Theoritical Implementation of Rigid diaphragm

[Eigen]

Hi all,

I'd like to know where can I find documentation on how OpenSEES implements the rigid diaphragm of 3D structures. It's also possible to study it from code but it would be very hard to understand. So your help will be appreciated ?

Best Regards,

[fmk]

RIgidDiaphragm command assumes infinite in-plane stiffness of the floor. The RigidDiaphragm command adds a muiti-point constraint to the model. A a multi-point constraint
simply defines a matrix equation that relates the motion between a set of dof at one node and another node.

If the slab is X-Y plane ( Z being out of plane axis). the constraint equation relating constrained dof (disp X, disp Y, rot Z) at constrained node to retained node is Uc = [1 0 -dY; 0 1 dX; 0 0 1]Ur
where dX and dY are the differences in coorrdinates between retained and constrained node.

How the matrix equation is imposed in the analysis depends on the constraint handler chosen.

[Eigen]

The thing with MPC and master-slave relation is conceivable to some extent. But I find it difficult to understand how the untransferable forces of slave nodes remains at the slave nodes and are eliminated during the Guyan reduction, so are they included in solution of overall linear algebraic system or simply we assume them as zero?
Additionally if assuming the untransferable loads are zero does that imposes any modification on right hand size of local matrix of element?

I also find it difficult to understand the composition of constraint matrix, For example see the attached image.
http://tinypic.com/r/qyzght/6
The given matrix is constraint matrix for first node (End_I) of bracing element which is 6x3 matrix, composing the constraint matrix of other end of element we will get the 12x6 matrix of bracing element. This is the most confusing part for me, I was expecting it to be the 12x12 where I can multiply it directly with local stiffness matrix of element, ready to be inserted into global stiffness assembly. Due to the fact that we try to solve the K*U=F equation locally and globally that means any manipulation on LHS should be done on the RHS also, right?


Your help will be appreciated.

[fmk]

in OpenSees we seperate the definition of the constraint from the implementation. How the constraint is enforced depends on the constraint handler chosen by the user.
The transformations you are describing are performed if you speficy that the transformation method is to be used. if the transformatio method is used, then indeed the element
matrix, K, is modified by T^t K T and the resisting force, R, is modified by T^R before they are added to the system.

[ningxz]

Could nodeReaction get a force from the master node that rigidDiaphragm using?

[fmk]

no .. it gets the displacement from the master, when calculating the reactions all that happens is that all the node takes any forces acting and from each elements framing into the node subtracts their resisting force component