6.6.2 The Reference Models
Under contract to NIST, Leslie E. Robertson Associates (LERA) constructed a global reference model of each tower using the SAP2000, version 8, software. ...These global, three-dimensional models encompassed the 110 stories above grade and the six subterranean levels. The models included primary structural components in the towers, resulting in tens of thousands of computation elements. The data for these elements came from the original structrual drawing books for the towers. These had been updated through the completion of the buildings and also included most of the subsequent, significant alterations by both tenants and The Port Authority. LERA also developed reference models of a truss-framed floor, typical of those in the tenant spaces of the impact and fire regions of the buildings, and of a beam-framed floor, typical of the mechanical floors.
LERA's work was reviewed by independent experts in light of the firm's earlier involvement in the WTC design. It was that earlier work, in fact, that made LERA the only source that had the detailed knowledge of the design, construction, and intended behavior of the towers over their entire 38-year life span. The accuracy of the four models was checked in two ways:
* The two global models were checked by Skidmore, Owings & Merrill (SOM), also under contract to NIST, and by NIST staff. This entailed ensuring consistency of the models with the design documents, and testing the models, for example, to ensure that the response of the models to gravity and wind loads was as intended and that the calculated stresses and deformations under these loads were reasonable.
* The global model of WTC 1 was used to calculate the natural vibration periods of the tower. These values were then compared to measurements from the towers on eight dates of winds ranging from 11.5 mph to 41 mph blowing from at least four different directions. As shown in Table 6-3, the N-S and E-W values agreed within 5 percent and the torsion values agreed within 6 percent, both within the combined uncertainty in the measurements and calculations.
* SOM and NIST staff also checked the two floor models for accuracy. These reviews involved comparison with simple hand calculations of estimated deflections and member stresses for a simply supported composite truss and beam under gravity loading. For the composite truss sections, the steel stress results wer ewithin 4 percent of those calculated by SAP2000 for the long-span truss and within 3 percent for the short-span truss. Deflections for the beams and trusses matched hand calculations to within 5 percent to 15 percent. These differences were within the combined uncertainty of the methods.
The few discrepancies between the developed models and the original design documents, as well as the areas identified by NIST and SOM as needing modification, were corrected by LERA and approved by NIST. The models then served as reference for more detailed models for aircraft impact damage analysis and for thermal-structural response and collapse initiation analysis.