NIST NCSTAR 1-6D

Federal Building and Fire Safety Investigation of

the World Trade Center Disaster

Global Structural Analysis of the

Response of the World Trade Center

Towers to Impact Damage and Fire

(Chapter 4 - Appendix C)

Mehdi S. Zarghamee

Yasuo Kitane

Omer O. Erbay

Therese P. McAllister

John L. Gross

National Institute of Standards and Technology • Technology Administration • U.S. Department of Commerce

Chapter 4

Global Analysis

4.1 CONVERSION FROM SAP2000 TO ANSYS

Simpson, Gumpertz & Heger, Inc. (SGH) performed global analysis of the WTC 1 and WTC 2 towers

using global models of the two towers developed in ANSYS as described in Chapter 2. The models were

subjected to the aircraft impact damage and the temperature time histories resulting from the ensuing fire enviroimients. The global models described in this report, and the reference models in NIST NCSTAR 1- 2A, used the same coordinate system. As illustrated in Fig. 4-1, the z-axis in this coordinate system is parallel to the vertical axis of the building, the x axis is parallel to the long direction of the building's

central core, and the y-axis is parallel to the short direction of the central core. In the WTC 1 models, the origin of the coordinate system is located at the southeast comer of the building with the y-axis extending

to the north. In the WTC 2 models, the origin is located at the northeast comer of the building with the yaxis extending west.

(a) Isometric view

Figure 4-1. Coordinate system used In the analysis models.

The SAP2000 global models in NIST NCSTAR I -2A were linearly elastic and included interior and

exterior columns, spandrels, hat truss members, and floor slabs at mechanical floors. Only the

mechanical floors were individually modeled. The other floor slabs were modeled using a set of coupling

equations in the softw are to slave the displacement of certain nodes to the displacement of other nodes.

In this case, these coupling equations provided full rigidity within the plane of the floor slabs (the x-y

plane) and full flexibility out of this plane.

As most of the structural action that led to the collapse of the buildings took place within and above the aircraft-impacted floors, the reference models were tmncated for each building below the lowest damaged

floors. The model of WTC 1 was tmncated at Floor 89, five floors below the zone of impact, and a series of equivalent vertical linear springs were introduced at the base of this tmncated model to represent the

NIST NCSTAR 1-6D, WTC Investigation 167
Chapter 4

stiffness of the interior columns and exterior walls beneath the level of truncation. Similarly, the model

of WTC 2 was truncated at Floor 73.

The truncated SAP2000 models were converted to ANSYS and modified to capture the failure modes of

floors and columns and to enhance numerical efficiency. The global models included geometric and

temperature-dependent material nonlinearities, including creep.

4.1.1 ANSYS Models

The ANSYS models were the direct translation of the truncated SAP2000 models. During the translation

of the models, the coordinates of the nodes, cross sectional properties of members, including orientation

and offset of the cross sections, nodal loads, material properties, and member end releases were

automatically converted from each SAP2000 database into an ANSYS database. Table 4-1 summarizes

the conversion used in translating the element types between SAP2000 and ANSYS. Comparison of the

results obtained for the gravity analysis of WTC 1 and WTC 2 from the SAP2000 models and translated

ANSYS models are discussed in the next section.

Table 4-1 summarizes the correspondence between element types containd in the SAP2000 model and

those in the converted ANSYS model. Table 2-1 previously presented a description of the various

ANSYS elements used in the global models. Gravity load analyses of the two buildings were then

performed using both the truncated SAP2000 and converted ANSYS models to verify the fidelity of the

conversion.

Table 4-1. Conversion from SAP2000 element types to ANSYS element types

SAP2000 Element Types ANSYS Element Types

Frame/Cable elements

Shell elements

Springs

BEAM188/189 later changed to BEAM24

SHELL63 later changed to SHELL181

LINKS

Following these analyses, the linear, elastic material properties of the converted ANSYS models were

replaced with temperature-dependent inelastic material properties as defined for all material types in Chapter 3 of NIST NCSTAR 1-6C. These material types were assigned to the elements according to their

material and cross sectional properties and their locations in the buildings. In the SAP2000 global model,

each cross section was assigned a yield value representing the material capacity for that cross section.

During the translation to ANSYS, a different name was given to each cross section and material

combination, which resulted in a unique material index. Using this material index, the material properties

of all elements were replaced with temperature-dependent inelastic material properties. In the actual

buildings, the rectangular tube columns in the exterior wall were typically fabricated from four plates,

Plate 1 (see Chapter 6 of NIST NCSTAR 1-6C for more information) and could have a different specified

yield strength than the rest (Plates 2 and 3). Examination of drawings in the region of interest showed

that all these plates had the same yield strength. Therefore, in the translation process, all plates in the same column cross section were considered to be of the same material.

The ANSYS models were also modified to include representation of the floor slabs, which except at mechanical floors, were not included in the SAP2000 models. Floor elements added into the ANSYS

model included the core slabs, those core beams that were framed with moment connections at their ends,

168 NIST NCSTAR 1-6D, WTC Investigation
Global Analysis

and the office area slabs. Figure 4-2 shows the analytical representation of the core and office area floors and the core beams included in the models. Beams in the core that were framed without moment

connections were not included in the model because they cannot transfer shear between columns without

significant relative displacement. However, their axial stiffness was combined with in-plane stiffness of

the floor slab, and then shell elements with this composite in-plane stiffness were used to model the floor.

An equivalent concrete thickness and modulus was calculated for the office area floors to match the in- plane stiftness of the composite floor system which included the concrete slab, the floor trusses, and the

floor seats. The thickness of the core slab was taken from the PANYNJ drawings, but the elastic modulus was adjusted to match the in-plane stiffness of the composite floor that included the steel beams and the concrete slab. Both core and office area floor slabs were modeled with linear-elastic material properties

for lightweight concrete. Later analyses with these models indicated that these slabs, composite with their

framing members, could redistribute load locally amongst neighboring columns and transfer lateral loads

to the exterior walls as collapse initiated and WTC 2 began to tilt.

Floors in the global models also provided diaphragm stiffness at each level. However, the floors were not modeled with sufficient detail to capture such floor behaviors under elevated temperatures as sagging and

failure of floor-wall connections. Instead, these effects were incorporated into the global analyses as fire- induced damage, as described in Section 2.5.

(a) Office and core area floor (b) Core area floor and core beams

Figure 4-2. Office and core area floors and core beams.

NISTNCSTAR 1-6D, WTC Investigation 169
Chapter 4

Figure 4-3. Location and IDs of outriggers and supporting columns.

Due to the limitations of the BEAM 188 element used to model spandrels, columns, and truss members, a

set of preliminary global analyses were conducted without including creep and inelastic buckling in the core and exterior wall columns, as discussed in Appendix C of this report. Plasticity and large deflection were the only nonlinearities included in those analyses. Later, the BEAM! 88 element was replaced with

the BEAM24 element to eliminate the limitations on creep and inelastic buckling. As shown in the global

analyses that included consideration of creep and buckling, described in Section 4.2, creep strains and

inelastic column buckling played a very significant role in the collapse of the towers.

Figure 4-3 shows the hat trusses in the global models. The hat trusses connected the exterior walls and

the core columns. As seen in the figure, four outrigger members on each face of the core extended

outward from the core to the exterior walls. Hat truss members were provided with plasticity in the

preliminary global models without creep and in the final WTC 1 global model with creep. The hat truss of the WTC 2 global model with creep was part of the "superstructure" where elastic properties were

used. Further discussion of this is presented in Section 4.2.2. The hat trusses were not modeled with

sufficient detail to capture the onset of buckling. However, the yield strength of the outrigger elements in the final WTC 1 model was set so that compressive yielding would occur when axial load reached the

compressive capacity of the members.

4.1 .2 Validation of Translated ANSYS Global Models

In order to verify the accuracy of the conversion of the building models from SAP2000 to ANSYS, prior

to adding material nonlinearities and elements representing the floor slabs to the ANSYS models, the

translated ANSYS models were subjected to gravity dead and live loads, and the ANSYS results were compared to the results of SAP2000 global models. The comparison included the calculated overall

displaced shapes, the maximum displacements, vertical base reactions at each construction stage, and

element forces for a set of randomly selected members from different parts of the buildings.

170 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

The gravity analysis was performed in three stages to simulate construction sequencing in the actual

erection of the buildings. In Stage 1 the portion of the towers up to and including Floor 106 was analyzed

under self-weight. In Stage 2 the members above Floor 106 were added, and the analysis was performed

for the effects of dead loads of the newly added members. In Stage 3, the superimposed dead load and 25

percent of the design live load was added at each floor level to obtain an estimate of the deformations and

stresses in each building under normal occupancy conditions.

Figure 4-4 shows the deformed shape calculated for WTC 1 by the ANSYS model and the truncated

SAP 2000 model, following Stage 3 analysis. Figure 4-5 provides a similar comparison for WTC 2.

Maximum displacement = 5.07 in

(a) WTC 1 ANSYS Model at Stage 3

Figure 4-4. Displaced shape of WTC 1 at the end of gravity analysis.

(b) WTC 1 SAP2000 Model at Stage 3

(Displacement is only shown on shell elements.)

Maximum displacement = 8.14 in

(a) WTC 2 ANSYS Model at Stage 3 (b) WTC 2 SAP2000 Model at Stage 3

(Displacement is only shown on shell elements.)

Figure 4-5. Displaced shape of WTC 2 at the end of gravity analysis.

Table 4-2 summarizes the maximum displacement and vertical reactions at the base for all stages of the

gravity analysis of WTC 1, and Table 4-3 presents similar data for WTC 2. As can be seen, the deformed

shapes as well as the maximum displacements and vertical reactions obtained from the analyses

performed with the ANSYS models agree well with the results of the similar analyses performed with

NISTNCSTAR 1-6D, WTC Investigation 171
Chapter 4

SAP2000. The maximum difference in displacements between the two models was less than 1.4 percent

for WTC 1 and 0.7 percent for WTC 2. The maximum difference between base reactions predicted by the

two analyses was 1 .2 percent for WTC 1 and 0.3 percent for WTC 2.

Table 4-4 presents a comparison of the axial forces computed from the ANSYS and SAP2000 analyses

for a randomly selected set of elements from different parts of WTC 1. Table 4-5 presents similar data

for WTC 2. The agreement between the results obtained from the ANSYS and SAP2000 analyses is quite

good.

Table 4-2. Comparison of maximum displacements and base reactions of WTC 1 from

translated ANSYS and SAP2000 models.

Stage

Maximum Vertical Displacement (in.) Base Reaction Sum (kip)

ANSYS SAP2000

Percent

Difference ANSYS SAP2000

Percent

Difference

1 -2.87 -2.83 1.4 55,600 54,940 1.2

2 -4.76 -4.74 0.4 98,470 97,850 0.6

3 -5.09 -5.07 0.4 107,040 106,450 0.6

Table 4-3. Comparison of maximum displacements and base reactions of WTC 2

obtained from translated ANSYS and SAP2000 models.

Stage

Maximum Vertical Displacement (in.) Base Reaction Sum (kip)

ANSYS SAP2000

Percent

Difference ANSYS SAP2000

Percent

Difference

1 -5.87 -5.91 -0.7 125,050 124,680 0.3

2 -7.67 -7.71 -0.5 166,950 166,980 -0.02

3 -8.10 -8.14 -0.5 180,250 180,360 -0.06

Table 4-4. Comparison of axial forces in randomly selected elements from WTC 1 model

at the end of gravity analysis.

Location and Type of Selected Element

Axial Force (kip)

ANSYS SAP2000

Exterior Coluirm 302 at Floor 104 -77 -69

Spandrel between Columns 124 and 125 at Floor 102 0 0

Outrigger member between at Floor 1 10 -39 -48

Vertical hat truss member at 1005 core column line at Floor 109 -74 -91 Horizontal hat truss member at Floor 107 21 19 Horizontal hat truss member at Floor 108 170 150

Core Column 602 at Floor 97 -738 -745

Core Column 501 at Floor 93 -2,180 -2,190

Core Column 1001 at Floor 89 -2,570 -2,590

Spandrel between Columns 339 and 340 at Floor 100 0 0

172 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

Table 4-5. Comparison of axial forces in randomly selected elements from WTC 2 model

at the end of gravity analysis.

Location and Type of Selected Element

Axial Force (kip)

ANSYS SAP2000

Core beam at Floor 107 11 6 Inclined truss member at hat truss at Floor 107 -34 -4 Inclined truss member at hat truss at Floor 108 36 8 Inclined truss member at hat truss at Floor 108 -580 -670

Core Column 502 at Floor 87 -1,930 1,940

Core Column 1001 at Floor 82 -3,270 -3,290

Core Column 1002 at Floor 87 -1,910 -1,920

Core Column 1008 at Floor 82 -3,400 3,520

Core Column 1003 at Floor 107 -590 -608

Exterior Column 122 at Floor 82 -313 -313

Exterior Column 329 at Floor 82 -228 -230

Exterior Column 130 at Floor 107 -222 -202

Spandrel between Columns 138 and 139 at Floor 83 0 0

Spandrel between Columns 447 and 448 at Floor 87 0 0

4.2 GLOBAL ANALYSIS WITH CREEP

4.2.1 Introduction

This section presents the results of analyses conducted with global models that included consideration of

plasticity, geometric nonlinearity relating to large displacements, inelastic buckling, and creep, and are referred to hereafter as global models or global analysis with creep. As noted earlier, a preliminary set of

global analyses were conducted on models that did not include creep and could not simulate inelastic buckling of columns with fidelity. The results of these preliminary analyses are presented in Appendix C

of this report, and are referred to as global analysis without creep. Due to the limited non-linear features

in the preliminary global models without creep, global instability could not be captured during

temperature time history analyses.

The results of the global analyses with creep are presented in Section 4.2.4 for WTC 1 and in Section 4.2.5 for WTC 2.

4.2.2 Modifications to the Global Model with Creep and Inelastic Buckling of

Columns

Preliminary global analyses with creep resulted in an unacceptably slow rate of convergence. This was

due to the size of the models and the nonlinear effects of temperature-dependent material properties,

especially creep. To reduce the size of the global models and to enhance the computational efficiency

without adversely affecting the fidelity of the results, a set of modifications were made. These

modifications and their effects on the analysis results are discussed in this section. Table 4-6 summarizes

the number of degrees of freedom, number of elements, and number of constraint equations in WTC 1 and WTC 2 global models before and after the modifications.

NIST NCSTAR 1-6D, WTC Investigation 1 73
Chapter 4

Table 4-6. Global model properties before and after modifications for computational

efficiency.

WTC 1 WTC 2 Before After Before After

Item Modifications Modifications Modifications Modifications

Number of Degrees of Freedom 291,670 265,760 487,260 196,900

Number of Constraint Eqs. 31,680 28,330 53,890 12,560

Number of Elements 63,880 57,680 106,460 38,130

Number of Beam Elements 48,200 43,600 81,280 32,540

Number of Shell Elements 15,680 14,080 25,180 5,490

Removal of Floors below Impact Zone

The parts of structures below the impact zones (Floor 89 to Floor 91 in WTC 1 and Floor 73 to Floor 77

in WTC 2) contributed little to the overall behavior of the buildings. Previous analyses of subsystem

models and preliminary global models showed that the elements below the impact zone did not experience plastic deformations or buckling. Therefore, they were eliminated to further reduce the size of

the models. With this modification, the global model for WTC 2 was truncated at Floor 77 just above the

mechanical floors and the global model for WTC 1 was truncated at Floor 91.

Release of Axial Degree of Freedom of Spandrels

The spandrel elements in the exterior wall were modeled using BEAM 188 elements. These elements

caused convergence problems when thermal expansion caused buckling of spandrels. Based on visual

evidence, buckling of spandrels did not compromise their ability to transfer shear and bending moment

and did not play a very important role in the collapse sequence. Therefore, the axial degree of freedom was released on these spandrel elements, avoiding buckling due to development of large axial force in the

spandrels. However, these BEAM 188 elements could still transfer shear and bending moments. The

coefficient of thermal expansion of spandrels was also removed so that the spandrels would not expand

with temperatures.

Removal of Coefficient of Thermal Expansion from the Slab in the Office Area

Since trusses were not modeled individually, the office area slab buckled easily when thermal expansion was restrained by the exterior wall. Artificial buckling of the slab caused convergence problems in the

global analysis. Since buckling of the slab in the actual buildings was resisted by the joists, and was not observed in any of the detailed full floor models, this slab buckling mode was considered unlikely to represent real building behavior. Consequently, the coefficient of thermal expansion for the slab in the

office area was set to zero.

Neglecting the thermal expansion of the office area slabs did introduce small errors in the out-of-plane

bending of columns extending between a hot floor and a cool floor, but such errors were small for columns extending between two hot floors. The error introduced by this modification was not expected to change failure modes or collapse sequence in the global analysis, because thermal expansion of floors was

hmited to less than a few inches (see Appendix A). The full floor models thermally expanded and pushed

174 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

outward on the columns until the thermal expansion was overcome by the floor sagging and the floors pulled inward on the exterior columns..

Use of Superelement in WTC 2

The term "superelement" is used to indicate substructuring, in which a portion of a large model expected

to remain elastic is condensed out from the model as a whole. In this technique, the stiffness, damping

and mass matrices for the substructure elements are calculated once and used throughout the analysis

without any further change. One can calculate stresses and strains in individual elements in the

superelement allowing verification of the assumption that the substructure elements remain elastic, or nearly so. The WTC 2 model was suitable for such modification as earlier analyses indicated that the

section of the building above Floor 86 would remain nearly elastic. Therefore, this portion of the

structure was converted into a superelement.

The use of this superelement in the WTC 2 analyses reduced the solution time required to complete a

single iteration by a factor of three. However, it was recognized that if the hat truss members became

inelastic and highly nonlinear, such nonlinearities could not be captured. Moreover, when the

superelement is used, the effects of construction sequence on the load distribution between core and wall

elements cannot be represented, since the birth and death option carmot be used in a superelement. As

shown below, the effect of not including construction sequence was evaluated and found to introduce an

error of less than 12 percent for vertical displacement.

To evaluate whether any member in the hat truss exceeded its elastic limits, the stresses in all elements

within the superelement were calculated at the end of each time interval. For this purpose, a separate

model that included the elements at and above Floor 86 was created. In this model, the material

properties of all elements were replaced with elastic material properties. At each time interval, the

displacements that were obtained from the global model at Floor 86 were imposed on the new model at the same level. Dead and live loads were also applied on the model. Member forces were calculated and

compared with their capacities. The results are discussed in Section 4.2.5.

Change from BEAM188 to BEAM24 Elements

In the global models without creep, columns were modeled by BEAM188 (3D hnear finite strain beam)

elements. The analysis could not be conducted with elements of this type capmring time dependent creep

behavior of steel. Frequent convergence problems occurred when thermally induced creep and buckling

of columns was in process. Different element types were tested to determine whether thermally induced

buckling and creep could be capmred. Finally, BEAM24 element was selected, and the element type for the columns was changed from BEAM 188 to BEAM24 (3D thin-walled beam).

Construction Sequence

Construction sequence was not included in the global models with creep. The effect of neglecting

construction sequence was examined for both buildings. When construction sequence was not included in the analysis, the total axial loads in columns along the exterior walls increased by 7 percent to 15 percent.

Similarly, the total column loads supported by the core columns decreased by about 10 percent.

NISTNCSTAR 1-6D, WTC Investigation 175
Chapter 4

Tables 4-7 and 4-8 indicate the differences in column loads when construction sequence either was or was not considered.

Table 4-7. Comparison of total column loads between WTC 1 models with and without

construci ion sequence

North

w/ Const w/o Con.st

South

w/ Const w/o Const

East w/ Const w/o Const

West

w/ Const w/o Const

Core

w/ Const w/o Const

Floor 93 - 94

Floor 94 - 95

Floor 95 - 96

Floor 96 - 97

Floor 97 - 98

Floor 98 - 99

12.307 13.145

11,922 12,760

11.450 12.281

1 1 .065 1 1 ,895 10.602 11,426

10.217 11.040

12,383 13,191 11,999 12.806

11,530 12,329

11,145 11.944 10.686 11.478 10.302 11.092

8,910 10,036 8,580 9,708

8,339 9,475

8,012 9,151

7,763 8,911 7.439 8.591

8,933 10,049

8,605 9,723

8,365 9,492 8,040 9,170

7,793 8,932

7.471 8,613

47,525 43,638

45,573 41,682

43,598 39,703

41,633 37,735 39,669 35,767

37.714 33.808 Note: Compression is positive. Units are in kip.

Table 4-8. Comparison of total column loads between WTC 2 models with and without

North South East West Core

w/ Const w/o Const w/ Const w/o Const w/ Const w/o Const w/ Const w/o Const w/ Const w/o Const

Floor 78 - 79 13.536 15.304 13.442 1 5.000 18.861 20.169 18,805 20.1 19 78,104 72,156 Floor 79 -80 12.965 14.723 12,877 14.424 18,650 19,970 18,596 19.923 76,197 70,246 Floor 80 -81 12,892 14,675 12,810 14,379 17,959 19,257 17,903 19.207 74,160 68,206 Floor 81 -82 12,367 14.141 12,292 13,851 17,728 19,036 17,673 18,989 71,824 65,866

Floor 82 -83 12,279 14.078 12,208 13.789 17,064 18,353 17.008 18,301 69,777 63,815 Floor 83 -84 1 1.775 13.567 1 1.712 13.284 16.816 18.1 14 16.761 18.1 14 67.793 61,828 Note: Compression is positive. Units are in kip.

The calculations showed that the outriggers in the WTC 1 simulations were more highly stressed when

the construction sequence was not considered. Since it was believed that the hat truss played an important

role in transferring loads in WTC 1, the yield strengths of the materials for these outriggers in WTC 1 were artificially increased to account for the incorrect increase in compressive stresses when construction

sequence was not considered.

The difference in maximum displacement calculated with and without consideration of construction

sequence was within 12 percent for both WTC 1 and WTC 2. Figures 4-6 and 4-7 present the differences

in calculated displacements for analyses in which construction sequence either was or was not considered,

respectively, for WTC 1 and WTC 2. In these figures, the results presented for global analyses with creep

for the state of the structure before aircraft impact are for the analyses in which construction sequence was neglected; they differ from the corresponding results presented in Appendix C for global analyses

without creep as those analyses included the effects of the construction sequence.

176 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

(a) Core w/ construction sequence (b) Core w/o construction sequence

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Figure 4-6. Comparison of vertical displacement between WTC 1 models with and

without construction sequence.

NISTNCSTAR 1-6D, WTC Investigation 177
Chapter 4

(a) Core w/ construction sequence (b) Core w/o construction sequence

(c) South face w/ construction sequence (d) South face w/o construction sequence

(e) East face w/ construction sequence (f) East face w/o construction sequence

Figure 4-7. Comparison of vertical displacement between WTC 2 models with and

without construction sequence.

178 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

4.2.3 Boundary Conditions and Loading Steps

The global models with creep were vertically supported on elastic springs at Floor 9 1 for WTC 1 and

Floor 77 for WTC 2. These elastic springs represented the axial flexibility of the portion of the building

below these floors. The models were fixed against horizontal translation at these floors.

The collapse analysis of WTC 1 considered creep and was performed only for Case B damage conditions

and temperature time histories; and that for WTC 2 was only performed for Case D. Section 2.2.3 of this report provides a description of these damage conditions. Severed and heavily damaged core columns

were removed in the global model with creep, while only severed columns were removed in the global

models without creep.

To reduce the size of the global models as much as possible, members that were predicted to have been

severed or heavily damaged by the aircraft impact were removed from the models before applying the

gravity load. The floor dead and live loads were applied at each column node at the floor levels. These

forces were taken directly from the ANSYS global models converted from the reference SAP2000 global

models. WTC 1 and WTC 2 global models were then subjected to Case B and Case D temperature

conditions, respectively. NIST provided temperature data at 10 min intervals ranging from 0 min to 100 mm for WTC 1 and to 60 min for WTC 2. For the first loading step of temperature analysis,

temperatures of the structural elements were linearly ramped up from room temperature to the

temperatures at 1 0 min. After the first step, the temperatures were linearly ramped from the temperatures

at the end of the pre\'ious time step to those at the end of current time step.

4.2.4 Simulation of WTC 1 Collapse

The global model of WTC 1, described in the previous section, was used to simulate the response of the

building to aircraft impact damage and the ensuing fire environment. Studies performed on the isolated

exterior wall and core models and on the full floor subsystem models indicated that the calculated

response of these models to the Case B impact damage and temperature time history set, as described in Section 2.2.3, more closely matched the structural behavior observed in the visual evidence than did

analyses using the Case A data set. Therefore, only the Case B impact damage and temperature time

history set was used in the final global analyses.

The gravity loading, consisting of the structure's self weight, superimposed dead load, and 25 percent of

the design live loads, was applied as a concentrated joint load at each column-floor node, without

consideration of construction sequence effects. Then the temperature time history was applied in a series

of load steps. Table 4-9 summarizes the sequence of analyses that were performed. The results of each

analysis step were used as the initial conditions for the next analysis step. The steps consisted of alternate applications of fire damage, in the form of floor/wall disconnections or pull-in forces, followed by

application of temperature change. Section 2.5 describes the methods by which floor/wall disconnections

and pull-in forces were determined and applied.

After application of the Case B aircraft impact damage set, which included severe damage on the north

face and to the north side of the core, the results of analysis showed slight tilting of the portion of the

structure above the damaged area, to the north. In early stages of the application of the temperature time

history, temperatures increased significantly in the core columns where thermal insulation was projected

to be damaged. The resulting thermal expansion of these core columns was larger than the thermal

NISTNCSTAR 1-6D, WTC Investigation 179
Chapter 4

expansion of the exterior walls which occurred at the same time. Therefore, as the core columns in the

model expanded, they were restrained by the stiff hat truss, resulting in increased compressive forces in the core columns. This effect first became significant at 20 min. By 50 min some of the core columns

under the influence of the high temperatures and high compressive loads began to exhibit buckling and

large creep strains. As buckling and creep strains accumulated, the core began to displace downward.

Again, the movement of the tops of the core columns was restrained by the hat truss which now began to redistribute loads from the core columns to the exterior walls. At 80 min, pull-in forces were applied to the south wall, based on the observed evidence. At 87 min, the south wall started to bow inward

significantly, initiating the buckling of the south wall that triggered the collapse sequence.

Table 4-9. Analysis steps of WTC 1 ANSYS global model.

Analysis

Step Description

1 Dead and 25 percent of the design live loads were applied on the model of WTC 1 with impact damage.

2

r-> 1 / 111* A

' 1 ii'r* jIj "jii ii r\ ' y t r\ ' Floor/wall disconnections and pull-in lorces that were projected to occur between 0 mm and 10 min

were applied.

3 Column and spandrel temperatures were linearly ramped up from room temperature of 20°C to

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were applied.

5 (^nliimn V^VJlMlllil ^nrl dllU oL/ullVild t^nfinHrpl 1pmt>prritiirp<; tCll IL/vl dlLll C O \A/prp linparlv lilJCdl 1 y pHjincrprl dldllLL,CU frnm llMlll tpmtipratiirpQ IK^II lUd £11 V.11 Co ^\cl I \.\J 10 min lllill fn\\j ^.\J '^O mm111111.

yj 1Flnnr/wall k\J\J\.l Weill Hi^rnnnppfinn^i VJloCwllllC CllUllo Jinrl ClllLl niill-in IJLlll 111 fnrrp*; IV^lCCo tVial llldl wpvp WCIC nroiPftpH Lfl\JJvClW>l toWJ omir \J\^\,\X\. liptwppn L/ClWCdl '^O min 111111 ClllVJ anrl ^0 min \\.x\.\.\ were applied.

7 1 r»l 1 1 mn ^inn cr^finnrpl tpmr\pi*fi ti i vpc \x/prp 1 1 nparlA/ c n

opH Trr^m tpmnpr^i ti ii"PC t '?0 mm \c\ ^0 mm

sO 1F"lnnr/\A/Pill Wj\jYi Weill ni<ipnnnpptinn<; UloCVJllllCC IIVJIIO Jinrl clllVJ niill-in lJUll 111 Tnrpp<s IV/lWCo tn?it llldl w/prp WCIC nrnippfprl L/iC^JCClCU toIVJ oppiir VJCC Lll hptwppn UClWCCll J\J "^0 min 111111 finH dllU 40i \J min 111111 were applied.

Q ("'nliimn V.CIL11111I JinH dllU oLfdllVil *;nanrlrplCl tpmnpmtiirpQ ICllipCl dltll CO wprp WClC linp^irlv llllCdllV plifmcrprl ClJdll^CCl frr^m llVJlll tpirrnprjitiirpQ LClIlL/Cl dltll C O dlat ^0 llJilJ min to\\J 40 mm111111.

1 f) 1Rlnor/wall kKjyJil Wdll rli<ipnnnpptinn<s UloCCIllll'*. C llCllo Jinrl dllU mill-in L/Llll 111 ICICCO inrpp*; tVi^if llldl \\/prp WCIC nrnipptprl UIVJICCICVJ toWJ oppiir MCCLll hpfwppn UClWCCll 40"v/ min 111111 dllVi imH SO mm111111 were applied.

\ \ r^olinTin jinH ^n^inrirpl fpmnprjitiirp*; w/prp linp^irlv pViJincrpH frnm tPTTir^prjitiirpQ 40 min to SO min

12 Floor/wall disconnections and pull-in forces that were projected to occur between 50 mm and 60 mm

were applied.

13 Column and spandrel temperatures were linearly changed from temperatures at 50 min to 60 min.

14 Floor/wall disconnections and pull-in forces that were projected to occur between 60 min and 70 min

were applied.

15 Coluirm and spandrel temperatures were linearly changed from temperatures at 60 min to 70 min.

16 Floor/wall disconnections and pull-in forces that were projected to occur between 70 min and 80 min

were applied.

17 Column and spandrel temperatures were linearly changed from temperatures at 70 min to 80 min.

18 Floor/wall disconnections and pull-in forces that were projected to occur between 80 min and 90 min

were applied.

19 Column and spandrel temperatures were linearly changed from temperatures at 80 min to 90 min.

20 Floor/wall disconnections and pull-in forces that were projected to occur between 90 min and 100 min

were applied.

21 Column and spandrel temperatures were linearly changed from temperatures at 90 min to 100 min.

180 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

Figures 4-8 to 4-23 show the calculated vertical displacements for the exterior walls of WTC 1, before

the aircraft impact, immediately after impact, at 80 min after impact (at the end of Step 17), and 100 min

after impact. Figures 4—24 to 4—32 show similar data for the core columns. Figure 4-33 shows the

calculated vertical displacement of Floor 99 before the aircraft impact. Figures 4-34 to 4-37 show

changes in vertical displacement at Floor 99 from the state before the aircraft impact. Before aircraft impact, the maximum vertical displacements of the exterior walls and the core were respectively

calculated as 3.3 in. and 4.2 in. (see Figs. 4-8 and 4—24). As indicated in Fig. 4—33, the core had larger

vertical displacements by about 1 in. than the exterior walls at Floor 99. Since the construction sequence was not considered in the analysis, this difference in the vertical displacements changed initial loading

conditions of columns. As shown in Table 4-7, the total column loads on the north and south walls

increased by 7 percent at the impacted floors, the total column loads on the east and west walls increased

by about 14 percent, and the total column loads on the core decreased by about 9 percent, by ignoring the

construction sequence. Owing to impact damage on the north face and the north side of the core, WTC 1

tilted slightly to the north after the aircraft impact as can be seen in Fig. 4—34. The maximum calculated

displacement of the north wall increased from 3.1 in. to 5.9 in. as shown in Figs. 4-12 and 4—13, and the maximum displacement of the south wall decreased from 3.2 in. to 3.0 in. as shown in Figs. 4—20 and

4—21 . The calculated vertical displacement for the east and west walls only increased slightly.

