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Steel truss in cantilever

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I'm working on the design of the roof of an amphitheater stage consisting of 62' long steel trusses supported on two columns 25' apart, so the trusses project in cantilever 37'. Two conditions will be investigated:
1.- The structure at service, using the code load combinations and assuming the cantilever bottom chord is laterally braced @ 9'-0"
2.- During installation, using the truss self-weight only and assuming the cantilever bottom chord is not laterally supported.
The second condition will control the size of the cantilever bottom chord. The question is: What is the appropriate k-value for this compression member? If the load was applied as a concentrated force at the end of the cantilever k would be about 2, but in fact the load linearly increases from zero at the end to a maximum value at the support, and therefore k=2 seems conservative. Could anybody please comment on this issue? Regards,
Javier Encinas
Encinas & Associates