For a span of time that lasted thousands of heartbeats and spared thousands of lives, the World Trade Center towers withstood the crashes of two jetliners and the flames stoked by their fuel. But eventually, the fires softened the steel structures, and the twin towers collapsed in a terrifying avalanche.
Now engineers think they are closing in on the specific structural failures that, like a few loose stones on a mountain, set off the deadly sequence of events inside the burning, partly smashed buildings. It could all come down to the sagging steel underpinnings of a few floors, which then tore away connections held by pairs of three-quarter- inch bolts and a pattern of welds where the floors were bound to columns.
Exactly which failure began the sequence - which occurred under extraordinary conditions never envisioned in the buildings' design - remains a matter of intense debate. Some analysts hold that too much evidence was destroyed in the collapses to say for certain.
But a leading theory has emerged as teams have sifted through the wreckage, examined photographs and videos and run computer simulations on aspects of the disaster. Many engineers now believe that relatively lightweight steel trusses holding up the reinforced concrete floors sagged in the heat and failed first when the connections that held them to the tightly spaced palisade of steel columns on the outside of the buildings gave way.
Each failure rapidly led to a larger and more serious one until the buildings plummeted with incredible fury, their upper floors striking the ground at an estimated 120 miles per hour.
"The most likely series of events would involve the floor supports," said Jon Magnusson, chairman and chief executive of Skilling Ward Magnusson Barkshire in Seattle, a structural engineering firm involved in the towers' original design.
Mr. Magnusson, who is also a member of a forensic team assembled by the American Society of Civil Engineers to determine the causes of the collapses, said attention had focused on the connections, around the outside of the floors. "If a member like that failed in a fire, that could mean the whole floor could go," he said.
The initial failures, in the impact zones between Floors 94 and 99 in the north tower and Floors 78 and 84 in the south, would not have directly caused the collapses, the engineers say. Rather, as the first floor to go fell and took out one or two more, the tightly spaced steel columns within the aluminum facade, themselves weakened by the fire, would have had no lateral support.
"Then all of a sudden your skin becomes detached and it becomes like a piece of paper," said William F. Baker, a partner in charge of structural engineering at the architectural firm Skidmore, Owings & Merrill, who is also part of the American Society of Civil Engineers team.
The exterior columns, or skin, could then have buckled under the tremendous weight above them, said Mr. Baker, who noted that the team had not reached a consensus and that its conclusions could change.
But Eduardo A. Kausel, a professor of civil and environmental engineering at the Massachusetts Institute of Technology, believes that the avalanche theory is correct. Once the columns on those few floors buckled, he said, the rest of the columns had no chance of stopping the collapse.
"They simply popped out of the way of the avalanche like matchsticks," Dr. Kausel said. "The collapse front accelerates as it progresses downward." Computer simulations reveal that after the first buckling, the upper floors probably reached the ground almost as quickly as a rock dropped from the same height would have, he said.
The studies also show that the surviving columns redistributed their load after the initial impacts, saving thousands of lives by preventing an immediate collapse. The studies may also explain why the south tower, struck second, fell first.
In describing their structural autopsy, the engineers strike a delicate balance. No building could be expected to survive such an onslaught, they say, and the trade towers performed admirably. But it is possible that skyscrapers with a different structure would not have ultimately collapsed, and the engineers say it is essential to understand what happened and why. That knowledge, Mr. Baker said, could help reduce the likelihood of future collapses, with all the human devastation and political upheaval they imply.
"It's important that we understand how these buildings behaved," he said, "because we don't have much other evidence of similar collapses that are useful for the industry to learn."
The structural ideas that guided the twin towers' design, considered innovative in the 1960's, became popular in the 70's and 80's before high- rise engineers turned to newer concepts, said William Faschan, a partner at Leslie E. Robertson Associates in Manhattan, one of the principal engineering firms that created the trade center's design.
"At the time of the World Trade towers," which were completed in the early 1970's, Mr. Faschan said, "tall buildings meant steel."
So rather than the combination of concrete and steel structural members common today, he said, the towers would be held up by beams, columns, plates and trusses of pure steel. But the twin towers and other structures like them were set apart by a design that divided the load between the tightly spaced columns around the outside of the building and a smaller core of heavier beams at the center.
Seen from above, the 110-story twin towers were approximately squares, 209 feet on a side, with 59 columns on each face. The core, containing the elevators, stairwells and mechanical equipment, consisted of a rectangular arrangement of 47 heavier columns. The core columns carried about 60 percent and the exterior columns 40 percent of the towers' weight, which totaled 276,000 tons each above the plaza level.
