Bentley Success Factors Webinar: Modeling and Analysis of Diaphragms
Webinar Date: October 2017
Building structure behavior in response to earthquake or wind is heavily dependent upon the nature, extent and stiffness of floor and roof diaphragms. It is important that the building model used in the analysis and design of a building accurately captures the effects of these diaphragms.
This webinar addresess the challenges of determining the proper way to perform the analyses, while balancing accuracy with business demands of speed and simplicity.
In this webinar learn about:
The recording of this webinar can be viewed free on-demand and can be found at: Modeling and Analysis of Diaphragms
The slides of the presentation can be downloaded here: ModelingAndAnalysisOfDiaphragms.pdf
Many questions were received during the Question and Answer period but time did not allow them to all be answered, nor to be answered in-depth. The questions of general interest are reproduced here, with answers.
Keep in mind that the conclusions presented in the webinar were based on a limited set of models. If there is any question on the applicability of those recommendations you should experiment with your models, trying different mesh sizes and different diaphragm properties. Always use good engineering judgement.
Question: Since IBC and ASCE 7 don’t have the same classification of diaphragms, which should I use?
Response: You will need to use your engineering judgment on this. If the building code in your jurisdiction requires conformance to the IBC, you probably have a choice on which to use. This is the case in most of the United States. If the building code in your jurisdiction references ASCE 7 but not the IBC (or is not based on the IBC), you will need to use the ASCE 7 classification.
Question: The rules for determining whether a diaphragm is Rigid or Flexible requires that a diaphragm analysis be performed in order to compare the diaphragm deflections with the frame drift. Since this requires a semirigid diaphragm analysis, what is the advantage of doing this?
Response: Once you have performed this semirigid diaphragm analysis for the structure it probably won’t be necessary to repeat that analysis again and again even if you modify the model. Usually such an analysis will show that the diaphragm is clearly Rigid or it is clearly Flexible. In that case it only requires that you perform a semirigid analysis once. Otherwise, you must perform the semirigid diaphragm analysis every time you make changes to the framing.
Question: What are the disadvantages of always specifying Semirigid diaphragms?
Response: The semirigid diaphragm analysis takes longer, so when you are in the process of refining and modifying your model to determine the ideal framing configuration you must repeatedly perform the analysis. These waits add up, and can make you less productive.
The properties of the diaphragm must be determined, defined and assigned.
The semirigid analysis is a more complicated analysis, with many more elements in the analysis model. This increases the chances of encountering analytical problems such as instabilities on nonconvergence in the analysis. These can then require considerable time and effort to investigate and correct.
Question: When does the Eurocode allow a diaphragm to be modeled as Rigid?
Response: EN 1998-1:2004+A1:2013 Eurocode 8: Design of structures for earthquake resistance has a NOTE in Clause 4.3.1(4) that says:
NOTE: The diaphragm is taken as being rigid, if, when it is modelled with its actual in-plane flexibility, its horizontal displacements nowhere exceed those resulting from the rigid diaphragm assumption by more than 10% of the corresponding absolute horizontal displacements in the seismic design situation.
Question: For many structures, we have a roof with metal deck and insulation. Can we consider the floors with metal deck and concrete to be rigid below and roof as flexible?
Response: Yes. The diaphragm type is determined independently for each diaphragm. Therefore, in the model there may be a mix of Flexible, Semirigid, and Rigid diaphragms.
Question: Can you give an example of what would tell an engineer that a bare metal deck diaphragm is not flexible?
Response: ASCE 7-16 Clause 188.8.131.52 Flexible Diaphragm Condition explicitly states that diaphragms constructed of untopped steel decking in a structure consisting of braced frames or shear walls can be considered to be Flexible. That means that diaphragms constructed of untopped steel decking in a structure consisting of moment frames does not qualify as Flexible (therefore must be analyzed as Semirigid), unless it can be analytically shown that it qualifies as Flexible per Clause 184.108.40.206.
Question: It is tough to define diaphragm stiffness properties for wood deck and metal deck for connections to prove it is semi-rigid. Explain if it is the case of it only having to do with deflection of the diaphragm.
