Shape factors and material indices have been recently developed for the opt
imal design of load-bearing beams and shafts. These shape factors and mater
ial indices are generally only applicable where there are no dimensional co
nstraints. However, dimensional constraints are very common in mechanical d
esign because of the integrated nature of modern machinery and equipment. T
his paper extends the methodology of a previous paper by Ashby by developin
g the shape factors and material indices for the case of constrained diamet
er in shafts. The paper also shows that dimensional constraints can have a
very significant effect on the optimal selection of material and shape.