# 1-10 - 32 Finite Element Analysis and Design 10 With...

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32 Finite Element Analysis and Design 10. With respect to the coordinate system xyz , the state of stress at a point P in a solid is 20 0 0 [ ] 0 50 0 MPa 0 0 50    (a) m 1 , m 2 and m 3 are three mutually perpendicular vectors such that m 1 makes 45º with both x - and y -axes and m 3 is aligned with the z -axis. Compute the normal stresses on planes normal to m 1 , m 2 , and m 3 . (b) Compute two components of shear stress on the plane normal to m 1 in the directions m 2 and m 3 . (c) Is the vector n = {0, 1, 1} T a principal direction of stress? Explain. What is the normal stress in the direction n ? (d) Draw an infinitesimal cube with faces normal to m 1 , m 2 and m 3 and display the stresses on the positive faces of this cube. (e) Express the state of stress at the point P with respect to the x y z coordinates system that is aligned with the vectors m 1 , m 2 and m 3 ? (f) What are the principal stress and principal directions of stress at the point P with respect to the x y z ′ coordinate s system?

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1-10 - 32 Finite Element Analysis and Design 10 With...

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