Beam/column

[chigozie]

I think the discussion started from the seismic point of view (read post#1). Comment:- Post post#1 reads “To avoid catastrophic failure or collapse (brittle collapse), it is required that the hinges (at the plastic stage) form on the
beams, rather than on the columns. For this reason, the codes required the designers to provide a margin of security on the
strength of the column over that of the beam. Having this in mind, is there a situation in which it is justified to provide a
beam of dimension greater than that of the column (say a beam of 500mm x 1200mm which is to be supported on columns
of dimension 500mm x 500mm, assuming that the beam is continuous with the column)? Again, how do we meet-up with
this requirement (I mean, what calculations do we have to carry out as to provide this margin of security between the beam
and the column)?”. This did not at any point refer to seismic analysis nor design, unless if you are saying that structural failure could only be verified if and only if there exists seismic loading.
2. The non-linear analysis offers you the possibility to view the sequence of formation of the plastic hinges. Plastic design is
a different matter. Codes means EC8, our national seismic design code and others. Where have I said that codes forbid
plastic analysis? Don't misinterpret what I have written! If plastic design of structures is the topic of the discussion, please
state it Same source wrote previously “Codes do not require non-linear analysis, so if you design a building using any type of linear analysis you won't be able to
see if hinges appear in columns. Only nonlinear analysis can tell you this. Comment:- is plastic analysis different from non-linear analysis????
3. About the post #2, Where is it said that it is OK to have plastic hinges in columns? The meaning of what it is written in
post #2 is: plastic hinges can form in columns, but in order to have a story mechanism which can lead to collapse, all the
columns in a story must have plastic hinges at the top and at the bottom.
4. The codes allow the following situation: the formation of plastic hinges in the top story columns. The reasons are quite
Obvious. Comment:- Could you please state these obvious reasons?. Remember that what could be an obvious reason to you might not be the same to me.
5. The codes do not require non-linear analysis for current building design. It is rather a designer's choice. Comment:- Please correlate this with yours previously quoted in 2; “…Where have I said that codes forbid plastic analysis?…” Comment continued:-.If the code does not require it, then how can a designer make it a choice to choose from?. Will the designer be operating within or outside the requirements of the code???. Incredible. Please remember that we are discussing engineering but not the legal or court interpretation of terms.
6. The formation of plastic hinges is due to the bending moment. An increased axial force in columns can increase the
bending column capacity (up to a certain limit, of course). But if it is assumed that the columns are designed according to
modern codes (the axial force is limited) than an increased axial force will be better than a decreased axial force. Comment:- Certainly, that is the case and I do not think that we had had any point to disagree on this, except that initially, you were, talking of the column design as if it were a beam design (where moment is the predominant action) .
7. Now returning to plastic hinges I will quote a few things from 'Seismic Design of Reinforced Concrete and Masonry Building':
"The primary aim of the capacity design of columns is to eliminate the likelihood of the simultaneous formation of plastic hinges at both ends of all columns of a story". From same source ”If you do a non-linear dynamic analysis you will see that hinges can appear in columns. If this is the case the overall
stability of the building is not jeopardized. Also, plastic hinges can form in the top story columns (the codes allow the
situation)” Comment:- Note the contradictions between the two statements!!!””..
"Moreover, during the inelastic dynamic response of a frame, when frame distortions similar to those of higher mode shapes
occur, moments may significantly increase at one or the other end of a column, and hence the formation of plastic hinge at
either ends must be expected. Accordingly, relevant codes specify that each end of the such a column be designed and
detailed for adequate rotational ductility." Read again:- “.....that hinges can appear in columns. If this is the case the overall stability of the building is not jeopardized Comment:-”If the stability of the structure is not jeopardized, why should code require that you guide against it by designing and detailing for adequate rotational ductility ?
Same source:-Regardingto to the capacity design of frames against plastic hinging in columns.
"The objective of Eurocode 8 rules for the design of (concrete, steel or composite) moment-resisting frames is to force
plastic hinges out of the columns and into the beams, so that a beam-sway mechanism develops and a soft-story is
prevented". Again …” But, you must take into consideration the fact that the building will not fail if a plastic
hinge forms in a column, rather than in a beam (it is necessary to have plastic hinges in all the columns). Further more the
plastic hinges must form in all the columns both at the top part and at the bottom part”. Comment:- If this statement is true, then why should the objective of Eurocode 8 rules for the design of (concrete, steel or composite) moment-resisting frames be that to force plastic hinges out of the columns and into the beams, so that a beam-sway mechanism develops and a soft-story is prevented. Are there no contradictions?
Also regarding to primary and secondary seismic elements,( from the same source):
"The building structures is taken in design to rely for its earthquake resistance only on its primary seismic elements....The
strength and stiffness of secondary elements against lateral loads is to be neglected in the analysis for the seismic action.
However, their contribution in resisting other actions (mainly gravity loads) should be fully accounted for" Comment:-This issue has nothing to do with either secondary or primary structural members. Comment:- Please read the lead post and interpret accordingly. Again, not all designs concepts adopt the braced frame philosophy. Structures could be design as completely moment resisting, as such this assertion has nothing to do with this discuss.
There is also a section about "Special Requirements for the design of secondary seismic elements" which describes the
design of these elements in the same above-mentioned source. Comment:- Like I sounded several times before now, seismic design is a different issue from the case at hand. Please interpret original post in its original context. I hope that we are done with this. How differently we could understand same simple issue.!!!

