Asymmetric beam torsion balance with shear flow

[tracker890 Source h]

Homework Statement

For the asymmetric beam, why the torque of external load to the centroid is different from the torque of internal shear flow to the centroid?
Therefore, please help me to understand why ∑Mc not equal to (∑Mc)_by AA section.
(ref. the link Question version)

Relevant Equations

∑Mc = (∑Mc)_by AA section

∑Mc = P*(b/2)
(∑Mc)_by AA section = (1/2)*F1*b+F2*h-(1/2)*F3*b

Dear Everyone：
Q：
Please help me to understand why the torque of external load to the centroid is different from the torque of internal shear flow to the centroid in the asymmetric beam?
Attached please refer to the following link for more details.
Question version
Original version

Thank you for your time and consideration.

 

[Lnewqban]

For some reason, I can’t clearly see the details of the problem in the link you have provided.
It seems to be a thin shell C-shape beam being loaded over the solid web.

The centroid of the cross section is located at some distance from the shear center.
Twisting moments caused by load and shear may or may not be at balance, according to the point of application of the load respect to the cross section.

These links may help you better than I could:
https://www.ae.msstate.edu/tupas/SA2/chA14.7_text.html

http://www.engineeringcorecourses.com/solidmechanics2/C3-transverse-shear/C3.2-shear-centre/theory/