Structural Analysis of Impact Damage to World Trade Center Buildings 1, 2, and 7

The National Institute of Standards and Technology (NIST) conducted an extensive investigation of the collapse of World Trade Center towers (WTC 1 and WTC 2) and the WTC 7 building. This paper describes the reconstruction of impact damage to each of the WTC buildings, as well as analytical studies related to the WTC building collapses. In addition, data and evidence that were collected, tests of the floor truss systems in the WTC towers that were conducted, the overall structural analysis approach, and the development of the collapse hypotheses are discussed to provide a basis for the impact analyses and the fire and structural response analyses in a companion paper. Three companion papers address the primary structural systems of the WTC towers and WTC 7, the effects of fire on the three buildings, and how these events contributed to building collapse. The papers provide an overview of the complex and extensive investigations undertaken by NIST at a level of detail that has scientific merit but presents key aspects from the voluminous official reports at a level suitable for the technical literature. The aircraft impact damage to structural members and their passive fire protection in WTC 1 and 2 were estimated through detailed aircraft impact simulations. The impact damage to WTC 7 was estimated from photographs after the collapse of WTC 1, where falling debris damaged the southwest corner of WTC 7. Based on the aircraft impact simulation, over half of the exterior columns on the north face of WTC 1 were severed and approximately 20% of the core columns were severed or heavily damaged. Spray-applied fire resistive material (SFRM) was dislodged by direct debris impact over five floors (Floors 94 to 98). WTC 2 structural damage was concentrated on the east side of the building. Over half of the exterior columns on the south face were severed and approximately 25% of the core columns were severed or heavily damaged. SFRM was dislodged by direct debris impact over six floors (Floors 78 to 83). WTC 7 was structurally damaged by debris from the collapse of WTC 1. Photographic evidence showed that seven exterior columns were severed near the southwest corner at the lower floors. Unlike the towers, the SFRM in WTC 7 likely remained intact except for local areas around the debris impact damage at the southwest corner. All three buildings were stable with the impact damage, but the WTC 2 building section above the aircraft impact damage leaned to the east and south.     

Overview of the Structural Design of World Trade Center 1, 2, and 7 Buildings

This paper summarizes the primary structural systems that comprised World Trade Center (WTC) 1, 2, and 7, which were destroyed in the terrorist attacks of September 11, 2001. There were four major structural subsystems in the towers: the exterior walls, the core, the floor system, and the hat truss. The major structural systems within WTC 7 were the foundation, exterior moment frames, floor system, interior columns, and column transfer trusses and girders. At the time of design and construction, the WTC towers were innovative in many ways, and resulted in a tremendous increase of open-plan commercial office space in downtown Manhattan. As the first of four papers, this paper summarizes the structural and passive fire protection features of each building, and focuses on the structural systems which played a critical role in the outcome of the attacks of September 11, 2001. Three companion papers address the effects of aircraft impact damage on the WTC towers and debris damage on WTC 7, the effects of fire on the three buildings, and how these events contributed to building collapse by describing the contribution of key structural systems to the overall building behavior and collapse, such as the floor systems and hat trusses in WTC 1 and WTC 2 and the floor connections around Column 79 in WTC 7.     

Reconstruction of the Fires and Thermal Environment in World Trade Center Buildings 1, 2, and 7

The National Institute of Standards and Technology (NIST) conducted an extensive investigation of the collapse of the three tall World Trade Center (WTC) buildings. A central part of this investigation was the reconstruction and understanding of the initiation and spread of the fires. This paper describes the reconstruction of the fires, the thermal environment they created within the buildings, and the raising of the temperatures of the structural components. NIST analyzed thousands of documents, interviews, photographs, and videos to obtain information on the layout of the floors and the progress of the fires. Experiments provided information on the factors likely to have determined the fire growth. Simulations using the Fire Dynamics Simulator gave good agreement with the fire spread as observed at the windows. Imposition of the probable thermal environment on the structural steel produced maps of the probable temperature profile of the steel as the fires progressed. For WTC 1 and WTC 2, even in the vicinity of the fires, it was unlikely that the columns and floor trusses with intact insulation heated to temperatures where significant loss of strength occurred. This was in part due to the short time between aircraft impact and building collapse. There were regions of the towers in which the loss of structural strength of floors and columns, whose insulation had been damaged by aircraft impact, was likely. For WTC 7, even though the insulation was intact, the long periods of heating resulted in floor components whose temperatures exceeded 600°C, but columns did not exceed 300°C.     

