Lect5_streTR_II - CE 231 Engineering Materials I Fall 2004...

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Olek, CE 231,Fal 2004 STRESS TRANSFORMATION • In-plane principal stresses • Maximum in-plane shear stress • Mohr’s circle for the general state of stress • Absolute maximum shear stress Olek, CE 231,Fal 2004 Center and Radius of the Circle X Y θ = 0 ( σ x + σ y ) /2 τ xy ( σ x - σ y ) /2 Center: ( σ avg ,0) σ x σ τ σ x τ xy A To get the point A in the circle (Radius), Use σ x and τ xy (known values) Make sure the SIGNS are Right Curtsey of N. Neithalath Olek, CE 231,Fal 2004 Rotation in Mohr’s Circle • Rotate the axes by 90 o CCW • These are the co- ordinates of G” Note : A rotation of 90 o ( θ ) on X-axis results in a rotation of 180 o (2 θ ) in the circle x x’, y θ = 90 y’ σ y = σ x τ x’y’ = - τ xy τ xy τ A ( σ x , τ xy ) Center: ( σ avg ,0) σ x ( σ x + σ y )/2 G ( σ y , - τ xy ) θ = 0 - τ xy C θ = 90 2 θ =180 o σ Curtsey of N. Neithalath
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Olek, CE 231,Fal 2004 Principal Stresses ( τ = 0) τ xy τ A ( σ x , τ xy ) Center: ( σ avg ,0) σ x ( σ x + σ y )/2 G ( σ y , - τ xy ) θ = 0 - τ xy C θ = 90 σ B D B and D represents the principal stresses σ 1 and σ 2 σ 1 > σ 2 σ 2 σ 1 Here, τ = 0 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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Lect5_streTR_II - CE 231 Engineering Materials I Fall 2004...

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