Problem_11_04 - b 2 a 2 − 1 b 2 r 2 + ⎛ ⎜ ⎝ ⎞ ⎟...

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Problem 11.4 a=100 mm b=250 mm p 1 =80 Mpa p2=0 Given: A long closed cylinder has an internal radius a = 100 mm and an external radisu b = 250 mm. It is subjected to an internal pressure p 1 = 80 MPa (p 2 = 0). Find: the maximum radial, circumferential, and axial stresses in the cylinder. a 100 mm := b 250 mm := p 1 80 MPa := p 2 0 := P0 := Eq. 11.20, 11.21, and 11.22 σ rr 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 zz p 1 a 2 p 2 b 2 b 2 a 2 P π b 2 a 2 + = σ θθ 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 () + = Using p 2 = 0 and P=0 we get: σ rr r () p 1 a 2 b 2 a 2 1 b 2 r 2 := σ θθ r () p 1 a 2 b
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Unformatted text preview: b 2 a 2 − 1 b 2 r 2 + ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ ⋅ := σ zz r ( ) p 1 a 2 ⋅ b 2 a 2 − := The maximum stresses occur at r=a. σ rr a ( ) 80 − MPa ⋅ = σ θθ a ( ) 110.476 MPa ⋅ = σ zz a ( ) 15.238 MPa ⋅ = Defining a range variable for the radius: r a a 1 mm ⋅ + , b .. := then we can plot the stresses. 0.1 0.15 0.2 1 − 10 8 × 5 − 10 7 × 5 10 7 × 1 10 8 × 1.5 10 8 × σ rr r ( ) σ θθ r ( ) σ zz r ( ) r...
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This note was uploaded on 01/11/2011 for the course MAE 3040 taught by Professor Mechanicsofsolids during the Spring '10 term at Utah State University.

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