Shelf strength technical query

[JJ1]

Hi,

I was wondering if someone could help me with the following question please;

I have an alcove in my hall and I would like to put in three shelves to hold large hardback books. The alcove depth is 28cm and the width (shelf span) is 76cm. I'm unable to put a rear shelf support at the back of the alcove, so the shelves would only be supported by a timber batten on each side.
Previously, I did a quick, temporary job using 28mm kitchen worktop with some decorative moulding glued to the front edge of the shelves. This has been fine for a number of years, except for the shelves have now bowed and I would like to redo it but using something more substantial. The shelves will be painted so looks isn't a primary concern and I would like to use 18mm MDF as I have plenty of surplus. I've cut the MDF to size and I've glued two pieces face to face, giving me a chunky, and more substantial, 36mm shelf. My initial plan was to support this on either side by sitting the shelves on top of a wooded batten fixed to the sides of the alcove. I'm guessing that a 36mm MDF shelf would be more than man enough for the weight and wouldn't have a problem with bowing over time.
However, I've been thinking that I wouldn't mind having the side supporting battens invisible, thus giving the impression of free-floating shelves. So, I thought why not glue another 18mm piece of MDF onto each shelf, giving me extra thick 54mm shelves. My plan was to then cut a rebate in each side of the shelf, from the back, to stopping just short of the front edge. It would then be a simple matter of just sliding the shelves onto the side-supporting battens, thus, having the battens 'hidden' in the shelf, as opposed to just having the shelves sitting on top of the battens.

And now for my query. If I was to make the rebate in the side of the shelves 18mm wide and I had it positioned in the middle of the shelf's 54mm thickness, that would give me 18mm of shelf thickness above the side support and 18mm below it.
So, what strength would that shelf have?
Would it be the same as a single piece of 18 MDF, as that's all that's sitting above the batten? Or, would it be 54mm's worth of strength, as that's the total shelf's thickness?

I'm not the best at explaining things, so I hope my question makes sense.

Any help would be much appreciated, thank you

 

[kostello]

Hi there


If you Google the sagulator.......


It should come up with a website that will calculate shelf lengths and sizes for you


It's got lots of options for materials and construction techniques

http://www.woodbin.com/calcs/sagulator.htm

Eta web address

 

[Steve Maskery]

This is a very interesting mathematical exercise. What you are asking for is Beam Strength. The strength of a beam is measured by the SQUARE of its thickness. So a 2" thick shelf is 4x the strength of a 1" shelf.

In your shoes I would make my shelves about 30mm thick, consisting of two 6mm skins over a honeycomb centre 18mm thick. You could make the ends so that they slide over an 18mm batten screwed to the wall, thus making it all invisible. Provided that the skin overhang was fairly short, I'd have though it was a perfect solution.

S

 

[Chrispy]

Your shelf will be fine, the only concern would be the shelf spliting in line with the top of the supporting battons so maybe to be sure put a few screws through the shelf top to bottem right at the endsto stop any split developing, thats the one main weakness with MDF it does split very easily.

 

[Phil Pascoe]

Find a bit of ply for the middle layer, maybe?

 

[GazPal]

Weight, load and structure influence the way a shelf performs and the heavier a shelf is, the more likely it is to sag unless adequately supported.

Span = 760mm
Depth = 280mm

I'd tend to use a double skin - sandwiching an internal frame - for this kind of shelf and lip both front and back for finish and added support. Namely a torsion box. The internal frame can be the same timber as used for the lipping, but rectangular in cross section with it's widest section vertical. Although heavy, MDF has no grain and lacks the integral strength found in solid timbers, so needs additional support when used to span openings.

http://en.wikipedia.org/wiki/Torsion_box

Given more time and a little more experience, a pre-stressed shelf could be made. This would bow upward very slightly at the centre without loading, but set itself straight once loaded. This is especially handy if dealing with heavily loaded shelving and - even if the shelf remained very slightly bowed upward - would visually appear perfectly flat. A similar method is used when bridging openings in masonry and is named a flat arch.

 

[AndyT]

While the box construction shelves would work, if I were you I'd be looking for some real wood instead of MDF - the strength to thickness ratio is so much better. It's not a huge project so you would not need very much.

Also, even if you can't fix battens across the backs of the shelves, you can gain extra strength by glueing battens along the front and rear edges of the shelves - like your doubling up idea, but localised.

 

[siggy_7]

This is a very interesting mathematical exercise. What you are asking for is Beam Strength. The strength of a beam is measured by the SQUARE of its thickness. So a 2" thick shelf is 4x the strength of a 1" shelf.