Response: As we saw in the Case Studies, as long as the property values that you use for a semirigid diaphragm are reasonably close to the real stiffness, there is not much impact on the analysis results. The exception to this was the displacement of the diaphragm at points away from the frames. And for the displacement values it is important to remember that there is probably more stiffness in the diaphragm in the real structure than is represented in the model, when the stiffening influence of gravity framing is considered.
Question: When modeling a semirigid un-topped metal deck, what type of stiffness modification factors would you recommend? How would you calculate effective E?
Response: This is beyond the scope of my presentation, and I can’t give you a definitive answer. The difficulty of determining these values was part of the motivation for conducting the case studies; I wanted to see how critical it was to be precise. Fortunately we saw from those results for those models that the precision doesn’t make much difference, except for deflection of the diaphragm at points away from the frames. The Steel Deck Institute Diaphragm Design Manual has some discussion and examples on how to calculate the diaphragm properties.
Question: For a metal deck diaphragm, how do you model the different stiffness in the orthogonal directions?
Response: The Steel Deck Institute Diaphragm Design Manual doesn’t make the distinction, it implies that the same stiffness is used in both axes. It is common to do so. For those who want to use different stiffnesses in the two directions, the RAM Structural System allows Stiffness Modification Factors to be assigned to each of the six components of a slab element.
Question: Does modeling composite/non-composite metal decks on steel beams with plate elements need to consider the spacing of the metal connectors to the steel beams or spacing of the studs?
Response: For modeling of composite decks that would not need to be considered when determining the diaphragm stiffness properties of the composite deck. However, after the analysis has been performed, the transfer of the diaphragm shear into the frame beams (and drags and cords) needs to be investigated, and sufficient studs and/or connectors should be provided to adequately transfer those forces.
For modeling of noncomposite metal decks, the spacing of connectors has an impact on the diaphragm stiffness properties. More on this can be found in the Steel Deck Institute Diaphragm Design Manual.
Question: In order to consider a composite floor as Rigid, what shear studs are necessary?
Response: In the Codes the definition of Rigid Diaphragm is not dependent upon the connection of the deck to the framing. However, it is of course necessary to attach the diaphragm to the framing sufficiently to transfer the horizontal forces from the diaphragm to the frames. This is done with shear studs, welds, or mechanical fasteners.
The RAM Structural System will design composite beams, automatically determining the required number of studs, but this is for gravity loads only; it is necessary to manually determine the number of additional studs required to transfer the diaphragm forces into the chords, drags and Frame beams.
Question: Do you have any recommendations for cracked factor for concrete diaphragms? How does cracked E affect the results for concrete diaphragms?
Response: ACI 318-14 Table 220.127.116.11.1(a) lists a crack factor of 0.25 for flat plates and flat slabs; I suspect however that this is for bending, not for diaphragm action. Otherwise that code appears to be silent. I would expect the diaphragm to crack under the extreme seismic event, but I wouldn’t expect the stiffness to be reduced 75%. I don’t have any recommendations, other than to point out that from the case study we saw that even if the diaphragm properties vary by a factor of 48, the results only varied by less than 4% for the frame forces and by less than 25% for the diaphragm forces. So at least for a structure like this model, whether you used a cracked factor of 0.25 or 0.5 or none at all, the impact on the results would be very small.
Question: For seismic analysis, to account for cracking, EC8 4.3.1 (7) suggests that we should use a E=0.5E_concrete. Do you think that this clause also covers diaphragms?
Response: Yes, it appears that this does apply to diaphragms. In a large earthquake the diaphragm will almost certainly crack (although it seems very conservative to assume that cracking of the diaphragm would reduce its stiffness by 50%). Two considerations: first, for diaphragms consisting of concrete fill on steel deck it is common to simply define the diaphragm properties based on the concrete fill and ignore the steel deck (because of the complexity and effort it would add to the modeling), but the steel deck certainly contributes to the stiffness; therefore for such decks it may be acceptable to ignore the crack factor and the contribution of the steel deck; and second, as was shown in the case study, the change in the stiffness of the diaphragm from applying the crack factor would likely have little impact on the analysis results.
