx zy O z z zx xy xz x x Shear Reaction Stresses and Sign Conventions y yz yx zy O z zx xy xz x 2 D Stress State 2 D Stress State y y O O z x x Special Cases of Plane Stress
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