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Calculation of Kz, Ky, Ly and Lz
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suresh_sharma
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Joined: 23 Mar 2011
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PostPosted: Tue Apr 12, 2011 3:16 pm    Post subject: Reply with quote

Now I come to the conclusion after going into the posting of Mr. Sarkar that Kz and Lz have nothing to do with slenderness ratio or effective length factor.
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bijay sarkar
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PostPosted: Tue Apr 12, 2011 3:30 pm    Post subject: Reply with quote

No No...

Kz, Ky, UNF are effective length factors and Lz, Ly, UNL are effective lengths. Only one set of data are to be provided in staad...either factors or Eff. lengths. If u provide factors, staad will itself calculate the effective lengths for further calculation of the slenderness ratio of the member.

If you provide effective lengths Lz, Ly, UNL then staad will simply calculate the slenderness ratio of the member for calculating the permissible stress of the member for design verification.


regards,

bijay sarkar
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suresh_sharma
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PostPosted: Tue Apr 12, 2011 6:21 pm    Post subject: Reply with quote

Mr. Sarkar, do you mean to say that Ly and Lz which in majority of the cases are node to node distance are the effective length of the member for the purpose of design in compression but IS 456 utlises sway and non sway definition coupled with Beta1 and beta2 factors for determning effective length factor. In majority of the sway frames the effective length factor will work out to more than 1. In fact the minimum value of the factor for the sway frame is 1. If this is the case then Staad is not considering effective length for design in the true spirit of the code.
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bijay sarkar
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PostPosted: Wed Apr 13, 2011 2:27 am    Post subject: Reply with quote

As the discussion was going on based on a staad file of steel structure, my all above postings are related with steel structures where effective length factors may be less than 1 such as truss members and bracing members. It depends on end fixity condition of the member. In steel structure, i have not found any engineer to calculate it from Beta1 and Beta2 which are cumbersome. Before Beta1 and Beta2, we are to decide which structure is a sway frame & which one is a non-sway frame. In case of columns, this factor is considered greater than unity in the direction of moment frame which is assumed as sway frame direction. In the braced direction, it is assumed as unity i.e for non-sway frame.

regards,

bijay sarkar
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debayan
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PostPosted: Wed Apr 13, 2011 3:10 am    Post subject: Reply with quote

Some people have the habit of giving one length only, which they usually give by multipliying the kx or kz factor along with the actual length.

That is absolutely permissible provided you don't ge confused.

Personally I feel it is better to give Ly, Lz seperate and Ky, Kz seperate just because it is easy for someone to verify if the particular STAAD file is given to someone for checking.
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debayan
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PostPosted: Wed Apr 13, 2011 3:21 am    Post subject: Reply with quote

@Suresh Sharma:- Actually I have yet to work thoroughly on the new IS code. It is based on limit state method, so it might have a new method to calculate Ky and Kz. But I clearly remember in the older code the Max value of K was 2 (for cantilever members).

But if you go according to AISC or BS codes you can have K values greater than 2 and that too for non-cantilever members. Actually in these codes they calculate the total rotational stiffness of the joint based on the column stiffness and the stiffnesses of the members framing into it. That, I feel gives a far accurate picture.

Anyways, lets not get confused and you stick to the code that you are following at present.

K factor cannot be calculated in STAAD. That is a input parameter which has to be given in STAAD or else it will take the default value as 1 which can have disastrous consequences.
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suresh_sharma
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PostPosted: Wed Apr 13, 2011 3:49 pm    Post subject: Reply with quote

The factors beta1 and beta2 are applicable even to steel structures for determining effective length factor of sway and non sway frames In this connection please refer to Fig C1 and C2 of appendix C of IS 800 -1984. Similar clause is also in IS 800-2007. Under the circumstances please guide me as to how to go about it. One of my fellow designer has told me that he used to determine effective length factor with the help of beta1 and beta2 during his previous assignment and that his company had developed an Excel sheet for working out effective length factor based on beta1 and beta2
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JVCSNL
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Joined: 26 Jan 2003
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PostPosted: Wed Apr 13, 2011 4:34 pm    Post subject: Reply with quote

