Why Do Sagging Floors or Trusses Pull Walls Inwards

[econ41]

I've been following this debate but probably wont participate in any depth.

However - since I seem to have been the first member to refer to the issues of underlying physics without concern for either Mick's creditable and innovative model OR whatever NIST may have said I think I should put the following comments on record:

This statement by Tony is wrong as Mick correctly identifies in a couple of later posts.

Catenary loads are only possible when the structural member can no longer take moments and will only transmit tensile loads like a cable..

The base point of disagreement is that the two effects are NOT mutually exclusive. They co-exist and can be treated as separate factors in analysis THEN added. There is no benefit in me speculating as to how the error has arisen.

This statement by Mick identifies the key issues of the true situation:

Catenary loads are possible whenever a stiff structural member suffers a reduction in it's ability to resist moments. If it's actively sagging then it's no longer fully resisting the moment forces, and hence must be acting less like a rigid structure, and more like a chain.

Mick correctly identifies the key point when he says "...must be acting less like a rigid structure, and more like a chain" i.e. it is somewhere between the two and each "mode" contributes to the overall situation.

The key factors are:
1) There is a range of possibilities between the extremes of "fully rigid beam" and "fully flexible rope";
2) Any one of those "grey area" scenarios involves a mix of rigid beam effects and flexible rope effects;
3) The proportion contributed may vary depending on situational specifics.

Whilst the two effects are NOT mutually exclusive as Tony suggests the interaction is not as simple as it may appear - and Tony's references to bending moment go partially to explaining the true situation.

The following suggestion by Mick MAY help.

Perhaps your objection here is a bit of a tautology, using "catenary loads" as the idealized loads from an idealized infinitely flexible rope dangling from two points? Perhaps we should adopt the more general term "pull-in forces", as used by NIST?

....as long as participants dont lose sight of the reality that both factors co-exist and that the pull in can be validly separated as if it was "the idealized loads from an idealized infinitely flexible rope".

 

[Tony Szamboti]

I still think aluminum might be the way to go. We are not going to get accurate numbers with steel anyway due to various scale issues. So aluminum should still demonstrate the principle.

I only had this 16"x1"x1/8" piece laying around. But let's do some investigatory experiments
View attachment 32182

#6x3/4 wood screws (it's all I have!) every 2" in 1/8" holes, as shear studs.
View attachment 32183
View attachment 32184

Add grout as a concrete substitute. Note I drilled some holes on the end for anchoring. Not sure how yet.
View attachment 32186

I'll let that set, then see it it takes a load without cracking, then try heating it.

This all is just investigation, not intended to demonstrate anything yet. The grout might just crack. A trip to Home Depot might be in my near future.

Mick, what you are doing so far looks good, although like you I am not sure grout can be used as a substitute for concrete as far as compressive strength.

Don't forget you should also use something to reinforce the grout/concrete with something like 1/16" diameter steel/stainless steel wire to mimic the welded wire fabric in the concrete.

 

[Mick West]

Don't forget you should also use something to reinforce the grout/concrete with something like 1/16" diameter steel/stainless steel wire to mimic the welded wire fabric in the concrete.

Yeah, I thought of that after the grout was setting. I've got some 1/2" mesh wire cloth.

 

[Oystein]

No reinforcing within the grout necessary at all - that's a wild goose chase and unseemly distraction as long as scaling issues have not been carefully addressed and evaluated.

I get why Tony is keenly interested in this silliness, but hope Mick will see it for what it is.

 

[Tony Szamboti]

That NIST explanation sounds like garbledy gook to me.

The core columns WERE laterally restrained by the bracing. Look at the plan of the core NIST.

The pull in of the facade was because the CORE side of the floor where you see pull in had no core side support... the floor at that point was essentially cantilevered and the connection pulled at the facade until the bolts sheared and the connection failed. Shear strength of a 5/8"Ø bolt is 1,500#. If the claimed pull in force was 15,000#... each connection would have had to have more than 7 bolts. I don't think the top chords of the double truss had 10 bolts... each one had 2. if the truss had buckled / sagged as they claim the 2-1"Ø did nothing.

http://www.rdfasteners.com/pdf/boltstrength.pdf

No?

Jeffrey, while looking over the truss connection details in the NIST report yesterday I found that the floor trusses were actually welded to their seats at the perimeter and the 5/8" diameter bolts there were considered construction bolts which remained in place after welding. This would make the truss to perimeter spandrel connection even stronger than I said earlier.

