2. The state of stress at a point in a machine part is given by the following stress tensor. The uniaxial yield stress for a steel material is oyp =950 MPa: 300 []= -400 MPа 300 -800 Calculate (a) the stress invariants I1, I2, I;; (b) the principal stresses by expansion of the characteristic stress determinant. (c) Determine using (i) the Tresca criterion and (ii) the von Mises criterion whether or not yielding occurs at the point with the above stress tensor. (Hint: Determine the principal stresses, o,, o,, and 0,, by solving the cubic Equation: o,-1,0,+I,0,-I, =0). Note: Failure occurs when lhs of the Equation for the Failure Theory being tested is greater than the rhs; FS is not needed for this problem (why?).

2. The state of stress at a point in a machine part is given by the following stress tensor. The uniaxial yield stress for a steel material is oyp =950 MPa: 300 []= -400 MPа 300 -800 Calculate (a) the stress invariants I1, I2, I;; (b) the principal stresses by expansion of the characteristic stress determinant. (c) Determine using (i) the Tresca criterion and (ii) the von Mises criterion whether or not yielding occurs at the point with the above stress tensor. (Hint: Determine the principal stresses, o,, o,, and 0,, by solving the cubic Equation: o,-1,0,+I,0,-I, =0). Note: Failure occurs when lhs of the Equation for the Failure Theory being tested is greater than the rhs; FS is not needed for this problem (why?).

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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