Structural Response of World Trade Center Buildings 1, 2 and 7 to Impact and Fire Damage

The National Institute of Standards and Technology (NIST) conducted an extensive investigation of the collapse of World Trade Center towers (WTC 1 and WTC 2) and the WTC 7 building. This paper describes the component, subsystem, and global analyses performed for the reconstruction of the structural response of WTC buildings 1, 2, and 7 to impact and fire damage. To illustrate the component and subsystem analyses, the approach taken for simulating the performance of concrete slabs and shear stud connectors in composite floors subject to fire conditions are presented, as well as steel floor framing connections for beams and girders. The development of the global models from the component and subsystem analyses is briefly described, including the sets of input data used to bound the probable conditions of impact and fire damage. The final analysis results that were used to develop the probable collapse hypotheses, and a comparison of the results against observed events, are presented for each building. A review of research activities focused on improving understanding of structural system response to multi-floor fires following the WTC disaster is also provided.     

Seismic collapse risk assessment of super high‐rise buildings considering modeling uncertainty: A case study

Based on the multiple stripes analysis method and the first‐order second‐moment method, a seismic collapse risk assessment considering the modeling uncertainty is carried out for a 118‐story super high‐rise building with a typical mega‐frame/core‐tube/outrigger resisting system. The sensitivity of the median collapse capacity of the building to eight main parameters is analyzed, and then the modeling uncertainty is determined. Both the effects of the characterization methods of bidirectional ground motion intensities and the selection of the ground motion intensity measure (IM) on the aleatory randomness are investigated. The mean estimates approach and the confidence interval method are used to incorporate both the modeling uncertainty and the aleatory randomness, and then the annual collapse probability, the collapse probability at the maximum considered earthquake (MCE) intensity level and the acceptable values of the collapse margin ratios (CMRs) with different confidence levels for the building are calculated. The results show that the influence of the modeling uncertainty on the collapse capacity of the super high‐rise structure is negligible, the aleatory randomness caused by the record‐to‐record variability is significant, and an appropriate ground motion IM can significantly reduce the aleatory randomness.     

核电站在大型商用客机撞击下损伤破坏研究进展

2001年9·11事件后,美国核能管理委员会、核能研究院和能源部以及我国核安全局相继出台相关规范,明确规定核电站设计必须考虑大型商用客机的意外和恐怖性撞击作用。从飞机机身的整体撞击效应、引擎局部撞击效应以及核岛厂房结构振动3方面,回顾了核电站重要基础设施在飞机撞击下损伤破坏的理论模型、原型和缩尺试验以及数值仿真研究等的工作进展,对课题组近年来在该领域的研究工作进行了简要介绍,包括4种典型飞机（F4战斗机、空客A320、A380和新舟MA600）和4类核岛设施（预应力钢筋混凝土屏蔽厂房、普通钢筋混凝土屏蔽与附属厂房、钢板混凝土屏蔽与附属厂房,普通钢筋混凝土大型冷却塔）的精细化有限元模型及其撞击全过程的数值仿真分析。此外,介绍了引擎撞击普通钢筋混凝土和超高性能混凝土靶板的缩尺试验和数值模拟分析工作,以及引擎撞击局部效应的计算方法。最后,指出了该领域已有研究在撞击力计算、整体响应、局部破坏、振动效应和多灾害作用方面的不足和进一步研究方向的建议。     

