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ME_423_lecture_3 - = = yy xx xy = 2 2 tan Maximum shear...

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ME 423 09/7/2011 Lecture 3 Transformation of stresses 2.1.1 Review of 2D stresses AB=1, OA=cos θ , OB=sin θ Stress transformation equations θ θ σ θ σ θ σ σ cos sin 2 sin cos 2 2 ' xy yy xx xx + + = θ θ σ θ σ θ σ σ cos sin 2 cos sin 2 2 ' xy yy xx yy + = θ θ σ σ θ θ σ σ cos sin ) ( ) sin (cos 2 2 ' xx yy xy xy + = or θ σ θ σ σ σ θ σ θ σ σ σ σ σ θ σ θ σ σ σ σ σ 2 cos 2 sin 2 2 sin 2 cos 2 2 2 sin 2 cos 2 2 ' ' ' xy yy xx xy xy yy xx yy xx yy xy yy xx yy xx xx + = + = + + + =
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Mohr’s circle 2 yy xx c σ σ + = 2 2 2 xy yy xx R σ σ σ +
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Unformatted text preview: = = yy xx xy = 2 2 tan Maximum shear stress ) ( 2 1 2 2 1 2 2 max = + = = xy y x R...
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