Stresses in a rotating object?

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Has anyone considered the following. If I have a really big disc and rotate it at a certain angular velocity. Then at some distance from the centre the tangential speed of the disc will equal the speed of light and any distance beyond will have a speed greater than that of light. Obviously this cannot be the case and some strange time dilation and length contraction effects will take place. Can anyone explain exactly what does happen? Presumably some stresses are set up in the disc which could be calculated?
 
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