In the early stages of thermal loading, the temperatures in the core area were rising. At 50 min, the calculated downward displacement of the core from plasticity, creep, and buckling of core columns was

1 .6 in. on average at Floor 99, as shown in Fig. 4—35. At 100 min, the downward displacement of the core was at 2.0 in. on average at Floor 99. Average increases of the downward vertical displacement at Floor 99 of the north, east, south, and west faces were 1.7 in., -0.24 in., -0.51 in., and -0.24 in. at 100 min,

respectively. As the bowing of the south wall increased, a section of the south wall above the bowed-in

area moved downward as shown in Fig. 4—37.

Figures 4—38 to 4—41 show the calculated out-of-plane displacements for the south wall before and after the aircraft impact, at 80 min (at the end of Step 17), and 100 min after impact. In these figures, inward

displacement is shown as positive. Figure 4-42 shows a plot of the variation of maximum calculated out- of-plane displacement in the south wall between 80 min and 100 min. Until pull-in forces were applied to the columns on the south wall over Floor 95 to Floor 99 at 80 min (Step 18), no inward bowing had

occurred. This matches the available video evidence. After the pull-in forces were applied, the bow

initiated and grew to 15.5 in. At about 87 min into the analysis, the inward bow began to increase

significantly. By 90 min, the rate of increase in inward bowing of the south wall slowed, and gravity

loads were redistributed to the east and west walls and the core. The predicted inward bowing gradually

increased to approximately 43 in. at 100 min. However, the south wall did not show instability (buckling)

at 100 min.

Analyses of isolated exterior wall substructure models and of the global model showed that the amount of

inward bowing predicted for the wall was highly sensitive to the magnitude of the applied pull-in forces. For a comparison, when pull-in forces were revised from the 5 kip magnitude used in the analyses

discussed above to 4 kip, the predicted inward bowing of the south wall decreased dramatically from

nearly 43 in. at 100 min to approximately 15 in. Minor upward adjustment of the pull-in forces, from the

5 kip used in the analyses, would have produced wall instability by 100 min. It is likely that the pull-in

forces in the actual building increased with time, and that likely, this inward bowing of the south wall did

trigger instability, which initiated the global structural collapse.

NISTNCSTAR 1-6D, WTC Investigation 181
Chapter 4

Figures 4-44 to 4-55 show calculated axial loads in exterior columns before and after the aircraft impact,

at 80 min (at the end of Step 17), and 100 min after impact. Figures 4-56 to 4-59 show the variation of

calculated axial loads in exterior columns along the different building faces at Floor 98 at different points

in time. Figures 4-60 to 4-63 show axial loads for the core columns before and after the aircraft impact,

at 80 min (at the end of Step 17), and 100 min. Figures 4-64 to 4-67 show the magnitude of axial load in each column at Floor 98; the size of axial load is proportional to the size of the circles. Tables 4-10 and

4-1 1 show the total column loads on each of the exterior walls and the core at Floor 98 and Floor 105,

respectively. Tables 4-12, 4-14, 4-16, 4-18, and 4-20 show total column loads on each of the exterior

walls and the core at different floors from Floor 93 to Floor 105. Tables 4-13, 4-15, 4-17, 4-19, and

4-2 1 show the predicted changes in the total column loads of each of the exterior walls and the core at various times in the analysis. Tables 4-22 to 4-24 show the difference in total column loads at Floor 98

and Floor 1 05 between the states before and after aircraft impact, just after aircraft impact to 80 min (at the end of Step 17), and between 80 min (at the end of Step 17) and 100 min.

After aircraft impact, gravity loads that were previously carried by severed columns were redistributed to other columns within the building. For example. Table 4-10 shows that the exterior columns of the north

wall at Floor 98 carried 10,974 kip load before the aircraft impact, and 10,137 kip just after aircraft impact, a net reduction of 837 kip. Table 4-1 1 shows that columns along the north wall at Floor 105 lost 732 kip of column loads as a result of the impact damage. Therefore, 732 kip out of 837 kip was

transferred by the hat truss to other portions of the structure, and the rest was redistributed to the adjacent

walls by the Vierendeel behavior of the walls themselves. Table 4-22 shows this load redistribution.

Due to the impact damage and the northward tilting of the building after impact, the south wall also lost gravity loads. Approximately 600 kip was transferred from the south wall by the hat truss. The east and

west walls and the core gained respectively gained 466 kip, 472 kip, and 400 kip, respectively.

As described above, during early stages of the thermal analysis, thermal expansion of the core area was

greater than that of the exterior walls. As this expansion occurred, the total column loads in the core

increased until 20 min into the analysis, as shown in Tables 4-20 and 4-21. After 20 min, the core began

to shed gravity loads as it displaced downward, under the influence of column creep and buckling. This

behavior continued until the south wall initiated inward bowing. At 80 min, about 6,800 kip of the

gravity load in the core was transferred by the hat truss to the exterior walls, as shown in Table 4-1 1. The

north, east, south, and west walls respectively gained 1,234 kip, 2,470 kip, 1,063 kip, and 2,021 kip from

this behavior. As shown in Table 4-23, the primary load redistribution path during the thermal loading

up to 80 min was through the hat truss.

Figure 4-58 shows that after 80 min. Columns 318 to 346 on the south wall unloaded as they bowed

inward. The vertical displacement of the south wall simultaneously increased as shown in Figs. 4-23 and

4-37, and the south wall shed 1,485 kip of the gravity load between 80 min and 100 min. As a result, the

east and west walls and the core all gained gravity loads. Figure 4-58 also shows load redistribution

within the south wall. As the columns near the center of the south wall unloaded after 80 min, the axial

loads on the columns on the east and west sides of the south wall increased.

Figures 4-68 to 4-71 show the calculated axial load demand-to-capacity ratio of each core column before

and after the aircraft impact, at 80 min (at the end of Step 17), and 100 min. Compressive capacities of

the core columns were calculated using Eq. E2-1 in the American Institute of Steel Construction's Manual

of Steel Construction Load and Resistance Factor Design (AISC LRFD) for inelastic buckling with an

effective length factor, K, of unity and a resistance factor of unity. At 100 min, a large number of core

182 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

columns (501. 601, 603, 606, 701, 703, 705, 707, 801, 804, 806, 807, 901, 903, 904, 905, 906, 908, and

1001) exhibited demand-to-capacity ratios larger than 0.7. Eight columns (501, 606, 705, 707, 804, 806,

807, and 908) exhibited ratios larger than 1.0. Although there is some significant uncertainty associated

with calculation of both the load on these columns and the buckling capacity, this indicates that at this time step, the core had either initiated or was close to initiating buckling-induced failure.

Figures 4-72 to 4-77 show the maximum strains in each column between Floor 93 and Floor 99 before

and after aircraft impact, at 10 min (at the end of Step 3), 40 min (at the end of Step 9), 80 min (at the end

of Step 18), and 100 min. These figures include elastic and inelastic strain, but no creep effects. Figures 4-78 to 4-81 show the same data, but include the additional effects of creep. Before the aircraft impact, all of the columns were loaded within their elastic range. After the aircraft impact, columns close

to removed columns (which included both severed and highly damaged columns) developed plastic strain. Plastic strain of the core columns increased significantly for the first 40 min, and then remained almost

constant until 100 min. At 100 min, the maximum elastic-plus-plasfic strain was 0.98 percent at Column

603. From 80 min to 100 min, plastic strain increased in almost all the bowed columns on the south face. However, creep strain was found to be far greater than plastic strain as can be seen in Figs. 4-78 to 4-81,

especially in the core. At 40 min, 22 of 38 core columns that were not severed or highly damaged by

aircraft impact had creep strains larger than 1.0 percent. After 40 min, the creep strains of core columns

on the south side of the core slowly increased. The maximum elastic-plus-plastic-plus-creep strain at 100 min was 7.3 percent in Column 1006. As temperature increased on the south wall in the later times,

creep strain in columns on the south wall also increased. By 1 00 min, creep strain increased in about 20

columns on the south face; the maximum elastic-plus-plastic-plus-creep strain in the columns on the south

face reached 2.9 percent.

At 100 min. the core was weakened on the south side and had shortened by 1.6 in., and the south wall had

bowed inward to approximately 43 in. from pull-in forces at Floors 95 to 99 and was unloading to the core and the adjacent east and west walls.

Based on the observ ations and the calculated results of the analysis, reported above, the following

sequence of events likely occurred as the south wall reached instabihty and buckled:

• As columns buckled, they shed load through Vierendeel action to adjacent columns in the

south wall, in turn buckling these columns.

• The inward bowing of the south wall increased as additional columns buckled.

• As a result of this behavior, instability progressed horizontally across the wall.

• When instability engulfed the enfire south wall, the wall continued to shed load to the east and west walls and to the core.

The onset of this load redistribution can be found in Table 4-24. The section of the building above the

impact zone began tihing to the south as column instability progressed rapidly from the south wall along

the adjacent east and west walls, resulting in increase of the gravity load on the core columns and in turn contributing to the buckling failure of these columns and initiating global collapse of the structure.

NISTNCSTAR 1-6D, WTC Investigation 183
Chapter 4

Since the global model did not include elements capable of capturing failure of column or hat truss element splices, nor buckling of hat truss outriggers, the conditions of the connections and the members

in the primary load path to and through the hat truss were evaluated at different time intervals. This

evaluation included the core column splices for tension, outriggers and supporting columns for compression, and the hat truss connections that were in the primary load path for tension.

Before the aircraft impact, core column splices were under compression. After the impact and with

increasing plastic and creep strains, the core displaced downward, and some core columns became

suspended from the hat truss. In fact, as shown in Table 4-26 and Fig. 4-82, Columns 503, 504, 505,

602, 603, 604, 605, 702, and 802 were calculated to be in tension at Floor 105 at 100 min. To evaluate

the condition of the core column splices at Floor 106, the tension capacities of these splices were

calculated using the AISC LRFD procedures and compared to the calculated tensile forces at each time

interval. Table 4-25 shows the calculated tension capacities of core column splices at Floor 106, and Fig.

4-83 shows tensile demand-to-capacity ratios for the core column splices at Floor 106 at 100 min. It was

found that tension forces in core columns were less than the capacities of the splices.

Sixteen outrigger members (four on each face) were present and participated in transfer of gravity loads

between the core columns and the exterior walls, as shown in Fig. 4-3. In the global model, each of these

outriggers was represented by one BEAM24 element; therefore, buckling of the member could not be

captured, although material nonlinearity was included. Table 4—27 presents axial load demand-tocapacity ratios of the outrigger members. Capacities of outriggers were calculated using AISC LRFD Eq.

E2-1 with an effective length factor K=0.75 and a resistance factor of unity. To check against calculated

capacities, axial loads obtained from the global model were adjusted for the additional axial load caused

by ignoring construction sequence. Analyses predicted that Outrigger E reached its axial load capacity

(see Fig. 4-3 for designations of outrigger members). Because the material properties of the outriggers in the global model were set so that they would yield when the axial load in the outrigger reached its compressive capacity, the axial load in Outrigger E did not change after reaching its capacity as unloading

in the post-buckling regime was not modeled. This may have resulted in an underestimate of the force

redistribution to the other outriggers.

Table 4-28 shows the computed demand-to-capacity ratios for axial loads of exterior columns supporting

the outriggers. Each of these exterior columns was also modeled by only one element (BEAM 1 88) in the

global model; therefore, buckling of the columns were not captured in the analysis. Compressive

capacities of these columns were also calculated using AISC LRFD Eq. E2-1 with an effective length

factor K=0.75 and a resistance factor of unity. This analysis showed that the axial loads in these columns

were well below their inelastic buckling capacities.

For effective load transfer from the core columns to the outriggers to occur, the capacities of the hat truss connections in the intermediate load path could not be exceeded. To investigate this issue, the hat truss connections that were in this load path were identified, and their capacities were compared to the

calculated forces transferred through them. The load path was identified by selecting the hat truss members that were predicted to have an absolute axial stress of 25 ksi or more. The hat truss stresses were evaluated at 80 min (at the end of Step 17) as at this time they had reached their predicted maxima.

Only the connections that were transferring tensile forces were evaluated. Figure 4-84 shows the

members determined to be in the primary load path. Figure 4-85 shows the location of the critical hat

truss connections that were evaluated. The capacities of the connections were calculated using the AISC

LRFD procedures. Table 4-29 summarizes capacities, demands, and the conditions of the connections

184 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

identified in Fig. 4-85. As can be seen in Table 4-29, none of the connections exceeded their capacities.

The state of the outriggers and core column splices at Floor 105 were discussed in the earlier paragraphs.

Based on these evaluations, it can be stated that even though one outrigger reached its capacity, the hat

truss was capable of redistributing loads between the core and the exterior walls, and therefore, the

evaluations described above are valid.

NISTNCSTAR 1-6D, WTC Investigation 185
Chapter 4

(a) North and east sides

(b) South and west sides

Figure 4-8. Vertical displacement of exterior wall of WTC 1 before aircraft impact

(downward displacement is negative).

186 NIST NCSTAR 1-6D, WTC Investigation
Global Analysis

(a) North and east sides

(b) South and west sides

Figure 4-9. Vertical displacement of exterior wall of WTC 1 after aircraft impact for

Case B conditions (downward displacement is negative).

NISTNCSTAR 1-6D, WTC Investigation 187
Chapter 4

188 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

NODAL SOLUTION

STEP=33

SUB =1437 TIME=150

UZ (AVG) RSYS=0

DMX =42.97 9 SMN =-6.499

SMX =.177856

Figure 4-11. Vertical displacement of exterior wall of WTC 1 at 100 min for Case B

conditions (downward displacement is negative).

NISTNCSTAR 1-6D, WTC Investigation 189
Chapter 4

^^^^81mm !WmlnMM ^^HH[I

^^^^^llllllllll IIIIIIIII IIIIIHI lllllllllillllllll ii^^^^^HI

^^^^^iiiiiiiiii IIIIIIIII iiiiiiiiiiiii lllllllllillllllll ii^^^^^n

^^^^^iiiiiiiiii IIIIIIIII IIIIIIIIIIIII lllllllllillllllll ii^^^^^ll

^^^^^liiiiiiiii IIIIIIIII IIIIIIIIIIIII lllllllllillllllll ii^^^^^ll

^^^^^iiiiiiiiii IIIIIIIII IIIIIIIIIIIII lllllllllillllllll iiHili^^HI

^^^^^iiiiiiiiii IIIIIIIII IIIIIIIIIIIII lllllllllillllllll iiHIii^^n

^^^^^iiiiiiiiii IIIIIIIII IIIIIIIIIIIII lllllllllillllllll iiHII^^HI

^^^^^iiiiiiiiii IIIIIIIII IIIIIIIIIIIII lllllllllillllllll iiHIil^^n ^^^^^liiiiiiiii IIIIIIIII IIIIIIIIIIIII lllllllllillllllll iihIII^^HI

^^^^^iiiiiiiiii IIIIIIIII IIIIIIIIIIIII lllllllllillllllll iiHIII^^HI

^^^^^iiiiiiiiii IIIIIIIII IIIIIIIIIIIII lllllllllillllllll iiHIIi^^ll ^iiiiiiiiii IIIIIIIII IIIIIIIIIIIII lllllllllillllllll iiHIif^^n

Figure 4-12. Vertical displacement of north wall of WTC 1 before aircraft impact.

iiiiiiiiiiimiiiiiiiiiii ^mmn

^^^^^H IIIIIIIIIIIII IIIIIIIIIII i^^^^^ll ^^^^^1 IIIIIIIIIIIII i^HB IIIIIIIIIII ^^^^^l ^^^^^H IIIIIIIIIIIII I^^B IIIIIIIIIII l^^^^^ll ^^^^^B IIIIIIIIIIIII i|H luiiiiiiii iii^^^^^HI

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Figure 4-13. Vertical displacement of north wall of WTC 1 after aircraft Impact for Case B

conditions (downward displacement is negative).

190 NIST NCSTAR 1-6D, WTC Investigation
Global Analysis

NODAL SOLUTION

STEP=25

SUB =170 TIME=120

UZ (AVG) RSYS=0

DMX =7.323

SMN =-6.94

SMX =.154595

101 ANSYS

-6.94 -5.363 -3.787 -6.151 -4.575 -2. WTCl Severe Temperature at 4800 sec - North Face

MAR 2 2005 19:45:29

- FL99 - FL97 - FL95 - FL93

-2.21 -.633642

-1.422 .154595

Figure 4-14. Vertical displacement of north wall of WTC 1 at 80 min for Case B

conditions (downward displacement is negative).

Figure 4-1 5. Vertical displacement of north wall of WTC 1 at 1 00 min for Case B

conditions with 5 kip pull-in forces (downward displacement is negative).

NISTNCSTAR 1-6D, WTC Investigation

1
Chapter 4

NODAL SOLUTION

STEP=1

SUB =2 TIME= . lOOE-02

UZ (AVG) RSYS=0

DMX =3.274

SMN =-3.273

201 ANSYS

FEB 14 2005 09:51:44

-3.273 -2.546 -1.818 -1.091

-2.91 -2.182 , -1.455 WTCl Gravity before Impact w/o Const - East Face

- FL99 - FL97 - FL95 - FL93

.727376 0

Figure 4-16. Vertical displacement of east wall of WTC 1 before aircraft impact

(downward displacement is negative).

NODAL SOLUTION

STEP=1

SUB =4 4 TIME=. lOOE-02

UZ (AVG) RSYS=0

DMX =3.894

SMN =-3.473

II 1

II 1 1

IIII

II

II

II

II

II

II

II

II

1 II

1 II

1 N

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IIIIII iiiiiiiiiniiiN linn

-3.473 -2.701 -1.929

-3.087 -2.315 -1.54

tWjBiai Gravity w/ Severe Impact Damage - East Face

201 ANSYS

FEB 11 2005 14:26:44

- FL99 - FL97 - FL95 - FL93

-.335876

.771751 0

Figure 4-17. Vertical displacement of east wall of WTC 1 after aircraft impact for Case B

conditions (downward displacement is negative).

192 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

Figure 4-18. Vertical displacement of east wall of WTC 1 at 80 min for Case B conditions

(downward displacement is negative).

NODAL SOLUTION

STEP=33

SUB =1437 -IME=150

UZ (AVG) RSYS=0

DUX =3.875

SMN =-3.493 iUI

nnnmnii

2Q^ ANSYS

MAR 30 2005

10:24 :27

- FL99 - FL97

- FL93

-3.453 -2.717 -1.94 -1.164 -.388082 -3.103 -2.328 -1.552 -.776164 0 WTCl Severe Tenro at 6000s w/5kiD pull - East Face

Figure 4-19. Vertical displacement of east wall of WTC 1 at 100 min for Case B

conditions with 5 kip pull-in forces (downward displacement is negative).

NISTNCSTAR 1-6D, WTC Investigation 193
Chapter 4

^^^^H 11 iiiiiiiiiiiiiiiiiiBiiiiiiiiiiiiiiiiii ri i^^^^^HI ^^^^^B lllllllllllllllilllllllllllllllllllllllllllllH l^^^^^ll ^^^^^i II iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii i^^^^Hl ^^^^^ II iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii i^^^^HI ^^^^^B II iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii II iHili^^HI

II iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii iH|ii^^H| ^^^^B II iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii ihII^^HI ^^^^^B ^^^^H iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii iHHi^^H iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii iHlii^^HI ^^^^^H lllllllllllllllllilllllllllllillllllllllllllllll H||^^H| ^^^^^B ^^^H iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii ihIII^^HI

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Figure 4-20, Vertical displacement of south wall of WTC 1 before aircraft impact

(downward displacement is negative).

H^^Hilil III!! II mm I III II I^^^^HI ^^^^^iiiii II iiiiiiiiimHniiii nil ii ii i^^^^^H ^^^^^iiii II iiiiiiiiiiiHiriiiiii nil II II i^^^^^H ^^^^^lII II II Hill II III Hill nil I I III II II i^^^^HI ^^^^^llll II lllllllll Hill IIHI I HI H II l^^^^^n ^^^^^hH H IIHIHII HIH IIHI I HI H II iHili^^HI ^^^^^hH H IIHIHII HIH IIHI I HI I II iHHg^^HI ^^^^^hH H IIHIHII HIH IIHI I HI I II IBII^^HI ^^^^^hH H IIHIHII n IIHI I HI I II iHlil^^H ^^^^^hH H IIHIHII l| IIHI I HI I H IHIII^^HI ^^^^^hH H IIHIHII l| IIHI I HI I H iHii^^HI ^^^^^hH H IIHIHII ll IIHI I HI I H iHill^^Bl ^^^^^hH H IIHIHII HIH IIHI I HI I H HHf^^H ^^H^H|||||||||H^^

Figure 4-21 . Vertical displacement of south wall of WTC 1 after aircraft impact for

Case B conditions (downward displacement is negative).

194 NIST NCSTAR 1-6D, WTC Investigation
Global Analysis

NODAL SOLUTION

STEP=25

SUB =170 TIME=120

UZ (AVG) RSYS=0

DMX =3.498

SMN =-2.839

lllllllllllllli

I UN

11

-2.839 -2.208 -1.577

-2.524 -1.893 -1.262

WTCl Severe Te.mserature at 4800 sec - South Face

301 ANSYS

MAR 2 2005 19:45:34

- FL99 - FL97 - FL95 - FL93

5378 -.315459 -.630919 0

Figure 4-22. Vertical displacement of south wall of WTC 1 at 80 min for Case B

conditions (downward displacement is negative).

Figure 4-23. Vertical displacement of south wall of WTC 1 at 100 min for Case B

conditions with 5 kip pull-in forces (downward displacement is negative).

NISTNCSTAR 1-6D, WTC Investigation 195
Chapter 4

(a) North and east sides

(b) South and west sides

Figure 4-24. Vertical displacement of core of WTC 1 before aircraft impact (downward

displacement is negative).

196 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

(a) North and east sides

(b) South and west sides

Figure 4-25. Vertical displacement of core of WTC 1 after aircraft impact for Case B

conditions (downward displacement is negative).

NISTNCSTAR 1-6D, WTC Investigation 197
(a) North and east sides

(b) South and west sides

Figure 4-26. Vertical displacement of core of WTC 1 at 50 min for Case B conditions

(downward displacement is negative).

198 NISTNCSTAR 1-6D, WTC Investigation
(a) North and east sides

(b) South and west sides

Figure 4-27. Vertical displacement of core of WTC 1 at 80 min for Case B conditions

(downward displacement is negative).

NISTNCSTAR 1-6D, WTC Investigation 199
Chapter 4

(a) North and east sides

(b) South and west sides

Figure 4-28. Vertical displacement of core of WTC 1 at 100 min for Case B conditions

with 5 kip pull-in forces (downward displacement is negative).

200 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

(a) 500 series columns (b) 600 series columns

- FL99 - FL97

~ - FL95

- - FL93

1^^^^ (in.

C: Gravity before I^ipact w/o

(c) 700 series columns (d) 800 series columns

(e) 900 series columns (f) 1000 series columns

Figure 4-29. Vertical displacement of core columns of WTC 1 before aircraft impact

(downward displacement is negative).

NISTNCSTAR 1-6D, WTC Investigation 201
Chapter 4

(e) 900 series columns (f) 1000 series columns

Figure 4-30. Vertical displacement of core columns of WTC 1 after aircraft impact for

Case B conditions (downward displacement is negative).

202 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

(e) 900 series columns (f) 1000 series columns

Figure 4-31. Vertical displacement of core columns of WTC 1 at 80 min for Case B

conditions (downward displacement is negative).

NISTNCSTAR 1-6D, WTC Investigation 203
Chapter 4

(e) 900 series columns (f) 1000 series columns

Figure 4-32. Vertical displacement of core columns of WTC 1 at 100 min for Case B

conditions with 5 kip pull-in forces (downward displacement is negative).

204 NISTNCSTAR 1-6D. WTC Investigation
Global Analysis

-2.5 in.

-2.8 in.

-3.6 in. o o O OO 0 o o

o o o oo c o o

o o OOQO o o

o o o oo o o

o o o oo o o o

o o o oo @ o Q

® 0)

1

N

-2.8 in.

Note: downward

displacement is shown as positive

displacement

>)>)>))))))))))))))))))))))))))))))))))))))))))))))))))IW

-2.5 in.

Figure 4-33. Vertical displacement at Floor 99 of WTC 1 before aircraft impact.

-+0.5 in.

-+3.2 in.

^(xza3aocoocccC32ISnt((((((((((((((CC(S23in^

-+1.8 in.

o © © @@ m

o o o © © ©

-+0.5 in. 1"

—0.1 in. :

Goo©

O O ©

O o e

-+0.1 in.

Note: increase in downward

displacement is shown as

positive value

-0.2 in. DOOOOOOOOOOOOOOOOOOOOOOOO —0.1 in.

Figure 4-34. Change in vertical displacement at Floor 99 of WTC 1 from the time before

impact to the time after impact for Case B conditions.

NISTNCSTAR 1-6D, WTC Investigation 205
Chapter 4

--+4.1 in.

~+0.4 in. i 8 -+0.3 in.

~+3.3 in.

) OO <

' OG

@ ®© O

© ©o

~+1.5 in.

I"

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@ o Note: increase in downward

displacement is siiown as

positive value

—OA in. 1—0.5 in. ooococcccicooooccoccccoaxxxxxxxxxxxxxxoo^ —0.6 in.

Figure 4-35. Change in vertical displacement at Floor 99 of WTC 1 from the time before

impact to 50 min for Case B conditions.

~+0.1 in.

~+4.1 in.

~+3.5 in.

~+0.2 in.

I"

—0.7 in.

Note: increase in downward

displacement is shown as

positive value

—0.8 in.

—0.9 in.

Figure 4-36. Change in vertical displacement at Floor 99 of WTC 1 from the time before

impact to 80 min for Case B conditions.

206 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

• V eooooOOl -0.2 in.

~+3.7 in.

-+3.5 in.

—0.1 in.

1

N

—0.4 in.

O

O

O

O

O

G

OOOO

O OO

oo

OO

~+1.9 in

@

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0

Note: increase in downward

displacement is shiown as

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1—0.5 in.

—0.1 in. ~+1.8 in.

OOOOOOOO —0.3 in.

Figure 4-37. Change in vertical displacement at Floor 99 of WTC 1 from the time before

impact to 100 min for Case B conditions with 5 kip pull-in forces.

NISTNCSTAR 1-6D, WTC Investigation 207
Chapter 4

Figure 4-38. Out-of-plane displacement of south wall of WTC 1 before aircraft impact

(inward displacement is positive).

NODAL SOLUTION

STEP=1

SUB =44

TIME=. lOOE-02

U^ (AVG) RSYS=0

DMX =3.241

SMN =-.093137

SMX =1 . 639

m ANSYS

-.093137 .291852 .676841 1.062

.099357 .484346 .859336 WTCl Gravity w/ Severe Impact Damage - South Face

MAR 15 2005 20:43:47

- FL99 - FL97 - FL95 - FL93

Figure 4-39. Out-of-plane displacement of south wall of WTC 1 after aircraft Impact for

Case B conditions (inward displacement is positive).

208 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

NODAL SOLUTION

STEP=25

SUB =170 TIME=120

UY (AVG) RSYS=0

DMX =3.498

SKN =-2.207

SMX =2.42 6

m ANSYS

MAR 2 2005 19:45:34

- FL99 - FL97 - FL95

I illll^^TMil^»..,JIII!llllllll!l,,l 1 1.1 .LILJiUILli i (in.) -2.207 -1.178 -.14807 .881588 1.911 -1.693 -.6629 .366759 1.396 2.426

Severe Temperature at 4800 sec - South Face

Figure 4-40. Out-of-plane displacement of south wall of WTC 1 at 80 min (at the end of

Analysis Step 17) for Case B conditions (inward displacement is positive).

Figure 4-41. Out-of-plane displacement of south wall of WTC 1 at 100 min for Case B

conditions with 5 kip pull-in forces (inward displacement is positive).

NISTNCSTAR 1-6D, WTC Investigation 209
Chapter 4

45

3

E

X 10 - ^

n>

5

" III'

0 ^ i 80 85 90 95 100

Time (min)

Figure 4-42. Time history of maximum out-of-plane displacement of south wall of WTC 1 for Case B conditions with 5 kip pull-in forces (from Analysis Step 18 to Step 21).

Figure 4-43. Out-of-plane displacement of south wall of WTC 1 at 100 min for Case B

conditions with 4 kip pull-in forces (inward displacement is positive).

210 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

Figure 4-44. Axial load in exterior columns of north wall of WTC 1 before aircraft impact

(compression is negative).

Figure 4-45. Axial load in exterior columns of north wall of WTC 1 after aircraft impact

for Case B conditions (compression is negative).

NISTNCSTAR 1-6D, WTC Investigation 211
Chapter 4

Figure 4-46. Axial load in exterior columns of north wall of WTC 1 at 80 min for the

Case B conditions (compression is negative).

Figure 4-47. Axial load in exterior columns of north wall of WTC 1 at 100 min for Case B

conditions with 5 kip pull-in forces (compression is negative).

212 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

Figure 4-48. Axial load in exterior columns of east wall of WTC 1 before aircraft impact

(compression is negative).

Figure 4-49. Axial load in exterior columns of east wall of WTC 1 after aircraft impact for

Case B conditions (compression is negative).

NISTNCSTAR 1-6D. WTC Investigation 213
Chapter 4

Figure 4-50. Axial load in exterior columns of east wall of WTC 1 at 80 min for the

Case B conditions (compression is negative).

Figure 4-51. Axial load in exterior columns of east wall of WTC 1 at 100 min for the

Case B conditions with 5 kip pull-in forces (compression is negative).

214 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

Figure 4-52. Axial load in exterior columns of south wall of WTC 1 before aircraft impact

(compression is negative).

Figure 4-53. Axial load in exterior columns of south wall of WTC 1 after aircraft impact

for Case B conditions (compression is negative).

NISTNCSTAR 1-6D, WTC Investigation 215
Chapter 4

-360559 -275812 -191064 -106317 -21570 -318185 -233438 -148691 -63943 20804 WTCl Severe Temp at 6000s w/5kip pull - South Face

Figure 4-55. Axial load in exterior columns of south wall of WTC 1 at 100 min for Case B

conditions with 5 kip pull-in forces (compression is negative).

216 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

1,000 ^ —Before Impact —After Impact

800 - —20 min —50 min — 80 min

-200

160 150 140

Column ID

110 100

Figure 4-56. Variation of axial load in exterior columns at Floor 98 of north wall of WTC 1 for Case B conditions with 5 kip pull-in forces (compression is positive).

—Before Impact —After Impact —20 min —50 min —80 min —100 min

260 250 240 230 220

Column ID

210 200

Figure 4-57. Variation of axial load in exterior columns at Floor 98 of east wall of WTC 1 for Case B conditions with 5 kip pull-in forces (compression is positive).

NISTNCSTAR 1-6D, WTC Investigation 217
Chapter 4

Figure 4-58. Variation of axial load in exterior columns at Floor 98 of south wall of

WTC 1 for Case B conditions with 5 kip pull-in forces (compression is positive).

300

50

460

—Before Impact —After Impact —20 min —50 min —80min —100 min

450 440 430

Column ID

420 410 400

Figure 4-59. Variation of axial load in exterior columns at Floor 98 of west wall of WTC 1 for Case B conditions with 5 kip pull-in forces (compression is positive).

