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Example 72

A circular disc 150 mm diameter and 12 mm thickness is clamped around the periphery and built into a piston of diameter 60 mm at the centre. Assuming that the piston remains rigid, determine the maximum deflection of the disc when the piston carries a load of 5 kN. For the material of the disc E — 208 GN/m2 and v = 0.3.

Solution

From eqn. (7.29) the deflection of the disc is given by

slope 0 = ———[2 log, r — 1] H—^—I----(2)

Now slope = 0 at r — 0.03 m. Therefore from eqn. (2)

8 tzD

But D

208 x 1728

= 32900

87T x 32900

Also the slope = 0 at r = 0.075. Therefore from eqn. (2) again, o= -5000 x 0.075[21ogg0,075 _1]+0,0375Cl+ C2

0 0

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