The compound cylinder shown below with a=160mm,b=190mm is fabricated from a hollow outer brass cylinder and a solid steel shaft by using a shrink fit process. For this assembly, the relationship between the shrinking allowance, \delta , and the interfacial pressure, p, is of the form p=c\delta , where c is a constant. It is found that for a \delta =0.01mm,p=10MPa. If \delta is increased to 0.1 mm , determine:
(a) Radial stress, \sigma _(r), and tangential stress, \sigma _(\theta ), on either side of the interface ( 12 points)
(b) Determine if failure occurs on either side of the interface using Tresca failure theory ( 6 points)
Given equations for special cases of thick-walled cylinders:
Internal Pressure Only:
\sigma _(r)=(a^(2)p_(i))/(b^(2)-a^(2))(1-(b^(2))/(r^(2)))
\sigma _(\theta )=(a^(2)p_(i))/(b^(2)-a^(2))(1 (b^(2))/(r^(2)))
External Pressure Only:
\sigma _(r)=-(b^(2)p_(o))/(b^(2)-a^(2))(1-(a^(2))/(r^(2)))
\sigma _(\theta )=-(b^(2)p_(o))/(b^(2)-a^(2))(1 (a^(2))/(r^(2)))