In 2002, the Chinese researchers Xinzheng Lu and Jianjing Jiang of the Department of Civil Engineering at Tsinghua University presented a finite element analysis of the complete collapses of WTC 1 and 2 at the International Conference on Protection of Structures Against Hazards. The results of the analysis can be found in their paper, Simulation for the Collapse of WTC after Aeroplane Impact.
Few details of the Lu-Jiang model are given in the paper. While they mention the inner core and outer perimeter, they only give some of the data related to dimension of the perimeter components (columns and spandrels). The data is gathered in the following tables:
- Dimension Table
| Component | L-J Dimensions | NIST dimensions | Material |
|---|---|---|---|
| Perimeter Column | width: 476.25 mm depth: NA thickness: NA spacing: 1.04 m |
width: 355.6 depth: 342.9 thickness: VH spacing: 1.02 m |
steel |
| Perimeter Spandrel | width: NA depth:1219.2mm |
width: VH (9.53 mm to 34.93 mm) depth: 1321.0 mm |
steel |
| Core Column | NA | VH | steel |
| Core Beam | NA | NA | steel |
| Floor Truss | NA | TBD | steel |
| Floor Slab | NA | TBD | concrete |
- Lu-Jiang Model Material Property Table
| Property | Steel | Concrete |
|---|---|---|
| Density | 7800 kg/m3 | 2500 kg/m3 |
| Young's Modulus | 200 GPa | 30 GPa |
| Poisson's Ratio | 0.27 | 0.2 |
| Yield Strength | 310 MPa | 30 MPa |
| Hardening modulus | 2 GPa | 0 |
| Plastic limit | 0.5%, 1.0%, 5.0% | 0 |
As the dimension table indicates, the values used by Lu-Jiang disagree with those that are given by NIST in its study. Also, It appears that the authors use the same column dimensions throughout the building, although this is not stated explicitly by the authors and would need to be verified.
In setting up their collapse simulation, Lu-Jiang do not simulate the aircraft impacts nor the fires. Elements of the building model are removed to approximate the effects of the impacts. To simulate the effects of the fires, they set the Young's modulus of the steel on the affected floors to 1/20 of its normal value in order to, in their words, "approach the performance of steel at 700oC". In the paper, they do not discuss their choice of elements to be removed from the model, nor do they indicate which columns they treat as being affected by the fires. It should be noted that other sources indicate that steel at 700oC should have 20% the strength it has at room temperature which indicates that the factor of 1/20 may not be the appropriate value.
A full evaluation of the Lu-Jiang model is hampered by the various unknowns, an extensive discussion with the authors would need to be initiated to fill in the missing blanks. In spite of these difficulties, some observations can be made. Lu-Jiang discuss the results they achieved in the cases where the plastic deformation limit of the steel has the value 0.5%, 1.0%, and 5.0%. A complete collapse of the towers can only be achieved for the value of 0.5%. In the case that the plastic deformation limit is 1.0%, the collapse haults about 100m below the aircraft impact area. For the 5.0% case, there is no collapse and only a part of the building near the impact area is damaged. For a value of 0.5%, the buildings collapse completely. The simulated collapse time in this case is about 110 seconds for WTC 1 and 90 seconds for WTC 2. Hence, it can be seen that the Lu-Jiang model does not adequately characterize the collapse of WTC 1 and 2.
The Lu-Jiang model is a valuable contribution to the study of the collapses of the WTC towers. It demonstrates that it is possible to perform finite element analyses of the collapses of the WTC towers. However, since the model does not adequately characterize the collapses, further study is warranted.
