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Abishek_Siingh
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PostPosted: Tue Aug 30, 2011 4:19 am    Post subject: Reply with quote

Dear Ms. Kajal Chopra,

It is nice to know that you are reading the same book which I read during my student days. I don't have the book with me but I remember a few things which as follow:

1. The book by Prof. chopra generally covers examples of plane frames. In plane frames 1 mode per storey is required and that is why the example that you are reading (also attached in your post) has only 5 modes because it is a plane frame five stories high.

2. For a 3D building say 12 stories high, we will have to extract 12X3=36 modes minimum to get a proper picture of earthquake dynamics as three modes per floor exist, two being lateral and one torsional. Yes, I know that in 12 stories, it is possible that first 7 to 10 modes give you 90%+ mass participation, but then in typical building constructed these days, many local modes also participate so it is always better to extract large number of modes but not less that 3 X number of stories. This is a personal preference of mine.

3. The response, whatever it may be, say reactions, moments etc. shall be extracted for every mode and suitably combined in CQC to get the final response. You will learn this when you move ahead in reading that book.

4. Typically for a tall building I would expect mass participation of 50-60% for the first and second modes each.

5. For a G+1 structure, static analysis, that is only for first mode will give you 90%+ mass participation which would be enough to get a response enough accurate for design. The same mass participation will be achieved for the other lateral direction.

Please revert with your views, as I am feeling interested in this academic discussion.

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Abishek Siingh

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prashant.ambulkar
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PostPosted: Tue Aug 30, 2011 6:13 am    Post subject: Reply with quote

Dear Prasad,

As whole area of india has been divided in earthquake zones with different zone factor (Z), whatever size of structure, it shall be designed for minimum earthquake load as per IS1893 - I.

Now Earthquake load can be calculated by two procedures -
1.0 Equivalent static procedure (Cl 7.5.3)
2.0 Dynamic procedure (Cl. 7.8 )


Equivalent static procedure -
If your structure is not coming under Cl 7.8.1 a) & b) criteria, use equivalent static procedure. Here in earthquake load combination you will count this load case.


Dynamic Procedure -
If your structure is coming under Cl 7.8.1 a) & b) criteria, use Dynamic Procedure.
Both static and dynamic earthquake loads shall be applied on the structure.
Then increase dynamic earthquake load as per clause 7.8.2.
In load combination, dynamic load case shall be used for earthquake load.


I hope, ur query has been resolved.
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kajal.chopra
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PostPosted: Tue Aug 30, 2011 9:45 pm    Post subject: Reply with quote

Dear Kumar Abhishek Singhji,

Further queries to your reply (if you don't mind answering);

Point 1:

You mentioned that in plane frames, 1 mode per storey is required. How is this thumb rule valid? What is the physics of the reasoning that in plane frame only one mode is required?

What is it is a 3D frame (sapce frame) or what if I have modelled using 2D walls and plates? How many modes are required then?

Point 2:

You said;

For a 3D building say 12 stories high, we will have to extract 12X3=36 modes minimum to get a proper picture of earthquake dynamics as three modes per floor exist, two being lateral and one torsional.

Do you mean, two for in plane horizontal displacements (in plane with the slab/diaphragm) and one vertical rotation?

Again, what is the physical reasoning when you say " it is possible that first 7 to 10 modes give you 90%+ mass participation"

What you mean by local modes?

Point 3:

What is CQC?

I have more to discuss from Prof Chopra's book? Do you have a copy? Since you have read it in depth, I would like to know your point of view? Or email me your id, I can send you a scanned copy Sir.

Thanks,
Kajal
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suresh_sharma
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PostPosted: Wed Aug 31, 2011 3:14 pm    Post subject: Reply with quote

Dear Kajal

I can throw very limited light on the matter raised by you. I have the book by Mr Anil K chopra. But very little of the book goes into my mind because the book mainly deals with American code which I am not familiar with.

You have raised one question - what is local mode?
I was going through a literature on the topic today and found the term local mode. I am reproducing below the content from the literature.

"A structure has several modes of vibration. If the structure were free to vibrate, the modes of vibration will follow the ascending order of strain energy. Consequently, if Y is the weakest direction of the structure, a Y direction mode will be the first mode. If the next weakest direction is Z, then the second mode will be a Z direction mode. Structures have local modes, where a small region within the model vibrates while the rest of the model remains stationary. It is entirely possible that a local mode is the lowest energy mode."

CQC is a very common term in response spectrum analysis which can be found in any text book.


Last edited by suresh_sharma on Thu Sep 01, 2011 12:58 am; edited 1 time in total
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Abishek_Siingh
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PostPosted: Wed Aug 31, 2011 7:22 pm    Post subject: Reply with quote

Dear Ms. Kajal Chopra,

It is good and I appreciate your reply and enthusiasm for a technical discussion. I will try to answer to the best of my knowledge.

Firstly, you are aware that masses are lumped at a story and on a story, the diaphragm action is rigid (rigid diaphragm action means that it is rigid in it's own plane but flexible in the vertical direction) thereby implying that the diaphragm will have two translational and one rotational degree of freedoms only (total 3). Out of plane bending and rotation at nodes is neglected in case of earthquake forces because we assume that earthquake forces are only horizontal at a floor level and have no component that will excite the vertical or rotational degree of freedom of the diaphragm.

