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

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More on the arcane subject of master/slave relationships in structural 
analysis programs.  Bruce Bates seems to have the best grasp of the 
subject when he states "Classically, a "master/slave" relationship 
involves two or more joints sharing one or more degrees of freedom 
(DOF)," but IMHO seems to miss the point on diaphragms.  In a 3-D 
environment (6 DOF at each node), a diaphragm is merely the invocation 
of the master/slave relationship for the in-plane DOF's (say x, y and 
rotation about z).  The remaining DOF's at each "slave" node (z, and 
rotations about x and y) remain independent.  The slaved DOF's are 
removed (actually folded into) the master DOF's by a process known as 
static condensation.

Probably the best known program that uses this process for the 
creation of diaphragms is the ETABS program and its forerunner TABS 
(developed at Berkeley in the early 60's by Clough, King & Wilson). 
 The early SAP programs (also originally developed at Berkeley) 
allowed slaving of nodes to masters on a DOF-by-DOF basis.

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. 
 Master/slave relationships can be used to model concrete beam/column 
finite rigid joints.

Many years ago I used SAP IV (running on an IBM 370) to model both 
rigid joints and diaphragms together in a cascading series of 
master/slave relationships (i.e., the z, xx and yy DOF's of node 
representing the column face was slaved to the node representing the 
centerline of the column.  At the same time the x, y and zz DOF's of 
the column centerline node were slaved to the master diaphragm node. 
 Interestingly, the SAP IV manual implied you couldn't do this, but it 
worked anyway).

The upshot of all this is that the software writers must fully 
document what assumptions they are using.  Terms like "classical 
master/slave" can be misleading.  Your "classical" (circa 1997) may 
not fit my definition (circa 1974).  About 7or 8 years ago I tried 
using STAAD (version ???) to model a diaphragm using their obviously 
predefined "master/slave" relationship.  The STAAD output showed the 
slave x, y and zz displacements matching exactly the master's.  This 
of course is not correct for a diaphragm, as the master zz rotation 
adds/subtracts to the x and y displacements of the slave (assuming the 
slave is some distance from the master. If the slave is concurrent 
with the master, as in Bates' X-bracing example, then the rigid body 
rotation is not coupled with the translation displacements).  When I 
pointed this out to STAAD, their response was that I was wrong and 
their formulation was correct.  This was the last time I used STAAD.

Warren Stewart, SE
Frederic R. Harris, Inc
San Pedro, CA

>----------------------------------------------------------------------  
----
>To: seaoc(--nospam--at)seaoc.org
>Subject: Re: SAP, RISA3D, STAAD
>
>Greg,
>
>To elaborate further on torsional warping, you're right that a 
typical moment
>connection will not fully develop warping restraint, but a moment 
connection
>....
>....
>....
>Regarding master/slave and rigid diaphragms, let me address this in a 
more
>general sense (rather than in a "program specific" sense). 
Classically, a
>"master/slave" relationship involves two or more joints sharing one 
or more
>degrees of freedom (DOF). A typical application for this is in 
modeling X
>bracing where the braces are pinned at their crossing point. They 
would share
>the same translational DOF at that point, but be released from each 
other for
>rotation. To model this, two nodes representing the midpoints of the 
two
>braces would be slaved to each other for translations, but not for 
rotations.
>
>Rigid diaphragms must be modeled using rigid links rather than 
master/slaves
>in order to maintain translation consistency. Granted all the nodes 
on the
>diaphragm should, in a strict sense, have the same inplane rotation, 
their
>global translations will not be numerically equal. This a brief and 
incomplete
>answer to your question, I know, but for more on this, I recommend 
you review
>the section "Diaphgrams" in the RISA-3D user's guide (anyone else who 
is
>interested and doesn't have access to the RISA-3D manual can email 
me
>PRIVATELY and I will fax this to you).
>
>Regarding STAAD specifically, the last time I used that program they 
modeled
>master/slave in the classical sense.
>
>Bruce Bates
>RISA Technologies