Posts by retug (3)

The Humble 3-Sided Diaphragm

Diaphragm Analysis - My Journey

Most engineers will find a certain area  of structural engineering that really excite them and areas that  they absolutely despise, and for the longest time, I absolutely despised diaphragm design. Diaphragm design is complicated and confusing, my project managers loved to throw around the buzz phrases they had learned throughout their time in the industry:

  • Did you consider that reentrant corner?
  • Should we use full depth collectors?
  • How are you analyzing the hole in your diaphragm?

These were all very valid questions, but when I asked them how they handle this, I was often left with responses that left me longing to dig deeper. Stuff like, "this hole is tiny, we don't need to consider it", "full depth collectors aren't needed, our forces are small"... etc. I wanted to know more.

This all changed when I discovered the book by Terry Malone, The Analysis of Irregular Shaped Structures Diaphragms and Shear Walls, he seemed to layout a logical, albeit math intensive, way to consider everything and anything one may encounter in diaphragm analysis.

The Humble 3 Sided Diaphragm

I present to you the humble 3 sided diaphragm in the image below:

Many structural engineers would like to analyze this like a cantilevered beam, but this cantilevered beam analogy falls short in a lot of regards.

Cantilevered beam analogy: Incorrect Chord Forces

Drawing the shear diagram for this diaphragm is pretty simple, the shear increases linearly within the diaphragm from right to left. It could yield a diagram like the following:

We know from structural analysis that moment is the area under the shear force diagram and it would yield the following moment diagragm:

​​​A concerned engineer would know that this diagram creates some inherent problems when designing their chords. At the very left hand side of the diaphragm, there would be a very large axial chord force, e.g. from the image above ~950 kip*ft / (depth between your chords). Where does this axial force go? It can't just disappear into the abyss. Just recently I was reviewing a 3 sided diaphragm design by another engineer and they went on their merry way designing chords according to a diagram similar to that above.

In reality, this moment diagram (and corresponding chord axial force) need to close to 0 at each end of the diaphragm in order for the diaphragm to be stable.

How does the moment diaphragm close to 0? One needs to consider the corresponding lateral resisting system (LRS) in the direction perpendicular to the applied loading; these LRS elements take an equal and opposite reaction (also fun fact, these reactions will always be equal and opposite, independent of stiffness of the elements) that stabilize the diaphragm due to the eccentric applied load relative to the resisting lateral force resisting system.

Considering these perpendicular lateral force resisting elements, we get a diagram similar to this:

Horray! The diagram closes to 0 on both ends, oddly similiar to a WL^2/8 type appearance.

I also performed some computer modelling of this 3 Sided Diaphragm to see if the Terry Malone analysis  methodology matched up with some finite element software. The results showed the exact same trends, the dipahragm moemnt and correspodning chord axial force in the diaphragm must go to 0 at the ends of the diaphragms. 

Below is a plot of axial force in chord elements in the diaphragm, note how they close to 0 at the ends.

 

One of the other areas that the cantilevered beam analogy fails is the deflected shape of the diaphragm. For loading applied from page down to up, I would expect there to be a smile face up deflection deflected shape. ETABs and RAM deformed shapes of the diaphragm showed the exact opposite, a smilely face down deflection.

You can read about the counter intuitive deflection here: https://www.eng-tips.com/viewthread.cfm?qid=450755 

The Takeaway

Diaphragm analysis is now something I enjoy doing, having the tools and techniques to analyze these complicated elements makes the engineering fun again.

Diaphragm design cannot be reduced to a simple stick model. The 2 dimensional nature of diaphragms and the corresponding in-plane and out-of-plane lateral resisting elements all play a role in stabilizing the diaphragm. A stick model can not account for the out-of-plane lateral elements.

One of my pipe dreams is develop a diaphragm analysis tool that can analyze any arbitrary diaphragm. I have added the "sketching" tab at the top ribbon of the website in attempt to begin the probably 20 year process of developing a diaphragm analysis computer tool. You can now draw a wonderful arbitrary polygon (hopefully soon to represent your diaphragm), only about 1000 more steps to get to a diaphragm analysis tool.

I would love to hear how you analyze diaphragms, leave a comment below!

ASCE 41 - What Gives?!?

Lately I have found myself doing a lot of seismic retrofits of existing structures.

These buildings are often analyzed utilizing ASCE 41 and I have a few complaints with the standard that I have not found answers too... hopefully someone reading this site can help me out with these.

  • Soil bearing pressures

    • In traditional ASCE 7 seismic design, you get to divide your equivalent lateral forces (ELF) or MRSA forces by an "R" factor... In ASCE 41, there is no "R" factor. There is an "m" factor that is ~"R" from my understanding, but these two terms should not be mixed and matched.
    • Given that your seismic loads from ASCE 41, e.g. BSE-1E or BSE-2E, are not divided by "R", the loads are MASSIVE! If I were to report these loads to my geotech engineer, they would laugh at me
    • I thought that maybe ASCE 41 would allow me to divide by the "m" factor, but instead, you get a measly factor of 3 when design your foundations
    • Coming from a high seismic area where I typically have an "R" of 8 and get to reduce my soil pressures by ~%10 with ASCE 7, only getting to divide by 3 is a real pain on my foundations. Contractors do not like these massive foundations.
  • Drift Limits

    • From the reading I have done, there are no drift limits in ASCE 41! What's up with that? It makes my life easier as a designer, but I have to feel like it should be considered.
    • Lots of moment frame designs according to ASCE 7 are drift controlled...
  • M Factors

    • M factors and R factors between ASCE 41 and ASCE 7 often do not match at collapse prevention. For example, BRB "m" factor is 7.5, while a BRB "R" factor is "8", what's the difference?
  • Force displacement curves

    • As innocent looking as this graph is, it is often extremely confusing to decipher
    • I will dig into this graph in the future

All images are taken from ASCE 41, I do not own these images and all rights belong to ASCE 41.

Website Creation - Part 1

While this website will mostly focus on items in the architecture, engineering, and construction (AEC) field, I figured I could start with posting about how I made this website.

This website was created with the Django framework (a term I just learned throughout this process). It seems to be popular among those in the python community and I learned about it from being a part of the local python club here in Utah. 

I started on this project on July 1st of 2021, the day my wife started up her night float rotation in the hospital. She works crazy hours during this rotation and I figured now would be the best time to start to learn web development.  I had (2) months to do the heavy lifting before the wife returned home. The heavy lifting of the project was completed today, August 23rd; a 54 day project. I would estimate that I spent ~ 2 hours a night working on this website bringing my total time to build this website to around 100 hours. 

In retrospect, I wish I would have gone with a preconfigured blog website like wordpress or wix; but I learned a ton thorough this process. Terms like "sudo," "nano," and "linux" "databases" all mean something to me now. I know the basics of how to configure a linux machine; how to setup website domains etc.

The process has been fun. Stay tuned! (I clearly need to add a spell check to my text editor as well; it is kind of ugly how many misspelled words I see)

 

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