This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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)...
View
Full
Document
 Spring '08
 Voulgaris,P

Click to edit the document details