Matthys P. Levy



Study Absolves Twin Tower Trusses, Fireproofing 11/04/02

By Nadine M. Post

The most comprehensive study yet on the destruction of the World Trade Center concludes that columns robbed of fireproofing failed first--not floor trusses--when the twin 110-story towers collapsed after being hit by terrorist plane attacks on Sept. 11, 2001. The proof is in the smoke that emanated from the burning towers before the collapses.

"There is no doubt left about the sequence of failure," says Matthys P. Levy, chairman of Weidlinger Associates Inc., the New York City-based engineer that led the study.

"Failure of the floors...was shown not to have had any significant role in the initiation of the collapses," says the report. Levy describes the floor truss system as "not unsubstantial," acting more like a membrane than a one-way system. "There was nothing wrong with it," he says. If the floor trusses had collapsed first, there would have been a mass of smoke as opposed to differentiated smoke, floor by floor, he adds.

HITS Planes caused different damage (Graphics courtesy of Weidlinger Associates Inc.)

The report also exonerates the steel's sprayed-on fireproofing. Computer models that identify the columns affected by the planes' impacts and flying debris confirm that columns with intact fireproofing did not succumb to the jet- fuel-triggered fire. The report also says, of the fireproofing knocked off the steel, that "no fireproofing is designed to withstand such devastating impacts."

Levy echoes preliminary reports. "The buildings were well-designed, rugged and withstood a tremendous impact," he says. "The fact that they did not collapse on the planes' impacts saved tens of thousands of lives."

SMOKE PROOF Engineers say smoke patterns are evidence that columns failed first, not floors. (Photo by Tom Sawyer for ENR)

Questions brought into the limelight by Sept. 11 include whether there is a better way to fight fires in tall buildings, says the engineer. "It's always been a problem," says Levy.

Another issue is whether less-frangible fireproofing should be considered for steel structures considered vulnerable to blasts and attacks. Experts might also reconsider location of fire stairs and the strengthening of the core, says Levy. But he cautions, "You can never anticipate exactly what the threat is going to be."

Regarding building materials, Levy says: "Concrete is not foolproof either."

The Weidlinger-led study was commissioned by Silverstein Properties Inc., the New York City-based leaseholder of the World Trade Center, to help support a $7-billion insurance claim. The research team also included LZA Technology/Thornton-Tomasetti Group; ARUPFire; Hughes Associates Inc.; SafirRosetti; Hillman Environmental Group; RWDI; W. Gene Corley, who led the ASCE-FEMA WTC study; Professor Sean Ahearn; and Z-Axis Corp.

Silverstein's insurers claim the collapse of the south tower, Two WTC, rendered the north tower, One WTC, unsalvageable even before it collapsed. If they prevail, Silverstein would receive only $3.5 billion (ENR 10/7 p. 11). Click here to view one WTC collapse sequence

The insurers commissioned their own engineering study, written by Exponent Failure Analysis Associates Inc., Los Angeles. Also released, the report disagrees with the Weidlinger findings, but mostly on points relating to the insurance battle. Engineers from Wiss, Janney, Elstner and Associates Inc., Northbrook, Ill., also working for the insurers, would not comment on their work.

In the Silverstein study, engineers put forth similar but not exact failure scenarios for both towers: The planes and flying debris hobbled the buildings at the zones of impact. Intact columns, their fireproofing knocked off by flying debris, ultimately lost strength and failed in the fuel-triggered fire.

Though hit by the second plane later than One WTC, Two WTC fell first, "primarily" because the plane struck it off-center and at an angle and caused damage that compromised the southeast corner of the core. "This confirms an earlier theory," says Levy. Click here to view two WTC collapse sequence

At each tower, exterior wall and core columns, connected by a steel "hat truss" at the building's top, initially redistributed loads away from the damaged areas to remaining columns. In Two WTC, the hat truss eventually could not deal with the situation of the corner columns gone, says Levy.

The team determined that the initial hits destroyed 33 of 59 perimeter columns in the north face of One WTC and 29 of 59 perimeter columns in the south face of Two WTC. Computer analysis showed that the impact of the planes also destroyed or disabled some 20 of 47 columns in the center of the core of One WTC and some five of 47 columns in the southeast corner of the core of Two WTC.

The Silverstein findings are based on analysis of original structural drawings, thousands of photos and dozens of videos. The team used computer modeling, including a program called FLEX developed by Weidlinger for the Dept. of Defense, and fire evaluation techniques to simulate the condition of each tower at critical times, creating impact and collapse sequences.

The National Institute of Standards and Technology, which recently began a two-year technical study on the World Trade Center disaster, is using both team's studies to perform a "very systematic" analysis, says S. Shyam Sunder, chief of NIST's materials and construction research division, Gaithersburg, Md. "The real question is whether there was one dominant failure mechanism or a combination," he adds.

Silverstein Report

Report Ties WTC Collapses to Column Failures - 10/25/02

By Nadine Post

The collapses of the 110-story twin towers of the World Trade Center after terrorists slammed hijacked planes into them were separately initiated in the impact zone of each tower due to failure of the columns, says a recent engineering report, not the floor trusses. Two WTC, though hit by the second hijacked plane after One WTC, fell first "primarily" because the plane struck it at an off-center angle and caused damage that compromised the corner of the core of the building, concludes the report's authors, a team of engineers from several firms working for Silverstein Properties Inc., the New York City-based leaseholder of the World Trade Center.

The findings are based on analysis of original structural drawings, thousands of photos and dozens of videos, says Silverstein. The team used computer modeling, some programs developed for the Dept. of Defense, and fire evaluation techniques to simulate the condition of each tower at critical points from impact to collapse.
Click here to view diagram 1 Click here to view diagram 2

The team determined that the initial hits destroyed 33 of 59 perimeter columns in the north face of One WTC and 29 of 59 perimeter columns in the south face of Two WTC. Computer analysis showed that the impact of the planes also destroyed or disabled some 20 of 47 columns in the center of the core of One WTC and some five of 47 columns in the southeast corner of the core of Two WTC. The crashes stripped fireproofing from columns in the path of debris created by the planes penetrating the buildings, it continues.

One frame from the computer model of the initiation of the collapse of Tower 2 performed by Weidlinger Associates

The team says the towers' columns of the redundant exterior tube and core columns, connected by a steel "hat truss" at the top of the buildings, redistributed loads away from the damaged areas to remaining columns. This allowed the towers to stand as long as they did, says the report. In a release, Matthys Levy of Weidlinger Associates Inc., one of the engineers on the study team, states, "The fact that tower one stood for 103 minutes.... and tower two for 56 minutes" after the loss of so many columns, "is a testament to the strength of the buildings and the skill of Leslie Robertson and the other engineers who designed them. I believe that few, if any, other buildings could suffer that amount of damage and not collapse immediately."

The computer models, says the report, identify the failure of columns that either lost fireproofing or were destroyed on impact as the specific cause of the collapse of each tower. "No fireproofing is designed to withstand such devastating impacts," says the report.

