What is the unbalanced moment 4

[Akeee]

Hi guys,
I try to design a flat slab and at punching shear check i have to use the unbalanced moment. Please help me understand what is the unbalanced moment and how do i calculate it. Thank you

 

[KootK]

The unbalanced moment is simply the moment that is drawn to a column in a column slab/beam assembly.

If you imagine a three column frame perfectly symmetric with respect to geometry and load, there would be no rotation at the center column joint and thus no moment would be drawn into the column. The moments on either side of the center column joint would "balance". Now, if you take that same frame and make one slab/beam span twice as long as the the other, the moment on either side of the center column joints would be unbalanced and a portion (not all) of that unbalanced moment would flow into the column via eccentric punching shear and flexure in the slab/column joint.

Functionally, the unbalanced moment is represented by the vertical step in the moment diagram that manifests itself where the slab/beam system passes over the columns below.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[Akeee]

Oh thank you very much KootK for your help. It seems very logic what you said, thank you very much. I have understood very well what you explained, for gravity load type, but if i have, say on that frame you draw, lateral load, seismic load, what moment diagram (only for seismic laterla force) will look like this :

That vertical step you are talking about is very large, the theory you said, can be applied here ?
Thank you again.

 

[KootK]

You're most welcome Aketr.

That vertical step you are talking about is very large, the theory you said, can be applied here ?

Absolutely. In fact, your findings highlight the Achilles heel of the slab/column lateral system: moment transfer at the joint. In my opinion, when flat plates/slabs are used for lateral resistance, the joints should be designed in a more rigorous fashion than we typically do for Gravity loads (Link).

If you're doing a 2D analysis instead of plate element FEM, make sure that you're using something akin to the equivalent column method to capture the fact that the column/slab moment connection is quite flexible. That will bring your moments down a fair bit.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[Akeee]

Thank you very much! When you have beam-column connection it's quite simple to create an image of how moment (i mean how the joint rotate if you consider that is infinite rigid ) transfers from one element to another, but in slab-columns its not that obvious. I'm using finite element method based software's, i just put that image to show what i meant. So when you have slab without beams punching shear problem is the main thing and i personally dont recommend this type of system in strong seismic zones, like this one where i live where seismic acceleration is 0,25...0,35g,for the main reason because you don't have structural elements ( and by elements i mean beams) where the steel yielding is controlled with formulas and methods that where verified with a lot of experiments. The base idea, the main concept, of concrete seismic design it that you dissipate earthquake energy by reinforcement yielding in elements that can take safely,and safely is the key, this kind of load , i mean in elements where plastic rotation due don't jeopardize the hole system stability, like the plastic hinges in the columns. So if you dont have this safe dissipation elements you just can't divide the lateral force by that factor who take yield in account, which is 3....6 so you will be designing your structure at a force 4..6 times bigger, not economically at all. So in slab-column system that slab is suppose to yield and form plastic hinges or you just raise up the lateral force and consider, what we call, elastic seismic force ?
That you again for helping me KootK, i really like speaking with you about this domain.

 

[KootK]

So in slab-column system that slab is suppose to yield and form plastic hinges or you just raise up the lateral force and consider, what we call, elastic seismic force ?

While this is a rational approach, I would still be pretty hesitant to employ it. One of the nice things about using ductility to dissipate seismic energy is that you don't have to be particularly accurate in estimating your seismic loads. Once you commit to "elastic" design, being right all of a sudden becomes more important. Once you go over, it's all over so to speak.

