Help With Figuring Steel Beam Size

LeChatNoir · Post by **LeChatNoir** » Thu Nov 30, 2006 8:51 pm

So it looks like Iâ€™m going to be building a new shop this spring and I want to have a steel beam that spans the length of the building for using a trolley/chain hoist. This will not only allow my back to get a rest, but facilitate larger playa projects. I knew I needed to calculate the Moment of Inertia for the cross section of the Wide Flange Beam that is supported on each end. After searching, I found a formula the I believe allows me to calculate this, but Iâ€™d really like for an engineer, architect, or someone with access to the correct tables to double check me. Hereâ€™s is the formula that I came up with:

P= Point Load
L= Length
E= 30,000 psi (err on side of caution)
I= Moment of Inertia
D= Maximum Deflection for Wide Flange Beams

First I must calculate the maximum allowable deflection for a beam spanning 54 feet total:

D=L/360
D=54 ft/360
D=1.800 inches

Then I can plug that number into the larger formula:

I=PL/48ED
I=(3000lbs*54ft)/(48*30000*1.800)
I=(162,000ftlbs/2,592,000)
I=0.0625
It is my understanding that this should then be multiplied by 1728 (perhaps to to account for cubic inches?), yielding:

I=108

With that number I can cross reference a chart in the Machineryâ€™s Handbook and find that a W12x19 will work because it has an I value of 130. Iâ€™ll probably go with a W12 x 22 (I of 156) just to be on the safe side.

But not having a complete grasp for the inner workings of the formula, can anyone tell me if I am correct here?

MikeVDS · Post by **MikeVDS** » Thu Nov 30, 2006 10:19 pm

Hmm. My source is "mechanics of Materials" by Beer, Johnston and DeWolf. My charts don't include W12x19, but they do have W12x16 and W12x22 which have values of Ix of 103in^4 and 156in^4 respectively. Ix is moment of inertia about the x axis, which seems like what you want. So that part seems ok.

I can run the calcs. I remember using the formula you used but it's been a while. I'm reading about them again to double check but while I do that can you clarify a few things? E= Youngs Modulus of Elasticity? I believe for steel it's about 30x10^6 which would be 30,000,000 psi. Also is the entire span going to be 54 feet? Also is it only supported by the ends? And the formula "I=PL/48ED" was that for a beam supported from each end? I don't believe I have that formula but I have the tools to derive the correct one. I'm guessing you pulled that out of some book?

Looks like there is at least that one error. Also don't forget to add in a safety factor. You do not want your beam to fail at 3001lbs, do you? And remember that hanging a 3000 lbs object from it means that you will have more force if the object jerks, swings etc. I'd recommend a safety factor of at least 2. I personally like to use 3 because it's my life, but in this case 2 would probably be acceptable to most standards. The only safety factor I can tell is using 30x10^6 instead of 29x10^6 (which looks like you used 30x10^3 accidentally, which is an easy mistake because your book might be using ksi instead of psi). That's way too small. Hang your max weight from the beam and in motion your beam should yield.

Don't forget you also need to support the beam plus it's load when you build the shop. An interesting formula is the way they name the I beams. For example your guess is W12 x 19. The 12 means the height of the beam in inches and the 19 means that it will weight 19lbs/foot. So at 54 feet the beam will weight just over 1000lbs.

LeChatNoir · Post by **LeChatNoir** » Fri Dec 01, 2006 1:41 pm

Your rightâ€¦ I mistakenly took E as the minimum yield strength of mild steel (36,000psi), and it should infact be the Modulus of Elasticity. The formula I found was on some old site where a fellow had figured a beam size for an similar circumstance. I used his formula, which used E= 30,000 which I'm most certain now, was in ksi. When I thought it was the yield stregth (36,000psi), I figured that he had lowered the number as a safety factor.

Okâ€¦ I went back to my pile of notes and noticed something. I left out part of the formula in my first post and it actually reads I=PL^3/48ED. This would mean a larger beam would be needed, which would not surprise me, since a W12x22 still intuitively seemed small for such a span.

So here's the situationâ€¦ The maximum load Iâ€™d wish to lift with this would be 2000lbs. I used 3000 as a safety factor, but like your idea of going with at least twice the static weight, so 4000lbs seems like a good number. The complete span of the beam would be 54â€™ with 6â€

LeChatNoir · Post by **LeChatNoir** » Fri Dec 01, 2006 2:03 pm

Ok... so unless I'm totally doing this wrong and only think I have a vague understanding of it.

D=54â€™/360
D=1.800

I=PL^3/48ED
I=(4000*54â€™^3)/(48*30,000,000*1.800)
I=629,856,000/2,592,000,000
I=0.243

*1728

I=419.904

Beams fitting this would be (per the Machineryâ€™s Handbook, Edition #24):

W12x53 (Ix=425)
W14x43 (Ix=428)
W16x36 (Ix=448)
W18x35 (Ix=510)

Post by **mdmf007** » Fri Dec 01, 2006 3:21 pm

LaChatNoir -

Marks Standard Handbook for Mechanical Engineering (one of the books behind me on the wall) has a little section about trolley rails, and how to size them.

