Calculating strength of steel?

This is sort of alternative modding... I'm fixing my house and doing various computer related modifications at the same time. I'm considering strengthening some roof beams with steel "L" structures, but wonder if it will really help.

So, a 40mm*40mm steel "L", 3 mm thick, over a 6m span, what weigth can it hold in the middle? How much can it bend before breaking?

Don't need exact calculations, just some calculated guesses..

L beams make for crappy load load supporting beams. Unless the load is placed on the corner on the L, then not only does the beam have to deal with bending forces, it has to deal with torsional forces as well. In addition the centroid will be quite a distant from the farthest point, so it leads to reduced load bearing strength.

Anyways, assuming you are using quality structural steel, your maximum load in the middle is 206.6 N or 46.45 lbs. The defection of the beam at this amount of load will be .129 m. These number assume no safety margin and are the actually numbers of yeilding of the metal. Anymore weight or deflection and your beam will enter the plastic deformation range (not good).

The load needed cause failure of the steel is 330.6 N or 74.32 lbs. I can not give a beam deflection for this cause all the formulas I know are only valid for metal that hasn't exceded it yield strength and would need to formulate new formulas.

Anyways this numbers are assuming alot as you were not specific on your materials. I could not find that size bar in my table of beams, so I don't know the weigh of the beam/ft so beam weight wasn't accounted for in the above numbers. Take these numbers to be ball park numbers you were asking for and do not trust for life to a junior mechanical engineering major.

Use additional wood beams.
You could also get premade plywood trusses. These have plywood capped on top & bottom with a "2x2"

Wow, some great info here! Thanks a lot!

Thing is, I want to keep the beams visible. They are about 12cm, and I'll drop the roof down about 5cm (to get downlights in) and still have the other 7 cm visible.. So additional beams won't work, and no wooden structure can support much weigth when just 5cm thick and 6 meter span..

But the steel "L" would support like 20kg in the middle, and the beams weigh about 10kg on their own. So about 10 kg of actual support... 8 of the "L" beams, so about 80kg.. Not much..

Does the way they're fixed make any difference? After all, the "L" beams won't move any and the "stretching" will be limited since it will be fixed to the wooden beam several places.. But the holes for fixing it will weaken it as well..

Anyway, the structural integrity is still good, the second floor won't fall on my head, it's just me thinking about making the structure even more rigid so it'll last even longer en move even less.

After all, the main beams have done their work for over 200 years and the have for the last 80 years

How about steel "I" or "H" beams, or just box sections (still no more then 5cm high)? That should support more, right?

Veland said:

Does the way they're fixed make any difference? After all, the "L" beams won't move any and the "stretching" will be limited since it will be fixed to the wooden beam several places.. But the holes for fixing it will weaken it as well..

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By fixing the beams numerous times, you reduce the span of beam carrying the load into smaller spans. This will decrease deflection and should increase the max load as you'll have a higher moment of resistance.

But you'll have to be careful on how you attach the beam to the wood. If you use insufficient connections, and load the beam, while the beam may carry the load, the connections could fail (tear out of the wood or break the bolt).

I imagine you'll be using bolts to secure the beam to the wood. If you plan on using the L beam, I would plan on using more bolts rather then less. The "weakening" effect is far dwarfed by the need for numerous good connections to reduce the beam's span and therefore moment. Make sure you use good bolts. Secured deeply into the wood.

Either way you look at it. More connections means more places for the beam to transfer the load into the wood frame. More connections = less load on each connection.

Veland said:

How about steel "I" or "H" beams, or just box sections (still no more then 5cm high)? That should support more, right?

Click to expand...

I beams are by far much stronger and more common then L beams. And it's easy to see why. The I beam is a symetrical beam, so the centroid of loading would be located at the center within the beam, eliminating the torsional "off center" forces created in using an unsymetrical beam like an L beam.

I don't have my steel handbook sitting around, it's back at university, but I'd expect an equvialent I beam to hold at least 30-40% more load because of it's superior shape before plastic deformation.

Gives more of a factor of safety at least.

If you rigidly attached the ends of the beam to prevent the ends from tilting downward then yes the bearing load would increase slightly and the deflection would decrease. Nothing in this world however is perfectly rigid as everything flexes under load.
Also, typically beam fail due to bending moments before any other form of loading but due to the thinness of your beam I would be worried about ripout. I am on vacation right now and don't have access to the data I need to do the calculations right now, I can get back to you on this.
Lasty, if you have not yet bought these beams I would highly recommend you buying "I" beams or boxed beam with the better of the two being the I-beam. Given beams of equal weigh/length the I-beam would beable to support much more load than the L beam due to the increased moment of inertia and the centroid being equal distance from the top and bottom of the beam.

Fixing thru I beam

Will fixing thru i beams with to attach a web cleat which holds a high performance drywall weaken the i beam? As an engineer would you allow such a fixing?

It has been a while since I helped build a house (last one was in Ann Arbor) but holes are allowed in the I-beam. You will need to check with local code first as that varies. Also check how big a hole is allowed and the spacing (how far apart each holes) is allowed. This may have a bearing on if you can hang the drywall or not.