218 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

(a) 500 series columns (b) 600 series columns

ANSYS

r=-=i(lb)

(c) 700 series columns (d) 800 series columns

(e) 900 series columns (f) 1000 series columns

Figure 4-60. Axial load in core columns of WTC 1 before aircraft impact (compression is negative).

NISTNCSTAR 1-6D, WTC Investigation 219
Chapter 4

ANSYS

- FL99

-FL97 - FL95' - FL93

(a) 500 series columns (b) 600 series columns

(c) 700 series columns (d) 800 series columns

ANSYSi

1001 '^.'^l

-FL99

-FL97

-FL95 - FL93

-FL99

-FL97

-FL95

.-FL93

vity w/ Severe iTipac

(e) 900 series columns (f) 1000 series columns

Figure 4-61. Axial load in core columns of WTC 1 after aircraft impact for Case B

conditions (compression is negative).

220 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

ANSYS

-FL99

-FL97 - FL95

.-:.EJLJ3.

(a) 500 series columns

(c) 700 series columns

(b) 600 series columns

ANSYS!

(d) 800 series columns

ANSYS

-FL99

FL97

-FL95

-FL93,

(e) 900 series columns (f) 1000 series columns

Figure 4-62. Axial load in core columns of WTC 1 at 80 min for Case B conditions

(compression is negative).

NISTNCSTAR 1-6D, WTC Investigation 221
Chapter 4

(a) 500 series columns (b) 600 series columns

b:;:^./' " '"^ '^ mmmmmmmmmm,^.^. i (lb) I i^^^^,^^^^ .(lb)

W7C: Severe Temp at 600Cs v)/5kip pi;!: - 900 Colunn line H W?C1 S^v^re T°7ip aC 60C0s w/5kip pull - 1000 Colu-nr. Litis

(e) 900 series columns (f) 1000 series columns

Figure 4-63. Axial load in core columns of WTC 1 at 100 min for Case B conditions with

5 kip pull-in forces (compression is negative).

222 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

I

N

501 508

Scale

4000 kip

2000 kip

Q 1000 kip

O 500 kip

O 250 kip

O -500 kip

OOOCDOOO

O O O CD O O O

8 8 8°88 8 8

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1001 1008

Figure 4-64. Axial load in columns at Floor 98 of WTC 1 before aircraft impact

(compression is positive).

I

N

501 508

Scale

4000 kip

2000 kip

Q 1000 kip

O 500 kip

® 250 kip

O -500 kip

o -o oOO

O O O o o

8°8S 8 8

o o o oO o o o OOOCDOOO

1001 1008

Figure 4-65. Axial load in columns at Floor 98 of WTC 1 after aircraft impact for Case B

conditions (compression is positive).

NISTNCSTAR 1-6D, WTC Investigation 223
Chapter 4

I"

Scale

4000 kip

2000 kip

^ 1 000 kip

O 500 kip

@ 250 kip

O -500 kip

OC.COGO.OO.O..OO -ocxsi^^ggnno^

501

U ° O °c O

)0OO

508

oo

o o °o o

o o o O

1008

Figure 4-66. Axial load in columns at Floor 98 of WTC 1 at 80 min for Case B conditions

(compression is positive).

I

N

Scale

4000 kip

2000 kip

Q 1000 kip

O 500 kip

© 250 kip

O -500 kip

501 508

yo o o@ o o O

o o °o O ® @

o oQO

Oo

o O °o o O

o O OO o O

1001 1008

Figure 4-67. Axial load in columns at Floor 98 of WTC 1 at 100 min for Case B conditions

with 5 kip pull-in forces (compression is positive).

224 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

Table 4-10. Total column loads at Floor 98 of WTC 1 for Case B conditions.

Row Analysis Step North East South West Core Total

(1) Before Impact 10.974 8,545 11,025 8.572 34,029 73,144

(2) After Impact 10.137 9,071 10,356 9,146 34,429 73,139

(3) 10 min 9.796 8,490 9,848 8.536 36,473 73,143

(4) 20 min 10.437 9,108 9,900 9.202 34,495 73,143

(5) 30 min 10.913 10,034 10.420 9,715 32,060 73,142

(6) 40 min 11.068 10.599 11.004 10,178 30,294 73,142

(7) 50 min 11,149 10,908 11,192 10,458 29,435 73,141

(8) 60 min 11,205 11,168 11,285 10,716 28,766 73,141

(9) 70 min 11,286 11.366 11,343 10,939 28,205 73,138

(10) 80 min 11.376 11,555 11,409 11.119 27.681 73,140

(11) 90 min 10,916 11,991 9,949 11.657 28.587 73,099

(12) 100 min 10.828 12,249 9.638 11.905 28.478 73,098

(13) (2)-(l) -837 526 -668 574 400 -5

(14) (10) -(2) 1,239 2,484 1,052 1.973 -6.748 1

(15) (12) -(2) 692 3.178 -719 2,759 -5,951 -41

(16) (12)-(10) -548 694 -1.771 786 797 -42

Note: Compression is positive. Units are in kip.

Table 4-11. Total column loads at Floor 105 of WTC 1 for Case B conditions.

Ron Anal\ sis Step North East South West Core Total

(1) Before Impact 8.026 6.562 8,092 6,604 20,361 49,645

(2) After Impact 7,294 7,028 7,488 7,076 20,761 49,646

(3) 10 min 6.944 6.461 6,981 6,469 22,790 49,646

(4) 20 min 7,551 7.075 7,057 7,158 20,806 49,647

(5) 30 min 8,020 7,998 7,569 7,685 18,377 49.648

(6) 40 min 8,193 8.571 8,129 8.147 16,608 49,649

(7) 50 min 8.285 8,878 8,315 8,428 15.743 49,650

(8) 60 min 8,351 9,130 8,414 8,687 15,069 49,650

(9) 70 min 8,435 9,319 8,481 8,914 14.502 49,651

(10) 80 min 8.528 9.497 8.551 9,097 13,978 49.651

(11) 90 min 8,096 9,847 7,327 9,506 14,876 49,652

(12) 100 min 8,023 10.076 7.066 9,720 14,767 49.653

(13) (2)-(l) -732 466 -604 472 400 1

(14) (10)-(2) 1.234 2,470 1,063 2.021 -6,783 5

(15) (12) -(2) 730 3,048 -422 2,644 -5,993 7

(16) (12)-(10) -504 579 -1,485 623 790 2

Note: Compression is positive. Units are in kip.

NISTNCSTAR 1-6D. WTC Investigation 225
Chapter 4

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228 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

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NISTNCSTAR 1-6D, WTC Investigation 229
Chapter 4

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230 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

Table 4-22. Change in total column loads before and after aircraft impact.

(Loads after impact) - (Loads before impact)

Row Floor North East South West Core

(1) Floor 98 -837 526 -668 574 400

(2) Floor 105 -732 466 -604 472 400

(3) (2)-(l) 105 -60 64 -103 0 Note: Increase in compression is shown as positive. Units are in kip.

Table 4-23. Change in total column loads after aircraft impact and at 80 min for Case B

conditions.

(Loads at 80 min) - (Loads After Im pact)

Row Floor North East South West Core

(1) Floor 98 1.239 2,484 1.052 1,973 -6,748

(2) Floor 105 1.234 2.470 1.063 2,021 -6,783

(3) (2)-(l) -5 -15 11 48 -35

Note: Increase in compression is showTi as positive. Units are in kip.

Table 4-24. Change in total column loads at 80 min and at 100 min for Case B

conditions.

(Load s at 100 min) - (Loads at 80 min)

Row Floor North East South West Core

(1)

(2)

Floor 98

Floor 105

-548 694 -1,771 786 797

-504 579 -1.485 623 790

(3) (2)-(l) 44 -115 285 -163 -7

Note: Increase in compression is shown as positive. Units are in kip.

NISTNCSTAR 1-6D, WTC Investigation 231
Chapter 4

501 508

(Qi (037) (^Qj (S) (g)

0.63)

(jf^v^fj) ^'^^

0.42I 0.48]

0.48|

0.48^ 0.50 I

N

1001

(^0^ (0^ (0^ l^f^^f^ ^^i!^ ^^f^

@ Q (Q) (oM) @

1008

Figure 4-68. Maximum demand-to-capacity ratio for axial load in core columns between

Floor 93 and Floor 99 of WTC 1 before aircraft impact.

501

0.45) ( 0-60

fo.44i

0.69 I { 0.64 ) ( 0.95 j

(^0^ fo.52

(0.3t| 10 451

1001

(0.41) (qM^I^AS) (0.45|

= Severed or heavily damaged column

508

0.49:

^^0^3^ ( 0.63

j ( 0.66

fo.55|

(o.50| (0.53)

j^ol2^

^^0^64^

[0.441 1031

1008

I

N

Figure 4-69. Maximum demand-to-capacity ratio for axial load in core columns between

Floor 93 and Floor 99 of WTC 1 after aircraft impact for Case B conditions.

232 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

# = Severed or heavily damaged column

Figure 4-70. Maximum demand-to-capacity ratio for axial load in core columns between

Floor 93 and Floor 99 of WTC 1 at 80 min for Case B conditions.

# = Severed or heavily damaged column

Figure 4-71. Maximum demand-to-capacity ratio for axial load in core columns between

Floor 93 and Floor 99 of WTC 1 at 100 min for Case B conditions with 5 kip pull-in forces.

NISTNCSTAR 1-6D, WTC Investigation 233
Chapter 4

Scale

8.00 %

4.00 %

2.00 %

1.00 %

0.50 %

O 0.20 %

Q 0.10 %

COL501

o o

O

COL1001

o o o o

o o o o

o o o

o o

o o

COL508

o o o o

O0.07

o

o

o COL1008

I"

cxxccccccxxrxxxxxDoaxcoxooaxax)cc^

Figure 4-72. Maximum elastic-plus-plastic strain for columns between Floor 93 and

Floor 99 of WTC 1 before aircraft impact (compressive strain is positive; strain values are

in percent).

Scale

8.00 %

4.00 %

2.00 %

1.00 %

0.50 %

O 0.20 %

G 0.10 %

0.57

COL501

o o • • o

COL508

o O o o •O o o 0

o

o

o

o o o#

o

o

o

o

o o o #o o o o

o COL1001 o o o o o o o COL1008

I"

# = Severed or heavily damaged column

Figure 4-73. Maximum elastic-plus-plastic strain for columns between Floor 93 and

Floor 99 of WTC 1 after aircraft impact for Case B conditions

(compressive strain Is positive; strain values are in percent).

234 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

ccxxxxxxxxo^

Scale

8.00 %

4.00 %

2.00 %

1.00 %

0.50 %

O 0.20 %

O 0.10 %

COL501

o

o COL1001

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o • • G ©

7) o O o o o

8 s*6: o O o fQ o o

O o OO o

o

o o COL1008

A N

ocooooooocaxaxrocxxjcCDX]

# = Severed or heavily damaged column

Figure 4-74. Maximum elastic-plus-plastic strain for columns between Floor 93 and

Floor 99 of WTC 1 at 10 min for Case B conditions (compressive strain is positive; strain

values are in percent).

Scale

8.00 %

4.00 %

2.00 %

1.00 %

0.50 %

O 0.20 %

O 0.10 %

COL501 ^

o O

COL508

O o o 0@ O O o o

o Q 0#A? o o

o O o O o o

o O O «0 O o o

O o O GD o

COL1001

o o

COL1008

I"

°oocxiOococoxiQj211)^QQIj^lJi02)S^

# = Severed or heavily damaged column

Figure 4-75. Maximum elastic-plus-plastic strain for columns between Floor 93 and

Floor 99 of WTC 1 at 40 min for Case B conditions (compressive strain is positive; strain

values are In percent).

NISTNCSTAR 1-6D, WTC Investigation 235
Chapter 4

Scale

8.00 %

4.00 %

COL501

o O • •

COL508

o

o

O o

COL1001

o OC

o CD "

o o

O O

O O

O O

o o

COL100

I

N

2.00 %

1.00 %

0.50 %

O 0.20 %

O 0.10 % _ .^OOOCXXCOCXXOCQininT) ))) 5^nf"lTnT>3X)000000000000COC)0OO° # = Severed or heavily damaged column

Figure 4-76. Maximum elastic-plus-plastic strain for columns between Floor 93 and

Floor 99 of WTC 1 at 80 min for Case B conditions (compressive strain is positive; strain

values are in percent).

Scale

8.00 %

4.00 %

2.00 %

O O

O o

COL1001

COL508

O o oo ®

o O o

®

o

COL1008

I

A/

O 0.10 %

# = Severed or heavily damaged column

Figure 4-77. Maximum elastic-plus-plastic strain for columns between Floor 93 and

Floor 99 of WTC 1 at 100 min for Case B conditions with 5 kip pull-in forces

(compressive strain is positive; strain values are in percent).

236 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

"ocraxnxocrxixmxoocCCCcaJKl

# = Severed or heavily damaged column

Figure 4-78. Maximum elastic-plus-plastic-plus-creep strain for columns between Floor

93 and Floor 99 of WTC 1 at 10 min for Case B conditions

(compressive strain is positive; strain values are in percent).

# = Severed or heavily damaged column

Figure 4-79. Maximum elastic-plus-plastic-plus-creep strain for columns between Floor

93 and Floor 99 of WTC 1 at 40 min for Case B conditions

(compressive strain is positive; strain values are in percent).

NISTNCSTAR 1-6D. WTC Investigation 237
Chapter 4

# = Severed or heavily damaged column

Figure 4-80. Maximum elastic-plus-plastic-plus-creep strain for columns between Floor

93 and Floor 99 of WTC 1 at 80 min for Case B conditions

(compressive strain is positive; strain values are in percent).

Figure 4-81. Maximum elastic-plus-plastic-plus-creep strain for columns between Floor

93 and Floor 99 of WTC 1 at 100 min for Case B conditions with 5 kip pull-in forces

(compressive strain is positive; strain value are in percent).

238 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

Table 4-25. Tension capacity of core column splices at Floor 106

Col#

Column Line

500 600 700 800 900 1000

1 460 335 335 335 335 460

2 335 335 335 335 335 335

3 335 335 335 335 460 460

4 335 335 335 335 335 335

5 335 335 335 335 335 335

6 335 335 335 335 335 335

7 335 335 335 335 335 335

8 460 335 335 335 460

Note: Units are in kip.

NIST NCSTAR 1-6D, WTC Investigation 239
Chapter 4

Table 4-26. Axial load in core columns at Floor 105 of WTC 1 for Case B conditions

Column ID

Impact

After Impact

10 min 20 min 30 min 40 min 50 min 60 min 70 min 80 min 90 min 100 min

501 753 1.033 976 1,326 1,504 1,634 1,690 1,703 1,661 1,635 1,595 1,563 502 567 751 996 569 416 353 303 266 210 156 90 44

503 632 469 631 312 129 57 23 -13 -63 -118 -190 -240 504 486 1 -49 -17 -34 -39 -32 -34 -36 -44 -70 -82 505 576 82 27 18 3 -8 -8 -8 -8 -16 -42 -52 506 629 512 544 311 311 324 320 313 314 315 281 266

507 558 676 774 466 328 313 304 296 303 312 284 275

508 743 1.057 1 .185 1,108 587 493 469 455 448 430 399 389

601 219 272 239 341 383 413 423 432 432 427 427 420

602 395 524 612 310 206 153 103 69 30 -5 -21 -45 603 408 475 525 315 1 18 1

-28 -64 -94 -126 -130 -137 604 275 131 85 45 7 -16 -28 -38 -45 -51 -50 -52 605 320 149 70 20 -3 -17 -23 -28 -34 -38 -36 -37 606 408 428 415 334 327 325 313 303 295 291 298 299

607 371 447 470 350 286 268 247 232 224 222 230 235

608 224 296 335 255 165 149 134 123 116 113 123 128

701 355 418 363 518 594 658 684 705 718 -J-)-) 733 733 702 395 529 652 232 145 85 ] 7 -34 -73 -98 -88 -89 703 266 288 380 456 456 425 407 387 368 351 344 334

704 224 221 237 214 189 165 147 132 121 113 1 19 1 17 705 181 159 146 135 125 117 1 10 103 99 96 98 95 706 276 227 195 178 167 161 153 146 141 137 138 133 707 386 447 472 514 524 514 491 471 456 445 448 449

708 391 491 540 420 448 470 462 451 446 445 470 482

801 398 450 374 536 630 706 742 762 777 788 818 834

802 398 473 622 167 110 69 1 -55 -91 -108 -73 -54 803 298 298 417 542 521 470 445 423 402 383 389 383 804 192 173 179 166 146 136 125 119 119 116 127 127

805 329 188 145 105 85 85 76 72 73 71 86 86

806 395 454 502 567 631 652 642 635 630 620 626 624

807 362 432 439 399 449 480 489 493 497 498 528 540

901 253 273 217 280 343 398 422 436 450 460 496 517

902 385 425 470 268 241 193 152 1 12 95 88 135 167

903 523 606 833 847 653 491 435 393 358 336 358 349

904 298 287 397 322 192 1 16 71 47 43 42 76 77 905 278 271 332 259 150 96 66 55 60 59 89 89 906 406 464 507 646 616 516 477 455 409 354 351 319

907 413 457 485 534 513 468 456 458 455 441 438 425

908 239 274 242 274 321 350 366 378 387 392 425 438

1001 762 735 605 721 915 1,112 1,212 1,301 1,370 1.405 1,595 1,685 1002 614 611 759 560 527 432 405 382 367 353 453 465

1003 745 744 855 1,079 990 555 426 286 214 182 299 271 1004 522 525 809 719 416 194 106 46 15 15 148 150

1005 534 546 830 685 359 176 94 50 27 20 135 132

1006 637 634 682 904 661 408 348 321 288 242 273 230

1007 587 578 582 727 624 500 478 476 463 435 438 408

1008 758 785 687 770 902 991 1,030 1,055 1.067 1.070 1,216 1,274

Note: Compression is positive. Units are in kip. Note: Shading indicates when core columns were in tension.

240 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

Col 501

{ 1563 j O

44O

-45

o

-89 O

-54 o167

Q 2 s

O o o

.137 -52 -37

@ 9 S

O271 OO^50 13

266) (275

^^ o O ^ 117 95 133

:383) o O

127 86

o230

Col 508

§> o128

Col 1001

4081

Col 1008

I"

Figure 4-82. Axial load (kip) in core columns at Floor 105 of WTC 1 at 100 min for Case B

conditions with 5 kip pull-in forces (compression is positive).

Col 501

O

O

O

O

o 0 @0 o

©o o

(o!l6)

0.11 o o o o

o o o

Co! 508

o o

o o

o

o

o

o r

o o o o o o o o

o

Col 1001

o o o o o

O = column in compression

o o

Col 1008

Figure 4-83. Tension demand-to-capacity ratio for core column splices at Floor 106 of

WTC 1 at 100 min for Case B conditions with 5 kip pull-in forces.

NISTNCSTAR 1-6D, WTC Investigation 241
Chapter 4

Table 4-27. Demand-to-capacity ratio for axial load in outriggers of WTC 1 for Case B

conditions (outrigger IDs are indicated in Fig. 4-3).

Outrigger ID Bfr Imp Aftr Imp 1U min 20 min 30 min 40 min 50 min 60 min 70 min XO min 90 min 100 min

North A (1.26 0.35 0.26 0.40 0.49 0.53 0.56 0.59 0.62 0.65 0.54 0.52 B (1.22 -0.07 -0.13 -0.04 0.02 0.04 0.06 0.07 0.08 (1.09 0.03 0.03 C 0.21 -0.05 -0.1

-0.02 0.04 0.06 0.08 0.08 0.09 0.1

0.05 0.04 D 0.25 0.35 0.29 0.45 0.61 0.67 0.70 0.72 0.73 (1.75 0.65 0.63 East E 0.32 0.4S 0.38 0.56 0.75 0.83 0.88 0.92 0.94 0.97 0.95 0.96 F 0.23 0.28 0.21 0.30 0.41 0.48 0.52 0.55 0.57 0.59 0.62 0.64 G 0.23 0.26 0.20 0.26 0.35 0.42 0.46 0.49 0.51 0.54 0.58 0.61 H 0.33 (1.31 0.23 (1.25 0.36 0,46 0.51 0.55 0.58 0.60 0.72 (1.77 South

1 0.25 0.12 0.04 0.03 (1.12 0.20 0.23 0.26 0.27 0.28 0.28 0.28

J (1.21 0. 1

(1.01 0.03 0.13 0.24 0.28 0.29 0.30 0.31 0.04 -0.02 K 0.21 0.10 0.01 0.03 0. 1

0.24 0.27 0.28 0.30 0.31 0.02 -0.04

L 0.26 0.12 0.02 0.05 0.11 0.20 0.24 0.27 0.29 0.31 0.19 0.18

\\est M 0.33 0.33 0.22 0.29 0.36 0.44 0.49 0.53 0.56 0.58 0.69 0.73 N 0.24 0.27 0.20 0.28 0.34 0.40 0.44 0.47 0.50 0.52 0.56 0.58 O (1.24 0.29 0.22 0.31 0.38 0.43 0.47 0.50 0.53 0.55 0.59 0.61 P 0.33 0.4S 0.39 0.54 (1.64 0.71 0.75 (1.79 0.83 (1 87 0.88 0.90

Table 4-28. Demand to capacity ratio for axial load in exterior columns supporting

outriggers at Floor 107 of WTC 1 for Case B conditions.

Column ID Bfr Imp Aftr Imp 10 min 20 min 30 min 40 min 50 min 60 min 70 min 80 min 90 min 100 min

North

1 10 0.30 0.40 0.35 0.43 0.48 0.51 0.53 0.54 0.56 0.58 0.52 0.51

1 1

0.24 0.31 0.28 0.33 0.36 0.37 0.38 0.39 0.40 0.41 0.37 0.37 129 0.28 0.00 -0.05 0.02 0.08 0.10 0.11 0.11 0.12 0.14 0.09 0.08

130 0.30 0.04 0.00 0.06 0.11 0.13 0.14 0.15 0.16 0.17 0.12 0.11

131 0.30 0.02 -0.03 0.04 0.10 0.12 0.13 0.13 0.14 0.16 0.10 0.10 149 0.25 0.30 0.28 0.33 0.39 0.41 0.42 0.43 0.43 0.44 0.41 0.40

150 0.25 0.31 0.29 0.36 0.43 0.46 0.48 0.49 0.49 0.50 0.45 0.44

East 217 0.20 0.26 0.23 0.29 0.38 0.41 0.43 0.45 0.46 0.47 0.46 0.47 218 0.25 0.34 0.28 0.38 0.51 0.57 0.60 0.63 0.65 0.67 0.66 0.67 228 0.30 0.35 0.28 0.36 0.47 0.53 0.57 0.59 0.62 0.64 0.67 0.69 229 0.22 0.25 0.20 0.26 0.34 0.38 0.41 0.43 0.45 0.46 0.49 0.50

231 0.22 0.25 0.20 0.25 0.32 0.37 0.40 0.42 0.43 0.45 0.48 0.49 232 0.30 0.33 0.27 0.33 0.42 0.48 0.52 0.55 0.57 0.59 0.63 0.65 242 0.25 0.25 0.20 0.21 0.28 0.33 0.36 0.39 0.40 0.42 0.50 0.53 243 0.20 0.20 0.17 0.18 0.22 0.25 0.27 0.29 0.30 0.31 0.36 0.38 South

310 0.30 0.23 0.19 0.19 0.23 0.28 0.29 0.3

0.31 0.32 0.33 0.33

311 0.24 0.20 0,18 0.17 0.20 0.22 0.23 0.24 0.24 0.25 0.25 0.25 329 0.27 0.17 0.10 0.12 0.20 0.29 0.32 0.33 0.33 0.34 0.10 0.05 330 0.34 0.23 0.14 0.16 0.26 0.37 0.40 0.41 0.41 0.43 0.13 0.07

331 0.27 0.18 0.10 0.12 0.21 0.30 0.32 0,32 0.33 0.34 0.10 0.05 349 0.24 0.20 0.17 0.18 0.20 0.22 0.23 0.25 0.25 0.26 0.22 0.22 350 0.31 0.23 0.18 0.20 0.23 0.27 0.30 0.31 0.33 0.33 0.28 0.28 West

417 0.21 0.21 0.17 0.19 0.22 0.25 0.27 0.29 0.30 0.31 0.35 0.37 418 0.25 0.25 0.19 0.23 0.27 0.32 0.34 0.37 0.38 0.40 0.46 0.49 428 0.30 0.34 0.27 0.35 0.41 0.46 0.49 0.52 0.55 0.56 0.60 0.62 429 0.23 0.26 0.20 0.26 0.31 0.35 0.37 0.40 0.41 0.43 0.46 0.47

431 0.23 0.26 0.21 0.27 0.32 0.36 0.39 0.41 0.43 0.44 0.47 0.48 432 0.30 0.35 0.28 0.37 0.43 0.48 0.51 0.54 0.57 0.59 0.62 0.64 442 0.25 0.34 0.28 0.37 0.44 0.48 0.51 0.54 0.57 0.59 0.60 0.62 443 0.21 0.26 0.23 0.29 0.33 0.36 0.37 0.39 0.41 0.43 0.43 0.44

242 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

Figure 4-84. Primary load path within the hat truss of WTC 1.

Figure 4-85. Location of the hat truss connections in the primary load path.

NISTNCSTAR 1-6D, WTC Investigation 243
Chapter 4

Table 4-29. Demand and capacity of the hat truss connections (kip) in the primary load

path at 80 min (connection IDs are shown in Fig. 4-85).

Connection

ID

Location Tension Capacity Demand Force

(tension)

State

Floor Column Yield Ultimate

1 110 501 1,250 1,250 680 Safe

2 108 502 1,250 1,250 680 Safe

3 111 502 1,930 1,930 80 Safe

4 108 502 520 520 100 Safe

5 110 701 1,340 1,340 390 Safe

6 107 702 950 950 370 Safe

7 110 801 1,340 1,340 140 Safe

8 107 802 335 260 140 Safe

9 110 1001 1,250 1,250 400 Safe

10 110 1008 1,250 1,250 290 Safe

1110 708 1,340 1,340 360 Safe

12 108 217-218 4,520 5,880 1,810 Safe

13 108 508 870 760 410 Safe

14 110 508 1,250 1,250 530 Safe

15 108 507 1,250 1,250 530 Safe

16 108 149-150 2,640 2,640 1,310 Safe

17 108 110-111 2,640 2,640 1,170 Safe

18 108 442-443 4,520 5,880 1,650 Safe

19 108 417-418 4,520 5,880 1,200 Safe

20 108 242-243 4,520 5,880 1,230 Safe

21 108 231-232 3,010 3,920 1,070 Safe

22 108 228-229 3,010 3,920 1,150 Safe

244 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

4.2.5 Simulation of WTC 2 Collapse

The global model of WTC 2, as described in Sections 4. 1.1 to 4.2.3, was used to simulate the response of

the building to aircraft impact damage and the ensuing fire enviroimient. Studies perfomied on the

isolated exterior wall and core models and on the full floor subsystem models indicated that the calculated

response of these models to the Case D damage and temperature time history set more closely matched

the structural behavior observable in photographic and video evidence than did analyses using Case C. Therefore, in this global analysis only the Case D damage and temperature time history set were used.

Section 2.2 of this report provides a description of the Case D structural impact damage set. The analysis

started with dead and 25 percent of the design live loads taken directly from the reference SAP2000

models and applied as concentrated loads at each column-floor node. Table 4-30 summarizes the

sequence of analyses that were performed. Section 2.5 gives the locations of floor/wall disconnections

and pull-in forces at different analysis steps. The results of each analysis step were used as the initial conditions for the next analysis step.

Table 4-30. Analysis Steps of WTC 2 ANSYS global model with Case D conditions.

Analysis Step Description

1 Dead and 25 percent of the design live loads were applied on the model ofWTC 2 with impact

damage.

2 Floorwall disconnections and pull-in forces that were projected to occur between 0 min and 10 min were applied.

3 Column and spandrel temperatures were linearly ramped up from room temperature of 20 °C to temperatures at 10 mm.

4 Floor wall disconnections and pull-in forces that were projected to occur between 10 min and 20

min were applied.

5 Column and spandrel temperatures were linearly changed from temperatures at 10 min to 20 min.

6 Floor/wall disconnections and pull-in forces that were projected to occur between 20 min and 30

min were applied.

7 Column and spandrel temperatures were linearly changed from temperatures at 20 min to 30 min.

8 Floor/wall disconnections and pull-in forces that were projected to occur between 30 min and 40

min were applied.

9 Column and spandrel temperatures were linearly changed from temperatures at 30 min to 40 min.

10 Floorwall disconnections and pull-in forces that were projected to occur between 40 min and 50

min were applied.

11 Column and spandrel temperatures were linearly changed from temperatures at 40 min to 50 min.

Figures 4-86 through 4-133 summarize the results of the global analyses with creep for the analysis steps

described in Table 4-30. The vertical displacements of the exterior wall and the core area are presented

in Figs. 4—86 through 4—98. For the exterior wall, the vertical displacements were about 2.0 in. to 3.0 in. before the aircraft impact. As indicated in Fig. 4-88, the core had larger vertical displacements by about

1 in. than the exterior walls at Floor 83 before aircraft impact. Since construction sequence was not considered in the analysis, this difference in the vertical displacements changed initial loading conditions

of the columns. As shown in Table 4—8, the total column loads on the east and west walls increased by 7 percent at the impacted floors, the total column loads on the north and south walls increased by about 13

percent, and the total column loads on the core decreased by about 8 percent, by ignoring the construction

sequence. After aircraft impact, the vertical displacements increased to 7.4 in. on the south wall

NISTNCSTAR 1-6D, WTC Investigation 245
Chapter 4

(Fig. 4-86). Due to thermal expansion of columns, the vertical downward displacements recovered

slightly initially and eventually increased as shortening due to plastic and creep deformations became

larger than the thermal expansion. However, the vertical displacements remained around 7.5 in. until 43

min at which point they increased rapidly to 11. 3 in. on the east and south faces with the bowing of the

east wall. When the east wall reached instability and buckled, the northwest comer of the exterior wall

lifted up about 2.0 in., which indicated that the tower was tilting toward the southeast around an axis

passing through the southwest and the northeast comers (Fig. 4-87). The tilting of the tower is also

illustrated in Figs. 4-88 and 4-89, where the vertical displacements at Floor 83 are presented. As can be

seen, with increasing time the displacements on the southeast comer increased, whereas the displacements on the northwest comer decreased. The likely axis about which the tower was tilted is indicated in Fig. 4-89. The axis location in Fig. 4-89 was based upon the distribution of plastic and creep strains,

which is presented later in this Section. Figure 4-90 shows the total displacements above Floor 86 when

the east wall buckled and collapse initiated. For reference, the undeformed tower is also shown. The tilt toward the southeast is clearly visible.

Analysis of the stmcture without aircraft impact damage indicates vertical displacements at the top of the

building of approximately 4 in. (Figs. 4-91, 4-93, 4-95, and 4-97). Analysis with the estimated aircraft impact damage in place indicates that vertical displacements at the southeast comer of the core increased

to approximately 10 in. (Figs. 4—91 and 4-97). As with displacements on the exterior wall, vertical

downward displacement of the core was predicted to be somewhat recovered in the initial periods of the

fire, due to thermal expansion, and then increased with time as inelastic and creep deformations of the

heated and heavily loaded columns increased substantially. When the east wall reached instability and

buckled, at 43 min, the core displacements suddenly increased to 13 in. at the southeast comer (Figs. 4-

92, ^94, 4-96, and 4-98).

