Any engineers available?

[chopnhack]

I am trying to improve my intelligence by actually working out the math to design an overhead rack......... it's not going well.

Materials:
I would like to use 1" square tubing, 1/8" wall (probably aluminum 6031 or 6036).

Dimensions:
The shelf will be 7' long by 1' deep. The shelf itself will be a rectangle by the above dimensions with 6 pieces to span the width (about 1 cross piece every 1'). Decking will probably be some type of open coated steel wire like below, really cheap at $7.26 for 6'.

Support:
The back 7' rail of the rack will be lag bolted every 16" to existing 2x4 stud partition wall. I will try to center it, but the likely hood is that it will be off center. So this load will be a shear load on 5 bolts at best 4 at worst. I am thinking of using 1/4" lag bolts 3" in length (1" bar, 1/2" drywall leaving 1.5" embedded into stud). The balance of the load will be suspended from overhead 2x6 trusses with 2x4 bottom chords. Square tube to angle connection with bolt and nut and then lagged into ceiling. The intent is to place 2x4 sections between the truss's bottoms and lag into these from below if perpendicular, if parallel (2) 2x4 on edge across the truss bottom chords and use threaded rod with large washer.

A lot of variables to be worked out....uh huh..but I wanted to just get a rough order to see if 1" tube is capable of what I want it do.

Estimated weight for storage - no more than 360 lbs.

I need help with deflection calculation, bending stress calculations and how to evaluate the component and then the item as a system if that is possible.

So far:

moment of inertia of the square tube = I =(a^4-b^4)/12
answer = 0.05697 inch^4

section modulus = S = (a^4-b^4)/6a
answer = 0.11393 inch^3

beam moment? = M = wl/8 using 360lbs/7ft /8
answer = 6.428lbs/ft? (wasn't sure of the units to use
after the division with "8") or in psi (x12) 77psi

this would be assuming that all the weight would bear on this one beam which is not the case, but this is where I am unsure as to how to proceed. How can I evaluate the system? Do I assume uniform loading and then apportion weight accordingly to sections?

[JimD]

It seems like you are over engineering this. The first thing I would do is to check the capabilities of the wire shelving with it's normal supports. If the home center you saw it at does not have that information you should be able to find it on the manufacturers website. You probably do not need the aluminum structure nor do you need 1/4 lag screws is my guess.

You also should not normally go more than 1 inch into the studs in the wall unless you know for sure what is in there. If the plumber or electrician put something closer than an inch to the surface they should have put a metal plate to keep you from screwing into it. But if they are more than an inch away from the surface they count on you not driving long screws into their pipe or wire. So your lag screws are also a little long unless you've seen those studs and know they do not have plumbing or wiring going through them in the area of the shelf.

I made a shelf supported like you describe except it was all wood in my garage for storage. It is 4 feet wide and I've walked on it (ready to work I was over 200 lbs when I put it up). I am a mechanical engineer but I did not work it all out. Takes too much time. I consulted some span tables but mainly just used prior experience.

Jim

[jking]

You mistakenly put the length (7 ft) in the denominator when calculating the moment. You had the equation correct, but, made the mistake when putting in the numbers. M=(360*7)/8 = 315 lb-ft. You then need to calculate the bending stress, fb = M/S & compare to allowable stress for aluminum. This is all assuming the tube is only supported on the ends. If you are lagging into the framing more often, then the span changes.

Assumptions - you are the best judge of what to design the shelf to since you know what you're likely to store on it. You could design it for the 360 lbs to be evenly distributed, but, in reality it's unlikely. I would probably look at it from the evenly loaded standpoint & then also make an assumption on some point loads. Condition 1 being even loading, condition 2 being maybe 3 or 4 boxes (point loads). Point load require a different set of equations, though.

I'm at work, so, I can't spend a lot of time on this. Maybe when I'm home tonight, I'll run through some scenarios. You won't be able to get the 1" tube to span 7ft between supports. Is there a reason you want to use 1" aluminum tube vs. something else? Are you fighting some serious space/clearance issues?

[JimD]

I did a little googling after I got off work. I did not find a great reference but I am even more convinced the aluminum frame is unnecessary. I found a simple 3 foot long shelf system 1 foot wide rated a minimum of 500 lbs per shelf. That tells me the shelf is plenty strong without the frame. I also found another source comment the brackets are the weak link. This is typically a simple stap type bracket wraping the shelf giving you a space to screw on the wall and a thin metal angle bracket. Of these the bracket was cited which makes sense to me.

If you don't think the stock brackets are strong enough, I would come up with some metal straps over the shelf at the wall held in place with a couple screws. And maybe a screw eye into a ceiling joist plus a chain to the front edge of the shelf. Or a sturdy wooden bracket to the front edge on every other stud.

