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

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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 = 12 = 21 = 0 13 = 31 = 0 22 = 23 = 32 = 0 33 = (b) = = = = = 0 = = = 0 = 0 2. The state of stress at a point P in a material is given by: 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, 123 1 3 , 1 1/ 3 nnn = = . (b) Compute the normal nn and tangential ns components of traction on this plane. (c) Repeat the above exercise for the stress state: 10 2 1 2 15 5 1 53 ij KPa   = 
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3. Determine the body forces for which the following stress field describes a state of equilibrium: σ ij [ ] = yz + 4 z 2 + 2 x 5 y + z xz + 3 y 8 x 3 sym . 2 xyz KPa . 4. The stress tensor at a point P referred to an
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HW#2 - AE 322 Homework #2 Due Monday, February 8, 2010...

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