Figures 4-99 through 4-101 show the out-of-plane displacements of the east wall at various analysis

steps. As shown in Fig. 4-99, there was no out-of-plane displacement on the east wall before the aircraft impact. After aircraft impact, the south side of the east wall at Floor 86 displaced outward about 2.0 in., whereas the north side at the same floor remained approximately at the same displacement as before

aircraft impact. This shows a slight twist about the z-axis. With increasing time and temperatures, the

east wall bowed and the inward displacements increased (Fig. 4-100). At 20 min the maximum inward

displacement reached 9.5 in. toward the center of the east wall. This maximum inward displacement

agrees well with the maximum inward displacement (~10 in.) that was measured from the photographs

and videos at the same time (at 9:21 am which is approximately 18 minutes after the aircraft impact).

After 20 min, the inward displacements steadily increased until at 43 min they rapidly increased to 62 in. (Figs. 4-100 and 4-101). At this point, the east wall reached instability and buckled over the entire width

of the wall.

Figures 4-102 and 4-103 show the lateral displacements of the exterior wall above Floor 86 after aircraft impact and at the instant of the east wall buckling. After aircraft impact. Floor 1 1 0 moved toward the east about 5.0 in. and toward the south about 5.1 in. There was also a slight twist about the z-axis of the tower

which was about 0.0007 radian at Floor 110. The twist about the z-axis was calculated by taking the

difference between the average in-plane displacement of the two opposing exterior walls (such as the east and the west walls) at Floor 110 and dividing the result by the distance between these walls (-200 ft). With the buckling of the east wall, the lateral displacements increased rapidly. The lateral displacements

246 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

of the north exterior wall increased to 15.2 in. toward the east, and of the south exterior wall increased to 6.7 in. toward south. The twist around the z-axis of the tower increased to 0.0010 radian at Floor 1 10.

Figures 4-104 through 4-1 1 1 show the variation of axial loads on the exterior wall columns at different

analysis steps. Typically, before aircraft impact, the load distribution along the width of the walls was

symmetric with respect to the centerline of each wall. After aircraft impact, the loads in the severed

columns redistributed. As a result of this redistribution, the column loads on the south side of the east and

west walls and on the east side of south wall increased. This was due to leaning of the tower toward the

southeast as the aircraft impact severed columns on the east side of the south wall and on the southeast comer of the core (Figs. 4-104, 4-106, 4-108, 4-110, and 4-1 1 1). After redistribution, at Floor 83 the

column loads on the south wall increased from about 250 kip before aircraft impact to 400 kip to 800 kip

in general and to 1,500 kip at the edges of the severed area after aircraft impact. The column loads on the

south side of the east wall at Floor 83 increased from about 350 kip before aircraft impact to about 450

kip after aircraft impact. The column loads on the east side of the north wall at Floor 83 did not change

significantly; however, the column loads on the west side of the north wall at Floor 83 decreased from

about 250 kip before aircraft impact to about 200 kip after aircraft impact. The column loads on the south

side of the west wall at Floor 83 increased from about 300 kip before aircraft impact to about 380 kip

after aircraft impact. The column loads on the north side of the west wall at Floor 83, however, decreased

from about 300 kip before aircraft impact to 250 kip after aircraft impact. Over the duration of the fires the column load distributions remained constant except for some localized changes due to relative

temperatures. When the east wall buckled, the load distribution significantly changed. The columns over

nearly the whole width of the east wall unloaded about 400 kip on the average at Floor 83. Similarly, the

columns on the west face unloaded about 65 kip on the average. This was due to the increased tilting of

the tower toward the east, as the east wall buckled. A part of the loads from the east and the west walls were redistributed to the east side of the south and the north walls. The column loads on the east side of

the south wall increased from about 500 kip to 800 kip after aircraft impact, and to 800 kip to 1,100 kip

after east wall buckling. The column loads on the east side of the north wall increased from about 200 kip

to 250 kip after aircraft impact, and to 300 kip to 500 kip after east wall buckling.

Figures 4-112 through 4-1 19 show the core column loads at different analysis steps. Before the aircraft impact the loads on the core columns were distributed symmetrically with respect to the center of the

core. The slight difference between comer columns on the south side (Columns 501 and 1001) and north

side (Columns 508 and 1008) of the core was due to slightly higher dead and live loads in the north side

columns. After aircraft impact, some portion of the loads in the severed columns was redistributed to the

adjacent intact columns within the core. The tilt toward the southeast also influenced the load

redistribution within the core. Columns 506, 507, 508, and 1008 at the northwest and northeast comers

unloaded; other intact core columns increased in load (Fig. 4-1 18). The maximum load in the 800 series core columns increased from about 1,400 kip before aircraft impact to about 1,700 kip after aircraft impact (Fig. 4-1 12). The maximum load in the 900 series core columns increased from about 1,250 kip

before aircraft impact to about 1,900 kip after aircraft impact (Fig. 4-1 14). Although the maximum load

in the 1000 series core columns reduced from about 4,300 kip before aircraft impact to about 3,000 kip

after aircraft impact (Fig. 4-116), the average load on the remaining intact 1000 series columns increased

about 360 kip at Floor 83 (Fig. 4-118).

Over the duration of the fires, some of the core columns, especially the ones on the east side of the core, unloaded due to yielding and creeping at high temperatures. Loads in softening columns were

NISTNCSTAR 1-6D, WTC Investigation 247
Chapter 4

redistributed to the adjacent columns with lower temperatures. During buckling of the east wall, the loads

in the core columns, especially the ones at the northeast comer of the core, increased significantly. For

instance, at Floor 83 the load in core column 1008 increased from 2,820 kip after aircraft impact to 5,320

kip at 43 min, the load in core coluinn 907 increased from 1,290 kip to 2,330 kip, and the load in core column 805 increased from 950 kip to 1,480 kip (Figs. 4-118 and 4-119).

Figure 4-120 shows the axial loads in the columns at Floor 83 before aircraft impact and after the

buckling of the east wall. This figure illustrates the load redistribution among the exterior wall and core columns. The tilting of the building about an axis likely located through the shaded area occurred after the buckling of the east wall and weakening of the core. Comparison of column loads before aircraft impact and after the east wall buckled clearly shows the unloading over the entire width of the east wall

and increased loads at the east side of the south and north walls.

Figures 4-121, 4-122, and 4-123 show the maximum of the elastic-plus-plastic strains and elastic-plusplastic-plus-creep strains in the columns between Floor 78 and Floor 83 for different analysis steps. The

elastic-plus-plastic strains, which were less than 0.05 percent before the aircraft impact, reached about

0.60 percent in the exterior columns and about 0.35 percent in the core columns after the aircraft impact.

With increasing temperatures the plastic strains increased, especially on the east wall and the east side of

the core. When the east wall buckled, the elastic-plus-plastic strains reached their maximum of

2.2 percent in the east wall and 0.9 percent in the east side core columns. The creep strains also increased

with increasing temperatures to the same level as the elastic-plus-plastic strains in the east wall

(1.0 percent to 2.0 percent), to about 2 to 6 times that in the core columns (2.0 percent to 6.0 percent), and

to about 10 times that in the east side of the north wall (4.0 percent to 5.0 percent).

The state of the hat truss members and the connections were checked as the global model did not include

break elements to capture column and hat truss splice failures or sufficient beam elements to capture

buckling of hat truss outriggers. The condition of the connections and the members in the primary' load

path of the hat truss was evaluated at different time intervals. Evaluations were performed for the core column splices for tensile capacity, outriggers and supporting columns for compressive capacity, and hat

truss connections in the primary load path for tensile capacity. The demand forces that were used in the

evaluation were obtained from the "superelement" since the hat truss was part of it for the WTC 2 global

model with creep. The results for elements within the superelement were obtained by back-substitution.

For this purpose the elastic model that was used to generate the stiffness matrix for the superelement was

used. This elastic model essentially represents the portion of the building from Floor 86 and above and is referred to as the "top model" hereinafter. The displacements obtained at the interface nodes between the

"superelemenf and the nonlinear portion of the building (Floor 86 and below) were applied to the base of

the "top model" at the end of each analysis step together with the nodal loads representing the dead and

the 25 percent of the design live loads.

Figures 4-124 and 4-125 show the loads on the core column splices at the hat truss level at different

analysis steps. As can be noticed, each splice was under compressive load before the aircraft impact.

After the aircraft impact, the splices at severed core column lines started to carry tensile loads. To

evaluate the condition of the core column splices at Floor 106, the tensile capacities of these splices were

determined using the AISC LRfD procedures and were compared to the tensile forces obtained at 40 min,

since at this time point the tensile forces at core column splices were at their maxima. The evaluation of

core column splices required an iterative procedure as splice failures were not modeled in the "top

model". The iteration procedure was required due to the slight nonlinearity of the problem where the

248 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

failure of a few splices did not alter boundary conditions of the "top model" significantly. In the first Iteration, the state of the "top model" was calculated using the interface nodal displacements at 40 min.

Once equilibrium was reached, the columns exceeding their splice capacity were identified (in the first iteration Columns 1001 and 1002 were identified (see Fig. 4-126) and removed). This removal

represented the splice failure at that column location. Before removing the columns, the displacement

boundary' conditions applied at the bottom of these column lines (at Floor 86) were replaced with the reaction forces that were obtained at the end of the first iteration. This conversion from displacement to force boundary condition allowed the remaining portion of the column lines to displace in the vertical direction when the columns were removed at Floor 105 to simulate splice failure. After the removal of

the columns, the "top model" was reanalyzed to redistribute the released tensile force due to splice failure. Once equilibrium was reached, the remaining core colunnn splices were reevaluated and any additional

splice failures were identified. This iterative procedure was repeated until none of the remaining splices

exceeded their tension capacity. A stable state was reached at the end of the fourth iteration. Figure 4-

126 summarizes the iteration sequence and the splices that failed at each iteration. Figure 4-127 shows

the state of the core column splices at the end of the fourth iteration.

In the global analyses, none of the splice failures were represented as those elements were part of the "superelement" which remained elastic throughout the analysis. However, the inclusion of splice failures

is not expected to significantly affect the load redistribution in the global analysis. The loads on columns

with failed splices would have redistributed through the core slab and core beams with moment

connections to adjacent core columns, which in turn would transfer these extra loads to the hat truss. To

quantify the amount of load that was redistributed to the hat truss through the adjacent core columns, the

total column loads on each face and at the core area were extracted at Floor 105 at the end of each

iteration. Table 4-3 1 summarizes these total column loads together with the magnitude of total tensile load released and total tensile load retransferred to the hat truss at each iteration. In Table 4-3 1 , the Column "TTLRSF" represents the total tensile load that was released due to splice failure and is equal to the summation of the load carried by the circled columns in Fig. 4-126 up to and including the current

iteration. In Table 4-31, the Column "Core" between Rows 6 and 9 represents the load that was

transferred to the base of the "top model" through the core colurrms. The sum of Column "TTLRSF" and

Column "Core" represents the total tensile load that was transferred to the hat truss after the splice

failures (labeled as "TTLRHT" in Table 4-31). As can be seen, about 73 percent (= 2,728 kip /3,717 kip)

of the released tension load was transferred to the hat truss after the fourth iteration. The core slab and

the core beams with moment connections were the primary components that transferred the released load

to the adjacent core columns and to the hat truss. Capacity calculations have shown that the core slab and

the core beams in the top 20 stories had enough cumulative capacity to redistribute the released load to the adjacent core columns. As a result of load redistribution, the loads on the southeast comer outriggers were reduced, but the loads on adjacent outriggers increased.

Figures 4-128 through 4—130 show the axial loads and stresses in the hat truss members at different

analysis steps. With the aircraft impact, the maximum axial load on the outriggers, which was about

1,900 kip before the aircraft impact, increased to about 3,400 kip at the southeast corner. This increase

remained almost constant over the duration of the fires. After the buckling of the east wall the maximum

load shghtly increased to 3,500 kip. The axial stresses in the outriggers also increased as a result of the

aircraft impact. The maximum axial stress of 28.4 ksi before aircraft impact increased to 55.0 ksi after the buckling of the east wall. The specified grade of steel for the outriggers was 50 ksi. The tests conducted on this grade of steel showed an average yield strength of about 54 ksi. Considering this yield

NISTNCSTAR 1-6D, WTC Investigation 249
Chapter 4

strength and the 10 percent increase in the hat truss forces due to neglecting construction sequence, it was

concluded that the outriggers of the hat truss did not exceed their elastic limits. To check against

buckling, the buckling capacities of these outriggers as well as the supporting coluiruis were calculated.

The buckling calculations were performed using the AISC LRFD Eqs. E2-1 and E2-3 with an effective

length factor "K" of 0.75 and a resistance factor of 1.0. The calculated capacities were then compared

with the axial compressive forces obtained from the analysis and con-ected to account for the load

increase due to construction sequence. The location of the outriggers and the supporting columns are shown in Fig. 4-3. Tables 4-32 and 4-33 summarize the resulting demand-to-capacity ratios for the

outriggers and the supporting columns, respectively. Except for one outrigger, designated Outrigger L, none of the outriggers or supporting columns was predicted to buckle.

Outrigger L was located at the southeast comer of the core, and above the severed core columns. With

the splice failures in Columns 1001, 1002, and adjacent core columns, the load on this outrigger reduced

and the load redistributed to other outriggers. With the load redistribution after sphce failures, the

demand-to-capacity ratio on Outrigger L reduced from 1.3 to 1.1 (Col "40* min" in Table 4-32). To

investigate whether the buckling of the Outrigger L would cause additional outriggers to buckle, the

element representing Outrigger L was removed from the "top model." Removal of Outrigger L from the

"top model" represents an upper bound solution as the load in the outrigger would not drop to zero after buckling. After removal of Outrigger L, the adjacent outriggers increased in load however, as presented

in Col "40** min" of Table 4-32, none of the remaining outriggers exceeded their buckling or yield

capacities.

In the global analysis, it was assumed that the connections in the hat truss area were adequate to transfer the loads from the core columns to the outriggers. The structural adequacy of the "primary" connections,

those hat truss connections between members that were predicted to have axial tensile or compressive

stress of 25 ksi or more, was evaluated. To perform this evaluation, the results at 40 min were used, since

at 40 min the stresses in the hat truss members were at their maxima. Only connections that transferred

tensile forces were evaluated. Figure 4-132 shows the members in the primary load path. Figure 4-133

shows the location of the critical hat truss connections that were evaluated in this study. The connections

between the horizontal tie-backs and the outriggers were not evaluated as they were found to have

significant capacity in the WTC 1 connection evaluations. Comiection capacities were calculated using

AISC LRFD procedures. Table 4-34 summarizes capacities, demands, and the predicted condition of the

evaluated connections. As can be seen in Table 4-34, before redistribution of load due to column splice

failure, none of the connections exceeded their capacities except the connections associated with the 1001

core column line. After load redistribution, the demand was less than the yield capacities for all connections. Based on this, and the other evaluations of column splices and hat truss members discussed

above, it was concluded that the hat truss was capable of transferring loads from core columns to the

outriggers without any connection failures.

Tables 4-35 and 4-36 summarize the total column loads at each exterior face and the core for Floor 83

and Floor 105. The first seven rows of Tables 4-35 and 4-36 provide the total loads at each analysis step.

The rows from 8 through 1 3 give the change in total column loads at each analysis step with respect to the

total column loads before aircraft impact. For instance. Row 8 gives the difference between the total column loads before and after aircraft impact. A positive value between Row 8 and Row 13 indicates that the total compressive load has increased in that analysis stage as compared to the total compressive load

before the aircraft impact. Based on these tables, after the aircraft impact, the core and the north wall

250 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

unloaded and their loads were redistributed to the south, west, and especially to the east wall at Floor 83. A similar load redistribution pattern was found for Floor 105. The comparison of the total column loads

before and after aircraft impact at Floor 83 and Floor 105 is presented in Table 4-37. The second row in this table represents the amount of load redistributed through the hat truss, and the third row represents

the amount of load redistributed through the spandrels and the floors. Based on this table, it can be stated

that about 94 percent (3.740 kip,4.000 kip) of the load that was unloaded from the core was redistributed

through the hat truss to the east, south, and west walls, and the remaining 6 percent was redistributed

through the floors to the exterior walls. A similar calculation for the east wall indicates that about 62

percent (2.699 kip/4,368 kip) of the load increase on the east wall came through the hat truss and the

remaining 38 percent came through the Vierendeel action of the wall. Rows 8, 9, 1 0, and 1 1 of Table 4-

35, show that the loads in the various walls and the core itself did not significantly change until the core imloaded at about 30 min. At 30 min the total column loads on the east wall increased by about 1,200 kip

(from 5,567 kip to 4,368 kip) and the core unloaded about 850 kip (from 4,861 kip to 4,007 kip) and the

north wall unloaded about 420 kip (from 1.797 kip to 1,374 kip) at Floor 83. Similarly, at Floor 105 and

at 30 min the total column loads in the various walls and core remained almost constant until initiation of

buckling of the east wall. After 40 min, the east wall suddenly unloaded about 8,540 kip, the west wall

imloaded about 2.860 kip, the core experienced a load increase of about 5,600 kip, the north wall

increased by about 2.310 kip. and the south wall increased by about 2.820 kip at Floor 83 (Table 4-38).

Comparison of the load redistribution that took place at Floor 105 with the one at Floor 83 indicates that about 1 00 percent of the additional core load came from the east and the west walls through the hat truss. For the east wall, about 46 percent (3,901 kip/8,539 kip) of the relieved load was redistributed through the

hat truss to the core, and the remainder was redistributed through Vierendeel action to the south and north

walls. After the redistribution, at 43 min. the load in the core had recovered to the same level as the total load before the aircraft impact.

Tables 4—39 through 4-43 summarize the loads in the east, south, north, west walls, and the core at se\ eral floor levels. The tables also indicate the change in column load at each stage of the analysis,

compared to the load present before aircraft impact. These load changes are provided in Columns 8 through 13. As described before, the changes in loads at Floor 105 represent the load redistribution

through the hat truss. The changes in loads along the height of the tower indicate the load redistribution

through the exterior wall and the floor system. In referring to the changes in loads after the aircraft impact (Col 8 in the tables), it can be concluded that the total column loads along the height of the core and the west wall remained almost constant. This indicates that almost all load redistribution from and to these portions of the tower went through the hat truss. The total column loads in the east wall increased at the hat truss level and continued to increase with distance from the hat truss. The north wall showed the opposite trend; at the hat truss level the wall unloaded and continued to unload further with distance from

the hat truss. The unloading took place primarily through Vierendeel action, to the east wall. After the

buckling of the east wall, the change in loads (Col 13 in the tables) indicates that the hat truss was the

primary load path for the portion of the load picked up by the core. The east and west walls unloaded at the hat truss le\'el and at lower floors. Both walls steadily picked up more load at lower floors through

the action of spandrels.

During the load redistribution, the floor slabs played a significant role in restraining the core in the lateral direction. The aircraft impact damage to the core and the ensuing fire environment caused the core to lean toward the south and east. In fact, calculations show that the isolated core would not have been

stable. The resistance to core leaning was provided by the exterior wall. The load was transferred to the

NISTNCSTAR 1-6D. WTC Investigation 251
Chapter 4

exterior walls by shear either through slabs or hat truss. To identify the contribution of the floor slabs to the lateral restraint of the core, the moment of the core column loads around the center of the building in the X- and y-directions at Floor 83 and Floor 105 were computed for WTC 2. Before impact, there was no

eccentricity in the load, and the moments thus calculated were small. After impact and at the end of

temperature histories, the moment in the x-direction was 5,905,640 kip-in at Floor 83 and

2,282,320 kip-in at Floor 105. Similarly, the moment in the y-direction was 5,051,130 kip-in at Floor 83

and 2,196,440 kip-in at Floor 105. The change in moment from Floors 83 to 105 was due to the lateral resistance of provided by the slabs and the exterior walls to the core. The results of calculations show that the overturning moment reduced by about 55 percent to 60 percent along the height of the tower. This

reduction was due to the lateral resistance provided by the floor slabs. The remaining 40 percent to 45 percent was resisted by the hat truss.

252 NIST NCSTAR 1-6D, WTC Investigation
Global Analysis

NODAL SOLUTION

TIKE=.100E-02

UZ (AVG) RSYS=0

D^QC -3.032

SKN =-2.971 SKX =-2

ANSYS

KAR 2 2005 10:51:30

-11.25 -8.75

-10 -7.5 WTC2 Reduced Model At Bfrimp

(a) Before impact

NODAL SOLUTION

STEP=1

SUB =68 TIME=.001

.RSYS=0 DMX =7.703

ANSYS

MAR 2 2005 10:36:04

-3.75 -1.25

-2.5 0 WTC2 Reduced Model At Aftrimp

(b) After impact

Figure 4-86. Vertical displacement of exterior wall of WTC 2 for Case D conditions

(downward displacement is negative).

NISTNCSTAR 1-6D, WTC Investigation 253
Chapter 4

NODAL SOLUTION

STEP=8

SOB =337 TIME=30

UZ (AVG) RSXS=0

DMX =9.831

SMN =-7

ANSYS

MAR 2 2005 10:40:07

-3.75 -1.25

-2.5 0 WTC2 Reduced Model At 1200s

(a) 'ZU mm

NODAL SOLUTION

STEP=17

SUB =523 TIME=63.523

UZ (AVG) RSYS=0

DMX =61.911

SMN =-11.096

AIMSYS

MAR 2 2005 10:45:47

-3.75 -1.25

-2.5 0 WTC2 Reduced Model At 2540s

(b)43 min

Figure 4-87. Vertical displacement of exterior wall of WTC 2 for Case D conditions

(downward displacement is negative).

254 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

r3)))))x )))) )))y )»))))Y ))m )))>x n ))))x n yym

-3.0 in C5 S

@ (2 O O

o o

N

oooo

o oo

-4.0 in O OO

O OO

O

O

-3.0 in

O

O

-3.0 in

O

O

O

G

'((( xcc(( x( ma x( xiai xda maai xauia x»»f

(a) Before impact

-3.0 in H

»»)))X n»^»x »nx n))x )X)n»t)3T^

-3.0 in

O O O OO O

O O O OO O

Q Oooo

O O OO

-4.0 in O O O OO o

O O O OO o

N

-3.0 in

o

o

o

o

G G

Va( m(( Y( K xaa xmai xaaa( Y(aa9^

(b) After impact

Figure 4-88. Vertical displacement at Floor 83 of WTC 2 for Case D conditions

(downward displacement is positive).

NISTNCSTAR 1-6D, WTC Investigation 255
Chapter 4

-7.3 in

O O O OO O Q

O O O CX) O O

o c

O 00 G

O 00 ®

-1.8 in

G

G

N

-3.7 in -3.0 in

(a) 20 min

y

; H \ -2.5 in

'

1^ r^j \

^ pi

-4.5 sr. I'^'

-10 in

Likely zone the

tower tilts around

-1.2 in 000 o5-^$

"©•X) O CO

rpO O O

( ) (

}

O O O OD O

O O O CD O

13 in 12 in 11 in

f ^ — N

[ -11 in -8.5 in k ICQ w ) w m !((((( m((( im

-5.0 in

(b) 43 min

Figure 4-89. Vertical displacement at Floor 83 of WTC 2 for Case D conditions

(downward displacement is positive; note the tilt toward east and south).

256 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

Figure 4-90. Total displacements of WTC 2 above Floor 86 at 43 min of Case D

conditions (deformed shape magnified 20 times). Note the tilt toward east and south.

NISTNCSTAR 1-6D. WTC Investigation 257
Chapter 4

(a) Before impact

(b) After impact

Figure 4-91. Vertical displacement of core of WTC 2 for Case D conditions (downward

displacement is negative).

258 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

(b) 43 min

Figure 4-92. Vertical displacement of core of WTC 2 for Case D conditions (downward

j displacement is negative).

!

NIST NCSTAR 1-6D. WTC Investigation 259
Chapter 4

(a) Before impact

SUB =68 TIME=.001

UZ (AVG

)

RSYS=0

DMX =8.916

SMN =-8.696

801AIMSYS

MAR 2 2005 10:36:34

FL77 —

WTC2 Reduced Model At Aftrimp - Core 800 Looking from West to East

(b) After impact

Figure 4-93. Vertical displacement of 800 series core columns of WTC 2 for Case D

conditions (downward displacement is negative).

260 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

807 FL86 r

STEP=8

SUB =337 TIME=30

UZ ' (AVC) RSYS=0

DMX =9.829 SMN =-9.809

FL77 —

-9.809

-8.71 WTC2 Reduced Model /

-12.212 -9.498 -6.785 -4.071 -1.357 -10.855 -8.142 -5.428 -2.714 0 WTC2 Reduced Model At 2540s - Core 800 Looking from West to East

(b) 43 min

Figure 4-94. Vertical displacement of 800 series core columns of WTC 2 for Case D

conditions (downward displacement is negative).

NISTNCSTAR 1-6D. WTC Investigation 261
Chapter 4

Figure 4-95. Vertical displacement of 900 series core columns of WTC 2 for Case D

conditions (downward displacement is negative).

262 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

(a) 20 min

(b) 43 min

Figure 4-96. Vertical displacement of 900 series core columns of WTC 2 for Case D

conditions (downward displacement is negative).

NISTNCSTAR 1-6D, WTC Investigation 263
Chapter 4

(a) Before impact

(b) After impact

Figure 4-97. Vertical displacement of 1000 series core columns of WTC 2 for Case D

conditions (downward displacement is negative).

264 NIST NCSTAR 1-6D, WTC Investigation
Global Analysis

UZ (AVG RSYS=0

DMX =9.881 SMS =-9.723

loo.ANSYS

MAR 2 2005 10:40:33

-9.723 -7.562 -5.402 -3.241 -1.08

-8.643 -6.482 -4.321 -2.161 0 WTC2 Reduced Model A:: 12C0s - Core 1000 Looking from Wesz Z-O East

(a) 20 min

looiANSYS Mil

SSYS=0

DKX =13.576 SX: =-12.982

MAR 2 2005

10:46:36

FL77—

-12.932 -10.097 -7.212 -4.327 -1.442

-11.54 -8.655 -5.77 -2.885 0 iuced Model Ac 254Cs - Core lOCC looking from West no East

(b) 43 min

Figure 4-98. Vertical displacement of 1000 series core columns of WTC 2 for Case D

conditions (downward displacement is negative).

NISTNCSTAR 1-6D, WTC Investigation 265
(a) Before impact

(b) After impact

Figure 4-99. Out-of-plane displacement of the east wall of WTC 2 for Case D conditions

(inward displacement is positive).

266 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

(b)43 min

Figure 4-100. Out-of-plane displacement of the east wall of WTC 2 for Case D conditions

(inward displacement is positive).

NISTNCSTAR 1-6D. WTC Investigation 267
Chapter 4

0 -\ < 1

i i

! 20 25 30 35 40 45

Time, min

Figure 4-1 01 . Variation of maximum inward bowing of the east wall of WTC 2 over time

for Case D conditions.

268 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

solution

S-J3 =1

TI.ME=.O07 UX (AVG) RSYS=0

DKX =20.662

SKN =--i.91i SMC =-.154533

^ (in.)

-7.C52 -5.327 -3.603 -1.879 -.154533 WTC2 Reduced Model At 2540s

Figure 4-102. Lateral displacements above Floor 86 of WTC 2 in the x-direction (northsouth) for Case D conditions.

NISTNCSTAR 1-6D. WTC Investigation 269
Chapter 4

Figure 4-103. Lateral displacements above Floor 86 of WTC 2 in the y-direction (eastwest) for Case D conditions.

270 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

(a) Before impact

ELEMENT SOLUTION

STEP=1 SUB =68 TIME=.00

SMISl TOP

DMX =4.5 SMN =-5S SMX =-16

12 3

; 92

ANSYS

MAR 2 2005 10:36:15 -FL86

359 y

-.:36E-07 -.:02E-07 WTC2 Reduced Model At Aftrimp - East Face

301-FL77

(lb) .

(b) After impact

Figure 4-104. Axial load in the east wall of WTC 2 for Case D conditions (compression is negative).

NISTNCSTAR 1-6D, WTC Investigation 111
Chapter 4

(b) 43 min

Figure 4-105. Axial load in the east wall of WTC 2 for Case D conditions (compression is negative).

272 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

ELEMENT SOLUTION

TIME=.100B-jO£ SMISl TOP

DMX =3.0i; SMN =-32l{ 5S SMX =-15,4810

ANSYS

MAR 2 2005 10:52:34

I I ! FFL86

I i 4— FT 77

401 ^ (lb)

WTC2 Reduced Model At Bfrimp - South

(a)

Face

Before impact

I

ELEMENT SOLUTION

STEP-1

SUB =68 TIME=.00l

SMISl TOP

DMX =7.7li: SMN =-.15(E+fl: SMX =884 1(

AIMSYS

MAR 2 2005 10:36:17

I I I I-FL86

r-FL77

-.lb3E*07 -.119E»07 -SbOOOO -.136E»07 -.102E*07 WTC2 Reduced Model At Aftrimp - South Face

-blOOOO -170000

80000 -340000

(b) After impact

Figure 4-106. Axial load in the south wall of WTC 2 for Case D conditions (compression

is negative).

NISTNCSTAR 1-6D, WTC Investigation 273
Chapter 4

(b)43 min

Figure 4-107. Axial load in the south wall of WTC 2 for Case D conditions (compression

is negative).

274 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

ELEMENT SOLUTION

STE?=1 SUB =1 TIfe=.1003-C£

SMISl TOP

DMX =3.0 6 SMN =-32?; 4S SMX =-15 I' 2 I

ANSYS

MAR 2 2005 10:52:05

I i ! FFL86

FL77

-900000 -700000 -500000 -300000 -100000

-800000 -600000 -400000 -200000 0 WTC2 Reduced Model Ac Bfrlmo - North Face

(a) Before impact

(b) After impact

Figure 4-108. Axial load in the north wall of WTC 2 for Case D conditions (compression

is negative).

NISTNCSTAR 1-6D, WTC Investigation 275
Chapter 4

ELEMENT SOLUTION

STEP=17

SUB =523 TIME=63.B33

SMISl

TOP

DMX =8.1 i! SMN =-87 1350 SMX =-60 'C

ANSYS

(b) 43 min

Figure 4-109. Axial load in the north wall of WTC 2 for Case D conditions (compression

is negative).

276 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

400

300

Q.

u

.5<

200

100

Before Impact

After Impact

20 min

43 min

160 150 140 130

Column ID

(b) West wall

120 110 100

Figure 4-110. Axial load in the east and the west wall columns at Floor 83 of

WTC 2 for Case D conditions (compression is positive).

NISTNCSTAR 1-6D. WTC Investigation 277
Chapter 4

1500

0

-\ 1 1 1 ^

1

: 260 250 240 230 220 210 200

Column ID

(b) North wall

Figure 4-111. Axial load in the south and the north wall columns at Floor 83 of WTC 2 for

Case D conditions (compression is positive).

278 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

FL86—SOLUTION

STEP=1

SUB =1 TIME=.10£IE-02 SMISl

TOP

DMX =4.311 SMN =-.147E+07

SMX =-51S455

ANSYS

MAR 2 2005

L0:52:52

807

-.I9SL07 -.154t>07 -.110EH)7 -660000 -220000 -.nSLOT -.132Et07 -BSOOOO -440000 WTC2 Reduced Model At Bfrln^j - Core 800 Looking from West to East

(a) Before impact

STEP=1

SUB =68 TIME=.001

SMISl TOP

DMX =8.916

SMN =-.169E+ SMX =29394

ANSYS

MAR 2 2005 10:36:35

FL77—

-.l93E<-07 -.lb<E«-0/ -.110E-f07 -660000 -220000

-.176E^07 -.132E-'07 -880000 -440000 pumgg

WTC2 Reduced Model At Aftrimp - Core 800 Looking from West to East o.u

(b) After impact

Figure 4-112. Axial load in 800 series core columns of WTC 2 for Case D conditions

(compression is negative).

