Question on design assumptions and structural modeling 4

[STpipe]

Hi everyone,

I've run into a scenario that has me puzzled with one of the projects I'm working on. I'm more interested in the theoretical aspect of the problem.

It's a retrofit, where I'm adding some beams and columns to provide additional support to a roof. The roof itself is made of material with a much lower stiffness than steel. I came up with the preliminary member sizes using hand computations using classical methods, and then subsequently modeled the structure (including the roof) in a commercial program to perform the detailed analysis.

The issue I'm having trouble resolving is that due to the nature of the analysis, the roof is providing significant lateral support to the beams, and is inducing significant axial loads into them. When analyzing the original structure, or in past projects where we have to interface a steel support structure with this same type of roof, the other engineers did not include any sort of lateral support that the it might provide in their analysis and calculations. However, based on what I'm seeing, not doing so may lead to the analysis missing a large axial load in the beams.

So my questions:

1) Are those axial forces in my beam "real", or simply a function of the modeling techniques used where I may need to revisit my assumptions.
2) Before the advent of these advanced 3D structural analysis programs, how would one go about making the correct assumptions for the structural behaviour when dealing with these scenarios which are not typical. The classical techniques which we learned typically would only consider the steel framing.

Thanks.

 

[BridgeSmith]

The axial forces would only be real if the modeling is accurate with respect to the stiffness and strength of the roof materials. Since you say the roof is much less stiff than the beams, this seems unlikely. Does your model have the roof acting compositely with the beam? If so, the capacity of the beam will be lower than what your model tells you it is. The model should be set up so that the roof provides lateral support (assuming there is a connection between the beam and the roof system), but ignores or accurately reflects the stiffness parallel to the beam.

To address Question 2, the beam would be analyzed using a simple f = M/S. That would be compared to the buckling stress if applicable, or the yield stress. The critical stress limit would be determined based on the bracing conditions of the compression flange (for lateral torsional buckling), and the compactness of the flanges and web (for local buckling).

 

[MotorCity]

If you modeled your roof as a diaphragm, applied a lateral load, and attached the beams to the deck, then the forces are real. Although, I would expect them to be very small.

 

[STpipe]

Thank you both for your responses!

HotRod10,

I double checked the material properties, so I would say the stiffness and strength properties of the roof material are accurate. However, since the stiffness is also dependent on the overall geometry, and the roof does contain stiffeners and ribs, then the stiffness difference may not be as significant as when one looks purely at the material properties. The beam is not modeled compositely with the roof, it is only connected at a discrete point to the roof and there would be a connection between the beam and the roof system.

For your modeling suggestion, that's sort of where I am hung up. Another engineer in my situation would face a similar decision. If the engineer takes option 1, which is to ignore the stiffness parallel to the beam, isn't there a risk that he might be missing some axial load in the beam? I see no downside with option 2, other than the additional time it takes to model this scenario accurately. However, this goes with the second part of my original question, which is, if I did not have access to the advanced computer modeling tool which allows me to accurately reflect the stiffness parallel to the beam, how would I go about accurately modeling that stiffness?

MotorCity,

I modeled the roof as shells, and the beams and columns with line elements. In that case, I believe the roof would be acting as a diaphragm.

 

[BridgeSmith]

If your model has the roof diaphragm rigidly attached to the beam, i.e. the connection is infinitely stiff (which is not the case in reality), whether continuously or at discrete points, it will act as a composite beam, will it not? I don't see how you get significant axial load into the beam otherwise. That being the case, unless the roof is modeled accurately with regard to stiffness, material strength, and restraint against buckling, then you could be significantly overestimating the capacity of the system. My experience with that type of software is limited, so I don't know whether the true buckling capacity of the roof can be modeled with a shell element, which would be perfectly flat and homogeneous (?), while the real roof is neither.

"...how would I go about accurately modeling that stiffness?"

The simple answer is that you wouldn't. You would ignore the roof in the structural model, other than assuming the beam is laterally braced at discrete points.

