A few people have written to me over the past few months regarding an article by Mr. Trevor Self, from Albuquerque I believe, styling himself Newton’s Bit. Rather than continue to answer these individually it will save time and effort if this reply is placed on the web and freely available. I have not previously bothered to answer this article because I did not believe that anyone would be taken in by his rubbish, riddled as it is with very basic errors, but for those who have not studied the subject it may prove beneficial to have some of these errors explained. Firstly I will deal with the arithmetical errors, then I will explain the engineering errors.
First of all the conversion from degrees to radians used by Mr Self is incorrect. There are pi (3.142) radians in 180 degrees, except apparently in New Mexico. This introduces an error of 200%.
There are four rotations in a three point buckle except in the mind of Mr Self who believes there are only three. A further error of 133%.
Mr Self uses a slenderness ratio which assumes that the columns in the towers were fitted with hinges on every storey. A casual glance at the towers proves this false, and the very fact that they stood for many years would help to confirm the non existence of these hinges. The error in slenderness ratio is 200%.
Mr Self chooses to call himself Newton’s bit for some reason but his refusal to accept Newton’s laws would have that famous man turning in his grave. Isaac Newton, or “whirling Isaac” as he is now known told us that each action has an equal and opposite reaction, but Mr Self chooses to ignore this fact conveniently allowing him to understate the energies involved by half. An error of 200%.
Mr. Self ignores the strengthening and bracing effect of the spandrel plates, core bracing, etc. The error is more difficult to quantify but is clearly significant. Why else would they have been included in the original design?
These errors when combined add up to ridiculous. It is easy to see therefore why I have previously dismissed this article without much comment. The only interesting part of this episode has been the manner in which supporters of the official story have latched onto it. There are those without the specialised knowledge to judge, who have betrayed their own unthinking bias by adopting Mr Self’s article without question. More importantly there are those who are or claim to be engineers and who do or should have that specialised knowledge and yet they have allowed the article to stand and allowed
Mr. Self to continue to embarrass himself, even when these most basic errors have been pointed out.
I hope that this clears up a few issues for some people, but if questions continue then please do not hesitate to contact me.
As an aside, I have always thought that the custom on the web of allowing everyone to choose their own nickname is a little bit strange. If this were the case in real life then all the Porkys and Kiffys of this world would be calling themselves Ace or Tiger. Mr Self, or Newton’s Bit, as he appears to prefer, is a definite case in point.
Things start to get a little bit more complicated. The first thing that should dawn on most people is that the floor is no longer being supported by the middle column which is going to cause some problems. The middle column will drop unless there is a force that can resist it, see Figure 3.
As the column drops, the top chord of the floor truss develops tensile forces (it is quite literally stretched). This tensile force has two parts, a vertical portion that pulls the column up and a horizontal force that pulls the rest of the structure in. This can be seen in Figure 4.
The other things to note here is that the left column is still under its full axial loading (P2, which will be important in the analysis). The left column is already shown pulled in to some degree, however it is not to scale. Further modifying the problem, we know that the fires caused the trusses to sag to some degree. If the fire is hot enough, the truss will become a tension only member. This means that the top chord of the truss will act something like a rope and pull inwards at its connections. This can be seen in Figure 5. There is another condition as well (which I have no illustrated) that will cause the heated floor to expand outwards without losing its bending capacity and thus not sagging. It is a condition that likely proceeded that of the sagging floor trusses.
NIST (1-6D) estimates that the total pull-in force at the exterior columns is roughly 6 kips (6,000lbs) at each column. The truss to column connection consisted of (2) 5/8” diameter bolts. Even non-structural grade bolts of this size will have a shear capacity of over 5kips each, so it is reasonable to assume that the top chord of the truss will not pull off of the columns at the connections due to a 6kip load.
Is this 6 kips enough to pull the column in several feet as seen in the photos of the tower?
Figure 7
What does the slenderness ratio of a structural steel column need to be to be in the inelastic buckling range?
What were the slenderness ratios of the central core columns at the collapse initiation sites of the 98th floor in the North Tower and 82nd floor in the South Tower?
Inelastic buckling occurs for all slenderness ratios under the Euler limit. That's 4.71 * SQRT(E/Fy). Of course extremely stout members won't buckle inelastically, however none of the columns in the upper floors of the WTC were that stout.
Do you have any clue as to what you're talking about? I recommend picking up an AISC Manual of Steel Construction and see exactly how steel is designed these days. We're not in the 1940's, we know how steel fails now. Maybe you should update you knowledge to modern information.
How did I know you would come on.This is where Mr. Szamboti shows his lack of knowledge as regards to structural engineering. The slenderness ratio that we are talking about, and what Mr. Szamboti struggles to understand, here is defined as K*L/r.
You used an effective length factor of 1.0 in your letter to Gordon Ross, which is for a pinned connection, when you should have used .5 to .65 for fixed both ends connections for the tower columns. The 1.0 gave you larger slenderness ratios and they still weren't greater than 40. Now you are going to say the tower columns weren't in the short column category and would have been subject to inelastic buckling. The AISC equations you show here and which you used in your paper are conservative for design.
You want to say the tower columns would fail due to buckling. Well how about a test case were an I beam with a slenderness ratio of 20 or lower failed due to inelastic buckling. Do you have any test cases? I have an AISC manual right here. I am familiar with the equations and monograph. You want to go around asking others if they have a clue and you seem to be the one who should be asked that question Mr. Smarty pants.