See NIST NCSTAR 1-3 section 4.2.4 (Connections, Bolts, and Welds) at the bottom.

 

[Tony Szamboti]

No reinforcing within the grout necessary at all - that's a wild goose chase and unseemly distraction as long as scaling issues have not been carefully addressed and evaluated.

I get why Tony is keenly interested in this silliness, but hope Mick will see it for what it is.

The concrete in floors in buildings is generally reinforced with rebar and welded wire fabric to prevent it from cracking underneath due to tensile forces from bending. What Mick is doing will bring his test a little closer to reality.

I would agree that the relationship between span, depth of the trusses/beams, and concrete thickness have to be scaled properly and it is somewhat complicated due to the exponential factors involved with moment of inertia and deflection, as well as two different materials with different moduli of elasticity.

 

[Oystein]

The concrete in floors in buildings is generally reinforced with rebar and welded wire fabric to prevent it from cracking underneath due to tensile forces from bending. What Mick is doing will bring his test a little closer to reality.

You say this without having assessed and evaluated scaling issues.

You could be easily wrong, and the exact opposite could be true: That the grout alone, if built into the model with random dimensions, is too STRONG in tension already in true scale with the original. In that case, adding wires or whatever as tensile reinforcement would remove the model even further from reality.

I would agree that the relationship between span, depth of the trusses/beams, and concrete thickness have to be scaled properly and it is somewhat complicated due to the exponential factors involved with moment of inertia and deflection, as well as two different materials with different moduli of elasticity.

And yet, without evaluating any of this, you make unfounded claims.

 

[Oystein]

Also, I doubt that the rebar in the WTC floors plays much of a role in making the floor assemblies stiffer. The trusses are composite with the (only 4 inches thin!) lightweight (!) concrete by having the bends (knuckles) of the diagonal web bars poking into the slabs. The system will lose that composition by having those knuckels tear out - laterally or vertically. The rebar would do little to prevent this, I think. It's then down to friction between top chord and slab.

 

[Mick West]

I'm fully aware that making a scale model of the truss+slabs+connections that's 18" (1.33 feet) long is an impossible task. Even getting the linear dimensions of the components is difficult enough. For the 36 foot slabs Reducing by 1.33/36 is a 1/27 reduction, taking the concrete from 4" to 4/27", or about 4mm. The material itself does not scale, with the granule size being much larger. It's impossible that spalling or cracks can be anywhere near as localized as they would be on a larger model.

And of course there's the issue of loading, 1/27 linear reduction means I need to load the "truss" with 27*27 = 729x its actual weight. The aluminum bar weighs 120g, so that's 87kg, a bit more than my weight. The bar cannot support that laying flat, but can support much more than that on its side.

There's many more complications of scale, materials, and structural accuracy. The intent of the original experiment is simply to demonstrate that a sagging horizontal structure (or a structure with reduced bending resistance) pulls in.

Unfortunate when I went to check on the grout this morning the test blob I left on the side was still pliable. Reading the instructions it says it takes 7 days to fully cure. So I'll set that aside for a while.

 

[Oystein]

... The intent of the original experiment is simply to demonstrate that a sagging horizontal structure (or a structure with reduced bending resistance) pulls in.
...

It's good to stick with that and not get lost in irrelevant details, and false claims about such.

For starters: Any solid, strictly horizontal structural member (truss, beam, anything), no matter how supported, will sag under its own weight. Perhaps by an imperceptibly little amount, but sag it will.

I you either increase load, or decrease capacity (i.e. by heating), it will sag more.
This changes the geometry of the assembly: If the length of the horizontal element stays the same, but it sags through deeper (cuvrves more), then its ends will (try to) move closer to each other. This results in a pull-in force.

Tony's claim that such a pull-in force does not occur as long as the member can resist moments is patently FALSE, and he needs to retract that claim, if he wants to be taken seriously. No adding of intricate details to the model can undo the falseness of his claim. Let's not get confused by bad engineering thinking!

Perhaps he imagines that making a truss composite with a 4-inch lightweight concrete slab will make a floor infinitely stiff no matter how hot fires get underneath - but that would of course be a dangerously unsound imagination.

