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

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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 σ = = ) ( or T n ( ) [ ] = σ [ ] n [ ] , (1) where ij σ 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: σ ij [ ] = σ 0 0 0 σ 0 0 0 σ 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 ( ) [ ] = σ 0 0 0 σ 0 0 0 σ 1 2 1 2 0 = 2 σ 2 2 σ 2 0 or T n ( ) = 2 2 σ e 1 e 2 ( ) (b) State of stress: σ ij [ ] = σ σ 0 σ σ 0 0 0 0 the plane under consideration is the same as in (a). Applying Equation (1) T n ( ) [ ] = σ σ 0 σ σ 0 0 0 0 1 2 1 2 0 = 0 2 σ 0 or T n ( ) = 2 σ 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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Solution3 - AE 321 Solution of Homework#3 1 The components...

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