Dear All,
Please refer to following definitions:
<xml><o> </o>
1.        Ly : Unsupported Length in local Y axis for a column modelled in STAAD it is Clear distance between beams parallel to local Z direction, the distance being Top of lower side element and bottom of upper element
2.       Lz : Unsupported Length in local Z axis   for a column modelled in STAAD it is Clear distance between beams parallel to local Y direction, the distance being Top of lower side element and bottom of upper element
3.       KY : Effective Length Factor for calculation of slenderness in Y axis
4.       KZ : Effective Length Factor for calculation of slenderness in Z axis
5.       Ley : Effective Length in Y Axis = KY x LY
6.       Lez : Effective Length in Z Axis = KZ x LZ
Ley and Lez are the end results that matter the member most, which is multiplication of K and L in appropriate direction.  They are design parameters required for design of elements and not used in analysis.
These parameters are necessary to calculate the slenderness ratio of member, which is very important parameter for strength of compression members.  Hence, these parameters are applicable to columns or beam-columns.  Whether it is steel or concrete column, the purpose of these parameters is to appropriately consider the compression capacity of the element under design.
Basically, effective length is the distance between two points between which the compression member buckle.  For example, in case of column fixed at both ends, the buckling will occur between 0.7m length (portion near ends not buckled).  In case of cantilever, the same is 2(two) as the first point is at fixed end and the second point is at imaginary end which is mirror from free end.
Effective length factor for braced (non-sway) frame is less than unity.  For un-braced (sway frame) frame it is greater than unity.  To calculate the effective length factors one has to understand the buckling phenomena.  The buckling of member depends on its rotational stiffness at each end. The rotational stiffness is calculated based on stiffness of column element and end condition of beam elements at column ends.  The terms beta1 and beta2 represent the stiffness of beam column element at two ends of compression members.  Buckling analysis an eigen value problem and difficult to solve manually and hence, Wood has suggested such simplified charts in early seventies.
Hence, if you can calculate the rotational stiffness of joint at both ends, whether it is steel or concrete, effective lengths can be calculated.  For a multi-storeyed steel structure having moment connections at floors, the calculation of effective length factors is very important and is being done.  Also, for crane columns, the same is very important in case of heavier cranes as stepped column is a non prismatic member and its buckling behaviour is quite complex.  According to my experience, the effective length factor of such crane columns in major axis is as high as 5.
For concrete structures, Ley and Lez are required to calculate the type of column in particular direction and do needful for the slenderness effects in particular direction.  
<o> </o>
In actual 3D models, the physical members are divided at many node points to form the geometry of the structures.  The members between such nodes can be termed as analytical members.  Usually, the programs do not identify the physical members unless they are defined using these parameters.  ETABS and SAP do have some features, whereby it calculates the appropriate length in each direction.  STAAD do have option of physical member modelling.
For design of steel beams in STAAD, the factor UNL is unsupported length to calculate the bending stress (based on lateral torsional buckling) and shall not be confused with Ly or Lz which are used for calculation of compressive stresses.
For more on the buckling and effective lengths, one may refer the paper published by Wood in the Structural engineer in seventies and book theory of elastic stability by Timoshenko.
<o> </o>
Regards,
Jignesh Chokshi
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suresh_sharma
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PostPosted: Thu Apr 14, 2011 1:45 am    Post subject: Reply with quote

Mr.Chokshi,
Now I understand from your posting that ELY and ELZ factor has to be detrmined as per Beta1 and Beta2 factor laid down in IS 456 and based on this input Staad will calculate l/r ratio otherwise Staad will take into account the default value which will be erroneous. Am I correct?
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JVCSNL
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Joined: 26 Jan 2003
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PostPosted: Thu Apr 14, 2011 2:00 pm    Post subject: Reply with quote

Dear Suresh,

Your understanding is correct. You need to provide necessary input (k and L) to calculate effective lengths.

I also suggest that after you perform design in any commercial software, you also check one or two designs manually for understanding and validating the design inputs.

Regards,

Jignesh Chokshi
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