Question: About clause 5.10 of EC8 that refers to a min 70mm thickness of the slab in order to consider that slab as a diaphragm. What is your opinion about composite floors? If we have a 120mm deck with a solid 61mm concrete layer (which is less than that 70mm minimum), do you think that we can consider it a semi-rigid diaphragm?
Response: In my opinion, yes you can consider that as a Semirigid (or possibly even a Rigid) diaphragm. Clause 5.10 is in Chapter 5 SPECIFIC RULES FOR CONCRETE BUILDINGS. It would apply to a formed concrete slab but I don’t believe it applies to a deck consisting of concrete fill on metal deck.
Question: Did you experiment with plate element thickness to mesh size? What are your recommendations?
Response: In my studies on the influence of mesh size on the analytical results I did not investigate varying deck thicknesses. I used a common configuration, 3.25” of lightweight concrete on 3” steel deck, for those models, only varying the mesh size. I would not expect the results to be different from those shown in the case study even if models with a different concrete thickness or with normal weight concrete were used.
Question: What G value can be considered as semirigid?
Response: If the question here is, what G value indicates that a deck is semirigid, the answer is that the G value is not an indicator. The determination of whether or not a diaphragm needs to be considered as semirigid or not is based on its flexibility versus the flexibility of the frames. This is a function of the frame layout and diaphragm geometry, as well as the effective G of the deck.
If the question is, what value of G should be used for a semirigid diaphragm, the answer is more complicated, and beyond the scope of the webinar and our discussion here. See the Steel Deck Institute Diaphragm Design Manual. The difficulty of determining this value and of converting it to an effective E’ value used in analytical software was what motivated me to conduct the case study presented in the webinar. As we saw from that case study it is important to be reasonably accurate in the properties used, but it is permissible to be approximately accurate without significant impact to the analysis results.
Question: When checking drifts, do you think that it is correct to use a medium value of the displacements in the slab or the maximum value? (for drift and second order effects susceptibility)
Response: For the purposes of this case study I wanted to look at the extremes, in order to see what the maximum impacts are. For design purposes, each Code has specific requirements. For example, in ASCE 7-10 Section 18.104.22.168 the determination of the Flexible diaphragm condition is based on the average drift; in Section 12.8.7 the stability coefficient is based on the drift at the center of mass; in Section 12.12.1 the drift limits are in reference to the drift at the center of mass. However, when checking the exterior cladding or interior partitions it may be necessary to consider the drifts at the extreme locations (see Section 12.12.2). As discussed in the webinar, this is where you need to use engineering judgement to decide how realistic the reported drift values are at these extreme ends/corners of the structure.
Similarly, Eurocode EN 1998-1:2004+A1:2013 Section 22.214.171.124 gives the limits on interstorey drift, where dr is defined in Section 126.96.36.199(2) as being based on the “average lateral displacements ds at the top and bottom of the storey…”.
Question: It seems intuitive that the flexibility and structural response of a diaphragm to out of plane loads would influence flexibility and structural response to in plane loads. Or is this interaction insignificant?
Response: A diaphragm may be very stiff in-plane, and very flexible out-of-plane. In general I would not expect one to impact the other. The deck may deflect vertically, but that wouldn’t significantly impact the deck’s horizontal stiffness unless the deflection is excessive and creates large p-delta moments. However, if the diaphragm is included in the lateral analysis model, portions of the diaphragm can act as beams framing from column to column, contributing to the stiffness of the frame, reducing the design forces take by the beams, and reducing the story drifts. I suspect, but haven’t verified, that this is only significant for thick slabs with frames with relatively small beams. In RAM Frame you can reduce that out-of-plane stiffness by specifying a stiffness modifier on the out-of-plane diaphragm stiffness.
Question: For buildings with multiple main force resisting lines we find the rigid diaphragm will cause much larger reactions to each wall including load reversals. Would you say this indicates the need for more seismic joints, or can we just use semi-rigid in order to tame those reactions?
