leg spacing for best structural support thought experiment - Woodworking Talk - Woodworkers Forum
 
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post #1 of 16 Old 09-16-2014, 10:51 PM Thread Starter
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leg spacing for best structural support thought experiment

I am making a bed. I am considering the spacing of the legs. On most beds, the legs are at the very ends of the boards that run the length of the bed (I don't know what if anything these are called).

But on the bed I am building, I am thinking that maybe I should place them inwards a bit. I'm not sure if this makes sense, but to illustrate what I am thinking, here is a thought experiment. Lets say my bed is 6 ft long. I have two legs attached to each side. If I place them right next to each other, at the halfway point (so it would kind of be like a seesaw), that would obviously be ridiculous because half of the weight of the bed (and occupant) will be pushing down on one side of that board that runs lengthwise, and the other half will be pushing down on the other unsupported side, and it will likely bow under all that unsupported weight (besides which it would likely fall to one side because it would indeed be see-saw like).


If I start to move the legs out towards the end, where should I stop in order to minimize the possibility of the wood sides distorting over time under that load? Intuitively, it kind of makes sense to me that each leg should be placed 25% in from the end. That way, each leg is supporting 25% of the total length on either side of the leg (25%, leg, 25%, 25%, leg, 25%). This seems like the most balanced distribution of load.

Am I thinking about this correctly?

Last edited by dlwalke; 09-16-2014 at 10:53 PM. Reason: attempted illustrations did not appear as intended
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post #2 of 16 Old 09-16-2014, 11:58 PM
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I think your thinking is correct re: weight distribution, but before going ahead with construction, you might want to consider a few factors.

First, gravity isn't the only force at play in a bed. The simple act of climbing into bed, and certain *ahem* movement while in bed result in lateral (side to side and head to foot) forces- in the x and y axes, as well as the gravity z axis.

The traditional positions of legs are as posts at the ends of the head and foot boards, which make for rigid resistance to side-side forces. Bolting or otherwise firmly attaching the rails (the term used for the long boards) to the head and foot boards give considerable head-foot rigidity.

Have you considered how you'd attach the legs in your plan? It seems to me that you'd have to really need some heavy duty construction to achieve the same rigidity.

Also, if the footboard is low, many people (well, at least my wife and I for sure), sit on the foot of the bed while putting on socks and shoes. If the legs are set in 25%, there really might be your see-saw effect!

It's always good to think outside the box, and the above isn't to crticize or discourage you. Keep the thought experiments coming!
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post #3 of 16 Old 09-17-2014, 12:12 AM
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That is an interesting question. Here's what came to my mind. The mattress usually sits on a "box" spring and buy design that helps to spread the load quite a bit. Would you accomplish your goal by simply making the side rails deeper? The side rails could also be built-up kind of like a hollow core door but no more than say 8". Looking forward to other's thoughts.

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post #4 of 16 Old 09-17-2014, 03:09 AM
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That is a very interesting thought experiment there. By moving the legs closer in, say 1.5 feet towards the center from the edges, you reduce the unsupported span of the board, which in theory would reduce any risk of sagging by a fairly good amount. That said, I've never seen a "traditional" bed with sagging issues across the rail.. I think what sweet Willy proposed makes a high degree of sense, a box spring or the slats on a box-spring-less bed would spread the load out by a significant degree, so the weight wouldn't be focused on the center enough to cause sagging. Certainly be an interesting thing to test out

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post #5 of 16 Old 09-17-2014, 08:00 AM
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static vs dynamic loads

A simple load diagram would show a "distributed" load evenly across the mattress area. In real life that ain't the case. As mentioned, people sit on sides and ends of the bed, not exactly in the center. The weight of 2 people may also change the loading depending on their activities.

Your theory is correct however, by moving the legs inboard from the ends you reduce the "bending" of the side rails. There would be an "overhang" on the ends, but that is manageable if not too much. On a 7 ft bed I would move the legs in from the ends about 15" to 18" just "off the top of my head" without making a loading/force diagram showing all the possible combinations.

Now you have a different issue which is how to attach the legs to the side rails, inboard, rather than at the ends. Probably a 1/2 lap joint would be best and depending on the materials, thicknesses you may want additional mechanical fastners.....

