The use of diaphragms in analysis programs has evolved over the last 15 years and this series will focus on some differences in the types of diaphragms that can be used and the corresponding results from using each type. We will also cover various tips and critical factors to keep in mind when using each type of diaphragm.
Prior to the mid- to late 1990s, most buildings were analyzed for lateral loads by simply modeling a series of 2D frames and applying nodal loads. Capabilities did not exist to automatically generate wind loads or seismic loads in programs. Therefore, the loads were typically calculated by hand (and the codes were much simpler for doing this) and the engineer decided how to distribute the loads to each frame. A 2D analysis program was then typically used to analyze each frame separately.
In the late 1990s, technology evolved so that lateral loads could be automatically generated for a building within a software program and these loads could be distributed to the lateral frames in the model. The RAM Structural System was one of the first tools to allow an entire building to be modeled and then designate "gravity" members and "lateral" members in an automated way. Only the members modeled as lateral would have wind and seismic loads distributed to them by the program. In other software programs, in order to achieve similar results, engineers could "pin" all the member ends that would not act as lateral members. When the software programs distributed the wind and seismic loads to the frames, this distribution was done via a rigid diaphragm assumption.
Why is all this history important? Hopefully it will help to show how this process has evolved, because when diaphragms started being used to automate the distribution of lateral forces, some interesting results occurred that often created confusion. In addition, when running hand calculations to verify results, it is helpful to understand how structural engineers analyzed frames before this automated technology existed.
Types of diaphragms in today's technology
We will focus on four different diaphragm scenarios for purposes of this series, discussing how they can be used, and critical items to keep in mind when using each type. The types of diaphragms include:
- No diaphragm or flexible diaphragm
- "Rigid" diaphragm
- "Semi-rigid" diaphragm using finite elements
- "Pseudo-flexible" diaphragm using simplified methods
This method doesn't require much discussion as it pretty much means what it says – there is no diaphragm being used to distribute lateral forces. It is sometimes referred to as a flexible diaphragm because it is so flexible that it is not capable of redistributing the loads between the frames in any way other than by the tributary area of the diaphragm to the frame. It is so flexible that it allows the frames to deflect independently of each other. Therefore, nodal loads need to be applied to the structure at appropriate points and only the stiffnesses of the members (beams, columns, braces and walls) comprise the finite element model. This method is the closest to the way that analysis was done before 3D programs became available. In programs such as RAM Structural System, Risa3D and ETABS that separate gravity and lateral members, the lateral members modeled would be the ones that receive lateral forces and the gravity members would have no contribution to the lateral stiffness.
This method of lateral force distribution requires considerably more discussion. When describing a diaphragm as "rigid," it means it is infinitely rigid, and it does not deform. A rigid diaphragm can rotate and it can translate, but it cannot deform. The lateral members in the structure are connected to the rigid diaphragm at the nodes that intersect with the diaphragm. This means that the lateral forces will be distributed (and redistributed at subsequent levels) based upon the relative stiffnesses of all the members resisting lateral loads at each level. This provides a convenient analytical tool for distributing the story forces to the various frames.
Because the diaphragm cannot deform in the analysis, the distance between any two points on the diaphragm cannot change, and this brings us to a key point that surprised many engineers when they first started using rigid diaphragms in software and saw that the beams in the lateral system had no axial force.
(In our next article, we will discuss in more detail some of the results when modeling rigid diaphragms, including the modeling of slab edges and openings, along with redistribution of lateral forces at various levels of a structure. Throughout this series, we will go into further depth on the use of different types of diaphragms in analysis software and the types of analysis results that might be expected. Stay tuned…)
Lisa Willard, P.E., and Brian Quinn, P.E., are with SE Solutions, LLC. They formerly worked for a combined 21 years at RAM International/Bentley Systems and can be reached at Lisa.Willard@LearnWithSEU.com or 805-482-8436, and firstname.lastname@example.org or 616-546-9420, respectively. Visit their technology website, www.LearnWithSEU.com
The authors would like to thank Allen Adams, S.E., Chief Structural Engineer at Bentley Systems, for his help in reviewing this article and providing comments.