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# Modern Steel Construction Steel Quiz12

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## Modern Steel Construction Steel Quiz

(OP)
I was looking at the steel quiz in the 10/17 issue of MSC. I was able to pick up the problem quickly as I'm sure others have. However, I had a slightly different answer, I came to the conclusions that the framing plan shown had beams that required themselves for support and therefore would not work. However the article simply states that the configuration is difficult to erect. Is the framing plan shown even structurally stable utilizing simple structural theory?

### RE: Modern Steel Construction Steel Quiz

I don't believe it is stable once the temporary is removed.

### RE: Modern Steel Construction Steel Quiz

2
It's stable. The deflection profile may be a Bessel function or something equally bizarre but it's stable. There's actually an entire branch of wood frame architecture devoted to this kind of thing: Reciprocal Architecture.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

### RE: Modern Steel Construction Steel Quiz

It may be stable, but I agree with their proposed solution of extending the W18. That seems the most practical. Even though its stable I bet the deflection calculations would be a bear.

### RE: Modern Steel Construction Steel Quiz

What is the grey x's? Is that supposed to stand for horizontal stability bracing or... I don't know?

### RE: Modern Steel Construction Steel Quiz

(OP)
Grey x's are openings in the floor.

I accidentally did this years ago and RAM flipped out. Hence the reason why I don't do it anymore.

### RE: Modern Steel Construction Steel Quiz

(OP)
OK, I took a quick look at your paper KootK and most of the framing that was shown would have an axial compression load associated with the framing. What was shown in MSC would I would guess you would end up with a catenary (tension) load. I can see how it would work, but I'm not daring enough to do it.

### RE: Modern Steel Construction Steel Quiz

I don't think it's stable without some kind of differential elevation in the beams, similar to the reciprocal framing in kootk's link. In FEA you'll get an instability warning, in practice it probably deflects into a funnel shape and destroys your floor and ceiling finishes.

### RE: Modern Steel Construction Steel Quiz

You could possibly make it stable via fixed beam ends putting torsion into the supporting beams; obviously not least cost but it would make the deflection calculations easier.

Professional Engineer (ME, NH, MA) Structural Engineer (IL)
American Concrete Industries
https://www.facebook.com/AmericanConcrete/

### RE: Modern Steel Construction Steel Quiz

- Conventional FEM chokes on this because it's (obviously) non-linear and recursive. No great surprise there.

- You tend to see this in sloped members simply because you tend to see this in roofs. Architects are usually a good deal less about the aesthetics of it in the underside of a floor. Also, you kinda need the oculus business for full dramatic effect. That's not unheard of in floors but pretty rare.

- I don't believe that axial/membrane effects are required for stability. If you've got a competent tension ring that'll certainly help. With no tension right, the slope exacerbates problems and lateral spread rears its ugly head.

- From a stability perspective, I believe this to be okay by inspection based on this observation: by definition, nothing here "grows without bound". The contributions to flexure and deflection get progressively smaller as you cycle round. Nothing runs away/amok on you.

- If you've got a vibration sensitive occupancy, that definitely warrants some attention.

- If you've got rain or concrete ponding potential, then there's a stability issue there. But that's a different animal and, other than trickier math, is little different than ponding issues in normally framed systems.

- This is actually quite a common morphology in old school heavy timber structures, particularly in the NE. Barns and churches where they mount a pergola on top and want no obstruction below. Back in my wood truss design days, I used metal plate wood connected trusses reciprocally to mimic these structures in certain applications.

- A useful way to think of these systems is as two, crossing beams, each constructed in two pieces that are moment spliced in a peculiar fashion.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

### RE: Modern Steel Construction Steel Quiz

Nice! There's a paper for darn near everything these days.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

### RE: Modern Steel Construction Steel Quiz

For what it's worth, I just created a quick RISA 3D model and it seems to work just fine.
Not saying I'd ever try to build this but I believe it does work.

The tough part for me to reconcile is "chasing" the load around the ring. In my first model (with only one distributed load) half the reaction gets passed to the connected beam over and over and over until it effectively is zero.

### RE: Modern Steel Construction Steel Quiz

My intuition says i can't believe it is stable without introducing some torsional, catenary, membrane or other in-plane effect. I can't check it myself as I only have a 2D FEA. Oh, well.

### RE: Modern Steel Construction Steel Quiz

Maybe i'll check it this week with some 2x4's and see what happens

### RE: Modern Steel Construction Steel Quiz

XR, please do! I'd love to see a real world test!

### RE: Modern Steel Construction Steel Quiz

Years ago, I actually saw a roof built out of glu-lam members which looked exactly like DETstru's model. I remember staring at it for quite sometime

DaveAtkins

### RE: Modern Steel Construction Steel Quiz

I was skeptical, but I built the same kind of model as DETstru and it worked. The deflection really wasn't that large either. I was very careful to make sure that I didn't have any weird torsional interaction between members. And, that's not including any kind of system non-linearity. So, it appears that it is a stable system... Though a very, very weird one.

