Lecture_Stress_transformation_Principal_Mohr_3D

Lecture_Stress_transformation_Principal_Mohr_3D - Class...

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Unformatted text preview: Class Workbook and Handouts - MME 412: Mechanics of Materials Prepared by: Kumar V. Singh -41- Stress Transformation and Principal Stresses in 3D Key Concept: Express unit normal for each of the primed (transformed) co-ordinate axis directions in terms of vector components of unprimed (original) system. Class Workbook and Handouts - MME 412: Mechanics of Materials Prepared by: Kumar V. Singh -42- Figure 2.1-8 [1] Class Workbook and Handouts - MME 412: Mechanics of Materials Prepared by: Kumar V. Singh -43- Three Dimensional Stress Equations: Class Workbook and Handouts - MME 412: Mechanics of Materials Prepared by: Kumar V. Singh -44- 3D Transformation as a combination of 2D rotations (Example 2.1-1) Given: Three dimensional State of the stress, ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ − − − − = 5 2 2 2 4 6 2 6 8 σ , determine transformed state of stress when this element is first rotated by o 45 about z-axis and then the resulting element is rotated o 30 about x-axis....
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This document was uploaded on 11/04/2011 for the course MME 512 at Miami University.

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Lecture_Stress_transformation_Principal_Mohr_3D - Class...

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