# How to obtain the principal stress lines in a floor?

Hi everyone,

For my project I am trying to get the principal stress lines in a concrete floor slab, like the isostatic stress lines in the floors of Pier Luigi Nervi.
First I tried the stress line component from Millipide and Karamaba, which worked, but I didn’t realy understand the outcome and didn’t have the full control over the stress lines. Here is a picture of it:

Then I tried it another way by using the vectorfield of the stress pattern which led to this:

Here I am stuck since I don’t know how to connect these small into bigger lines like in the first picture.
My goal is to be able to control the stress pattern in a floor slab and eventually to create an algorithm to print this pattern. ( I have already tried something like the ‘Travelling Salesman Problem’), but that would then be the next step.

But I first need to connect these smaller lines into bigger curves.

I hope someone has an idea how to do this.

This is my script in grasshopper: Principal stress lines problem.gh (32.7 KB)

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Hello Juma,

In my own search for an answer regarding the plotting of principle stress lines I have stumbled upon your topic. Perhaps by sharing what I have found so far we can help each other and find a way to create stress lines with a level of control the build in algorithms of Karamba and Millipide do not offer.

My finding so far point towards scripting an own plotting algorithm from the vector field (which can be retrieved from example from Karamba). I however do not know where to start when it comes to programming such an algorithm and personally have very limited knowledge of scripting in general.

The following papers might be of use to you as they were part of my literature review:

http://www.odysseasgeorgiou.com/Publications/Interactive%20Structural%20Analysis%20and%20Form%20finding.pdf

https://repository.tudelft.nl/islandora/object/uuid%3A84d79ea4-aa20-46f4-be61-5daf36be900c?collection=education

https://www.researchgate.net/publication/310645017_Stress_Line_Generation_for_Structurally_Performative_Architectural_Design

http://staff.ustc.edu.cn/~lgliu/Projects/2017_PG_RibShell/Paper/ribShell-lowres.pdf

Furthermore I have found several topics regarding stress lines on the grasshopper forum:
https://www.grasshopper3d.com/photo/principal-stress-grid

If you have found anything I would like to ask you to please share the information with me. You could do this by posting on this discussion, but also feel free to contact me on my personal email: nathanielrasmioen@gmail.com.

Best of luck with your project!

Kind regards,

Nathaniel

2 Likes

The isostatic lines that @j.y.h.a.juma obtained are not the ones of Pier Luigi Nervi’s Palace of Labor (the slab that appears in the photo he/she attached); instead they are extremely similar to this pattern of Nervi’s Gatti Wool Factory:

I believe that both of you would love to read this blog post from Princeton University’s Form Finding Lab: https://formfindinglab.wordpress.com/2019/01/23/pier-luigi-nervi-in-italy-part-1-his-ribbed-floor-slab-systems/ (also you, @DanielPiker). Compare the tedious and work intensive procedures that are shown in that article — a) Pier Luigi Nervi’s photoelasticity experiments and b) the slow methods used by the post’s author, e.g.: manual calculations, drawings, and SAP 2000 / MatLab — with the quick and efficient methods that Grasshopper allows us to use. Additionally, I believe that Daniel has lots of knowledge on this topic and his advice would be helpful (hence I tagged him).

I gladly support your initiative of helping each other @n.rasmioen, wish you the best with your thesis project! Please let me know what both of you have been able to do after all this time regarding this topic @j.y.h.a.juma and @n.rasmioen. Good luck and greetings from the Dominican Republic!