Lect4_streTR - CE 231 Engineering Materials I Fall 2004 Jan...

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Olek, CE 231,Fal 2004 STRESS TRANSFORMATION • Transformation equations • In-plane principal stresses - direction • In-plane principal stresses - magnitude • In-plane shear stress • Mohr’s circle- plane stress Olek, CE 231,Fal 2004 Stress Transformation σ x σ x σ y σ y τ xy σ y σ y σ x σ x τ x’y’ x y x’ Y’ θ X’ Y’ σ y σ x σ y τ x’y’ τ xy Y’ face - A Y’ τ xy σ x σ x X’ τ x’y’ σ y X’ face - A θ θ X Y Curtsey of N. Neithalath Olek, CE 231,Fal 2004 Normal and Shear Components - Preview Y’ τ xy A cos θ σ x A sin θ σ x A X’ τ x’y’ A σ y A sin θ X face - A θ τ xy A sin θ θ θ θ θ Σ F x’ = 0 Σ F y’ = 0 Curtsey of N. Neithalath
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Olek, CE 231,Fal 2004 Transformed Stress Equations ' cos 2 sin 2 22 xy xy xx y σ σσ θτ θ +− =+ + ' yx y =− '' 2 xy x y τ ⎛⎞ + ⎜⎟ ⎝⎠ Curtsey of N. Neithalath Olek, CE 231,Fal 2004 In-Plane Principal Stresses - Direction ' cos 2 sin 2 y σσσ + To find out the angle of maximum and minimum normal stress, differentiate the equation with respect to θ , and set to zero ' () ( 2 s i n 2 ) 2 c o s 2 0 2 x d d + = tan 2 / 2 xy p = Curtsey of N. Neithalath
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This note was uploaded on 01/06/2011 for the course CE 231 taught by Professor Jasonweiss during the Spring '08 term at Purdue University-West Lafayette.

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Lect4_streTR - CE 231 Engineering Materials I Fall 2004 Jan...

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