Questions about the SMF modeling

[Ya-HengYang]

Hello Prof. Elkady,

I have two questions about the SMF model in this repository:
(1) In the Spring_IMK.tcl (line 89), why do we need to correct rotations to account for elastic deformations?

set theta_y [expr $My/(6 * $E * $Ix / $L)];
set theta_p [expr $theta_p - ($McMyP-1.0)*$My/(6 * $E * $Ix / $L)];
set theta_pc [expr $theta_pc + $theta_y + ($McMyP-1.0)*$My/(6 * $E * $Ix / $L)];

If we follow the notation in the Appendix B of Ibarra (2005), does that imply that the response parameter (e.g., $\theta_p$) obtained from the regression equation (lines 78 & 79) actually corresponds to $\theta_{p,mem}$ instead of $\theta_{p,spring}$? If so, then it's necessary to eliminate the elastic beam-column term $\theta_{bc}$ to ensure that the sub-elements are connected in series and have the correct assembled member parameters. However, if it is the case, should we use (n+1)/n *6 * $E * $Ix / $L instead of 6 * $E * $Ix / $L for $K_{bc}$?

(2) In SMF4B.tcl (line545), what is the reason or reference for defining gravity frame element damping using $a1_mod/10?

region 3 -eleRange 900000 999999 -rayleigh 0.0 0.0 [expr $a1_mod/10] 0.0;

Thank you!
Best, YHY