Stress Trajectories of Slabs/Shells

[puszka]

Hi everyone,

I have been doing a lot of reading from prominent 20th century engineers (Eduardo Torroja, Nervi, Waclaw Zalewski etc.) and I am interested in learning more about stress trajectories and how to find them in different structural shapes. It is a really cool concept though it is hardly even mentioned in an undergrad, but has been used to in the past to create some amazing works. As I am playing around with Karamba 3D for fun and my own knowledge, I was hoping to learn some more basic theory behind it to improve my intuition. If anyone knows of any good resources/books/texts/entire subjects that are introductory into how forces are transferred through different materials and different shapes, I would love to know more. All I really understand now are the parallel, fan, and lattice networks in walls, beams, and prismatic members and I know there is a lot more to learn.

For example, Nervi designed the Gatti Wool Factory with the ribs aligned to the isostatics of the the maximum and minimum bending moments in the slab (pictured). I'm still not totally sure how to find these without the help of a software which for me is a black box in terms of understanding.

 

[KootK]

This won't be quite what your looking for but it has some interesting historical information on the use of thrust line concepts and the like in compression stuctures.

 

[puszka]

@KootK

Yes! A great rec but alas I have read it already

 

[JStephen]

See Timoshenko's Theory of Plates and Shells and similar references where a lot of flat plate problems are addressed. In that first picture, if those ribs were aligned with bending stresses in an un-ribbed flat plate, that kind of analysis is likely where it came from. Of course, if you have uneven loading, all that goes right out the window, too.

 

[centondollar]

"For example, Nervi designed the Gatti Wool Factory with the ribs aligned to the isostatics of the the maximum and minimum bending moments in the slab (pictured). I'm still not totally sure how to find these without the help of a software which for me is a black box in terms of understanding."
Designing is easy if the purpose is architectural and not structural. Nervi was an architect, and what you describe boils down to a gridwork model for a structure whose weight is dominated by uniform dead weight. Hardly complicated, if you ask me.

It is seldom possible to determine internal forces and stress trajectories for any shape more complicated than a simple beam or slab without resorting to FEA-software - this is particularly the case for shells (membrane-bending coupling), cables (geometric nonlinearity), beam-columns (membrane-bending coupling), curved beams (torsion-bending-membrane coupling) and many other interesting structural shapes. If the problem involves any type of non-linearity, such as bending-membrane coupling, plasticity or contact, the solution is almost always intractable by hand and the outcome of FE calculations is highly reliant on the robustness of the solver algorithm and correctness of user-input parameters e.g., critical time steps and damping models in dynamics.

Finally, as JStephen already noted, if the loading is not overwhelmingly dominated by a predictable load (such as uniform dead load), the "stress path optimization" concept becomes quite useless. In real life, you will resort to boring shapes (circles and rectangles (solid or hollow), I-shapes, C-shapes, stiffened plates, ribbed slabs) to deal with varying load, large load and dynamic effects. Bridges only come in a select few formats for a reason.

 

[puszka]

@JStephen
Yes, I have heard reference to Timoshenko and that sounds like a good rec. Might be time to delve in.

Hardly complicated, if you ask me.

Lol, draaag me

I guess what I meant to convey was not that I was interested in learning how to do this in complicated structures by hand per se, but just to understand more of the basic building blocks of the theory behind this kind of design to grow my intuition. Eduardo Torroja (Spanish engineer and contemporary to Nervi) spoke a lot about developing this intuition and visualization ability but didn't elaborate as to how to do so. The kind of playfulness they show in structural design is something I have become attracted to post-graduation since engineering education focused so heavily on technical aspects and largely ignores any kind of creativity. At least, it felt as though mine did.
I can say that there are a lot of resources out there that I have found, but I'm struggling with the inflection point between simple and advanced theory. I just need a boost to get over the hump.

 

[centondollar]

Real work requires producing robust and correct calculations and designs, which is why FEA and tried-and-tested methods and principles of structural mechanics are used in industry. As long as you understand what type of structural action is most preferable (tension, compression) and least preferable (torsion, bending and shear) and the principles behind typical structures (shallow trusses have larger member forces and vice versa, closed profiles are extremely torsionally stiff, I-profiles are superior in bending, panels and stiffened panels are useful in shell structures and weight-critical applications etc.), I'd say you already possess the most useful "intuition".

Engineering is mathematics, and optimal design even more so. Intuition is improved by doing structural design, learning technical material and choosing structural models (bar, beam, plate, shell, solid) fit for the task at hand.

Honestly, if you want to spend your days drawing fancy geometry that an engineer will never sign off on, you're better off applying to architectural school.