(That pull-in force may of course be counter-acted by other effects, e.g. by expansion if it is heated. But the mere fact that a horizontal member sags adds a pull-in force.)

 

[Mick West]

Mick correctly identifies the key point when he says "...must be acting less like a rigid structure, and more like a chain" i.e. it is somewhere between the two and each "mode" contributes to the overall situation.

The key factors are:
1) There is a range of possibilities between the extremes of "fully rigid beam" and "fully flexible rope";
2) Any one of those "grey area" scenarios involves a mix of rigid beam effects and flexible rope effects;
3) The proportion contributed may vary depending on situational specifics.

Here's an interesting illustration of this:

That's a bungee cord that I soaked in water and froze overnight. It is by no means rigid, but it has more moment resistance than an unfrozen cord.

The setup just after initial placement.

Result:


Source: https://www.youtube.com/watch?v=ikZlvl_vAVY


The cord sags as it defrosts. The right columns is pulled in (left column is fixed).

The important point here is that this is a small change in the moment resisting capacity of the cord. It's not going from stiff to flexible. It's going from somewhat flexible to slightly more flexible. It had a small moment resisting capacity, which was then reduced slightly. This small change was sufficient to increase the pull-in force at the end connections and move the 4x4 column measurably.

 

[qed]

Please can you guys help us "civilians" understand what @Tony Szamboti is predicting.

Source: https://www.youtube.com/watch?v=U967Ld5QPzs

Is Tony saying that, with an additional concrete layer above the aluminium tube, the loaded concrete/aluminium bar will not sag when heated?

 

[Mick West]

Is Tony saying that, with an additional concrete layer above the aluminium tube, the loaded concrete/aluminium bar will not sag when heated?

Ask Tony. I don't think he's made a specific prediction. He's aware there's too many variable to predict what will happen. The experiment with grout bonded to aluminum is not going to prove anything, it an illustration at best, an a possibly misleading exploratory test at worse.

 

[qed]

@Tony Szamboti

I just knocked up a quick proof of concept.

Source: https://www.youtube.com/watch?v=U967Ld5QPzs


The aluminum exhibits the same gradual sagging of the ice chain, yet is clearly still highly moment resisting. At the end it pulls in the the two blocks, even thought it's not attached to them.

Mick, you need concrete on top which is composite with a metal frame below for your simulation to have any validity.

Here is the basic concrete mix a material science teacher at the University of Illinois uses for lab experiments. He doesn't make them use aggregate and has them use just water, cement, and sand.

http://matse1.matse.illinois.edu/concrete/bm.html

• @Tony Szamboti What difference will we see with the addition of the concrete layer?

 

[Tony Szamboti]

To those like Oystein,

I want to make it clear that I certainly understand that any horizontal member will sag under its own weight and load. The point is that usually in structures it is imperceptible and the amount of tensile load from a horizontal member on a vertical support is negligible when the horizontal member retains stiffness in the vertical direction, which is a function of moment or bending resistance. Most of the load is transferred to the supports and handled in shear on the mounting brackets attaching the horizontal member to the vertical and then in compression by the vertical member.

The ability to take moments caused by a vertical load affects how much tensile force will develop in the horizontal direction in a significant way, as Mick showed above with the frozen bungee cord. The concrete will allow the composite floor to retain some moment resistance even when heated and thus will affect how much tensile force is developed by the composite floors. It will be different from the trusses themselves and I don't think anyone can simply say it would be negligible in a credible way.

The amount of concrete involved in the composite floor situation is also more than just that on top of the truss chords. The composite floor is essentially a "tee" shape. Structural engineers generally use a value for width of the slab involved to be the width of the truss + 16 x the slab thickness. In the case of the Towers the width of the slab used for calculating its contribution to moment of inertia would be 4 x 2 + 2 x 1.09 + 16 x 4 = 74.18 inches, with the first two terms multiplied being the calculation for width of the double truss which was 10.18 inches.

Additionally, everyone should be asking why the NIST FEA program did not realize the tensile force that would have been necessary to pull the columns inward.

 

[qed]

@Tony Szamboti

Mick, you need concrete on top which is composite with a metal frame below for your simulation to have any validity.
You say you used a 5/8" square tube earlier. Was it steel? What was the wall thickness? What was your span?
If you give me that I can tell you what an equivalent thickness of concrete on top of it would be to allow you to reasonably mimic the trusses and slab in the Twin Towers. You can put wires through it to simulate the welded wire fabric and screws through the top of the tube that would jut into the concrete to make it a composite beam and provide the effect of shear studs (knuckles from the trusses in the case of the Twin Towers).

