Ranking "by eye" bi-material cross sections for strength/stiffness

AI Thread Summary
The discussion revolves around ranking four thin-walled cross sections made of titanium and aluminum under pure torsion based on stiffness and strength. Participants are encouraged to provide reasoning for their rankings rather than numerical values, emphasizing a qualitative approach. The conversation highlights the importance of understanding material properties, specifically the shear modulus, and how they relate to torsional stiffness. Additionally, the analysis suggests using concepts like torque superposition and compatibility equations to derive individual contributions to the overall behavior of the cross sections. The thread ultimately seeks insights into the thought processes behind evaluating bi-material strips in torsional loading scenarios.
greg_rack
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Howdy guys,
Say we have been given the four thin-walled cross sections below loaded in pure torsion, where the material in black, titanium, has E=100GPa and the one grey one, aluminum, E=75GPa(no clue why Es are given, as I would have expected the shear modulus, G... maybe it is expected to use the equation G=##f(v, E)## to derive the latter).
But anyways, the point now would be to rank by eye each one of them once from the stiffest to the less stiff cross section, and then from the strongest to the weakest.
As the "by eye" might have led you to think, a reasoning is expected in place of numbers/ratios(or a maybe a more wordy version of the latter) to justify the resulting ranking.

Therefore, I would be curious to see how you guys would reason such an exercise and see the thought process behind a reasonable ranking. For the bi-material strips specifically, I really wouldn't know how to tackle this without relying on the bookkeeping process of:
-torques superposition, ##T=T_1+T_2##;
-compatibility equation for the deflection rate to be equal in both parts of the cs, ##\frac{d\theta}{dz}=\frac{3T_1}{G_1s_1t^3}=\frac{3T_2}{G_2s_2t^3}##
-solving for the individual torques and then computing the individuals ##\tau_{max}## and ##\frac{d\theta}{dz}##
Any ideas? :)

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A search using terms torsion thin wall open sections brought back memories of strength of materials class where this class of sections was analyzed. These sections are analyzed as the sum of three separate flat bars. The torsional stiffness of each bar is proportional to the shear modulus. This assumes that the sections are loaded only in torsion, and the ends are not restrained against warping.
 
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