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Lateral Loads and Area Objects(Slabs)

Oct 11, 2014 at 9:06 PM
Hi Ehsan,

To calculate Earthquake forces, we usually have some parameters for soil. We also need apply the calculated lateral load to gravity center of floor for a building. BriefFiniteElement is just allowing us to make loadings to Nodes and Elements, but we dont have a feature for area elements to whose center we can apply a load.

Thanks,

Sedat
Coordinator
Oct 12, 2014 at 6:30 AM
Hi Mr. Sedat,
Thanks for your comment. For calculating the lateral loads there is need to implementing rigid element (to use it as rigid diaphragm) which you can see in features section that is listed as planned feature, and i've sticked in formulation phase of rigid element.
For example consider a 6 roof structure with 6000 free nodes, the stiffness and mass matrix are about 6000 by 6000 matrices. It is very time consume task to find all eigen values and vectors for the 6k by 6k matrices (if we not say its nearly impossible on desktops), but if we can apply rigid elements to reduce the stiffness and mass matrix size (which as i can remember was doing in EQ. Engineering in university) then the stiffness and mass matrices are reduce to say 36x36 and simply possible to determine the eigens for that which is 36 eigen vectors and 36 eigen values.
I've found some documentations for applying the rigid elements available from here which other version are accessible through google as well. There are three methods listed in the document: Master Slave method, Penalty Function and Lagrange Multiplier. which there is a comparison table in page 52 of the document. What is important for this case is: it should retain positive definiteness of stiffness matrix and it should reduce the stiffness and mass matrix dimensions as well. But the thing i'm in doubt is that maybe other methods for our case be possible to do. Can anyone confirm that Master-Slave method which is described in above document gains exact values for this case? or even is suitable for this case?

Also about the area elements, they are also listed in features as planned to do, and will implement it soon.

Regards
Oct 14, 2014 at 9:40 PM
Hi Ehsan,

You know there are two kinds of methods in seismic design codes:
  1. Static Equivalent Force Method used for regular geometric and mass distributed structures, such as a 6 story building with all floors are covered and act as rigid diaphgram. It is a simple method and I have developed it for your lib for Turkish codes. I have tested your software against local Turkish software idecad and Sap2000 and is giving very close results for displacements and internal forces. I want to congratulate you on this!
  2. Dynamic Methods which are used in irregular geometric and mass distributed structures. Modal Analysis or Time-History are dynamic methods. Unfortunately, I am not much knowledable about this dynamic analysis. There is a C open source called Frame3DD, check internet, which does dynamic analysis. It is unfortunately not object based, but just console app.
Hope this helps.

Kind regards,

Sedat
Coordinator
Oct 17, 2014 at 6:12 AM
Edited Oct 17, 2014 at 6:13 AM
Hi Mr. Sedat,
Would you like to write the 6 story building problem (static equivalent method) as an tutorial (regarding Turkish code)?
If you do so, I'll give you technical support for this library (and probably other structural engineering libraries) for free and wherever you need it.
Oct 17, 2014 at 7:32 AM
Hi Coordinator,

Of course I will be happy to do this. But I need to know just one thing on which I am stuck.

According to Equivalent Static Force method for defining lateral earthquake forces, the Turkish code and American Seismic code reqires to calculate center of mass of a floor and apply the calculated equivalent static force on the point. This point is a fictitious point actually. Your library has only nodes, not the area feature. If it had area feature, then I would apply this force to center of that area and let the library calculate nodal displacements. Also, the standarts require you to calculate rigidity center of a floor and compare with center of mass. Furthermore, it asks you to apply the equivalent force to mass center with an eccentricity of 5% of perpendicular dimension to earthquake direction. If we can calculate mass and rigidity centers for each floor, then it is simpler to apply a 6 story tutorial.

There is another problem regarding distribution of lateral force to axis perpendicular to earthquake direction due to irregularities of mass distribution. Suppose there are no rigid diaphgrams on between some of the axis. How would you find mass center if there is no diaphgram !. Or there may be more diaphgrams on a floor.

Equivalent force method reqiures you to have a rigid diaphgrams on each floor reqularly( only 1/3 of floor can be empty acc. Turkish Seismic Code). Then you need dynamic analysis to account for irregular distributed diaphgrams or no diaphgrams at all. Equivalent force method is actually is the case of Mod 1 of Modal Analysis.

After dynamic analysis or equivalent method, you obtain one base shear force and you distribute vertically to floors with a formula and then you have to apply this force to mass centers with an eccentricity. You need to distribute also in Y direction supposing you calculate earthquake in X direction.

Kind regards,

Sedat
Coordinator
Oct 18, 2014 at 8:04 AM
Hi,
I'll reply on this soon. Have to think about it.

Regards
Jan 1, 2015 at 7:55 AM
Edited Jan 1, 2015 at 8:57 AM
Hi all,

As I know,static equivalent seismic load did not required area element.. only apply at nodes connected by rigid links were it's located at center of mass, additional torque moment apply due to eccentricity with center of mass with center of rigidity.

center of rigidity calculated based on column lateral stiffness in which below floor supported, and center of mass calculated from nodal mass in floor level being considered.

I'm new to BriefFE library, from quick view in featured there's rigid link with master ad slave nodes so I think can do with this library even user need to defined manually for master node position coordinates and additional torque moment due to mass eccetricity.

If BriefFE work as single exe solver with text input data availble, may I can create example and comparision.

Regards,