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# HW#2 - AE 322 Homework#2 Due Monday February 8 2010 NOTE If...

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AE 322 Homework #2 Due Monday, February 8, 2010 NOTE: If you use MATLAB ® , show command sequence and output. 1. Find the components of the traction n T on planes defined by n 1 = 1 2 , n 2 = 1 2 , n 3 = 0 and n 1 = 1 2 , n 2 = − 1 2 , n 3 = 0 for the following states of stress: (a) σ 11 = σ σ 12 = σ 21 = 0 σ 13 = σ 31 = 0 σ 22 = σ σ 23 = σ 32 = 0 σ 33 = σ (b) σ 11 = σ σ 12 = σ 21 = σ σ 13 = σ 31 = 0 σ 22 = σ σ 23 = σ 32 = 0 σ 33 = 0 2. The state of stress at a point P in a material is given by: σ ij [ ] = 20 2 1 2 15 2 1 2 3 KPa (a) Compute the components of traction n T on the plane passing through P whose outward normal vector n makes equal angles with the coordinate axes. Note: this is the octahedral plane, 1 2 3 1 3, 1 3, 1/ 3 n n n = = . (b) Compute the normal nn σ and tangential ns σ components of traction on this plane. (c) Repeat the above exercise for the stress state: 10 2 1 2 15 5 1 5 3 ij KPa σ  =

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3. Determine the body forces for which the following stress field describes a state of equilibrium: σ ij [ ] = yz + 4
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HW#2 - AE 322 Homework#2 Due Monday February 8 2010 NOTE If...

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