To catch up, here are links for part 1, part 2, and part 3.
The Brooklyn Bridge caissons were much bigger than the similar pneumatic caissons that had been used earlier. Their timber construction was based on a few ideas, all subject to engineering design or review. First, the roof had to be strong enough to carry the weight of the partially-completed tower during the sinking process. That was obviously a matter of structural design, and so relatively simple.
Second, the caisson had to be able to carry the weight of the tower and the load from the cables (in other words, half of the dead and live load of the main span and half the dead and live load of one of the side spans) when complete. After the caissons reached the final bottom elevation, they were filled solid with a combination of masonry and unreinforced concrete. The filling meant that the caisson roof was no longer spanning, although the timbers still had to be strong enough to transmit the full load without crushing. Again, this was a matter for reasonably normal structural deisgn.
Third, and perhaps most importantly, the wood had to be stable, in a material sense, indefinitely. Most experience with submerged wood structure at that time concerned the piles used to create piers and wharfs, which showed that various treatments (creosote was popular) would stop rot fungi from attacking the wood. Those treatments did not stop marine borers, small worms that eat wood, but their habitat was found to be from the river bottom to low tide elevation. In other words, the borers like to be where it is always wet. Since the caisson roofs would be entirely below the river bottom when in their final positions, Washington Roebling made the judgement call that the wood be safe from attack, and the empirical evidence is that he was entirely correct.
The other problem with wood is that it is flammable, and the work was taking place well before incandescent electric light was available. In other words, the interiors of these two wood boxes full of pressurized air were lit by flame. To make matters worse, the joints between timbers were caulked with oakum for waterproofing, as would be the joints in any wooden-hull ship. There was a major fire in the Brooklyn caisson in December 1870, that damaged the roof when the caisson was almost down to its final elevation. The damage was repaired and the New York caisson, still under construction, was given an iron lining to prevent a similar occurrence.
Above, the roof of one of the caissons while under construction in the shipyard.