Response: Before specifying more seismic joints (which are expensive) I would recommend analyzing the structure with all diaphragms defined as Semirigid (with the Roof as Flexible if appropriate). The ‘softer’, more realistic diaphragm will be less likely to transfer forces from one frame to another than does the Rigid diaphragm, for some frame configurations. The case study that I presented contained such a configuration, with a single frame on the left and two closely coupled frames on the right. In that case study the frame story shear for one of the frames differed by over 60% when analyzed with a Semirigid diaphragm versus a Rigid diaphragm. Note that this difference between the results for the two diaphragm types is not usually this great for structures where the frames are approximately uniformly distributed across the diaphragm and where the diaphragm is not long and narrow between frames; for most buildings the Rigid diaphragm and the Semirigid diaphragm give very similar results.
Question: Can gravity framing be modeled for lateral analysis?
Response: In most frame programs, everything included in the model is considered part of the frame, and is included in the lateral analysis. This requires careful modeling to try to prevent the Gravity members from taking lateral forces, that may then be required to be detailed as Frame members per the special seismic detailing provisions; most programs don’t make the distinction between Gravity members and Frame members. However, in the RAM Structural System each member is specified as either Gravity or Frame, and then in the lateral analysis only the Frame members are included (although the impacts of the Gravity members on the gravity loads, P-delta, and frame member bracing are included). If desired to determine the contribution of the Gravity members in the stiffening of the diaphragm, for example, the Gravity members can be modeled as Frame members, with care taken in their modeling as explained above. If this is done I recommend that it be done in a separate model specifically used for the investigation of the diaphragm so as not to impact all other aspects of the design of the Frames.
Question: Is there anything that needs to be considered when analyzing a two-story structure with a flexible roof diaphragm and 2nd floor rigid diaphragm?
Response: This is a very common situation, and is certainly permitted by the code. The roof diaphragm can be specified as Flexible (or Semirigid if desired), and the floor can be specified as Rigid. This is a very realistic model and captures the behavior nicely. The main considerations are, does the roof diaphragm qualify as Flexible, and does the floor diaphragm qualify as Rigid? If the roof diaphragm satisfies any of the conditions given in ASCE 7-10 Section 188.8.131.52 it can be modeled as Flexible; if the floor diaphragm satisfies the conditions given in Section 184.108.40.206 it can be modeled as Rigid. The type of diaphragm can also be determined analytically using Section 220.127.116.11.
Question: What about modeling of plywood diaphragms?
Response: ASCE 7-10 Section 18.104.22.168 indicates that plywood diaphragms in light-frame construction qualifies as Flexible, with some conditions given. I don’t know of any publications that give any guidance on what material properties to use if the plywood diaphragm is modeled as a Semirigid diaphragm.
Question: How does the diaphragm assumption impact results when P-Delta is included?
Response: For simplicity, in the case study models P-delta analysis was not included. However, I would not expect the inclusion of P-delta to have a significant impact on the conclusions presented. If anything, because P-delta in effect makes the frames less stiff I would expect to see the diaphragm mesh size and properties have even less impact on the results.
Question: Base shears are increased on the magnitude of 20% using rigid diaphragms when P-Delta is included. When P-Delta is turned off the base shears match between rigid and semi-rigid.
Response: That may be the case for a particular model; for other models you may well see differences between rigid and semirigid when P-Delta is turned off. And in many you will see very little differences at all. Take a close look at your model to determine what is happening; it is most likely due to differences in building period. Is the semirigid diaphragm also acting as “beams”, creating or stiffening moment frames? Are the slabs coupling shear walls? If so, this can have a big impact on the period, and therefore on the base shear. The stiffness of these “beams” is impacted by the P-delta analysis, whereas the Rigid Diaphragm doesn’t produce this effect and therefore its impact doesn’t change between P-delta and no P-delta. To reduce this effect, apply stiffness modifiers to the out-of-plane slab stiffness if necessary.
