Space Platform by Murray Leinster

The world turned over on its axis with unfailing regularity, and nights followed mornings and mornings followed nights according to well-established precedent. One man turned up in Bootstrap with radiation burns, but he had not offered himself for check over at the hospital. He was found dead in his lodging. Since nobody else appeared to have suffered any burns at all, it was assumed that he was the messenger who had brought the radioactive cobalt to Braun, who also had been doomed by possession of the deadly stuff, but who had broken the chain of fatality by not dumping it free into the air of the Shed. Under the circumstances, then, three-shift work on the Platform was resumed, and three times in each twenty-four hours fleets of busses rolled out of Bootstrap carrying men to work in the Shed, and rolled back again loaded with men who had just stopped working there.

Trucks carried materials to the Shed, and swing-up doors opened in the great dome's eastern wall, and the trucks went in and unloaded. Then the trucks went out of the same doors and trundled back for more materials. In the Shed, shining plates of metal swung aloft, and welding torches glittered in the maze of joists and upright pipes that still covered the monster shape. Each day it was a little more nearly complete. In a separate, guarded workshop by a sidewall, the Chief and Haney and Mike the midget labored mightily to accomplish the preposterous. They grew lean and red-eyed from fatigue, and short of temper and ever more fanatical -- and security men moved about in seeming uselessness but never-ceasing vigilance.