Note:
While you can create these type of model in a general purpose program (like RISA-3D) I don't believe you could create it in a program like RISAFloor or RAM or such. Very difficult to track tributary areas for live load reduction or such for a funky framing system like this.

### RE: Modern Steel Construction Steel Quiz

Huh. Sounds as though I was incorrect about linear methods not working for this. Which leads me to my next point of interest.

If we drop the pretense of "instantaneous load response", as they discuss in that article of slick's, it seems to me that the question should not be "why is load chased in this situation?" but, rather, "surely load is chased in every situation?".

It has long been my intuition that moment distribution is not just an expedient calculation method but, instead, a true description of how load response flows through an indeterminate structure. The handling of imbalances in moment distribution strikes me as too similar to "load chasing" here to be mere coincidence.

Even in an ostensibly determinate structure such as a simple span beam, I feel that you'd still get this "load chasing" at the atomic level as individual molecules rearrange themselves to produce load resistance (equilibrium) while continuing to obey their own version of material law (atomic repulsion and attraction). Every simple span beam is really a gazoolion interdependent, molecular springs after all.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

### RE: Modern Steel Construction Steel Quiz

DETstru, what happens if you have axial springs on the supports? The supporting beams are obviously not relatively stiff in their weak axis flexure and I feel this will change how your beams react.

Professional Engineer (ME, NH, MA) Structural Engineer (IL)
American Concrete Industries
https://www.facebook.com/AmericanConcrete/

### RE: Modern Steel Construction Steel Quiz

Good point. To heck with axial springs though, let's go axial wheels. Should still be stable externally.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

### RE: Modern Steel Construction Steel Quiz

Switching to springs made no difference at all. There are no horizontal reactions, only vertical.

### RE: Modern Steel Construction Steel Quiz

One thing that jumped out at me from the start is having a W18 frame into a W16. Not a fan of something like that.

### RE: Modern Steel Construction Steel Quiz

#### Quote (DETstru)

Switching to springs made no difference at all. There are no horizontal reactions, only vertical.

Hmmmmm, I was thinking there would be but that makes sense I suppose; each beam is statically stable in the axial direction. Maybe if you had large deflections this would come into play but sticking with the small displacement assumptions then I can see it having no effect.

Professional Engineer (ME, NH, MA) Structural Engineer (IL)
American Concrete Industries
https://www.facebook.com/AmericanConcrete/

### RE: Modern Steel Construction Steel Quiz

Okay, I fully encourage you to make one of these. I'm amazed how sturdy this is.

I'm now wondering what I can make around the house that utilizes this. Wife said she wanted a trellis arch out back, maybe it should have a reciprocal plane frame in the roof...

Professional Engineer (ME, NH, MA) Structural Engineer (IL)
American Concrete Industries
https://www.facebook.com/AmericanConcrete/

### RE: Modern Steel Construction Steel Quiz

#### Quote (KootK)

A useful way to think of these systems is as two, crossing beams, each constructed in two pieces that are moment spliced in a peculiar fashion

See it TME? It jumps out all over me when I look at your model.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

### RE: Modern Steel Construction Steel Quiz

#### Quote (KootK)

See it TME? It jumps out all over me when I look at your model.

I know, right?! I'm going nuts over this, it's simultaneously really hard to wrap my head around but it's just simple span beams! "Peculiar fashion", indeed.

I'm loving this, if I didn't have stuff I should be doing I'd totally fall down the rabbit hole with avscorreia. Used up too much time already.

Professional Engineer (ME, NH, MA) Structural Engineer (IL)
American Concrete Industries
https://www.facebook.com/AmericanConcrete/

### RE: Modern Steel Construction Steel Quiz

Mrs. TME totally deserves a reciprocally framed trellis.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

### RE: Modern Steel Construction Steel Quiz

2
Independent peer review incoming:

### RE: Modern Steel Construction Steel Quiz

#### Quote (DETstru)

Independent peer review incoming:

Love it. Would you say that is part of a "balanced" breakfast?

I'm just now realizing how interesting these are. With the proper bracing (or otherwise connecting the "peak") these frames become diaphragms! They can provide lateral stability as well as vertical.

Professional Engineer (ME, NH, MA) Structural Engineer (IL)
American Concrete Industries
https://www.facebook.com/AmericanConcrete/

### RE: Modern Steel Construction Steel Quiz

DETstru:
‘Pear review,’ what the hell do you mean? Those are just plane ol apples. And, V-8, that doesn’t have any peers in it ether, it’s a vegetable juice. I fiddled around with these structures years ago, they can drive you crazy, and become addictive too.

### RE: Modern Steel Construction Steel Quiz

Well I didn't have any pears so... I did my best!
Unfortunately I now only have 3 apples left...