Collapse simulation of reinforced concrete frame structures

Study of collapse‐resisting properties of structures has attracted widespread attention because of frequently occurring earthquakes and extreme events (e.g. blast) around the world. The developments in computational methods have enabled researchers to numerically simulate the collapse of structures under different kinds of loadings and provide reliable assessments of the collapse performance of structures. The dynamic nature of structural collapse requires a direct integration algorithm to solve the equations of motion of the numerical simulation model. A major concern in such simulations is the computational efficiency, which stems from the need to use a small time step size in both implicit algorithm and explicit algorithm. In this paper, modeling techniques to simulate typical failure mechanisms in reinforced concrete frame structures combined with the application of the recently developed explicit, unconditionally stable, parametrically dissipative KR‐α integration method to investigate collapse simulation are presented. A fiber beam‐column element is used to model the frame members, where the material nonlinearities, especially material softening, are simulated by a plastic damage model combined with a failure criterion. Numerical examples are presented to illustrate the proposed collapse simulation technique. The results indicate that the proposed technique provides an accurate result and has exceptional computational efficiency. Copyright © 2015 John Wiley & Sons, Ltd.     

Failure analysis of a transmission tower subjected to combined wind and rainfall excitations

Many transmission towers have collapsed during severe gales and thunderstorms, and these failures have traditionally been attributed simply to wind loading. This study attempts to reveal the full failure mechanism of tower structures under strong wind excitation considering the rainfall effect. First, the calculation of rain load for a tower‐line system is provided. Then, an uncertainty analytical method for estimating the strength capacity and predicting the failure pattern of transmission towers induced by wind and rain loads is presented. Next, a real collapsed transmission line is considered to establish the finite element model, followed by the determination of the most vulnerable tower, which is then used to perform the uncertainty analysis. The results illustrate that the collapse basic wind speed considering the rainfall effect is smaller than the pure wind condition. In addition, the failure probability of the tower body is the largest, which is consistent with the deterministic method, whereas the most vulnerable tower began to fail from the tower leg in reality, indicating that the initial broken position of the transmission tower may not occur in the location with the largest probability and that the deterministic method is invalid in some cases. Finally, the influence of the wind attack angle and bundle number of transmission conductor is investigated. The most unfavorable wind attack angle is 90°, and the rainfall effect becomes increasingly significant with increases in the bundle number; this relationship should be given particular attention.     

A cross‐scale refined damage evolution analysis of large commercial aircraft crashing into a nuclear power plant

Since the 9/11 attacks, whether nuclear power plants (NPPs) can withstand the malicious impact of large commercial aircraft has become a question that must be considered in the design phase. Refined model and fine‐scale element reflect more accurately the failure procedure and behaviour. However, due to the exceedingly complex structure of NPP, the traditional meshing method requires a substantial number of geometric operations involving point, line, area, and volume, leading to a tedious modelling process and very high computational costs, as well as making it difficult to modify and optimize the model. This paper combines the scaled boundary finite element method with the octree technique to refine nuclear engineering damage evolution analysis and establish a refined numerical model of the Generation III⁺ NPP, considering the detailed equipment hatch, air intake, and internal steel containment vessel structures. Subsequently, the refined damage evolution analysis of a large commercial aircraft crashing into an NPP was developed. The mesh size sensitivity, impact region shape comparison, and the influence of different impact heights were discussed. The results indicate that the cross‐scale refined meshing and analysis method provides a high‐quality discrete grid with fewer elements. Furthermore, this method is highly flexible, more accurately simulating the damage evolution and gradual destruction process. We recommend future structural optimization for the air intake and conducting detailed analyses at this location. The cross‐scale analysis method presented in this paper enables a rapid, refined simulation of a malicious impact by a large commercial aircraft. Additionally, it provides technical support for future studies of the responses of NPPs' internal structures, systems, and equipment under extreme earthquake and other disaster conditions.     

