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 stressstrain relationship in a different co
ordinate system. Stress transformation allows us to develop such relationship in a desired
coordinate system.
Stress Transformation in 2D:
So far we know that the components of stress are associated with the faces perpendicular
to the coordinate 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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 Fall '11
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 Coordinate system, Class Workbook, Kumar V. Singh

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