### RE: Modern Steel Construction Steel Quiz

I just realized that everyone makes these frames all the time without realizing it; cardboard boxes! When you fold up the top without taping it you make it into a reciprocal frame!

Professional Engineer (ME, NH, MA) Structural Engineer (IL)
American Concrete Industries
https://www.facebook.com/AmericanConcrete/

### RE: Modern Steel Construction Steel Quiz

I have no substance to add to this thread, I just love how this topic peaked all our interested and led to these small scale models that showed substantially more capacity than we all intuitively thought should be there. Maybe not all @KootK.

Goes to show always something new to learn/experience in our profession. Comes very timely behind the recent post about confidence in calculations as well and how to get comfy with them. TME wasn't comfortable with the results so threw together a small scale real world replica with material on hand and got "performance" in line with DETstru's RISA model, at least thats what I see in the deflected shape of the chopsticks :).

As an aside TME need a youtube clip of the erection sequence and any shoring that was needed prior to the system being stable.

### RE: Modern Steel Construction Steel Quiz

DETstru:
Well, you better hurry up then, there is a three legged, apple supported, variation of what you guys built. The center opening is a equal sided triangle.

### RE: Modern Steel Construction Steel Quiz

Learn something new everyday!

### RE: Modern Steel Construction Steel Quiz

(OP)
So I suppose the answer given in MSC is correct in that the only problem with the framing scheme has to do with erectibility and not my thought if stability. Still not going to do it IRL.

### RE: Modern Steel Construction Steel Quiz

Also redundancy. The structure is the epitome of non-redundant where failure of one member is guaranteed to result in a catastrophic collapse of the entire reciprocal frame. I'd only do this if it had an architectural feature and was skookum as frig.

Professional Engineer (ME, NH, MA) Structural Engineer (IL)
American Concrete Industries
https://www.facebook.com/AmericanConcrete/

### RE: Modern Steel Construction Steel Quiz

I love the photos and enthusiasm, but Im still not on board with the stability argument.
I've only seen one of these "in the wild" and the deflections were enormous. It was a wood framed structure, and too long ago to remember the specific spans or member sizes.

I ran a RAM elements analysis and it didn't show any problems and didn't show any axial forces or weak axis bending. Really, it only convinced me that RAM isn't a proper tool for this type of problem.
Each of the physical models shown here, and the photos of the shelter structure, show a significant overlap between the framing members. If there is any slip between these members it wouldn't matter and you can develop friction between these joints to help minimize slip.

What happens with a series of wood beams to nailed or end nailed together? There is no potential to develop axial resistance and the consequences of slip are much more severe.
With steel connections, youll get some axial capacity from a standard shear plate connections and maybe that's enough to provide stability, but I don't think its inherently stable.

### RE: Modern Steel Construction Steel Quiz

The book KootK linked to emphasises that the design of the notches and joints is crucial to success. To be honest the examples given where the joints are twisted wire (frapping as we called it in the Scouts) look a lot more robust, easier and uglier than the minimalist notched style used by the Japanese.

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

### RE: Modern Steel Construction Steel Quiz

This is similar to getting 20 kids in a row, standing them in a circle and getting them to all sit at the same time...
totally works until their legs wear out.

### RE: Modern Steel Construction Steel Quiz

The model posted by Detstru has been around for more than 40 years. If anyone has an old copy of Beer and Johnson Statics and Dynamics textbook, it's there.

### RE: Modern Steel Construction Steel Quiz

I'm trying to mentally calculate the reactions if only one of the beams was loaded and it's kind of driving me crazy...

### RE: Modern Steel Construction Steel Quiz

#### Quote (atrizzy)

I'm trying to mentally calculate the reactions if only one of the beams was loaded and it's kind of driving me crazy...

This was actually why I made my little chopstick model. It's actually fairly simple once you think about it but it does have "second-order" effects. Each beam acts simple span and thus a load on beam #1 causes a reaction of some percentage onto beam #2, that loads some percentage onto beam #3, then that loads back beam #1. Thus, you need to run multiple iterations to get the true load but the actual math is just simple span beams.

Professional Engineer (ME, NH, MA) Structural Engineer (IL)
American Concrete Industries
https://www.facebook.com/AmericanConcrete/

### RE: Modern Steel Construction Steel Quiz

Doing the iteration by hand, you find that you come to 99% of the reaction after the second iteration.

With one beam uniformly loaded in a system of four beams connected at their midpoint (like the DETstru model, I think) each reaction around the perimeter is half the adjacent reaction. (Look at the reactions in the first DETstru model above)

So, you'd expect the reaction to be 0.5*W in a simply supported beam. In this* reciprocal system, the reaction at the loaded beam is 0.533*W = 1/2W + 1/32W + 1/512W + ...

