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Effective Length Factors for X-Braced Frames

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In response to the question posed by Tarek Mokhtar concerning  the correct effective length factors for x-braced frames:

Several people have given references to theoretical and experimental studies which support the use of  K=0.5.  To this information I would add that these studies mostly deal with buckling out of the plane of the frame; they do not address in-plane buckling or seismic loading.

For frames whose end-gussets are configured to favor in-plane buckling, the brace in tension provides significant rotational stiffness (in addition to the translational stiffness addressed in the studies listed by Ed Marshall and Michael Valley) and an even lower effective length factor is justified (solving a differential equation gives a factor of 0.42).

For seismic design, two additional concerns should be addressed.  First, an upper bound value for buckling strength should be determined, in addition to the lower bound; this is necessary to determine the maximum (compressive) force that connections and adjacent elements will experience.  Second, thought must be given to how cyclic buckling will affect connections: for example, buckling of one brace may cause the other to twist its end gussets severely (especially with torsionally-stiff sections); this may lead to premature fracture.

Rafael Sabelli
DASSE Design, Inc.
33 New Montgomery, Suite 850
San Francisco, California 94105