NISTNCSTAR 1-6D, WTC Investigation 279
Chapter 4

FL86-

STEP=8 I SUB =337 ; TIME=30 ! SMISl

{ TOP I DMX =9.829 ! SMN =-.n9E+C7i

sMx =15381 ;

FL77 —

807

ANSYS

MAR 2 2005 10:40:28

801

(lb)

WTC2 Reduced Model At 1200s - Core 800 Looking from West to East

STEP=17 : SUB =523 i TIME=63.523 ; SMISl i TOP

DMX =12.253 , SMN =-.198E+07-i SMX =58951 I

ANSYS

MAR 2 2005 10:46:29

-.198E<-07 -.154E+07 -.llOEi-07 -660000 -220000 -.n6E+07 -.132E+07 -SSOOOO -440000 jgg^^^

WTC2 Reduced Model At 2540s - Core 800 Looking from West to East u.u

(b)43 min

Figure 4-113. Axial load in 800 series core columns of WTC 2 for Case D conditions

(compression is negative).

280 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

Figure 4-114. Axial load in 900 series core columns of WTC 2 for Case D conditions

(compression is negative).

NISTNCSTAR 1-6D. WTC Investigation 281
Chapter 4

STEP=n

SUB =523 i TIME=63.523 j SMISl TOP

DMX =12.694

SMN =-.282E+C7| SMX =3523 i

AISISYS

FL77 —

-.288E+07 -.224E+07 -.160EtO7 -960000 -320000 -.256E+07 -.192Et07 -.128E+07 -640000 |^^^^

WTC2 Reduced Model At 2540s - Core 900 Looking from West to East o.u

(b)43 min

Figure 4-115. Axial load in 900 series core columns of WTC 2 for Case D conditions

(compression is negative).

282 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

FL86—SOLUTION

STEP=1

SUB =1 TIME=.10OE-02

SMISl TOP

DMX =4.274 SMN =-.428E+07

SMX --.122E+07

ANSYS

mar! 2 2005 io:52:57

FL77-i^

1008

WTC2 Reduced Model At Bfrlrap - Core 1000 Looking from West to East

(a) Before impact

FL86

STEP=1

SUB =68 TIME=.001

SMISl TOP

DMX =10.229

SMN =-.306E+07

SMX =35385

ANSYS

MAR 2 2005 10:36:41

FL77 —

-.b-/2E*0V -.<;44E»0V -.318E-f07 -.ISOEtOV -635000 -.b08E»0T -.331E»07 -.254E+07 -.127Et07 WTC2 Reduced Model At Aftrimp - Core 1000 Looking from West to East u.o

(b) After impact

Figure 4-116. Axial load in 1000 series core columns of WTC 2 for Case D conditions

(compression is negative).

NISTNCSTAR 1-6D, WTC Investigation 283
Chapter 4

SUB =523 TIME=63.523

SMISl TOP

DMX =13.576

SMN =-.571E+0r7 SMX -35405

ANSYS

RA.R 2 2005 10:46:37

-.572E+07 -.44iE+07 -.SISE+OT -.190Et07 -635000 -.50eE+07 -.3eiE+07 -.254E+G7 -.127E+07 WTe2 Reduced Model At 2540s - Core 1000 Looking from West to East o.o

(b)43 min

Figure 4-117. Axial load in 1000 series core columns of WTC 2 for Case D conditions

(compression is negative).

284 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

501 508

2988 1 {''924) 1 1871 [1502)(1404) (20%) (1881

4a {861

(1195)

(l20£ 3 m

^

;782) ^ ^

(1168

1001

2320 1354 {1287) 2205

N

1039 (837|

18441

1008

(a) Before impact

501

^^^J^

^^m^ (2235) {16101(1475) {1887

(14S) ("^1698) (1561) {1121) (1172) (1247)

508

2678

10

(1068

(935) (951 11449)

(U38)

(l384)

1001

^^^^ ( 2351

N

(b) After impact

2085

1008

Figure 4-118. Core column loads (kip) at Floor 83 of WTC 2 for Case D conditions

(compression is positive).

NISTNCSTAR 1-6D, WTC Investigation 285
Chapter 4

508

^ IVI 1008

(b)43min

Figure 4-119. Core column loads (kip) at Floor 83 of WTC 2 for Case D conditions

(compression is positive).

286 NIST NCSTAR 1-6D, WTC Investigation
Global Analysis

Scale

5,000 kip

O 2,500 kip

Q 1,000 kip

O 300 kip

501 508

OOOODOOO

o o o oo o o o

OooO

o oo

o o o oo o o o OOOCDOOO

1001 1008

N

aD»)))}) )» »)))»)})»?)))))))?)}j. ».?))a).).mi).?.»nn)

(a) Before impact

Scale

5,000 kip

Q 2,500 kip

O 1,000 kip

O 300 kip

^(({(((((f {((.((<((<«.<({«(<<(«<( (a<<ta(r{{.{(frTmxx)ooo

Likely zone the

tower tilts around

508

WW w -^^^.^ O O m3 O aj G^^O

1001

CPOOa

o o oT--

1008

S

N

(b)43 min

Figure 4-120. Axial load in Floor 83 columns of WTC 2 for Case D conditions

(compression is positive).

NIST NCSTAR 1-6D, WTC Investigation 287
Chapter 4

-0.04

501

O G o o

o

o

G O

O ©

O

©

-0.05

o

o

1001

©

o o © o

o o o -0.05

© O © 0

o © o ©

508

o O

0 o

J ©

1 ©

©

©

1008

N

-0.05

-0.04

(a) Before impact

ai30CD3axD3ocaDooocaxxxx)ocxxxxx»

-0.04

-0.09

~0.60(

© © ©

O o @ ©©

-0.34

o ooo©

-0.150 ®

oO

508

O O

O O 9

© © © ©

1001

N

-0.04

-0.10 -0.04

iin:Dxa'oxcaxcexnxaxaxaxraxx3^^

(b) After impact

Figure 4-121. Maximum eiastic-plus-plastic strains for columns between Floor 78 and

Floor 83 of WTC 2 for Case D conditions (compressive strain is positive; strain values are

in percent).

288 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

-0.04

-0.09

-0.60i

501 508

o o o o o o O n G GO © © Q

-0.35

Oogo O O

O O

00 o © ©

-0.70 O O o ®

1001 1008

-0.04

N

-0.10 -0.40

-0.30

(a) 20 min

-0.09

-0.80

-0.03

-0.30

(roxnxaxctxxxxxxxoooooocxDoocoooocxaxx

-0.03

501 508 OOOOOO O o O O O OO O 0 o

-0.40 ^

-0.75 (p O O 9

O© o ^

1001 1008

N

-1.0 -1.3

2]SS"ii~2.20

-0.35

(b)43 min

Figure 4-122. Maximum elastic-plus-plastic strains for columns between Floor 78 and

Floor 3 of WTC 2 for Case D conditions (compressive strain is positive; strain values are

in percent).

NISTNCSTAR 1-6D, WTC Investigation 289
Chapter 4

N

~0.11 W -0.50 -0.70

())))))))) ))))]))))))))))m^mm)

(a) 20 min

Q33XUXmxXXXXXXXXXXXXXXXX)CiCXXDOOOC«CXXXXXXX)OOOooooooooo

(b) 43 min

Figure 4-123. Maximum elastic-plus-plastic-plus-creep strains for columns between

Floor 78 and Floor 83 of WTC 2 for Case D conditions (compressive strain is positive;

strain values are in percent).

290 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

501 508

(^72?) 1517 571 459 X 546

[237) (279

fe52)

(292) (3^ 134 {248)

(285)

695 552 695 560 0

1001 N 1008

(a) Before impact

501

^^^980^ ^^5^ ^708^ (^^^X^53 0 0

508

663

(180 (185

(17^ (367 383^

(229) Hi

1001

245) (227

N

(b) After impact

^(ais) (^toT) (^6^

(ss?)

1008

Figure 4-124. Axial load in core columns (kip) at Floor 105 (at hat truss level) of WTC 2

for Case D conditions (compression is positive).

NISTNCSTAR 1-6D, WTC Investigation 291
Chapter 4

508

1001 N 1008

(b)43min

Figure 4-125. Axial load in core columns (kip) at Floor 105 (at hat truss level) of WTC 2

for Case D conditions (compression is positive).

292 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

501 508

(335 33S

3S 33

(335 ( 335) (3351

(3S (335 0 0 00 0 0

1001 N

1008

(a) Tension capacities of core column splices

501 508 ©0 0 0 0 0 © © 03 © © ©

00 0 0 0 @ (300) (363) (^)(426 (452

©

0

@ o ®

(SS [595

1001 N

1008

(b) Before splices 1001 and 1002 fail

(t = 40 min)

501 508 501 508 000QQ000 ©©©0©©©©

9 353 4?S 455 (S3]

1001

• @ @ ® @ © @

m @ @ 0 0 @)

^

o @ © © © @

% @ -es ® 0 0 ©)

N

(c) After splices 1001 ancj 1002 fall

(t = 40 min) (l" iteration)

1008 1001

3^1 3551 4=2 (456 Si) o ® @ @ @ @

@ @

-©1 e — N

MSB 564

1008

(d) After splices 901 and 902 fail

(t = 40 min) (2"^^ iteration)

501 508 0 0 0 00 0 0 0

0 (S) (3a (BO (3) @

1001

" @ @ @ @ 0

^ @ @ @ ©

# © 8 © @ ©

• • <5 « 0 ©

N

(e) After splices 801 and 1 003 fail

(t = 40 min) (3"^ iteration)

1008

501

1001

[si) (0) 0)3) ©) ©^ ©)

508

332 (3i7 «2 451 (357 @ @ @ @ ©

@ @ © ©

@ © 0 0

^ e 0) (0

N

1008

(f) After splice 701 fails

(t = 40 min) (4*^ iteration)

o

Splices exceeding their tension ^_ , , , , •X 4 *i, * -4 4- A ready fai ed sp ices

capacity at that iteration ' ^

Figure 4-126. Progressive failure of core column splices at Floor 105 of WTC 2

(compression is positive; values are in kip).

NISTNCSTAR 1-6D. WTC Investigation 293
Chapter 4

501 508

o o o oo o o o

o o o oo o o o

• o ooo o o o

• o ooo o o

• • o oo o o o

1001

o • •

. oo

^ ooo

1^ 1008

^

Failing splices right after impact Splices failing after load redistribution

Figure 4-127. State of core column splices at Floor 105 of WTC 2.

Table 4-31. Total column loads (kip) at Floor 105 at different stages of splice failures at 40 min (compression is positive).

Row Analysis Status West East North South Core TLRSF* TLRHT**

(1) Before Splice Failure (t = 40 min) 9185 11913 6537 8706 12402 0 0

(2) Splices 1001 and 1002 fail 9221 11747 6577 8432 12761 -1436 -1077

(3) Splices 901 and 902 fail 9227 11644 6612 8206 13045 -2419 -1776

(4) Splices 801 and 1003 fail 9241 11550 6629 8043 13267 -3368 -2503

(5) Splice 701 fails 9229 11533 6649 7925 13391 -3717 -2728

(6) (2)-(l) 36 -166 40 -274 359 -1436 -1077

(7) (3)-(2) 6 -103 35 -226 284 -983 -699

(8) (4)-(3) 13 -93 17 -163 222 -949 -727

(9) (5)-(4) -11 -17 20 -117 124 -349 -225

(10) (6)+(7)+(8)+(9) 44 -380 1 12 -780 989 -3717 -2728

* Total load released by the splice failure ** Total load retransferred to the hat-truss

294 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

(a) Before impact

Figure 4-128. Axial force in hat truss members of WTC 2 for Case D conditions (tension

is positive).

NISTNCSTAR 1-6D. WTC Investigation 295
Chapter 4

V

Floor 106

WTC2 Reduced Model At 1200s

ANSYS

MAR 14 2005 11:10:57

Figure 4-129. Axial force in hat truss members of WTC 2 for Case D conditions (tension

is positive).

296 NISTNCSTAR 1-6D. WTC Investigation
Global Analysis

(a) Before impact

Figure 4-130. Axial stress in hat truss members of WTC 2 for Case D conditions (tension

is positive).

NISTNCSTAR 1-6D, WTC Investigation 297
Chapter 4

STEP=7

SUB =1 TIME=. 007 SX (NOAVG) RSYS=0

DMX =21.63

SMN =-54942

SMX =40634

ANSYS

MAR 14 2005 11:10:56

Floor 106

-54942 -33703 -12464 8775 -44322 -23083 -1844

WTC2 Reduced Model At 2540s

Figure 4-131. Axial stress in hat truss members of WTC 2 for Case D conditions (tension

is positive).

298 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

Table 4-32. Demand-to-capacity ratios for outriggers of WTC 2 for Case D conditions

(outrigger IDs are shown in Fig. 4-3).

Outrigger ID Bfr. Imp. .\ftr. Imp. 10 min 20 min 30 min 40 min 40* min 40** min 43 min

\Nest

A 0.23 0.61 0.61 0.64 0.66 0.63 0.63 0.38 0.25 B 0.19 0.30 0.30 0.32 0.33 0.31 0.31 0.25 -0.03*** C 0.19 0.27 0.27 0.28 0.30 0.27 0.28 0.22 -0.07 D 0.21 0.18 0.18 0.19 0.21 0.18 0.20 0.19 -0.29 North

E 0.29 0.11 0.10 0.10 0.13 0.14 0.17 0.09 -0.01 F 0.21 0.10 0.08 0.08 0.10 0.12 0.13 0.11 0.08 G 0.20 0.11 0.08 0.08 0.11 0.13 0.14 0.13 0.10 H 0.30 0.21 0.16 0.18 0.19 0.18 0.19 0.24 0.24 East

I 0.22 0.39 0.35 0.34 0.45 0.43 0.42 0.41 -0.18 J 0.18 0.56 0.52 0.53 0.66 0.65 0.61 0.71 0.02 K 0.18 0.62 0.58 0.59 0.72 0.72 0.66 0.79 0.09 L 0.22 1.12 1.09 1.12 1.24 1.30 1.11 0.00 0.72 South

M 0.30 0.68 0.64 0.64 0.70 0.75 0.52 0.72 0.87 N 0.22 0.34 0.32 0.33 0.36 0.38 0.28 0.34 0.40 O 0.22 0.30 0.28 0.30 0.32 0.33 0.27 0.31 0.33 P 0.31 0.51 0.50 0.52 0.53 0.53 0.50 0.57 0.49

* After load redistribution due to core column splice failures. After Outrigger L was removed.

* Negative value indicates tension

NISTNCSTAR 1-6D, WTC Investigation 299
Chapter 4

Table 4-33. Demand to capacity ratios for columns supporting outriggers at Floor 107 of WTC 2 for Case D conditions.

Column ID Bfr. Imp. Aftr. Imp. 10 min 20 min 30 min 40 min 43 min

West

110 0.26 0.46 0.46 0.47 0.48 0.47 0.28

111 0.26 0.39 0.39 0.40 0.41 0.40 0.26 129 0.27 0.37 0.37 0.38 0.40 0.37 0.06 130 0.31 0.39 0.39 0.40 0.41 0.39 0.09 131 0.27 0.35 0.34 0.36 0.37 0.35 0.05 149 0.25 0.24 0.24 0.25 0.25 0.24 0.08 150 0.25 0.23 0.23 0.23 0.24 0.23 0.00 North

217 0.17 0.11 0.11 0.11 0.12 0.12 0.07 218 0.23 0.12 0.11 0.11 0.13 0.14 0.05 228 0.27 0.17 0.15 0.15 0.17 0.19 0.15 229 0.22 0.14 0.12 0.12 0.14 0.16 0.13 231 0.26 0.18 0.15 0.15 0.18 0.19 0.17 232 0.26 0.18 0.15 0.15 0.18 0.20 0.18 242 0.20 0.15 0.12 0.13 0.14 0.14 0.17 243 0.19 0.16 0.14 0.14 0.15 0.14 0.17 East 310 0.25 0.34 0.32 0.31 0.36 0.36 0.05 311 0.27 0.33 0.32 0.31 0.35 0.35 0.13 329 0.26 0.61 0.57 0.58 0.69 0.69 0.12 330 0.31 0.68 0.65 0.66 0.77 0.77 0.19 331 0.27 0.63 0.60 0.61 0.72 0.72 0.16 349 0.26 0.56 0.55 0.56 0.60 0.62 0.42 350 0.26 0.71 0.69 0.71 0.77 0.81 0.51 South

417 0.18 0.30 0.29 0.29 0.31 0.33 0.37 418 0.24 0.46 0.43 0.44 0.47 0.50 0.57 428 0,28 0.38 0.36 0.37 0.39 0.41 0.43 429 0.23 0.30 0.29 0.30 0.32 0.33 0.34 431 0.26 0.33 0.31 0.32 0.34 0.36 0.36 432 0.27 0.35 0.34 0.35 0.37 0.38 0.38 442 0.21 0.32 0.31 0.32 0.33 0.33 0.31 443 0.20 0.28 0.28 0.28 0.29 0.29 0.27

300 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

Figure 4-1 32. Primary load path within the hat truss of WTC 2.

"

Critical connections in the main load path

I fin lliMpiBliPMipH^^ (psi) -54110 -31223 -8336 14551 37438

-42667 -19780 3107 25994 48881 WTC-2 Severe Case Temperature Analysis

Figure 4-133. Location of hat truss connections that were in the primary load path.

NISTNCSTAR 1-6D, WTC Investigation 301
Chapter 4

Table 4-34. Demand and capacity of the hat truss connections

path at 40 min (connection IDs are shown in Fig

(kip) in the primary load

4-133).

Con.

ID

Location Tension Capacity Demand Force (tension) Status

Floor Column Yield Ultimate Before Redist. After Redist. Before Redist. After Redist.

1 110 501 840 1,100 567 512 Safe Safe

2 108 601 840 1,100 567 512 Safe Safe

3 110 701 630 870 575 370 Safe Safe

4 110 801 840 1,100 950 510 Yielded Safe

5 109 801 630 870 575 370 Safe Safe

6 110 1001 760 870 1,370 760 Failed Safe

7 108 901 840 1,100 950 510 Yielded Safe

8 108 1002 1,250 1,250 440 110 Safe Safe

9 108 1003 1,470 1,470 1,000 700 Safe Safe

10 110 1003 1,250 1,250 750 550 Safe Safe

11 110 1004 1,470 1,470 1,000 700 Safe Safe

12 1 1

1004 1,250 1,250 750 550 Safe Safe

Table 4-35. Total column loads at Floor 83 of WTC 2 for Case D conditions.

Row Analysis Step West East North South Core Sum

(1) Before Impact 18,065 18,114 13,567 13,284 61,828 124,857

(2) After Impact 18,670 22,481 12,193 13,511 57,821 124,676

(3) 10 min 18,728 22,226 11,896 13,358 58.413 124,621

(4) 20 min 18.914 22,208 12,052 13,318 58,124 124,616

(5) 30 min 18,876 23,681 11,770 13,365 56,967 124,659

(6) 40 min 18.531 23,682 11,906 13,473 56.825 124,418

(7) 43 min 15,667 15,143 14,215 16,292 62.422 123,738

(8) (2)-(l) 604 4,368 -1,374 227 -4.007 -181

(9) (3)-(l) 662 4,112 -1,670 74 -3.415 -236

(10) (4)-(l) 849 4,094 -1,515 35 -3.704 -241

(11) (5)-(l) 811 5,567 -1,797 81 -4,861 -199

(12) (6)-(l) 466 5,568 -1,661 190 -5,003 -439

(13) (7)-(l) -2.398 -2,971 648 3.009 594 -1.119

Note: Compression is positive. Units are in kip.

302 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis

Table 4-36. Total column loads at Floor 105 of WTC 2 for Case D conditions.

Row i^UI III oUUIII Sum

(1) Before Impact 8,497 8 57'' 7 1 M

(2) After Impiict 9,170 1 1,272 4.8 749

1 0 min 9,182 11

11 ,v7U OfilX S ''7S 1 ^ Q7S 4R 74")

(4) 20 min 9,279 1 1,120 0 _> 1 4RHO, 74^ /

(5) 30 min 9,370 1 1.859 6,416 8,553 12,544 48 74''

(6) 40 min 9,198 1 1,927 6,524 8 691 40'' 48TO 74'' , / H*- (71 43 mm 7.086 8,026 6 546 1 7 Ql S 4S 74'^ HO, / HiL

(8) (2)-(l) 674 2,699 -895 1,263 -3 741 0

(9) (3)-(l) 685 2,489 -1,132 1,106 -3,148 0

(10) (4)-(l) 783 2,547 -1.071 1,182 -3,441 0

(11) (5)-(l) 873 3,287 -965 1,384 -4,579 0

(12) (6)-(l) 702 3,355 -858 1,522 -4,721 0

(13) (7)-(l) -1.411 -547 -835 2,000 792 0

Note: Compression is positive. Units are in kip.

Table 4-37. Change in total column loads before and after aircraft impact.

(Loads After Impact) - (Loads Before Impact)

Row Floor West East North South Core

(1) 83 604 4,368 -1,374 227 -4,007

(2) 105 674 2,699 -895 1.263 -3,741

(3) (2)-(l) 69 -1,668 479 1.035 266

Note: Increase in compression is shown as positive. Units are in kip.

Table 4-38. Change in total column loads between 40 min and 43 min.

(Loads at 43 min) - (Loads at 40 min)

Row Floor West East North South Core

(1) X3 -2,864 -8,539 2,309 2,819 5,596

(2) 105 -2.1 12 -3.901 23 479 5,513

(3) (2)-(l) 752 4,637 -2,286 -2,340 -84

Note: Increase in compression is shown as positive. Units are in kip.

NISTNCSTAR 1-6D, WTC Investigation 303
Chapter 4

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304 NISTNCSTAR 1-6D, WTC Investigation
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NISTNCSTAR 1-6D. WTC Investigation 305
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306 NISTNCSTAR 1-6D, WTC Investigation
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NISTNCSTAR 1-6D. WTC Investigation 307
Chapter 4

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308 NISTNCSTAR 1-6D, WTC Investigation
Chapter 5

Collapse Sequence

5.1 INTRODUCTION

This chapter summarizes the sequences of collapse of WTC 1 and WTC 2 from the analyses of global

models with creep. The basis of the conclusions derived here are as follows:

• Analyses of subcomponents, such as connections (truss seats and knuckles), components

(trusses and columns), subsystems (full floors and exterior walls), preliminary global models,

and isolated parts of the final global models (core and exterior wall) subjected to temperature

loads from fire, were performed to identify failure modes and failure loads. These models

included large deflection effects and temperature-dependent material nonlinearities due to plasticity and creep. Break elements were developed to capture various failure modes such as

truss seat failure and web diagonal buckling (NIST NCSTAR 1-6C). As they became larger,

the models were gradually reduced in complexity to enhance computational efficiency, while

ensuring that key failure modes and failure sequences were captured.

• The final global models included large deflection, and temperature-dependent plasticity and

creep.

• The final global models were developed based on the following assumptions:

- Floors were modeled by plate elements with elastic properties without the ability to simulate sagging and its effect on the development of pull-in forces at floor/wall

disconnections. Full floor analyses found that floors initially expanded outward but then

pulled inward as the floor sag increased. Pull-in forces resulting from floor sagging and

floor/wall disconnections were determined based on the results of full floor models and

isolated wall models and were modified by visual observafions. They were input in the

global model analyses at different times as fire-induced damage.

- Spandrels were modeled by beam elements. The axial degree of freedom of the beam

elements was released to enhance numerical efficiency and avoid thermally-induced

buckling; spandrel elements continued to transfer shear and bending moments. The

exterior wall subsystem analysis showed that large deformations and buckling of

spandrels would not affect the stability of exterior columns significantly.

- Columns were modeled to capture inelastic buckling, but not the kink-type buckling that

is initiated by the local buckling of plates and results in significant distortion of the cross

section. The analysis of columns showed that when buckling occurred in a column that spanned several floors and was at high temperatures, inelastic buckling, rather than kinktype buckling, governed its load deformation characteristic.

NIST NCSTAR 1-6D, WTC Investigation 309
Chapter 5

- The building sections below the impact zones were removed, and the vertical stiffness of

the removed sections was replaced with equivalent vertical springs. Preliminary analyses

of the global models showed that building sections below the impact zone did not

contribute much to the overall behavior of the towers.

- Construction sequence was not considered to enhance computational efficiency. A

comparative study showed that the total column load on each face of the exterior wall

increased by 7 percent to 1 5 percent and the total column load on the core decreased by

about 10 percent when the construction sequence was not included.

- Structural members that were severed or heavily damaged by aircraft impact were removed from the final global models before gravity loads were applied.

- Break elements were not used in the final global models to represent component failures

such as failure of column splices. However, the results of the global model analyses were examined to determine whether any component failure occurred and to what extent its failure impacted the collapse sequence.

The key structural events common to both towers are discussed below.

• Floor sagging sufficient to cause the observed inward bowing of the exterior wall was caused by

the elevated steel temperatures resulting from loss of thermal insulation. The elevated

temperature caused buckling of the truss web diagonals, as shown in Fig. 5-1 (NIST NCSTAR 1- 6C), which caused the floor sag to increase significantly and to approach a catenary shape. The

catenary action in this study refers to the combined action that results when the bending capacity

of the truss is exceeded and additional load is carried by the floor system acting as a tensile structure (Fig. 5-2). Note that in Fig. 5-2, Mrefers to the residual moment capacity in the floor

with highly deformed truss. Sagging of the floor resulted in pull-in forces at floor/exterior wall

connections, and led to inward bowing of the exterior wall

• Bowing and buckling of the entire exterior wall of a tower occurred under the combined effects of

temperature, redistributed gravity load, pull-in force from sagging floors, and loss of lateral support due to sagging or floor/wall disconnections. Floors with large sag did not restrain the

exterior wall columns from buckling.

• Downward displacement of the core was due to severed core columns from the aircraft impact

and redistributing column loads to non-severed core columns and due to shortening of the core columns caused by buckling, plasticity, and creep of core columns at elevated temperatures.

• Redistribution of gravity loads among exterior and interior columns resulted from aircraft impact

damage, restrained thermal expansion, shortening of core columns, tilting of the tower above the

impact area, and bowing and buckling of exterior walls. Gravity loads were redistributed from

columns with aircraft impact or fire-induced damage, both in the core and exterior walls,

primarily to neighboring columns. Loads were redistributed from the core to the exterior walls

and from the exterior walls to the core primarily through the hat truss. Loads were redistributed

between adjacent exterior walls primarily through the spandrels, and to a lesser extent through the

hat truss. Major load redistribution mechanisms were as follows:

310 NIST NCSTAR 1-6D, WTC Investigation
Collapse Sequence

- Aircraft impact reduced the load on the impacted wall and on the opposite wall through

the hat truss and redistributed the load to the side walls.

- Restrained thermal expansion caused increased loads in the heated elements.

- Shortening of the core columns caused a redistribution of the load from the core to the

exterior walls.

- Tilting of the tower redistributed the load among the exterior walls, resulting in increased

load on the compressed part of the exterior walls.

The collapse sequence of each tower is presented in detail below.

Buckling of diagonals

Exterior seat Interior seat

(in.) -42.11 -32.603 -23.095 -13.588 -4.081 -37.357 -27.849 -18.342 -8.834 .673211

Figure 5-1 . Vertical displacement of the truss model under thermal loading.

I I U I U I U U 1 1 U U U U U U I

t

V=0.5qL V=0.5qL

<! X

J

T=r0.5qx(L-x)-Ml/d

Figure 5-2. Catenary action in the floor system.

NISTNCSTAR 1-6D, WTC Investigation 311
Chapter 5

5.2 WTC 1 COLLAPSE SEQUENCE

The aircraft impacted the north wall of WTC 1 at 8:46 a.m. The aircraft severed exterior columns and

floors on the north side of the tower and core columns and floor members between Floor 93 and Floor 98. The subsequent fires weakened structural subsystems, including the core columns, floors, and exterior

walls. The core displaced downward, the floors sagged, and the south exterior wall bowed inward. At

10:28 a.m., about 102 min after the aircraft impact, WTC 1 began to collapse.

The sequence of main structural events that led to the collapse of WTC 1, starting from aircraft impact,

and the causes and effects of these structural events along with key observations, are discussed below.

The WTC 1 collapse sequence consists of five main events, listed in Table 5-1, which are discussed

below. Actual observations are summarized in Table 5-2, which are based on NIST's examination of

photos and videos (NIST NCSTAR 1-6).

Table 5-1. Summary of main events that led to the collapse of WTC 1, Event Number Event

1 Aircraft impact

2 Unloading of core

3 Sagging of floors and floor/wall disconnections

4 Bowing of south wall

5 Buckling of south wall and collapse initiation

Table 5-2. Observations on WTC 1 provided by NIST.

Time

Time from

Impact

(min) Observation

8:46:26 0 Aircraft impact on the north wall of WTC 1 between Floor 93 and

Floor 99 and Columns 1 1 2 and 151.

9:25:28 39 Fire on west side of south wall.

9:40 54 No bowing of columns was observed between Columns 301 and 323 on

the east side of south wall.

10:18:43 92 Smoke suddenly expelled on Floor 92 north wall. Floor 94 east side of

north wall. Floor 95 to Floor 98 on west side of north wall. Floor 95

and Floor 98 on north side of west wall, lower floor on south side.

10:22:59 97 Inward bowing from Floor 95 to about Floor 99 between Columns 308

and 326 (maybe to 340) on the south wall, maximum amplitude

approximately 55 in. at Floor 97.

10:28:18 102 Smoke puff out of north edge and center of west wall; smoke and

debris clouds out of the north, east, and west walls on Floor 98. Fire out of windows on the north, east, west, and south walls between

Floor 92 and Floor 98, and on Floor 104.

10:28:20 102 WTC 1 began to collapse. First exterior sign of collapse was at Floor 98. Rotation of at least 8 degrees to the south occurred before the building section began to fall vertically under gravity.

312 NIST NCSTAR 1-6D, WTC Investigation
Collapse Sequence

Aircraft Impact

The aircraft impacted WTC 1 at the north wall. The aircraft severed or heavily damaged Columns 112 to 151 between Floors 94 and 98 on the north wall. After breaching the building's perimeter, the aircraft continued to penetrate into the building. The north office area floor system sustained severe structural damage between Columns 1 12 and 145 at Floors 94 to 98. Core Columns 503, 504, 505, 506, 604, 704,

706, 805. and 904 were severed or heavily damaged between Floor 92 and Floor 97. The aircraft also severed a single exterior panel at the center of the south wall from Columns 329 to 33 1 between Floor 93

and Floor 96. In summary, 38 of 59 columns of the north wall, three of 59 columns of the south wall, and

nine of 47 core columns were severed or heavily damaged. In addition, thermal insulation on floor

fi-ammg and columns was also damaged from the impact area to the south perimeter wall, primarily

through the center of WTC I and over one-third to one-half of the core width. Figures 2—2, 2—14, and 2—

18 summarize aircraft impact damage to exterior and core columns and floors of WTC 1.

Gravity loads in the columns that were severed were redistributed, mostly to the neighboring columns.

Due to the severe impact damage to the north wall, the wall section above the impact zone moved

downward as shown in Figs. 4-9 and 4-13. The hat truss resisted the downward movement of the north

wall and rotated about its east-west axis, which reduced the load on the south wall. As a result, the north

and south walls each carried about 7 percent less gravity loads at Floor 98 after impact, the east and west

walls each carried about 7 percent more loads, and the core carried about 1 percent more gravity loads at Floor 98 after impact (Table 5-3). Column 705 buckled, and Columns 605 and 804 showed minor

buckling.