You sound pretty knowledgeable about the seismic side of things. As such, I'm sure that you know that the slab/column lateral system is not permitted by code in some seismic jurisdictions.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[Akeee]

Yes, "plastic" design, where you count on ductility, it pretty easy because if you respect the minimum conditions imposed by seismic codes you don't have to worry about a lot of stuff that will happen "under the hood" and more importantly it is far more economically (conditions like stirrups maximum step size, maximum compressed zone in beams - will ensure a "long" yield in bars - applying this ones you will have a large capable plastic rotation which is the key here because you can count of large amount of energy to be dissipated - so you will have a smaller lateral seismic force - and you can count on large moment redistribution ). So it's a great idea this concept, this methodology, of design of concrete structures in seismic zones but you can apply it only on structures with ductile elements, as i said elements that can "afford" to yield "hard".
In my opinion the slabs without beams is far far away from this type of elements so what i think i will do is to consider a ductility factor of 2 ( 1 will be elastic but counting for large safety factors of strength of material i think 2 is a more realistic elastic ductility factor) then apply the lateral force, which will be a lot bigger using 2, and design the slabs (calculate the reinforcement) for those stresses, the slab and the columns too. So when the earthquake will happen, designing on elastic phase, in my structure will be no yielding, or very small local portions, so no ductility, yes i lost the main advantage - economically part - so will be a lot more reinforcement so a lot more expensive but will be safe, safety always will be first.
About the restrictions of seismic code, i know i posted on ACI section but i did this because i saw other conversations where about this topic, i'm from Europe and in my country we are under EUROCODE jurisdiction but on seismic design (eurocode 8) the EN1998 is not, yet, implemented, so we have a national design code, in which, don't ask my why, this type of structures are not explicit forbidden so i can use this argument.
PS: I forgot to mention that the main stress in this slab due the seismic load is shear stress so typically this kind of stresses will produce fragile break so another plus for elastic method.

 

[rapt]

Too bad if the elastic moment at the column slab connection is so high that the connection fails in punching shear before plastic hinges form!

Punching shear is a brittle failure mechanism and cannot be ignored simply because there is no moment differential under plastic conditions!

 

[KootK]

I don't think that anyone is suggesting plastic design here rapt. At least not any longer. We're toying with designing for elastic or near elastic seismic loads in order to avoid exactly the kinds of issues that you've mentioned.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[Akeee]

It's true that it may be some plastic incursions if the earthquake will be bigger then the one i design the elastic forces and that will be probably true, this earthquake from seismic codes, the "design" earthquake force value it's calibrated with some probability that will occur in some time period (usually 50 years), return period in US i think is 475 year, here in my country is 225 years. For 475 => probability that in one year the earthquake with that magnitude will NOT occur is 99.78% and for 225 will be 99.55%. The lever of safety (by this i mean the magnitude of force) is defined basically on one major parameter country economic wealth. I, as engineer, am responsible only for earthquake maximum value that is written in the seismic code that is valid when i design the building.

 

[Akeee]

KootK thank you again for your info's, was very very good. Could you recommend me please a good structural analysis book?

 

[KootK]

This is my favorite: Link. It doesn't get into plate and shell FEM or anything like that though.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[Akeee]

Hehe i have it on my library I didn't had time to read it all but some parts yes, why do you like it that much ? It's good i dont say it's not, maybe if i do all the examples there i will change my opinion.

 

[KootK]

I found that the clarity of the presentation was excellent. Great graphics and a nicely structured approach. In college, we were assigned a different book which the entire class struggled with. A week before mid-terms, someone brought the Hibbeler book in. By the end of the week, everyone had their own copy. True story.

If you have the time to spend, and you want something more sophisticated, this would be my recommendation: Link. This one too: Link

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[Akeee]

Yeap that's true, the book is pretty clear about what it says but lacks on theoretical approach, for example i struggle to have a good understanding (because is really counter intuitive) how you can compute a displacement if you use a virtual force (equal to 1) which will "ride on" with the actual force (i think that this expression is used on the book) and from internal and external work you will get the real thing. I know how to apply it, i see and understand the math, but i always try to find text that shows the problem from another angle (more like real world examples), i know it's hard to explain complicated stuff with easy and understandable ideas but in my opinion that make a good book. In college i was only caring about doing to problems and to remember the formulas, now i started wondering why is this this way and i am reading a lot so i will get a better understanding in this matter.
The book in the second link sounds interesting, a like the idea of comparing matrix and classical approach, i will try it after.
Nice talking to you, to bad there is no private message function here..

