Solution_Exam-Fall2010-1_2

Solution_Exam-Fall2010-1_2 - EML 4507 Fall 2010 Exam 1-2...

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EML 4507 Fall 2010 Exam 1-2 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 4 0 0 [ ] 0 4 0 0 0 2 If the yield strength Y of the material is equal to 8 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 4; 4; 2. (a) 1 8 2 4 Y SF (b) 13 max max 4 ( 2) 3 22 8 1.33 26 Y SF (c) 2 2 2 1 2 2 3 3 1 2 36 6 8 1.33 6 VM Y VM SF Problem 2 : The state of stress at a point is given by: 300 [ ] 0 3 0 003 Calculate the normal stress n and shear stress n on a plane whose normal is given by (2/3, 2/3, 1/3). Solution : The traction on an arbitrary plane is given by Tn Since is a diagonal matrix, the matrix multiplication is simple: 3 0 0 2 2 1 0 3 0 2 2 3 0 0 3 1 1 T Magnitude of this traction is: 4 4 1 3 T The normal stress is obtained as the scalar (dot) product of T
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Solution_Exam-Fall2010-1_2 - EML 4507 Fall 2010 Exam 1-2...

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