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

• greg_rack
In summary, the conversation discusses four thin-walled cross sections loaded in pure torsion, with two different materials (titanium and aluminum) and different shear moduli. The task is to rank the sections from stiffest to least stiff and from strongest to weakest. The conversation also mentions the difficulty in tackling this task without relying on mathematical equations and equations for torque and deflection rate.
greg_rack
Gold Member
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? :)

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.

## 1. What is the purpose of ranking "by eye" bi-material cross sections for strength/stiffness?

The purpose of ranking "by eye" bi-material cross sections is to visually compare and evaluate different cross sections for their strength and stiffness properties. This method is often used in preliminary design stages to quickly identify potential candidates for further analysis.

## 2. How is the ranking "by eye" process conducted?

The ranking "by eye" process involves visually examining the cross sections and comparing their geometric features, such as width, height, and thickness, to determine their potential for strength and stiffness. This can be done by hand or with the aid of software tools.

## 3. What factors should be considered when ranking "by eye" bi-material cross sections?

When ranking "by eye" bi-material cross sections, factors such as material properties, loading conditions, and design constraints should be taken into account. The geometry of the cross section, including its shape and dimensions, should also be considered.

## 4. What are the limitations of ranking "by eye" bi-material cross sections?

One of the main limitations of ranking "by eye" bi-material cross sections is that it is a subjective method and relies heavily on the experience and judgment of the evaluator. It also does not take into account the full complexity of the structural analysis, and may not accurately predict the actual strength and stiffness of the cross sections.

## 5. How can the results of ranking "by eye" bi-material cross sections be used in the design process?

The results of ranking "by eye" bi-material cross sections can be used as a preliminary guide in the design process to narrow down potential cross section options for further analysis. However, it should not be the sole basis for selecting a cross section, and more rigorous analysis should be conducted to ensure the structural integrity of the final design.