John L. Gross, Ph.D., P.E.

Building and Fire Research Labora

National Institute of Standards and Techno

U.S. Department of Commerce

John.Gross@nist.gov

Federal Building and Fire Safety Inves

of the World Trade Center Disast

National Construction Safety T

Advisory Committee Meetin

Project 6 – Structural Fire Resp

Collapse Analysis

June 22, 2004
Disclaimer Disclaimer

Certain commercial entities, equipment, producare identified in this presentation in order to desprocedure or concept adequately or to trace the procedures and practices used. Such identificaintended to imply recommendation, endorsemeimplication that the entities, products, materialsare necessarily the best available for the purpo
Project Tasks Project Tasks

This project has the following tasks:

 Evaluate the structural response of floor and colu

under fire conditions.

 Evaluate the response of the WTC towers under f

with and without aircraft impact damage.

 Identify and evaluate candidate hypotheses for in

propagation of collapse and estimate the uncertaicollapse initiation and propagation mechanisms.

 Conduct tests of structural components and syste

conditions.

 Report on the performance of open-web steel trus

in fire. 

 Analyze the response of WTC Building 7 under fir
Relationship to other projects... Relationship to other projects...

Project 6 relies heavily on information provided 

projects, specifically,

 Reference structural models of typical floor a

subsystems and of each WTC 1 and WTC 2 t

 Extent of aircraft damage to WTC 1 and WTC  Mechanical properties of the steels, welds an

the construction of the towers including elasticreep properties from 20oC to 700oC (Project 

 Thermal properties of spray-on fire resistant m

(Project 5)

 Temperature-time histories for various compo

systems and systems for both standard fires 119) and real fires based on fire dynamics sim(Project 5).
Objectives Objectives

To determine the structural response of the WT

aircraft impact and internal fires and to identprobable structural collapse mechanisms.

 Task 1: Components and Subsystems Task 2: Global Analysis without Impact Dama Task 3: Global Analysis with Impact Damage Task 4: Evaluation of Collapse Hypotheses
Task 1: Components and Subsyst

Task 1: Components and Subsyst

Develop detailed nonlinear structural models of the 

exterior wall section and evaluate performance foand elevated structural temperatures. 

 Single exterior panel section for strength und

 Floor section behavior for strength under ther

(80-in wide section)

 Truss seat connection for strength under ther

 Full floor models of mechanical floor and typi Multi-panel exterior wall section with connect

Identify dominant failure modes and parameters tha

influence the analysis results for critical componesubsystems.

Develop approaches to simplify structural analyses 

modeling and analyses.
Status - Task 1The truss model, with knuckle and seat components

potential failure modes that may occur under loadconditions, though the actual sequence of failure other loading and fire conditions.

The truss model can capture the following:

 Temperature-dependent elastic material prop

steel and concrete

 Temperature-dependent steel plasticity Buckling of truss members Failure of knuckle causing loss of composite  Failure of studs on the strap Failure of stud on the spandrel Failure of the exterior and interior truss seats
Status - Task 1The exterior wall model consists of 3x3 exterior wall 

columns by 9 spandrel beams) and includes all pmodes (columns and splices) that may occur und

thermal conditions.

The exterior wall model can capture the following:

 Column collapse due to large lateral deflectio Column buckling due to loss of lateral bracin Failure of column splice bolts and spandrel s
Status - Task 1The full floor model consists of all steel trusses (main trus

trusses), truss connections, perimeter and core columbeams, and concrete floor slab and includes all potentthat may occur under loading and thermal conditions.

The full floor model can capture the following:

 Floor sagging due to:

• Loss of stiffness at high temperatures• Yielding or buckling of critical truss members• Loss of composite action due to knuckle failure

 Loss of floor support (failure of interior or exterior 

connections) 

 Expansion of floor system and resulting column fo
Task 2: Global Analysis Without Im

Task 2: Global Analysis Without Im

Determine the structural response to large fires with

damage.

 Develop global model of one tower without im

nonlinear analysis of building regions affecte

 Analyze the structural response to ASTM sta

one to three (1-3) representative building fire 

Project 5. 