 

[KootK]

Can you provide a bit more information with respect to the situation? Geometry and the load condition creating the axial forces?

My belief is that we should never base our work on the expectation that we know anything with any great degree of accuracy. That, because we really do not know anything with any great degree of accuracy. Rather, I think that it's a game of "somewhat intelligent general proportioning" rather than "knowing". It was a lot easier to see it that way back before software allowed us know things with considerably more precision than we once did.

Whenever this kind of thing comes up, you'll get some folks mentioning that often one kind of failure doesn't necessarily mean that your member is no longer fit to address another type of failure. Ductility and redistribution. Sometimes that's true but not always. If buckling is involved, that's usually non-ductile and the argument gets murky. In your case, one could see the beams possibly buckling torsionally under axial and then not being available to resist lateral loads. It's unlikely, and the beam may well unbuckle as you transition from one load case to another, but it's possible.

Adopting a "rough proportioning" mindset as a opposed to a "knowing" mindset has made the work a lot more enjoyable for me, truly. And I don't care if the codes do not explicitly allow this. The codes don't have to live with the vagaries and complexities of my work, I do.

My gut says that these axial loads can be ignored and probably should be for the sake of your own market competitiveness. If you're interested in taking this further, post some sketches and I'm sure that we can devise a plausible story for you to tell. That, right there, is the lion's share of what engineering management boils down to on the technical side. The plausible story that makes things easy and cheap.



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.

 

[MrHershey]

I double checked the material properties, so I would say the stiffness and strength properties of the roof material are accurate. However, since the stiffness is also dependent on the overall geometry, and the roof does contain stiffeners and ribs, then the stiffness difference may not be as significant as when one looks purely at the material properties. The beam is not modeled compositely with the roof, it is only connected at a discrete point to the roof and there would be a connection between the beam and the roof system.

For your modeling suggestion, that's sort of where I am hung up. Another engineer in my situation would face a similar decision. If the engineer takes option 1, which is to ignore the stiffness parallel to the beam, isn't there a risk that he might be missing some axial load in the beam? I see no downside with option 2, other than the additional time it takes to model this scenario accurately. However, this goes with the second part of my original question, which is, if I did not have access to the advanced computer modeling tool which allows me to accurately reflect the stiffness parallel to the beam, how would I go about accurately modeling that stiffness?

You mention the beam is connected to the roof at a discrete point (I assume this is actually discrete points, plural) and things aren't modeled compositely. But if things are connected together without any force/moment releases then you'll get composite action whether you like it or not. Depending on how things are modeled, that may be where your axial is coming from.

Think of just a simply supported composite beam, steel wide flange with slab on deck. At midspan you'll have tension in the wide flange portion and compression in the slab. If you modeled things discretely and asked the program for the forces in just the beam, you'll get axial and it's real. But it's from composite action, it's not some global axial force. To check I'd turn shell stiffness parallel to the beams way, way down and see what you get. If axial goes away, that's your answer. You should also see your moments in the beam increase if composite action was the culprit.

Assuming that's your answer I'd tend to ignore the composite action (this assuming your diaphragm isn't concrete). That means either ditching the model or getting things modeled correct so you don't get composite action. While in real life you may get some composite action, it's not typically considered in design for lighter roofs. And to actually count on it you have to do way more than just look at beam axial. If you were in theory to consider this composite action, you would also need to design the actual diaphragm for its resultant axial force, ensure continuity of that axial force across any diaphragm joints or laps, and design the connectors from beam to diaphragm for horizontal shear transfer. One important thing in modeling is making sure you're consistent. If you're not discounting the composite action for the beam design, you need to follow through and not discount it for diaphragm and connection design either.

 

[STpipe]

Again, thank you very much for everyone's comments. I was concerned that my original post was too vague to get a substantial discussion going, but you've given me a lot of food for thought.