 

[KootK]

I've struggled with the virtual work stuff for over a decade. It's voodoo I say! I get that it's about energy/work balance but that's just sooo difficult to "feel". If I couldn't check it would other methods, I'd never have developed any faith in it at all. It is often the simplest route to solution, however.

I have this book which has helped some: Link. Unfortunately, at true mathematical understanding of virtual work actually requires variational calculus and perpetration theory. Pretty high end for your rank and file structural engineer.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[Akeee]

It's appears to me that you have a lot of experience and knowledge in our domain, structural engineering, i know that is not the topic, that is why i said to bad this website doesnt have private messages, but i need to ask your opinion on this question: what makes the differences between a very good structural engineer and a medium one ? (except from the obvious answer "it holds"). It have to be a combination of speed, good understanding of the structural concepts (and be this i mean the capacity to spot potential very dangerous situations that are not so clear) and open mind for the strangest concepts that come this days. This is only my opinion.

 

[KootK]

Hey, it's your thread so you can wander as you see fit. All of the traits that you've mentioned are necessary, but not sufficient to being highly successful in structural engineering. I'm an convinced that the most important traits are actually project management aptitude and the ability to sell (bring in work).

Think of it this way. When a big sexy project comes in the office, who will management assign it to? The technical rock star who can ETABS up a storm? Or the successful project manager who has delivered large projects in the past with happy clients and steady profits? It's the second guy, without question. And if that second guy also brought in the work via his relationship with the client? Then that guy gets to cherry pick the work as he sees fit.

I consider myself to be a very capable technical engineer. However, I am, at best, a middle of he road project engineer and salesman. Don't get me wrong, I've done well for myself. My rise has not been meteoric however.

I've actually had the pleasure meeting Bill Baker of SOM, arguably the only living "rock star" of structural engineering. If you spent 15 minutes with each of us at a party, I'd defy you to identify which of us is the true structural genius. Bill, however, can self promote and bring home a monster project in a way that I probably cannot. Bill wins. As he should.

My recommendation to junior engineers is to never neglect project management and sales. It's a bit sad for someone of my constitution to admit but, should you find yourself at the highest echelons of our field, fancy technical work will be the domain of the nerds working for you rather than you yourself.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[Akeee]

Thank you, what you said is very important, i never thought in this way, probably because i don't have your experience. You brought up recommendations to junior engineers, i am a junior, two years ago i got my bachelor degree, 1 yr and a bit as structural engineer and i struggle with a decision that i have to make, i didn't apply for master program because i wanted to work in the field, to find out what i like most and what i should focus on in my carrier and i consider that, at the time, from books and story's i couldn't make such a big decision that will affect the rest of working time so i need it to see for myself. Now i think that structural engineering it's what i should follow so i want, next year or maybe later, to enroll in a master program in this domain. I live in a Easter European country and the master programs here are not that bright so i read online a lot and found some colleges in Sweden called Chalmers and one in Denmark DTU, they are a lot more but i can't afford to pay fee that big like in US or Canada. On this 2 i found programs that will cover what i would like to learn but the problem is that my job is here and i can't work from far away so i will lose my job if i will go and i dont know if i will find one, as structural engineer, there in the next 2 years for study, on the other hand i can stay here, go to a much much lower master program. If you have this choices what you choose? A master program there will open a lot of doors to much much bigger companies and so i will make projects which now i only dream of but come with some disadvantages, like away from family, working with strangers so on.. I really respect your how you see things so it will be very important for me to hear your thoughts on this, thank you.

 

[KootK]

Absolutely, without question, go abroad to the best school that you can get into. Illinios, Berkely, Cambridge... It'll be a great experience and you should maximize it. Neither the money nor the time will matter when you look back at it 20 years from now, I guarantee it. The University of Toronto has an excellent program and it is relatively cheap to live and study in Canada (I'm Canadian). Heck, you can sleep in my basement for a month while you get set up.

Things are booming pretty good in the US these days. If you were willing to emigrate, I wouldn't worry about finding a job in the US after obtaining a North American M.Sc. We live for stealing brains from abroad.

The above statements only apply if you don't have a wife and/or children who would be unduly inconvenienced by your academic adventures. People come first.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.