What is the optimal width for shelves in a curved-wall closet?

[MattF]

Hi, I've been trying to work this problem that someone needs for a closet project. I tried to get some help in the general math forum, but that didn't work. Hopefully I'm targeting the right group now :)

Basically we're trying to build custom (cut to fit) shelves in a walk-in closet. There's a little problem though; the back wall is curved. Now, the shelves themselves will not be curved to fit the wall, they will be straight-back ones. Here's a picture of what I'm talking about; http://img.photobucket.com/albums/v449/MJF/closetexample.gif

Just a sidenote, the thin lines (83" markings) are just measurements, not walls.

I have all the measurements (all in inches, and then the angle), some of which i calculated to fill in the blanks. I need three shelves, all the same width, to fit against that curved wall. To make it easier, the depth of the shelves will be 16.5", and height is not an issue. Because of the two side walls, there will be some dead space. Obviously the front corner of a shelf will hit the walls on the side. http://img.photobucket.com/albums/v449/MJF/shelf.gif

Now, the question is, how do I find the optimum shelf width so that the three shelves make the best fit? I tried to find it, but I'm pretty much stumped. I know there's a mathematical solution to this. A practical solution would be even better, since of course I can actually be in the closet taking measurements. Thanks!

 

[yourdadonapogostick]

use more than one board for each shelf

 

[faust9]

What do you mean, why not go wall to wall(72")?
Are you worried about support conditions?

Why not cut the shelves with the same curvature as the wall?

Here, let's standardize our terminology:
Width is how far the shelf projects from the wall(you called it depth) and length is how many pairs of shoes you can line up from one end to the other(you called this width).

The optimal placement for the shelf supports is(I'm not going to prove this you can do it using castigliano's thm's):
Assuming a distributed load with a shelf of length 'L' and the supports loacted at some distance 'a' from either end and a uniform shelf cross section:
$$a=L\frac{\sqrt{2}-1}{2}=0.207L$$

Basically, the shelf will be able support the largest load if you place the supports 21% of the shelf length from either end.

I'm kind of lost as to what is vexxing you though. Most people don't know the above and don't really care about it because there is no guarantee you'll find a stud at the exact loaction and if you don't find a stud then you'd have to use a fastener weaker than the shelf so the exact placement of the support becomes moot. Are you trying to figure out how long you supports need to be when you eventually determine the value of 'a' in order to support a 16.5" wide shelf?

 

[MattF]

Clarification

Maybe this will clear up some things; http://img.photobucket.com/albums/v449/MJF/shelfplacement.gif

All the images I have linked to are top-down views of the closet. I need three shelves, all of the same width. Looking at the picture, you can see that the corners of the left and right shelves hit the side walls. The depth of the shelves are 16.5". Taking into account the dead space in each corner, and so on, I need to figure out how to get optimum shelf size and placement.

 

[MattF]

Thanks for replying, faust. What I'm trying to do is place three shelves, with straight backs, following the back wall like in the picture. What's getting me are those two corners (one in the left and one in the right) where there's dead space. I need to find an accurate width for each shelf so that they fit as well as possible without going "into" the side walls, if you know what I mean. The front left corner of the shelf on the left hits the sidewall, and likewise for the shelf on the right.

Maybe this helps? I'm sorry if I'm not making things clear very well :/

 

[faust9]

Thanks for replying, faust. What I'm trying to do is place three shelves, with straight backs, following the back wall like in the picture. What's getting me are those two corners (one in the left and one in the right) where there's dead space. I need to find an accurate width for each shelf so that they fit as well as possible without going "into" the side walls, if you know what I mean. The front left corner of the shelf on the left hits the sidewall, and likewise for the shelf on the right.

Maybe this helps? I'm sorry if I'm not making things clear very well :/

Trial and error possibly. Do you have access to CAD? That would help too. I wouldn't attempt to do this as a hand calculation myself. I'd use pencil and paper and a ruler or CAD to determine the correct lengths.

Good luck.

 

[Danger]

Good luck.

As one who unfortunately can't afford CAD, I should point out that the same thing can be accomplished with an art programme (I use Illustrator). Just define shapes according to your own scale (I go with 1"=1' for stuff of this size) and manipulate them with the movement tools to check the fit.

 

[Moonbear]

Why not just start out with slightly oversized boards, fit the first one, cut the edge at an angle, match the angle on the second board to butt the two ends together, then do the same for the third board? Actually, just for convenience, I'd start with the two ends first, then just bring the center board in, set it up on the first two and draw a pencil line of where you need to cut just by tracing the underside. I'll try to draw a sketch of what I mean...I'll come back and edit in an attachment if I'm successful.

Okay, I'm adding an attachment. Then all you need to do to determine the length of the boards needed is get out your handy dandy ruler and measure straight lines between each of the arrows I've drawn in the picture. This also means you won't have gaps between the shelves, making them more useful and attractive.

 

[FredGarvin]

I am guessing by your responses that you want to do as little cutting as possible, if any. What exactly are you calling "optimal?" Does that imply the most amount of area or simply the easiest to fit?

 

[Moonbear]

I am guessing by your responses that you want to do as little cutting as possible, if any. What exactly are you calling "optimal?" Does that imply the most amount of area or simply the easiest to fit?

I was assuming he just didn't want to cut curves, not that he didn't want to do any cutting, but I could be wrong. If he just wants to buy pre-cut shelving and not mess around with any mitered cuts, then the lengths need to be determined on the wall side by finding the "pivot" points on the wall he wants to use and then measure the length of the three lines tangent to those three points. I honestly would just do it the practical way of buying boards a little longer than you're going to need, mount the brackets for the center points, rest your shelving boards on the brackets and use pencil lines to mark where to make your cuts. It's a shelf in a closet, so you don't need to have the angles perfect, just cut them so the two boards butt into each other at whatever angle looks good to you. Even if in the end you wind up with some small gaps between them, it'll be better than leaving the edges square with large gaps between them.