*edit: the summation applies to this geometry

### RE: Modern Steel Construction Steel Quiz

#### Quote (TME)

but it does have "second-order" effects.

I believe not. I stated this myself at first but later retracted it after all the successful RISA results started rolling in. As I mentioned previously, I believe all the "load chasing" to be no more second order than the remainder chasing in moment distribution. Just business as usual with an indeterminate structure organizing itself to resist load. This is a minor clarification but an important one I think. At least is it for me as I was wrong headed about it initially.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

### RE: Modern Steel Construction Steel Quiz

I did an iterative analysis in ram and it came back fine.

Reminds me of how you close a cardboard box lid. One flap overlapping the other.

Also works in a 3-member system.

### RE: Modern Steel Construction Steel Quiz

#### Quote (KootK)

remainder chasing in moment distribution

This is a better term of what I was trying to describe, hence why I put "second-order" in quotes as it's not really second order.

#### Quote (kipfoot)

Doing the iteration by hand, you find that you come to 99% of the reaction after the second iteration.

Very neat! I'm amazed with only 4 beams that only 2 iterations are needed but there it is. I feel this kind of mathematically demonstrates why these frames are so much stiffer than I would expect at face value.

Professional Engineer (ME, NH, MA) Structural Engineer (IL)
American Concrete Industries
https://www.facebook.com/AmericanConcrete/

### RE: Modern Steel Construction Steel Quiz

#### Quote (TME)

I put "second-order" in quotes as it's not really second order.

Ahh... my bad. I didn't register the significance of the air quotes. Which is odd as I tend to overuse that device myself.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

### RE: Modern Steel Construction Steel Quiz

Here are my tests, with 3, 4 and 5 elements.
Now my wife and kids think that I'm a nerd. They're probably right.

### RE: Modern Steel Construction Steel Quiz

Another independent peer review for anyone left in need of convincing...

### RE: Modern Steel Construction Steel Quiz

What I find most interesting about this is our physiological reaction to what seems to be effectively little more than linear elastic load distribution in an indeterminate structure (erection / vibration / redundancy excepted). For consideration, I've created what I believe to be an analogous in plane model. Does that raise anybody's stability hackles? I've also compared the system to a moment splice in timber to try and drive home what I believe to be a fundamental characteristic of these things.

In the model below, I've intentionally stripped the boundary conditions down to as few as I believe can be had while keeping the thing stable.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

### RE: Modern Steel Construction Steel Quiz

This is pure conjecture but I wonder if we're simply bad at thinking about grillages. Most of us spend most of our time investigating and thinking about in plane models. I did some grillage stuff in college and haven't looked at a grillage of any complexity since.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

### RE: Modern Steel Construction Steel Quiz

I remember when I was a kid, my Mom doing this with our silverware. It was a puzzle you had to figure out.

You put the four knives flat in the formation we're all familiar with now (support the end of each knife with an upside down cup). Then you put an upside down bowl over the square made by the knives to hide how they interlock.

You show that to someone, then tell them to look away while you disassemble it. See if they can figure out how to assemble it.

I guess my mom would've made a top notch structural engineer :)

### RE: Modern Steel Construction Steel Quiz

A similar application my mom taught me was ninja "bombs" made out of popsicle sticks.

You throw them against something (your brother's head for example) and they explode on impact. And by explode I mean their strain energy due to bending is converted into kinetic energy.

So yeah, you could say my Mom is the coolest. :)

### RE: Modern Steel Construction Steel Quiz

Actually, now that I think about it, the ninja bomb has nothing to do with this. Nevertheless, it is awesome.

### RE: Modern Steel Construction Steel Quiz

The ninja bomb has something to do with it, I think...
It's just that instead of an external load the applied loads are all internal (between one member and another) and the friction force holds them together. Your throwing it at your brother's head would be analogous to knocking one of the reciprocal members off of another with a lateral force.

### RE: Modern Steel Construction Steel Quiz

I am not a structural guy, however, I can visualize a catastrophic failure of a roof with that system similar to the catastrophe of the Hartford civic center space frame roof.

### RE: Modern Steel Construction Steel Quiz

#### Quote (KootK)

Just business as usual with an indeterminate structure organizing itself to resist load.

Assuming small deflections, I would not say that it is indeterminate but rather quite determinate.

### RE: Modern Steel Construction Steel Quiz

I believe that the structure is statically determinate, contrary to some of the comments above. If plan dimensions are provided, all reactions can be obtained by statics alone. An iterative process is unnecessary to solve the problem.

BA

### RE: Modern Steel Construction Steel Quiz

#### Quote (Heuvo)

Assuming small deflections, I would not say that it is indeterminate but rather quite determinate.

Huh. It seems that the reciprocal framing plot just won't stop thickening. Like delicious Thanksgiving gravy.