Unloading of Core

Temperatures in the core area rose quickly, and thermal expansion of the core was greater than the

thermal expansion of the exterior walls in early stages of the fire. This increased the gravity loads in the core columns until 10 min after impact (Table 5-3). The additional gravity loads from adjacent severed

columns and high temperatures caused high plastic and creep strains to develop in the core columns in early stages of the fire. More columns buckled inelastically due to high temperatures. Creep strain continued to increase to the point of collapse (see Fig. 4-81). By 30 min, the plastic-plus-creep strains exceeded thermal expansion strains. Due to high plastic and creep strains and inelastic buckling of core columns, the core columns shortened, and the core displaced downward. At 100 min, the downward

displacement of the core at Floor 99 became 2.0 in. on the average, as shown in Fig. 4-37.

The shortening of core columns was resisted by the hat truss, which unloaded the core over time and

redistributed the gravity loads from the core to the exterior walls, as can be seen in Table 5-3. As a

result, the north, east, south, and west walls at Floor 98 carried about 12 percent, 27 percent, 10 percent,

and 22 percent more gravity loads, respectively, at 80 min than the state after the impact, and the core

carried about 20 percent less loads as shown in Table 5-3. The net increase in the total column load on

the south wall, where exterior wall failure initiated, was only about 10 percent due to the downward

displacement of the core (see Fig. 5-3). At 80 min, the total core column loads reached their maximum.

As the floor pulled in starting at 80 min on in the south side, the south exterior wall began to shed load to adjacent walls and the core.

NISTNCSTAR 1-6D, WTC Investigation 313
Chapter 5

Sagging of Floors and Floor/Wall Disconnections

The long-span trusses of Floor 95 through Floor 99 sagged due to high temperatures. While the fires were on the north side and the floors on the north side sagged first, the fires later reached the south side,

and the floors on the south side sagged. Figure 5-4 shows vertical displacements of Floors 95 through 98

determined by the full floor models at 100 min. Full floor models underestimated the extent of sagging

because cracking and spalling of concrete and creep in steel under high temperatures were not included in the floor models, and because the extent of insulation damage was conservatively estimated. The sagging

floors pulled in the south wall columns over Floors 95 to 99. In addition, the exterior seats on the south

wall in the hot zone of Floors 97 and 98 began to fail due to their reduced vertical shear capacity at around 80 min, and by 100 min about 20 percent of the exterior seats on the south wall of Floors 97 and

98 failed, as shown in Figs. 5-^ and 5-5. Partial collapse of the floor may have occurred at Floors 97 and

98, resulting from the exterior seat failures, as indicated by the observed smoke puff at 92 min ( 10: 19

a.m.) in Table 5-2, but this phenomenon was not modeled.

Bowing of South Wall

The exterior columns on the south wall bowed inward as they were subjected to high temperatures, pull-in

forces from the floors beginning at 80 min, and additional gravity loads redistributed from the core. Figure 5-6 shows the observed and the estimated inward bowing of the south wall at 97 min after impact

(10:23 a.m.). Since no bowing was observed on the south wall at 69 min (9:55 a.m.), as shown in Table

5-2, it is estimated that the south wall began to bow inward at around 80 min when the floors on the south

side began to substantially sag. The inward bowing of the south wall increased with time due to continuing floor sagging and increased temperatures on the south wall as shown in Figs. 4-42 and 5-7.

At 97 min (10:23 a.m.), the maximum bowing observed was about 55 in. (see Fig. 5-6).

Buckling of South Wall and Collapse Initiation

With continuously increased bowing, as more columns buckled, the entire width of the south wall buckled

inward. Instability started at the center of the south wall and rapidly progressed horizontally toward the

sides. As a result of the buckling of the south wall, the south wall significantly unloaded (Fig. 5-3),

redistributing its load to the softened core through the hat truss and to the south side of the east and west

walls through the spandrels. The onset of this load redistribution can be found in the total column loads

in the WTC 1 global model at 100 min in the bottom line of Table 5-3. At 100 min, the north, east, and

west walls at Floor 98 carried about 7 percent, 35 percent, and 30 percent more gravity loads than the

state after impact, and the south wall and the core carried about 7 percent and 20 percent less loads,

respectively. The section of the building above the impact zone tilted to the south (observed at about 8°, Table 5-2) as column instability progressed rapidly from the south wall to the adjacent east and west

walls (see Fig. 5-8), resulting in increased gravity load on the core columns. The release of potential

energy due to downward movement of building mass above the buckled columns exceeded the strain energy that could be absorbed by the structure. Global collapse ensued.

314 NISTNCSTAR 1-6D, WTC Investigation
Collapse Sequence

Table 5-3. Total column loads at Floor 98 and Floor 105 of WTC 1 global model for

Case B conditions.

Row Analysis Morth \\ all East V\ all South Wall West Wall Core

Step Floor 98 Floor 105 Floor 98 Floor 105 Floor 98 Floor 105 Floor 98 Floor 105 Floor 98 Floor 105

( I

Before Impact 10.974 8.026 8.545 6.562 1 1.025 8.092 8.572 6.604 34.029 20,361

(2) Alter Impact 10.137 7.294 9.071 7,028 10,356 7.488 9.146 7,076 34,429 20,761

(3) 1 0 min 9.796 6.944 8.490 6,461 9.848 6,981 8,536 6.469 36.473 22,790

(4) 20 min 10.437 7.551 9,108 7,075 9.900 7,057 9,202 7,158 34.495 20,806

(5) 30 min 10.913 8.020 10,034 7,998 10.420 7,569 9,715 7,685 32.060 18.377

(6) 40 min 1 1 .068 8.193 10.599 8,571 1 1 .004 8.129 10.178 8,147 30.294 1 6.608

(7) 50 min 1 1.149 8.285 10.908 8.878 1 1.192 8,315 10.458 8,428 29,435 1 5.743

(8) 60 min 1 1 .205 8.351 1 1.168 9.130 1 1.285 8,414 10.716 8,687 28.766 1 5.069

(9) 70 min 1 1.286 8.435 1 1.366 9,319 1 1.343 8,481 10.939 8,914 28,205 14,502

(10) 80 mm I I .J /D 0 CIO 8.525 1 1 .555 9,497 1 1 .409 8,55

11,119 9,097 27,681 1 3,978

(111 90 min 10.916 8.096 11.991 9,847 9.949 7,327 11.657 9,506 28,587 14,876

(IZ) 100 min 10.828 8.023 12.249 10.076 9.638 7,066 1 1 .905 9,720 28.478 14,767

(13) (2)-(l) -837 -732 526 466 -668 -604 574 472 400 400

(14) (10)-(2) 1.239 1.234 2.484 2.470 1,052 1,063 1,973 2,021 -6,748 -6.783

(15) (12)-(2) 692 730 3.178 3.048 -719 -422 2,759 2.644 -5,951 -5.993

(161 (12)-(10) -548 -504 694 5 79 -1.771 -1,485 786 623 797 790

Note : Compression is positive. Units are in kip.

12,000

11.000 - r—

10,000 £

9,000

o 8,000 -

7,000

6,000

Before After 10 min 20 min 30 min 40 min 50 min 60 min 70 min 80 min 90 min 100

Impact Impact min Time

Figure 5-3. Total column loads at Floor 98 of the south wall of WTC 2 global model for

Case B conditions (compression is positive).

NISTNCSTAR 1-6D, WTC Investigation 315
Chapter 5

(a) Floor 98

AN

AN

(b) Floor 97

(c) Floor 96 (d) Floor 95

Figure 5-4. Vertical displacements of full floor models of WTC 1 for Case B; temperature

condition at 100 min (downward displacement is negative).

(a) Floor 97 (b) Floor 98

Figure 5-5. Loss of vertical supports obtained in Floor 97 and Floor 98 full floor models

of WTC 1 for Case Bj temperature condition at 100 min (1x displacement magnification).

316 NISTNCSTAR 1-6D, WTC Investigation
Collapse Sequence

Figure 5-6. Inward bowing of exterior columns of the South wall of WTC 1 at 10:23 a.m.

(97 min after impact). Displacements were estimated by NIST from the analysis of this

photograph.

NISTNCSTAR 1-6D, WTC Investigation 317
Chapter 5

NODAL SOLUTION

STEP=33

SUB =1437 TIME=150

UY (AVG) RSYS=0

DMX =42.979

SMN =-.701059

SMX =42.826

ANSYS

MAR 3 0 2005

10':23:38 ,

Col301

Col359

(in.) 4^

-.701059 8.972 18.644 28.317 37.99

4.135 13.808 23.481 33.153 42.826 WTCl Severe Temp at 6000s w/Skip pull - South Face (5X)

Figure 5-7. Inward bowing of south wall of WTC 1 global model with creep at 100 min for

Case B conditions with 5 kip puil-in forces (5x displacement magnification).

318 NISTNCSTAR 1-6D. WTC Investigation
Collapse Sequence

5.3 WTC 2 COLLAPSE SEQUENCE

The aircraft traveling in a north-northeast direction impacted the south wall of WTC 2 at 9:03 a.m. The

aircraft mostly severed columns and floors that were on the east side of the building between Floor 78 and

Floor 84. The subsequent fires were also on the east side of the building. At 9:59 a.m., about 56 min

after the aircraft impact, the building started to collapse with the east wall buckling inward, followed by

tilting of the building above Floor 82 to the east and south.

The section below discusses the sequence of main structural events that led to the collapse of WTC 2, and

the causes and effects of these structural events along with key observations, starting from aircraft impact.

The WTC 2 collapse sequence consisted of five main structural events. These events are chronologically

listed in Table 5-4 and discussed below. Actual observations for WTC 2 are summarized in Table 5-5,

which are based on NIST's examination of photos and videos (NIST NCSTAR 1-6).

Table 5-4. Summary of main events that led to the collapse of WTC 2

Event number Event

1 Aircraft impact

2 Sagging of floors and floor/wall disconnections

3 Bowing of east wall 4 Unloading and leaning of core

5 Buckling of east wall and collapse initiation

Table 5-5. Observations on WTC 2 provided by NIST.

Time

Time

from

Impact

(min) Observation

9:03 0 Aircraft impact on the south wall of WTC 2 between Floors 77 and 85. Columns 404 to 443.

9:21 18 Columns of the east wall bowed inward over the entire width of Floors 78 to 83; maximum of

7-9 in. at Floor 80.

9:38 35 Floor 83 disconnections on the east wall appeared to extend.

9:54 51 Columns of the east wall bowed inward between Floor 78 and Floor 84, 12 - 20 m. at Floor 80. East side of Floor 83 draped between Columns 310 to 342.

9:59 56 WTC 2 began to collapse.

Column splices failed at every third panel and columns sprung back from inward bowing as collapse initiated on the east wall near the northeast comer Smoke and debris clouds were expelled from Floor 8 1 on the east, north, and west walls of

the building.

WTC 2 appeared to tilt around the base of Floor 82 and initial downward motion was visible

at the same location.

Tilt of approximately 3 to 4 degrees to the south and 7 to 8 degrees to the east occurred

before building section fell. Kink (change in slope) on the southeast comer near Floor 94 (halfway along building section above failure). Kink (change in slope) and offset about at the Floor 106.

NIST NCSTAR 1-6D, WTC Investigation 319
Chapter 5

Aircraft Impact

The aircraft impacted the south wall of WTC 2, severing a number of exterior columns on the south wall

from Floor 78 to Floor 84. The south office area floor system sustained severe structural damage between

Columns 410 and 436 from Floor 79 to Floor 83. Core columns 701, 702, 801, 802, 803, 901, 903, 1001,

1002, 1003, and 1004 were severed or heavily damaged between Floor 77 and Floor 84. The aircraft also

severed Column 253 of the north wall. The aircraft damaged the floor framing and core columns at the

southeast comer of the core. In summary, 32 of 59 columns of the south wall, two of 59 columns of the

north wall, and 11 of 47 core columns were severed or heavily damaged. Thermal insulation was

damaged from the impact area through the east half of the core to the north and east exterior walls. The

floor truss seat connections over about one-quarter to one-half of the east side of the core were severed on

Floor 80 and Floor 81 and over about one-third of the east wall on Floor 83. Figures 2-3, 2-15, and 2-19

summarize aircraft impact damage to the exterior wall and core columns and floors of WTC 2.

Gravity loads in the columns that were severed on the south wall and in the southeast comer of the core were redistributed to adjacent intact columns and also to the columns on the east wall (see Table 5-6). In

this redistribution, the total axial load on the core columns reduced by 6 percent, and the total axial load on the north wall columns reduced by 10 percent. The total axial load on the east wall columns increased

by 24 percent, and the total axial load on the west and south wall columns increased by 2 percent to 3 percent. The large increases in loads on the east wall resulted from their proximity to the severed core columns at the southeast comer of the core. The total load on the south wall at Floor 83 did not change,

as some of the loads from the core area were redistributed to that wall through the hat tmss.

At Floor 105, splices in the columns at the southeast comer of the core failed (Columns 1001 and 1002

and most likely Columns 701, 801 , 901, 902, and 1003). This increased the core tendency to lean toward

southeast and also increased the vertical downward displacement of the core at the impact zone. After the core column splices failed, 73 percent of the loads released from the failing core columns were

redistributed through the hat tmss to the exterior walls.

As can be seen in Table 5-6 for Floor 83, about 20 percent (= 227 kip / 1,263 kip) of the redistributed

load at the hat tmss level of the south wall was transferred through columns, and the rest of the load

(about 1,000 kip) was transferred to the coluinns of the east and west walls through the spandrels.

After load redistribution following impact, the core was prevented from tilting excessively toward the east by the north and south exterior walls through the action of the floors and the hat tmss.

Sagging of Floors and FloorA/Vall Disconnections

Aircraft impact and high temperatures due to subsequent fires caused Floor 79 through Floor 83 to sag. The sag was greater at Floor 80 and Floor 81 where the tmss seats on the east side of the core failed at

aircraft impact (see Fig. 5-9). High temperatures weakened the tmss seats on the east exterior wall and

caused tmss seats to fail at Floor 83 and Floor 82 (see Fig. 5-10) which in tum increased the sag in those

floors. Floor sagging induced pull-in forces on the east wall columns, beginning approximately 10 min

after impact and increasing with time.

320 NISTNCSTAR 1-6D, WTC Investigation
Collapse Sequence

Bowing of East Wall

The east wall columns bowed inward as a result of increasing temperatures (reduced strength and

stiffness) and pull-in forces induced by sagging floors (see Fig. 3-98). The inward bowing in the east wall increased with time due to the combined effects of pull-in from sagging floors (see Fig. 4-101),

increased axial loads, and a continuous increase in plastic and creep strains. As columns bowed, they

shed load to adjacent unbowed columns, but the total column load on the east wall did not change

significantly after impact until buckling of the east wall started near the collapse time (see Fig. 5-11).

Unloading and Leaning of Core

With increasing time and temperatures, the core columns developed high plastic and creep strains,

especially on the east side of the core. Plastic and creep strains exceeded the thermal expansion strains beginning about 30 min after the aircraft impact (see Fig. 5-12). High plastic and creep strains caused

unloading on the east side core columns. This increased leaning of the core toward the east and

transferred more loads to the east wall (Table 5-6). Calculations showed that resistance to core leaning was provided by the north and south exterior walls, partly through the floors and partly through the hat

truss. Leaning of the core resulted in tilting of the upper part of the tower as the east wall buckled.

Buckling of East Wall and Collapse Initiation

With continuously increased bowing and axial loads, the entire width of the east wall buckled inward.

The instability' started at the center of the wall and rapidly progressed horizontally toward the sides. As a resuh of the buckling of the east wall, the east wall significantly unloaded, redistributing its load to the

softened core through the hat truss and to the east side of the south and north walls through the spandrels

(see Figs. 5-13 and 5-14 and Table 4-38). The section of tower above the buckled wall suddenly moved

downward, and the building tilted toward the east (see Fig. 5-15).

The section of the building above the impact zone tilted to the east and south (observed at about 7° to 8°

to east and about 3° to 4° to south. Fig. 5-16) as column instability progressed from the east wall to the

adjacent south and north walls. The release of potential energy due to downward movement of the

building mass above the buckled columns exceeded the strain energy that could be absorbed by the

structure. Global collapse ensued.

NISTNCSTAR 1-6D. WTC Investigation 321
Chapter 5

Tab e 5-6. Total column loads at Floor 83 and Floor 105 of WTC 2 for Case D conditions.

Row Analysis West Wall East Wall North Wall South Wall Core

Step Floor 83 Floor 105 Floor 83 Floor 105 Floor 83 Floor 105 Floor 83 Floor 105 Floor 83 Floor 105

(1) Before Impact 18,065 8.497 18,114 8,572 13,567 7,382 13,284 7,169 61,828 17,123

(2) After Impact 18,670 9,170 22,481 11,272 12,193 6,487 13,511 8,432 57,821 13,382

(3) 1 0 min 18,728 9,182 22,226 11,061 11,896 6,250 13,358 8,275 58,413 13,975

(4) 20 min 18,914 9,279 22,208 11,120 12,052 6,311 13,318 8,351 58.124 13,682

(5) 30 min 18,876 9,370 23,681 11,859 11,770 6,416 13,365 8,553 56,967 12,544

(6) 40 min 18,531 9,198 23,682 11,927 11,906 6,524 13,473 8,691 56,825 12,402

(7) 43 min 15.667 7,086 15,143 8,026 14,215 6.546 16,292 9,169 62.422 17,915

(8) (2)-(l) 604 674 4,368 2,699 -1,374 -895 227 1,263 -4,007 -3,741

(9) (6H2) -138 28 1,201 656 -287 37 -38 259 -996 -980

(10) (7H6) -2.864 -2,112 -8,539 -3,901 2,309 23 2,819 479 5,596 5,513 Note; Compression is positive. Units are in kip.

322 NISTNCSTAR 1-6D. WTC Investigation
Collapse Sequence

TTC? n.^^ - Haxlff.UP. Dan.aq<; Case TePipcra-ure dt 2100

(e) Floor 79

Figure 5-9. Vertical displacements of full floor models of WTC 2 for Case Dj temperature

condition at 40 min (downward displacement is negative).

NISTNCSTAR 1-6D, WTC Investigation 323
Chapter 5

I.

(d) At 9:54 a.m.

(51 min after impact)

Figure 5-10. Floor sagging observed on the east wall of WTC 2 at different times.

324 NISTNCSTAR 1-6D. WTC Investigation
Collapse Sequence

_ 25,000

a.

22,500 -

^ 20,000

(0

^ 17,500 o

•Do 15,000

E

° 12,500

Too

10,000

Before After Impact Impact

lOmIn 20 min 30 min 40 min 43 min

Time

Figure 5-1 1 . Total column loads at Floor 83 of the east wall of WTC 2 global model for

Case D conditions (compression is positive).

NISTNCSTAR 1-60, WTC Investigation 325
Chapter 5

0.04

0.09

0.60

Oil

501 508

o o o o o o o o O o O o o o O O

0.35

• o Oogo oG

O

o

(fl.3j o O o O 0

1001 100

0.04

0.50 0.70 '

0.90

(a) At 20 min (b) At 30 min

XXXXX30CXXXXXXX300000OOOOCX)O0O000O

0.09

0.60

0.15

(c) At40 min

Figure 5-12. Maximum elastic + plastic + creep strain magnitudes for columns between

Floor 78 and Floor 83 of WTC 2 global model for Case D conditions at 20 min, 30 min, and

40 min (compressive strain is positive; strain values are in percent).

326 NISTNCSTAR 1-6D, WTC Investigation
Collapse Sequence

(a) View from east (b) View from southeast

Figure 5-1 3. Inward bowing of the east wall of WTC 2 global model for Case D conditions

at 43 min at the instant of collapse initiation (deformed shape scaled four times).

Figure 5-14. Inward bowing of exterior columns of the west wall of WTC 2 just before

collapse.

NISTNCSTAR 1-6D, WTC Investigation 327
Chapter 5

Figure 5-15. Total displacements of WTC 2 global model above Floor 86 for Case D

conditions at 43 min at collapse initiation (note the tilt toward east and south; deformed

shape magnified 20 times).

Figure 5-16. Initiation of Collapse of WTC 2. Note the tilt toward east and south.

328 NISTNCSTAR 1-6D, WTC Investigation
Collapse Sequence

5.4 DISCUSSION

The structural analyses of this study on components, subsystems, isolated exterior walls and cores, and

global models of WTC 1 and WTC 2, as well as observations from photos and videos taken during the event, showed that the tower collapses were caused by the combined effects of the structural and thermal

insulation damage from aircraft impact and the subsequent intense fires.

The structural impact damage alone did not cause the collapse of the towers, as they stood for periods of

time, and collapsed after fire-induced weakening of the cores, floor systems and exterior walls. In the

absence of impact damage, there would have been no insulation damage, and the likelihood of collapse of

towers under the intense fires would have been very small.

The damage to insulation was a result of direct impact by debris from the aircraft impact, which knocked

down walls and partitions and removed the insulation (NIST NCSTAR 1-6). Insulation is a key fire protection system for steel structural members. Without insulation, steel members may be heated during

the "effective duration" of the fires to an extent that causes significant stiffness and strength reduction.

According to the results of fire dynamics simulations by NIST (NIST NCSTAR 1-5), fire moved from

location to location, and the "effective duration" of the fire at any one location was roughly about 20

minutes, which was much shorter than the time to collapse. It was found in the results of the thermal

analysis conducted by NIST that temperatures of floor trusses and columns with insulation were lower

than 400 °C during the Case B fire (100 min long) for WTC 1. On the other hand, temperatures of steel members that lost insulation were found to be higher than 600 °C and even higher than 800 °C. Reductions in modulus of elasticity, yield strength, and ultimate tensile strength of steel in the WTC

towers were found to be 13 percent, 20 percent, and 10 percent at 400 "C, and 35 percent, 92 percent, and

80 percent at 700 °C. In addition, creep in steel may become more significant than plastic strain when the

steel is exposed to temperatures higher than 500 °C under high stress.

The temperatures in the steel members without insulation damage were lower than those with insulation

damage for the same fire (see Fig. 5-17 (c)), and the lower temperatures resulted in much reduced creep,

plasticity, and buckling. Without insulation damage, floor sag would have been significantly reduced (see

Figs. 5-17 (d) and (e)), and consequently the floors could not and would not have pulled inward on the exterior wall. Without insulation damage, the core columns and the exterior wall would not be

significantly weakened, and the likelihood of the exterior wall buckling would be negligibly small. Without insulation damage, the likelihood of collapse of the towers would have been very small.

NIST NCSTAR 1-6D, WTC Investigation 329
Chapter 5

ELEMENTS

TEI-irEWiTUkEC

(a) Temperatures on the top surface of the slab (b) Temperatures on the bottom surface of the slab

ELEMENTS TEHFERATUREE

THIK-^S.'iiS TMAX-Sor.ise AN

MP*'

L 20C AOC 6CC CCC

Area of insulation damage

Note: Structural members that were

severed by aircraft impact are also shown

in temperature plots (a), (b), and (c)

(c) Temperatures of steel members

AN

(d) Vertical displacement (entire model)

rrrrrru

Or

AN

in.

AC5 .27036 -2.567 3.1U

(e) Vertical displacement (top view without slab)

Figure 5-17. Full floor model of Floor 96 of WTC 1 for Case Bi temperature condition

at 100 min.

330 NISTNCSTAR 1-6D. WTC Investigation
Appendix A

FEAOF Floors

A.1 MODEL DESCRIPTION

A full floor model includes 1 ) both exterior and core columns extending from one floor below to one floor

above, 2) spandrels of the floor of interest, 3) floor slab, 4) floor trusses including primary and bridging

trusses, 5) strap anchors, 6) core beams, 7) deck support angles, and 8) break elements to capture failure modes including truss web diagonal buckling and weld failure, exterior and interior seat failure, stud

failure, strap anchor weld failure, connection failure between primary and bridging trusses, and

connection failure between long-span and transfer trusses. A full floor model without impact damage is shown in Fig. A-1.

The members listed below were found to fail in the early stage of thermal loading and cause large

nonlinearities in the subsequent stages; therefore, they were removed from the model to enhance

computational efficiency. Figure A-2 shows the full floor model with these members removed. Deck

support angles and bridging trusses buckled due to their themial expansion in the one-way area. Shear

studs and welds between strap anchors and truss top chords failed due to shear force caused by the

difference in thermal expansion between the floor and the exterior wall in the direction transverse to the

primary trusses. Although these members did not exist in the floor model, they were not expected to control the stability and ultimate failure mode of the full floor system under fire. Analyses perfonned

after remo\ al of the following members showed no premature failure mode such as torsional buckling of

primary trusses:

• Deck support angles

• Bridging trusses except in the two-way zone

• Shear studs connecting the slab and the spandrel

• Strap anchors

The visco-elastic dampers that connected the truss bottom chords to the spandrels were not included in the

full floor model because dampers were expected to be soft when subjected to slow loading rates.

Truss members (top and bottom chords and web diagonals) were modeled by BEAM188 elements.

Columns were modeled by BEAM189 elements. Spandrels were modeled by SHELL181 elements. The

concrete slab was modeled by SHELL181 elements with four layers through the thickness. Each layer of

the shell element for the slab had one integration point.

Nonlinear steel material properties were assigned to each structural member according to the drawings. A

bilinear model with a yield point at its compressive strength was used for the concrete slab, where the yield strength was the same in both tension and compression. Creep in the steel was not included in any

of the full floor analyses. It was found that creep in BEAM188/189 elements would cause severe convergence problems when those elements experience thermally-induced buckling.

NISTNCSTAR 1-6D. WTC Investigation 331
Appendix A

Both core and exterior columns were fixed in the vertical direction at the bottom. Core columns were free

in horizontal directions and fixed in all rotations at the top and bottom. Exterior columns were fixed in translation perpendicular to the face of building and in rotation about the axis parallel to the face of the

building at the top and bottom. They were also fixed in torsion at the top and bottom.

Elements corresponding to severed members due to impact were removed from the model in the

beginning of the analysis based on the results of the aircraft impact analysis (NIST NCSTAR 1-2 and

Chapters of NCSTAR 1-6).

(a) Top view

(b) Top view without concrete slab

Figure A-1. Full floor model without impact damage.

332 NIST NCSTAR 1-6D, WTC Investigation
FEA of Floors

The full floor model was first analyzed for dead and live loads, and then thermal loads were applied to simulate the path-dependent nonlinear response. Dead and live loads consisted of self-weight, 8 psf

superimposed dead load, and 25 percent of design live loads. Design live loads varied from 55 psf to 85 psf in the model. Vertical loads were not apphed to columns. For thermal loads, NIST provided two

sets of temperature time histories for each building. These temperature cases were designated as "Case Aj

temperature condition" and "Case B, temperature condition" for WTC 1 , and "Case C, temperature

condition" and "Case Dj temperature condition" for WTC 2. NIST later refined these temperatures, and

refined cases were referred to as "Case A temperature condition" and "Case B temperature condition" for WTC 1. and "Case C temperature condition" and "Case D temperature condition" for WTC 2. Since the

largest change in thermal insulation damage and temperatures occurred for WTC 1 Floor 97, Case A, and

Case A temperature conditions were used to analyze the difference in the floor behavior for the two cases. Since results from the WTC 1 Floor 97 analysis under Case A temperature condition was very similar to those from the analysis with Case A, condition, it was concluded that the refined temperature cases would

not change the floor behavior significantly. Therefore, analysis of other floors were not conducted with

the refined temperature conditions.

Temperature data sets were provided for every structural node at 10 min intervals up to 100 min for WTC 1 and up to 60 min for WTC 2 for each temperature case. In the first step of the thermal loading,

temperature was linearly ramped up from room temperature to the temperature specified at 10 min. After

the first step, the temperature was linearly interpolated between two data sets. Figures A-3 to A-8 show

NIST temperature distributions for WTC I Floor 97 for Case A, temperature condition, Case A

temperature condition, and Case Bj temperature condition. For each case, temperatures were plotted at only 10 min. 50 min. and 100 min. Figures A-9 to A-12 show NIST temperature distributions for WTC 2 Floor 82 for Case C, and Case D, temperature conditions. In the figures, severed members were

also shown; however, the severed members were removed from the floor models and did not exist in the

analysis.

Temperatures for truss members and spandrels were assigned at node locations and did not change within

the cross section. Temperatures for columns were assigned at node locations and had a gradient within

the cross section. Temperatures for the slab were assigned at node locations, and there were five points to define the temperature distribution through the thickness at each node location.

NISTNCSTAR 1-6D, WTC Investigation 333
Appendix A

Figure A-2. Full floor model after removal of deck support angles, spandrel studs,

bridging trusses outside of two-way zones, and strap anchors.

334 NISTNCSTAR 1-6D, WTC Investigation
FEA of Floors

(a) Top view at 1 0 min (b) Top view without concrete slab at 1 0 min

(c) Top view at 50 min (d) Top view without concrete slab at 50 min

(e) Top view at 1 00 min (f) Top view without concrete slab at 1 00 min

Figure A-3. Case Ai temperature distribution for Floor 97 of WTC 1.

NISTNCSTAR 1-6D. WTC Investigation 335
Appendix A

elemeiitl; TEHFEkAT'JREK WestAN

South North

iCC)

(a) Top surface at 10 min

ELEMENT;-

TEWrEKnT'-'KEK East

AN

South North

(b) Bottom surface at 10 min

AN

(c) Top surface at 50 min (d) Bottom surface at 50 min

West

AN

South North

(e) Top surface at 100 min (f) Bottom surface at 100 min

Figure A-4. Case Aj temperature distribution in the slab for Floor 97 of WTC 1.

336 NISTNCSTAR 1-6D, WTC Investigation
FEA of Floors

(a) Top view at 10 min (b) Top view without concrete slab at 10 min

AN

South JVest

East

(c) Top view at 50 min (d) Top view without concrete slab at 50 min

AN AN

(e) Top view at 100 min (f) Top view without concrete slab at 100 min

Figure A-5. Case A temperature distribution for Floor 97 of WTC 1.

NISTNCSTAR 1-6D. WTC Investigation 337
Appendix A

TEMPERATyKE:;

Tr-iiu-:o West

AN

South North

I m

\mm¥mh''''\'^'Sf' ^-fioiRtv ^)

(a) Top surface at 10 min

East

AN

South North

(°C)

(b) Bottom surface at 10 min

ELEMENTS AN

West TEMPERATUhEE East

AN

TMAX=S1C.40:-

m

South North South North

I

(c) Top surface at 50 min (d) Bottom surface at 50 min

AN

(e) Top surface at 100 min

East

AN

South North

(f) Bottom surface at 1 00 min

Figure A-6. Case A temperature distribution in tlie slab for Floor 97 of WTC 1,

338 NISTNCSTAR 1-6D. WTC Investigation
FEA of Floors

(a) Top view at 10 min (b) Top view without concrete slab at 10 min

AN

South JVest

%„

East

if!

North

4iP

ifC)

(c) Top view at 50 min

AN

TEHrEiAf.'RES

South JVest

East

111 ir'

(°C)

(d) Top view without concrete slab at 50 min

TQtPEMr.T'i--

South

AN

(e) Top view at 100 min (f) Top view without concrete slab at 100 min

Figure A-7. Case Bj temperature distribution for Floor 97 of WTC 1.

NISTNCSTAR 1-6D. WTC Investigation 339
Appendix A

West

AN

South North

(a) Top surface at 10 min (b) Bottom surface at 10 min

:EJ-lPEhATl.'PEB West

AN

South Sorth

(c) Top surface at 50 min (d) Bottom surface at 50 min

West

AN

North

(e) Top surface at 100 min (f) Bottom surface at 100 min

Figure A-8. Case Bj temperature distribution in the slab for Floor 97 of WTC 1.