Improve WTC Tower models for analysis with impa

 Identify parameters that strongly influence an

 Develop approaches to simplify models for g
Task 3: Global Analysis With Impa

Task 3: Global Analysis With Impa

Develop global model of each WTC tower with impa

nonlinear analysis of building regions affected by 

Analyze three to five (3-5) building fire scenarios pro

for each tower and determine: 

 Time-sequence of events, 

 Mode of failure or capacity reduction for each 

the sequence and associated temperatures, 

 Load redistribution during the sequence of ev Agreement between analysis and observed p

Conduct parametric studies of the global analyses to 

influential parameters.

Repeat analyses for final fire scenarios. Identify mos

collapse initiation sequence. 
Status – Tasks 2 and 3 Tasks 2 and 3

Work is under way to conduct global analyses:

 Global models have been developed in SAP 

based upon the Project 2 Reference Models

 Conditions include (median, upper bound, lo

values):

• Impact damage to structure• Impact damage to fireproofing• Debris distribution on floors• Structural time-temperature histories
 Structural system capacity for the following s

• Before impact damage• After impact damage• During fire growth and spread

 Extent of load redistribution within and betw

exterior framing systems via hat truss and/o

 Conditions required for global instability (col

Status – Tasks 2 and 3 Tasks 2 and 3
Probabilistic Approach to Evaluate 

Probabilistic Approach to Evaluate 

in Global Capacity in Global Capacity

Global Reserve Capacity RC(t)

tco

RC(t

c)=0

Aircraft 

Impact

Capacity

Before 

Impact

RC(0)

Fire Growth and 

Structural Response

Capacity

After 

Impact

Events with sign

contribution to ch

global capac

Variability in 

analyses
Task 4: Evaluation of Collapse Hyp

Task 4: Evaluation of Collapse Hyp

Identify candidate hypotheses for initiation and 

collapse.

Evaluate hypotheses for collapse initiation and 

including the role played by columns, floors, and hat truss.

Estimate variability of probable collapse initiatio

propagation mechanisms.

Identify most probable structural collapse sequ
Status – Task 4

NIST has developed a working hypothesis tha

the chronological sequence of major eventhe collapses. 

In progress...

 Specific load redistribution paths and d

scenarios are under analysis for the coeach tower.

 Timeline of fire and structural observa

photographic, video, and interview recdeveloped.
Review of Progress Under Task 1 Review of Progress Under Task 1

The scope of work under Task 1 includes:

 Develop and validate ANSYS models of 

exterior wall subsystems,

 Evaluate the structural responses of thes

under dead and live loads and elevated stemperatures,

 Identify failure modes and failure sequen

associated temperatures and times-to-fa

 Identify simplifications for the global mod

analyses.
Materials

 Concrete Steel

Exterior Wall M

 Column p Column S Exterior W

Full Floor Model

 Knuckle Truss Seats Truss

Review of Progress Under Task 1 Review of Progress Under Task 1

The following will be covered...
Materials Materials
Steel

 Project 3 has provided properties of 28 differ

steel used in WTC 1 and 2 and load-elongati

A325 bolts.

 Temperature-dependent properties that are t

types of steel

• Modulus of elasticity,• Poisson’s ratio,• Instantaneous coefficient of thermal expansion• Yield strength reduction factor, and• Tensile strength reduction factor.
Steel Properties at Elevated Temperature Steel Properties at Elevated Temperature

0 200 

0

0.20.40.60.8

1

ConstructioBolt Steel

Tensile Strength Reduction Factor

Yield Strength Reduction Factor

0 200 400 600 800 1000 0

0.20.40.60.8

1

Construction SteelBolt Steel

Temperature (°C)

Yield Strength Reduction Factor

Tensile Streng
Instantaneous Coefficient of Thermal Ex

Instantaneous Coefficient of Thermal Ex

0 200 400 600 800 1000

1.2 .10 51.3 .10 51.4 .10 51.5 .10 51.6 .10 51.7 .10 5

Temperature (°C)

Coefficient of Thermal Expansion (1/°C)

0 200 

0

1.10 5

2.10 53.10 54.10 55.10 5

Normal wLightwei

Coefficient of Thermal Expansion (1/°C)

Steel C
Steel – Plasticity Plasticity

0 0.05 0.1 0.15 0.2 0.25 

0

2 .104

4 .1046 .1048 .104

T=RTT=300°CT=500°CT=700°C

Elastic + Plastic Strain (in/in)

Stress (psi)

Material ID 1 Steel
Bolts

0

10,00020,00030,00040,00050,00060,00070,00080,000

0.000 0.050 0.100 0.150 0.20

Elongation (in.)