Regardles of the beam size, the flange also comes into play if you will be using a flange mounted trolley, a top mounted flange is way better by a factor of 3/1. This small section addresses the fact that the lower flange will deform and drop a trolley at a lot less than the rated load of the beam itself.
i.e. if the rail is rated at 10tons, the flange is definately not, and its safe load is related to its thickness, and how distance from the center of the beam the trolley wheels roll on. A top mounted rail trolley even if it deforms, simply gets stuck, a bottom mounted trolley will come off and drop to the floor..

The reson this section is highlighted in my book, is that we dropped a fire truck body when the lower edge of the I beam gave out, and deformed enough to let the trolley slip off.

later all

MikeVDS · Post by **MikeVDS** » Fri Dec 01, 2006 5:26 pm

If those formula are correct, that looks ok. I will try to get a chance to run things myself sometime this weekend. It'll probably take me a few hours to re-derive everything and remember exactly what is going on. It's good practice for me though. Someone who uses this stuff every day could probably tell you yes or no easily, but I understand the underlying principals and have to work from those.

I'd never seen the D=L/360 before. I know a simple formula like that can be used but I'll have to confirm that this works for your application. D,yeild should be linearly dependent on L so it looks promising.

The I=PL^3/48ED family of formula depend on how the beam is supported and how the load is distributed. I've seen formulas similar to this with 2, 12, 24, 64 instead of the 48. Also the exponents can differ. So I'll try to confirm this for you as well.

MikeVDS · Post by **MikeVDS** » Fri Dec 01, 2006 5:29 pm

Also, do you know the units on the "*1728 " factor? I can tell you what they should be based on how you're using it but I haven't figured out if those work out yet.

LeChatNoir · Post by **LeChatNoir** » Fri Dec 01, 2006 10:32 pm

I've only got a basic understanding for the stuff buried within the formula, so the best I can figure is that multiplying by 1728 is relative somehow to cubic inches (12*12*12=1728), but Iâ€™m not sure how. Again, this was just taken straight out of the formula I found online, which I can't find now, by the way.

My brain is now so full of numbersâ€¦ it hurts.

LeChatNoir · Post by **LeChatNoir** » Fri Dec 01, 2006 10:51 pm

mdmf007 wrote:The reson this section is highlighted in my book, is that we dropped a fire truck body when the lower edge of the I beam gave out, and deformed enough to let the trolley slip off.

you know... such a thought had crossed my mind too. Jeez... too much to ponder at such an hour. I've toyed with the idea of finding used bridge crane that's already rated for the load I need. But that's a bit more $$$$ than I was anticipating. Plus it seems like chickening out on figuring out the answers and formulas

Bob · Post by **Bob** » Sat Dec 02, 2006 5:16 pm

We could tell you how to derive beam formulae using calculus, but why don't you just rent a Hyster?

LeChatNoir · Post by **LeChatNoir** » Sat Dec 02, 2006 9:24 pm

Because renting the proper equipment would be far too sensible and easy. I prefer to punish myself for a while in order to feel like Iâ€™ve actually done something.

Tiahaar · Post by **Tiahaar** » Sat Dec 02, 2006 11:48 pm

how about one of these?

http://www.gorbel.com/gantrycranes/fixedgantry.asp
1-5 ton capacities, spans to 30 feet
(hey I would love to just have a shop...with a smooth concrete floor...in which to use one of these...someday)

Zulegoona · Post by **Zulegoona** » Sun Dec 03, 2006 7:10 am

I thought of one of those too Tiaharr, even with a set in floor track it seems like it could be more versatile because of the side to side capability .

LeChatNoir · Post by **LeChatNoir** » Sun Dec 03, 2006 7:30 am

The biggest problem with a floor gantry is that you gotta have room to maneuver it around whatever is in the shop. Most times, this isn't much of an option, unfortunately.

I'm leaning now towards an overhead mounted gantry crane. With the size/weight of the beam I need to use to span the entire shop length, I could build a much more versatile option for just a bit more. But i still need to verify the size of the beam to span the 30' width.

Here's pretty much what I'd be looking at, only spanning 30' instead of 24':

http://www.lkgoodwin.com/more_info/seri ... anes.shtml

LeChatNoir · Post by **LeChatNoir** » Sun Dec 03, 2006 7:39 am

Along with complete crane kits, they also sell the trucks that you can add your own beam to:

http://www.lkgoodwin.com/more_info/cran ... kits.shtml

Pretty affordable too.

EspressoDude · Post by **EspressoDude** » Sun Dec 03, 2006 8:16 am

LCN: is this a "business" shop you are putting your crane in?? If so, your insurance company, OSHA, state crane inspectors, etc. may have a whole lot to say about your project.