Now I have a pavilion with two end access staircases leading unto a central platform. The end staircases are each of span 6.5m on plan, rising from the ground level onto the platform at 3m above the ground level. The platform itself is of span 30m. So how do we proportion this pavilion? (see the uploaded image above for further details )
Regards
Teddy

[DamirDz]

Hello everyone!

Nice discussion...

To avoid catastrophic failure or collapse (brittle collapse), it is required that the hinges (at the plastic stage) form on the beams, rather than on the columns. For this reason, the codes required the designers to provide a margin of security on the strength of the column over that of the beam. Having this in mind, is there a situation in which it is justified to provide a beam of dimension greater than that of the column (say a beam of 500mm x 1200mm which is to be supported on columns of dimension 500mm x 500mm, assuming that the beam is continuous with the column)? Again, how do we meet-up with this requirement (I mean, what calculations do we have to carry out as to provide this margin of security between the beam and the column)?
Regards
Teddy

The same issue has been bothering me for a long time as well. The answer here is that the reinforcement makes the final difference. As i recall EC8 (EN version) states that we need to the design the column in the matter to achieve:

McRd>or=1.3MbRd.

And reinforcement has a big deal here. But you are right regarding the beam height; the code should limit the depth of the beam ( i can't remember that the code actually does) in order to meet the requirements for hinge forming(just in case you can't change the column size, and you can't use endless amounts of reinforcement).

But, what bothers me more is this:

For Capacity Design (weak beam strong column), in design you can take beam stiffness 50% of its full stiffness while still maintaining column stiffness to 100% of its full stiffness or :
Beam, I design = 50% I gross beam
Column, I design = 100% I gross beam

ACI uses :
Beam, I design = 35% I gross beam
Column, I design = 70% I gross column

or in general, I beam reduction factor is half of that I column reduction factor.

These apply to Ix, Iy & J (Torsional constant; - not polar moment of inertia).

Reinforcement detailing is also important provide this mechanism.

Yes, i know we reduce the stiffness in order to take account for cracking of concrete. But we already neglect concrete in tension(where cracking mainly appears) and leave it for the reinforcement, and now this.
I agree that we should reduce the gross I of the beam to account for hinge forming, but this concerns only the seismic design situation. This leads to reduced moments and thus to less reinforcement. But how does the gravity load case affect the hinge forming?
Here is what I mean:
Let's say we have this 2 load cases mentioned above, and at some beam-column joint in the structure we have the following:
(the numbers are just figurative)
1) Gravity load case - M=300 kNm => As=25cm2 (i assume here 100% I of the beam; please show me facts to do otherwise).

2) Seismic load case - M=150 kNm => As=13cm2 (assuming the gross section I is reduced by some amount).