It adds that the fireproofing on the structural elements of the towers had been inspected regularly and that the inspection program "represented a greater standard of care than is generally followed for high-rise office buildings in New York City."

The report exonerates the floor trusses for the collapses. "Failure of the floors...was shown not to have had any significant role in the initiation of the collapses," it says. Studies by Hughes Associates and ARUPFire led the team to conclude that tower floors survived the initial impact of the planes, suffering only localized damage. On the basis of a review of smoke plumes and fire spread, for each tower, the engineers concluded that the fires did not lead to the collapses of the floors affected before the towers fell. Additionally, the engineers claim that computer modeling shows that the failure of columns alone, independent of the floors explains the collapses.

Diagram illustrating the way Tower 1 redistributed loads to other columns on its north face and started off immediate collapse, as modeled by Weidlinger Associates

The findings are intended to build on the study initiated by the American Society of Civil Engineers and sponsored by the Federal Emergency Management Agency, called World Trade Center Building Performance Study. Released last May, it suggested subjecting the floor truss system to "more detailed evaluation." But the study also stated the truss systems "should not be regarded" as design deficiencies, says the Silverstein report.

The Silverstein report also concludes that fire temperatures were lower than typical "fully developed" office fires. The fires were fueled by office furniture and floor contents initially ignited by the jet fuel, which burned out quickly. Dust and debris distributed by the crashes inhibited the fires, which at the impact floors were between 750°F and 1,300°F.

The engineering team is comprised of: Weidlinger Associates Inc., led by Matthys Levy and Najib Abboud; LZA Technology/Thornton-Tomasetti Group, led by Daniel Cuoco and Gary Panariello; ARUPFire, led by Richard Custer; Hughes Associates Inc., led by Craig Beyler; SafirRosetti, led by Howard Safir; Hillman Environmental Group, led by Christopher Hillmann and John B. Glass Jr.; RWDI, led by Peter Irwin; Dr. W. Gene Corley, who led the ASCE-FEMA study; Professor Sean Ahearn; and Z-Axis Corp., led by Gary Freed and Alan Treibitz.

Silverstein commissioned the reports for its insurance claim on the World Trade Center. The organization has already given the reports to the National Institute of Standards and Technology, which is studying the collapses of the towers and Seven World Trade as part of a two-year study.

Van Romero

Albuquerque Journal
September 21, 2001

Fire, Not Extra Explosives, Doomed Buildings, Expert Says

By John Fleck

Journal Staff Writer

A New Mexico explosives expert says he now believes there were no explosives in the World Trade Center towers, contrary to comments he made the day of the Sept. 11 terrorist attack.

"Certainly the fire is what caused the building to fail," said Van Romero, a vice president at the New Mexico Institute of Mining and Technology.

The day of the attack, Romero told the Journal the towers' collapse, as seen in news videotapes, looked as though it had been triggered by carefully placed explosives.

Subsequent conversations with structural engineers and more detailed looks at the tape have led Romero to a different conclusion.

Romero supports other experts, who have said the intense heat of the jet fuel fires weakened the skyscrapers' steel structural beams to the point that they gave way under the weight of the floors above.

That set off a chain reaction, as upper floors pancaked onto lower ones.

Romero said he believes still it is possible that the final collapse of each building was triggered by a sudden pressure pulse caused when the fire reached an electrical transformer or other source of combustion within the building.

But he said he now believes explosives would not have been needed to create the collapse seen in video images.

Conspiracy theorists have seized on Romero's comments as evidence for their argument that someone else, possibly the U.S. government, was behind the attack on the Trade Center.

Romero said he has been bombarded with electronic mail from the conspiracy theorists.

"I'm very upset about that," he said. "I'm not trying to say anything did or didn't happen."

BELOW IS THE ORIGINAL STORY AS IT APPEARED ON SEPT. 11, 2001 hours after the attack

September 11, 2001

Explosives Planted In Towers, N.M. Tech Expert Says
By Olivier Uyttebrouck

Journal Staff Writer

Televised images of the attacks on the World Trade Center suggest that explosives devices caused the collapse of both towers, a New Mexico Tech explosion expert said Tuesday.

The collapse of the buildings appears "too methodical" to be a chance result of airplanes colliding with the structures, said Van Romero, vice president for research at New Mexico Institute of Mining and Technology.

"My opinion is, based on the videotapes, that after the airplanes hit the World Trade Center there were some explosive devices inside the buildings that caused the towers to collapse," Romero said.

Romero is a former director of the Energetic Materials Research and Testing Center at Tech, which studies explosive materials and the effects of explosions on buildings, aircraft and other structures.

Romero said he based his opinion on video aired on national television broadcasts.

Romero said the collapse of the structures resembled those of controlled implosions used to demolish old structures.

"It would be difficult for something from the plane to trigger an event like that," Romero said in a phone interview from Washington, D.C.

Romero said he and another Tech administrator were on a Washington-area subway when an airplane struck the Pentagon.

He said he and Denny Peterson, vice president for administration and finance, were en route to an office building near the Pentagon to discuss defense-funded research programs at Tech.

If explosions did cause the towers to collapse, the detonations could have been caused by a small amount of explosive, he said.

"It could have been a relatively small amount of explosives placed in strategic points," Romero said. The explosives likely would have been put in more than two points in each of the towers, he said.

The detonation of bombs within the towers is consistent with a common terrorist strategy, Romero said.

"One of the things terrorist events are noted for is a diversionary attack and secondary device," Romero said.

Attackers detonate an initial, diversionary explosion that attracts emergency personnel to the scene, then detonate a second explosion, he said.

Romero said that if his scenario is correct, the diversionary attack would have been the collision of the planes into the towers.

Tech President Dan Lopez said Tuesday that Tech had not been asked to take part in the investigation into the attacks. Tech often assists in forensic investigations into terrorist attacks, often by setting off similar explosions and studying the effects.

John Osteraas

Looking in on COLLEGE OF ENGINEERING alumni

John Osteraas

John Osteraas, center, salvages materials from the collapsed World Trade Center buildings in the shadow of Manhattan. (32K JPG)

John Osteraas may not be a household name, but he's been at the center of one of the most important stories in recent times — the collapse of the World Trade Center buildings.

Osteraas, director of the civil engineering practice at California-based Exponent Failure Analysis, has been one of a handful of civil engineers who has extensively studied the collapse of the World Trade Center buildings up close. His work has proved critical in assessing exactly why the two towers collapsed after being struck by airplanes on Sept. 11, 2001.

Osteraas' research on the World Trade Centers is an outgrowth of his work with the Federal Emergency Management Agency's Urban Search and Rescue Team, established 10 years ago to respond to and investigate natural disasters such as earthquakes and hurricanes. The team was established in the wake of an earthquake in Mexico City, when haphazard rescue efforts led to deaths beyond those originally caused by the earthquake.

But Osteraas says the team's role has expanded in the wake of incidents such as the bombing of Murrah Federal Building in Oklahoma City in 1995. Beyond extracting victims trapped in structures, members of the team investigate building sites to determine how they collapsed, where victims might be found, and how rescue and clean-up efforts can go forth without endangering workers.

