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Problem_11_23

# Problem_11_23 - Problem 11.23 Given Two cylinders are...

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Problem 11.23 Given: Two cylinders are slip-fitted together to form a composite open cylinder. Both cylinders are made of a steel having a yield stress Y=700 MPa. The inner cylinder has inner and outer diameters of 100 and 150+ mm, respectively. The outer cylinder has inner an outer diameters of 150 and 300 mm , respectively. Find: a) the shrink pressure p s and maximum internal pressure p 1 that can be appplied to the cylinder if it has been designed with a factor of safety of SF = 1.85 for simultaneous initiation of yielding at the inner radii of the inner and outer cylinders. Use maximum shear-stress criterion of failure. b) Determine the outer diameter of the inner cylinder required for the design. E=200 GPa and ν =0.29. Solution: Note that Units are not used because it interferes with the MathCad solve block for some reason. a 0.050 := b 0.150 := c 0.075 := P 0 := SF 1.85 := E 200000 := ν 0.29 := Y 700 := Eq. 11.20 σ rr r a , b , p 1 , p 2 , ( ) 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 ( ) := Eq. 11.21 σ θθ r a , b , p 1 , p 2 , ( ) p 1 a 2 p 2 b 2
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