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RE: Partial Rigidity (was ALGOR, EAGLE, ETABS, STAAD etc.)

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> ----------
> From: 	YHHuang(--nospam--at)aol.com[SMTP:YHHuang(--nospam--at)aol.com]
> Reply To: 	seaoc(--nospam--at)seaoc.org
> Sent: 	Monday, June 08, 1998 1:39 AM
> To: 	seaoc(--nospam--at)seaoc.org
> Subject: 	Re: Partial Rigidity (was ALGOR, EAGLE, ETABS, STAAD
> etc.)
> 
> I have to admit that I need more help from you.  You can certainly
> have more
> freedom to assume whatever value you wish to release in your model and
> analyses.  But, what I don't know is how can I select values that are
> good and
> realistic value?  How do I judge if the results are accurate?  Is
> there a good
> source for this information?
> 
> Thanks!
> 
> Y. Henry Haung
> 
> 
(1) How to select a value for connection?

This may be determined by the "purpose of members" or by the "member and
connector strength". First, let us consider a structure, for example,
having X- and Z- direction lateral forces. There is a secondary
component (substructure, i.e., or a diaphragm)  that is designed to
resist X lateral forces only, but not for Z lateral forces. In this
situation, reduce the connection rigidity for Z- direction lateral
forces to a small value (i.e., 1%, ***0% is not so good for numerical
procedure***), and keep the connection rigidity for X-direction lateral
forces in full strength. The joints do not transmit the Z-direction
lateral forces into the secondary component.

Secondly, let us consider the member and connector strength. Keeping the
connection rigidity in the full value means the connector is designed to
absorb more energy. Reducing the connection rigidity may release the
connector burden, and the extra energy may be re-distributed to
member(s). It is inappropriate to define the full rigidity for a weak
connector. If the member is stronger than the connector, properly
reducing the connection rigidity is possible. A decision on a proper
value can be made by examining which component (member or connector) has
a potential to absorb more energy. However, a decision by the component
purpose is more important.



(3) How to verify if the results are accurate?


Any analysis must satisfy the equilibrium and compatibility conditions.
Certainly, formulating partial-rigid analysis must follow the same
requirement.

The accuracy of a partial-rigid analysis can be verified by checking
equilibrium, compatibility, and eigen-solution. Computer output contains
nodal displacements, internal forces, and mode shapes with eigenvalues.

(a) At each joint, check the equilibrium of external forces (if
applied), reaction (if a support) and internal forces.

(b) On each member, check the equilibrium of external member forces (if
applied) and internal forces.

(c) On each member, use the displacement_1 (analysis output at node 1),
external member forces (if applied), and internal forces (analysis
output) to calculate the displacement_check at node 2. And, compare
displacement_check and displacement_2 (analysis output).  The difference
must be close to zero. --> "Compatibility Test"

(d) For each mode, calculate the relative error "( {X}^T[K]{X}-[lambda]
) / [lambda]" where {X} is eigenvector, normalized with respect to
[mass]



Or, you can verify a partial-rigid analysis by the following procedure.
Use a well-known program to start an analysis with full-strength
connections. Then, select some members, and adjust the connection
rigidity to 99%, and have a partial-rigid analysis. Those results should
be close. Then, try 98%, 97%,....., and 50%,,,. The results should
gradually change. Partial-rigid connections can apply to static and
dynamic analyses. I also apply partial-rigid connections to effective
length analysis. 



J. Luo
Luo(--nospam--at)Equation.com