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**Unformatted text preview: **, = I1 7 I2 5 3 3 11 I3 5 Hence, the cubic equation for principal stresses is:-+-= 3 I12 I2 I3 0 or-+- = 3 72 11 5 0--- = 5 1 1 0 Problem 2 : It is determined that n =5 is one of the principal stresses for the state of stress in Problem 1. (i) Write the three linear equations you will use to determine the corresponding principal direction. (ii) Solve the above equations to determine the principal direction. If there are multiple principal directions for n =5, then show them in a parametric form. Solution ( - )-- ( - ) ( - ) = 3 5 20 2 3 5 000 1 5 nxnynz 000 The first two equations are the same:--= =-2nx 2ny 0 nx ny The last equation yields n z =0 Then the principal direction is given by ,- , 121 1 0...

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