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I can't understand what why they don't put Reaction momentum of torsional spring in FBD of whole system at B in instability analysis of column
You would be right, even though the effect of moment $K_r \alpha$ at hinge C and A is zero, but there is shear due to this moment that should be added to A and C
$$V_a=V_c= \frac {K_r\alpha}{2l}$$
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