Concrete 3D-printing, which consists in the layer-by-layer deposition of a concrete filament, results in the formation of a textured surface, the geometry of which highly depends on the printing process. Resulting heterogeneities typically lead to anisotropic behaviour, which is not accounted for in design codes for standard concrete construction. However, explicitly representing the layer geometry in a detailed 3D model is not computationally feasible. In this study, periodic homogenisation is therefore used to determine the anisotropic behaviour of 3D-printed concrete plates and recover the 3D stress state under a given load in the elastic regime. Additionally, unlike traditional cast concrete structures, most printed structures are not reinforced, leading to brittle behaviour and scale effects. While such effects are negligible when using rebars, they pose challenges for unreinforced 3D-printed concrete. A two-scale Weibull model is therefore used to estimate the probability of failure of a shell structure accounting for the layer geometry and inclination, using the stress recovery resulting from homogenisation. A parametric study is conducted considering a wide range of layer aspect ratios and inclinations, assuming uniform and non-uniform material properties across the layer cross-section, showing that the presence of heterogeneities at the surface may significantly reduce stiffness. Additionally, scale effects resulting from the layer dimensions are estimated from the two-scale Weibull model, and a decrease in the mechanical strength of printed structures compared to homogeneous structures is shown in some configurations. The proposed model is therefore a relevant tool for a better estimation of the elastic behaviour and failure load of printed structures given the material stiffness and strength. In doing so, it starts fulfilling the promise of 3D printing: to optimize concrete structures.