340 NISTNCSTAR 1-6D, WTC Investigation
FEA of Floors

AN

( C)

(a) Top view at 10 min (b) Top view without concrete slab at 10 min

AN

(c) Top view at 30 min (d) Top view without concrete slab at 30 min

AN

East 'lij,. South

"'hi.

I iht^^

North

5^'

West

tCC)

(e) Top view at 60 min

North

AN

.» > Sow//?

lit" res?

CO

(f) Top view without concrete slab at 60 min

Figure A-9. Case Ci temperature distribution for Floor 82 of WTC 2.

NISTNCSTAR 1-6D. WTC Investigation 341
Appendix A

ELEHENTr, tehEEFATURe;; SouthAN

East West

(a) Top surface at 10 min

TEMl'EhATl.m:.' North

AN

East t West

(b) Bottom surface at 10 min

element;; tempemtubes SouthAN

(c) Top surface at 30 min (d) Bottom surface at 30 min

South

AN

r

East West

|L ~ 1 .

(e) Top surface at 60 min (f) Bottom surface at 60 min

Figure A-10. Case Cj temperature distribution in the slab for Floor 82 of WTC 2.

342 NISTNCSTAR 1-6D, WTC Investigation
FEA of Floors

AN

East South

(a) Top view at 10 min

AN

>ii,i. South

(b) Top view witliout concrete slab at 10 min

AN

TOlIS-J'-.tiO .

East '^%^South

'lilll North

(c) Top view at 30 min

AN

Tt<IN-15.eo:-i TMAX-3:i.S:-G

,'0

South

1 -4,''^' li^'

North

(d) Top view without concrete slab at 30 min

(e) Top view at 60 min

AN

South

"1

North West

(°C)

(f) Top view without concrete slab at 60 min

Figure A-11. Case Dj temperature distribution for Floor 82 of WTC 2.

NISTNCSTAR 1-6D, WTC Investigation 343
Appendix A

element:: TEHPEkATURES South

AN

West

t(°C)

(a) Top surface at 10 min

South

AN

(c) Top surface at 30 min

AN

South

East West

(e) Top surface at 60 min

TEMPEKATURES North

AN

East

I

West

(b) Bottom surface at 10 min

North

AN

East West

(d) Bottom surface at 30 min

(f) Bottom surface at 60 min

Figure A-12. Case Dj temperature distribution in the slab for Floor 82 of WTC 2.

344 NISTNCSTAR 1-6D. WTC Investigation
FEA of Floors

A.2 WTC 1 FLOORS

A.2.1 Case Aj Temperature Condition

Table A-1 gives the maximum vertical displacement of WTC 1 floors, and Figs. A-13 to A-19 show the

vertical displacements of the floors when the maximum displacement was obtained. Floor 95 to Floor 98

showed a significant vertical displacement in the north office area near the impact damage. The

maximum vertical displacement of all floors was 32 in. for Floor 97 at 60 min. The vertical displacement

in the south office area was found to be insignificant on all the floors throughout the thermal loading.

Figure A-20 shows the average total thermal expansion of floors over the entire width of the building at 100 min in tu o orthogonal directions. The total floor expansion ranged from 4 in. to 8 in. Many web

diagonals of Floor 95 to Floor 98 buckled in the hot zones of the north office area. Although gusset plates

fractured at several locations, a complete disconnection of the floor from the exterior wall was not observed. Figure A-21 shows horizontal reaction force at individual columns of the north and south faces

of Floor 97. A positive reaction force in the figure means that the column is pulled inward by the floor,

and a negative reactions force means that the column is pushed out by the floor. Since columns that were

not at floor trusses were not connected to the floor in the model because of the removal of strap anchors

and studs, reaction forces at those columns were small, and the plots became jagged. As can be seen in the figure, almost all the columns were pushed out by the floor. This was also the case for other floors.

Table A-1. Maximum vertical displacement of WTC 1 floors for Case Aj temperature

condition.

Floor

Max. Displacement

(in.)

Time at the Maximum

(min)

93 5.4 30

94 13.5 100

95 30.9 10 96 23.3 10 97 31.5 60

98 26.4 30

99 7.0 50

Note: Downward displacement is positive.

I

NISTNCSTAR 1-6D. WTC Investigation
Appendix A

J

(a) Entire model

AN

E(in.

(b) Top view without slab

AN

(in.)

Figure A-13. Vertical displacement of WTC 1 Floor 93 for Case A, temperature condition

at 30 min (downward displacement is negative; 5x displacement magnification).

Figure A-14. Vertical displacement of WTC 1 Floor 94 for Case Ai temperature condition

at 100 min (downward displacement is negative; 5x displacement magnification).

346 NISTNCSTAR 1-6D, WTC Investigation
FEA of Floors

(a) Entire model (b) Top view without slab

Figure A-15. Vertical displacement of WTC 1 Floor 95 for Case Aj temperature condition

at 10 min (downward displacement is negative; 5x displacement magnification).

(a) Entire model (b) Top view without slab

Figure A-16. Vertical displacement of WTC 1 Floor 96 for Case Aj temperature condition

at 10 min (downward displacement is negative; 5x displacement magnification).

NISTNCSTAR 1-6D, WTC Investigation 347
Appendix A

(a) Entire model (b) Top view without slab

Figure A-17. Vertical displacement of WTC 1 Floor 97 for Case Aj temperature condition

at 60 min (downward displacement is negative; 5x displacement magnification).

(a) Entire model (b) Top view without slab

Figure A-18. Vertical displacement of WTC 1 Floor 98 for Case Ai temperature condition

at 30 min (downward displacement is negative; 5x displacement magnification).

348 NISTNCSTAR 1-6D, WTC Investigation
FEA of Floors

AN

(a) Entire model (b) Top view without slab

Figure A-19. Vertical displacement of WTC 1 Floor 99 for Case Ai temperature condition

at 50 min (downward displacement is negative; 5x displacement magnification).

100

99

98

97

O 96

North-South

• East-West

2 3 4 5 6 7 Total Slab Expansion (in)

Figure A-20. Thermal expansion of floors of WTC 1 for Case Aj temperature condition at 100 min.

NISTNCSTAR 1-6D. WTC Investigation 349
Appendix A

160 150 140 130 Column ID

(a) North face

120 110 100

-150

-200 340 330 320 Column ID

(b) South face

300

Figure A-21. Horizontal reaction force per column of WTC 1 Floor 97 for Case Aj

temperature condition.

A.2.2 Case Bi Temperature Condition

Table A-2 gives the maximum vertical displacement of WTC 1 floors for Case B, temperature condition,

and Figs. A-22 to A-28 show the vertical displacements when the maximum displacement was obtained.

The maximum vertical displacement of Floor 95 to Floor 98 increased due to higher temperature when

compared to Case A, temperature condition. Especially, the vertical displacement in the south office area of those floors became significant. The maximum among the floors was 49 in. in the south office area of

Floor 98 as shown in Fig. A-27. The large displacement on the south side of Floor 98 was caused by the

exterior seat failure between Column 329 and Column 343 that started at 90 min (see Fig. A-29).

Exterior seats between Column 337 and Column 347 of Floor 97 also failed, which caused a vertical

displacement of 37 in. in the south office area (see Fig. A-29). These exterior seats failed due to loss of

vertical shear strength under the extreme temperatures encountered. Figure A-30 shows the average total thermal expansion of floors over the entire width of the building at 100 min of Case B, temperature

condition. The total floor expansion ranged from 5 in. to 8.5 in. Figure A-3 1 shows horizontal reaction

force at individual columns of the north and south faces of Floor 98. It can be seen in the figure that reaction forces of columns between Column 329 and Column 343 became close to zero after the trusses attached to these column lost their vertical support at the exterior seats. Almost all the columns were

found to be pushed out by the floor. This was also the case for other floors.

350 NISTNCSTAR 1-6D, WTC Investigation
FEA of Floors

Table A-2. Maximum vertical displacement of WTC 1 floors for Case Bi temperature

condition.

Floor

IVIsx. Displsc^mcnt

(in.)

Time at the Maximuin

(min)

93 -5.8 100

94 12.7 100

95 29.2 10 96 28.6 10 97 37.4 100

98 49.0 100

99 6.8 100

Note: Downward displacement is positive.

(a) Entire model (b) Top view without slab

Figure A-22. Vertical displacement of WTC 1 Floor 93 for Case Bi temperature condition

at 100 min (downward displacement is negative; 5x displacement magnification).

NISTNCSTAR 1-6D. WTC Investigation 351
Appendix A

(a) Entire model

AN

--MK =-11 .585

i:mx -C.116

(b) Top view without slab

AN

N

i(in.)

Figure A-23. Vertical displacement of WTC 1 Floor 94 for Case Bi temperature condition

at 100 min (downward displacement is negative; 5x displacement magnification).

AN

(a) Entire model

.liiiiiiB —jHBiBiCin.)

(b) Top view witliout slab

Figure A-24. Vertical displacement of WTC 1 Floor 95 for Case Bj temperature condition

at 10 min (downward displacement is negative; 5x displacement magnification).

352 NISTNCSTAR 1-6D, WTC Investigation
FEA of Floors

AN

(a) Entire model (b) Top view without slab

Figure A-25. Vertical displacement of WTC 1 Floor 96 for Case Bj temperature condition

at 10 min (downward displacement is negative; 5x displacement magnification).

-li.l'.- ature it 600C

(a) Entire model

iir::;::

J...1.1

rrr

-4+-

TtT

AN

—t

,

(b) Top view without slab

i(in.)

Figure A-26. Vertical displacement of WTC 1 Floor 97 for Case Bj temperature condition

at 100 min (downward displacement is negative; 5x displacement magnification).

NISTNCSTAR 1-6D. WTC Investigation 353
Appendix A

(a) Entire model ^ (b) Top view without slab

Figure A-27. Vertical displacement of WTC 1 Floor 98 for Case Bj temperature condition

at 100 min (downward displacement is negative; 5x displacement magnification).

-i' .-h.^ . - ., .547425

V.'T^: - v^x-iTi^n, Do:t.5oe Case Tetro'rrst'jre gCCC sec

I '--4 < \- i ' ! —..l ,L„ :

: , —(in.)

(a) Entire model (b) Top view witliout slab

Figure A-28. Vertical displacement of WTC 1 Floor 99 for Case Bj temperature condition

at 100 min (downward displacement is negative; 5x displacement magnification).

354 NISTNCSTAR 1-6D, WTC Investigation
FEA of Floors

(a) Floor 97

Figure A-29. Loss of vertical supports i temperature condition at 100 mir

I AN

(b) Floor 98

WTC 1 Floor 97 and Floor 98 for Case Bj

(1x displacement magnification).

100

92 23456789

Total Slab Expansion (in)

Figure A-30. Thermal expansion of floors of WTC 1 for Case Bi temperature condition at 100 min.

NISTNCSTAR 1-6D. WTC Investigation 355
Appendix A

100

-200160 150 140 130 120 Column ID

(a) North face

110 100

100

50 -

O -100

-200

-150 +-!

360 350 340 330 320 Column ID

(b) South face

310 300

Figure A-31. Horizontal reaction force per column of WTC 1 Floor 98 for Case Bj

temperature condition.

A.3 WTC 2 FLOORS

A.3.1 Case Cj Temperature Condition

Table A-3 gives the maximum vertical displacement of WTC 2 floors for Case C, temperature condition,

and Figs. A-32 to A-36 show the vertical displacements when the maximum displacement was obtained.

Floor 79 to Floor 83, except Floor 82, had the maximum vertical displacement in the southeast area near

the impact damage. Floor 82 had the maximum vertical displacement in the northeast area. The

maximum displacement was projected to occur at 60 min on all floors. The vertical displacement in the

west office area was found to be insignificant on all the floors throughout the thermal loading. Floor 80

had a fair amount of vertical displacement in the north half of the west office area although the maximum

displacement was 15 in. A significant amount of web diagonals of Floor 82 to Floor 83 buckled in the hot zones of the east office area. Seat failures were not observed on Floor 79 to Floor 81. Trusses at Column

301 to Column 317 on the east face of Floor 82 and at Column 325 to Column 333 on the east face of

Floor 83 lost their vertical support at the exterior seats at 50 min as shown in Fig. A-37. Figure A-38

shows the average total thermal expansion of floors over the entire width of the building at 60 min in two

orthogonal directions. The total floor expansion ranged from 2.5 in. to 5.5 in. Figure A-39 shows

horizontal reaction force at individual columns of the north and south faces of Floor 81 . When the

reaction force is positive, the column is pulled inward by the floor. Columns between Column 353 and

Column 359 were pulled in by the floor. This was caused by the floor sagging in the southeast area that was primarily due to the impact damage to the interior truss seats. A few columns at the southeast comer

of Floor 80 and Floor 83 were also pulled in by the floor.

356 NISTNCSTAR 1-6D, WTC Investigation
FEA of Floors

Table A-3. Maximum vertical displacement of WTC 2 floors for Case Ci temperature

condition.

Max. Displacement Time at the Maximum

Floor (in.) (min)

79 19.0 60

80 30.1 60

81 31.0 60

82 45.2 60

83 38.9 60

Note: Downward displacement is positive.

:f2

, |iffTM(in.1

-11.493 -i^.Wj ^.Vi:. :ure at 3600 sec

(a) Entire model (b) Top view without slab

Figure A-32. Vertical displacement of WTC 2 Floor 79 for Case Ci temperature condition

at 60 min (downward displacement is negative; 5x displacement magnification).

NISTNCSTAR 1-6D, WTC Investigation 357
Appendix A

STEF-7 AN

•(in.)

(a) Entire model (b) Top view without slab

Figure A-33. Vertical displacement of WTC 2 Floor 80 for Case C, temperature condition

at 60 min (downward displacement is negative; 5x displacement magnification).

(a) Entire model (b) Top view without slab

Figure A-34. Vertical displacement of WTC 2 Floor 81 for Case Cj temperature condition

at 60 min (downward displacement is negative; 5x displacement magnification).

358 NISTNCSTAR 1-6D, WTC Investigation
FEA of Floors

-18.15

(a) Entire model (b) Top view without slab

Figure A-35. Vertical displacement of WTC 2 Floor 82 for Case Ci temperature condition

at 60 min (downward displacement is negative; 5x displacement magnification).

NISTNCSTAR 1-6D, WTC Investigation 359
Appendix A

(a) Entire model ^ (b) Top view without slab

Figure A-36. Vertical displacement of WTC 2 Floor 83 for Case Cj temperature condition

at 60 min (downward displacement is negative; 5x displacement magnification).

(a) Floor 82 (b) Floor 83

(1X displacement magnification) (3X displacement magnification)

Figure A-37. Loss of vertical supports in WTC 2 Floor 82 and Floor 83 for Case Cj

temperature condition at 60 min.

360 NISTNCSTAR 1-6D, WTC Investigation
FEA of Floors

84

North-South —A— East-West

78 < < : ,

. 2 3 4 5 6 7 8 9 Total Slab Expansion (in)

Figure A-38. Thermal expansion of floors of WTC 2 for Case Cj temperature condition at 60 min.

Figure A-39. Horizontal reaction force per column of WTC 2 Floor 81 for Case Cj

temperature condition.

A.3.2 Case Di Temperature Condition

Table gives the maximum vertical displacement of WTC 2 floors for Case D, temperature condition,

and Figs. A^O to A-44 show the vertical displacements when the maximum displacement was obtained.

Due to more impact damage and different temperature histories than Case Cj temperature condition, all floors had larger vertical displacement. Floor 80 and Floor 81 suffered damage to many interior seats in the east office area due to the aircraft impact. Bridging trusses that had been removed in Case Cj

temperature condition were replaced in these two floors in order to support primary trusses of the east

NISTNCSTAR 1-6D, WTC Investigation 361
Appendix A

office area after the impact. The maximum vertical displacement of 97 in. was calculated at Floor 81 near

the impact damage at 50 min as shown in Fig. A-42. Significant sagging of the floor was observed at Floor 79 to Floor 83. Gusset plates and bolts at more than 75 percent of all the exterior seats of the east face of Floor 82 and Floor 83 failed due to horizontal shear force that was caused by the difference in the

thermal expansion between the floor and the exterior wall in the direction transverse to the primary

trusses. The truss at Column 357 of Floor 81 was the only truss that lost its vertical support at the exterior

seat among all the floors. This truss walked off the truss seat. Figure A-45 shows the average total thermal expansion of floors over the entire width of the building at 60 min of Case Dj temperature

condition. The total floor expansion ranged from 1 in. to 5 in. Figures A-A6 and A-47 show horizontal

reaction force at individual columns of the north and south faces of Floor 80 and Floor 82, respectively.

Column 101 to Column 1 1 1 on the west face and Column 347 to Column 359 on the east face were pulled

in by the floor at 60 min on Floor 80 because of the floor sagging occurring in the southeast area. Since

core columns were not restrained in the horizontal directions, when the floor pulled in one face of exterior

wall, the opposite face of the exterior wall would also be pulled in. Columns at the southeast comer were

pulled in by the floor at Floor 79 and Floor 8 1 . Many columns of the west face of Floor 82 were pulled

inward, while reaction forces at many columns of the east face were close to zero. As described above,

gusset plates and seat bolts failed at a number trusses on the east face of Floor 82. Because columns at these locations were not supported in the horizontal direction by the floor, the reaction force became close

to zero at these columns.

Table A-4. Maximum vertical displacement of WTC 2 floors for Case D, temperature

condition.

Max. Displacement Time at the Maximum

Floor (in.) (min)

79 35.8 60

80 65.6 40

81 96.7 50

82 49.4 60

83 44.6 60

Note: Downward displacement is positive.

AN

I (in.)

(a) Entire model (b) Top view without slab

Figure A-40. Vertical displacement of WTC 2 Floor 79 for Case Dj temperature condition

at 60 min (downward displacement is negative; 5x displacement magnification).

362 NISTNCSTAR 1-6D, WTC Investigation
FEA of Floors

Figure A-41. Vertical displacement of WTC 2 Floor 80 for Case Dj temperature condition

at 40 min (downward displacement is negative; 5x displacement magnification).

(a) Entire model (b) Top view without slab

Figure A-42. Vertical displacement of WTC 2 Floor 81 for Case Di temperature condition

at 50 min (downward displacement is negative; 5x displacement magnification).

NISTNCSTAR 1-6D, WTC Investigation 363
Appendix A

(a) Entire model ^ (b) Top view without slab

Figure A-43. Vertical displacement of WTC 2 Floor 82 for Case Dj temperature condition

at 60 min (downward displacement is negative; 5x displacement magnification).

Figure A-44. Vertical displacement of WTC 2 Floor 83 for Case Dj temperature condition

at 60 min (downward displacement is negative; 5x displacement magnification).

364 NISTNCSTAR 1-6D, WTC Investigation
FEA of Floors

—0—North-South —A— East-West

0 1 2 3 4 5 6 7 Total Slab Expansion (in)

Figure A-45. Thermal expansion of floors of WTC 2 for Case Dj temperature condition at 60 min.

100

-150

-200

—600 sec —1 ,200 sec — 1 .800 sec —2,400 sec — 3.000 sec —3,600 sec

100

160 150 140 130 120 Column ID

(a) West face

110 100

-200

—600 sec —1,200 sec —1,800 sec —2,400 sec — 3,000 sec —3.600 sec

360 350 340 330 320 Column ID

(b) East face

310 300

Figure A-46. Horizontal reaction force per column of WTC 2 Floor 80 for Case Dj

temperature condition.

NISTNCSTAR 1-6D. WTC Investigation 365
Appendix A

100

50 -

-50

q -100

-150

-200

—600 sec —1 .200 sec — 1.800 sec 2.400 sec —-3,000 sec —3,600 sec

160 150 140 130 120 110 Column ID

100

(a) West face

100

50

-50

-150

-200

im

—600 sec —1,800 sec —3,000 sec— 1 ,200 sec

2,400 sec —3,600 sec

360 350 340 330 Column ID

320

(b) East face

310 300

Figure A-47. Horizontal reaction force per column of WTC 2 Floor 82 for Case Dj

temperature condition.

A.4 SUMMARY OF RESULTS

Figures A-48 and A-49 show conditions of the connections between the exterior wall and the floors predicted by the WTC 1 floor models at 100 min for Case Aj and Case B, temperature conditions, and

Figs. A-50 and A-51 show conditions of the connections between the exterior wall and the floors

predicted by the WTC 2 floor models at 60 min for Case C, and Case D, temperature conditions. The

figures show the following conditions:

• Condition 1: gusset plate failure + seat failure due to vertical shear (loss of vertical support)

• Condition 2: gusset plate failure + bolt shear-off + truss walk-off (loss of vertical support)

• Condition 3: gusset plate failure + bolt shear-off + significant displacement (>25 in.) of the

floor in that area (floor remains vertically supported)

• Condition 4: tensile force between the exterior wall and the floor system (floor remains

vertically connected, but exerts pull-in force on the exterior wall)

Conditions 1 and 2 were treated as the case of floor/wall discoimections. Conditions 3 and 4 were treated as the case where the floor pulled in the exterior wall.

The behaviors of the floor system found in the full floor models subjected to impact damage and elevated

temperatures from the fires can be summarized as follows:

• Bridging trusses subjected to elevated temperatures buckled between primary trusses.

• When significant differences in thermal expansion of floors and exterior walls in the direction transverse to the axes of primary trusses occurred near the comers, studs, diagonal strap

anchors, gusset plates, and seat bolts at exterior truss seats failed due to the lateral shear. Web diagonals of floor trusses with damaged thermal insulation buckled.

366 NISTNCSTAR 1-6D. WTC Investigation
FEA of Floors

• Floors sagged into catenary forms.

• Truss seats disconnected from the exterior walls.

Pull-in forces were expected to develop whenever the floor sagged. Although the floor sagging was

captured by the floor models in the heated area, the pull-in force on the exterior columns was not captured

in most of the full floor model analyses. To accurately calculate pull-in forces between the floor and the exterior columns in the full floor model, much more detailed modeling would be required. Such

modeling includes accurate boundary conditions on columns, creep in steel, friction at the truss seats, accurate e\'aluation of failure of strap anchors and studs, and concrete cracking and spalling. In addition,

temperature time histories that were used in the full floor model analyses may be different if improved

estimates of impact damage to insulation were obtained. Further discussion on the pull-in force can be

found in Section 2.5.2 of this report.

NISTNCSTAR 1-6D. WTC Investigation 367

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Appendix A

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FEA of Floors

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A//S7 NCSTAR 1-6D. WTC Investigation 369
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NISTNCSTAR 1-6D. WTC Investigation 371
Appendix A

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372 NISTNCSTAR 1-6D, WTC Investigation
Appendix B

Floor Truss Dynamic Response

Due to Impact of Dropping Floor

B.1 impact of dropping floor

The failure of dropping floor may occur due to thermal and/or additional debris weight on the truss, and'or as a result of the aircraft impact. A floor truss or a group of floor trusses could lose support at both

the exterior and interior supporting ends and drop onto the floor below. This failure mode, which is shown in Fig. B-1, will be referred to as full truss drop. Alternatively, a floor tmss or a group of floor trusses could lose support on one side and drop down to impact the target floor below. This failure mode,

which is also shown in Fig. B-1, will be referred to as partial truss drop.

Schematic of full truss drop Schematic of partial truss drop

-^1 T

Before impact

Before impact

After impact After impact

Figure B-1. Schematic of full truss or partial truss drop

and web diagonal crushing at impact.

B.2 purpose and scope

The purpose of this study is to determine the dynamic response of the target truss from the impact of full and partial truss drop, to determine whether the target truss seats can resist such an impact load, and to determine whether the target truss will lose its composite action, sag significantly, and consequently fail

to restrain the exterior column to which it is connected against instability.

NISTNCSTAR 1-6D. WTC Investigation 373
Appendix B

B.3 METHOD OF ANALYSIS

The simulation of a floor drop is idealized with a truss drop. This has inherent assumptions that all seats for the floor fail simultaneously to cause a full or partial drop. The dynamic response of the target truss from the impact of a dropping truss is calculated using conservation of energy principle. The potential

energy of the truss just before drop, which is a function of drop height, converts to the kinetic energy of

the truss just before impact. As the dropping truss starts to impact the target truss, the web diagonal

members of the dropping truss are assumed to deform plastically to absorb some of the kinetic energy.

The energy absorption due to crushing of the furniture and partitions are neglected in this study. The

energy absorption due to web diagonal member crushing reduces the kinetic energy available at impact to deform the target truss. All the web diagonal members are assumed to deform plastically for the full truss drop case, while only one quarter of the web diagonal members are assumed to deform plastically for

partial truss drop, representing one quarter of the length of the truss that may come in contact at impact

with the floor below. The kinetic energy loss at the time of impact of the dropping truss and the target

truss is calculated based on conservation of momentum. The two trusses are assumed to travel together

after the impact, at one-half of the velocity of the dropping floor before impact.

The dynamic load due to the impact of the dropping truss onto the target truss will cause the target truss to deform plastically beyond the static load due to the weight of the two trusses. The maximum dynamic

deformation of the trusses is calculated by conservation of energy principle assuming that the resistance

of the truss is a bilinear function of displacement. This assumption is based on fitting the accelerationdeflection relationship of target truss, calculated with finite element analysis, as shown in Fig. B-2.

Finite element results

Assumed resistance

Knuckle No. 4 fail

1 1 knuckles from the

interior end fail

Increase T

from 20 T to 400"C

Knuckle No. 1 to 6 and No. 13 fail, and

truss walks off the interior seat

Bolts at the interior seat shears off

Diagonals start to buckle and 2 knuckles from the interior end fail

0 20 40 60 80

Truss mid-span defection (in.)

Figure B-2. Target truss resistance against increasing acceleration

374 NISTNCSTAR 1-6D, WTC Investigation
Floor Truss Dynamic Response Due to Impact of Dropping Floor

B.4 RESULTS

The ratios of demand-to-seat capacity for the gravity loads of the dropped and impacted trusses moving

together for temperamres of 20 °C, 400 °C, 600 °C, and 700 °C, and the gravity plus dynamic impact loads

for temperatures of 20 ''C and 400 °C, are calculated. A demand-to-capacity ratio of less than one shows

that the truss seat has sufficient capacity to resist the load, and a demand-to-capacity ratio of larger than one implies that the seat could fail. The range of the demand-to-capacity ratios is due to the different

assumptions for the amount of energy loss due to crushing of the web diagonal members of the dropped

truss.

The demand-to-capacity ratio of the long-span truss for gravity loads is shown in Table B-1 and for gravity plus impact loads is shown in Table B-2. The result for gravity loads alone shows the both the

exterior and interior truss seats have sufficient capacity to support the weight of two floors for all temperatures considered. The result for gravity plus impact loads shows that at temperatures below

400 ''C neither the exterior nor interior truss seats is expected to fail. Peak deflection response due to gravity and the dynamic impact of the dropping truss is given in Table B-3. The results show that at room temperamre, and more so at 400 °C, the impacted truss will deflect to an extent that it loses

composite action and becomes a catenary. At 400 the truss walks off the interior seat. Obviously, a

catenar\' truss is not able to restrain the exterior column against transverse movement and cannot restrain

it from instability. Although a truss response to increasing acceleration at 700 "C was not developed, the

strength reduction of the truss seats clearly indicates that the failure of truss seats will occur.

Table B-1. Demand-to-capacity ratio of long-span truss for static gravity load.

Temp.

CC)

Demand

(kip)

Capacity (kip) Demand/Capacity

Int. Seat Ext. Seat Int. Seat Ext. Seat 20 26.4 187.3 140.0 0.14 0.19 400 26.4 166.9 125.7 0.16 0.21 600 26.4 81.6 77.8 0.32 0.34 700 26.4 37.2 35.5 0.71 0.74

Table B-2. Demand-to-capacity ratio of long-span truss

for dynamic impact load from full truss drop.

Temp.

CC)

Demand (kip) Capacity (kip) Demand / Capacity

Int. Seat Ext. Seat Int. Seat Ext. Seat 20 38.6 65.3 187.3 140.0 0.21 0.35 0.28 0.47 400 39.1 45.2 166.9 125.7 0.23 0.27 0.31 0.36

Table B-3. Peak deflection response due to static gravity and dynamic impact

Temp.

("C)

Static Deflection (in.) Dynamic

Deflection (in.)

20 2.3 7.6 25.4 400 24.2 66.4 89.6

NISTNCSTAR 1-6D. WTC Investigation 375
Appendix B

B.5 CONCLUSIONS

At room temperature, the impact of a dropping truss will not cause failure of truss seats, but will cause the

impacted truss to deform into a catenary. At 400 "C, the impacted truss will walk off the interior seat. In

either case the impacted floor will not restrain the exterior column against transverse movement and

instability. The impact of a dropping truss at 700 ''C will cause failure of truss seats.

376 NISTNCSTAR 1-6D, WTC Investigation
Appendix C

Global Analysis Without Creep

The anah^sis results presented in this Appendix were obtained from the prehminary global analyses that were performed neglecting the effects of creep and inelastic buckling of columns. These analyses were

primarily used to study the interaction between various structural components in the overall global

response of the towers. Because of the significant role that creep played in the collapse process, the resuhs from these analyses are presented without making any conclusive remarks about the collapse

sequence of the towers.

C.1 WTC 1 GLOBAL ANALYSIS WITHOUT CREEP

The WTC 1 ANSYS model without creep was analyzed with Case A, structural damage condition and

subjected to Case A, temperature time histories. Temperature-dependent plasticity and the nonlinear

geometry were the major sources of nonlinearity in the model. Table C-1 summarizes the sequence of

analyses that were conducted with the WTC I ANSYS model with Case A, conditions (see Section 2.2 for Case A, structural damage condition). The results of each analysis step were used as the initial conditions

for the next. Case Bj was not considered for preliminary global analysis, as the lack of creep and inelastic buckling behaviors limited the usefulness of repeating this analysis.

Table C-1. Analysis Steps of WTC 1 ANSYS global model for Case Aj conditions.

.Analysis

Step

Description

1 WTC 1 model below Floor 106 was analyzed under its own self-weight.

2 Structures above Floor 106 were added in a stress-free state, and the model was analyzed for dead

load including those above Floor 106.

3 Superimposed dead load and 25 percent of the design live loads were superimposed on the model.

4 Columns, spandrels, and floor elements that were severed during aircraft impact were removed,

and the model w as analyzed.

5 Column and spandrel temperatures were ramped up linearly to temperatures at 10 min.

6 Column and spandrel temperatures were changed linearly from temperatures at 10 min to 20 min.

7 Column and spandrel temperatures were changed linearly from temperatures at 20 min to 30 min.

8 Column and .spandrel temperatures were changed linearly from temperatures at 30 min to 50 min.

9 Column and spandrel temperatures were changed linearly from temperatures at 50 min to 100 min.

The model was first analyzed to capture the effects of the construction sequence (analysis steps 1, 2, and 3). The results of analysis for Step 3 represent the state before the aircraft impact. In analysis step 4,

the columns, spandrels, and floor elements that were severed during the aircraft impact were removed

from the model, and the building was reanalyzed to redistribute the load to the non-severed members.

The results of this analysis represent the state of the building after the aircraft impact. After load

redistribution, the column and spandrel temperatures provided by NIST at 10 min intervals were applied

to the model (analysis steps 5 through 9). Temperatures were calculated by linear interpolation for times

in between 1 0 min intervals. In order to reduce computation time, the temperature data sets for which

NISTNCSTAR 1-6D. WTC Investigation 377
Appendix C

temperatures remained approximately linear with time during the interval from the previous and the

following temperature data sets were eliminated from the analyses. Based on this elimination,

temperature analyses were performed at 10 min, 20 min, 30 min, 50 min, and 100 min. Temperatures were not applied to the floor elements to prevent unrealistic buckling of floors. As discussed earlier, the

floors in the global models did not include the floor trusses and were modeled by plate elements to match

their membrane stiffness; the bending stiffness of the floors was not modeled accurately.