Also, determine if CuTa, rather than the actual building period, is being used to calculate base shears. If so, that can obscure your investigation of what is causing differences between P-delta and no P-delta, Rigid and Semirigid.
Question: By what magnitude can the in-plane flexibility of the diaphragm influence the story drift for say a one-story building (with braced frames) from a nonlinear dynamic analysis?
Response: The flexibility of the diaphragm does impact the drift, but that impact is relatively small compared to the impact of the stiffness of the frames. There is no simple answer for this question, you would need to investigate for each structure.
Question: Does this apply to STAAD.Pro?
Response: Although the case studies were performed using RAM Structural System, the results that were presented were not peculiar to any particular software. If you performed similar studies in STAAD or any other program you would get similar results.
Question: On page 75 [and 76], why is the bottom shear less than the story shear above? This is only applicable to the moment frame. The braced frame results are as expected.
Response: In these models the columns were modeled fixed in both axes. As a result of that, at the lowest level the columns in the moment frames in the perpendicular direction took about 12% of the total shear in their weak axis; at the other levels those columns took very little shear in their weak axis. Hence the seemingly odd change of shear at the lowest level. Because braced frames are so stiff, the columns in the perpendicular frames took very little shear in the weak axis. Whether or not the columns should be pinned at the base is a debate for another day, but although this would change some numbers in the charts it would not change the conclusions drawn from the case studies.
Question: Can a sloped roof be analyzed as semi-rigid in RAM Structural System?
Response: Yes it can, but you have to be careful in the modeling and somewhat skeptical of the results. Roof diaphragms are often modeled using the thickness (the gauge) of the steel deck; this is appropriate for horizontal diaphragm action because it best represents the area. This results in a very small moment of inertia for out-of-plane bending, but in reality the roof decks have a reasonably large moment of inertia because of the corrugations. When the horizontal forces are applied, the deck modeled merely based on the gauge of the steel will show extremely large deformations (because since it is sloped there is a component of the horizontal force causing bending in the diaphragm, which was modeled with a very small moment of inertia resisting that bending). These extreme deformations aren’t real, since the roof deck has a moment of inertia much large than that of a flat plate of the gauge thickness, as is modeled. Recently a feature was added to the program whereby Stiffness Modification Factors can be assigned to any of the six components of a slab element. It may be possible to resolve this problem by assigning a very large modification factor to the bending components; in this way the program would use a diaphragm area correctly based on the gauge, but would use an out-of-plane bending stiffness appropriate for the corrugated roof deck. I recommend that you investigate this, and the impact that various Factors have on the results for your structure, and then decide what is appropriate.
Question: Will chord members only receive load if the diaphragm is set to semi-rigid and beams set to lateral type (pin-pin fixity)? Same question for collectors.
Response: One short-coming of the Rigid diaphragm assumption is that when the beams are attached to the diaphragm they are analytically constrained so that they can’t shorten or elongate. As a result of that the analysis reports no axial force in those beams. This is true for beams in frames as well as beams that are intended to be collectors or chords. And this is the case regardless of what software you use. In some cases this may be inconsequential, but not in others. One solution is to disconnect some nodes from the diaphragm, for example at one end of the beam or interior node where chevron braces frame in (RAM Frame automatically disconnects these interior nodes). Another solution is to model the diaphragm as Semirigid.
For drags and chords, they need to be included as Frame members in the model and the diaphragm needs to be specified as Semirigid. You may need to pin the ends so that they don’t act as frame beams, so that they only act as axial members.
Question: Should you consider diaphragm and frame deflections combined to determine story drifts?
Response: ASCE 7-16 Section 12.12.1 merely says “story drift”; it doesn’t explicitly state what that includes. I use the results from the program: if the diaphragm was analyzed as Rigid, the drift results won’t include any deflection of the diaphragm (ok since it will be a small value if the diaphragm qualifies as Rigid); if the diaphragm was analyzed as Semirigid, the drift results will include whatever the deck deflection adds to the results at the point that I am investigating. This is a practical approach that I feel is adequate.
