The minimum weight problem of a shallow circular beam is studied in th
e case when the beam has a piece-wise constant thickness. The minimum
of the weight is sought under the condition that the deflections of th
e beam of piece-wise constant thickness do not exceed those of the ref
erence beam of constant thickness for given values of the external loa
ding. The beam is subjected to uniformly distributed transverse pressu
re and to axial dead load. The material of the beam is assumed to be i
deally rigid-plastic. Moderately large deflections are taken into acco
unt. Necessary optimality conditions are derived and used in order to
establish the optimal values of the design parameters.