4 cf 20 2 p 674 tan 2 p p 337 0 1237 0 oa

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Unformatted text preview: (FX )2 = (20)2 + (48)2 = 52MPa 6 3 x • Principal planes and stresses XF 48 = = 2.4 CF 20 2θ p = 67.4° tan 2θ p = θ p = 33.7 0 , 123.7 0 σ = OA= OC+ CA max = 80+ 52 σ max = +132MPa σ min = OA= OC− BC = 80−52 σ min = +28 MPa 7 • Stress components after rotation by 30o φ = 180° − 60° − 67.4° = 52.6° σ x ′ = OK = OC − KC = 80 − 52 cos 52.6° = +48.4 MPa σ y ′ = OL = OC + CL = 80 + 52 cos 52.6° = +111.6 MPa τ x ′y ′ = KX ′ = 52 sin 52.6° = 41.3MPa 8 4 7.6 Out of plane τmax • For plane stress, z axis normal to plane of stress (xy plane) is principal axis ( τ = 0 ) τ max • a) τ max for element is = to max “in-plane” (xy plane) shearing stress b) Planes of τ max are at 45o to principal planes. σ σ min σmax max σmin σ max &σ min opposite sign τ max = 1 (σ max − σ min ) = R 2 9 1 2 τ max = σ a • σ max & σ min same sign τ max for element is equal to half σ max σ min = 0 σ max = σ a 1 2 τ max = σ max (out of plane ie, not in xy plane)...
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