exam1-sample-sol

# exam1-sample-sol - Solution of sample problems first exam 1...

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Solution of sample problems first exam 1. The non-zero components of the stress tensor are xy = xz =4Mpa . What is the normal component of the stress on a plane perpendicular to the vector (1,2,2). First normalize the vector to unit length =(1/3,2/3,2/3). Now 0 4 4 1/3 16/3 400 2 / 3 4 / 3 / 3 4 / 3 t       So t =(4/3)(4 i + j + k ) Mpa. The normal component of t is t  =32/9Mpa 2. For the stress state defined in Problem 1, verify that the direction of the vector (0,1,-1) is a principal direction. What is the principal stress associated with that direction? A principal direction is an eigenvector, and when you multiply it by the matrix it gets multiplied by the eigenvalue (which is the principal stress) without changing direction. 044 0 0 0 400 1 0 01 0 1          so indeed the vector is an eigenvector, and the eigenvalue, equal to the principal stress, is zero. 3. The displacement field in meters is given by v=0.01xyz, with the other components being zero. What are the components of the engineering strain at x=y=z=1m?

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exam1-sample-sol - Solution of sample problems first exam 1...

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