But the exterior columns, 14 inches square in cross section, had another function that proved crucial.
The columns gave the towers enough stiffness to withstand hurricane-force winds of greater than 100 m.p.h. During the buildings' construction, the columns were assembled in modular fashion by stacking triplets of 36-foot-long sections held together by steel plates, or spandrels.
When a hijacked Boeing
Those structures played another lifesaving role as the jets, 156 feet from wingtip to wingtip, each tore out about 35 exterior columns before plunging inside. Because of their close spacing and tight connections, the surviving columns on each damaged face instantly formed a kind of arch - the technical term is a Vierendeel truss - over the holes and prevented an immediate collapse.
"It's fair to say that the close spacing of the exterior columns was one of the key elements that allowed those buildings to remain standing," Mr. Faschan said.
The aluminum wings and the planes' fuselage would have been almost instantly shredded into pieces the size of an adult's fist, said Tomasz Wierzbicki, director of the impact and crashworthiness laboratory at M.I.T. Engines and other heavy parts continued to the core, but by working out the amount of energy involved, Dr. Wierzbicki and a student, Liang Xue, determined that at most half the inner columns could have been broken or severely mangled.
The buildings stood. Then the fires broke out.
Under terrific loads, said John D. Osteraas, director of civil engineering practice at Exponent Failure Analysis Associates in Menlo Park, Calif., steel columns have much in common with a wooden yardstick or an uncooked spaghetti noodle: only with lateral support can they hold up much weight.
"If you brace it so it can't buckle, it can carry quite a bit of load," Mr. Osteraas said.
So the exterior columns, for example, were braced laterally by their connections to the floor trusses themselves. The trusses, made largely of lightweight, zigzagging webs of steel rod a little over an inch in diameter, held up a steel deck covered with four or five inches of reinforced-concrete flooring.
The trusses were welded to pieces of angle iron, or light steel beams with an L-shaped cross section, which were in turn fastened with pairs of three-quarter-inch bolts to a small plate jutting from the exterior columns.
The jets would have knocked loose large amounts of fireproofing that had been sprayed in thick layers on all of the steel in the building, said Mr. Osteraas, who has examined the debris at ground zero.
Even more important, jet fuel, about 10,000 gallons per plane, spilled and immediately began burning at much higher temperatures than those of ordinary office fires. At the center of the impact zone, the temperature would have "jumped exponentially," said Yogesh Jaluria, a professor of mechanical and aerospace engineering at Rutgers.
Steel begins losing much of its strength at roughly 1,100 degrees Fahrenheit, Dr. Jaluria said. Some places inside the buildings probably shot above 2,000 degrees within seconds, he said. In minutes, that heat would be spread by rising air and flames and by conduction through the steel itself, he said.
Engineers are still not sure whether the hot fires or the lack of fireproofing posed the greatest danger. Either way, the light steel of the trusses heated up first, and in the next 20 or 30 minutes, the floors began to sag between the interior and exterior columns.
Because they were not designed to withstand that kind of force, the links of the trusses to the columns may have been the first to go, Mr. Osteraas said.
"Those bolts were essentially the weak link in the system," Mr. Osteraas said. "In engineering terms, we refer to something like that as a mechanical fuse."
Once begun, the avalanche took only seconds. If one floor fell and tore out at least part of another, it would mean that many exterior columns, themselves hot and weakened, were suddenly without lateral bracing for 36 feet or more. (The columns in the core had a separate set of heavier side braces.)
The columns then buckled under the colossal weight above them and the avalanche reached its horrible conclusion.
While that is the leading theory, other engineers are pushing the idea that the columns in the center, where the fires may have been hottest, lost their strength and buckled first.
"I don't disagree that the floors must have collapsed at some point," said Matthys Levy, a founding partner at Weidlinger Associates, who has written a new chapter on the core-collapse theory for his 1992 book, "Why Buildings Fall Down," and plans to release a new edition in January. "I don't think that's enough to cause the buildings to go down."
But however that debate resolves itself, most engineers seem to agree that damage to the core was probably a factor in why the south tower collapsed more quickly than the north.
That seems to be because the second plane rammed the south tower well to the right of its center line, in such a way that the wreckage struck a shorter side of the rectangular core. The first plane hit near the center of one long side.
That means that any piece of debris from the second plane could take out as many as eight interior columns in a row, perhaps greatly weakening the east side of that core and making that tower more susceptible to a collapse.
The south tower, its top listing noticeably to the southeast, fell at 9:59 a.m.; the north tower followed at 10:28 a.m.
Workers have been removing debris and human remains from the site ever since.