Bending Stiffness of Twisted Beams

Hello!

I was looking to analytically obtain the local bending stiffness of a uniform selender beam which has been twisted along the longitudinal axis (please note that the beam is not 'pre-twisted', i.e, it not twisted in its unstressed state). The exact problem statement is written below. I would be extremely grateful if I can get directions on how to approach the problem or references where such a problem is addressed. Thank you very much!

Problem statement:

A uniform slender beam of rectangular cross-section is clamped at one end and twisted by applying a longitudinal moment at the free end. The resulting total twist at the free end is 'alpha'.  'Alpha' is not small ( it can be in the range 30-90deg. ) but the twist per unit-length of the beam can be assumed to be small (i.e, the strain is not large). How do we derive the local bending stiffness of the beam in this configuration? I.e., if small concentrated forces are applied at the end of the beam normal to the longitudinal axis when it is twisted, what is the resulting local displacement of the beam?

Sincerely,

Jayanth