Vulnerability and Robustness of a Security Skyscraper Subjected to Aircraft Impact

Abstract: Ultra‐high‐performance concrete (UHPC) is particularly suitable for application in aircraft‐impact‐resistant high‐rise buildings for combined load‐bearing and protective structures. The material provides very high—steel‐like—compressive strength, sufficient ductility, and fire resistance due to the addition of steel and polypropylene fibers. The following contribution is focused on two key aspects: hydro‐code simulations of structural UHPC walls which protect vertical escape and rescue routes and structural dynamic simulations of the global structure to investigate the impact resistance considering the sudden loss of external columns. A high‐speed dynamic material model for UHPC is obtained by implementing the results of a series of Hopkinson‐Bar experiments which were recently published. The strain‐rate‐dependent material properties are implemented in the established RHT‐Concrete‐Model for hydro‐code applications being furthermore extended by a tensile softening law for fiber‐reinforced UHPC. Based on this material model a series of aircraft‐engine impact experiments are configurated supported by three‐dimensional nonlinear hydro‐code prognosis simulations. With a total of six impact experiments on combined fiber‐ and rebar‐reinforced UHPC panels, all relevant damage states of the structural wall are obtained. The experimental results are compared to the hydro‐code prognosis simulations to validate the simulative approach and the material model for UHPC. In addition to the local impact behavior, structural dynamic numerical simulations of a global high‐rise structure are presented being focused on the effect of the sudden and notional loss of columns in coincidence with the aircraft impact load function.     

Progressive-Failure Analysis of Buildings Subjected to Abnormal Loading

Abstract: This article presents a progressive‐failure analysis procedure to evaluate the performance of a building framework after it has been damaged by unexpected abnormal loading, such as an impact or blast load caused by a natural, accidental, or deliberate event, or as a result of human error in design and construction. To begin with, it is assumed that some type of short‐duration abnormal loading has already caused some form of local damage to the structure. The residual load‐carrying capacity of the remaining framework is then analyzed by incrementally applying the prevailing long‐term loads and any impact debris loads, and progressively tracing the strength deterioration of the structure until either a globally stable state is reached or progressive collapse occurs for part or all of the structure. The computer‐based procedure is based on the displacement method of analysis. The effect of both axial force and shear deformation on member and structure stiffness is accounted for in this article (Liu, 2004; Xu et al., 2004). The stiffness matrices for framework members account for elastic–plastic bending, shearing, and axial deformations, and are progressively updated under incrementally increasing loads through the use of degradation factors that characterize stiffness deterioration. The computational model allows the incremental analysis to proceed beyond loading levels at which structural instabilities occur, including the formation of plastic collapse mechanisms and the disengagement of members from the building superstructure. The progressive‐failure analysis procedure is quite general and, with the appropriate choice of material constitutive model, may be applied to building frameworks of any type (concrete, steel, composite, etc.). Herein, a constitutive model for structural steel is adopted to account for elastic–plastic behavior under single or combined forces, and the progressive‐failure analysis procedure is illustrated for two example planar steel moment frames.     

Zum Einfluß der Temperatur auf die Bemessung von Kühlturmschalen aus Stahlbeton

Temperature effects on the design of cooling tower shells. Bending moments caused by temperature constraints substantially influence required reinforcement quantities in cooling tower shells. Important parameters in linear structural analyses are the extents of characteristic thermal actions and their combinations as well as global reduction factors that account for the loss of stiffness by cracking. The sensitivity to variations in temperature scenarios is presented using numerical simulations of a representative cooling tower shell and the design specifications of “BTR‐Kühltürme (2005)”. The characteristic design‐scenarios are simulated in geometrically and materially nonlinear computations to realistically estimate the loss of stiffness by cracking, the influence of temperature effects on the ultimate load bearing capacity as well as actual extents of steel and concrete stresses.     