Steve, I think you will find that the stiffness of a shelf is related to the cube of its thickness - a rectangular section's second moment of area is w.h³/12. So making it thicker is even more beneficial.

 

[JJ1]

Many thanks for all the superb information.

Originally, I was going to go for the honeycomb/torison box idea, but because I already had plenty of 18mm MDF lying around, I decided to use that instead, just to use it up.
I had already cut it all to size and glued it up, hence the reason I wanted to continue using that, rather than starting from scratch again.
I'm completely new to woodworking and in my ignorance I didn't realize MDF was actually a fairly weak material. I had wrongly assumed that because it felt so dense and heavy, it was probably pretty strong. The extra strength of 'proper' wood makes sense and that's something new I've learnt (and remembered for future projects )

I've decided to go with the three 18mm pieces to give me a good thick 56mm shelf. The size quite appeals and it will fit well within the alcove and work out ok for the different heights of the various books.

Thanks for the tip about screwing the MDF together to prevent it splitting. I hadn't thought of that and will certainly do that. I will also be adding an extra piece to the front edge of the shelf to add further strength and to give a better appearance to the front.

Regarding the actual positioning of the rebate in the side of the shelves, for the supporting batten. Does it matter (strength wise to prevent bowing) where it is positioned, i.e. towards the top, middle or bottom? Taking into account I'll add some screws to prevent any splitting, as mentioned above?
I've added an illustration to try and show what I mean. Excuse my terrible drawing, but of the three examples, the first one is the strongest, I presume, because the shelf supports are supporting the full 56mm shelf thickness. What about examples 2 and 3. Are they just as strong as example 1? That was what I was trying to fathom out with my original question.

 

[Chrispy]

As for the shelf bowing no it won't make any difference where the batton is.

 

[JakeS]

What about examples 2 and 3. Are they just as strong as example 1?

I would say that there's a marginal benefit to having the batten lower down the thickness of the shelf (as in 1 or 3), simply because when the shelf sags the sides that meet the wall (and rest on these battens) will pivot slightly away from the wall. So if your batten is lower, the shelf has to sag more before it slips off the batten and drops your stuff all over the floor and/or anyone who happens to be passing.

But it's a marginal benefit. It's probably more important to not overload your shelf than to worry too much about the exactly positioning of the mounting battens!

 

[AndyT]

I can't be definitive - I'm not a structural engineer - but I think number 3 would be strongest.

However; another suggestion:

Don't worry about concealing the fixing battens from below. Nobody will be peering in underneath the shelves, which will be filled up with books any way. Cut your bottom layer of mdf shorter than the top two - the difference being equal to the amount that your wall battens stick out. That way you can drop each shelf down onto its battens, rather than pushing it in like a drawer - which will make it much easier to see and adjust any minor inaccuracies. (Alcoves are almost never square or true.)

The battens won't be as they are in your drawing - unless you want to start making grooves in the walls! - but will be flat against the wall, held in by screws into wall plugs.

It's tempting to say that you should make the batten depth equal to the thickness of the bottom layer, so everything is flush. This might work if you use hardwood such as oak or ash for the battens, but 18x18mm strips of mdf have almost no strength. So you might need to make the battens deeper and have some of the batten showing beneath each shelf, if each one is say, 18mm thick by 36mm deep. They don't have to come all the way to the front edge of the shelves, so they can mostly hide in the shadows.

 

[JJ1]

Thanks all for the info.

Don't worry about concealing the fixing battens from below. Nobody will be peering in underneath the shelves, which will be filled up with books any way.

That's true,. But me being a bit of a perfectionist, will know they're there :lol: and I'm determined to have them concealed It shouldn't be much more work to conceal them and have the shelves slide on the battens because I had some old shelves already there which fitted the alcove just right, which was, as you mention, definitely not square or true, so it was just a simple job of using the old shelves as templates.
As I've already got two 18mm pieces of MDF glued up, I thought I could route the rebates with a straight cut router bit. Being a novice woodworker, I'll benefit from using the router anyway, having only ever used one a couple of times before. I can then glue on the third sheet.

The battens won't be as they are in your drawing - unless you want to start making grooves in the walls! - but will be flat against the wall, held in by screws into wall plugs.

That was just my feeble attempt at trying to use drawing software :roll:

I was going to use some pine 18mm x 30mm battens and securely screw them to the wall on the 18mm side, giving me 30mm on which to support the shelves. I'm assuming this will be fine, as I had battens before, but with the shelves only supported on the 18mm side.

I appreciate all your help and advice, many thanks