Looks like 3/32" (13 gauge).

I think it is a 3/64" wall thickness tube, not 3/32". Each mark is 1/32" and it looks like it is 1.5 times that wide which would be 3/64". It is probably 18 gauge which is .0478" and is close to the .0468" decimal equivalent of 3/64".
I don't think you need any large aggregate in the concrete. Sand alone with Portland cement should work to provide the same reaction as concrete.
I don't think you even need to heat it evenly. If you get a stretch of 6 inches of the metal frame to 700 C it should take the compressive resistance away from the metal enough.
I will calculate how much cement and sand you need proportionately along with its height dimension to stay 5/8" wide. Give me a day.

Here is the basic concrete mix a material science teacher at the University of Illinois uses for lab experiments. He doesn't make them use aggregate and has them use just water, cement, and sand.http://matse1.matse.illinois.edu/concrete/bm.html

You state that the addition of your concrete layer "should take the compressive resistance away from the metal enough."

• In this simulation, will the addition of the concrete layer you propose prevent the aluminium bar from significantly sagging when the composite concrete/aluminium bar is heated?

Yes or no? In your expert opinion.

 

[Ray Von Geezer]

As another civvy, I think Tony is referring to how the concrete and steel components effectively prevent each other from sagging by the use of components like shear studs attached to the beam and embedded in the concrete.

I could be wrong, but if so then I think it's going far beyond the intention of Mick's model (to show simply how the sagging/pull in occurs) into modelling things like when did the studs fail due to thermal expansion, how many failed and which ones - that would be a whole different level of complexity.

It seems to me that once the studs do start to fail then the contribution of the slabs to preventing sagging is lost and they're simply supported weight which increase it. Is there any point modelling the post-failure sagging by adding the cement/concrete/grout? Intuitively if the "beam" sags under its own weight it'll sag more when supporting extra, but again I could be wrong about that too.

Ray Von

 

[qed]

Is there any point modelling the post-failure sagging by adding the cement/concrete/grout?

Yes. Since this was suggested by @Tony Szamboti.

What Mick has here (I think) is a "minimal viable product" which can be honed to cater for objections, etc. For example adding shear studs from the aluminium bar into the concrete.

 

[Ray Von Geezer]

Yes. Since this was suggested by @Tony Szamboti.

What Mick has here (I think) is a "minimal viable product" which can be honed to cater for objections, etc. For example adding shear studs from the aluminium bar into the concrete.

Tony, I think, wants Mick to model whether the floors (beams & slabs) would sag, so far as I can see the purpose of this demonstration was to show what would happen when they did, and to this layman it meets that purpose.

Mick already pointed out several issues of scale, differences in materials and such and how the demonstration as envisaged by Tony is unlikely to be of much use. The layer of "concrete" seems particularly odd - weren't the beams supporting slabs much wider than the beams themselves? Mick's use of aluminium makes sense in the context of the original experiment, but for Tony's suggestion it's just another difference between the model and reality.

I guess my pont is; if this is Tony's suggestion, and Mick is happy to accommodate it, then shouldn't Tony define some parameters and predict outcomes to show why it's worthwhile?

To me it just looks like make-work.

Ray Von

 

[Oystein]

I want to make it clear that I certainly understand that any horizontal member will sag under its own weight and load. ... The ability to take moments caused by a vertical load affects how much tensile force will develop in the horizontal direction in a significant way, as Mick showed above with the frozen bungee cord. The concrete will allow the composite floor to retain some moment resistance even when heated and thus will affect how much tensile force is developed by the composite floors. It will be different from the trusses themselves and I don't think anyone can simply say it would be negligible in a credible way.

But earlier you had claimed the opposite:

Catenary loads are only possible when the structural member can no longer take moments and will only transmit tensile loads like a cable.

That was clearly, unequivocally FALSE, and you should come out admitting that you made an utterly FALSE claim tight there, if credibility is important to you.

The point is that usually in structures it is imperceptible and the amount of tensile load from a horizontal member on a vertical support is negligible when the horizontal member retains stiffness in the vertical direction, which is a function of moment or bending resistance. Most of the load is transferred to the supports and handled in shear on the mounting brackets attaching the horizontal member to the vertical and then in compression by the vertical member.