Since in our buildings these degrees of freedom are defined at the center of mass of each floor diaphragm, the mass of the diaphragm in say x and y (z being vertical) direction will determine the mass associated with the translational degree of freedoms along x and y.

Important: If you don't define the degree of freedoms where the mass is lumped, your mass matrix will never be diagonal. A diagonal mass matrix does not have coupling terms.

The moment of inertia of the diaphragm about the vertical axis passing through it's center of mass will provide the mass associated with the rotational(torsional) degree of freedom, of the diaphragm about it's own plane.

Suppose you have a plane frame, like the example you uploaded. You will agree with me on the fact that this frame, being planar will have 2 degree of freedoms(DOF), one translational and one rotational. Also, in a plane frame you have columns and horizontal beams (in the same plane as the diaphragm).

Additionally, in the case of plane frames, the masses are lumped at nodes. This lumping can be easily arrived at by tributary area method. The mass is transferred to each beam column junction node through the diaphragm by tributary area method and unfactored loads are used to get that mass.

It is assumed that;

1. The flexural rigidity of the beams is infinite.

2. The rotational inertia of point mass(lumped mass at node) is zero.

3. Rigid Diaphragm action will help in preventing the rotation of nodes (beam -column junction) under horizontal loads, to some extent.

Due to the 3 assumptions above, under the action of horizontal loads, the beam moves horizontally without bending vertically. Therefore, there will be no rotation of nodes.This leaves us with only one degree of freedom per floor and that is translational.

Practically, there will always be some rotation at nodes, but they are of negligible influence to strucural dynamics.

Now, the pattern of vibration is qualitatively is the mode shape of a structure. Hence, number of possible mode shapes depends on the degree of freedom of that structure. In the plane frame case we have deduced that there is one degree of freedom per floor hence my statement that only one mode per floor is required. So it is a fact and not a thumb rule.

Secondly, the tall buildings are modeled using 2D walls oriented along both x and y direction so the logic remains the same.

Thirdly, Mr. Suresh Sharma's post on local modes is correct. To give an example, I would say the lift machine room and the overhead water tanks which are located on the terrace of most buildings are called appendages. These appendages have very less mass and stiffness as compared to the whole building. The entire building will vibrate as one unit under earthquake, but these appendages will vibrate independent of the building thereby giving rise to local modes. Their vibration will not entirely be independent because they are attached to the building at terrace level, but will majorly be independent.

Fourthly, CQC is called "Complete Quadratic Combination" as it is nothing but a mathematical rule as to how the responses from all modes have to be clubbed together to get the final response.

Hope these help...

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Abishek Siingh



Last edited by Abishek_Siingh on Thu Sep 01, 2011 3:25 am; edited 1 time in total
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kajal.chopra
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PostPosted: Thu Sep 01, 2011 12:24 am    Post subject: Reply with quote

Dear Abhishek Singhji,

Your example of local modes was really good.

One question: Can these (if yes, how) local modes be captured while doing the modal analysis? Be it by hand (for relatively very few DOF) or software?

Kajal
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Abishek_Siingh
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PostPosted: Thu Sep 01, 2011 3:43 am    Post subject: Reply with quote

Dear Ms. Kajal,

Yes, the local modes can be captured. The mass and stiffness matrix, which is formulated to get hold of the modal matrix will have to include the mass of the appendage(which will produce local modes) and the stiffness of the appendage.

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atul_123
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PostPosted: Thu Sep 01, 2011 5:28 am    Post subject: Reply with quote

this might be useful document.



www.iitk.ac.in/nicee/IITK-GSDMA/EQ21.pdf

file is attached here



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atul_123
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PostPosted: Thu Sep 01, 2011 5:31 am    Post subject: Reply with quote

kajal.chopra wrote:
Dear Kumar Abhishek Singhji,

Further queries to your reply (if you don't mind answering);

Point 1:

You mentioned that in plane frames, 1 mode per storey is required. How is this thumb rule valid? What is the physics of the reasoning that in plane frame only one mode is required?

What is it is a 3D frame (sapce frame) or what if I have modelled using 2D walls and plates? How many modes are required then?

Point 2:

You said;

For a 3D building say 12 stories high, we will have to extract 12X3=36 modes minimum to get a proper picture of earthquake dynamics as three modes per floor exist, two being lateral and one torsional.

Do you mean, two for in plane horizontal displacements (in plane with the slab/diaphragm) and one vertical rotation?

Again, what is the physical reasoning when you say " it is possible that first 7 to 10 modes give you 90%+ mass participation"

What you mean by local modes?

Point 3:

What is CQC?

I have more to discuss from Prof Chopra's book? Do you have a copy? Since you have read it in depth, I would like to know your point of view? Or email me your id, I can send you a scanned copy Sir.

Thanks,
Kajal



here i am attaching one pdf downloaded from  from sefindia document.

for cqc & srss methods

www.sefindia.org/?q=system/files/sp22_ex2.PDF



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kajal.chopra
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PostPosted: Thu Sep 01, 2011 11:55 pm    Post subject: Reply with quote

Abhishek Singhji,

Thanks a lot.

Can you throw some light on the physical interpreattion of classical damping and non classical damping?

Mathematically, classical damping has diagonalised damping matrix (uncoupled) and non classical has non diagonalised damping matrix. Fine, this is math.

What is the physical interpreattion of classical damping and non classical damping?

Kajal
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