Beam/column
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Author: chigozie
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Beam/column
#1
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
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#2
You can provide beams with dimensions greater than that of the columns if you have shear walls which provide the necessary lateral strength.
If you don't have shear walls and you have beams with large dimensions, you can increase the reinforcement (and the dimensions) of the column until it's ok. 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
So, in my opinion the best solution is to provide an adequate amount of reinforcement in the column and detail it accordingly, but keeping in mind the fact that a plastic hinge is very likely to form there (the rest of the columns must be detailed according to capacity design rules).
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#3
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.
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#4
@tamboon:

Can you tell me the reference to your first sentence? Why 50%? How to explain that?
Is there some calculation to be made to proof this claim or?

With regards
G


p.s. once I saw the above mentioned 50% (in some publication) but can't remeber where...
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#5
iceman84 wrote:-
...You can provide beams with dimensions greater than that of the columns if you have shear walls which provide the necessary lateral strength....

Comment:-
I do not think that this provision was made with respect to provision of lateral stability as such, the case of shear wall does not come in. If you are contrary to this please give me a reference to this provision.

,,,,you can increase the reinforcement (and the dimensions) of the column until it's ok,...
Comment:-
This is a verge statement. Please indicate on how you will know when it is ok (what calculations do you have to accomplish)
,,,,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:-
I beg to disagree with that statement. If not, why is it that the code (EUROCODE) requires that the hinges be formed in the beams rather than in the column, This will amount to suicide if the hinges are to be formed in the columns rather than in the beams (like you are suggesting). This will result in brittle collapse which will be fatal as there will be no pre-failure warning

.....So, in my opinion the best solution is to provide an adequate amount of reinforcement in the column and detail it accordingly, but keeping in mind the fact that a plastic hinge is very likely to form there (the rest of the columns must be detailed according to capacity design rules).....

Comment:- how much is adequate as to comply with this requirement?

tamboon wrote:-
.....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.....


Comment:-
Like was pointed out by Grunf, colud you please cite these clause or how you arrived at the figures that you quoted?
Regards
Teddy
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#6
1. EC8 allows you to choose primary and secondary members for seismic resistance. In the case of secondary elements, their strength and stiffness can be neglected. This elements may not be designed according to the rules for primary structural members. So if you have a structural wall system which takes practically all the lateral load, other members can be designed as secondary members.
2. Increase the reinforcement in the column and/or the dimensions of the column until you satisfy the capacity design checks.
3. 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). The formation of plastic hinges in columns will lead to story mechanisms (any form of brittle failure is excluded).
4. An adequate amount of reinforcement is the minimum amount of reinforcement according to the seismic design code.
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#7
You were citing the Eurocode 8. Could you please indicate the articles and the paragraphs in the code that infer the statements “....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?????? ). [The formation of plastic hinges in columns will lead to story mechanisms (any form of brittle failure is excluded).......”
Comment:-
In the non-linear analysis, hinges could appear anywhere but you have to design against that which is most critical as such will lead to collapse. It is for this reason that the code require that you should not allow a situation in which hinges form in the column as this will lead to the condition of brittle collapse.
Please remember that the analysis of a structure is different from code requirements.

Again, taking this reasoning into the design of primary and secondary members for seismic design (which is a different topic) detract from the original post “.....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......”
Please note that I did not mean seismic loading/design. I meant the general requirement of the code as cited inter-alias.
Regards
Teddy
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#8
The articles in EC8 refer to primary and secondary members. For further information about the formation of plastic hinges in columns go to: Seismic Design of Reinforced Concrete and Masonry Buildings by T.Paulay&N.Priestley.
By choosing some structural members as secondary members, they can be designed without considering the requirements given in EC8. So, in my opinion, this solution can be applied if you have beams with very large dimensions, compared to the columns.
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. How can you design a building so as not to have plastic hinges in columns without the use of nonlinear analysis?
I have never said that it is OK to have plastic hinges in columns, but this situation can occur and this does not mean that you will have a structural collapse.
What do you mean by brittle collapse?
The formation of plastic hinges in columns is due to the bending moment. From the beginning it is assumed that any form of brittle failure is forbidden. So of what type of brittle collapse are you talking about?
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#9
The articles in EC8 refer to primary and secondary members. For further information about the formation of plastic hinges in columns go to: Seismic Design of Reinforced Concrete and Masonry Buildings by T.Paulay&N.Priestley. By choosing some structural members as secondary members, they can be designed without considering the requirements given in EC8. So, in my opinion, this solution can be applied if you have beams with very large dimensions, compared to the columns.

Comment:-
Like I had sounded several times before now, this requirement has nothing to do with seismic design (which is a different topic). Please refer to my previous posts.
Your last post reads and I quote: -

...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. How can you design a building so as not to have plastic hinges in columns without the use of nonlinear analysis?.....
Comment: -
Please read: -
“As result, work started on plastic theory and plastic method of design was first permitted in the country in 1948 when a clause was inserted in the new edition of BS 449”. -Quoted from the “Steel Designers Manual” (page 531)(Note: - as far back as 1948!!!!! that plastic design was included in the BS).
Pushover analysis is a non-linear analysis and it is used in the analysis and design of most non-simple structures.
Ultimate limit state method of design is a non-linear design. Is it true that the codes do not require ultimate limit state method of design in structural design and/or forbids Pushover analysis? If not, then which codes are you talking about; which articles in Euro code 8 are you talking about. Please cite them. You wrote:-

".... I have never said that it is OK to have plastic hinges in columns". . . In line with this, please refer to POST #2 (that arrived in your name) and I quote you verbatim. "....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.." . Also refer to Post # 6 and I quote you line for line:-
...."3. 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). The formation of plastic hinges in columns will lead to story mechanisms (any form of brittle failure is excluded)..
Or am I quoting another person?
. Again:-
"....but this situation can occur and this does not mean that you will have a structural collapse....". "the codes allow the situation" when you said before now that "the Codes do not require non-linear analysis." Reasoning along the lines, are these statements not contradicting themselves? Or are you talking of a none engineering code here?
I quote you again:-
".....What do you mean by brittle collapse?
The formation of plastic hinges in columns is due to the bending moment..."

Comment: -
Yes it is assume that the formation of plastic hinges in columns is due to the bending moment, but this is not the actual fact as in the analysis and design of columns, the dominant action is axial force and not bending and for this fact, adjustments have to be made to the results obtained in assuming that the plastic hinges are due to bending. Please read that part again and confirm.
regards
Teddy
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#10
1. I think the discussion started from the seismic point of view (read post#1).
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!
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.
5. The codes do not require non-linear analysis for current building design. It is rather a designer's choice.
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.
I hope that things are clear, now!
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". It refers to columns above level 2.
"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."
Regarding the use of concrete shear walls I will quote some relevant things from the "Designer's Guide to EN1998-1 and EN 1998-5'
"So, in the horizontal direction of the building that has walls resisting at least 50% of the seismic base shear, Eurocode 8 expects these walls to prevent the occurrence of a soft -story mechanism, and waives the condition of satisfaction of equation D4.23 at the joints of primary seismic columns with beams".Equation D4.23 refers to the capacity design of frames against plastic hinging in columns.
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".
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".
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.

So, I hope I made myself clear now: the objective of the capacity design is to avoid the formation of a soft story mechanism (which means to have simultaneous f plastic hinges at both ends of all columns of a story)!
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