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

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I agree with Warren's point that master/slave, diaphragm and
rigid link are all synonymous mathematically. The displacements,
actions and stiffness matrices corresponding to slave DOF's are
transferred to master DOF's by the following relations :

(See section 16-7 of "Structural Analysis" by Ghali & Neville)

                    {q} =  [C].{D}
                    {F} =  transpose [C] . {Q)
                    [Sm] = transpose [C] . [Ss] . [C]
where

{q}  = displacements at slave DOF's
{D}  = displacements at master DOF's
{Q}  = actions at slave DOF's
{F}  = equivalent actions at master DOF's
[Ss] = stiffness matrix at slave DOF's
[Sm] = stiffness matrix at master DOF's

       | 1  0 -y |
[C]  = | 0  1  x |
       | 0  0  1 |

x,y  =  co-ordinates of slave node with origin at master node

I have verified that the master/slave method when applied in
this fashion gives correct results for translations *and*
in-plane rotations.

Incidentally, static condensation is a process of folding
(usually) internal DOF's into external DOF's of an element. This
process is not applicable to master/slave DOF's.

Rudra Nevatia
Central Computing Facility