Biomech-Principal_Stress-Lecture

Biomech-Principal_Stress-Lecture - Principal Stresses...

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Unformatted text preview: Principal Stresses Introduction to Biomechanics 14:125:208 Definition Principal Stress Principal stresses are normal stresses that are found in planes where there is no normal shear stress They are perpendicular to principal planes, point in principal directions. Transforming Stresses How do we discover the effects of stresses on different planes Not just parallel or perpendicular to the applied stress rotate Transforming Stresses Today well look at how stresses are transformed under rotation of the coordinate axis These equations can be used to find the maximum and minimum stresses in an element Well look at plane stress Transforming Stresses In our example, This is true for thin plates and columns Transforming Stresses Now what happens when we rotate Transforming Stresses Take a look at one triangular slice of the cube and look at the forces Transforming Stresses Sum the forces sin cos 2 sin cos sin cos 2 sin cos 2 2 ' 2 2 ' xy y x x xy y x x dA dA dA dA Transforming Stresses From trigonometry So therefore Transforming Stresses Apply this to our equation So Transforming Stresses For y , just replace with +90 Since Transforming Stresses What about the shear stress?...
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Biomech-Principal_Stress-Lecture - Principal Stresses...

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