I have been working through some complicated diaphragm designs with a newer engineer recently and have been learning a lot about transfer diaphragms. I realized I was falling into some pitfalls and it was good working through this with the newer engineer. One of the great things about working with newer engineers is the fresh perspective and inquisitive nature.

The Sample Building

The building shown at the start of this blog post is a 20 story tall building, with the lower (2) floors being the typical transfer diaphragm type building, where the building core shifts a lot of its lateral load out to the perimeter concrete walls. See image below for large jump in shear at the transfer diaphragm in the building we inspect in this post.

I want to note that this building is completely made up, please take all numbers with a grain of salt and let’s focus on the relative values, not the values themselves. Please also let me know if you do diaphragm design differently, this is one person's perspective on diaphragm design.

A few notes on the building.

• Total height 248ft
• Typical story height is 12ft
• 24” thick concrete core with moment frame outrigger system
• 12” thick concrete slab for typical floor
• 24” transfer diaphragms at levels 2 and 1
  • We will study a few differing transfer diaphragm setups
  • Level 2 Shown below

• Building is subjected to an ELF type load
  • Base ETABs seismic seismic parameters
    • R = 8
    • Sds = 1.374
  • Total base shear is 1600 kip under ELF loading

My Previous Design process for Diaphragm Design

Let me outline the way I used to design diaphragms

• Calculate the ELF applied story forces that a program like ETABs/RAM elements produces
  • For our sample building, which I have uploaded to github, we have the following applied diaphragm forces for an ELF type load case
  • Note at story 2, we have an applied force of 34.2kip

• From here, I would then calculate the diaphragm design force according to ASCE 7.
  • For fun, let’s do a quick calc based on the seismic parameters input into the ETABs model. Controlled by Fpx_min and we are checking level (2)
  • Fpx = 0.2*Sds *Wp = 0.2*1.374*(5064kip) = 1392 kip
  • This works out to about 96.67psf over the 120’x120’ level 2 transfer diaphragm
• Next, I would take the ratio of applied diaphragm force in the ELF case and compare that to the Fpx value, this would be the ratio I would use to amplify my section cut results by to do the design of my chords and collectors, you can maybe start to see the problem.
  • Amplification factor Fpx/Fx = (1392kip)/34.249kip =~ 40.5
• A small aside, I built this tall 20 story building to demonstrate my point, but when working with smaller buildings that often do not have as explicit of transfer diaphragms, 6-8 stories, built into a hillside for example, the addition of lateral force resisting elements, these ratios are much smaller and seem like they might be reasonable.
• With the amplification factor, in attempt to capture the minimum diaphragm design force, I amplify my shear force and moment diagram and design my design to resist these amplified forces. You can see that a factor of 40.5 is unreasonable and does not capture what the code is truly trying to capture with minimum diaphragm design forces and higher level mode effects. More on this later.

Sample buildings and iterations with level 2 Transfer Diaphragm

I have uploaded (3) differing ETABs models to github.

1. The base model with a 24” thick transfer diaphragm

2. The model with a 12” thick diaphragm and stiffness modifiers to account for cracking
3. Same model as #1, but with a large hole in the transfer diaphragm

The new way of designing diaphragms:

Moving forward with diaphragm designs, I will not use this amplification method I outline above anymore. I think this method works for regular buildings, where there is little transfer of forces through diaphragms and for buildings where the lateral force resisting system is “regular”. My definition of regular is that shear force in the lateral force resisting system slowly accumulates on a story, by story basis. Backstay effects and transfer diaphragms are not "regular".

I will note that the sample building I have built, I would define as regular above level 2 and above, the shear force accumulates in the shaft as you move down the building until you hit level 2 and experience the large backstay effect.

The new way of designing diaphragms is running two overall design checks

1. Running the overall ELF model, reviewing results in the diaphragm with the slicer
2. Appling a diaphragm design force one level at a time and reviewing the results of the diaphragm with the slice

Please note that these forces need to be amplified for element being design, for example, a lot of collector forces need to be amplified by omega.

My understanding of diaphragm design forces is that they are to capture higher level mode effects where the max diaphragm design force at a specific level would not typically occur in the same assumed manner as the first mode. The first mode and corresponding ELF design forces is the correct way to design the lateral force resisting system and the design of transfer diaphragm forces. In a lot of cases for transfer diaphragms, the typical ELF load distribution will be the worst case diaphragm force.

Fun Sketches

You can see in the 1st mode assumed shape, the lateral load builds up and a majority of the lateral load will have to transferred at the transfer diaphragm to the stiff basement walls if the transfer diaphragm is stiff enough. In the case of the higher level mode deformed shape, the applied loads will typically cancel out as you move from story to story.

This approach is backed up by NEHPR Seismic Design Technical Brief #5, Seismic Design of Composite Steel Deck and Concrete Filled Diaphragms, a few excerpts below

Shear Results

­Onto the fun plots. All plots produced with results from the diaphragm slicer and matplotlib

Notes on the shear plots

• These are clickable for closer inspection, I realize they are quite tiny. Click to review and zoom
• You can see big differences in shear forces between the differing models
• Switching from a 24” thick transfer diaphragm to a 12” diaphragm with stiffness reduction for cracking led to a large decrease in diaphragm shear
  • 1335 kip (12”) / 2380 kip (24” diaphragm) = 0.56
• Note that this could lead to a negative feedback loop, I need more diaphragm strength, whoops, I have more diaphragm demand.
  • One thing to pay attention to
• Note that the diaphragm Fpx graph (red line) is tiny in comparison to the other transfer diaphragm forces. This illustrates the pitfalls with my old design method. You live and learn and get better.
• I was also surprised to see how little impact the large hole had on the shear diagram (black and yellow plot)

Moment Plot

Not much to note here, moment results are in line with what you would expect after reviewing the shear diagrams.

The Takeaway

If you have a transfer diaphragm, be sure to do two diaphragm designs, one based on the overall ELF response and one based on the diaphragm design force applied as individual load case. Even on buildings where diaphragms are not immediately obvious as transfer diaphragms, doing this procedure can reduce your transfer diaphragm forces significantly. Any change in building geometry or the addition of a new lateral force resisting line, consider doing a little extra work of two diaphragm designs and the savings could be well worth it.