Many, many years ago I graduated college as a Mechanical Engineering Technologist but my career path took me elsewhere. I therefore can use and comprehend most of the "tools of the trade" but I'm very rusty in that usage. I therefore don't feel fully confident in my own calculations and would like some input.

I want to use a 12" long Stainless Steel solid rod to support approximately 200 lbs of weight equally distributed between two mounted bearings on each end with the rod itself only supported in the center.

In addition to the rod supporting the weight, it needs to remain straight enough that the bearings do not bind due to a bend in the rod.

For unrelated reasons the rod cannot exceed 2.375" diameter But I'm hoping the actual required size is much less than that.

I'd appreciate either an answer with some supporting calculations or a link to somewhere the info can be found. Small Bio