"It's a little bit like archeology and a little bit of investigative work and a little bit of engineering," he says. "Typically we never find all of the puzzle pieces. You have to infer with the best pieces available."

Osteraas was born in Wausau, but moved to Madison in the sixth grade. He enrolled at UW-Madison, and took a liking to engineering. He quickly found mentors in now-Emeritus Civil & Environmental Professors C.K. Wang and Chuck Salmon. To this day, Osteraas says, he applies lessons he learned from his classical methods of structural analysis course. "I attribute that class to my understanding of structural behavior," he says. "I see something and say, 'Aha, I remember that.'"

For Osteraas, the collapse of the World Trade Center towers represented an obvious challenge. Almost all of the buildings were destroyed in the collapse, resulting in the destruction of much of the evidence that engineers like Osteraas rely on to reconstruct collapses.

But debris from "Ground Zero," which Osteraas inspected, as well as sophisticated computer modeling, has allowed engineers to reconstruct the events that led to the buildings' collapse.

Although there is considerable ongoing debate about exactly how the towers collapsed, Osteraas says most engineers agree that the towers' floors began to sag due to the stress put on the buildings' support columns. Those columns, and the bolts used to attach them to the floors, were weakened by the impact of the airplanes and the incredibly hot temperatures from the resulting explosion.

Once one floor collapsed, the others were sure to follow, according to Osteraas' analysis, comparing the collapsing floors to a giant hammer going through the towers.

"It was far beyond anything ever anticipated or designed for," he says. "It was amazing they stood for as long as they did."

Despite the tragedy of the attack on the World Trade Center, and the subsequent collapse of its towers, Osteraas firmly believes that engineers can learn lessons from it about how to make buildings structurally more sound and safer.

"We don't learn much from our successes," he says. "The curse of engineering is that when it does its job, it's taken for granted. Our work is totally invisible."

Dr. W. Gene Corley

Speaker contends fire caused towers to collapse

Dr. W. Gene Corley spoke Tueday on the collapse of New York’s Twin Towers.

Katie O'Boyle
Associate News Editor

The twin towers of the World Trade Center did not fall because they were struck by two aircrafts.

They fell because of the fires that broke out in both towers.

Dr. W. Gene Corley was the head of a team of engineers who investigated the collapse of the towers in the period following the Sept. 11 terrorist attacks. Tuesday night, Corley came to UD to share his findings with the campus community. His speech, entitled “World Trade Center Attack: Why the Towers Fell,” was a part of the Distinguished Speakers Series and this year’s Humanities Symposium.

With a new task set before him after the Sept. 11 terrorist attacks Corley worked with a team of structural engineers, fire protection engineers and firefighters. Investigators found that the two buildings could have stood indefinitely without the fires.

On the morning of the attacks, Corley was engaged in somewhat of an ironic conference call with five other engineers. They were discussing improvements in building designs to prevent damage from potential terrorist attacks. One man on the call had pulled into the Pentagon parking lot to engage in the conference. Their call was cut short with an explosion just around the corner.

A number of organizations came together to help keep people safe and collect data in the aftermath of the attack. Using pieces of scrap metal and debris, Corley and his team began to collect and analyze data to get the structural explanation for the collapse. Corley also discussed several of the misinterpretations he has encountered from people, who received much of their information from the press.

Unknown to some, a total of seven buildings were severely damaged, if not destroyed, from the attack. Specifically, a nearby 47-story building across the street from the towers was completely demolished, something Corley believes could have made headlines on its own.

“I couldn’t believe the actual damage that was caused around the Twin Towers,” freshman civil engineering student Karalyn Snider said. “Dr. Corley’s presentation really made me aware of the structural aspects of the collapse. I think a lot of his findings could help make us more prepared in the future.”

Corley’s study has included collection of data, preliminary analysis and recommendations for additional studies as well as improvements. He went into great detail about each part of the buildings that individually played a role in the collapse.

His presentation included animation of the second plane hitting the second tower, which Corley analyzed structurally in regards to his studies.

Fireproofing also became an important aspect of the investigation, as Corley emphasized how the impacts of the aircrafts alone were not enough to cause the complete collapse.

“The impact of the crafts did however dislodge much of the fire proofing on the structure,” Corley said. “And this is what brought it down quicker.”

With the main water supply cut from the sprinklers, the fire burned for an extended period of time.

Corley also focused parts of his talk on ways to improve buildings that are potential targets for terrorist attacks. Lessons learned included better fire resistance tactics, more reliable sprinkler systems and fireproofing sticking under impact.

“‘I've been asked the question, if they had enough fire protection, would they have stood?’” Corley said. “Yes they would.”

In a question and answer session, Corley was asked if he suggested any major recommendations for changes in building codes to prevent such damage in the case of future terrorist attempts. Corley feels however, that money would be better spent toward keeping aircrafts out of terrorist hands.

Along with his investigation of the World Trade Center collapse, Corley was selected in 1995 to head the team investigating the Murrah Federal Building in Oklahoma City, better known as the site of the Oklahoma City bombing.

Much of Corley’s research has changed aspects of his profession overall, highlighting the need for safer and more economical structures.

As senior vice president of Construction Technology Laboratories, Corley has been the recipient of 16 national awards and authored more than 150 technical papers and books.

Corley’s presentation is part of the Humanities Symposium, which this year has been focused on the Benjamin and Marian Schuster Performing Arts Center, a new construction in downtown Dayton.

Vincent Dunn

Why the World Trade Center Buildings Collapsed

A Fire Chief ’s Assessment

By: Deputy Chief Vincent Dunn ret.

After the 767 jet liner crashed into the world trade center building creating the worst terror attack in history, a fire burned for 56 minutes inside the World Trade Center building number two. The top 20 floors of the building collapsed on the 90 floors below. The entire one hundred and ten-story building collapsed in 8 seconds... After a fire burned inside WTC tower number one for 102 minutes, the top 30 floors collapsed on the lower 80 floors. And the entire one hundred and ten stories of this building collapsed in 10 seconds. You can say the reason they collapsed was they were struck with a 185 ton jet airliner and the 24,000 gallons of jet fuel caused a fire of 1500 to 2000 degrees F which weakened the steel and cause the collapse. Or you can take a closer look at the buildings construction of the WTC buildings. And ask yourself why did these structures collapse so fast and so completely. The answer can be found by examining high-rise construction in New York City over the past 50 years

World Trade Center tower construction

In terms of structural system the twin towers departed completely from other high-rise buildings. Conventional skyscrapers since the 19th century have been built with a skeleton of interior supporting columns that supports the structure. Exterior walls of glass steel or synthetic material do not carry any load. The Twin towers are radically different in structural design as the exterior wall is used as the load-bearing wall. (A load bearing wall supports the weight of the floors.) The only interior columns are located in the core area, which contains the elevators. The outer wall carries the building vertical loads and provides the entire resistance to wind. The wall consists of closely spaced vertical columns (21 columns 10 feet apart) tied together by horizontal spandrel beams that girdle the tower at every floor. On the inside of the structure the floor sections consist of trusses spanning from the core to the outer wall.

