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Case 2: Fixed Radius, R
Fixed size tubing is commonest for the traditional market of road bicycles. Minimum weight is still important for many users, but cost may dominate for others (considered below). The same constraints are imposed as before: adequate stiffness, and resistance to fatigue failure.
For this case, the relevant performance indices for minimum weight, for bending of tubes of fixed radius (variable thickness) are:
Note that these are the same as for tension, but here they also apply to bending, with the appropriate geometric constraint.
These indices are plotted against one another in the chart below. As before, the best materials are towards the top right hand corner and ceramics are excluded, on account of their brittleness and unsuitability for bicycles; frame materials are highlighted with blue labels.
With this change in geometric constraint, all the metals compete closely on stiffness; Ti and Mg alloys are better for fatigue than steels, Al alloys and Al-SiC MMC.