Well yes, "usually".
You are kinda forgetting the unusual circumstances like planes crashing into the towers, fire protection getting stripped from the trusses, and huge, unfought, multi-story fires raging through those floors.

Obviously, trusses did not retain stiffness and sagged when subjected to intense fires. Sagged much more than they did while cold.

That, obviously, created a catenary force, which you previously denied.

And I don't think anyone can simply say it would be negligible in a credible way.

The amount of concrete involved in the composite floor situation is also more than just that on top of the truss chords. The composite floor is essentially a "tee" shape. Structural engineers generally use a value for width of the slab involved to be the width of the truss + 16 x the slab thickness. In the case of the Towers the width of the slab used for calculating its contribution to moment of inertia would be 4 x 2 + 2 x 1.09 + 16 x 4 = 74.18 inches, with the first two terms multiplied being the calculation for width of the double truss which was 10.18 inches.

Additionally, everyone should be asking why the NIST FEA program did not realize the tensile force that would have been necessary to pull the columns inward.

10.18 inches.
Can you explain what relevance that number with 4 significant digits has towards the topic of this thread? What that the hell are you talking about??

 

[cloudspotter]

View attachment 32194
View attachment 32195
This shorter piece of the Al was heated by seven candles. It reached thermal equilibrium at 75°C. Thinner candles would increase the heat flow in (more flames). I guess I could also make a mega-candle with two rows of wicks down the middle.

So: possibly viable for heating aluminum, but would require lots of candles, and the proximity of the candles would limit deflection.

Would something like this do the job?

https://www.roofingsuperstore.co.uk/product/roofers-single-furnace.html


(also useful for roofing jobs and clearing weeds)

 

[econ41]

Ray Von Geezer raises a couple of significant issues as shown by parts of his two comments:

I could be wrong, but if so then I think it's going far beyond the intention of Mick's model (to show simply how the sagging/pull in occurs) into modelling things like when did the studs fail due to thermal expansion, how many failed and which ones - that would be a whole different level of complexity....

Ray Von

I have always admired Mick's efforts at physical modelling and have commended them and linked to them on other forums on numerous appropriate occasions.

BUT as the record of recent years shows I have regularly questioned the purpose of the modelling and the implicit target which I will loosely describe as "helping lay persons understand the physics". My concerns usually about extending the modelling into areas more complex than the layperson needs or can benefit from. And where the modelling becomes less appropriate. I think that Ray Von Geezer is correct when he suggests that the "inform the lay person" purpose has been met - at least in Ray's case:

Tony, I think, wants Mick to model whether the floors (beams & slabs) would sag, so far as I can see the purpose of this demonstration was to show what would happen when they did, and to this layman it meets that purpose.

Tony may have a different objective BUT Ray's lay person need is met.

Now there have been two strands of discussion in the thread:
1) The OP topic involving modelling; AND
2) The relevant issues of underlying physics.
...and I am conscious of the preference of this forum to stay strictly with one topic. So I will make a brief comment on each of the two topics and leave it for guidance as to whether the second should be pursued here in this thread.

Topic #1 As far as the modelling is concerned the modelling process and discussion is heading down the path of more rigorous modelling of detail. The same path was followed a year or more back with the several threads discusing modelling of the "progression stage". My question at that time - the same point I make here - has the modelling gone far enough for the likely laypersons who would benefit? Because pursuing details is not likely to increase benefit to such lay persons.

Topic #2 - The underlying physics. Tony Szamboti address some issues "To those like Oystein,...."

That post and others preceding identify many of the key aspects of physics but there are two issues of principle which Tony relies on which I would dispute. They are:
(a) The first - which Oystein has already addressed - is the false reliance on "ordinary" conditions and their misapplication to the physics of the WTC real situation and of Mick's modelling - neither of which are "ordinary". I agree Tony's analogous reliance on "ordinary" is wrong - my reasons more tightly focussed than Oystein's but no need to go into details here.

(b) The second is the actual physics involving a balance of "beam" and "catenary" actions. Tony correctly identifies in this recent post the relevant factors but does not state how they "share the load". In fact in earlier posts he has stated both explicitly and by implication that the two are mutually exclusive. That is not so. Both are present concurrently.