I disagree and believe that the system is indeterminate and that the reactions can only be found by equilibrium when you have symmetry in play. Here's my reasoning by way of thought experiment:

As I mentioned above a few times now, this system has the characteristic of being quite similar to two moment spliced, orthogonal crossing beams. Hopefully that is not in dispute. And, just like two crossing beams, the loads distribute based on relative stiffness.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

### RE: Modern Steel Construction Steel Quiz

I disagree. The reactions are not related to stiffness. The problem is determinate.

For example, suppose each beam is 10' long and the square opening in the middle is 5'x5' such that each beam is supported at one end by an external support and at the other end by another beam. In all cases, the reaction occurs at midpoint of the supporting beam.

If all beams are loaded with uniform load W then the total load on the grid is 4W. Each of the four reactions is W due to symmetry.

Assume that only Beam B1 carries uniform load W. The others are not loaded. Beam B1 bears on B2 which bears on B3 which bears on B4 which bears on B1. The reaction of B4 on B1 is P. B1 reaction is W/2 + P/2 which falls at the midpoint of B2. B2 exerts a reaction of W/4 + P/4 on B3 which in turn dumps W/8 + P/8 on B4.

B4 reacts with W/16 + P/16 on B1, but we called that P, so:
P = W/16 + P/16
Solving, P = W/15 and the reaction of B1 can be found to be R = 8W/15
The remaining three reactions are 4W/15, 2W/15, and W/15 for B2 to B4 respectively.
The sum of all reactions is W as expected.

BA

### RE: Modern Steel Construction Steel Quiz

#### Quote (BAretired)

Each of the four reactions is W due to symmetry.

Right. But does this not invalidate your example since the symmetric situation is the one unique case where equilibrium alone can yield a solution?

Take your geometrically symmetric example and run these two thought experiments on it:

1) All members W21.

2) The North-South members Wx21; the East-West members 2X4 SPF.

Think the four reactions are still W for both cases? I don't. And that implies indeterminacy.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

### RE: Modern Steel Construction Steel Quiz

Just realized that your example is two seperate examples, one symmetrically loaded and one not. I'll have to leave that for another day. It's a bit of a mouthful for digesting tonight.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

### RE: Modern Steel Construction Steel Quiz

Yes KootK, there are two examples, one with all beams loaded, the other with only one beam loaded.

If the problem is statically determinate, the reactions must be the same even if the beam size is variable. If a 2x4 SPF is capable of carrying the load, then the external reactions must be equal with all beams equally loaded.

BA

### RE: Modern Steel Construction Steel Quiz

#### Quote (BA)

If the problem is statically determinate, the reactions must be the same even if the beam size is variable.

Right, but my contention is that the problem is not statically determinate.

#### Quote (BA)

If a 2x4 SPF is capable of carrying the load, then the external reactions must be equal with all beams equally loaded.

Is the distribution below not valid with unequal reactions and symmetric loading?

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

### RE: Modern Steel Construction Steel Quiz

In your latest example, the external equilibrium is satisfied but you have not specified how the 100# load gets into the system. If the load is applied uniformly on each beam, i.e. 25# each, I believe the external reactions will be equal by statics. If the load is applied unsymmetrically, say 50# each to B1 and B3 and zero load to B2 and B4, I'm not so sure the external reactions would be equal. It could be determined by statics but my poor old brain doesn't feel like tackling that problem right now.

To take your example a bit further, you could have external reactions of 50# and 0# instead of 30# and 20# which would still satisfy external equilibrium.

BA

### RE: Modern Steel Construction Steel Quiz

Beams have been numbered B1 through B4 in the attached sketch. As noted, the only applied load is W on B1 which is assumed to occur at 0.75L from the left end where L is the beam length. The external reactions are labeled R1, R2, R3 and R4 which apply to B1 through B4 respectively. The reaction of B1 to B2 is assumed to be P which is to be determined by statics.

Beams B2, B3, and B4 have a beam reaction applied at midspan from B1, B2 and B3 respectively. Consequently, their reaction at each end is half of that load.

All beams are simple spans, so the calculation is relatively simple.
It was found that for load W at the location shown:
R1 = 0.3W
R2 = 0.4W
R3 = 0.2W
R4 = 0.1W

R1 + R2 +R3 +R4 = W as expected.

If all four beams have a load W acting at 0.75L from the external end, the principle of superposition can be used to find that each external reaction is equal to W.

BA

### RE: Modern Steel Construction Steel Quiz

If load W is placed only on B1 and B3 at 0.75L from the end, using superposition, reactions are R1+R3 or R2+R4 which means they are all equal, namely W/2. The sum of all four external reactions is 2W as expected.

BA

### RE: Modern Steel Construction Steel Quiz

I am finding your argument pretty persuasive BA. And you definitely get an A+ for effort. Although I do think it cruel of you to use my own sketches to dismantle my theories. You're retired... you shouldn't even have Bluebeam damn it!

