Solution_Exam-Fall2010-1_3

Solution_Exam-Fall2010-1_3 - EML 4507 Fall 2010 Exam1-3...

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EML 4507 Fall 2010 Exam1-3 Write only on the front side. If you want, write your name in the back. All problems carry equal points Solution Problem 1 : The state of stress at a point is given by MPa 1 0 0 [ ] 0 2 0 0 0 3 If the yield strength Y of the material is equal to 6 MPa, calculate the Safety Factor N using: (a) Maximum principal stress theory; (b) Maximum shear stress theory; and (c) von Mises’s Theory. Solution : The stress matrix is a diagonal matrix and hence the normal stresses themselves are the principal stresses. 1 2 3 3; 2; 1. (a) 1 6 2 3 Y SF (b) 13 max max 3 ( 1) 2 22 6 1.5 24 Y SF (c) 2 2 2 1 2 2 3 3 1 2 13 3.61 6 1.66 3.61 VM Y VM SF Problem 2 : The state of stress at a point is given by: 10 0 0 [ ] 0 10 0 0 0 10 Calculate the normal stress n and shear stress n on a plane whose normal is given by (1/3, -2/3, 2/3). Solution : The traction on an arbitrary plane is given by Tn Since is a diagonal matrix, the matrix multiplication is simple: 10 0 0 1 10 11 0 10 0 2 20 33 0 0 10 2 20 T Magnitude of this traction is: 1 100 400 400 10 3 T The normal stress is obtained as the scalar (dot) product
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Solution_Exam-Fall2010-1_3 - EML 4507 Fall 2010 Exam1-3...

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