Torsion in statically indetermined beam

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The discussion focuses on analyzing torsion in a statically indeterminate beam subjected to a central torque of Mt=10 kNm with a shear modulus G=80 GPa. The key challenge is determining the distribution of torque between the two components of the central cross-section. The approach involves using the relationship T1 + T2 = Mt and the angle of twist, but the participants highlight the importance of considering reactions and symmetry in the problem. Ultimately, the symmetry of the beam suggests that T1 and T2 will be equal, simplifying the calculations.

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Dell
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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

Capture.JPG


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

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