Torsion in statically indetermined beam

[Dell]

the beam below is subjected to a single torque of Mt=10KNm at its centre, G=80GPa

find the distribution of the torque between the 2 components of the central cross section

what i have done in similar questions (where i have had one free end) i have chosen T1 and T2 - the relative torque in each of the components and solved using dϕ/dx,- using the fact that the angle of twist from x=1m to x=0.8m must be the same for both components i could solve for T1 and T2 because in all the cases i have solved i knoew that T1+T2=Mt,
in this question i am not sure this is the case since Mt is not the internal Torque in this cross section,

 

[pongo38]

Have you considered the reactions, and the observation that the problem has symmetry?

 

[Mene]

i am not sure how to find the internal torque in this case

I would first clarify the question by asking for more information about the beam, such as its dimensions and boundary conditions, in order to accurately determine the distribution of the torque between the two components of the central cross section.

However, based on the given information, it seems that the beam is statically indeterminate and the torque is applied at the center of the beam. In this case, it is not possible to determine the internal torque in the central cross section without knowing the boundary conditions and the dimensions of the beam.

If we assume that the beam is simply supported at both ends and has a constant cross-sectional area, we can use the compatibility equation for torsion to solve for the distribution of torque between the two components. This equation states that the total twist in a beam is equal to the sum of the twist in each component.

Therefore, we can set up two equations using the compatibility equation at x = 0.8m and x = 1m, and solve for the two unknown torques, T1 and T2. This would give us the distribution of the torque between the two components of the central cross section.

However, if the boundary conditions or dimensions of the beam are different, the approach to solving for the distribution of torque would also be different. I would recommend further clarification and information to accurately determine the internal torque in the central cross section.