HW2Solution

HW2Solution - EGM 5533 Period 5 Assignment#2 ORIGIN 1 MPa...

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EGM 5533 - Period 5 Assignment #2 ORIGIN 1 Ξ ORIGIN MPa 10 6 Pa µε 10 6 Problem 2.5: T 80 20 40 20 60 10 40 10 20 MPa := Stress tensor at a point a.) Find the stress vector on the plane described by the vector v: v 1 2 1 := Vector describing a plane n v v := n 0.4082 0.8165 0.4082 = Normal vector on the plane described by v t i T ji n j = tT T n := t 65.3197 61.2372 32.6599 MPa = Stress vector on the plane described by v b.) Determine the principal stresses σ p: T ij σ p δ ij σ p 3 I 1 σ p 2 I 2 σ p + I 3 = 0 = Eigenvalue problem σ p reverse sort eigenvals T () := σ p 110 50 0 MPa = Principal stresses i Ξ last σ p .. := Indexing c.) Find the maximum shear stress: τ max 1 2 σ p 1 σ p 3 := τ max 55MPa = Maximum shear stress d.) Find the octahedral shear stress: I1 1 3 i σ p i = := I1 160MPa = First invariant σ oct 1 3 I1 := σ oct 53.3333MPa = Octahedral normal stress (hydrostatic pressure) np i 1 3 := np 0.5774 0.5774 0.5774 = Normal on the octahedral plane τ oct σ p 3 σ oct np := τ oct 44.9691MPa = Octahedral shear stress 1 of 4

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EGM 5533 - Period 5 Assignment #2 Problem 2.56: a.) Determine the displacement and strain fields for the x-y coordinate system: uxy , ()a 1 a 2 x
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HW2Solution - EGM 5533 Period 5 Assignment#2 ORIGIN 1 MPa...

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