Classical theories of the strength of solids, such as fracture mechanics or those based on the maximum stress, assume a continuum. Even if such a continuum hypothesis can be shown to work at the nanoscale for elastic calculations, it has to be revised for computing the strength of nanostructures or nanostructured materials. Accordingly, quantized strength theories have recently been developed and validated by atomistic and quantum-mechanical calculations or nanotensile tests. As an example, the implications for the predicted strength, today erroneously formulated, of a carbon-nanotube-based space elevator megacable are discussed. In particular, the first ab initio statistical prediction for megacable strength is derived here. Our findings suggest that a megacable would have a strength lower than ≈45 GPa.