If your model has the roof diaphragm rigidly attached to the beam, i.e. the connection is infinitely stiff (which is not the case in reality), whether continuously or at discrete points, it will act as a composite beam, will it not? I don't see how you get significant axial load into the beam otherwise. That being the case, unless the roof is modeled accurately with regard to stiffness, material strength, and restraint against buckling, then you could be significantly overestimating the capacity of the system. My experience with that type of software is limited, so I don't know whether the true buckling capacity of the roof can be modeled with a shell element, which would be perfectly flat and homogeneous (?), while the real roof is neither.

"...how would I go about accurately modeling that stiffness?"

The simple answer is that you wouldn't. You would ignore the roof in the structural model, other than assuming the beam is laterally braced at discrete points.

To your first point, you're right, the connection is infinitely stiff, and I now think this may be the issue. If I were to model it accurately, the rigid constraint should be replaced with some form of spring stiffness.

If I ignore the roof in the structural model, wouldn't there be a risk that I'm not adequately designing the beam? By virtue of connecting the roof to the steel, in reality there will be some load transfer through shear of the fasteners which in turn apply an axial load to the beam (albeit significantly smaller than the load calculated where I have the infinitely stiff connection between the two).

KootK,

Solid post. My comments are below:

Can you provide a bit more information with respect to the situation? Geometry and the load condition creating the axial forces?

The roof and beam are sloped, and the applied gravity loads are not perpendicular to its surface. So the applied reaction from the roof onto the beam would have one component that is normal to the surface of the roof and one that would be in-plane. However, as MrHershey correctly pointed out, when releasing the forces in the axial direction of the beam, the axial load went down significantly, so I was seeing an effect due to composite action.

My belief is that we should never base our work on the expectation that we know anything with any great degree of accuracy. That, because we really do not know anything with any great degree of accuracy. Rather, I think that it's a game of "somewhat intelligent general proportioning" rather than "knowing". It was a lot easier to see it that way back before software allowed us know things with considerably more precision than we once did.

That's precisely where I wanted to go with this thread and my own skills. Develop them further so that I can get a better sense of solving these problems, without having to over rely on the software, as its precision can be deceiving if the wrong assumptions are made.

Whenever this kind of thing comes up, you'll get some folks mentioning that often one kind of failure doesn't necessarily mean that your member is no longer fit to address another type of failure. Ductility and redistribution. Sometimes that's true but not always. If buckling is involved, that's usually non-ductile and the argument gets murky. In your case, one could see the beams possibly buckling torsionally under axial and then not being available to resist lateral loads. It's unlikely, and the beam may well unbuckle as you transition from one load case to another, but it's possible.

Adopting a "rough proportioning" mindset as a opposed to a "knowing" mindset has made the work a lot more enjoyable for me, truly. And I don't care if the codes do not explicitly allow this. The codes don't have to live with the vagaries and complexities of my work, I do.

So I guess, this is where the crux of this topic. How to determine whether I do get ductility and redistribution and ignore the axial loads to justify ignoring them.

My gut says that these axial loads can be ignored and probably should be for the sake of your own market competitiveness. If you're interested in taking this further, post some sketches and I'm sure that we can devise a plausible story for you to tell. That, right there, is the lion's share of what engineering management boils down to on the technical side. The plausible story that makes things easy and cheap.

One of the things my colleague and I discussed when reviewing the results, was specifically releasing the constraint in the axial direction of the beams. One possible justification we came up with was that since we know the roof material will fail in bearing long before shear failure of the fasteners, you would get excessive deformation in the hole, thus the axial load in the beam would never reach the values shown in the analysis.

You mention the beam is connected to the roof at a discrete point (I assume this is actually discrete points, plural) and things aren't modeled compositely. But if things are connected together without any force/moment releases then you'll get composite action whether you like it or not. Depending on how things are modeled, that may be where your axial is coming from.

