reinforced 25mm MDF

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I have built some cupboards and bookshelves into a couple of alcoves and I seem to have a problem with the shelves. They are approx 880mm span and made from 25mm veneered MDF. The thing is when they are populated with books there is a slight bow in the middle. Hard to believe I know. Not exactly a heavy load either!!! I do not wish to have them supported in the middle or have any visible brackets/supports so they are fixed at the ends.
I have considered a few things and the best i can come up with is to router a slot down the middle of each and insert a 12mm stainless steel shaft and then fill it in and have them re-veneered. Would any of you consider this a viable option?
I would be routering the top of the shelf so that the shaft does not force out the fillet when under load.

Any comments or suggestions?
 
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Aiken said:
I have built some cupboards and bookshelves into a couple of alcoves and I seem to have a problem with the shelves. They are approx 880mm span and made from 25mm veneered MDF. The thing is when they are populated with books there is a slight bow in the middle. Hard to believe I know.
Not really - the people who make MDF recommend a maximum span of 600mm. You will even get that (although less of it) with plywood. What you should have done was consult the Sagulator

Aiken said:
I have considered a few things and the best i can come up with is to router a slot down the middle of each and insert a 12mm stainless steel shaft and then fill it in and have them re-veneered. Would any of you consider this a viable option?
Not really as the steel will still sag. You need to put in a threaded steel rod (better still two) with a nut and washer at each end and tighten-up the nuts to keep the shelf under tension and increase its beam strength (rigidity). This will require housings to be cut which look something like those used in a kitchen worktop joint. Guitar makers use a similar technique in guitar necks

Scrit
 
Would the rod have to be the full width or could it run from say 100 -150mm in from each end as they are fixed at the sides? Would this have any bearing (excuse the pun) on the deflection?
 
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