Question: Regarding mixing diaphragm types across floors, if you have a lower floor with transfer beams though, doesn't that give inaccurate results if your upper floors were modeled as rigid diaphragms?
Response: The Rigid diaphragm is only rigid horizontally, but I suppose that the Rigid diaphragm could provide some “arching” stiffness as the column and the beams deflect downward. You need to experiment with this to determine the extent of the impact. Note that in the RAM Structural System, if these transfer members are Gravity members, the Rigid diaphragm will not have any impact.
Question: Is there a big difference between the result of semi rigid and rigid diaphragms to the amount of reinforcement of concrete beams and columns?
Response: That depends on whether or not the diaphragm would qualify as Rigid. If so, I would not expect much difference in the member forces between an analysis done with Semirigid diaphragm and one done with Rigid diaphragm, and therefore I would not expect much difference in the design of concrete members. As was shown in the Case Studies, the model did not qualify as Rigid diaphragm, and the frame forces for the worst frame differed by about 70%. Again, I recommend experimenting with your particular building, analyze and design with both, and then compare.
Question: Do you have any comments on diaphragms for precast parking garages or precast diaphragms?
Response: If there is a topping slab you may be able to use the full properties of the slab (precast plus topping), with whatever cracking factor you deem appropriate. If there is no topping slab you somehow need to account for the reduced stiffness due to the panels not being rigidly attached (there is some ‘give’ in the connection of the panels). Sorry, I don’t know what to tell you on that one.
Question: How can you reduce errors in "distorted shells" and does the distortion have a significant effect on the lateral analysis?
Response: In the meshing process, occasionally the result is mesh elements that are not relatively rectangular, they are long and narrow. Such elements don’t give as good of results as the more rectangular elements. I can’t speak for other software, but in the RAM Structural System these are almost always within the narrow slab edges around the perimeter, and they are very small. As a result they will have virtually no impact on the analysis results, and can safely be ignored.
Question: Is Chicago Building Code any different from IBC 2015 on the definition of rigid versus flexible diaphragms?
Response: I don’t know. Often local building officials will adopt the IBC as is, sometimes they will make changes. I don’t know what Chicago has done.
Question: Should a sunken slab be considered a horizontal irregularity?
Response: The definitions of Structural Irregularity are given in Section 12.3.2 of ASCE 7-16, and in Section 4.2.3 of Eurocode EN 1998-1:2004+A1:2013. The Eurocode does not define a sunken slab as an Irregularity. Type 3 in Table 12.3-1 in ASCE 7-16 does define a Diaphragm Discontinuity Irregularity; an “abrupt discontinuity” in the diaphragm qualifies as an Irregularity. However, you should use your engineering judgement on this. If the two slabs are sufficiently attached to each other they will act as a single diaphragm and will not be Irregular; if not, you will need to model them as separate diaphragms, and you will need to consider the structure to be Irregular.
Question: Is there any guideline to decide on rigidity with respect to the amount of openings in the slab?
Response: Type 3 in Table 12.3-1 in ASCE 7-16 defines a Diaphragm Discontinuity Irregularity to occur when the area of openings is greater than 50% of the gross diaphragm area. This is a generous limit.
Question: What is the correct diaphragm for a high-rise building, Rigid or Semirigid?
Response: The rules for determining whether a diaphragm can or should be analyzed as Rigid or Semirigid are the same regardless of the height of the building. You need to consider each floor; if it qualifies as Rigid you have your choice between Rigid and Semirigid (Rigid will substantially reduce the analysis time), otherwise you have to use Semirigid.
Question: How does the degree of rigidity affect the horizontal force in the braced frame?
Response: For the model in the case study, varying the diaphragm stiffness by a factor of 48 only impacted the shear in each frame by less than 4%.
Question: What is the difference between diaphragm and frame?
Response: The Diaphragm is the slab or deck, the Frame is the beams and columns. They do interact, the beams can stiffen the diaphragms, and the diaphragms can take axial forces away from the beams. In a flat plate concrete structure the slab is often considered to be part of the Frames, acting as moment frame ‘beam’ members between the columns.