Wind‐induced fatigue of large HAWT coupled tower–blade structures considering aeroelastic and yaw effects

An efficient approach for predicting wind‐induced fatigue in large horizontal axis wind turbine coupled tower–blade structures subject to aeroelastic and yaw effects is presented. First, aerodynamic loads under yaw conditions are simulated based on the harmonic superposition method and modified blade element momentum theory, in which wind shear, tower shadow, tower–blade interactions, aeroelastic, and rotational effects are taken into account. Then, a nonlinear time‐history of wind‐induced responses under simulated aerodynamic loads is obtained. Finally, based on these results, wind‐induced fatigue damage and lifespan are predicted according to linear cumulative damage theory. For completeness, the influences of mean wind speed, aeroelasticity, and yaw angle on horizontal axis wind turbine fatigue life are discussed. The results indicate that the aerodynamic loads and residual fatigue life can be estimated accurately by the proposed model, which can be used to simulate the 3D wind fields of wind turbines under given wind conditions. The wind energy of the wind turbine blade is mainly concentrated at its edge and is weaker at the hub. Estimation of wind turbine fatigue life is therefore suggested to be based on the component with the shortest life, being the blade root. Furthermore, yaw conditions significantly shorten fatigue life and should not be ignored. Fatigue life is also rather sensitive to mean wind speed.     

How did the WTC towers collapse: a new theory

This paper uses a finite-element model to investigate the stability of the Twin-Towers of the World Trade Center, New York for a number of different fire scenarios. This investigation does not take into account the structural damage caused by the terrorist attack. However, the fire scenarios included are based upon the likely fires that could have occurred as a result of the attack. A number of different explanations of how and why the Towers collapsed have appeared since the event. None of these however have adequately focused on the most important issue, namely ‘what structural mechanisms led to the state which triggered the collapse’. Also, quite predictably, there are significant and fundamental differences in the explanations of the WTC collapses on offer so far. A complete consensus on any detailed explanation of the definitive causes and mechanisms of the collapse of these structures is well nigh impossible given the enormous uncertainties in key data (nature of the fires, damage to fire protection, heat transfer to structural members and nature and extent of structural damage for instance). There is, however, a consensus of sorts that the fires that burned in the structures after the attack had a big part to play in this collapse. The question is how big? Taking this to the extreme, this paper poses the hypothetical question, “had there been no structural damage would the structure have survived fires of a similar magnitude”?A robust but simple computational and theoretical analysis has been carried out to answer this question. Robust because no gross assumptions have been made and varying important parameters over a wide range shows consistent behaviour supporting the overall conclusions. Simple because all results presented can be checked by any structural engineer either theoretically or using widely available structural analysis software tools. The results are illuminating and show that the structural system adopted for the Twin-Towers may have been unusually vulnerable to a major fire. The analysis results show a simple but unmistakable collapse mechanism that owes as much (or more) to the geometric thermal expansion effects as it does to the material effects of loss of strength and stiffness. The collapse mechanism discovered is a simple stability failure directly related to the effect of heating (fire). Additionally, the mechanism is not dependent upon failure of structural connections.     

Response Phase Behaviours and Response Time Predictors of the 9/11 World Trade Center Evacuation

The evacuation of the World Trade Center (WTC) Twin Towers on 9/11 is one of the largest full scale high-rise emergency evacuations to date and provides an opportunity to learn from survivor experiences. Here, quantitative and qualitative data extracted from the UK WTC High-rise Evacuation Evaluation Database (HEED) study were used to: (i) calculate more fine-grained response times useful for evacuation modelling; (ii) investigate Response Phase behaviours; and (iii) see which of these behaviours and other factors predicted the response times. Analyses revealed that the majority of participants’ response times were within 0 min to 1 min of WTC1 being hit (rapid responders) and 1 min to 4 min (moderate responders). Logistic regression indicated that rapid responders were more likely to be participants in WTC2 than participants in WTC1, the tower that was currently under attack. Higher perceived risk and undertaking fewer if any tasks prior to evacuation also significantly predicted rapid response times. Conversely, response times beyond 1 min from WTC1 impact were significantly predicted only by increased numbers of Information Tasks being undertaken prior to evacuation. These tasks appeared to be undertaken more frequently prior to evacuation than were Action Tasks.     

