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Solution_Exam-Fall2010-1_1

Solution_Exam-Fall2010-1_1 - EML 4507 Fall 2010 Exam 1-1...

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EML 4507 Fall 2010 Exam 1-1 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 2 0 0 [ ] 0 4 0 0 0 1 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 4; 2; 1. (a) 1 6 1.5 4 Y SF (b) 1 3 max max 4 ( 1) 2.5 2 2 6 1.2 2 5 Y SF (c) 2 2 2 1 2 2 3 3 1 2 19 4.36 6 1.38 4.36 VM Y VM SF Problem 2 : The state of stress at a point is given by: 13 0 0 [ ] 0 13 0 0 0 13 Calculate the normal stress n and shear stress n on a plane whose normal is given by (3/13, 4/13, 12/13). Solution : The traction on an arbitrary plane is given by T n Since is a diagonal matrix, the matrix multiplication is simple: 13 0 0 3 3 1 0 13 0 4 4 13 0 0 13 12 12 T Magnitude of this traction is: 9 16 144 13 T
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