Diaphragm Flexibility

[Badar (BAZ)]

*SEFP Consistent Design*
*Diaphragm Flexibility*
*Doc No: 10-00-CD-0004*
*Date: August 07, 2014*

I am writing this article about a very important, but mostly neglected topic of flexibility of diaphragm. I used to assume that all reinforced concrete slabs can be treated as rigid diaphragms. But as it turns out, only the slab with span-to-depth (depth is length of slab in direction of lateral loads) ratio of less than 3 and without horizontal irregularity can be treated as rigid diaphragm. The more important thing is that the span-to-depth ratio and horizontal irregularity is not the only criteria and one other factor also needs to be kept in mind before assigning rigid diaphragm to concrete slabs in numerical model of building.

Another important concept that I learned, and it was a moment of epiphany for me, is about TRANSFER diaphragms. I had posted a topic “Amplification Of Forces In Etabs” earlier in this forum but we were not able to reach at a satisfactory conclusion. Now, I have the answer to that query: Back Stay effect. Another article is required to explain it , and this concept is not discussed in this article. This article is about flexibility of diaphragm.

Diaphragms are horizontal members of the lateral-force resisting system of building structures. Their function is to distribute inertial forces, generated at its own level, as well as other levels, to vertical members of lateral-force resisting system.

One kind of diaphragm only distributes inertial forces generated at its own level. This kind of behaviour is observed in buildings where there is a continuity of vertical members of lateral-force resisting system: building should not have a setback or podium at lower levels, or below grade levels. The other kind of diaphragm, known as “Transfer diaphragm”, not only distributes inertial forces generated at its own level, but also re-distributes forces coming from upper levels. This type of behaviour is typical of a building having setback or podium at lower levels, or below grade levels. Transfer slabs can attract huge forces due to a behaviour dubbed as BACKSTAY EFFECT.

Now, coming to the issue of flexibility of diaphragm. According to ASCE 7-10,

“Diaphragms of concrete slabs or concrete filled metal deck with span-to-depth ratios of 3 or less in structures that have no horizontal irregularities are permitted to be idealized as rigid”.

In addition to considering aspect ratio and horizontal irregularity as a basis for assuming concrete slab as a rigid diaphragm, the relative stiffness of adjoining vertical lateral load resisting system. Buildings with shear walls at ends and flexible frames in between are the ones where the assumption of rigid diaphragm leads to underestimation of drifts and erroneous distribution of base shear in vertical as well as horizontal direction (1)(2)(3); shear forces in middle frames can be reduced to 23% if rigid diaphragm is assigned in the model (1) for buildings with this type of structural configuration.

M. Moeini et al. (2008) (3) conducted a parametric study using numerical analysis and proposed formulae that predicts the error associated with assuming concrete slab as rigid diaphragm. They also concluded that for buildings, without shear walls, rigid diaphragm assumption is suitable for irregular buildings as well. But, for long and narrow buildings with shear walls at ends, the assumption of rigid diaphragm is not suitable.

The objective of writing this article was to warn engineers about the tendency of blindly assigning rigid diaphragm to concrete slab in any type of building configuration. The result could be underestimation of forces as well as drifts.

• Nakashima, M., Huang, T., Lu, L-W. “ Effect of Diaphragm Flexibility on Seismic Response of Building Structures”, In proceedings of 8^th world conference on earthquake engineering.
• San Luis Obispo, MSc Thesis , “ An Investigation of influence of diaphragm flexibility on building design through comparison of forced vibration testing and computational analysis”, 2010.
• M. Moeini, B. Rafzey, W.P. Howsen, “Investigation into the floor diaphragm flexibility in rectangular reinforced concrete buildings and error formulae”, In proceedings of 14^th world conference on earthquake engineering.

The article is not finalized and would be completed in coming weeks.

[Waqar Saleem]

nice article

"The objective of writing this article was to warn engineers about the tendency of blindly assigning rigid diaphragm to concrete slab in any type of building configuration. The result could be underestimation of forces as well as drifts." these lines should be underlined

[EngrUzair]

Thanks for providing an interesting and practice-oriented article. I hope you will update the material very soon.

[Waqas Haider]

Baz bhai, I was studying your article and since, many of terms are used in this article about which i am unaware. And i am also studying a document regarding behavior of diaphragms. I am attaching the same document. I will keep asking about other terms and confusions but for the time being kindly clarify my this confusion. You have mentioned the term SPAN-TO-DEPTH ratio. You have clarified about depth i.e. length parallel to load direction. What do you mean by SPAN?? Is it perpendicular length to Lateral loads?? If yes then it means the same slab can behave as rigid diaphragm in one direction lateral force and non rigid diaphragm in other direction lateral force according to your this statement "the slab with span-to-depth (depth is length of slab in direction of lateral loads) ratio of less than 3 and without horizontal irregularity can be treated as rigid diaphragm."???

diaphragm Design.PDF

[Badar (BAZ)]

Span of the diaphragm is the distance between vertical  lateral load resisting elements. Yes, the same diaphragm can behave different in different directions.

Also read and understand following statement from the article:

 

In addition to considering aspect ratio and horizontal irregularity as a basis for assuming concrete slab as a rigid diaphragm, the relative stiffness of adjoining vertical lateral load resisting system

 

The statement implies that when your are using shear walls in the building, the span  of the diaphragm could be the distance (perpendicular to the lateral force) between shear walls, depending upon the relative stiffness of moment resisting frames and shear walls.

If the building has no shear walls, then the span is the distance (perpendicular to the lateral force) between column lines, or two consecutive frames.