Answer to Question #135334 in Physics for ANKIT

Question

Shrink fitting is a technique where two parts are joined or fitted together, for example, by (i) heating one of the parts causing it to undergo thermal expansion, (ii) then putting the two parts together, and (iii) then letting the heated part cool down to ambient temperature, whereby it shrinks and fits tightly to the other part.
A circular steel sleeve of small thickness t is to be shrunk onto a solid rigid circular shaft of diameter 10 cm. Find the proper initial inside diameter of the sleeve if the allowable hoop stress in the sleeve is 200 MPa. Take E of steel as 2×105 MPa.

Answer 1

$$\frac{d-d_i}{d}=\frac{\sigma}{E}\\1-\frac{d_i}{10}=\frac{200}{2\cdot10^5}$$

$$d_i=9.99\ cm$$