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# Re: SAP, RISA3D, STAAD - Master/Slave Relationships

• To: seaoc(--nospam--at)seaoc.org
• Subject: Re: SAP, RISA3D, STAAD - Master/Slave Relationships
• From: BRBATES <BRBATES(--nospam--at)aol.com>
• Date: Wed, 31 Dec 1997 16:35:57 EST

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In response to Warren Steward:

You state:

>>
The slaved DOF's are  removed (actually folded into) the master DOF's by a
process known as static condensation.
<<

I take this to mean you agree that a "master/slave" relationship means a given
DOF is shared by more than one node, i.e. the slave is assigned the master's
DOF.

>>
Bates seems to imply that a "rigid link" is somehow different than the
"classical master/slave."  It is not.  A truly rigid link in the 3-D
environment merely has all 6 DOF's of the slave node slaved to the
master node.  A diaphragm has 3 of 6, as discussed above.
<<

Yes, in fact they are different.

The difference between a "rigid link" connection between nodes and a
"master/slave" connection is that the rigid link retains independent DOF's for
both nodes, and the master/slave does not. Does this make a difference? You
bet it does.

Here's an example. Imagine a simple table top model, 4 columns with the tops
of the columns linked together via a diaphragm. If we model this top diaphragm
using in-plane master/slave links, this means the four top nodes will share
the same in-plane DOF's. We'll say this is the X- Y plane, so they share the
X,Y and Z Rotation DOF's.

Now, for the solution, a stiffness method program calculates one displacement
per DOF, so the four top nodes will all have the same X,Y and Z rotation
displacements because they all share the same DOF's. Is this right? Nope. If
this diaphragm rotates, the X,Y displacements for each of the nodes will be
different. Only the in-plane rotation is always the same for all the nodes on
the diaphragm.

Another point is the loading. If we apply a force to one of the top slave
nodes, a master/slave link will move that force to the master node because,
again, there is only one DOF and the load vector is formed on a DOF basis. So
if we have a master node in the center and we load one of the corners of the
tabletop, we won't get any rotation (as we should) because the load is moved
to the center of the diaphragm!

The master/slave method will give correct results for a diaphragm so long as
there is no in-plane rotation of the diaphragm (perhaps the case when you were
running SAP?), but it falls apart as soon as the first rotation appears.

>>
The upshot of all this is that the software writers must fully
document what assumptions they are using.
<<

Our documentation is crystal clear as to what assumptions we use.

Bruce Bates
RISA Technologies

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