11 сентября 2001   ::   Мейссан Тьерри

To calculate the per floor volume of steel used in the construction of the twin towers, we will divide the calculation into three parts, namely, the volume of steel in the perimeter wall, the volume in the central core and the volume used in the floor support system.

The perimeter wall was comprised of box columns welded to large spandrel plates. Two typical prefabricated sections are illustrated below. Each consists of three spandrel plates welded to three box columns and each is three floors high.

The first figure below shows the cross section of one of the perimeter box columns and its surrounds. The second and third figures detail the dimensions of two actual perimeter columns that were salvaged from the rubble.

The numbers in the figure denote:

• 36 — the steel column

• 38 and 39 — fire resistant plaster

• 40 — aluminum facade

• 42 — window glass

• 43 — the window frame.

To obtain an estimate of the «typical» perimeter column, the dimensions of the perimeter columns listed in the WTC Steel Data Collection documentation were averaged. Whether this accurately reflects the true distribution of perimeter column thickness, is unclear, but it is all one has to go on (till those who hold the architectural details release them).

So, our «average» perimeter column has dimensions:

d = 13.4, t_w = 0.48, b_f = 12.9, t_(tf) = 0.32 and t_(bf) = 0.32.

and cross-sectional area:

2 x (13.4 x 0.48) + (12.9 x 0.32) + (14 x 0.32) = 21.5 square inches,

The parameters d, t_w, b_f, t_(tf) and t_(bf) are as in the following diagram from Appendix D which is part of the report found at http://www.house.gov/science/hot/wtc/wtcreport.htm.

For the time being we will ignore the column end plates and the spandrel beams. Since each floor is 12 feet high, the per floor volume of steel in an average perimeter box column is:

12 x 21.5/144 = 1.792 cubic feet.

In total there are 240 such columns, so the volume of steel so far is

240 x 1.792 = 430 cubic feet.

Now lets deal with the volume of steel in the column end plates. Each end plate is 14 inches wide by 11.75 inches deep and 1.375 inches thick, giving a volume of

14 x 11.75 x 1.375 = 226.2 cubic inches = 226.2/1728 = 0.130896 cubic feet.

Since, on each floor, one third of the columns are joined, and each join involves two end plates, the per floor volume of steel in the end plates is

2 x 0.130896 x 240/3 = 20.9433 cubic feet.

The spandrel plates are large, being 52 inches high and 3/8 inches thick.