A sketch of the proposed design, or better yet a Google Sketch Up workout will allow for changes more easily if you have the 3 D skill for that program. I like to make scale models of new concepts:
http://www.woodworkingtalk.com/f9/i-...-22874/index2/


The answer to your question will only be as detailed and specific as the question is detailed and specific. Good questions also include a sketch or a photo that illustrates your issue. (:< D)
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post #6 of 16 Old 09-17-2014, 08:39 AM
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This question would be easier to answer if we knew why you would want to do this?

Or is this just an exercise in theory?

George

PS Having a headboard/footboard on the bed is accomplished easier if the legs are at the end.
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post #7 of 16 Old 09-17-2014, 09:13 AM
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might be echoing, but the side boards should be able to handle the weight at any point. legs at the corners means you need enough support to put some 200lbs right in the middle and not sag.

If you are considering some sort of minimalist design with thin sideboards, shortening the wheel base as it were would assist in that effort.

I wonder a bit how that would look though?
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post #8 of 16 Old 09-17-2014, 11:03 AM
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I've seen plenty of platform beds with the base recessed. I think the answer to your question is not in the physics of torsion/racking/stability, but in how far back do you need the legs to not stub your toe while walking next to it.

Regards,
Steve
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post #9 of 16 Old 09-21-2014, 02:47 AM Thread Starter
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responses to responses

Thanks for your responses. I have attached a picture of a practice leg as secured to a piece of 2X4, and a pic of 2 legs that I will actually use, up against the rail of an existing bed. I have tried to put all my weight on the practice leg and it seems to be secure (as I weigh about 200 lb and me or a guest plus the bed and mattress wouldn't weigh more than 400 I don't think, and since there would be 4 such legs, each would bear about half as much weight as I put on the demo leg). The leg is made from Padauk and joined with a biscuit and wood glue (and as seen in the pic, bolted to the rail). My plan is such that the bed, when viewed from the top, would look like a rectangular tic-tac-toe board but with 4 lines going across rather than 2. The 2 vertical lines would be 1X8 rails (~73" long) and the 4 lines going across would be 1X6" boards. The rails and cross pieces would fit together using lap joints (I have seen the specific joint referred to as an edge half lap). If the frame seemed loose (e.g., movement in response to racking forces), I would maybe reinforce some of the intersections of the rails and cross boards with a short piece of 2X4 or something to try to keep the right angles true. The rails would be in about 6" from either side (e.g., from the edge of the mattress and also from the end of the cross boards. A varnished piece of plywood would go on top of all of this (so the bed would basically be a platform to get things off the ground and give a bit of storage space underneath) and the mattress would sit on this. The plywood could also be screwed onto the frame as an alternative method of making the bed frame "tight" (i.e., no wiggles in the joints) but I am not very experienced in wood shrinkage/expansion issues and am not sure if this might lead to trouble if, for example, the frame shrunk or expanded or twisted a bit and the plywood didn't. Securing the plywood would be an easy way of tightening everything up though so I'd like to do that…just not sure. If this works out, I have some more nebulous plan for a headboard and a couple other optional flourishes. The rails and maybe cross boards will likely be cherry although since they are not going to be very visible, maybe I should use something less expensive (like I assume pine is here in the southeast).

The reason I'm designing it this way is basically just that I need to do something that is within and maybe stretches just a little, my competence level and is feasible with a miter saw, hand drill, hand saw, (no router or table saw or drill press or inside work area to speak of) and that I can finish in a reasonably short period of time. And I'd like it to look home-made…in a good way. I think the legs look better in a little, but also just didn't know initially if I would have any problems (with legs at end) with the rails sagging.
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post #10 of 16 Old 09-21-2014, 08:46 AM
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Quote:
Originally Posted by dlwalke View Post
Thanks for your responses. I have attached a picture of a practice leg as secured to a piece of 2X4, and a pic of 2 legs that I will actually use, up against the rail of an existing bed. I have tried to put all my weight on the practice leg and it seems to be secure (as I weigh about 200 lb and me or a guest plus the bed and mattress wouldn't weigh more than 400 I don't think, and since there would be 4 such legs, each would bear about half as much weight as I put on the demo leg). The leg is made from Padauk and joined with a biscuit and wood glue (and as seen in the pic, bolted to the rail). My plan is such that the bed, when viewed from the top, would look like a rectangular tic-tac-toe board but with 4 lines going across rather than 2. The 2 vertical lines would be 1X8 rails (~73" long) and the 4 lines going across would be 1X6" boards. The rails and cross pieces would fit together using lap joints (I have seen the specific joint referred to as an edge half lap). If the frame seemed loose (e.g., movement in response to racking forces), I would maybe reinforce some of the intersections of the rails and cross boards with a short piece of 2X4 or something to try to keep the right angles true. The rails would be in about 6" from either side (e.g., from the edge of the mattress and also from the end of the cross boards. A varnished piece of plywood would go on top of all of this (so the bed would basically be a platform to get things off the ground and give a bit of storage space underneath) and the mattress would sit on this. The plywood could also be screwed onto the frame as an alternative method of making the bed frame "tight" (i.e., no wiggles in the joints) but I am not very experienced in wood shrinkage/expansion issues and am not sure if this might lead to trouble if, for example, the frame shrunk or expanded or twisted a bit and the plywood didn't. Securing the plywood would be an easy way of tightening everything up though so I'd like to do that…just not sure. If this works out, I have some more nebulous plan for a headboard and a couple other optional flourishes. The rails and maybe cross boards will likely be cherry although since they are not going to be very visible, maybe I should use something less expensive (like I assume pine is here in the southeast).

