Lecture03

Since τ xz τ yz 00 mpa σ zz σ 3 0 mpa 2 θ σ τ

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Since τ xz = τ yz = 0.0 MPa, σ zz = σ 3 = 0 MPa 2 θ σ τ (40, 30) σ 1 σ 2 τ max (100, -30) σ 3 From before: σ 1 = 112.4 , σ 2 = 27.6 MPa Radius 1-2: τ 12 max = 42 MPa (as before) Radius 2-3: τ 23 max = (27.6 0.0)/2 = 14 MPa Radius 1-3: τ 13 max = (112.4 0)/2 = 56 MPa Largest shear stress is 56 MPa in 1-3 plane (not x-y plane) Different co-ordinate systems What happens if directions are not as given in notes? (say axis is in z -direction?) What happens if σ xx is principal stress (rather than σ zz ) What happens if co-ordinate system is r , θ , z or r , θ , φ , or 1, 2, 3? Make a consistent right-handed transformation table: x z x 1 x r x r x a x apples y x y 2 y θ y θ y b y bananas z y z 3 z z z φ z c z carrots All equations, diagrams and sign conventions given above will work with these transformations, provided each set is right-handed.
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