buckling strength of bracing with cut and reinforcement

[J1D]

Hi,
I have a situation in calculating bracing strength. The flanges of an existing W8x31 bracing is to be chopped at middle at one side, the cut is 3” deep curved. The disturbed length is about 2ft. The center to center support distance of the bracing is about 12’-6”. With a ½” plate welded to the other side of the cutting along the length, the sectional properties is equivalent to the intact section. Along the chopped length the member is offset 0” to 2.7”+/-, there will be bending moment along the length because of the eccentricity and axial force. Question: How to calculate the bracing strength in this case?
Thanks for comments

 

[J1D]

Nobody ever encountered this? It's like a straight bar with a shallow arc in a short portion.

My thought is the strength (with lateral-torsional buckling) is higher than the strength with the bending moment parabolically distributed to the whole length. The effect is somehow bending-moment length related.

The bending moment is usually very small except for in the bracing with huge axial force.