Problem 11.23Given: Two cylinders are slip-fitted together to form a composite open cylinder. Both cylinders aremade of a steel having a yield stress Y=700 MPa. The inner cylinder has inner and outer diameters of100 and 150+ mm, respectively. The outer cylinder has inner an outer diameters of 150 and 300 mm ,respectively.Find: a) the shrink pressure psand maximum internal pressure p1that can be appplied to the cylinder ifit has been designed with a factor of safety of SF = 1.85 for simultaneous initiation of yielding at theinner 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.a0.050:=b0.150:=c0.075:=P0:=SF1.85:=E200000:=ν0.29:=Y700:=Eq. 11.20 σrrr a, b, p1, p2, ()p1a2⋅p2b2⋅−b2a2−a2b2⋅p1p2−()⋅r2b2a2−()⋅−⎡⎢⎢⎣⎤⎥⎥⎦:=Eq. 11.21σθθr a, b, p1, p2, ()p1a2⋅p2b2⋅
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τmax, 300 mm, 150.292 mm, internal pressure p1