Bearing walls and Open floor design

When the jet liners crashed into the towers based upon knowledge of the tower construction and high-rise firefighting experience the following happened: First the plane broke through the tubular steel-bearing wall. This started the building failure. Next the exploding, disintegrating, 185-ton jet plane slid across an open office floor area and severed many of the steel interior columns in the center core area. Plane parts also crashed through the plasterboard-enclosed stairways, cutting off the exits from the upper floors. The jet collapsed the ceilings and scraped most of the spray-on fire retarding asbestos from the steel trusses. The steel truss floor supports probably started to fail quickly from the flames and the center steel supporting columns severed by plane parts heated by the flames began to buckle, sag, warp and fail. Then the top part of the tower crashed down on the lower portion of the structure. This pancake collapse triggered the entire cascading collapse of the 110-story structure.

Steel Framing

The most noticeable change in the modern high-rise construction is a trend to using more steel and shaping lightweight steel into tubes, curves, and angles to increase its load bearing capability. The WTC has tubular steel bearing walls, fluted corrugated steel flooring and bent bar steel truss floor supports. To a modern high rise building designer steel framing is economical and concrete is a costly material. For a high-rise structural frame: columns, girders, floors and walls, steel provides greater strength per pound than concrete. Concrete is heavy. Concrete creates excessive weight in the structure of a building. Architects, designers , and builders all know if you remove concrete from a structure you have a building that weights less. So if you create a lighter building you can use columns, girders and beams of smaller dimensions, or better yet you can use the same size steel framing and build a taller structure. In News York City where space is limited you must build high. The trend over the past half-century is to create lightweight high buildings. To do this you use thin steel bent bar truss construction instead of solid steel beams. To do this you use hollow tube steel bearing walls, and curved sheet steel (corrugated) under floors. To do this you eliminate as much concrete from the structure as you can and replace it with steel. Lightweight construction means economy. It means building more with less. If you reduce the structure’s mass you can build cheaper and builder higher. Unfortunately unprotected steel warps, melts, sags and collapses when heated to normal fire temperatures about 1100 to 1200 degrees F.

The fire service believes there is a direct relation of fire resistance to mass of structure. The more mass the more fire resistance. The best fire resistive building in America is a concrete structure. The structures that limit and confine fires best, and suffer fewer collapses are reinforced concrete pre WWII buildings such as housing projects and older high rise buildings like the empire state building, The more concrete, the more fire resistance; and the more concrete the less probability of total collapse. The evolution of high- rise construction can be seen, by comparing the empire state building to the WTC. My estimate is the ratio of concrete to steel in the empire state building is 60/40. The ratio of concrete to steel in the WTC is 40/60. The tallest building in the world, the Petronas Towers, in Kula Lumpur, Malaysia, is more like the concrete to steel ratio of the empire state building than concrete to steel ratio of the WTC. Donald Trump in New York City has constructed the tallest reinforced concrete high-rise residence building.

The computer designed high rise building

The computer has allowed engineers to reduce the mass of a structure by its ability to more accurately determine the load bearing capability of structural framework. Years ago before the computer, builders were not sure of a structural elements load bearing capability, so they over built by using a so called “safety factor”. This built in safety factor could result in a structure with twice the required load bearing strength. Because of computer calculation this no longer occurs. The older buildings use to have built in a so called “safety factor” of two-to-one. Not so today, if the building code requires a load bearing factor of 40 pounds per square foot that is exactly what you get. There is no margin for error.

Effects of jet crash and fire on a skeleton steel high rise

A plane that only weighted 10 tons struck the Empire State Building and the high-octane gasoline fire quickly flamed out after 35 minutes. When the firefighters walked up to the 79 floor most of the fire had dissipated. The Empire State Building in my opinion, and most fire chiefs in New York City, is the most fire safe building in America. I believe it would have not collapsed like the WTC towers. I believe the Empire State Building, and for that matter any other skeleton steel building in New York City, would have withstood the impact and fire of the terrorist’s jet plane better than the WTC towers. If the jet liners struck any other skeleton steel high rise, the people on the upper floors and where the jet crashed may not have survived; there might have been local floor and exterior wall collapse. However, I believe a skeleton steel frame high rise would not suffer a cascading total pancake collapse of the lower floors in 8 and 10 seconds. Hopefully some engineer using computer calculations, can reconstruct the effects of a 767 jetliner crashing into another New York City high building. In any other high rise in New York City, I say, the floors below the crash and fire, would not collapse in such a total a cascading pancake cave-in. Most of the occupants and rescuers killed in the WTC tower collapse were on the lower floors.

The Empire State Building

Perhaps builders should take a second look at the Empire State Buildings construction. There might be something to learn when they rebuild on ground zero. The empire state building has exterior Indiana limestone exterior wall, 8 inches thick. The floors are also 8 inches thick consisting of one-inch cement over 7 inches of cinder and concrete. All columns, girders and floor beams are solid steel covered with 1 to 2 inches of brick terracotta and concrete. There is virtually no opening in the floors. And there are no air ducts of a HVAC heating cooling and venting system penetrating fire partitions, floor, and ceilings. Each floor has its own HVAC unit. The elevators and utility shafts are masonry enclosed. And for life safety there is a 4-inch brick enclosed so-called “smoke proof stairway”. This stairway is designed to allow people to leave a floor without smoke following them and filing up the stairway. This is accomplished because this smoke proof stairway has an intermediate vestibule, which contains a vent shaft. Any smoke that seeps out the occupancy is sucked up a vent shaft.

Concrete removal

Since the end of WWII builders designed most of the concrete from the modern high-rise constriction. First concrete they eliminated was the stone exterior wall. They replace them with the “curtain walls of glass, sheet steel, or plastics. This curtain wall acted as a lightweight skin to enclose the structure from the outside elements. Next the 8-inch thick concrete floors went. They were replaced with a combination of 2 or 3 inches of concrete on top of thin corrugated steel sheets. Next the masonry enclosure for stairs and elevators were replaced with several layers of sheet rock. Then the masonry smoke proof tower was eliminated in the 1968 building code. It contained too much concrete weight and took up valuable floor space. Then the solid steel beam was replace by the steel truss. And finally the concrete and brick encasement of steel columns girders and floor supports was eliminated. A lightweight spray-on coating of asbestos or mineral fiber was sprayed over the steel. This coating provided fireproofing. After asbestos was discovered hazardous vermiculite or volcanic rock ash substance was used as a spray-on coating for steel. Outside of the foundation walls and a thin 2 or 3 inches of floors surface, concrete has almost been eliminated from high-rise office building construction. If you look at the WTC rubble at ground zero you see very little concrete and lots of twisted steel.