Load (lbs)

Based on test data for 7/8 in. diameter A325 bolt with 

load-elongation relationships at elevated tempera

A325 bolt have been constructed.
Concrete Concrete – Stress-Strain Relationship in 

Strain Relationship in 

0.015 0.01 0.005 

4000300020001000

0

RTT=300°CT=600°CT=700°C

Strain (in/in)

Stress (psi)
Full Floor Model Full Floor Model
Full Floor Model Full Floor Model

Component Models

 Knuckle Truss Seat Connections Truss and Exterior Column

web d

knuc

Truss Seat 

Connection
Detailed Knuckle Analysis Detailed Knuckle Analysis

Goals:

 Determine failure strength of knuckle-concre

connection at room and elevated temperatu

 Develop a simplified representation for glob

Failure Mode: 

 Cracking and crushing of concrete leading t

composite action of floor system. 

Validation: 

 Comparison with available test data. 

Analysis: 

 ANSYS – LS Dyna Concrete Material Model: Psuedo Tensor Knuckle/Concrete Interface

• Bonded• No Friction Contact 
Laclede Tests of 1967 Laclede Tests of 1967

Drawing provided by Laclede Steel.
Longitudinal Shear Model Longitudinal Shear Model 

– Compressiv

Compressiv

Crush Region in Gray
Knuckle Shear Strength Knuckle Shear Strength

Temperature (oC) Sh

Hot Gas Knuckle Concrete fc(T)/fc Longitud

(kip

RT - 450 <375 300 1.00 30 650 550 450 0.80 24 850 725 600 0.63 19 1050 900 750 0.50 15 

Knuckle shear strength is based on test /analysis results after concrete strength.Temperature effect on knuckle shear strength is proportional tThe knuckle is conductive and heats up the concrete in compr
Simplified model of knuckle Simplified model of knuckle

n3

n3

n5

n3 

4 n

4 n

n5

1 n

Py 

Pz

2 n

n6

n6

2 n

n7

n8

11 9 n

n

n10

Pz

Px

Py

knuckle

1 n

2 n - Node on slab

- Node on truss

12

n

Constraint equationsCoupling displacement DOF of node 1 and 7

Break element No. 8-9: Capture loss of horizontal resistance in the Y direction if knuckle fails horizontally in the X directionNo. 9: Control nodes: 8,2; DOF: UXNo. 10: Control nodes: 2,9; DOF: UX

Break element No. 10: Capture loss of horizontal resistance in the Y direction if knuckle fails verticallyControl nodes: 12,2; DOF: UZ

5 Beam elements:Make the knuckle capacity temperature-dependent

Point-to-point contact element to transfer vertical compressive force between node 1 and 2
Truss Seat Connections Truss Seat Connections

Stand-off plates -

Seat angle

5/8 in. diameter bolt

Truss top chord

Gusset plate

Strut

Column/spandrel

Bearing angle

Chan

Vertical plate stiffe

Truss top chord

Strut

Bearing angle

5/8 in. dia. bolt

Exterior Seat Interior 
Truss Seat Analysis Truss Seat Analysis

Goal:

 Determine failure of truss seats at room 

elevated temperatures.