The reason I'm designing it this way is basically just that I need to do something that is within and maybe stretches just a little, my competence level and is feasible with a miter saw, hand drill, hand saw, (no router or table saw or drill press or inside work area to speak of) and that I can finish in a reasonably short period of time. And I'd like it to look home-made…in a good way. I think the legs look better in a little, but also just didn't know initially if I would have any problems (with legs at end) with the rails sagging.
Please use paragraphs when you write. They were invented for a reason. I would not even attempt to read the above.

George
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post #11 of 16 Old 09-21-2014, 11:08 AM Thread Starter
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same text but with paragraph marks inserted

Sorry. I was typing this late and not paying much attention to formatting. Hopefully this will be easier to read/comprehend.

>Thanks for your responses. I have attached a picture of a practice leg as secured to a piece of 2X4, and a pic of 2 legs that I will actually use, up against the rail of an existing bed. I have tried to put all my weight on the practice leg and it seems to be secure (as I weigh about 200 lb and me or a guest plus the bed and mattress wouldn't weigh more than 400 I don't think, and since there would be 4 such legs, each would bear about half as much weight as I put on the demo leg).

The leg is made from Padauk and joined with a biscuit and wood glue (and as seen in the pic, bolted to the rail). My plan is such that the bed, when viewed from the top, would look like a rectangular tic-tac-toe board but with 4 lines going across rather than 2. The 2 vertical lines would be 1X8 rails (~73" long) and the 4 lines going across would be 1X6" boards. The rails and cross pieces would fit together using lap joints (I have seen the specific joint referred to as an edge half lap).

If the frame seemed loose (e.g., movement in response to racking forces), I would maybe reinforce some of the intersections of the rails and cross boards with a short piece of 2X4 or something to try to keep the right angles true. The rails would be in about 6" from either side (e.g., from the edge of the mattress and also from the end of the cross boards. A varnished piece of plywood would go on top of all of this (so the bed would basically be a platform to get things off the ground and give a bit of storage space underneath) and the mattress would sit on this.

The plywood could also be screwed onto the frame as an alternative method of making the bed frame "tight" (i.e., no wiggles in the joints) but I am not very experienced in wood shrinkage/expansion issues and am not sure if this might lead to trouble if, for example, the frame shrunk or expanded or twisted a bit and the plywood didn't. Securing the plywood would be an easy way of tightening everything up though so I'd like to do that…just not sure.

If this works out, I have some more nebulous plan for a headboard and a couple other optional flourishes. The rails and maybe cross boards will likely be cherry although since they are not going to be very visible, maybe I should use something less expensive (like I assume pine is here in the southeast).

The reason I'm designing it this way is basically just that I need to do something that is within and maybe stretches just a little, my competence level and is feasible with a miter saw, hand drill, hand saw, (no router or table saw or drill press or inside work area to speak of) and that I can finish in a reasonably short period of time. And I'd like it to look home-made…in a good way. I think the legs look better in a little, but also just didn't know initially if I would have any problems (with legs at end) with the rails sagging.<

Last edited by dlwalke; 09-21-2014 at 12:17 PM. Reason: wording not content
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post #12 of 16 Old 09-21-2014, 01:11 PM Thread Starter
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Quote:
Originally Posted by GeorgeC View Post
This question would be easier to answer if we knew why you would want to do this?