The results of the WTC 1 global model analyses for Case Aj conditions are summarized in Figs. C-1

through C-9.

Figure C-1 shows the total displacement at different analysis steps. The maximum displacement was

obtained right after aircraft impact and was equal to 4.9 in. This displacement was gradually reduced to

4.1 in. at the end of 100 min due to thermal expansion of core and exterior columns between Floor 93 and

Floor 98. Figures C-2 and C-3 show the total displacements for north, south, and east exterior walls

before and after aircraft impact and at 50 min and 100 min. The total displacements for the west exterior

wall are not shown as they were similar to the east exterior wall. The displacements were typically at their maximum right after aircraft impact around the hat truss and gradually decreased with time, reaching

their minimum value at 50 min to 100 min in the aircraft damage zone.

Figures C-4 and C-5 show the axial load variations over north, south, and east exterior wall columns and

spandrels before and after aircraft impact and at 50 min and 100 min. After the aircraft impact, the loads

carried by the severed columns of the north wall were primarily redistributed to the remaining columns of

the north wall and also to the core and other exterior walls. As a result of this redistribution, the

maximum column load increased from 265 kip to 1,200 kip on the north exterior wall and from 268 kip to 380 kip on the south exterior wall. The 1,200 kip load occurred in a column adjacent to the impact

damage area. The column loads on the east and west walls slightly increased in the south side of the

walls. With increasing time, the maximum column load in the south wall increased from 380 kip after aircraft impact to 670 kip at the end of 1 00 min. This increase was primarily due to the steady increase of

column temperatures on the south wall.

Figure C-6 shows the total column loads in the core columns and the north, south, east, and west exterior

walls for several floors at the end of each analysis step. Due to the removal of severed columns,

spandrels, and floor elements, the total column loads below Floor 98 after aircraft impact did not equal

the total column loads before the aircraft impact.

After the aircraft impact, the total load in core columns increased about 1 ,000 kip, in the east exterior wall

columns about 200 kip, and in the west exterior wall columns about 150 kip, whereas the total load

decreased in the north wall columns about 1,150 kip and in the south wall columns about 200 kip. With

increasing time, the temperatures in the core and the south exterior wall columns increased more than the other exterior wall columns, causing relative thermal expansion. Relative thermal expansion caused the core and the south exterior wall columns to attract more load, and the exterior walls on the north, east, and

west sides to unload. The increase in loads due to thermal expansion of the core columns increased the

plastic strains with time and the resulting shortening caused the unloading of the core columns at 30 min.

As time approaches 1 00 min, the temperatures of all columns dropped down, and the effects of thermal

expansion decreased. This can be seen in the loads at 100 min, where core columns unloaded and

redistributed load to each exterior wall (about 3,500 kip). About 32 percent of the redistributed load was

378 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis Without Creep

transferred to each of the east and west exterior wall columns, and 1 8 percent to each of the north and

south exterior wall columns.

Figures C-7. C-8, and C-9 show the ratio of elastic-plus-plastic strain to the temperature-dependent yield

strain of the core columns between Floor 96 and Floor 97 before and after aircraft impact and at 10 min,

20 min. 50 min, and 100 min. As can be noticed, the elastic-plus-plastic strain in the core columns before

aircraft impact was typically 50 percent to 60 percent less than the yield strains at room temperature.

After the aircraft impact, except for Column 504, the maximum strain ratio did not get beyond 1.0, indicating that almost all core columns remained in the elastic range. With increasing time and

temperatures, the strain ratios started to increase, especially in the west and the south sides of the core. Strain ratios reached their maximum at the end of 50 min and remained almost constant till the end at about 100 min. Higher strain ratios were clustered around west and south side core columns, indicating a tendency to tilt toward the south and west.

NISTNCSTAR 1-6D. WTC Investigation 379
Appendix C

(e)At50min (f)AtlOOmin

Figure C-1, Total displacement at different stages of WTC 1 for Case Aj conditions.

380 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis Without Creep

(a) North wall before impact (b) North wall after impact

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Figure C-2. Total displacement on the north, south, and east faces of the WTC 1 before

and after aircraft impact (looking from outside).

NISTNCSTAR 1-6D, WTC Investigation 381
Appendix C

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Figure C-3. Total displacement on the north, south, and east faces of the WTC 1 at 50 min and 100 min of Case Aj conditions (looking from outside).

382 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis Without Creep

(a) North wall before impact (b) North wall after impact

(c) South wall before impact (d) South wall after impact

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Figure C-4. Axial load variation on the north, south, and east faces of the WTC 1 before

and after aircraft impact (looking from outside; compression is negative).

NISTNCSTAR 1-6D, WTC Investigation 383
Appendix C

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compression is negative).

384 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis Without Creep

Row Analysis Stage North South East West Core Sum

(1) Before Impact 12375 12459 9006 9045 47101 89986

(2) After Impact 10330 12151 9222 9242 47812 88757

(3) 10 min 9649 1 1714 8429 8142 50762 88696

(4) 20 min 9528 11761 8260 8023 51 185 88757

(5) 30 min 9564 11931 8421 8060 50781 88757

(6) 50 min 9852 12228 9065 8714 48898 88757

(7) 100 min 10492 12880 10067 9880 45438 88757

(a) Above Floor 93

Row Analysis Stage North South East West Core Sum

(1) Before Impact 11119 11204 8126 8170 41216 79835

(2) After Impact 9598 11 004 8328 8339 42174 79443

(3) 10 min 8898 10573 7546 7237 45137 79391

(4) 20 min 8757 10620 7387 7128 45552 79444

(5) 30 min 8795 10780 7545 7176 45148 79444

(6) 50 min 9094 1 1068 8179 7840 43263 79444

(7) 100 min 9771 1 1668 9192 9014 39799 79444

(b) Above Floor 96

Row Analysis Stage North South East West Core Sum

(1) Before Impact 10264 10352 7564 761

37299 73090

(2) After Impact 9090 10171 7761 7770 38295 73087

(3) 10 min 8397 9739 6983 6661 41262 73042

(4) 20 min 8261 9783 6828 6546 41669 73087

(5) 30 mm 8299 9938 6990 6594 41266 73087

(6) 50 min 8588 10223 7625 7270 39381 73087

(7) 100 min 1 0824 8628 8466 35919 73087

(c) Above Floor 98

Figure C-6. Total column loads In the core and exterior walls of WTC 1 at different floors

and at different times (compression is positive).

NISTNCSTAR 1-6D. WTC Investigation 385
Appendix C

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strain for the core columns at Floor 96 of WTC 1 before and after aircraft impact.

386 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis Without Creep

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strain for the core columns at Floor 96 of WTC 1 at 10 min and 20 min for Case A

conditions.

NISTNCSTAR 1-6D, WTC Investigation 387
Appendix C

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strain for the core columns at Floor 96 of WTC 1 at 50 min and 100 min for Case A,

conditions.

388 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis Without Creep

C.2 WTC 2 GLOBAL ANALYSIS WITHOUT CREEP

The WTC 2 ANSYS model with no creep and no inelastic buckling of columns was analyzed with

Case C, and revised Case C, structural damage condition and subjected to Case C, and Case D,

temperature conditions. Temperature-dependent plasticity and the nonlinear geometry were the sources of nonlinearity in the model.

Case Dj temperature histories were analyzed with revised Case C, structural damage as there was little strucmral response to Case C, temperature histories, particularly in the core. The application of structural damage to the global model was a lengthy process, hence, only a different temperature history was

considered for prehminary analysis purposes.

C.2.1 Case Ci Structural Damage and Temperature Conditions

Table C-2 summarizes the sequence of analyses that were performed with the WTC 2 ANSYS global

model with Case C, conditions (see Section 2.2 for Case C, structural damage condition). The revised

Case C, structural damage condition was provided by NIST in the middle of the analysis for the thermal

loading. Additional core columns were removed in analysis step 6 as shown in Table C-2. The results of

each analysis step were used as initial conditions for the next analysis step.

Table C-2. Analysis Steps of WTC 2 ANSYS global model with Case d conditions.

Analysis Step Description

1 WTC 2 model below Floor 106 was analyzed under its own self-weight.

2

Structures above Floor 1 06 were added in a stress-free state, and the model was analyzed for dead

load including those above Floor 106.

-> Superimposed dead load and 25 percent of the design live loads were superimposed on the model.

4 Columns, spandrels, and floor elements severed during aircraft impact were removed, and the model was analyzed.

5 Column and spandrel temperatures were linearly ramped up to temperatures at 10 min.

6

Core Columns 1003 at Floor 80 and 903 between Floors 77 and 84 were removed from the model

to represent the additional severed columns that were identified by NIST at later stages of the investigation (see Seclion 2.2 for the revised Case C, structural damage condition).

7 Column and spandrel temperatures were changed linearly from temperatures at 10 min to 20 min.

8 Column and spandrel temperatures were changed linearly from temperatures at 20 min to 30 min.

9 Column and spandrel temperatures were changed linearly from temperatures at 30 min to 40 min.

10 Column and spandrel temperatures were changed linearly from temperatures at 40 min to 50 min.

11 Column and spandrel temperatures were changed linearly from temperatures at 50 min to 60 min.

The model was first analyzed to capture the effects of the construction sequence (analysis steps 1, 2, and

3). The results of analysis step 3 represented the structure state before the aircraft impact. In analysis

step 4, the columns, spandrels, and floor elements that were severed during the aircraft impact were removed from the model, and the building was reanalyzed to redistribute the load to the non-severed

members. This analysis represents the state of the building after the aircraft impact. After load

redistribution, the column and spandrel temperatures were applied to the model (analysis steps 5, 7, 8, 9,

10, and 1

1 ). The column and spandrel temperatures were provided by NIST at 10 min intervals. For

times between these time intervals, temperatures were calculated by linear interpolation. Analyses were

NISTNCSTAR 1-6D, WTC Investigation 389
Appendix C

conducted at every 10 min up to 60 min. In Analysis Step 6, after the analysis of 10 min temperatures,

two more core columns that were identified as severed during the aircraft impact were removed from the

model. Temperatures were not applied to the floors in the global model to prevent floor buckling, as discussed for the WTC 1 global model without creep.

The results of the WTC 2 global model analyses with Case C, structural damage and temperature

conditions are summarized in Figs. C-10 through C-20.

Figure C-10 shows the vertical displacement at different analysis stages. The maximum displacement

after the removal of additional severed core columns at analysis step 6 was equal to 7.2 in. This

displacement gradually decreased to 7.0 in. at the end of 50 min. This reduction was due to thermal

expansion of the core and the exterior wall columns between Floor 79 and Floor 83. Figures C-1 1 and

C-12 show the vertical displacements for south and east exterior walls before and after aircraft impact

and at 30 min and 60 min. The displacements were typically at their maximum near the hat truss at analysis step 6, after all severed members were removed, and gradually decreased to their minimum near Floor 77 through Floor 81 at 60 min. Figure C-1 1 shows that the displacement on the east wall, which was symmetric before the aircraft impact, became greater on the south side of this wall after the aircraft impact. This was due to the load redistribution to the south side of the east wall as a result of the removal

of the severed columns on the south wall and in the southeast comer of the core. This was the first sign of

tilting of WTC 2 toward the southeast.

Figures C-13, C-14, C-15, and C-16 show the axial loads before and after aircraft impact and at 30 min

and 60 min over the south, east, and north exterior wall columns and spandrels and in the 800, 900, and

1000 core column series. After the aircraft impact, the load carried by the severed columns of the south

exterior wall was primarily redistributed to the remaining columns on the same face and also to the core and other exterior wall columns. As a result of this redistribution, the maximum column load increased

from 334 kip to 1,410 kip on the south exterior wall and from 451 kip to 485 kip on the east exterior wall. Similar to displacement, the axial load on the east wall, which was symmetric before the aircraft impact,

became greater on the south side of this wall after the aircraft impact. This was due to the load

redistribution to the south side of the east wall as a result of the removal of the severed columns on the

south wall and in the southeast comer of the core. The axial load in core columns also was significantly

affected by the aircraft impact and fire-induced temperatures. The maximum column load increased from

4,930 kip to 5,120 kip in the 1000 core-column series, from 1,600 kip to 2,250 kip in the 900 core column

series, and from 1,740 kip to 2,630 kip in the 800 core-column series. After the removal of 1003 and

903 core columns, the column loads increased on the east and south side core columns.

With increasing time, the maximum column load on the east exterior wall columns increased from

485 kip after aircraft impact to 630 kip at the end of 60 min. This increase was primarily due to the

steady increase of column temperatures on the east wall as a result of the continuous fires. Similarly, the

axial loads in the 1000 core column series steadily increased due to continuous fires on the east side of the

core.

Figure C-1 7 shows the total column loads over the entire core and north, south, east, and west exterior

walls for different floors. Due to the removal of severed columns, spandrels, and floor elements, the total column loads below Floor 83 after aircraft impact are not equal to those before the aircraft impact.

Referring to the total column loads above Floor 83 in Fig. C-1 7, after the aircraft impact (including the

effects of additionally removed Column 903 and Column 1003 in the core), the total column load in the

390 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis Without Creep

east exterior wall columns increased about 2,600 kip, whereas the total column load decreased in the core by about 1.200 kip, in the north exterior wall by about 750 kip, in the west exterior wall by about 50 kip,

and in the south exterior wall by about 600 kip. With increasing time, the temperatures in the east, the

north, and the south exterior wall columns increased more than those in the west exterior wall and core columns. The higher temperatures resulted in higher thermal expansions and greater axial loads in the

exterior wall columns. In Floor 83, the temperamre effect alone resulted in unloading of the core by

1,820 kip and increased the total column loads by 140 kip on the south exterior wall, by 700 kip on the

west exterior wall, by 600 kip on the north exterior wall, and by 380 kip on the east exterior wall.

Figures C-18. C-19. and C-20 show the ratio of elastic-plus-plastic strain to the temperature-dependent

yield strain of the core columns between Floor 82 and Floor 83 before and after aircraft impact and at 10 min (analysis step 6), 30 min, 40 min, and 60 min. As can be noticed, the elastic-plus-plastic strain in the core columns before aircraft impact was typically 60 to 70 percent less than the yield strains at room

temperature. After the aircraft impact, the maximum strain ratio reached 0.6, indicating that all remaining

core columns were in their elastic range. After the removal of Core Columns 1003 and 903, Core

Columns 1004 and 1005 started to show strain ratios greater than 1.0 (indicating plasticity) with 10 min

temperatures. Strain ratios in Core Columns 1004 and 1005 continued to increase with increasing time

and temperatures, reaching their maximum at the end of 60 min. High strains were clustered around the

east side core columns, demonstrating possible tihing of the core.

NISTNCSTAR 1-6D. WTC Investigation 391
Appendix C

(a) Before impact (b) After impact

(c) At 10 min (Analysis step 6) (d) At 30 min

(e) At 40 min (f) At 60 min

Figure C-10. Vertical displacement at different stages of WTC 2 for

Case Cj conditions.

392 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis Without Creep

Figure C-1 1 . Vertical displacement on the south and east faces of WTC 2 before and

after aircraft impact (looking from outside; downward displacement is negative).

NISTNCSTAR 1-6D. WTC Investigation 393
Appendix C

(a) South wall at 30 min (b) South wall at 60 min

(c) East wall at 30 min (d) East wall at 60 min

Figure C-12. Vertical displacement on the south and east faces of WTC 2 at 30 min and

at 60 min of Case Cj conditions (looking from outside; downward displacement is negative).

394 NIST NCSTAR 1-6D, WTC Investigation
Global Analysis Without Creep

(a) South wall before impact (b) South wall after impact

(e) North wall before impact (f) North wall after impact

Figure C-13. Axial force variation on the south, east, and north faces of WTC 2 before

and after aircraft impact (looking from outside; compression is negative).

NISTNCSTAR 1-6D, WTC Investigation 395
Appendix C

Figure C-14. Axial force variation on the south, east, and north faces of WTC 2 at 30 min

and 60 min of Case Cj conditions (looking from outside; compression is negative).

396 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis Without Creep

FU3T to. 2 h

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(e) 1000 series columns before impact (f) 1000 series columns after impact

Figure C-15. Axial force variation on the 800, 900, and 1000 series core columns of

WTC 2 before and after aircraft impact (looking from west; compression is negative).

NISTNCSTAR 1-6D. WTC Investigation 397
Appendix C

(a) 800 series columns at 30 min (b) 800 series columns at 60 min

(e) 1000 series columns at 30 min (f) 1000 series columns at 60 min

Figure C-16. Axial force variation on the 800, 900, and 1000 series core columns of

WTC 2 at 30 min and 60 min of Case Cj conditions (looking from west; compression is negative).

398 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis Without Creep

Row Analysis Stage West East North South Core Sum

(1) Before Impact 18779 18837 13714 13529 77563 142423

(2) After Impact 18951 20394 12892 1 1880 76831 140949

(3) After Impact* 18774 21384 12800 12528 75166 140652

(4) 1 0 min 19499 20616 12997 11333 76504 140949

(5) 10 min (b) 19322 21606 12905 11981 74839 140652

(6) 20 min 19471 21616 12978 12130 74458 140652

(7) 30 min 19469 21637 • 13138 12309 74099 140653

(8) 40 min 19462 21692 13246 12427 73826

(9) 50 min 19472 21795 13305 12506 73574 140653

(10) 60 min 19500 21887 13388 12538 73341 140653

* Including the effects of additionally removed Columns 903 and 1003 in the core (= (2) - (4) + (5)).

(a) Above Floor 78

Row Analysis Stage West East North South Core Sum

(1) Before Impact 17642 17697 12558 12393 71319 1 3 1 609

(2) After Impact 17755 19295 11818 10982 71249 131099

(3) After Impact* 17557 20305 11756 11599 69754 130972

(4) 1 0 min 18310 19529 1 1942 10396 70924 131101

(5) 10 min (b) 18111 20539 11881 11014 69429 130974

(6) 20 min 18258 20479 11960 11230 69048 130974

(") 30 min 18251 20462 12137 11435 68688 1 3U9 /

(8) 40 min 18241 20502 12245 11570 68414 130972

(9) 50 min 18238 20603 12309 11660 68162 130972

(10) 60 min 18239 20690 12414 11700 67928 130972

* Including the effects of additionally removed Columns 903 and 1003 in the core (= (2) - (4) + (5)).

(b) Above Floor 81

Row Analysis Stage West East North South Core Sum

(1) Before Impact 16728 16782 1 1972 1 1820 67309 124611

(2) After Impact 16853 18337 1 1241 10561 67499 124490

(3) After Impact* 16664 19328 1 1 184 11 183 66115 124474

(4) 1 0 min 17398 18604 1 1346 9970 67172 124489

(5) 10 min (b) 17209 19595 1 1288 10592 65788 124473

(6) 20 min 17356 19511 11365 10833 65409 124473

(7) 30 min 17351 19482 11537 11054 65048 124473

(8) 40 min 17344 19521 11644 1 1191 64773 124473

(9) 50 min 17350 19619 1 1702 11280 64521 124473

(10) 60 min 17370 19709 11787 11320 64287 124473

* Including the effects of additionally removed Columns 903 and 1003 in the core (= (2) - (4) + (5)).

(c) Above Floor 83

Figure C-17. Total column loads in the core and exterior walls of WTC 2 at different

floors and at different times for Case Ci conditions (compression is positive).

NISTNCSTAR 1-6D. WTC Investigation 399
Appendix C

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Figure C-18. Ratios of axial elastic-plus-plastic strain to temperature-dependent yield

strain for the core columns at Floor 82 of WTC 2 before and after aircraft impact.

400 NISTNCSTAR 1-6D. WTC Investigation
Global Analysis Without Creep

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NISTNCSTAR 1-6D. WTC Investigation 401
Appendix C

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Figure C-20. Ratios of axial elastic-plus-plastic strain to temperature-dependent yield

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conditions.

402 NIST NCSTAR 1-6D, WTC Investigation
Global Analysis Without Creep

C.2.2 Case Di Temperature Condition and Case Cj Structural Damage Condition

Table C-3 summarizes the sequence of analyses that were performed with the WTC 2 ANSYS global

model with the revised Case C, structural damage condition from Step 4, and Case D, temperamre

condition. Revised Case C, structural damage refers to the removal of core columns 903 and 1003 in addition to the other core columns that were severed after the aircraft impact as shown in Section 2.2. Case D, structural damage condition was not used as this structural damage condition was not available at the time of analyses.

Table C-3. Analysis Steps of WTC 2 ANSYS global model with Case Di temperature

condition and Case Cj structural damage condition.

Analysis Step Description

1 WTC 2 model below Floor 106 was analyzed under its own self-weight.

-) Structures above Floor 106 were added in a stress-free state, and the model was analyzed for dead

load including those above Floor 106.

3 Superimposed dead load plus 25 percent of the design live loads were superimposed on the model.

4

Columns (including the 1003 and 903 core columns), spandrels, and floor elements that were

se\ ered during aircraft impact were removed, and the model was analyzed (see Section 2.2 for the

re\ ised Case Cj structural damage condition).

5 Column and spandrel temperatures were ramped linearly up to temperatures at 10 min.

6 Column and spandrel temperatures were changed linearly from temperatures at 10 min to 20 min.

7 Column and spandrel temperatures were changed linearly from temperatures at 20 min to 30 min.

8 Column and spandrel temperatures were changed linearly from temperatures at 30 min to 40 min.

9 Column and spandrel temperatures were changed linearly from temperatures at 40 min to 50 min.

10 Column and spandrel temperatures were changed linearly from temperatures at 50 min to 60 min.

The model was first analyzed for the effects of the construction sequence (analysis steps 1, 2, and 3). The

results of analysis step 3 represent the state of the structure before the aircraft impact. In analysis step 4, the columns, spandrels, and floor elements that were severed during the aircraft impact were removed,

and the structure was reanalyzed to redistribute the loads to other members. This analysis represented the

structure state after the aircraft impact. The column and spandrel temperatures were applied to the model

(analysis steps 5 through 10). The column and spandrel temperatures were provided by NIST at 10 min

intervals. Temperamres were calculated by linear interpolation for times in between 10 min intervals. Temperature analyses were performed at every 10 min up to 60 min. Temperamres were not applied to the floor elements, as discussed earlier.

The results of the WTC 2 global model analyses with Case D, temperature condition and the revised

Case C, structural damage condition are sunmiarized in Figs. C-21 through C-32.

Figure C-21 shows the vertical displacement at different analysis steps. The maximum vertical

displacement after the aircraft impact increased from 7.0 in. to 7.7 in. with the inclusion of the additional

severed core columns (1003 and 903). The 7.7 in. maximum vertical displacement after aircraft impact

gradually increased to 9.2 in. at the end of the 60 min temperamre analysis. The exterior columns

between Floor 79 and Floor 83 thermally expanded with temperature; however, the core columns

shortened due to plastic deformation, and the plastic strains in 1000 series core columns were greater than

the thermal expansion strains. Figures C-22 and C-23 show the vertical displacements for the south and

east exterior walls after aircraft impact, and at 30 min, 50 min, and 60 min. The displacements of these

NISTNCSTAR 1-6D, WTC Investigation 403
Appendix C

exterior walls were typically at their maximum after aircraft impact and gradually decreased to their

minimum value with time up to 50 min and then increased slightly beyond 50 min up to 60 min, as temperatures reduced.

Figures C-24, C-25, and C-26 show the axial load variation over the south, east, and north exterior wall

columns and spandrels after impact and at 10 min, 20 mm, 30 min, 50 min, and 60 min. The maximum

column load on the east exterior wall columns increased from 485 kip after aircraft impact to about

880 kip at the end of 30 min and then dropped down to 800 kip at the end of 60 min. The increase in column forces was mostly concentrated at the center portion of the east wall. The maximum column load on the north exterior wall columns increased from 355 kip after aircraft impact to about 550 kip at the end

of 30 min and then dropped down to 440 kip at 50 min; it then increased again to 700 kip at the end of

60 min.

Figures C-27, C-28 and C-29 show the axial load variations over the 800, 900, and 1000 core column

series after aircraft impact and at 10 min, 20 min, 30 min, 50 min, and 60 min. Over the duration of the

fires, the maximum column load after impact increased from 5,200 kip to 6,250 kip in the 1000 core column series and from 1,700 kip to 2,500 kip in the 900 core column series, and decreased shghtly from

3,400 kip to 3,200 kip in the 800 core column series.

Figure C-30 shows the total column loads in the core and the north, south, east, and west exterior walls

for different floors. Total column loads below Floor 83 after aircraft impact did not add up to the total coluinn loads before the aircraft impact. This difference is equal to the self-weight of severed members

and floor loads applied to severed columns.

In Floor 83, the temperature effect alone resulted in an unloading of the core columns by 2,000 kip and

increased the total load by 630 kip on the south exterior wall, by 300 kip on the west exterior wall, by

540 kip on the north exterior wall, and by 530 kip on the east exterior wall.

Figures C-3 1 and C-32 show the ratio of elastic-plus-plastic strain to the temperature-dependent yield

strain of the core columns between Floor 82 and Floor 83 at 10 min, 20 min, 50 min, and 60 min. After

10 min, except for Core Columns 801, 1004, and 1005, the strain ratios in the core columns were all less than 1.0. With increasing time, more columns from east side and center region of the core area started to show strain ratios greater than 1.0, indicating the onset of plasticity. A maximum strain ratio of 41 was

reached between 40 min and 60 min at Column 1005. Higher strain ratios were clustered around the east side of the core, indicating a tendency of the core to tilt toward east.

404 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis Without Creep

(e) At 50 min (f) At 60 min

Figure C-21. Vertical displacement at different stages of WTC 2 for Case Dj temperature

condition and the revised Case Ci structural damage condition (downward displacement

is negative).

NISTNCSTAR 1-6D, WTC Investigation 405
Appendix C

(a) South wall after impact (b) South wall at 30 min

(c) East wall after Impact (d) East wall at 30 min

Figure C-22. Vertical displacement on the south and east faces of WTC 2 after aircraft

impact and at 30 min of Case Di temperature condition and the revised

Case Cj structural damage condition (looking from outside; downward displacement is negative).

406 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis Without Creep

(a) South wail at 50 min (b) South wall at 60 min

(c) East wall at 50 min (d) East wall at 60 min

Figure C-23. Vertical displacement on the south and east faces of WTC 2 at 50 min and

at 60 min of Case Dj temperature condition and the revised Case Ci structural damage

condition (looking from outside; downward displacement is negative).

NISTNCSTAR 1-6D, WTC Investigation 407
Appendix C

(a) South wall after impact (b) South wall at 10 min

(c) East wall after impact (d) East wall at 10 min

(e) North wall after impact (f) North wall at 10 min

Figure C-24. Axial force variation on the south, east, and north faces of WTC 2 after

impact and at 10 min of Case D; temperature condition and the revised

Case Cj structural damage condition (looking from outside; compression is negative).

408 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis Without Creep

(a) South wall at 20 rnin (b) South wall at 30 min

AMSYS

JAN- 23 2005 21:07:53

(e) North wall at 20 min (f) North wall at 30 min

Figure C-25. Axial force variation on the south, east, and north faces of WTC 2 at 20 min

and at 30 min of Case Di temperature condition and the revised

Case Ci structural damage condition (looking from outside; compression is negative).

NISTNCSTAR 1-6D, WTC Investigation 409
Appendix C

ANSYS

^^^^^^^^^^

(a) South wall at 50 min (b) South wall at 60 min

(c) East wall at 50 min (d) East wall at 60 min

(e) North wall at 50 min (f) North wall at 60 min

Figure C-26. Axial force variation on the south, east, and north faces of WTC 2 at 50 min

and at 60 min of Case Dj temperature condition and the revised

Case Ci structural damage condition (looking from outside; compression is negative).

410 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis Without Creep

(a) 800 series columns after impact (b) 800 series columns at 10 min

(c) 900 series columns after impact (d) 900 series columns at 10 min

(e) 1000 series columns after impact (f) 1000 series columns at 10 min

Figure C-27. Axial force variation on the 800, 900, and 1000 series core columns of

WTC 2 after impact and at 10 min of Case Dj temperature condition and the revised

Case Ci structural damage condition (looking from west; compression is negative).

NISTNCSTAR 1-6D. WTC Investigation 411
Appendix C

(e) 1000 series columns at 20 min (f) 1000 series columns at 30 mIn

Figure C-28. Axial force variation on the 800, 900, and 1000 series core columns of

WTC 2 at 20 min and at 30 min of Case Dj temperature condition and the revised

Case Cj structural damage condition (looking from west; compression is negative).

412 NISTNCSTAR 1-6D, WTC Investigation
ANSIS

JAS 23 no 05

Global Analysis Without Creep

(a) 800 series columns at 50 min (b) 800 series columns at 60 min

(c) 900 series columns at 50 min (d) 900 series columns at 60 min

(e) 1000 series columns at 50 min (f) 1000 series columns at 60 min

Figure C-29. Axial force variation on the 800, 900, and 1000 series core columns of

WTC 2 at 50 min and at 60 min of Case Di temperature condition and the revised

Case Cj structural damage condition (looking from west; compression is negative).

NISTNCSTAR 1-6D, WTC Investigation 413
Appendix C

Row Analysis Stage West East North South Core Sum

(1) Before Impact 18779 18837 13714 13529 77563 142423

(2) After Impact 18824 21170 12812 12396 75450 140652

(3) 1 0 min 19668 21636 13148 11694 74506 140652

(4) 20 min 19984 21951 13004 1 1661 74053 140653

(5) 30 min 20005 22426 13129 11899 73195 140653

(6) 40 min 19980 22260 13252 12156 73005 140653

(7) 50 min 19617 22048 13211 12609 73168 140653

(8) 60 min 19161 21803 13294 12959 73436 140653

) Above Floor 78

Row Analysis Stage West East North South Core Sum

(1

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Before Impact 17642 17697 12558 12393 71319 1 3 1 609

(2) After Impact 1 76 1

20084 11761 1 1475 70039 130972

(3) 1 0 min 18453 20602 12152 10672 69094 130973

(4) 20 min 18759 20889 12005 10680 68640 130973

(5) 30 min 18755 21379 12146 10910 67782 130972

(6) 40 min 18718 21202 12290 11170 67593 130972

(7) 50 min 18340 20983 12237 11655 67756 130971

(8) 60 min 17876 20724 12316 12034 68022 130972

(b) Above Floor 81

Row Analysis Stage West East North South Core Sum

(1) Before Impact 16728 16782 11972 11820 67309 124611

(2) After Impact 16717 191 1

11188 11058 66400 124474

(3) 1 0 min 17551 19473 11596 10404 65449 124473

(4) 20 min 17864 19739 1 1443 10431 64996 124472

(5) 30 min 17875 20198 11573 10687 64138 124471

(6) 40 min 17847 20006 11709 10960 63950 124471

(7) 50 min 17482 19841 1 1651 11384 64113 124472

(8) 60 min 17025 19637 11734 1 1691 64384 124471

(c) Above Floor 83

Figure C-30. Total column loads in the core and exterior walls of WTC 2 at different

floors and at different times for Case Di temperature condition and the revised Case C; structural damage condition (compression is positive).

414 NISTNCSTAR 1-6D, WTC Investigation
Global Analysis Without Creep

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NISTNCSTAR 1-6D. WTC Investigation 415
Appendix C

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416 NISTNCSTAR 1-6D, WTC Investigation
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