Think of just a simply supported composite beam, steel wide flange with slab on deck. At midspan you'll have tension in the wide flange portion and compression in the slab. If you modeled things discretely and asked the program for the forces in just the beam, you'll get axial and it's real. But it's from composite action, it's not some global axial force. To check I'd turn shell stiffness parallel to the beams way, way down and see what you get. If axial goes away, that's your answer. You should also see your moments in the beam increase if composite action was the culprit.

Assuming that's your answer I'd tend to ignore the composite action (this assuming your diaphragm isn't concrete). That means either ditching the model or getting things modeled correct so you don't get composite action. While in real life you may get some composite action, it's not typically considered in design for lighter roofs. And to actually count on it you have to do way more than just look at beam axial. If you were in theory to consider this composite action, you would also need to design the actual diaphragm for its resultant axial force, ensure continuity of that axial force across any diaphragm joints or laps, and design the connectors from beam to diaphragm for horizontal shear transfer. One important thing in modeling is making sure you're consistent. If you're not discounting the composite action for the beam design, you need to follow through and not discount it for diaphragm and connection design either.

As mentioned in my response to KootK, doing as you suggested significantly reduced the axial loads, so this is an effect of composite action.

For your last paragraph, as you said typically for lighter roofs, composite action isn't considered because then you would need to design the roof for the resultant axial forces, continuity, joints etc., however in reality, the behaviour of that roof would be to act as a diaphragm and would see some of these forces. If the design doesn't take that into account, how is it that we don't see more roof failures because those forces were not taken into account in the design of the roof? I understand this concept when dealing purely with steel as we tend to limit the design to the yield strength of the material, so it has the capacity to go plastic and redistribute load etc.

 

[KootK]

The roof and beam are sloped, and the applied gravity loads are not perpendicular to its surface. So the applied reaction from the roof onto the beam would have one component that is normal to the surface of the roof and one that would be in-plane. However, as MrHershey correctly pointed out, when releasing the forces in the axial direction of the beam, the axial load went down significantly, so I was seeing an effect due to composite action.

This doesn't sound like composite action. Rather, it sounds like good old fashioned direct axial load. Then the question becomes whether or not that component of the deck load rightfully belongs in the beam or in the diaphragm. Two important questions for you:

1) What is this diaphragm made of? I haven't combed through everything here so forgive me if you'd stated that someplace.

2) What is it that provides direct, axial restraint to this beam here? What keeps if from sliding in the plane of the roof?

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.

 

[KootK]

3) The axial load that you're seeing in your beam produces how much axial stress? ksi etc.

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.

 

[STpipe]

KootK,

1) I hadn't stated it, but it's made of fiberglass
2) The beam would be bolted to the roof

There is definitely going to be an axial load in the beam, however the magnitude I was previously seeing was massive. Once I removed the restraint in the axial direction of the beam, there was still an axial force, but it was not as large.

 

[STpipe]

KootK,

3) In this case, it produced about 1 ksi stress.

 

[KootK]

2) The beam would be bolted to the roof

This doesn't make sense to me as the answer to my question. I wouldn't think that the diaphragm could both apply axial load to the beam and simultaneously resist axial moment in the beam. Not unless there's complexity involved that I'm not grasping.

3) In this case, it produced about 1 ksi stress.

Is the value before or after you removed the axial restraint? For the purpose of this discussion, we really need the before value.



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.

 

[BridgeSmith]

"If I ignore the roof in the structural model, wouldn't there be a risk that I'm not adequately designing the beam?"

Including the roof in the structural model (as a structural component and not just a load) makes it part of the beam. Think of the roof as analogous to a bolted cover plate attached to the top flange of the beam, or even as the top flange of the beam itself. Does the beam have greater capacity with the cover plate or without it? The large axial load you were seeing is essentially an internal shear on a composite section, and it only shows up because the software reports actions of the components separately.

"By virtue of connecting the roof to the steel, in reality there will be some load transfer through shear of the fasteners which in turn apply an axial load to the beam"

Whatever axial force you see inn the beam is the force carried by the roof through composite action, which increases the capacity of the section, thus the reason for making a section composite.