I think DETstr should step up and adjust her RISA model to run a test case of my specification:

- All members 10'
- Oculus N-S dim 2'
- Oculus E-W dim 4'
- Load applied at one of the oculus corner connections
- Case I: all members W8x21
- Case II: the N-S members switched to 2x4 SPF

How about it DETstu? I don't normally attempt to assign others homework but I'm not yet a RISA jockey and I'm so damn busy that I'm working at 9:30 pm on a Wednesday... There's a big, shinny magenta star in it for you?

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

### RE: Modern Steel Construction Steel Quiz

#### Quote (KootK)

As I mentioned above a few times now, this system has the characteristic of being quite similar to two moment spliced, orthogonal crossing beams. Hopefully that is not in dispute. And, just like two crossing beams, the loads distribute based on relative stiffness.

This is very much in dispute for me at least.

I don't agree that the orthogonal crossing beams with moment connections behaves at all similar to the reciprocal frame.

FWIW I also strongly believe that the timber moment splice posted above is also determinate.

The key to determinacy was if the member forces could be obtained without the use of a stiffness function. Symmetrical or not, the member forces can be found without the use of a stiffness function for the reciprocal frame in this discussion. This of course assumes that you also base your argument on there being small deflections and boundary conditions that prevent dubious tension ring and catenary behavior.

### RE: Modern Steel Construction Steel Quiz

#### Quote (Heuvo)

I don't agree that the orthogonal crossing beams with moment connections behaves at all similar to the reciprocal frame.

Really, not at all? You place a load among some members, none of which extends the full distance between supports. And somehow, like magic, that load is transferred out to the supports. That doesn't sound anything like splicing to you?

#### Quote (Huevo)

FWIW I also strongly believe that the timber moment splice posted above is also determinate.

I never suggested otherwise so we're in agreement there.

#### Quote (Huevo)

Symmetrical or not, the member forces can be found without the use of a stiffness function for the reciprocal frame in this discussion.

Can they? That really is the question. And perhaps they can. As I mentioned earlier, I'm coming around to BA's reasoning. That said, one must recognize the important logical distinction between being able to generate a solution (one of many perhaps) and being able to generate the solution (unique). BA's adroitly demonstrated that (a) solution can be found without invoking stiffness. In my mind,however, it has not yet been demonstrated that he has found a unique solution. And that's whole thing with indeterminate structures after all. There are infinite solutions that satisfy equilibrium when that is the only criterion applied. That's why I posted my latest sketch showing the statically admissible unequal reactions: to highlight that it's not enough just to find one solution; we need to also exclude all of the others.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

### RE: Modern Steel Construction Steel Quiz

Not sure if this counts as a reciprocal frame or not but here's a cool stair I saw while in Europe.

### RE: Modern Steel Construction Steel Quiz

Not reciprocal as the last beam in the spiral doesn't load up the first. Very cool framing though.

Professional Engineer (ME, NH, MA) Structural Engineer (IL)
American Concrete Industries
https://www.facebook.com/AmericanConcrete/

### RE: Modern Steel Construction Steel Quiz

So I decided to do my own modelling. The RISA file is attached for anyone who would like to critique it.

- At run time, I get a program complaint of "Z reactions do not sum to match Z loads". I'd be curious to know if anyone can resolve that as, to some degree, it casts a bit of doubt on the solutions.

- Presumably, because of the runtime error just mentioned, I'm unable to report joint reactions. They can be gotten indirectly via shear diagrams.

- I believe that this test supports the hypothesis that these are statically determinate systems. The response parameters, such as the moments shown below, do shift slightly from one model to the next. However, that's a very slight shift over what is about a 100 fold increase in vertical displacement.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

### RE: Modern Steel Construction Steel Quiz

The model's picking up some undesired torsion, particularly the wood version. Anybody know a simple solution to that? Updated model attached.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

### RE: Modern Steel Construction Steel Quiz

Are you releasing torsion at the ends connected to other beams? Conventionally you do not to prevent beams from spinning in space but in this case you would.

### RE: Modern Steel Construction Steel Quiz

Backing off on the extreme stiffness discrepancy between models, I went to W18x35 and W8x21. Bending and torsion shown below.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

### RE: Modern Steel Construction Steel Quiz

I've released torsion at one end of each member which is all I'm allowed to do. Perhaps I need to break up the physical members (RISA speak) into seperate, node to node members in order to introduce more torsional release.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

### RE: Modern Steel Construction Steel Quiz

FWIW, I ran it in STAAD with roller supports, found no issues, and beam stiffness didn't affect reactions. So it would appear it is determinate.

### RE: Modern Steel Construction Steel Quiz

Kootk,

If make each wood beam infinitely long, the system will still work. The wood beams will carry virtually no shear and serve to just maintain stability of the system. The wood beams will act as a make-shift moment connection between the two steel beam halves and will have 0 reaction at their supports. I think it helps to explain the behavior of the system.