Jim

[chopnhack]

Good stuff guys:

JimD - absolutely over engineering this but I need a little mental workout every once in awhile in the deep end outside of my circle of knowledge. You are correct on the lags, I omitted the fact that I installed the studs and the wiring and plumbing so its known to be safe. Of course the lags could always be smaller to err on the side of safety. The manufacturer of the wire shelf that I found locally states 50lbs for the shelf, no mention of per foot etc. so I assume they are claiming the capacity for the entire 6' section. Originally I was considering just decking the frame with 3/8" ply but I wanted this to look a little nicer and easier to clean so I looked at Home Depot's wire shelving. The thinner sections of the shelf are not the same construction as some of these other wire shelves that have higher capacities. The one's that you mention (I assume) are built with a double perimeter reinforced with trusses. The shelf I am considering in the photo does not.

jking - thanks for that:

moment of inertia of the square tube = 0.05697 inch^4

section modulus = S = 0.11393 inch^3

beam moment? = M = wl/8 using 360lbs*7ft /8
answer = 315 ft lbs or in psi (x12) 3780psi

fb=M/S
fb= 3780 psi / 0.11393 inch^3

stress experienced at load = 33.1k psi
allowable stress 9500 psi

deflection 4.87 inches
IIRC the allowable deflection was 12 inches but obviously this can't work from just two points of support. Can you briefly explain the thought process on how to evaluate for multiple support locations?

Thanks!

[jking]

moment of inertia of the square tube = 0.05697 inch^4

section modulus = S = 0.11393 inch^3

beam moment? = M = wl/8 using 360lbs*7ft /8
answer = 315 ft lbs or in psi (x12) 3780 in-lbs

fb=M/S
fb= 3780 in-lbs / 0.11393 inch^3

stress experienced at load = 33.1k psi
allowable stress 9500 psi

deflection 4.87 inches
IIRC the allowable deflection was 12 inches but obviously this can't work from just two points of support. Can you briefly explain the thought process on how to evaluate for multiple support locations?

Thanks!

Fixed your units in the above.

For what you're doing, if you want to look at multiple supports I'd simply use the distance between your supports as the length in the equations.

[cabinetman]

I am trying to improve my intelligence by actually working out the math to design an overhead rack......... it's not going well.

Materials:
I would like to use 1" square tubing, 1/8" wall (probably aluminum 6031 or 6036).

Dimensions:
The shelf will be 7' long by 1' deep. The shelf itself will be a rectangle by the above dimensions with 6 pieces to span the width (about 1 cross piece every 1'). Decking will probably be some type of open coated steel wire like below, really cheap at $7.26 for 6'.

Support:
The back 7' rail of the rack will be lag bolted every 16" to existing 2x4 stud partition wall. I will try to center it, but the likely hood is that it will be off center. So this load will be a shear load on 5 bolts at best 4 at worst. I am thinking of using 1/4" lag bolts 3" in length (1" bar, 1/2" drywall leaving 1.5" embedded into stud). The balance of the load will be suspended from overhead 2x6 trusses with 2x4 bottom chords. Square tube to angle connection with bolt and nut and then lagged into ceiling. The intent is to place 2x4 sections between the truss's bottoms and lag into these from below if perpendicular, if parallel (2) 2x4 on edge across the truss bottom chords and use threaded rod with large washer.

A lot of variables to be worked out....uh huh..but I wanted to just get a rough order to see if 1" tube is capable of what I want it do.

Estimated weight for storage - no more than 360 lbs.

I need help with deflection calculation, bending stress calculations and how to evaluate the component and then the item as a system if that is possible.

Chop,

I can appreciate your verve with coming up with the formulas for this project. Some years ago I fabricated and installed upper cabinets 42" high, 14" deep, with a 12' radius. There was also was a curved restaurant counter below that followed. The cabinets had a solid panel on the outside of the curve, and doors on the inside.

The methods available to decoratively suspend the weight were added to the construction of the ceiling. What showed above the cabinets needed to be minimal and failsafe.

We don't always have the option to get engineering on our projects. But in commercial use, and for in home use, there is a liability factor that cannot be ignored.

You didn't say what the walls were clad with if anything. If there is sheetrock/drywall, then the fastened tubing may have the ability to compress the applied board. If there is just plain 2x4's, you have a good structural mounting media.

I'm guessing the use of the square tubing is for a decorative and structural appeal. The wire type closet shelving is usually supported by a gusset from the wall to the front edge of the shelf. Believe it or not, that shelving will hold quite a bit of weight.

Assuming you make that rectangle out of the tubing, that would be more than adequate for a frame. Adding the wire shelving to it IMO would make for a sturdy shelf. To install, the rear tube could be bolted/screwed to the studs. To support the front, you could use 3/8" threaded rod. It could be drilled through the top of the tube, with an acorn nut to cap the bottom.

Up at the top, you could also run a 7' square tube across the joists/rafters, and fasten with angle brackets to the side of the joists/rafters. If you want to decorate the threaded rod, you could use a sleeve to slip the rod. Or, you could use the square tube as a suspension support. Doing that you would have the look from the front of a square tube face frame.

I'm thinking that four (4) of those will yield a 28" span (3 openings) in between which will offer good support. In thinking of an alternative to the wire shelving, an aluminum diamond mesh grate, or something similar, might work out well. HD carries a similar grill.
.

