Granite overhang on island

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I am building an island from individual magnet carcass units. At present island is 1400mm (w) x 560mm (d) x 870mm (h) With the units standing on the plastic legs. I plan to add end and back panels (16mm deep) that will be secured to the unit and then to wood blocks that are secured to the floor to hold the island in place.
I then want to place a piece of 3cm deep granite on top so it matches the main kitchen units with an overhand over one side to use as a breakfast bar (see image, overhang marked in grey).

My question is based on the width of the island base being 560mm what is a safe amount (in mm) of overhang that I can have in grantie. Also I have been looking on line and found an american product (http://www.counterbalanceshop.com/) that can strengthen the unit to support granite but could not find a UK equivalent, any suggestions?
 

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I then want to place a piece of 3cm deep granite on top so it matches the main kitchen units with an overhand over one side to use as a breakfast bar

My question is based on the width of the island base being 560mm what is a safe amount (in mm) of overhang that I can have in grantie.

Not very much. Google tells me that the tensile strength of granite is 4.8 MPa, compared to 400 for steel and 117 for oak. So it would snap with about 25 times less load than an oak overhang of the same dimensions.
 
Plan to anchor the carcass on back and both sides to the floor, not the front where the plinth would go. I am reading that some people say they have 300mm (12") of overhang unsupported and some up to 380mm (15"), but I think sourcing some material is my best bet
 
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Tensile strength resists the material being stretched. There is a different "strength" rating to be used when something is being bent before it snaps.
 
They are related. The material at the outside of the bend is under tension and the material at the inside of the bend is under compression. Failure starts when either the outside reaches the tensile strength or the inside reaches the compressive strength.

See e.g.
https://en.m.wikipedia.org/wiki/Flexural_strength

But anyway, here are flexural strengths from random googled websites:
Granite: 10 - 20 MPa
Oak: 100 Mpa

So 5 times weaker than oak.

But anyway we can calculate the answer. Let the max size of the overhang be L. Say the safety criteria is that we want to be able to sit on the edge without it breaking, with a safety factor of 2. Say that's 100kg over a width of 50cm of worktop. That's 1kN of force, and L kNm of torque. At the fulcrum, assume that the top and bottom are under equal and opposite stress, with the top half contributing half of the supporting torque i.e. 0.5L kNm. If this were all at the surface, 15mm from the middle, that would be a force of 33L kN. Distributed over an area of 50cm x 15mm that would be a pressure of 4.4L Mpa, but it is twice that at the surface, 8.8L Mpa. So with a breaking stress of 10 Mpa, L = 1.1m. Hmmmm, that's the right order of magnitude but larger than I was expecting! Perhaps I should have allowed a greater safety factor.
 
You could add a sheet of ply rebated into top and allow it to overhang half the length of your overhang for support.
 
Just remember that sometime, somebody is going to either jump up and sit on it, or drop three hundredweight of shopping onto it.
Belt and braces! It needs to be supported well somehow either by legs or brackets, and screwed to the floor as necessary to stop tipping.
 

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