Problem_11_07 - σ rr a 100 − MPa ⋅ = σ θθ a 60 MPa...

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Problem 11.7 Given: A closed cylinder has an inside diameter of 20 mm and an outside diameter of 40 mm. It is subjected to an external pressure p 2 = 40 MPa and an internal pressure of p 1 = 100 MPa. Find: the radial and circumferential stress at r=a. Solution: a1 0 m m := b2 0 m m := p 1 100 MPa := p 2 40 MPa := P0 := Eq. 11.20, 11.21, and 11.22 σ rr r () p 1 a 2 p 2 b 2 b 2 a 2 a 2 b 2 p 1 p 2 () r 2 b 2 a 2 () := σ θθ r () p 1 a 2 p 2 b 2 b 2 a 2 a 2 b 2 r 2 b 2 a 2 () p 1 p 2 () + := σ zz r () p 1 a 2 p 2 b 2 b 2 a 2 P π b 2 a 2
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Unformatted text preview: σ rr a ( ) 100 − MPa ⋅ = σ θθ a ( ) 60 MPa ⋅ = σ zz a ( ) 20 − MPa ⋅ = Note that the force due to the external pressure creates a larger load in the z direction than the internal pressure and thus σ zz is negative. r a a 1 mm ⋅ + , b .. := 0.01 0.012 0.014 0.016 0.018 1 − 10 8 × 5 − 10 7 × 5 10 7 × 1 10 8 × σ rr r ( ) σ θθ r ( ) σ zz r ( ) r...
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