• “Exact” model utilizing a detailed finite element representation of all important structural entities.  This exact model attempts to predict the actual behavior of the building without making any significant a priori assumptions regarding the overall behavior of the building structure. In other words, rather than making approximate and often arbitrary (albeit convenient) assumptions regarding how the building behaves, the exact modeling approach is intended to predict the actual behavior of the building in a manner consistent with the fundamental principles of  structural mechanics. Exact modeling techniques are somewhat more tedious and time consuming to perform, but usually result in far more accurate predictions of building response.
• “Approximate” model based on a priori assumptions regarding the behavior of the building (i.e., assumptions that are made without prior detailed knowledge of the actual behavior of the building structure). Such assumptions provide a convenient means to significantly simplify modeling and analysis procedures of buildings resulting in rather quick and low cost analysis and design, but often produce highly inaccurate predictions of building response.

• Willingness of the client to pay for exact modeling techniques
•  Time constraints on design
•  Design code requirements
•  Professional standards of practice
•  Structural characteristics of the building to be modeled
•  Extent of knowledge and experience of the responsible engineers
•  Business issues involving competitiveness and profitability
•  Quality of construction practices and materials (or lack thereof)
•  Willingness to accept high risk and high liability
•  Level of concern for safety of the public
•  Other factors

Unfortunately, in recent years it appears that economic considerations have become the primary driving force behind the extensive use of approximate modeling techniques in substitution for exact modeling techniques.  Although approximate techniques have a long history of use, their formulations are predicated on the requirement that the building structure being modeled conform to very stringent limitations on the irregularity of the geometry of the structure, member and finite element properties, the stiffness attributes of the structure, the permissible loading conditions, member and finite element boundary conditions, overall deformation behavior of the structure, and numerous other factors.

In the time before computers became the primary modeling and analysis tool for structural engineers, approximate techniques were the only means of modeling and analyzing high rise buildings.  In those times, clients and building designers were fully aware of the limitations of such approximate techniques.  Thus, it was expected that the structural engineer would specify constraints on the structural configuration of the buildings being designed in order to assure that analysis results computed on the basis of approximate methods of analysis would
have a reasonable possibility of predicting reasonably correct building behavior. In other words, it was normal for the structural engineer to dictate to the building designer/architect that the building have structural characteristics that were consistent with the known limitations of the available approximate modeling and analysis tools in use at the time.

Such is not the case today.  Rather, the client expects, and often requires, that the structural engineer use the latest computer technology to perform modeling and analysis of any building structure conceived by the architect, no matter how complex and irregular the physical structure may be.  Further, both the client and architect, and often the structural engineer, mistakenly believe that the very use of the computer will assure correct modeling and analysis of building structures independent of whether or not an exact or approximate method is used.  Based on such an incorrect belief, and in response to unreasonably low fees paid for structural engineering services and to unreasonably limited time allocation to complete the structural engineering of the building, the engineer is generally forced into the use of the lowest cost and most approximate techniques of modeling and analysis whether or not such techniques have the ability to correctly predict the behavior of the building.  Further, there are several computer programs in use today that implement such highly approximate procedures which are extremely inexpensive, and which require very few engineering and computer resources, to use.

Unfortunately, if only approximate techniques are used, the structural engineer has no way to know whether or not the solutions obtained are anywhere near the correct solutions.  Approximate methods of modeling and analysis today become extremely dangerous in view of the fact that modern buildings are generally very tall structures with high aspect ratios, and which incorporate exceedingly complex and highly irregular geometries, highly nonuniform stiffness distributions throughout the structure, large open interior atrium spaces, extremely limited use of structural materials (especially when compared to high rise buildings in the days before computers), lower inherent factors of safety in design, etc.

Since approximate techniques have become so widely used, it has become essential to investigate the actual errors inherent in such methods by performing controlled computational experiments which create analysis results for models of actual high rise building structures which are modeled using various commonly used approximations, and comparing such approximate results to benchmark solutions created using the far more exact finite element formulations.
This paper documents one such investigation on a 67 story reinforced concrete building structure that is 867 ft (264m) tall with a square footprint of 160.63 feet (48.96 m) by 160.63 feet (48.96 m), and which is located in the southeastern part of the U.S.A. The building was completed in 1992 and consisted of 2,600,000 gross square feet (241,548 m² ) of building area and 1,200,000 net rentable square feet (111,484 m²) of office space.  The aspect ratio of the building is approximately 5.4. The structure has four different floor plans ranging from
stories 2 -15, 16-28, 29-42 and 43-53. Outriggers are used at different floors and the building is supported by 16 exterior columns and a concrete core shear wall. The columns are connected by a 4.5 in. (11.43 cm) thick concrete slab and beam system. Stories 4-10 are an open atrium lobby.
The investigation involved the analysis of the building structure for both dead and wind load cases. Three different models were considered for the dead load case, and five different models were considered for the wind load case.