quiz12_solution

quiz12_solution - 2 + 2 xy max = x y 2 2 + 2 xy a) 1,2 = 10...

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Name: _____________________________ 1 Quiz 12, Spring 2005 Mechanics of Materials (CVEN 305--505) Problem 1: For the state of stress shown in Fig. 1, determine the principal stresses and the maxi- 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 = 5ksi
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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
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Unformatted text preview: 2 + 2 xy max = x y 2 2 + 2 xy a) 1,2 = 10 ( 10) 2 2 + 5 2 = 5 5 ksi max = 5 5 ksi b) | z | < 5 5 Since the principal stresses and masimum shear stresses are: Note: principal stresses: 1 > 2 > 3 1 = 5 5 ksi 3 = 5 5 ksi 2 = 10 ksi (for part b) 2 = 10 ksi (for part c) max = 5 5 ksi...
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quiz12_solution - 2 + 2 xy max = x y 2 2 + 2 xy a) 1,2 = 10...

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