(3 + v) + —--tf where — B is a second convenient constant of integration,

B pa>2r2

B pa>2r2

For a solid disc the stress at the centre is given when r — 0. With r equal to zero the above equations will yield infinite stresses whatever the speed of rotation unless B is also zero, i.e. B — 0 and hence B/r2 = 0 gives the only finite solution.

Now at the outside radius R the radial stress must be zero since there are no external forces to provide the necessary balance of equilibrium if o> were not zero. Therefore from eqn. (4.7), or = 0 = A - (3 + v)


pco R

2 p2

Substituting in eqns. (4.7) and (4.8) the hoop and radial stresses at any radius r in a solid disc are given by oco2R2 , „ pco2r2 cjh = (3 + v--(1 + 3v)~

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