The ultrastructure of protein materials such as spider silk, muscle tissue or amyloid fibers in natural adhesives consists primarily of beta-sheets structures, composed of hierarchical assemblies of H-bonds. These H-bond assemblies form the most fundamental interfaces in these protein materials, and therefore control their macroscopic properties. Despite the weakness of H-bond interactions - intermolecular bonds 100 to 1,000 times weaker than those in ceramics or metals - these materials combine exceptional strength, robustness and resilience. We discover that the rupture strength of H-bond assemblies is governed by geometric confinement effects, suggesting that clusters of at most 3-4 H-bonds break concurrently, even under uniform shear loading of a much larger number of H-bonds. This universally valid result leads to an intrinsic strength limitation that suggests that shorter strands with less H-bonds achieve the highest shear strength. We present a quantitative analysis of our predictions with experimental results, illustrating excellent agreement of the predicted strength values with a large range of experimental data. Our results further explain recent experimental proteomics data, suggesting a correlation between the shear strength and the prevalence of beta-strand lengths in biology. We also compare our results with the characteristic dimensions of beta-helical and alpha-helical protein domains and illustrate that similar confinement effects may be the key to explain their characteristic structures. Our hypotheses are confirmed by direct large-scale full-atomistic MD simulation studies of beta-sheet structures in explicit solvent. Our study illustrates how the formation of such hierarchical structures can lead to a manifold increase of the shear strength, while increasing their ability to undergo large deformation, explaining some of the characteristic properties of spider silk. Our study provides new insight into the multi-scale failure mechanisms in biological protein materials, which may eventually enable the de novo design of structural nanomaterials.