Difference between wood and steel beams in theory 2

[LittleInch]

There was a recent post here which disappeared as the poster was asking for a design, but I was intrigued enough to do some research into this.

So on a theoretical level, if a wooden beam ( the example was about 4.5m of 4 x 12, so basically half a tree) is accepted by various parties as being sufficiently strong to resist loads and deflection limits, how do you show that a substitute square steel tubing 2 x 10 is as good?

Looking at deflection calcs the term EI as a denominator is always there.

So ignoring anything else, is it simply a matter of showing that if the EI of the steel tube is bigger than the EI of the wooden beam then it is at least as good?

I did some quick calcs and using an E of 10 GPa for wood and 200 GPa for steel plus the I calculation, the steel bean was about twice as good in terms of deflection calcs and I would assume similar for bending moment / shear etc. Of course it is harder to nail other bits of wood into the steel beam, but you take the rough with the smooth.

Does that work as simple ready reckoner? This doesn't mean you can design anything and still need sign off etc but does it work?


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[1503-44]

Basically yes, for deflection you compare EI.
But you also need to check actual tension stresses and shear mostly because Section Modulus for a solid rectangle and a square tube is nothing similar, and that would also apply to lateral buckling properties. Shear allowables perpendicular to the wood grain is also very low, as is crushing shear near bearings.

 

[XR250]

I think for starters, you have to define "as good"

 

[1503-44]

OK
Then make that a No for termites and a Yes for rust.

 

[LittleInch]

"As good" means that the steel beam is capable of replacing the wooden beam (or vice versa!) without exceeding either bending moment / shear / tension / bearing load or displacement.

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[gte447f]

This is very basic stuff, nothing magical. You are on the right track.

What is the same? span, load, shear, bending moment

What is different? allowable stresses, section modulus, moment of inertia, modulus of elasticity

Compare. Have fun.

What other potential issues might also require consideration? connections, beam bracing, lateral torsional buckling, etc.

 

[LittleInch]

I just wanted to see if I was on the right track. Clearly there are many other issues to consider when changing from a bit lump of timber to a more slender lump of metal which might be channel, tube, I beam or similar solid form item.

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[Celt83]

The wood will also be more sensitive to Shear deformations and experience creep deflection over time.

On a material level steel is isotropic while wood is anisotropic.

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[dik]

might be orthotropic...

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

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[KootK]

What you have to worry about will kind of depend on the direction that you're going. Switching from wood to steel, as you have proposed, will be easier than switching from steel to wood. Steel is much stronger than wood in shear and is not afflicted by the creep issues that plague wood. So, in switching from a 4x12 to a 2x10 HSS, you would merely need to:

1) Meet or exceed the EI values as you have suggested.

2) Ensure that lateral torsional buckling of your tube isn't a problem. I'd want to do this with actual loads but, I suppose, you could do it by meeting or exceeding the buckling capacity of the wood.

3) Ensure that local HSS wall buckling doesn't govern. This you could do by way of b/t ratio or by way of an analysis using the load.

 

[HTURKAK]

to resist loads[/b] and deflection limits, how do you show that a substitute square steel tubing 2 x 10 is as good?]

This thread reminds me the idiom "The devil is in the details" ..are the loads static ? If yes, the comparison and substitute of two beams with shear and bending stiffness, other stability checks is reasonable.

However,in case of dynamic loading , the mass and dynamic properties are important factors..( e.g. the damping ratio of timber is around 10 times of steel ).

Other factors; durability,corrosion, fire resistance....

 

[liam1369]

You get much more section strength from steel and with the much more efficient I sections typically, you end up with more likely member failure and flange / web buckling.

Standard timber joists for example are mostly for simply bending and axial for studs.

 

[LittleInch]

Thanks for the responses - I was a bit worried I would be chewed up and spat out, but it was good information for the future. It's been a looooong time since I studied beams and structures so just wanted to make sure I hadn't got this completely wrong.

Many thanks.

LI

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[RWW0002]

2) Ensure that lateral torsional buckling of your tube isn't a problem. I'd want to do this with actual loads but, I suppose, you could do it by meeting or exceeding the buckling capacity of the wood.

LTB for HSS beam??

I would lump LTB in with shear and creep under "less likely to be an issue that with wood" if HSS is being used. (If other steel sections, it will definitely be a necessary check.)

If deflection (thru equivalent EI), bearing, LTB, shear, and creep are "not-likely-issues, this leaves mostly bending stress checks. If you look at stress from an allowable stress standpoint (don't shoot me LRFD folks, this is just an exercise) with some conservative assumptions regarding allowable stress of the various materials, it quickly turns into a simple algebra exercise to see if stress will control over deflection. I will not ruin your fun by going through the math for you..

I will echo everyone else in saying that each member should be checked individually for its specific design conditions, but if you are looking for a "rule of thumb" so to speak, you should be able to come up with one with a bit of math..

 

[strucbells]

LTB could control design in tall and skinny rectangular HSS beams..there's a check for it in the flexure section of the steel manual. Obviously not a concern for square and relatively square rectangular sections.

 

[KootK]

LTB for HSS beam??

substitute square steel tubing 2 x 10

That's practically flat plate from an LTB perspective.

 

[RWW0002]

Fair enough, there may be a tall and skinny enough member to have LTB issues, I will not rule it out, but section F7 of AISC steel manual does not even address the failure mode in the spec. the commentary notes it is not typically and issue (see attached)

As far as "rules of thumbs" go, I would say it is not likely an issue (but should be checked in a final design)

 

[strucbells]

There actually is a section under F7 in the 15th edition, F7.4. But fair enough, I ran a few calcs on a HSS10x2x1/4..and for typical spans the effect is fairly limited...only an 8% reduction in Mn for a 20ft unbraced length. Deflection probably makes it a moot point in most cases. Still worth being aware of.

 

[RWW0002]

Agree.

 

[KootK]

One difficulty with the AISC checks is that I believe that they implicitly assume in plane support restraint of each of the four walls of the HSS. That's often not the case for practical HSS support connection. The result being that overall section warping will reduce LTB capacity more than the AISC equations would suggest.

If rules of thumb are the order of the day, here's one: keep HSS h/b ratios in the 1.5 - 2.0 range.