### RE: Modern Steel Construction Steel Quiz

That does help Jeremy and I see it the same way. Even in that hyperbolic example, however, the apparent determinacy of the system is still in play though, right?

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

### RE: Modern Steel Construction Steel Quiz

I think about it like this. Imagine the steel beams are together and the wood beams are framed into the side. This system is determinant right? Then you slowly slide the steel beams apart until they're in the current configuration. Should the determinancy be maintained?

I mean, based on the if r = 3n its determinant, I get r = 16 (2 at each support and 2 at each hinge) and 3n = 12 which means its indeterminant but it's only a "general rule".

### RE: Modern Steel Construction Steel Quiz

#### Quote (BAretired)

B4 reacts with W/16 + P/16 on B1, but we called that P, so:
P = W/16 + P/16
Solving, P = W/15 and the reaction of B1 can be found to be R = 8W/15
The remaining three reactions are 4W/15, 2W/15, and W/15 for B2 to B4 respectively.
The sum of all reactions is W as expected.

Yes! This shows algebraically what I did numerically with the same geometry. I determined the first reaction to be 0.533W but really it's 8W/15, which is an important distinction in this thread. ;) Either way, the reactions are determined without regard to the member properties.

### RE: Modern Steel Construction Steel Quiz

No matter how many beams there are, the system is determinate. We've been talking about four beams... But 3 beams, and 12 beams and 87 beam systems are also determinate.

Here's the proof, (which is how you should all be determining a structure's determinancy, not by running fancy computer programs! Shame!)

Let's say you have X number of beams.

There are 2X unknowns (the number of reactions is 2 per beam... Y-direction on the left end, and Y-direction on the right end of each beam).

There are also, 2X static equations. Make a free body diagram of each beam. One equation is summing the forces in the Y direction. The other equation is summing the moments about a point.

You then have a system of 2X linear equations with 2X variables.

### RE: Modern Steel Construction Steel Quiz

Nice. That's a much stronger proof and I accept it.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

### RE: Modern Steel Construction Steel Quiz

#### Quote (KootK)

Nice. That's a much stronger proof and I accept it.

I got the KootK approval! :)

### RE: Modern Steel Construction Steel Quiz

Wow, it was quite the busy evening for everyone...

### RE: Modern Steel Construction Steel Quiz

#### Quote (cal)

I got the KootK approval!

You certainly did. You won't often seem me post FEM as proof and, when you do, it'll often represent a personal failure of sorts. My preference is to have a working theory in hand for why something is a certain way BEFORE I do FEM to confirm it it. FEM up front usually means that I've failed in the working theory department which was the case here. And I guess there was no way around that in this instance as I appear to have been altogether wrongheaded.

I'm actually really bad at the whole quantitative indeterminacy evaluation thing. It's a gap that needs addressing. When we covered that college, I was in the midst of a really intense whirlwind romance. Very little sleep, copied homework, and sporadic class attendance for a few weeks. It's a gap that needs addressing as it comes up often here and I feel foolish being at a disadvantage on stuff that is so fundamental.

I have a LOT of structural analysis books and have actually struggled to find one that treats the subject rigorously enough for my liking. Usually just the equations, some reference to systems of equations, and a few examples. I want to be able to "feel" it if I'm going to invest the time.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

### RE: Modern Steel Construction Steel Quiz

#### Quote (KootK)

Well your humility is as impressive as your brilliance. I learn a great deal from you and appreciate the time you spend to write out thorough responses. It is quite helpful to a young engineer.

And that's as sappy as I'll make it. Good day sir.

### RE: Modern Steel Construction Steel Quiz

#### Quote (cal91)

...not by running fancy computer programs! Shame!

I just want to go on record saying that I remembered how to check for determinancy by hand; but I'm lazy. Thus, fancy computer programs. :P

Awesome proof, thanks for confirming my "engineering judgement".

Professional Engineer (ME, NH, MA) Structural Engineer (IL)
American Concrete Industries
https://www.facebook.com/AmericanConcrete/

### RE: Modern Steel Construction Steel Quiz

#### Quote (TME)

Awesome proof, thanks for confirming my "engineering judgement".

No problem! :)

### RE: Modern Steel Construction Steel Quiz

I was thinking about this last night and I thought a good analogy might be a steel plate suspended by cables. (I.e. it would have vertical stability.) Still trying to get my head around the analogy of the plate to the beams.

### RE: Modern Steel Construction Steel Quiz

WARose - not sure I follow?

### RE: Modern Steel Construction Steel Quiz

#### Quote:

WARose - not sure I follow?

Not 100% sure I do either.

Some of the moments goes into the beams (that run to the supports) in the 4 beam model we are talking about.....but in my analogy, all moments are in the plate in the center: Reactions from plate rotation and vertical forces run to the supports via the cables (or T/C only members).