 

[STpipe]

This doesn't make sense to me as the answer to my question. I wouldn't think that the diaphragm could both apply axial load to the beam and simultaneously resist axial moment in the beam. Not unless there's complexity involved that I'm not grasping.

I'm not following this particular train of thought. Perhaps I completely misunderstood your original question?

Is the value before or after you removed the axial restraint? For the purpose of this discussion, we really need the before value.

It is the before value. The magnitude of the loading is not particularly critical and the size of the beam was chosen more so for practicality and ease of installation rather than for any strength or serviceability consideration.

Including the roof in the structural model (as a structural component and not just a load) makes it part of the beam. Think of the roof as analogous to a bolted cover plate attached to the top flange of the beam, or even as the top flange of the beam itself. Does the beam have greater capacity with the cover plate or without it? The large axial load you were seeing is essentially an internal shear on a composite section, and it only shows up because the software reports actions of the components separately.

This part I understand, and theoretically, the amount of composite action that can develop is dependent entirely on how much relative sliding between the components the shear connectors can prevent. By having the rigid constraint, 100% of the shear force between the beam and the roof is able to be transferred because relative sliding between the two components is prevented. Taking a standard composite steel beam with concrete deck, if the number of shear connectors is not sufficient to get 100% composite action, then at ultimate loads, the studs will plastically deform which causes a small amount of relative sliding between the slab and the beam. As long as the beam is sized accordingly (whether for no or partial composite action), then the design will be fine.

Whatever axial force you see inn the beam is the force carried by the roof through composite action, which increases the capacity of the section, thus the reason for making a section composite.

Ok, I think I'm seeing what you're trying to say. So essentially, I have two options.

Option 1 - connect the beam to the roof as I originally did, however in this case I need to design the beam as a composite section by including the roof as part of the beam (using an effective width for the roof and a transformed cross section). In this scenario, I would need to extract my shear, bending and axial forces for the composite cross section as a whole (so I would need to take section cuts that include the roof shell elements to get an accurate internal forces). Since I'm no longer looking at just the steel beam, that larger axial force would disappear, and I would be left with only the externally applied axial force which is from the geometry of the problem.

Option 2 - release the axial component of force in the connection from the beam and roof. The beam in this case sees a higher moment and the axial force in the member is the real direct axial load and should correspond be the same value as in Option 1 when considering the composite cross section.

 

[MrHershey]

If the design doesn't take that into account, how is it that we don't see more roof failures because those forces were not taken into account in the design of the roof?

In order for that diaphragm to actually see that load you need to make sure you provide sufficient methods to transfer the load and maintain continuity within the diaphragm. I'd argue this typically isn't provided. We provide continuous load paths for lateral loads, but those paths typically are not solely contained within the decking material.

Think of a wood panel roof. Typically diaphragm loads transfer from panel to panel through edge nailing. But that edge nailing is to supporting members, typically the panels themselves are not nailed together. Load path across panel joints is panel->nail->supporting member->nail->panel. This a perfectly acceptable load path for lateral loads, but doesn't really provide the continuity in the panels that you would need for them to act compositely.

You may get a little bit of action from edges of panels bearing on each other, but the panels would have to be consistently bearing tight to each other to keep the load path continuous.

 

[KootK]

I'm not following this particular train of thought. Perhaps I completely misunderstood your original question?

My understanding of your statements so far is:

1) You think that the diaphragm is delivering axial force to the beam.

2) You think that the diaphragm is restraining the beam from moving in the plane of the diaphragm.

For most any situation other than composite action, I'd consider those statements to be in opposition to one another. Something can't be both the source of load and resistance to it at the same time. So I guess we really just need to figure out if this is composite action we're talking about. To that end:

a) Is the axial load tension or compression? I'd think tension for composite action unless you're running continuous beams, either on purpose or by accident.

b) Given that you've obviously got this modeled already, can you post the axial load diagram for the beam? If composite action is the culprit here, I'd expect to see a diagram reminiscent of a shear diagram in shape.

