Classical theories on the strength of solids, based on fracture mechanics or maximum stress, assume a continuum. Even if this robust hypothesis has been demonstrated 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 recently have been formulated and validated by atomistic and quantum-mechanical calculations or nanotensile tests. As an example, we will discuss the implications on the strength prediction for the carbon nanotube-based space elevator's megacable.