Now, my questions are:
How do we meet the plastic hinge requirements now?
(we assume the beam is properly detailed to prevent shear failure)
I know i would design the beam for the first case.
So, how can we be sure(it's all relative :P) that the hinge will form in the beam designed with this reinforcement? Or it won't form at all? And, is it justified to modify the column reinforcement for this case of beam reinforcement?

Regards

[RedHorse]

i do encounter such cases most of my designs calculations,
my solution... may not be academic.

i design the members (coulmns and beams) with the stress envelop, if the strong column weak beam requirement fails, i modify the columns to meet such requirement to insure; as chigozie points out to; quote "To avoid catastrophic failure or collapse (brittle collapse)", increasing the column "I" generally satisfies the requirement, then again you tend to over design the columns, with that in mind, i would like to err on the side of safety.

my two cents on the matter.

[DamirDz]

I agree with you on that; i myself encounter this on all my calculations. Everyone with a sane mind will design anything just to stay on the "safe" side.
But (un)fortunately we are talking about the modern code requirements here which guide us to design not only safe but also economic strctures.. All these scientific papers and books are working with simple, regular, 2D structures; but 90% of the time we don't have a clear code "prescribed" situation. We are then left with our engineering intuition to decide what to do; and that's the fun part of this profession.
Where i'm going with this is that this particular problem(topic) should be a little more detailed and more clear(perhaps someone with more exp here will make it clear for us plz). I do NOT want to rely on the "pure" statement that proper detailing will take care of plastic hinges. Maybe it's just me, but i like to see numbers that will prove me i'm right.

Another thing here, that was mentioned in this topic and concerns the primary and secondary members in seismic analysis and design:

How do we treat the secondary members during analysis? Do we neglect their stiffness during EQ and account them only for their mass and for gravity load transfer?
And, if so, how do we know when to do this? Is this the paragraph that talks about dual, frame, wall etc. systems?

Regards

[iceman84]

I don't agree with the fact that for gravity loads we should use 100% of I because the design of RC elements is made for behavior stage II (cracked section). If the concrete were in stage I (uncracked) the reinforcement stress would be very small (30-40 N/mm2). The reduction of I is clearly visible on the relation M-phi (curvature) for a section in bending.

[DamirDz]

My apologies for not mentioning the code...i work with the eurocodes.
I don't know what code you are referring to, but i don't seem to recall that the eurocode requires the reduction of I. I would appreciate it if someone would show me the section of the EC where it says to do so.
As far as the stress in the reinforcement is concerned, i design the amount of reinforcement by assuming full stress in the same.

Regards

[iceman84]

The reduction of I is not a code matter. No code can force you to use I for cracked or I for uncracked section (I don't refer to seismic codes). If we make the assumption that the section is uncracked (I is 100%) then the reinforcement stress will be a lot smaller than the yielding stress of the reinforcement. As an example: for a section 300x700mm, with 4x20mm bars as bottom reinforcement the cracking moment (the maximum moment for stage I behavior of the section-uncracked concrete is 60 kNm; the yielding moment of the section is 299 kNm, while the ultimate moment is 306 kNm).
So if somebody wants to use I for the uncracked section for ULS design, then the reinforcement computation must be taking into account the fact that the reinfrocement stress is a lot smaller than the yielding stress. Otherwise the section capacity should be computed using I for the cracked section.

[chigozie]

DamirDz wrote:-
...but i don't seem to recall that the eurocode requires the reduction of I. I would appreciate it if someone would show me the section of the EC where it says to do so.
...
Comment:-
I think that you are absolutely correct. The issue of reduction or none reduction of the moment of inertia does not have anything to do with analysis at the ultimate limit state. I have never come about the provisions being mentioned by the proponents of this so-called reduction anywhere either in the code or in engineering literature. Since the deign of the beam and or column and or any other structural component at the ultimate limit state is being performed under same loading conditions, if we should follow this proposition or stipulation in the code (of which I had never come across) the modification of the I should apply to all the components and at last you will find out that you wasted time to achieve nothing. It will amount to dividing the whole component of an equation by say, 100, which will not give you any result different from that of the original. I had request the proponents of this clause to cite their sources but none was able to do that. So any one who still maintains that this so-called reduction in I is supported in any literature, let him please cite the article, paragraph and commas of the code or give reference to the literature from which he lifted this information. We are here and ready to learn.
Reagrds
Teddy

