LECTURE #4 :3.11 MECHANICS OF MATERIALS F03INSTRUCTOR : Professor Christine OrtizOFFICE : 13-4022 PHONE : 452-3084WWW : http://web.mit.edu/cortiz/www• Review Lecture #3• Multiaxial Stress States1. Definition of Elasticity : when a material is deformed it recovers it's original shape anddimensions, strain is recoverable, linear vs. nonlinear elasticity, molecular origins2. Poisson's Ratio :3. Shear Stress and Strain :Review : Lectures #30.25 0.35 ( , )0.5 ( )0 ( , exp )yzxxmetals ceramicsvolume conservationauxetic volume ansionεενεεννν−−===−=<Puniaxial loadingLoyzxδδδδxδδδδzδδδδy©2001 Brooks/Cole, a division of Thomson Learning, Inc. ThomsonLearning™is a trademark used herein under license., , , , , , , (' )oooVshear stress V shear force A force parallel to AAshear strain shear displacement Lo initial lengthLG G shear modulus Hooke s Law for Shearττδγγ δτγ== = === = ===xyz•OσxxσyyσzzτyxτyzτxyτxzτzxτzyGeneralized Multiaxial 3D Stress StatesMost 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 normalsNormal Reaction Stresses and Sign Conventionsxyz•OσxσyσzτyxτyzτxyτxzτzxτzyConditions of Static EquilibriumConditions of Static Equilibrium: 2D and 3DNormal Reaction Stresses and Sign Conventionsxyz•OσxσyσzτyxτyzτxyτxzτzxτzyzShear Reaction Stresses and Sign Conventionsxyz•Oτyxτyzτxyτxzτzxτzy2-D Stress State2-D Stress Statezxyy•Ox•OSpecial Cases of Plane
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