The performance building code

How did lightweight high-rise construction evolve since WWII? It evolved with the help of the so-called performance code. After WWII the builders complained about building codes. They said they were too restrictive and specified every detail of construction. They called the old building codes “specification codes”. They complained the codes specified the size and type and some times even the make of a product used in construction. They decried the specification code as old fashion. They wanted the building codes changed to what they called “performance codes.” They wanted the building codes to specify the performance requirements only; and, not specify the size and type of building material to use. For example, with fire resistive requirements they wanted the code to state just the hours of fire resistance (one, two, three or four hours) required by law; and not to state the specific type and material used to protect structural steel and enclosures for stairways and elevators shafts. For example, a performance building code states: the steel has to be protected against heat of flames for one, two, three or four hours during a fire. It does not state what to use as a fire resisting material. This performance code signaled the end to concrete encasement fire protection and allowed a spray on fire protection for steel and plasterboard enclosed stairs and elevator shafts. Builders hailed the New York City building code of 1968 as a good performance code. However, some fire chiefs decried it as a law that substituted frills for real construction safety. The asbestos spray on coating of steel trusses used in the WTC towers was considered by Chief of the New York City Fire Department, at the time, John T. O’ Hagan to be inferior to concrete encasement of steel. Writing in his book, High Rise Fire and Life Safety. l976, he listed the following problems of spray-on fire protection of steel:

  1. Failure to prepare the steel for spray-on coating adhesion. Rust and dirt allowed spray-on fire retarding coating to scale and fall away from steel during construction
  2. Poor or uneven application of the spray-on fire retarding was discovered during post fire investigations
  3. Variation of spray-on material during manufacture makes it ineffective
  4. Lack of thoroughness in covering the steel during application is a problem
  5. Failure to replace spray-on material dislodged by other trades people performing work around the steel during the construction of the building.

The WTC started construction in the 1970s. And the WTC towers built by the Port Authority of New York did not have to comply with the minimum requirements of the new1968 performance building code.

Recommendations for constructing the new high rise buildings on ground zero

  • The steel columns, girders and floor beams should be encased in masonry or other more effective fire retarding material. Spray-on fire retarding is ineffective. Post fire investigations reveals the spray on fire retardant has scaled off and steel beams and concrete and steel floor slabs crack and allow flame spread.

  • Lightweight bar joists should not be used to support floors in high-rise buildings. The National Fire Protection Association has shown unprotected steel bar joist fail after five or ten minutes of fire exposure.

  • For life safety in high-rise buildings bring back the smoke proof tower. This allows people to escape fire using smoke free stairways.

  • Stairs and elevator shaft ways should be enclosed in masonry to prevent smoke spread.

  • Heating ventilation and air condition HVAC systems should be provided by unit system serving only one or two floors. Central air system serving 10 or 20 floors creates shaft ways and duct systems that penetrate fire rated floors walls partitions and ceilings. Smoke spreads throughout ducts of central HVAC systems.
  • The high rise building framework should be skeleton steel framing not center core steel column framing. There should be no bearing wall high rise construction. Reduce the size of open floor design.
  • Increase the thickness of concrete in floor construction. The two or three inches of concrete over corrugated steel fails during most serious high rise fires and must be replaced.
  • Automatic sprinklers should protect all high rise buildings. Firefighters can extinguish approximately 2,500 square foot of fire with one hose line. Two hose steams may quench 5,000 square feet of fire. The World Trade Center floor areas were 40,000 square feet in area.
  • Federal, State and Port Authority buildings should comply with New York City building codes and actually in some cases should exceed them. Remember building codes are only minimum standards.

Zdenek P. Bazant, Yong Zhou

Journal of Engineering Mechanics ASCE, in press
9/13/01, Expanded 9/22/01, Appendices 9/28/01)
Why Did the World Trade Center Collapse?—Simple Analysis

By Zdenek P. Bazant, Fellow ASCE, and Yong Zhou

Abstract: This paper3 presents a simplified approximate analysis of the overall collapse of the towers of World Trade Center in New York on September 11, 2001. The analysis shows that if prolonged heating caused the majority of columns of a single floor to lose their load carrying capacity, the whole tower was doomed. The structural resistance is found to be an order of magnitude less than necessary for survival, even though the most optimistic simplifying assumptions are introduced.
Introduction and Failure Scenario

The 110-story towers of the World Trade Center were designed to withstand as a whole the forces caused by a horizontal impact of a large commercial aircraft (Appendix I). So why did a total collapse occur? The cause was the dynamic consequence of the prolonged heating of the steel columns to very high temperature. The heating lowered the yield strength and caused viscoplastic (creep) buckling of the columns of the framed tube along the perimeter of the tower and of the columns in the building core. The likely scenario of failure is approximately as follows.

In stage 1 (Fig. 1), the conflagration caused by the aircraft fuel spilled into the structure causes the steel of the columns to be exposed to sustained temperatures apparently exceeding 800°C. The heating is probably accelerated by a loss of the protective thermal insulation of steel during the initial blast. At such temperatures, structural steel suffers a decrease of yield strength and exhibits significant viscoplastic deformation (i.e., creep—an increase of deformation under sustained load). This leads to creep buckling of columns (e.g., Bazant and Cedolin 1991, Sec. 9), which consequently lose their load carrying capacity (stage 2). Once more than about a half of the columns in the critical floor that is heated most suffer buckling (stage 3), the weight of the upper part of the structure above this floor can no longer be supported, and so the upper part starts falling down onto the lower part below the critical floor, gathering speed until it impacts the lower part. At that moment, the upper part has acquired an enormous kinetic energy and a significant downward velocity. The vertical impact of the mass of the upper part onto the lower part (stage 4) applies enormous vertical dynamic load on the underlying structure, far exceeding its load capacity, even if it is not heated. This causes failure of an underlying multi-floor segment of the tower (stage 4), in which the failure of the connections of the floor-carrying trusses to the columns is either accompanied or quickly followed by buckling of the core columns and overall buckling of the framed tube, with the buckles probably spanning the height of many floors (stage 5, at right), and the upper part possibly getting wedged inside an emptied lower part of the framed tube (stage 5, at left). The buckling is initially plastic but quickly leads to fracture in the plastic hinges. The part of building lying beneath is then impacted again by an even larger mass falling with a greater velocity, and the series of impacts and failures then proceeds all the way down (stage 5).
Elastic Dynamic Analysis

The details of the failure process after the decisive initial trigger that sets the upper part in motion are of course very complicated and their clarification would require large computer simulations. For example, the upper part of one tower is tilting as it begins to fall (see Appendix II); the distribution of impact forces among the underlying columns of the framed tube and the core, and between the columns and the floor-supporting trusses, is highly nonuniform; etc. However, a computer is not necessary to conclude that the collapse of the majority of columns of one floor must have caused the whole tower to collapse. This may be demonstrated by the following elementary calculations, in which simplifying assumptions most optimistic in regard to survival are made.

For a short time after the vertical impact of the upper part, but after the elastic wave generated by the vertical impact has propagated to the ground, the lower part of the structure can be approximately considered to act as an elastic spring (Fig. 2a). What is its stiffness C? It can vary greatly with the distribution of the impact forces among the framed tube columns, between these columns and those in the core, and between the columns and the trusses supporting concrete floor slabs.

