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If the effective crank length is the same (bb to pedal) and they are made similarly you would need more metal to produce a curved crank.
If you are comparing two cranks with the same weight and length then the staight one would most likely be stronger (this is assuming both are solid cranks or both are similarly made hollow forged cranks).
Arches in buildings are stronger because of how the spread the load into compression in the bricks, a straight lintel bears a lot of the weight in tension (the underside) which is not ideal for concrete etc.
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I'm not an engineer so forgive any mistakes in my use of terminology.
The first thing you need to know about loading on bicycle cranks is that bending isn't your problem. The load you have to resist is torsion about the long axis, caused by the pedal load being a long way off this axis. Once you've solved that, bending is solved too. Making the crank anything other than a straight line connection from the pedal eye to the BB spindle as close to the BB bearing as possible always makes both load cases worse, so you have to use more material to achieve the same rigidity and strength. The best design is a round tube, a conic frustum is simpler to integrate to the differently sized ends than a cylinder but you'd have to dive into the weeds to optimise the termination points.
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dancing james
gbj_tester
@Batman
Ignoring the disproven power advantages of a curved crank, is the shape itself stronger than a straight crank? I'm basing this question on the understanding that arches are stronger than a straight lintel in buildings. However im not sure if the load needs to be applied in the center of the arch for this to be true, as opposed to at the end in the case of a crank i.e. is the force applied at the pedal of the crank arm producing a tensile force across the crank? I'm not an engineer so forgive any mistakes in my use of terminology.
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