[iceman84]

I quote from a book called "Design of Reinforced Concrete Structures" -Chapter 6 by M.N.Hassoun:
"The moment of inertia, in addition to the modulus of elasticity, determines the stiffness of the flexural member. Under small loads, the produced maximum moment will be small and the tension stresses at the extreme tension fibers will be less than the modulus of rupture of concrete; in this case the gross transformed cracked section will be effective in providing rigidity. At working loads or higher, flexural tension cracks are formed...In both locations only the transformed cracked sections are effective in determining the stiffness of the member; therefore, the effective moment of inertia varies considerably along the span. At maximum bending moment, the concrete is cracked, and its portion in the tension zone is neglected in the calculations of the moment of inertia....Once cracks have developed, the assumption of uncracked section behavior under small loads does not hold."
I quote from a book called " Reinforced Concrete Structures" -Chapter 11 by R. Park, T.Paulay:
"Commonly, the flexural stiffness values used in the structural analysis are based on the gross concrete section; no allowance is made for concrete cracking and the steel is ignored...However, the change in the ratios of the flexural stiffnesses resulting from cracking may be significant in some cases...In fact, in may frames the beams will be cracked but the columns will remain uncracked in the service load range. the reduced flexural rigidity of cracked beams may lead to a bending moment to the columns larger than that calculated on the basis of gross section stiffnesses....To avoid significant moment redistribution, it may be better to base the moment of inertia of the beams on an approximate transformed cracked section (e.g. 0.5Ig) and the moment of inertia of columns on a the gross section Ig."

[chigozie]

Present post is in reference to post #11. I will come back to post #19. later.
If you should take a look at this structure, you will notice that the ultimate limit state condition or strength will not govern the design. The dimensions of the frame components will be determined, rather by serviceability condition, particularly deflection.
If we should adopt the span/effective depth ratio of 26 (BS 8110) for continuous beam and concentrate at the platform (30m span), then required effective depth = 30000/26 = 1154mm; add cover and the dimension of the link plus diameter of 25mm diameter main reinforcement (say a total of 100mm), we have 1254mm which is practically 1260mm. if we should follow strictly the provision of the BS 8110, we will have to modify this further for the fact that 30m is outside the base length of 10m (actually, it should be between 1.5 and 3 times the figure calculated above if we should proportion the beam following to the letter, the stipulation in the standard). If we are to follow the weak beam strong column doctrine, what will be the right dimension for the column, if we cannot hide the strength of the column in the reinforcement? In that case, the column should be at least as thick as the beam i.e., if we have a beam of say 450mm x 1260mm (as estimated for the platform as above), then the column should be of dimension at least of 450mm x 1260mm. Considering the span of the column of 6.5m (which could also be treated as another span on a continuous beam with the central platform), we will notice that it will amount to the waste of material if we should provide this dimension, when a column of dimension 450mm x 325mm could have served our purpose (if we had used the slenderness ratio of 20 for the column i.e. 6500/20 = 325mm). Note that this is in the absence of the provision that Mr.col should be greater than or equal to 1.2 Mr.bm as stipulated in the code. (Mr.col = capacity of the column and Mr.bm= capacity of the beam). So if we are to put this fact into consideration, we will have to further increase the dimension of the column, thus the moment of inertia as to have an Mr.col greater than or equal to 1.2 Mr.bm. Though this may serve the provision of the code, but my question is:- “Is it necessary to meet up with this requirement even in the light of the analysis as done above, which showed that the dimension of 450mm x 1260mm is in excess as such will amount to wastage of material, in as much as the dimension of 450mm x 325mm is enough and could comfortably support the beam. If not, then what do we do in order not to run afoul of the code’s provision?”
Regards
Teddy