Here is a more detailed explanation of reserve capacity and factor of safety. The following appeared in my 2008 book. No one has shown any errors in this discussion.
The Issue of Reserve Capacity
As the NIST report states,
“both towers had considerable reserve capacity. This was confirmed by analysis of the post-impact vibration of WTC-2, the more severely damaged building, where the damaged tower oscillated at a period nearly equal to the first mode period calculated for the undamaged structure.” [my emphasis]61
The above passage informs us that WTC-2 gave no sign of instability after the impact of Flight 175. Unfortunately, although NIST’s summary report provides a wealth of information about how the World Trade Center was constructed it fails to clarify the matter of the WTC’s “considerable reserve capacity.” At any rate, I scoured the report in vain for a clear discussion of this important issue. In frustration, I finally called NIST for assistance and was guided to several of the project reports and supplementary documents. I also consulted with Gary Nichols, an expert at the International Code Council (ICC), and with Ron Hamburger, a leading structural engineer. These conversations were an education. I learned that estimating the overall reserve capacity of a steel structure is by no means a simple matter. Numerous factors are involved. Moreover, there are different ways to approach the problem.
Perhaps the simplest measure of reserve capacity are the standards for the material components of a building. In the late 1960s when the WTC was constructed the applicable standard was the New York City Building Code, which required a builder to execute computations for the various structural members to show they met the specified requirements. However, the code also allowed for actual testing of members in the event that computations were impractical. The testing standards applicable in 1968 give a reasonable idea of the required level of reserve strength in the steel columns and other materials used in the WTC. For example, in the most stringent test a steel member had to withstand 250% of the design load, plus half again its own weight, for a period of a week, without collapse.62
Factor of Safety
Another widely used measure of reserve capacity is the so called “factor of safety.” This varies for different structural elements, but for steel columns and beams typically ranges from 1.75 - 2.0.63 The NIST report actually breaks down this more general figure into two separate and slightly different measurements for stress: yielding strength (1.67) and buckling (1.92).64 For our purposes, however, the more general figure is adequate. So, for example, a steel column with a factor of safety of 1.75 must support 1.75 times the anticipated design load before it begins to incur damage. While this value is typical of steel beams in general, the actual reserve strength of the steel columns in the WTC was higher. When NIST scientists crunched the numbers for the 47 core columns of WTC-1 (in the impact zone, between the 93rd and 98th floors) they calculated that the factor of safety ranged from 1.6 to 2.8, the mean value being 2.1.65 This means that the average core column in the impact zone of WTC-1 could support more than twice its design load before reaching the yield strength, i.e., the point where damage may begin to occur. My grateful thanks to the NIST investigative team for helping me locate these numbers, which were buried in the report.
It is important to realize that the factor of safety is not a threshold for collapse, but a value beyond which permanent damage may begin to occur. As the NIST report admits, even “after reaching the yield strength, structural steel components continue to possess considerable reserve capacity.”66 This is why steel beams and columns typically do not fail in sudden fashion. The loss of strength is gradual. No doubt, this helps to explain why, although fires have ravaged many steel frame buildings over history, none had ever collapsed–––until 9/11–––nor has any since. What all of this means, of course, is that even in the most improbable worst case, in which many or all WTC core columns lost half of their strength, there was still sufficient reserve capacity to support the building.
The Perimeter Wall
With regard to the WTC’s perimeter columns, the factor of safety fluctuated from day to day and even from hour to hour, because, in addition to supporting 47% of the WTC’s gravity load, the perimeter wall also had to withstand the lateral force of the wind, which is highly variable given the whims of Mother Nature. A single face of the WTC presented an enormous “sail” to the elements, for which reason John Skilling vastly overbuilt this part of the structure. According to the NIST report, the outer wall’s factor of safety against wind shear on September 11, 2001 was extraordinary, i.e., in the 10-11 range.67 Why so high? The answer is simple: On the day of the attack there was essentially no wind, only a slight breeze.68 For this same reason nearly all of the perimeter wall’s design capacity was available to help support the gravity load. As the NIST report states, “On September 11, 2001 the wind loads were minimal, thus providing significantly more reserve for the exterior walls.”69 When NIST crunched the numbers for a representative perimeter column in WTC-1 (column 151, between the 93rd and 98th floors), they arrived at a factor of safety of 5.7.70 Assuming this average figure is a typical value we arrive at a reasonable estimate of the perimeter wall’s amazing reserve capacity. Even if we subtract those columns severed/damaged by the impact of Flight 175, and the lost capacity due to the alleged (but unproven) buckling along the eastern perimeter wall, there was still a wide margin of safety, more than enough by several times over to support the outer wall’s share of the gravity load, with plenty to spare.71 I must emphasize: These are not my numbers. They are NIST’s own figures.
The WTC’s tremendous reserve capacity was no secret. In 1964, four years before the start of construction, an article about the planned WTC appeared in the Engineering News-Record. The article declared that “live loads on these [perimeter] columns can be increased more than 2,000 percent before failure occurs.”72 A careful reading of the piece also gives insight into why the plane impacts were not fatal to the integrity of the outer wall. The reason is simple: the perimeter columns were designed to function together as an enormous truss, specifically, a Vierendeel truss. The wall was inherently stable. After the plane impacts it behaved like an arch, simply transferring the load to the surrounding columns. As the 1964 article states,
“the WTC towers will have an inherent capacity to resist unforeseen calamities. This capacity stems from its Vierendeel wall system and is enhanced through the use of high-strength steels.”73
In short, NIST’s own data fails to support its conclusions about the cause of the WTC collapse. The official theory requires the fatal weakening of both sets of columns, and NIST came up short on both counts due to insufficient evidence. Indeed, I would call it woefully insufficient.
Notes:
61 NIST NCSTAR 1, Full Summary Report, WTC Investigation p. 144.
62 In the code his was sub-article 1002.0, adequacy of the structural design. See NIST NCSTAR 1-1A, WTC Investigation, p. 32.
63 Conversation with Ron Hamburger, structural engineer, Dec 7, 2006.
64 NIST NCSTAR 1-2, WTC Investigation, p. 66.
65 In the NIST report the reserve capacity data is expressed in the form of demand/capacity ratios, which is simply another way of expressing the factor of safety. I use the latter because I feel it’s more comprehensible to the average lay person. Personal communication, December 14, 2006. See NIST NCSTAR WTC Investigation 1-6, Figure 8-9, p. 233.
66 NIST NCSTAR 1-2, WTC Investigation, p. 66.
67 NIST NCSTAR 1-2, WTC Investigation, p. cxii; also see NIST NCSTAR 1-2, WTC Investigation, p. 84.
68 The NIST report states: “on the day of the attack the towers were subjected to in-service live loads (a fraction of the design live loads) and minimal wind loads.” NIST NCSTAR 1-2 WTC Investigation, p. liv.
69 NIST NCSTAR 1-2, WTC Investigation, p. 66.
70 I received clarification about this from the NIST WTC Investigation Team. Personal communication, December 14, 2006. The number 5.7 is derived from values presented in Figure 4-35, NIST NCSTAR 1-6, WTC Investigation, p. 101.
71 NIST NCSTAR 1-2, WTC Investigation, p. 66.
72 “How Columns Will Be Designed for 110-Story Buildings,” Engineering News-Record, April 2, 1964.
73 Ibid.
His statement is refutable by simply running a search in Acrobat:
