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Lecture_Stress_transformation_Principal_Mohr_2D_2

# Lecture_Stress_transformation_Principal_Mohr_2D_2 - Class...

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Class Workbook and Handouts - MME 412: Mechanics of Materials Prepared by: Kumar V. Singh -29- Stress Transformation: It is a process of determining the state of stress that act on a plane of arbitrary orientation. Why it is important? We should be able to find planes that contain the maximum stresses. These maximum stresses are known as principal stresses and the corresponding plane is known as principal planes (these planes have no shear stress). These maximum stresses and their respective planes can be the basis for design for avoiding failure. It helps us determine that a given material is weak or strong in a particular direction. Some time it will be convenient to derive stress-strain relationship in a different co- ordinate system. Stress transformation allows us to develop such relationship in a desired co-ordinate system. Stress Transformation in 2D: So far we know that the components of stress are associated with the faces perpendicular to the co-ordinate axes. We will now derive stress components acting on arbitrarily oriented faces by considering a small element of a solid body which is cut at an arbitrary angle θ .

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Class Workbook and Handouts - MME 412: Mechanics of Materials Prepared by: Kumar V. Singh
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Lecture_Stress_transformation_Principal_Mohr_2D_2 - Class...

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