The "missing bit of physics" as far as I can see is an explanation of how the loads share between residual "stiffness" as a beam allowing the "normal" style of force distributions and the transfer of part loads to the catenary mechanism with resulting "pull-in" forces.

What would happen can be explained - initially in broad outline - and sort of "first order" like this:

Assume for simplicity the beam has a single central point load "2W" - therefore vertical reaction at each end = "W"
As the temperature of the beam rises it weakens and starts to sag. The weakened beam cannot support 2W - with W at each end. So "Wba" (Residual load carried by beam action) is less than W and the lost portion is taken up by "Wca" load due catenary action. Where somewhat obviously Wba + Wca = W - we have the same vertical load irrespective of which mechanism carries what part of it.

And this is where some of the complexities alluded to by Tony start to complicate the analysis. (Don't "prevent" - just "complicate" ) The "inwards pull" results simply from the vectors of the downwards angle of the tension pull in the sagging beam. Which - if we refer back to what got us to this point - is why such high "pull in forces" can be developed - and which will probably show up as Mick starts measuring. BUT it is not simply the angle of the sag in this "heat weakened" beam scenario. It would be if it was only a rope. Or Mick's chain with all the ice melted.
But let's leave this preliminary explanation there - see if there is any interest and whether it should be a separate thread.

 

[James W Wing]

I think you might need a diagram there

Yes, I guess so. Maybe I missed the point of your experiment, but it seems like the heating of the beam from the top would cause the beam to extend slightly on the top and actually bend upwards as shown in B of my diagram, assuming that the beams are pinned top bottom or both, the lengthening of the material would cause a momentary outward motion. Your experiment did not pin them so there is definitely an outward motion.

As the beam heats up the elastic properties become such that it no longer holds its shape and the beam will sag due to weight, if heated from the bottom (C) the sag will occur sooner, but whether from top or bottom the heating will cause a momentary outward motion of an inch or two on both sides until the beam begins to fail.

As the beam begins to fail further outward push will occur until the chord of the sagging beam becomes less than that of the nominal beam length and the whole thing will begin to pull the walls inward until the pins break and the whole floor crashes to the floor below. It will hit in the center, overloading the beams again and breaking the pins and the two will fall together to the next floor bam bam bam bam - all the way to the point where a floor has enough underpinning to withstand the weight of the onslaught.

 

[Mick West]

Maybe I missed the point of your experiment

The point is simply to demonstrate that a sagging floor pulls the sides in.

Thermal expansion of the beam breaking connections is another issue. NIST did discuss this as I remember, but it was much more of an issue in WTC7.

 

[James W Wing]

The point is simply to demonstrate that a sagging floor pulls the sides in.

Thermal expansion of the beam breaking connections is another issue. NIST did discuss this as I remember, but it was much more of an issue in WTC7.

Sorry, I was only trying to explain why the momentary outward movement of the vertical poles occurred in your earlier experiment, not that they might have broken some bolts. BTW I doubt that it could have - not purely thermal expansion, maybe along with the crash or explosions, but who knows?

There is no doubt in my mind that the walls will come inward if the beams are connected to them. I am at a loss as to how your myriads of experiments show that they will or won't - the closest is that of the melting ice on the chain - that should have made it perfectly clear. You must be having way too much fun!

I might have missed something though, was the question also posing that a different scenario than that of falling inward might have occurred - if so, what and how were they suggesting that it might have happened? For a few milliseconds I thought it was strange that it was all maintained within the confines of the building walls, but then it was clear to me - how else could it fall - sideways? That could happen only if the underpinnings were removed - so all of this discussion appears to be quite meaningless unless it is for the pure scientific aspects of understanding what happened. In other words - it is debunked already, isn't it? You have proved your point as far as I can see - who is disputing it further?

 

[Mick West]

Cascading floors is off-topic. Feel free to discuss elsewhere.

 

[Seymour]

Sorry, I was only trying to explain why the momentary outward movement of the vertical poles occurred in your earlier experiment, not that they might have broken some bolts. BTW I doubt that it could have - not purely thermal expansion, maybe along with the crash or explosions, but who knows?

There is no doubt in my mind that the walls will come inward if the beams are connected to them. I am at a loss as to how your myriads of experiments show that they will or won't - the closest is that of the melting ice on the chain - that should have made it perfectly clear. You must be having way too much fun!

