Solution3 - AE 321 Solution of Homework #3 1. The...

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1 AE 321 – Solution of Homework #3 1. The components of the traction at a given plane is given by j ji j ij n i n n T σ = = ) ( or T n () [] = n , ( 1 ) where ij represent the symmetric stress tensor and j n represents the j component of the outward normal unit vector of the plane under consideration. (a) State of stress: ij = 00 0 0 with unit vector normal to the plane: n j = 1 2 1 2 0 After substituting into Equation (1), we obtain the traction on the plane under consideration T n = 0 0 1 2 1 2 0 = 2 2 2 2 0 or ± T n = 2 2 ² e 1 ² e 2 (b) State of stress: ij = 0 0 000 the plane under consideration is the same as in (a). Applying Equation (1) T n = σσ 0 0 1 2 1 2 0 = 0 2 0 or ± T n = 2 ² e 2
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2 2. a. Compute the components of traction on the plane passing through P whose outward normal vector n makes equal angles with the coordinate axes.
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This note was uploaded on 01/18/2010 for the course AE 321 taught by Professor Waller during the Fall '07 term at University of Illinois at Urbana–Champaign.

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Solution3 - AE 321 Solution of Homework #3 1. The...

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