1-18 - CHAP 1 Stress-Strain Analysis 45 18. Strain at a...

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CHAP 1 Stress-Strain Analysis 45 18. Strain at a point is such that xx = yy = 0, zz = 0.001, xy = 0.006, and xz = yz = 0. Note: You need not solve the eigen value problem for this question. (a) Show that n 1 = i + j and n 2 = i + j are principal directions of strain at this point. (b) What is the third principal direction? (c) Compute the three principal strains. Solution: (a) The strain matrix is 3 0 6 0 [ ] 6 0 0 10 0 0 1     In order to show a direction n is a principal direction, it is enough to show that [] nn . After normalizing n 1 and n 2 , 33 11 0 6 0 1 6 10 10 [ ] 6 0 0 1 6 22 0 0 1 0 0                                                0 6 0 1 6 10 10 [ ] 6 0 0 1 6 0 0 1 0 0    
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