I might have missed something though, was the question also posing that a different scenario than that of falling inward might have occurred - if so, what and how were they suggesting that it might have happened? For a few milliseconds I thought it was strange that it was all maintained within the confines of the building walls, but then it was clear to me - how else could it fall - sideways? That could happen only if the underpinnings were removed - so all of this discussion appears to be quite meaningless unless it is for the pure scientific aspects of understanding what happened. In other words - it is debunked already, isn't it? You have proved your point as far as I can see - who is disputing it further?

For what it's worth NIST predicted thermal expansion of the trusses that would push on the columns, followed by sagging when heated further that results in pulling.

If Mick's thing shows that, then it's confirmation

 

[Mick West]

For what it's worth NIST predicted thermal expansion of the trusses that would push on the columns, followed by sagging when heated further that results in pulling.

If Mick's thing shows that, then it's confirmation

I'm not sure about "confirmation" however if you look back at this post:

No thermal expansion was visible to the naked eye, HOWEVER there's some interesting effects. When I first heat the beam in the middle with the smaller blue propane torch, the two block rise up. I'm heating the bar on top, the thermal expansion is greater on top, so it makes the bar want to curve upwards. So the blocks rise very slightly and rotate outwards
View attachment 32141

The beam then does seem to expand a bit (maybe 1mm) up until the sag starts to set in. Watch the top of the "column" on the right here.
View attachment 32143

(Note the background shifts slightly too. I think this is due to the image stabilization in my Nikon P900)

There is distinct thermal expansion. It's not very significant compared to the sagging though.

 

[econ41]

For what it's worth NIST predicted thermal expansion of the trusses that would push on the columns, followed by sagging when heated further that results in pulling.

If Mick's thing shows that, then it's confirmation

Confirmation of what? That NIST was right? The physics is straight forward and independent of whether NIST was right. (And NIST was right...)

A beam (joist if you prefer but the terminology is not important) subjected to heating will expand along its length while still maintaining "rigidity" (stiffness if we want to be more pedantic).

THEN - if it gets hot enough - it will lose stiffness and start to sag. It will STILL continue to expand in length but that aspect is swamped by the other factors which are:
1) The "beam" will lose beam strength and start to sag because it can no longer carry all the applied load. AND
2) The "sagging" will put the "length" into a curve which means the horizontal vector of the now curved length will start to reduce; AND
3) Because it sags catenary action will start to pull inwards.

(And - subject of my previous comment and some errors in earlier posts - the catenary action applies concurrently with the now reduced strength of "beam" action - the heated beam can no longer carry the full load so catenary action takes up the shortfall.)

And the inwards pull from catenary will be more that the outwards push from linear expansion. Simple geometry of the relevant vectors.

So there are two topics implicit in your contribution to this discussion - (1) Was NIST right >> yes and (2) is the physics understood >> yes .. and the physics of the situation is straightforward AND independent of whether NIST was right or wrong.

 

[econ41]

I'm not sure about "confirmation"....

...it certainly DEMONSTRATES - and I suggest it "confirms" the physics for those who need such confirmation.

There is distinct thermal expansion. It's not very significant compared to the sagging though.

Yes. And "not very significant" is guaranteed by the geometry of the vectors.

 

[Hierophant]

Could you also do an experiment that shows the behavior or 2 attached steel beams instead of one? I'm asking because the floors were held up by a sort of girder that basically looks like 2 steel beams connected by diagonal beams.

If the lower horizontal beam is heated more than the upper one, thermal expansion will cause the 2 beam system to bend, because one becomes longer than the other. A bit like a bi-metal thermometer/thermostat, except that its the same kind of metal with one having a higher temperature (and therefor higher length).

Even if the lower beam expands, it will make the (non expanding) upper beam bend, which will make it effectively pull in. It's and additional effect to the one of bending by weakening that you showed. Bending by differential heating/expansion. I'm curious how that would look, even though it's probably harder to reproduce.

 

[Mick West]

Could you also do an experiment that shows the behavior or 2 attached steel beams instead of one? I'm asking because the floors were held up by a sort of girder that basically looks like 2 steel beams connected by diagonal beams.

A truss.

I'm not sure if the differential expansion of the lower part (the lower chord) would do anything, as it's not attached to the inner columns.

 

[econ41]

....I'm not sure if the differential expansion of the lower part (the lower chord) would do anything, as it's not attached to the inner columns.

