ultimate moment

It is really quite frightening to think that you are designing any kind of structure when you ask a question like that. My advice to you is stay within your level of competence, whatever that may be. It is certainly not structural design.

and if i did is not a structural design..can you give me an idea what is structural designing to you? and what is the problem of my questioning?

"Based on my experience as a civil engineer, am preparing structural analysis of two storey residential building. My question is... is it correct my judgment using ultimate moment on any of my floor beams equivalent to wl*l/12? because if i use wl*l/8 as a max moment rebar's is too many."

You cannot expect a comprehensive answer to such a question on CR4. Your usage of the term "ultimate moment" is not clear. I know what the term means, but I'm not sure that you do.

A simple beam under uniform load w has a bending moment wl²/8. The factored moment M_f = w_fl²/8 where w_f is the factored uniform load, determined in accordance with the provisions of the code you are using. In my code, the Alberta Building Code:

w_f = 1.25D + 1.5L where D = dead load and L = live load

I don't know which code you are using, so cannot comment on that.

The ultimate moment at any section is the moment occurring simultaneously with failure of the beam. It cannot be determined with complete certainty as there are uncertainties respecting material properties and construction practices. In general, the ultimate moment is higher than the factored moment because of these uncertainties.

The negative moment in a two span continuous beam with equal spans and hinged ends is also wl²/8. For any other type of continuous beam, the moment coefficient is variable depending on the ratio of spans and the location for which moments are being calculated. The value of wl²/12 may be adequate in some places but not others. My code gives values for a variety of conditions and I expect yours does too. Why don't you look at your code instead of asking CR4?

And finally, you do not select a moment coefficient based on the notion that "the re bars is too many". You adopt a coefficient which is in close proximity with the way the structure is going to behave under load. If you are unable to determine that with reasonable accuracy, you have two options, (1) analyze the structure using either hand methods or computer methods and (2) select a moment coefficient which you know to be conservative.

I hope I have answered your question, but if not, please respond.

I am new here so I am a little nervous about submitting something, but I figure this would be a good time to say something since I have a little bit of experience with this type of thing. Therefore to address the above question and agree with ba/ael, I would add this. The denominator of the Moment formula is based on the fixity of the connections of the supports at the end of the beam. The (wl*l)/8 is based on the beam ends being pinned to the supports with no resistance to rotation in the joint. The (wl*l)/12 is based on a completely fixed connection to the supports and not allowing any rotation. Even with one end fixed and the other end pinned the formula given in the AISC steel manual is the more conservative (wl*l)/8. Since a fully fixed connection is difficult at best to achieve, and since some resistance to rotation will exist even in a wood framed building, choosing a denominator between 8 and 12 can be done. However, the resistance of the connection needs to be determined, and then an experienced structural engineer can make a judgement about what number to put in the denominator of the moment formula. Example: a steel moment frame would be closer to 12 than to 8 since it is very stiff, but in a wood structure only 8 should be used. Having said that, I would never determine what formula to use based on anything but how the fixity of the connections would be. Therefore the original question of whether or not to use a fixed end formula instead of a pinned end formula without taking into consideration the end fixities because a more favorable design outcome would emerge is folly at best.

Nice post.

Perhaps it comes down to the "rebars he too many" portion of the original post. My guess is that the beam will NOT be fixed sufficiently for this reason but that the work will proceed as if it were so and the result will be less than satisfactory.

My apology to all, am not trying to confuse everyone. The ultimate moment which I mentioned before is already equated to factored moment under uniformly distributed load. Where ultimate moment M_u = M_d = ø A_s f_y (d –a/2) if;

= w_ul²/12; w_u = 1.4 w_dl + 1.7 w_ll

1. Strain in reinforcement and concrete shall be assumed directly proportional to the distance from the neutral axis.
2. Maximum usable strain at extreme concrete compression fiber shall be assumed equal to 0.003.
3. Tensile strength of concrete shall be neglected in axial and flexural calculation of reinforced concrete.

My assumption here is the concrete floor beam is under uniformly distributed load. Hence, w_ul²/8 (factored moment) is conservative enough. That's why I adopt w_ul²/12 considering the concrete floor beam is fixed. And I want "economic" and of course "safe" structure. Fast and safe calculation using hand calculation. Is this factored moment reliable to the situation like this? Sorry of my English also.

Your ultimate moment formula is correct for concrete; sorry for the misunderstanding. The problem is still fixity of the connection. For a concrete "moment frame connection" (which is the closest "thing" to what will be needed to use (wl*l)/12) you will need a large amount of rebar at the connection to resist the tension from the moment forces at the connection plus extra rebar for containment for the beam and column, etc. Because of the nature of concrete I would venture a guess that a connection like this could be considered fixed under these circumstances, but I would never consider this a completely fixed connection. However, I believe you are correct in using a fixity somewhere in between pinned and fixed. This is where good judgement must be used since we as engineers need to be confident not just in our design, but also in the execution of that design. If you feel that your design is safe using a larger denominator than 8, that would seem fine, but remember you must have confidence that your design will be built properly to ensure that it will respond and react to the forces you designed for. That means keeping track of how the design is built as best you can.

Long story short I would pretty much stick to using a denominator of less than 10, for a concrete structure, if I really needed to push my design to work. I do however, try everything I can to get my design to work before even beginning to look at this option. For me it is pretty much a last ditch effort, and I prefer to change the design before I put my neck out in this way.

Hope this helps

wl/12 is the moment at the ends for fixed end beams, and wl/24 is the center moment. However, this is kind of the best case scenario and the pinned end is the worst case for the moment at the center. If it is truly a fixed end, you will be transferring all these moments from the beam to the walls or columns. So you may benefit by the reduction in steel in the two way slabs, but you will need to stiffen the columns to resist the added moments. Usually i have found though that since the negative moment to the positive moment is still wl/8 total, it just changes the side the tension steel lies on and for simplicity, unless the slab is long, you extend the steel in top and bottom all the way through (however, you could just extend it part way with overlap for the development lengths on the top). You should review the requirements in ACI 318 for 2-way slabs. Also, seismic loads and wind loads will need to be factored in.

You sound like a different person than the one who originally posed the question. Please see moment and shear coefficients below for various conditions of support mentioned in CSA A23.3. What code are you using? Does it not have similar coefficients?

You guys give me a lot of idea handling problem like this. Thanks to Engr. Bruce (ba/ael), RCE, and to you Indrivetrains. Even though Engr. Bruce intimidated me he deserves my thanks. I am using ACI 318 for Method of Analysis and NSCP.

I do not have a recent copy of ACI 318, but my old ACI 318-63 (don't laugh) has coefficients similar to the ones I gave you from the current Canadian code. Some things don't change with time.

I apologize for the intimidation. I felt your original question reflected a lack of understanding of basic structural design principals. I see now that I may have jumped to unwarranted conclusions. Sorry!

dear every one,

sorry, for participating this beautiful discussion at late. structural design is not so easy as you can think. i am telling this beacause the formula which you gives are apprximate. when I analyse a multispan beam (in deeper meaning frame), I see that most of the case when span is not equal or equal these formula can not give correct result. in every case a redistribution can occured about moment. if any one want analyze a frame by 2-D frame, I suggest him please analize by substitute frame or Kani's model for gravity load analysis and Portal frame/ Cantilever frame for latarel load analysise.

Thank all of you-

RAHUL