The work described in the paper complements previous work concerned with the investigation of the causes of size effects in structural-concrete members. It is based on the use of a finite-element model found to yield realistic predictions of structural-concrete behaviour in all cases investigated to date. In fact, the previous use of this model in investigations of size effects in reinforced-concrete beams with a shear span-to-depth ratio larger than 2 indicated that such effects reflect the dependence of load-carrying capacity on small unintended eccentricities of the applied load and/or load-induced anisotropy, rather than, as widely considered, on fracture-mechanics characteristics. The present work extends the scope of the above investigation so as to include the case of beams with a shear span-to-depth ratio smaller than 1.15, the behaviour of which is already established experimentally. It is found that, unlike the beams with a shear span-to-depth ratio larger than 2, the beams investigated in the present work, in contrast with the interpretation given to recently published experimental findings, are size-effect independent.