Eccentricity with Rigid Diaphragm and without Rigid Diaphragm

[sonyablade2010]

Dear all,

How Robot is taking into account the calculated seismic forces when the case is with or without rigid diaphragms. ?

1.) with Rigid Diaphragm 

Robot is supposed to apply the calculated seismic loads to rigid diaphragm mass center and with the +-%5 eccentricity of mass center. Can we visually see the calculated seismic loads applied at the rigid diaphragm?

2.) Without  Rigid Diaphragm 

If the building floors are not composed to behave as rigid diaphragm, where is the sense of having +-%5 eccentricity in that case? How Robot implements that if the nodal masses are assumed lumped only translational and there is no rotational masses in each node? The key point here is How Robot is taking the eccentricity in that case?

And again can we visually see the generated seismic acting on nodal masses?

Regards,

[sonyablade2010]

Your help will be appreciated!

Regards,

[Pawel.Pulak]

I will answer in "reverse order" starting from question 2) because it give more clear explanations I suppose.

2.) Without  Rigid Diaphragm

If the building floors are not composed to behave as rigid diaphragm, where is the sense of having +-%5 eccentricity in that case? How Robot implements that if the nodal masses are assumed lumped only translational and there is no rotational masses in each node? The key point here is How Robot is taking the eccentricity in that case?

And again can we visually see the generated seismic acting on nodal masses?

Eccentricity is generally corresponding to inaccuracies of the structure and possible non-uniformity or inaccuracies of loads. It is not directly related to diaphragms. In general case (structure with or without diaphragms) when mass eccentricity is defined in modal analysis using "Add nodal masses" method (the default setting):

• Robot is calculating the position of center of mass (CM) of whole structure or separately for each story if stories are defined
• for nodes with non-zero masses (for all nodes if "Disregard density" is not active) masses on one side of CM are increased while masses on the opposite side of CM are decreased. It is done in such way that the total mass remains constant and only the position of CM changes according to required eccentricity in specific direction. It is done or for whole structure or separately for each story

Above method requires at least 2 nodes with different coordinates along specific direction because the change of CM can be obtained only by increase of mass in one of them and decrease in another. This method does no require rotational masses because eccentricity is obtained by the changes of translation masses

 Seismic forces acting on masses can be seen on View or in tables using pseudostatic forces:

1.) with Rigid Diaphragm

Robot is supposed to apply the calculated seismic loads to rigid diaphragm mass center and with the +-%5 eccentricity of mass center. Can we visually see the calculated seismic loads applied at the rigid diaphragm?

When diaphragm with FE mesh is used its mass is distributed in nodes of FE mesh.

When diaphragm without FE mesh is used its mass is applied to calculation node in CM of the diaphragm - it is both translation and rotation (mass moments of inertia) mass. In case of nodal mass with rotation components these rotation components are considered even if lumped mass without rotations is declared in modal analysis.

When using "Add nodal masses" method to define mass eccentricity for structures containing such diaphragms Robot is not changing CM of diaphragms but only changing their masses together with masses of other components (beams, walls, columns) to obtain desired eccentricity of CM of whole structure or story.

In Robot there is also another method available to define mass eccentricity in modal analysis: "Offset of the mass matrix". When using this method for nodes with non-zero masses appropriate masses are offset (as if virtual rigid links) to obtain required eccenticity of CM. Such offset is used also for calculation node in CM of the diaphragm without FE mesh.

This method requires consistent mass matrix.

It is not set as default method because this type of offsetting can result in additional "unphysical" vibration modes with drilling rotations of nodes not connected to diaphragms or in nodes of diaphragms with FE mesh.

I hope these explanations will be helpful.

[sonyablade2010]

Thanks Pawel for enlightement,

Regarding the 2nd technique 

Is that second technique (2. Without  Rigid Diaphragm) is Robot's proprietary design tecnique in FEM?

Because I have nowhere seen that such a technique can be used in literature by manipulating nodal masses nominal value to get the eccentricity, how that technique is called in literature?

When the values on side is increased, is it done on element basis or you simply manipulate the local/global mass mass matrix inner products ? 

In that case the content of the matrix is important, if it is diagonal it should be very easy to locate the which row/column belongs to which side of eccentricity but if it's comprised from consistent matrix then there will be another hassle.

Regarding the 1st technique 

Offset mass value is a bit tricky IMHO as you depicted, it may mislead an engineer to  the unnphysical frequencies. In that case I'd do the normal modal analysis and  get familiarize with structures natural vibrations.  Then I'll do offset technique and will try to capture the frequency which are around those found in the normal modal anlaysis, the rest simply will be ignored.  Please comment on that , whether it is right or wrong way to follow?

AFAIU, rigid diaphragm without FE Meshing is almost same as 2nd technique only difference is this time you increase the mass of structural objects.

Your help will be appreciated!

Regards,

[Pawel.Pulak]

Regarding the 2nd technique ("Add nodal masses" active)

It is our proprietary technique developed to avoid unphysical modes possible in "Offset of the mass matrix" method.

The idea is based on practical "engineer's" assumption that mass eccentricity means that in one place the structure is heavier than it should be while in another it is lighter than it should be (but keeping the total mass constant).

As concerns details of implementation (on element level  or on node/DOF level of mass matrix) I will give you some info later today.

Regarding the 1st technique ("Offset of the mass matrix" active)

Yes, of course it is better to compare vibration modes found without mass eccentricity and the modes found using this technique to find possible "drilling" ones to eliminate them (or to use the other technique - the default one).

Regards,

[Pawel.Pulak]

Additional explanations.

As concerns details of implementation of "Add nodal masses" method it is done on the element level when assembling mass matrix. So in case of defined stories the mass from elements belonging to various stories is precisely distinguished.

Regards,