quiz12_solution - 2 τ 2 xy τ max = σ x − σ y 2 2 τ 2...

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Name: _____________________________ 1 Quiz 12, Spring 2005 Mechanics of Materials (CVEN 305--505) Problem 1: For the stateof stressshown inFig. 1,determine theprincipal stressesand themaxi- mum shear stresses when a) σ z =0 b) σ z =--10 ksi c) σ z =10 ksi Figure 1 A stress element. z y x σ x σ x σ y σ y τ xy σ z σ x = 10 ksi σ y = − 10 ksi τ xy = 5 ksi
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Name: _____________________________ 2 Solution: The principal stresses and maximum shear stresses in the plane problem can be obtained using: σ 1,2 = σ x + σ y 2 σ x σ y 2 2 +
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Unformatted text preview: 2 + τ 2 xy τ max = σ x − σ y 2 2 + τ 2 xy a) σ 1,2 = 10 − ( − 10) 2 2 + 5 2 = 5 5 ksi τ max = 5 5 ksi b) | σ z | < 5 5 Since the principal stresses and masimum shear stresses are: Note: principal stresses: σ 1 > σ 2 > σ 3 σ 1 = 5 5 ksi σ 3 = − 5 5 ksi σ 2 = − 10 ksi (for part b) σ 2 = 10 ksi (for part c) τ max = 5 5 ksi...
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