Beyond unicellular and multicellular organisms, there is a third type of structural complexity in living animals: that of the mechanical self-assembly of groups of distinct multicellular organisms into dynamical, functional structures. One of the most striking examples of such structures is the army ant bivouac, a nest which self-assembles solely from the interconnected bodies of hundreds of thousands of individuals. These bivouacs are difficult to study because they rapidly disassemble when disturbed, and hence little is known about the structure and rules that individuals follow during their formation. Here we use a custom-built Computed Tomography scanner to investigate the details of the internal structure and growth process of army ant bivouacs. We show that bivouacs are heterogeneous structures, which throughout their growth maintain a thick shell surrounding a less dense interior that contains empty spaces akin to nest chambers. We find that ants within the bivouac do not carry more than approximately eight times their weight regardless of the size of the structure or their position within it. This observation suggests that bivouac size is not limited by physical constraints of the ants' morphology. This study brings us closer to understanding the rules used by individuals to govern the formation of these exceptional superorganismal structures, and provides insight into how to create engineered self-assembling systems with, for instance, swarms of robots or active matter.