Simulation of offshore wind turbine response for long-term extreme load prediction

When there is interest in estimating long-term extreme loads for an offshore wind turbine using simulation, statistical extrapolation is the method of choice. While the method itself is rather well-established, simulation effort can be intractable if uncertainty in predicted extreme loads and efficiency in the selected extrapolation procedure are not specifically addressed. Our aim in this study is to address these questions in predicting blade and tower extreme loads based on stochastic response simulations of a 5 MW offshore turbine. We illustrate the use of the peak-over-threshold method to predict long-term extreme loads. To derive these long-term loads, we employ an efficient inverse reliability approach which is shown to predict reasonably accurate long-term loads when compared to the more expensive direct integration of conditional load distributions for different environmental (wind and wave) conditions. Fundamental to the inverse reliability approach is the issue of whether turbine response variability conditional on environmental conditions is modeled in detail or whether only gross conditional statistics of this conditional response are included. We derive long-term loads for both these cases, and demonstrate that careful inclusion of response variability not only greatly influences such long-term load predictions but it also identifies different environmental conditions that bring about these long-term loads compared with when response variability is only approximately modeled. As we shall see, for this turbine, a major source of response variability for both the blade and tower arises from blade pitch control actions due to which a large number of simulations are required to obtain stable distribution tails for the turbine loads studied.     

Wind-driven rain on the facade of a monumental tower: Numerical simulation,full-scale validation and sensitivity analysis

Wind-driven rain (WDR) is one of the most important moisture sources that affect the hygrothermal performance and the durability of building facades. The facades of the Dutch monumental building St. Hubertus show severe deterioration caused by WDR. Assessment of the amount and intensity of WDR falling onto the facades is necessary as input for numerical heat-air-moisture (HAM) transfer models to analyse the causes of the moisture problems and the impact of remedial measures. In this study, a numerical simulation method based on Computational Fluid Dynamics (CFD) is used to predict the amount of WDR impinging on the south-west facade of the tower of the building. The paper focuses on the numerical simulation results, the validation of these results and their sensitivity to two parameters: the level of geometrical detailing of the computational building model and the upstream terrain aerodynamic roughness length. Validation is performed by comparison of the numerical results with a dataset obtained from on-site WDR measurements. It is shown that the CFD simulations provide fairly good predictions of the amount of WDR impinging on the south-west facade of the tower, except for the lower part. It is also shown that the local effects of geometrical facade details are significant and can yield differences in WDR exposure up to 40%, while their effect at other positions is negligible. Finally, the sensitivity of WDR simulations to the upstream aerodynamic roughness length is discussed.     

高层钢框架考虑损伤累积效应的地震倒塌分析方法

针对结构倒塌破坏的不确定性,提出一种用于高层钢框架结构在强震作用下结构倒塌全过程模拟的数值方法,该方法采用基于中心差分法的显式积分格式,通过定义结构的层损伤,将修正的K&K模型应用到结构中,以考虑结构在地震作用下强度和刚度的退化规律。通过编制有限元程序将该方法用于分析20层benchmark模型结构倒塌全过程和倒塌机理。分析表明,该考虑材料损伤累积效应的方法能更精确地确定高层钢框架结构的失效极限荷载,且在未知结构的失效破坏模式前提下,可较好地模拟在地震作用下结构的失效路径以及倒塌全过程和揭示结构的倒塌机理。     

The Thiel–Zsutty earthquake damage model,reformulated and extended

The Thiel–Zsutty (TZ) model predicts mean and the probability distribution function for earthquake damageability of building as a function of peak ground acceleration. ATC‐13‐1 provides an alternate damageability model based on modified Mercalli intensity characterization of ground motion and a beta distribution function for selected building types. This paper provides a reconciliation of the TZ and Applied Technology Council (ATC) methods. It is shown that the beta distribution can provide a continuous representation of the step‐wise TZ Markov distribution function. When the TZ model uses a compression factor for the standard deviation to represent the degree of uncertainty in the parameters, then the TZ results are found to be consistent with the ATC‐13‐1 distribution function for a specific compression factor of 0.40. This paper provides a new, simply applicable method to determine the damage distribution function for a given site, building type, and site conditions; using a beta distribution and allowing inclusion of the degree of confidence the assessor has in the determination of the parameters. New equations are provided to estimate the mean, standard deviation, and upper confidence limit of the damage ratio.