It is the before value.

While I know that you wanted to keep this theoretical, I think that the answer to your question may in the practical. 1 ksi axial should be pretty low compared to your flexural stresses.


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.

 

[BridgeSmith]

STpipe, I would be very cautious about your Option 1. Real materials, especially a roof diaphragm such as you describe, is very difficult to model accurately. In fact, if it was me, I would not even entertain Option 1 due to the uncertainties involved. In any case, if the steel beam alone is sufficient for the loads, why would you complicate the analysis by making it composite with a roof diaphragm of questionable capacity with connections of undetermined strength and stiffness?

 

[STpipe]

In order for that diaphragm to actually see that load you need to make sure you provide sufficient methods to transfer the load and maintain continuity within the diaphragm. I'd argue this typically isn't provided. We provide continuous load paths for lateral loads, but those paths typically are not solely contained within the decking material.

Think of a wood panel roof. Typically diaphragm loads transfer from panel to panel through edge nailing. But that edge nailing is to supporting members, typically the panels themselves are not nailed together. Load path across panel joints is panel->nail->supporting member->nail->panel. This a perfectly acceptable load path for lateral loads, but doesn't really provide the continuity in the panels that you would need for them to act compositely.

You may get a little bit of action from edges of panels bearing on each other, but the panels would have to be consistently bearing tight to each other to keep the load path continuous.

Ok, that makes sense.

But what if the diaphragm is continuous? In that situation if I want to design the beam as non-composite, but still need to tie down the diaphragm to it, does it mean that similar to shear studs in a concrete slab, if there aren't enough shear connectors to fully develop composite action, the shear connectors will plastically deform as you approach the ultimate limit state, thus as long as the beam is properly designed to take all the loads on its own, it will adequately handle this scenario.

My understanding of your statements so far is:

1) You think that the diaphragm is delivering axial force to the beam.

2) You think that the diaphragm is restraining the beam from moving in the plane of the diaphragm.

For most any situation other than composite action, I'd consider those statements to be in opposition to one another. Something can't be both the source of load and resistance to it at the same time. So I guess we really just need to figure out if this is composite action we're talking about. To that end:

a) Is the axial load tension or compression? I'd think tension for composite action unless you're running continuous beams, either on purpose or by accident.

b) Given that you've obviously got this modeled already, can you post the axial load diagram for the beam? If composite action is the culprit here, I'd expect to see a diagram reminiscent of a shear diagram in shape.

a) When the force is released along the axial direction of the beam, the axial force is in tension.

b) The axial diagram is reminiscent of a shear diagram with a point load of a beam at mid-span.

STpipe, I would be very cautious about your Option 1. Real materials, especially a roof diaphragm such as you describe, is very difficult to model accurately. In fact, if it was me, I would not even entertain Option 1 due to the uncertainties involved. In any case, if the steel beam alone is sufficient for the loads, why would you complicate the analysis by making it composite with a roof diaphragm of questionable capacity with connections of undetermined strength and stiffness?

It was definitely not my intent to make it composite originally. I was just saying out loud what the two options were just for a better understanding of the concepts and the different behaviours I was seeing. So as I mentioned in my response to MrHershey, I will release the the force component in the axial direction to eliminate the effects of composite action in the beam and go from there.

 

[racookpe1978]

I like the the earlier analogy of a bolted cover plate attached to the top flange of several beams.

Problem is: I see no recognition that the (very flexible) fiberglass cover plate is not only restricting (somewhat) the movement (reactions) of the beams under the roof, and thus the columns attached to the beams), but is the source of the loads (live and dead) onto the those same beams and columns.

If not modeled correctly as a flexible membrane attaching to all of the roof's beam supports, how can the OP assume his model is transmitting those loads that create his force model of the reactions to the assumed loads?