I actually modeled this thing (i.e. a steel plate suspended) in STAAD and got some (stable) results. (And some warnings about instability unless I used fixed supports.) I also had to abandon the cables/truss members suspending it as it became too unstable. I wound up using beams....but released at the supports. (Which is like the 4 beam model.) So not sure about my original analogy.

EDIT/UPDATE: I was able to get the model above to work with the members connecting the plate to the supports designated as truss members by doing a enforced displacement at the plate corners. Sort of forcing the cables to engage (Designating the members as cable and having some initial tension didn't work.) This resulted in minimal instability.

### RE: Modern Steel Construction Steel Quiz

I don't understand the need for a plate and cable analogy. Four simple span beams is about as straightforward as it could possibly be.

BA

### RE: Modern Steel Construction Steel Quiz

I had nothing to do this morning & the weather wasn't conducive to painting.

### RE: Modern Steel Construction Steel Quiz

Ta-da!

It's quite strong and stiff. Though lesson learned; if you're going to build one of these, don't use old wood from a decommissioned deck. The halved joints work great but when you're trying to get the reciprocal frame together it involves quite a bit of twisting, bending, hammering, and all the resulting cross-grain tension did not go over well on this old, weathered wood.

Oh well, nothing a few curse words and some long screws can't fix.

Makes a decent pull-up frame for exercise, too.

Professional Engineer (ME, NH, MA) Structural Engineer (IL)
American Concrete Industries
https://www.facebook.com/AmericanConcrete/

### RE: Modern Steel Construction Steel Quiz

TME...... this is amazing!

I can't believe one ET question about not even a real project has led to this! Fantastic!

### RE: Modern Steel Construction Steel Quiz

I wonder if this was inspired by an engineer reading this post.

Human Reciprocal Frame

### RE: Modern Steel Construction Steel Quiz

Hah! That was hilarious. It would be immensely gratifying if it was due to this thread but I don't have that much faith in serendipity.

Professional Engineer (ME, NH, MA) Structural Engineer (IL)
American Concrete Industries
https://www.facebook.com/AmericanConcrete/

### RE: Modern Steel Construction Steel Quiz

gravityandinertia - that's great!

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### RE: Modern Steel Construction Steel Quiz

...anything more difficult?

Dik

### RE: Modern Steel Construction Steel Quiz

I showed this video to someone who made a claim they did it in a class at school with 40 people! I know the math works out that everyone is essentially carrying about 1 body weight on their legs, but I still can't picture a 40 person circle of this. It would look insane!

### RE: Modern Steel Construction Steel Quiz

I thought that the group might enjoy this example from my real life work this week. Precast hollow core plank. It's not sexy like the heavy timber but the erection and, to a lesser extent, performance concerns are there. It shall be rectified.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

### RE: Modern Steel Construction Steel Quiz

Naw, leave it, take pictures of the construction afterwards for fake internet points. All the cool engineers are doing it. :P

Professional Engineer (ME, NH, MA) Structural Engineer (IL)
American Concrete Industries
https://www.facebook.com/AmericanConcrete/

### RE: Modern Steel Construction Steel Quiz

You need to tell your mechanical guy he missed putting full width holes in the other two planks adjacent these two.

### RE: Modern Steel Construction Steel Quiz

This thread made it's way back to AISC's Modern Steel Construction. Take a look at the editor's letter on page 6.

[link http://digitaleditions.walsworthprintgroup.com/pub...#{"issue_id":453364,"page":6}]Link[/link]

Reading that letter made me think back to the video below. The Atlanta Falcon's new roof has to at least be partially considered a reciprocal frame!

Link

### RE: Modern Steel Construction Steel Quiz

#### Quote (EZBuilding)

This thread made it's way back to AISC's Modern Steel Construction. Take a look at the editor's letter on page 6.

That brought a huge smile reading that. Much appreciated for the link EZ. Of course I shouldn't be surprised that they saw the thread but I'm glad our exuberance of "nerding out" over this topic made it back to them and even beyond to Mr. Kruth. Definitely shows that the passion for structural engineering is alive and well at all levels of the profession.

All in favor of a monthly discussion thread on future steel quiz topics say "aye"?

Professional Engineer (ME, NH, MA) Structural Engineer (IL)
American Concrete Industries
https://www.facebook.com/AmericanConcrete/

### RE: Modern Steel Construction Steel Quiz

That is awesome! Haha I love the recap of this infinitely long thread.

### RE: Modern Steel Construction Steel Quiz

I missed the discussion, but jumping back to the matter of determinancy.

The practical definition of determinancy make it pretty obvious (in additional to the mathematical definition that Cal pointed out):

Removal of any degree of freedom from the supports will result in failure.
Addition of a hinge or roller or other release within a member will result in failure

There is no redundancy, therefore it is statically determinant.

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