For our purpose, we may assume that all the impact forces go into the columns and are distributed among them equally. Unlikely though such a distribution may be, it is nevertheless the most optimistic hypothesis to make because the resistance of the building to the impact is, for such a distribution, the highest. If the building is found to fail under a uniform distribution of the impact forces, it would fail under any other distribution. According to this hypothesis, one may estimate that C 71 GN/m (due to unavailability of precise data, an approximate design of column cross sections had to be carried out for this purpose).

The downward displacement from the initial equilibrium position to the point of maximum deflection of the lower part (considered to behave elastically) is h + (P/C) where P = maximum force applied by the upper part on the lower part and h = height of critical floor columns (= height of the initial fall of the upper part) 3.7 m. The energy dissipation, particularly that due to the inelastic deformation of columns during the initial drop of the upper part, may be neglected, i.e., the upper part may be assumed to move through distance h almost in a free fall (indeed, the energy dissipated in the columns during the fall is at most equal to 2πX the yield moment of columns, X the number of columns, which is found to be only about 12% of the gravitational potential energy release if the columns were cold, and much less than that at 800°C). So the loss of the gravitational potential energy of the upper part may be approximately equated to the strain energy of the lower part at maximum elastic deflection. This gives the equation mg[h + (P/C)] = P2/2C in which m = mass of the upper part (of North Tower) 58·106 kg, and g = gravity acceleration. The solution P = Pdyn yields the following elastically calculated overload ratio due to impact of the upper part:

where P0 = mg = design load capacity. In spite of the approximate nature of this analysis, it is obvious that the elastically calculated forces in columns caused by the vertical impact of the upper part must have exceeded the load capacity of the lower part by at least an order of magnitude.

Another estimate, which gives the initial overload ratio that exists only for a small fraction of a second at the moment of impact, is

where A = cross section area of building, Eef= cross section stiffness of all columns divided by A, ρ = specific mass of building per unit volume. This estimate is calculated from the elastic wave equation which yields the intensity of the step front of the downward pressure wave caused by the impact if the velocity of the upper part at the moment of impact on the critical floor is considered as the boundary condition (e.g., Bazant and Cedolin, Sec. 13.1). After the wave propagates to the ground, the former estimate is appropriate.

An important hypothesis implied in this analysis is that the impacting upper part, many floors in height, is so stiff that it does not bend nor shear on vertical planes, and that the distribution of column displacements across the tower is almost linear, like for a rigid body. If, however, the upper part spanned only a few floors (say, 3 to 6), then it could be so flexible that different column groups of the upper part could move down separately at different times, producing a series of small impacts that would not be fatal (in theory, if people could have escaped from the upper part of the tower, the bottom part of the tower could have been saved if the upper part were bombed, exploded or weakened by some "smart" structure mechanism to collapse onto the lower part gradually as a pile of rubble, instead of impacting it instantly as an almost rigid body).
Analysis of Inelastic Energy Dissipation

The inelastic deformation of the steel of the towers involves plasticity and fracture. Since we are not attempting to model the details of the real failure mechanism but seek only to prove that the towers must have collapsed and do so in the way seen (Engineering 2001, American 2001), we will here neglect fracture, even though the development of fractures is clearly discerned in the photographs of the collapse. Assuming the steel to behave plastically, with unlimited ductility, we are making the most optimistic assumption with regard to the survival capacity of the towers (in reality, the plastic hinges, especially the hinges at column connections, must have fractured, and done so at relatively small rotation, causing the load capacity to drop drastically).

The basic question to answer is: Can the fall of the upper part be arrested by energy dissipation during plastic buckling which follows the initial elastic deformation? Many plastic failure mechanisms could be considered, for example: (a) the columns of the underlying floor buckle locally (Fig. 1, stage 2); (b) the floor-supporting trusses are sheared off at the connections to the framed tube and the core columns and fall down within the tube, depriving the core columns and the framed tube of lateral support, and thus promoting buckling of the core columns and the framed tube under vertical compression (Fig. 1, stage 4, Fig. 2c); or (c) the upper part is partly wedged within the emptied framed tube of the lower part, pushing the walls of the framed tube apart (Fig. 1, stage 5). Although each of these mechanism can be shown to lead to total collapse, a combination of the last two seems more realistic (the reason: multi-story pieces of the framed tube, with nearly straight boundaries apparently corresponding to plastic hinge lines causing buckles on the framed tube wall, were photographed falling down; see, e.g., Engineering 2001, American 2001).

Regardless of the precise failure mode, experience with buckling indicates that the while many elastic buckles simultaneously coexist in an axially compressed tube, the plastic deformation localizes (because of plastic bifurcation) into a single buckle at a time (Fig. 1, stage 4; Fig. 2c), and so the buckles must fold one after another. Thus, at least one plastic hinge, and no more than four plastic hinges, per column line are needed to operate simultaneously in order to allow the upper part to continue moving down (Fig. 2b, Bazant and Cedolin 1991) (this is also true if the columns of only one floor are buckling at a time). At the end, the sum of the rotation angles θi (i = 1, 2, . . ) of the hinges on one column line, Σθi, cannot exceed 2π (Fig. 2b). This upper-bound value, which is independent of the number of floors spanned by the buckle, is used in the present calculations since, in regard to survival, it represents the most optimistic hypothesis, maximizing the plastic energy dissipation.

Calculating the dissipation per column line of the framed tube as the plastic bending moment Mp of one column (Jirasek and Bazant 2002), times the combined rotation angle θi = 2π (Fig. 2b), and multiplying this by the number of columns, one concludes that the plastically dissipated energy Wp is, optimistically, of the order of 0.5 GN m (for lack of information, certain details such as the wall thickness of steel columns, were estimated by carrying out approximate design calculations for this building).

To attain the combined rotation angle Σθi = 2π of the plastic hinges on each column line, the upper part of the building must move down by the additional distance of one buckle, which is at least one floor below the floor where the collapse started. So the additional release of gravitational potential energy Wg ≥ mg · 2h 2 X 2:1 GN m = 4.2 GN m. To arrest the fall, the kinetic energy of the upper part, which is equal to the potential energy release for a fall through the height of at least two floors, would have to be absorbed by the plastic hinge rotations of one buckle, i.e., Wg=Wp would have to be less than 1. Rather,

if the energy dissipated by the columns of the critical heated floor is neglected. If the first buckle spans over n floors (3 to 10 seems likely), this ratio is about n times larger. So, even under by far the most optimistic assumptions, the plastic deformation can dissipate only a small part of the kinetic energy acquired by the upper part of building.