[chopnhack]

Thanks jking - I was having a hard time with the units.

So if supported every 28" starting at 0 going to 84", 4 upright supports would be used. I am assuming dividing the load equally across those three sections or 120lb per 28" span so:

3,686 psi of experienced stress or a safety factor of ~2.5 at maximum load with 1" square tube. I could always go with the 1.5"x 1" rectangular tube of the same wall thickness, and that would drop the max stress to 1480 psi. Price should be about the same. That would give a safety factor of ~6.4. At this point I can see that this should be plenty strong. Have I come to correct conclusions?

C-man - Thanks for the info, I too was thinking about splitting the uprights in that fashion! And you bring up a great point, the tubing was going to be installed over drywall. I'm not too concerned because drywall can take 350 psi in compression before deforming, so as long as the front supports are balanced, I think it should be ok. The expanded metal sheet, I had not seen in HD before, in what section did you see it? I can always get it from my supplier, but it would be good to know the pricing before ordering. I like the threaded rod idea, I originally nixed it because I thought it would sway, but with the rear being fixed to the wall, there's no way! Thanks for making me rethink that. I would use washers and hex nuts of course, the acorn is a good idea to make sure the bottoms of the all thread are covered, nice touch. The reason for using aluminum box or rectangle is aesthetics, I don't feel like using steel because of the difficulty in cutting and drilling and then priming and painting. The aluminum is easy to cut and drill and looks good in the buff and low maintenance. The reason for the skimpy support is low clearance in that section.

Thanks for the help guys, really appreciate it.

[jking]

So if supported every 28" starting at 0 going to 84", 4 upright supports would be used. I am assuming dividing the load equally across those three sections or 120lb per 28" span so:

3,686 psi of experienced stress or a safety factor of ~2.5 at maximum load with 1" square tube. I could always go with the 1.5"x 1" rectangular tube of the same wall thickness, and that would drop the max stress to 1480 psi. Price should be about the same. That would give a safety factor of ~6.4. At this point I can see that this should be plenty strong. Have I come to correct conclusions?

Sounds about right. I would try to make an educated guess about what size box or tub you'll be putting on the shelf. The last thing you want to do is find out you have supports hanging down & spaced close enough that you can't use a convenient size box.

I assume you're planning to weld the tube frame together. Have you welded Al before? It's not as forgiving as welding steel.

[cabinetman]

I assume you're planning to weld the tube frame together. Have you welded Al before? It's not as forgiving as welding steel.

Using fitted connectors (similar to these) may eliminate the need to weld.
.

[chopnhack]

I have only welded a few times and was less than pleased. I could sure go for a new toy (TIG welder) lol but could hardly justify that one. I have some 3" equal angle with 1/8" wall that I had intended to use as "brackets" cutting 1.5" wide pieces and then turning them on their side to wrap around the corners of the rack. Through bolt with 1/4" bolt in a w pattern. There are a few areas that are just not accessible for me to place a nut behind - namely along the back that is to be lagged into the wall so I got some 1/4" self tapping screws to join the strapping to the middle span supports and back piece. I intend to use a strap on either side of the middle span to account for this type of fastener. I actually picked up all the materials today, nuts, bolts, all thread, acorns, 6' shelf, rect. tubing, angle, drill bits, lock washer, washers all told with tax $128.66. Not bad for a custom solution. I have seen online numerous places to order these prefabbed overhead storage for the garage, but with shipping they are kinda pricey. The real important reason above price is that this is an odd area to fit what I want into. Height and side restrictions. Jking, I did start the design with a couple of different shapes of sterilite in mind but I think I have settled with a 30q straight side container, 18-by-12-1/8-by-12-In I will be able to fit 6 of these wide with just a bit overhanging in the front. I seriously doubt that any would ever contain 60lbs, but you never know I have a story stick drawn out that gives each one some space for easy removal and I made sure the center upright supports are landing in between the totes. I hope to have some time next week to get started on it!

[gsmittle]

All this m*th makes my brain hurt. You might also try 80/20 for tubing and connectors. The last time I looked through their catalog they had solutions for problems I didn't even know were problems.

g.

[chopnhack]

I promise no more math, here is the final product on which I did some pullups off the corner (thats the final check )

I made it a little longer than anticipated so I used some plate I had left over to patch the ends up. I was able to get 5 lags in. The last photo was a fathers day gift

Thanks for all the help guys!

[sailor55330]

After reading this thread, all I can say is "wow".

What are you storing on this? Gold Bars? That is one serious shelf you have there sir. I am not criticizing because it is obviously what you wanted, but I think as someone said, the word "overkill" might be applicable for 350lbs.

At any rate, nice job.

[chopnhack]

If I had gold bars....lol, thanks, but I just needed an area to store as much as possible without having the shelving material take up too much vertical space. As for overkill, probably, but you never know how much you will end up storing up there, plus my son sleeps on the other side of that wall so a safety factor of 6 lets me sleep at night