The NIST NCSTAR1 report can be extremely amusing at times if you can stomach it. One of the most astounding events of 9/11 was the top of the south tower tilting before coming down and disappearing in a dense cloud of dust. So I figured any discussion of that occurence had to refer to either the “center of mass” or “center of gravity” of at least 25 stories of the building. So I searched my DVD download of the report to see what turned up. Definitely not what I expected.
Center of mass is only used 4 times and the only real object it references is the airplane. It appears that they were extremely concerned about ceiling tiles and devoted an entire report to them. The only Interesting thing about it that I can tell is that the plane decelerated at 60 g’s and came to a stop in 0.63 seconds. Suspended ceilings must be of major concern in the collapse of a 500.000 ton building.
NCSTAR 1-5D Ceilings.doc (offset 34)
Reaction of Ceiling Tile Systems to Shocks
center of mass page 77(*3)
Some of the airplane debris would not likely have traveled this far into the tower, while some parts of the plane and some of the fuel passed through the building and exited the far side. It was, therefore, assumed that the center of mass of the airplane penetrated slightly more than one-half of the tower’s depth. Assuming that the center of mass of the airplane is located at approximately the center of its length, the center of mass of the airplane would have traveled approximately 197 ft (60 m) between when the nose impacted the face of the tower and when the airplane remnants came to rest.
center of mass page 79
where, x p (t ) was the position of the center of mass of the airplane at time t. Given the initial and final velocities of the airplane and the differential displacement, described above, Equations 2–3 and 2–4 were solved to determine the acceleration parameters. The estimated peak acceleration of the airplane was found to be –62g (–610 m/s2), and the estimated duration of the impact was found to be 0.63 s. The resulting acceleration history is shown in Fig. 2–45.
They don’t use the term “center of gravity” in relation to any real physical object from 9/11. They only use it in explaining how they configured their simulation software in specifying columns for the simulator. I find this truly amazing for a 11,305 page report that took 3 years. I guess the centers of mass and gravity don’t matter for the tons of material that was hurled hundreds of feet from the buildings.
NCSTAR 1-6.doc (offset 82)
Structural Fire Response and Probable Collapse Sequence of the
World Trade Center Towers
center of gravity page 182
Shell elements were used to model the plates comprising the box column and the spandrels. Rigid elements connected the center of gravity of the column to its component plates and the spandrel at both the top and the bottom of the model. The column was simply supported in three directions at the bottom and simply supported in the horizontal directions at the top. Increments of axial displacement were applied at the top of the model.
center of gravity p186
In the ANSYS panel model, beam elements replaced shell elements to model the columns, while shell elements were used to model the spandrels, and beam elements attached the center of gravity of the columns to the mid-plane of its corresponding spandrel component at each shell element through the depth of the spandrel.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - -
NCSTAR 1-6C.doc (offset 48)
Component, Connection, and Subsystem Structural Analysis
center of gravity page 44
Four-node finite strain shell elements were used to model the plates of the column and the spandrels. Nodes of column plates at the top and the bottom of the model were rigidly tied to the center of gravity of the column cross section. The column was pinned at the bottom and fixed in the two horizontal directions at the top. Increments of axial displacement were applied at the top of the model at room temperature and 700 ̊C.
center of gravity page 216
The model also represented Column 151 from Floor 96 to Floor 97 since the dimensions, plate thicknesses, and material properties were identical to those of Column 151 from Floor 95 to 96. SHELL181 plate elements modeled the plates of columns and spandrels. CERIG rigid elements connected the center of gravity of the column to its component plates and to the spandrel at both the top and the bottom of the model. The column was pinned at the bottom and restrained in the two horizontal directions at the top. Axial displacement was applied incrementally at the top of the model.
center of gravity page 222
To capture the gravity load effects from upper floors (those above Floor 99), internal forces and moments at midheight of the columns between Floors 99 and 100 in the LERA SAP2000 global model, caused by dead plus 25 percent of design live load, were applied as loads at the tops of the corresponding columns in the exterior wall model at the center of gravity of the columns. To capture the gravity load effects from individual floors, floor loads were extracted from the LERA SAP2000 floor model and applied to each column.
center of gravity page 222
For columns that were modeled by BEAM189 elements, temperatures were provided for nodes at the center of gravity of the column, and their linear gradients transverse to the exterior wall were also provided. Gradients parallel to the wall were found to be negligible. Temperatures for SHELL181 elements were provided at each node. NIST did not always provide temperatures for the bolts at column splices. When bolt temperatures were provided, they matched temperatures at the nearest interior or exterior tips of columns.
All of the page numbers refer to the PDF pages, not the official NIST page numbers. Doing searches in Adobe reports the PDF numbers. I specified the offset for each report so the NIST page numbers can be computed. Just subtract the offset from the PDF page to get the official government sanctioned, approved and certified page number.
Since for some reason our brilliant government officials locked this PDF document, even though taxpayers payed for it, it is impossible to cut and paste from it with Adobe. But never fear, I was able to cut and paste from it with the Linux Evince document viewer.