Support and Span Limits for a Concrete Top

      A discussion of table design involving issues of wood deflection and concrete span capability. June 15, 2009

Question
I am building a four post workbench type caster table with a 65" span. The top will be 2" concrete and lower shelf will be holding 400lbs. of stuff. Is there an online calculator that will give me a load span maximum for 1x4x65" vs. 1.25x4x65 etc. aprons? I need to minimize the thickness and width of the aprons. Wood species is variable as well.

Forum Responses
(Cabinetmaking Forum)
From contributor o:
No help on an on line calculator (in fact I doubt that a reliable one exists - perhaps some rough rules of thumb)? The deflection of a beam of such and such a cross section, made of a material with a certain modulus of bending strength (from tables of the strength of wood) assuming uniform loading is in any first year engineering text.

Your problem is complex in that your answer is not the breaking strength of the apron supports, but the deflection of those members as related to the allowable bending of the slab. The critical factor is the bending of the two inch concrete slab. That would require calculating the failure point of a two inch slab of concrete, in bending, involving the psi strength of the concrete, and the aggregate size. If the stress exceeds a certain amount then a crack will start in the bottom and the crack will travel through the slab. Concrete is weak in tension. I would estimate that the calculation ultimately of the apron cross section would be very inexact due to the variability one would need to allow for in the strengths assumed for the wood and the cured concrete. Some small rebar or wire in the bottom would help strengthen the concrete a lot. If you already know all this, please excuse my posting in its entirety.



From the original questioner:
You lost me big time - I do understand psi strengths. I guess my question is if you support a one inch thick, four inch wide, five foot long piece of cypress and place it on its edge how much weight could you put on it before sags or breaks, versus a piece of oak. I know the bending strength is 10,500 psi, stiffness is 13,350 psi, but how much weight will it hold? Are you saying the concrete will warp with the wood?


From contributor O:
I am saying that with a little bit of load the board on edge will bend a little, and as the load goes up the bending increases. Ultimately the board would break, but the problem is, is that any concrete slab can only stand so much bending before it will crack through. So the limiting thing here is how much the apron board bends before the concrete snaps. Coming up with an apron size that will not bend too much (and allow the slab to crack through) depends on the weight of the slab, the strength of the slab (which varies with the strength of the mix, the curing time (temperature and water content), if the slab has rebar (and how much), the weight on the bench top, the strength of the wood (which varies not only by species, but from piece to piece) and that with so many variables it would be very hard to come up with a number, say like: a 1x4 won't work but a 1 3/16 x4 will work.

I am saying that the board does not bend at some exact weight supported, but rather bends continuously with applied weight. More like a given board will bend 1/8 inch with 100 pounds, and 2/8 inch at 200 pounds and 3/8 inch at 300 pounds. Yes the concrete slab will bend too. When the supporting apron bends more than the concrete slab can take, it will break. What I am saying is that with so many variables it is very hard (or impossible) to calculate how thick or deep that apron needs to be. I am sure that someone can tell you to use a 2x4 or a 2x5 or a 2x8 and be safe by vastly overbuilding the project, but you seemed to be wanting to know a safe minimal number, and I am only suggesting that is very hard to calculate.



From contributor Z:
Contributor O is right on the money. There are too many variables. Let me tell you how I would build this. What you want is to keep the concrete from bending past its limit. 400 lbs is not a lot depending on where itís at in the apron length. At the ends a 3/4 " oak board could hold it. In the middle itís going to deflect. Use 3/4 oak or any other hardwood like beech or maple. Apply 1/8 steel plate to the back of the apron slightly smaller that the width so it won't be easily seen. You could even go as far as inserting it into a groove as a spline. Like a truss bar in a guitar neck. Another option is to have an entire sub frame made if tube steel and hidden by wood. I would be more concerned with the casters holding out.


From contributor J:
Are you pouring the concrete yourself or are you buying the top premade? The reason I ask is that if you are making it yourself you probably don't need any support bracing if you build it right. Rebar is not randomly placed it needs to be controlled. I would have to do some homework again but I think that you would want to put your wire mesh about 1/4 of the way into the slab from the bottom and then you want to pull the wire tight before you pour the concrete. The less moisture in the concrete when you pour the better. Pour with at least a six bag mix, possibly more. I used to work for a company that did suspended concrete decks on homes.


From the original questioner:
Contributor O - you are correct I do not want to over beef it - only because I canít. I have a 28" restriction on the top width with a 24" cutout. Tight framing is not a problem with oak but Spanish cedar is very weak.

Contributor Z - that is an excellent idea. I was thinking of splining in a 1/4" angle iron. I agree with the oak holding, but this is going to be Spanish cedar. It does not score well on bending strength. My instincts tell me a 1.5"x4.5" would not hold. I have re-worked the design to incorporate a 4" stile at the midpoint which will deflect the load but by how much? Correct on the casters but I spend $35 each on a 2" wheel. How I mount the casters to the posts is another engineering challenge with Spanish cedar.

You are correct contributor J. I donít need much support to hold the concrete. The wood sag is an issue. Thanks guys I really appreciate your time and thoughts. What would my job description be on a resume - Part Designer, Engineer, Architect, Sales Person, Cost Accountant, JIT expert, Product Inspection Expert - we donít get paid enough. I know I left out something.



From contributor J:
I think that you won't need any support if you put a piece of 1/8" plate steel underneath the piece and weld a bunch of bolts sticking up into the piece so that it is tied to the plate. If all else fails just make one and see what it takes to break it.


From the original questioner:
As usually the client has changed the design after two days of me designing the Spanish cedar unit. We are going with 1.75"x4" corner posts. .75x4.5x60" aprons a vertical divider board at the half point so the span will only be 28" - white oak. Sag still hangs in the back of my mind but it will take many years if at all.


From contributor J:
I did some more research and I am pretty sure that 4" wire mesh is fine. I actually talked to my old boss and he said that 2" thick 65" span might not need rebar and doesn't need any wood skirts underneath. By the way the biggest deck we ever built was 16' x 64' x 6" thick with only posts on the outside.



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