HW2_Soln_r1 - 1. Find the components of the traction n T r...

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Unformatted text preview: 1. Find the components of the traction n T r on planes defined by n 1 = 1 2 , n 2 = 1 2 , n 3 = and n 1 = 1 2 , n 2 = - 1 2 , n 3 = for the following states of stress: (a) 11 = 12 = 21 = 13 = 31 = 22 = 23 = 32 = 33 = (b) 11 = 12 = 21 = 13 = 31 = 22 = 23 = 32 = 33 = Solution a) g G = 1/2 1/2 = /2 /2 g G = 1/2 1/2 = /2 /2 b) 1/2 1/2 = 2 2 1/2 1/2 = 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 r on the plane passing through P whose outward normal vector n r 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 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 5 3 ij KPa =- (a) g G = 20 2 1 2 15 2 1 2 3 1/3 1/3 1/3 = 23/3 11/3 23 b) = T n = - + 23 = 6 = |T | = 17 = 13.88 c)...
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HW2_Soln_r1 - 1. Find the components of the traction n T r...

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