T-section for curved beam

  • Thread starter Will
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This question is based on a design project for my intro to machine part design class. We are designing frame that is in the shape of a half-circle, with force being applied at the center, directed toward the center of curvature via pin/hole, and reactive forces at the ends. We decided on a t-section only because our teacher mentioned as a good design choice for loads like this, which cause a lot of bending moment. But we are having trouble explaining why in words.

Should the wider part of the cross section always be along the inner radius? We had trouble optimizing the stress and making the inner and outer bending stresses of similar magnitude(our teacher said this was desirable). The equations of stress for curved cross section have the neutral axis pushed in even further inward than the centroid is already, which would make the ratio of co/ro greater, resulting in more stress due to bending on the outer surface, correct? Or would it be optimal to get the ratio co/ro as close as possible to ci/ri? If so, how would that be done? The math is tricky!

If someone could explain to me why this is a good design choice based on fundamental equations, this would be helpful in our write up about reasons for choosing this cross-section. I aploligize for rambling on, there are just so many dimensions to this problem!

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