It would affect the overall performance/effect of the joist as a sub system Mick. The "fight" between bottom chord and top chord defines how the joist overall acts in the bigger picture. Let me try to put it in context.....it is a "systems" v "sub-systems" issue.

I read Hierophant's post and thought of how I could meaningfully respond. It raises some potentially complex issues which may hinder rather than help understanding. Let's see if we can explore the issues at a simple level....."(first??).,

The simplest way I can address it - which may not communicate well - is that is is an issue of "systems level".

The top and bottom chords of the floor joist truss are within the system of "floor joist". The issue if we think of the whole building structure is "what effect do the mechanism of floor joists" have on the overall structure.

The issue as raised by Hierophant is WITHIN the sub-system of "joist". It affects how the joist overall interacts with the"bigger picture" of the whole structure.

So think about what a "joist" does within the whole system of the building. It - the "joist" including its competing bottom and top chords - initially expands due to thermal expansion thereby pushing the perimeter columns outwards. (Yes - and pushing the core columns inwards but the perimeter ones would lose the "tug of war" AKA "push of war". So initial "push out" of the perimeter would be the effect.) (I won't derail to explore why that is so.....)

Now in the context of Hierophant's questions that "macro" effect is the result of the action of the whole truss.....which is the NET result of the "top chord" fighting the "bottom chord" conflict he identifies. The OVERALL result in the early stages is "Joist pushes OUT".

Later - as the whole joist gets hotter - it - the whole joist - starts to sag and the force on the perimeter becomes "pull in" as per all the previous discussion and explanations. Once again it is NET pull in - independent of the "state" of the battle between the top and bottom chords.

Let's see if we can discuss it further - or even if we need to go further.

 

[Hierophant]

A truss.

I'm not sure if the differential expansion of the lower part (the lower chord) would do anything, as it's not attached to the inner columns.

What I was trying to say was that the expansion of the lower part would force the truss (sorry for using the wrong words) to bend.

The bending is what will make the truss pull inwards. The weakening through fire combined with the weight of the truss would make the truss bend (thereby pulling inwards), which is what you showed in your experiment.

But differential expansion of upper and lower parts of the truss alone would also force it to bend, even without weight and weakening. Or, if the diagonal rod at the end of the truss is able to give way in some way when pushed (its intended to pull not push), the lower part of truss would not fulfill its function of supporting the upper part anymore.

(sorry not a native speaker)

 

[econ41]

What I was trying to say was that the expansion of the lower part would force the truss (sorry for using the wrong words) to bend.

<< Yes.

...But differential expansion of upper and lower parts of the truss alone would also force it to bend, even without weight and weakening....

<< Yes. the key word is "also" - two different causes but the same end result.... the truss bends causing inwards pulling.

 

[Mick West]

It would affect the overall performance/effect of the joist as a sub system Mick. The "fight" between bottom chord and top chord defines how the joist overall acts in the bigger picture. Let me try to put it in context.....it is a "systems" v "sub-systems" issue.

That was badly put on my part. Of course it will do something - I was thinking more along the lines of something that would also show up in a model. I don't think it's really plausible to model the effects of the geometry of the trusses on a very small scale.

 

[econ41]

That was badly put on my part.** Of course it will do something - I was thinking more along the lines of something that would also show up in a model***. I don't think it's really plausible to model the effects of the geometry of the trusses on a very small scale.****

** Understood - my interest was in getting the "parts of system" versus "whole system" point posted to see if it would help Hierophant. And taking a risk of using "system language" tho his later post shows he "gets" the key points. Realised them for himself without my risky higher level conceptual explanation.

*** Understood that - as we know you and I tend to take partially different approaches to the use of models. Differences aside I doubt it would be possible to model that aspect in a meaningful way - easy to demonstrate the "sub-system" effects BUT not in a model of a more extended part of the building.

**** Probably true. And the main point is independent of the "truss" setup with discrete upper and lower chords spaced by diagonals. The issue of temperature differential between top and bottom would apply to a rolled section "I" beam, a boxed fabricated beam - even a solid bar. The macro effect on the "joist" would behave analogously. Initial linear expansion pushing the ends outwards followed by inwards pull from sagging as the beam became heat softened.

 

[Abdullah]

The main reason why the trusses pulled in was web buckling. This web buckling was itself a result of sagging caused by expansion. From NCSTAR 1-6C