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steel PL over RC slab

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Quick problem, somewhat theoretical:

You have a reinforced slab that spans between two beams, in a ribbed slab
type of construction. Next place a steel plate continuous over two or more
of the spans. The steel plate is not bonded or bolted, just laying on top of
the floor. Next pass a moving load from a wheel over this plate. How do you
calculate the portion of the load carried by the steel plate and the slab? I
don't have any FEA software either. I think there is a somewhat simple
solution involving the various EI's of the two materials. In my head I see
the steel deflecting under the load, carrying some of the load, then passing
the remainder into the slab, until it starts deflecting, then so and so
forth until some type of equilibrium is reached.

Also is there a way to : a) size the plate so that it carries a specific
portion of the load
b) the slab carries no load at all, the plate carries all of it

I think b) is nearly impossible because you would have to have such a thick
plate that it virtually had zero deflection. Noone could transport such a
theoretical plate :)

Sorry if this is confusing, I am a bit confused but I am sure one of you
will clear it up...

Thanks in advance,

Andrew Kester, EI
Longwood, FL

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