Note in the crane kits the top "channel if needed" that strengthens the beam and keep the top of the I beam from buckling. It appears that the cross sections they use are marginal for the rated loads.

Also be aware that as the load tries to sag the center of the bridge crane, the forces push the columns/walls of your building apart.

Not to throw water on your fire, but a serious injury may cost way more than a crane design stamped by a licensed engineer and properly inspected.

Wish I had one of those too, and a shop big enough to put one!!!

LeChatNoir · Post by **LeChatNoir** » Sun Dec 03, 2006 4:46 pm

Your advice is true, ED... and duly noted. I've thought of these things also. Technically it's an artist's studio with no employees at this time, so I'm not too worried about being inspected for such things. But that being said, I'm in no way attempting to avoid any sort of code or correctly built device. Should I wind up doing it this way, then I'll certainly build it the way I build my railings... over engineered and stout as an oak tree.

However... I am going to contact the company I found earlier and ask them about a price on a 30' span. But even if I go that route, I want to understand the physics/math behind it all.

EspressoDude · Post by **EspressoDude** » Sun Dec 03, 2006 5:53 pm

yes, it is a great opportunity to learn the mechanical design behind such things...Still learning at our ages, imagine!!

WHEN IN DOUBT, BUILD IT STOUT is my motto also. And it usually ends up too heavy to be practical

Tiahaar · Post by **Tiahaar** » Sun Dec 03, 2006 10:21 pm

Oh yes LeChatNoir if you can swing the extra the bridge crane will be your new love! I worked with a guy who had one, all manual with a chain hoist, and have envied him ever since. He somehow found a big one surplus and built his shop to fit the crane beams. Lucky fellow.

I seem to have a hazy recollection of some civil engineering statics coursework on beam loading...point loads vs loads distributed across a surface, maximum allowable deflections, etc etc... are you delving into all that??

As it turns out I have never used it and would have to go back and relearn it all now.

Bob · Post by **Bob** » Mon Dec 04, 2006 12:49 am

[hits head against desk]

Might want to consider more seriously what similar shops in your area do, who they've consulted on similar projects, and what local code requires. Even pallet racks need engineering stamps in some jurisdictions. Engineering is more than cookbook crap you can plug numbers into. Good luck.

LeChatNoir · Post by **LeChatNoir** » Mon Dec 04, 2006 8:39 am

Might want to consider more seriously what similar shops in your area do, who they've consulted on similar projects, and what local code requires

I am continuing to seriously consider all aspects of this. I am in an agricultural area and the building is considered a farm shop. It'll actually be one of the smaller ones around. I am not considered an industry, I am an artist with a studio.

Bob... you should know that I'm not just flying by night here. And I don't think I can just plug a number in and get a crane out (Though I admit that my public fleshing out of the math contained within may appear to the contrary). I want to understand what is happening inside the formula in order to gain better understanding and a feel for whether or not this is a realistic option for me.

I've been planning a new shop for years and its finally starting to come together. I never just jump into anything without digging into it as deeply as I can and what you are seeing here is one small part of it. I'm not at all unfamiliar with working with steel or with cranes or other types of heavy material handling devices. I've been working metal professionally for 15 years, often in large shops. I've checked into buying new cranes and having someone do a turn-key job for me. If $25,000 were no big deal to me (and that's a small one) I'd do it that way. But I've got little more than that to put into the entire building. I haven't yet even come to the final decision of building or not since I'm still weighing the costs.

New shop or retrofitted old one... either way, I've got to figure something out or continue to damage my back.

Bob · Post by **Bob** » Mon Dec 04, 2006 10:51 am

Just seems like a floor hoist or gantry would be a lot more versatile, with more of a guarantee it's going to work to the rated capacity right out of the box as long as the floor slab can support the loads, it could be maintained & repaired from the floor instead of climbing, used in places in the shop an overhead beam setup couldn't reach, & used in the yard outside the shop or on remote jobs. You'd know better what you need or the county requires, of course. If the shop is a kit building they might have something pre-engineered available.

LeChatNoir · Post by **LeChatNoir** » Mon Dec 04, 2006 3:38 pm

A floor gantry is certainly a versatile critter, but the way the forging station is laid out, it would be hard for one person to maneuver it around with any degree of efficiency. An overhead bridge crane would reach every spot in the shop quickly and easily (minus the amount of offset for the bridge system and crane trucks of course). And if Iâ€™m going to build a new shop, now is the time to go ahead and do it.

Today I talked with a fellow at the company I linked to earlier and explained what I needed to do. He said it was certainly doable and is working up a price on both a finished crane (28â€™ span) and the crane end trucks alone. If I choose to use my own beam, all I would need to do is assemble it with their product using their included diagrams of where to drill holes, etc. Niceâ€¦