When the next buckle with its group of plastic hinges forms, the upper part has already traveled many floors down and has acquired a much higher kinetic energy; the percentage of the kinetic energy dissipated plastically is then of the order of 1%. The percentage continues to decrease further as the upper part moves down. If fracturing in the plastic hinges were considered, a still smaller (in fact much smaller) energy dissipation would be obtained. So the collapse of the tower must be an almost free fall. This conclusion is supported by the observation that the duration of the collapse of the tower, observed to be 9 s, was about the same as the duration of a free fall in a vacuum from the tower top (416 m above ground) to the top of the final heap of debris (about 25 m above ground), which is It further follows that the brunt of vertical impact must have gone directly into the columns of the framed tube and the core and that any delay Δt of the front of collapse of the framed tube behind the front of collapsing (‘pancaking’) floors must have been negligible, or else the duration of the total collapse of the tower, 9 s + Δt, would have been significantly longer than 9 s. However, even for a short delay Δt, the floors should have acted like a piston running down through an empty tube, which helps to explain the smoke and debris that was seen being expelled laterally from the collapsing tower.
Problems of Disaster Mitigation and Design

Designing tall buildings to withstand this sort of attack seems next to impossible. It would require a much thicker insulation of steel, with blast-resistant protective cover. Replacing the rectangular framed tube by a hardened circular monolithic tube with tiny windows might help to deflect much of the debris and fuel from an impacting aircraft sideways, but regardless of cost, who would want to work in such a building?

The problems appear to be equally severe for concrete columns because concrete heated to such temperatures undergoes explosive thermal spalling, thermal fracture and disintegration due to dehydration of hardened cement paste (e.g., Bazant and Kaplan 1996). These questions arise not only for buildings supported on many columns but also for the recent designs of tall buildings with a massive monolithic concrete core functioning as a tubular mast. These recent designs use high-strength concrete which, however, is even more susceptible to explosive thermal spalling and thermal fracture than normal concrete. The use of refractory concretes as the structural material invites many open questions (Bazant and Kaplan 1996). Special alloys or various refractory ceramic composites may of course function at such temperatures, but the cost would increase astronomically. It will nevertheless be appropriate to initiate research on materials and designs that would postpone the collapse of the building so as to extend the time available for evacuation, provide a hardened and better insulated stairwell, or even prevent collapse in the case of a less severe attack such as an off-center impact or the impact of an aircraft containing little fuel. Lessons should be drawn for improving the safety of building design in the case of lesser disasters. For instance, in view of the progressive dynamic collapse of a stack of all the floors of the Ronan Point apartments in the U.K., caused by a gas explosion in one upper floor (Levy and Salvadori 1992), the following design principle, determining the appropriate ff of redundancy, should be adopted: If only a certain judiciously specified minority of the columns or column-floor connections at one floor are removed, the mass that might fall down from the superior structure must be so small that its impact on the underlying structure would not cause dynamic overload.
Closing Comments

Once accurate computer calculations are carried out, various details of the failure mechanism will doubtless be found to differ from the present simplifying hypotheses. Errors by a factor of 2 would not be terribly surprising, but that would hardly matter since the present analysis reveals order-of-magnitude differences between the dynamic loads and the structural resistance. There have been many interesting, but intuitive, competing explanations of the collapse. To decide their viability, however, it is important to do at least some crude calculations. For example, it has been suggested that the connections of the floor-supporting trusses to the framed tube columns were not strong enough. Maybe they were not, but even if they were it would have made no difference, as shown by the present simple analysis.

The main purpose of the present analysis is to prove that the whole tower must have collapsed if the fire destroyed the load capacity of the majority of columns of a single floor. This purpose justifies the optimistic simplifying assumptions regarding survival made at the outset, which include unlimited plastic ductility (i.e., absence of fracture), uniform distribution of impact forces among the columns, disregard of various complicating details (e.g., the possibility that the failures of floor-column connections and of core columns preceded the column and tube failure, or that the upper tube got wedged inside the lower tube), etc. If the tower is found to fail under these very optimistic assumptions, it will certainly be found to fail when all the detailed mechanisms are analyzed, especially since there are order-of-magnitude differences between the dynamic loads and the structural resistance.

An important puzzle at the moment is why the adjacent 46-story building, into which no significant amount of aircraft fuel could have been injected, collapsed as well. Despite the lack of data at present, the likely explanation seems to be that high temperatures (though possibly well below 800°C) persisted on at least one floor of that building for a much longer time than specified by the current fire code provisions.
Appendix I. Elastic Dynamic Response to Aircraft Impact

A simple estimate based on the preservation of the combined momentum of the impacting Boeing 767-200 ( 179,000 kg X 550 km/h) and the momentum of the equivalent mass Meq of the interacting upper part of the tower ( 141 ·106 X v0 ) indicates that the initial average velocity v0 imparted to the upper part of the tower was only about 0.7 km/h = 0.19 m/s. Mass Meq, which is imagined as a concentrated mass mounted at the height of the impacted floor on a massless free-standing cantilever with the same bending stiffness as the tower (Fig. 2d), has been calculated from the condition that its free vibration period be equal to the first vibration period of the tower, which has been roughly estimated as T1 = 14 s (Meq 44% of the mass of the whole tower). The dynamic response after impact may be assumed to be dominated by the first free vibration mode, of period T1. Therefore, the maximum horizontal deflection w0 = v0Ti/2π 0.4 m, which is well within the design range of wind-induced elastic deflections. So it is not surprising that the aircraft impact per se damaged the tower only locally.

The World Trade Center was designed for an impact of Boeing 707-320 rather than Boeing 767-320. But note that the maximum takeoff weight of that older, less effcient, aircraft is only 15% less than that of Boeing 767-200. Besides, the maximum fuel tank capacity of that aircraft is only 4% less. These differences are well within the safety margins of design. So the observed response of the towers proves the correctness of the original dynamic design. What was not considered in design was the temperature that can develop in the ensuing fire. Here the lulling experience from 1945 might have been deceptive; that year, a two-engine bomber (B-25), flying in low clouds to Newark at about 400 km/h, hit the Empire State Building (381 m tall, built in 1932) at the 79th floor (278 m above ground)—the steel columns (much heavier than in modern buildings) suffered no significant damage, and the fire remained confined essentially to two floors only (Levy and Salvadori 1992).
Appendix II. Why Didn’t the Upper Part Pivot About Its Base?

Since the top part of the South Tower tilted (Fig. 3a), many people wonder: Why didn’t the upper part of the tower fall to the side like a tree, pivoting about the center of the critical floor? (Fig. 3b) To demonstrate why, and thus to justify our previous neglect of tilting, is an elementary exercise in dynamics. Assume the center of the floor at the base of the upper part (Fig. 3b) to move for a while neither laterally nor vertically, i.e., act as a fixed pivot. Equating the kinetic energy of the upper part rotating as a rigid body about the pivot at its base (Fig. 3c) to the loss of the gravitational potential energy of that part (which is here simpler than using the Lagrange equations of motion), we have equationb.gif where x is the vertical coordinate (Fig. 3c). 5 This provides

where θ = rotation angle of the upper part, H1 = its height, and the superposed dots denote time derivatives (Fig. 3c). Considering the dynamic equilibrium of the upper part as a free body, acted upon by distributed inertia forces and a reaction with horizontal component F at base (Fig. 3d), one obtains equationc.gif. Evidently, the maximum horizontal reaction during pivoting occurs for θ = 45°, and so

where, for the upper part of South Tower, m 87 · 106 kg.