Or is this just an exercise in theory?

George
Only thing I hope to accomplish is not paying a whole lot of money for a bed that looks nice and functions well when I think I can probably construct one myself for a lot less, and maybe learn a few things in the process. The constraint for exactly how I build it has to do with my current level of carpentry skills, and needing to get it done within a month or two working a few hours on Sunday's. FWIW, I do not trust my competence with nice clean tight mortise and tenon joints (I do own but have not used a Rockler kit with loose tenons that fit into drilled mortises) nor do I have a table saw or router, etc.

Although its not just an exercise in theory, I am interested in the theoretical aspects of load distribution as it relates to this type of project. It is not solely for the practical aspects of constructing this, but thinking about the practical aspects got me interested in the theoretical aspects.

Here is a slight digression that is necessary to get to what I am wondering. If a 3 ft beam is supported by a single post, then the best placement of the post would obviously be in the middle of the beam. So one might think that if you had two posts and a 6 ft beam (rail), the best placement of the posts (legs) would be at 1.5 and 4.5 ft, so that you would basically just be duplicating the best placement with the post and 3 ft rail described above, and placing the duplicates side by side. However, if the load is placed on the beam in-between the 2 posts, no matter where it is placed within that span (in this example, a 3 ft span), both posts will pick up some of that load, so it really ISN'T comparable to the situation with one post (unless the load were placed somewhere other than in between the two posts).

I assume there is some logical relation that equates distance with force (that engineering students probably learn in Engineering 101), and my guess is that it is not a linear function of distance, but I don't really know. And I would guess that knowing this might be necessary in order to solve the question of where best to place two posts holding up a single beam (it seems like it would be something less than 25% in from the end). Perhaps the properties of the specific materials involve also come into play. I may have to search out an engineering forum.

Dave
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post #13 of 16 Old 09-21-2014, 02:15 PM
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Well Dave, design and stepping outside the box are important and I like to work with posters within their design. Looks like a nice plan from the second picture. But going to be a real toe stubber. Just making the bed each day will make the task that much more of a pain.

Also the joints are almost never strong enough to resist the little annoying squeak so try to make them tight as possible.

Al


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post #14 of 16 Old 09-21-2014, 03:09 PM
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that's a toe stubber for sure

Having been there, done that,I would opt for a different design. You have successfully redistributed the load over 4 points, then down to 2 points, but all the framing is right on the exterior of the rails, making it in the way of toes who can't see in the dark. The screams alone will give neighbors cause to report domestic violence...just sayin' ......

There's good reasons for beds to be floated over the base OR to have the feet at the corners where you expect them to be. Now you can make it however you wish, but that's my free advice, no charge, it's the internet.

The answer to your question will only be as detailed and specific as the question is detailed and specific. Good questions also include a sketch or a photo that illustrates your issue. (:< D)
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post #15 of 16 Old 09-21-2014, 04:14 PM Thread Starter
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toes will be protected

Quote:
Originally Posted by Al B Thayer View Post
Well Dave, design and stepping outside the box are important and I like to work with posters within their design. Looks like a nice plan from the second picture. But going to be a real toe stubber. Just making the bed each day will make the task that much more of a pain.

Also the joints are almost never strong enough to resist the little annoying squeak so try to make them tight as possible.

Al
Keep in mind though that the legs, unlike the picture of the legs up against my store-bought bed, will be inset not only from the ends of the rails but also in about 6 inches from the edge of the bed (the plywood that the mattress sits on will extend about 6" from rails) so I think my toes are actually more at risk from a normal bed with posts at the corners. I will try to remember to post a pic of the project once I get a few more of the components together, along with some notes as to whether or not it is as functional as I hope.

Happy for all free advice.

Last edited by dlwalke; 09-21-2014 at 04:17 PM.
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post #16 of 16 Old 09-22-2014, 08:24 AM
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Quote:
Originally Posted by dlwalke

Keep in mind though that the legs, unlike the picture of the legs up against my store-bought bed, will be inset not only from the ends of the rails but also in about 6 inches from the edge of the bed (the plywood that the mattress sits on will extend about 6" from rails) so I think my toes are actually more at risk from a normal bed with posts at the corners. I will try to remember to post a pic of the project once I get a few more of the components together, along with some notes as to whether or not it is as functional as I hope.

Happy for all free advice.
Well there you go.

Al


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