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ME_423_lecture_4 - ME 423 Lecture 4 3D Stresses p Unit...

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1 ME 423 09/9/2011 Lecture 4 3D Stresses Unit vectors to the (x,y,z) axes : i, j, k Unit normal vector to plane ABC: p Direction cosines of p : p i = l ; p j = m ; p k n = 1 2 2 2 = + + n m l If area ABC=1, then OBC= l , OCA= m , OAB= n If p is a principle direction zx yx xx n m l l σ σ σ σ + + = zy yy xy n m l m σ σ σ σ + + = zz yz xz n m l n σ σ σ σ + + = From a non-trivial solution for the homogeneous equation of l,m,n ( ) ( ) ( ) 0 = - - - σ σ σ σ σ σ σ σ σ σ σ σ zz yz xz yz yy xy
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