Could the combined plastic shear resistance Fp of the columns of one floor (Fig. 3f) sustain this horizontal reaction? For plastic shear, there would be yield hinges on top and bottom of each resisting column; Fig. 3e (again, aiming only at an optimistic upper bound on resistance, we neglect fracture). The moment equilibrium condition for the column as a free body shows that each column can at most sustain the shear force F1 = 2Mp/h1 where h1 2:5 m = effective height of column, and Mp 0:3 MN m = estimated yield bending moment of one column, if cold. Assuming that the resisting columns are only those at the sides of the framed tube normal to the axis of rotation, which number about 130, we get Fp 130F1 31 MN. So, the maximum horizontal reaction to pivoting would cause the overload ratio

if the resisting columns were cold. Since they are hot, the horizontal reaction to pivoting would exceed the shear capacity of the heated floor still much more (and far more if fracture were considered).

Since F is proportional to sin 2θ, its value becomes equal to the plastic limit when sin 2θ = 1/10.3. From this we further conclude that the reaction at the base of the upper part of South Tower must have begun shearing the columns plastically already at the inclination

The pivoting of the upper part must have started by an asymmetric failure of the columns on one side of building, but already at this very small angle the dynamic horizontal reaction at the base of the upper part must have reduced the vertical load capacity of the remaining columns of the critical floor (even if those were not heated). That must have started the downward motion of the top part of the South Tower, and afterwards its motion must have become predominantly vertical. Hence, a vertical impact of the upper part onto the lower part must have been the dominant mechanism.

Finally note that the horizontal reaction Fmax is proportional to the weight of the pivoting part. Therefore, if a pivoting motion about the center of some lower floor were considered, Fmax would be still larger.
Appendix III. Plastic Load-Shortening Diagram of Columns

Normal design deals only with initial bifurcation and small deflections, in which the diagram of load versus axial shortening of an elasto-plastic column exhibits hardening rather than softening. However, the columns of the towers suffered very large plastic deflections, for which this diagram exhibits pronounced softening. Fig. 5 shows this diagram as estimated for these towers. The diagram begins with axial shortening due to plastic yielding at load P10 = A1fi where A1 = crosssection area of one column and fy = yield limit of steel. At the axial shortening of about 3%, there is a plastic bifurcation (if imperfections are ignored). After that, undeflected states are unstable and three plastic hinges (Fig. 5) must form (if we assume, optimistically, the ends to be fixed). From 6 the condition of moment equilibrium of the half-column as a free body (Fig. 5), the axial load then is P1 = 4Mp/L sinθ, while, from the buckling geometry, the axial shortening is u = L(1 - cosθ), where L = distance between the end hinges. Eliminating plastic hinge rotation θ, we find that the plastic load-shortening diagram (including the pre- and post-bifurcation states) is given by

which defines the curve plotted in Fig. 5. This curve is an optimistic upper bound since, in reality, the plastic hinges develop fracture (e.g., Bazant and Planas 1998), and probably do so already at rather small rotations. The area under this curve represents the dissipated energy.

If it is assumed that one or several floor slabs above the critical heated floor collapsed first, then the L to be substituted in (8) is much longer than the height of columns of one floor. Consequently, P1(u) becomes much smaller (and the Euler elastic critical load for buckling may even become less than the plastic load capacity, which is far from true when L is the column height of a single floor).

It has been suggested that the inelastic deformation of columns might have ‘cushioned’ the initial descent of the upper part, making it almost static. However, this is impossible because, for gravity loading, a softening of the load-deflection diagram (Fig. 5) always causes instability and precludes static deformation (Bazant and Cedolin 1991, Chpt. 10 and 13). The downward acceleration of the upper part is ü = N[P10 - P1(u)]/m where N = number of columns and, necessarily, P10 = mg/N. This represents a differential equation for u as a function of time t, and its integration shows that the time that the upper part takes to fall through the height of one story is, for cold columns, only about 6% longer than the duration of a free fall from that height, which is 0.87 s. For hot columns, the difference is of course much less than 6%. So there is hardly any ‘cushioning’.

* American Media Specials, Vol. II, No. 3, September 2001, J. Lynch, ed., Boca Raton, Florida.
* Bazant, Z.P., and Cedolin, L. (1991). Stability of structures: Elastic, inelastic, fracture and damage theories. Oxford University Press, New York.
* Bazant, Z.P., and Kaplan, M.F. (1996). Concrete at high temperatures. Longman – Addison-Wesley, London.
* Bazant, Z.P., and Planas, J. (1998). Fracture and size effect of concrete and other quasibrittle materials. CRC Press, Boca Raton, Florida, and London.
* Bazant, Z.P. (2001a). ”Why did the World Trade Center collapse?” SIAM News (Society for Industrial and Applied Mathematics, M.I.T., Cambridge), 34 (8), October (submitted Sept. 14).
* Bazant, Z.P. (2001b). “Anatomy of Twin Towers Collapse.” Science and Technology (part of Hospodarske Noviny, Prague) No. 186, Sept. 25, p.1.
* Jirasek, M., and Bazant, Z.P. (2002). Inelastic Analysis of Structures. J. Wiley and Sons, London and New York.
* Levy, M., and Salvadori, M. (1992). Why buildings fall down. W.W. Norton and Co., New York.
* “Massive assault doomed towers” (editorial), Engineering News Record 247 (12), September 17, 2001, pp. 10–13.


1. Walter P. Murphy Professor of Civil Engineering and Materials Science, Northwestern University, Evanston Illinois 60208;
2. Graduate Research Assistant, Northwestern University.
3. The original version with equations (1) and (2) was originally submitted to ASCE on September 13, and an expanded version with equation (3) was submitted to ASCE on September 22. Appendix II was added on September 28, and I and III on October 5. The basic points of this paper, submitted to SIAM, M.I.T., on September 14, were incorporated in Bazant (2001a,b). Posted with updates since September 14 at,, and


* Fig. 1 Stages of collapse of the building (floor height exaggerated).
* Fig. 2 (a) Model for impact of upper part on lower part of building. (b) Plastic buckling mechanism on one column line. (c) Combination of plastic hinges creating a buckle in the tube wall. (d) Equivalent mass Meq on a massless column vibrating at the same frequency.
* Fig. 3 Pivoting of upper part of tower about its base; (a,b) with and without horizontal shear at base; (c) model for simplified analysis; (d) free-body diagram with inertia forces; (d,e) plastic horizontal shearing of columns in critical floor at base.
* Fig. 4 Scenario of tilting of upper part of building (South Tower).
* Fig. 5 (a) Plastic buckling of columns; (b) plastic hinge mechanism; (b) free-body diagram; (d) dimensionless diagram of load P1 versus axial shortening u of columns of the towers if the effects of fracture and heating are ignored; and (e) the beginning of this diagrams in an expanded horizontal scale (imperfections neglected).

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