Failure Modes: 

 Material yield or fracture Bolt shear failure Weld failure Bearing angles “walk off” support

Analysis: 

 Linear elastic for load distribution Strength calculations per AISC LRFD
Truss Seat Analysis Truss Seat Analysis

Gusset plate fails Bolt comes into bearing 

and shears off

Possible failure sequence under horizontal load...
Finite Element Model of Exterior Se

Finite Element Model of Exterior Se

1

'Truss Seat 1411 detail E62' 

Stand-o

Seat angle

Truss top chord

Gusset plate

Strut

Bearing an
Failure Sequence of Exterior Seats 

Failure Sequence of Exterior Seats 

Tensile Force Tensile Force

(A) Seat details 1111, 1311, 1411, 1511, and 1611 at all te(B) Seat detail 1013 at temperatures below 100

oC 

(C) Seat details 1212 and 1313 at all temperatures, and detemperatures more than or equal to 100

oC 

(C)

(B)

(A) Gusset plate 

Yields

Gusset Plate 

Fractures

Fillet Weld 

Fractures

Bolt Shears 

Off

Bolt Shears 

Off

Fillet Weld 

Fractures
0

20406080

100120140160

0 0.2 0.4 0.

Horizontal Tensile Force Resistance of E

Horizontal Tensile Force Resistance of E

Truss travel distance (in)

Tensile force resistance (kip) 600oC 500oC 400oC 300oC 20oC 50oC 200oC 100oC

700oC

Gusset plate yields Gusset pla

Bolt shears o

Slip resistance 

bolt connection

At travel distan

truss walks off 
Horizontal Tensile Force Resistance of E

Horizontal Tensile Force Resistance of E

182

156

67

32

20C 400C 600C 700C

100 115

42

20

20C 400C 600C 700C

134 120

62

31

20C 400C 600C 700C

104 93

49

25

20C 400C 600C 700C

1411 

1411 

1411 

1411 

1411 

1411 

1411 

1411 

1411 

1511 

1411 

1411 

1311 

1311 

1313 

1013 1212 1212 1212 1611 1111 1111 1111 1111 1111 1111 1111

23 

23 

23 

23 

22 

22 

21 

21 

20 

20 226A, 

17 17 17 17 17 15 15

#1311, #1411, and #1511

#1013

#1212#1611#1111

For all interior seats 

44 34 9 4

20C 400C 600C 700C

134 120

62

31

20C 400C 600C 700C

#1313

182

156

67

32

20C 400C 600C 700C

Original drawing used with permission of PANYNJ
Vertical Force Resistance of Exterior Sea

Vertical Force Resistance of Exterior Sea

207

184

90

20C 400C 600C 

1411 

1411 

1411 

1411 

1411 

1411 

1411 

1411 

1411 

1511 

1411 

1411 

1311 

1311 

1313 

1013 1212 1212 1212 1611 1111 1111 1111 1111 1111 1111 1111

23 

23 

23 

23 

22 

22 

21 

21 

20 

20 226A, 

17 17 17 17 17 15 15

#1411 #1511 #1311 

#1013 and #1

#1212#1611

#1111

#20 #226A #15 and #17

#21 

#22 and #23 

385

343

167

76

20C 400C 600C 700C

226

201

98

45

20C 400C 600C 700C

94 84

60

27

20C 400C 600C 700C

187 167

82

37

20C 400C 600C 700C

94 84

45 

20C 400C 600C 

193 172

84

38

20C 400C 600C 700C

221

197

96

44

20C 400C 600C 700C

140 126

78

35

20C 400C 600C 700C

265

236

116

53

20C 400C 600C 700C

94 84

58

20C 400C 600C 

111 100

53 

20C 400C 600C 

Original drawing used w
Simplified Model of Exterior Truss 

Simplified Model of Exterior Truss 

Exterior column centerline 

4 n 

Beam elemMake gussetemperature

BCteC

Exterior seat model same as the interior seat

n3 2 n

1 n

n4
Single Truss with Floor Slab Analys

Single Truss with Floor Slab Analy

Goals:

 Capture the potential failure modes and failu

the truss under gravity when subjected to the

 Develop a simplified representation for full fl

model.

Failure Modes: 

 Material yield Member buckling Knuckle failure Truss seat failures

Analysis: 

 Nonlinear, inelastic analysis (ANSYS) under 

thermal load
WTC1, Floor 96 WTC1, Floor 96

143 144

507

Truss C32T1(most common)

Original drawing used with 
Single Truss with Floor Slab Model Single Truss with Floor Slab Model

 Exterior columns are fixed at 12 ft above and below 

floor slab.

 Channel supporting the interior truss seat is not mod

assumed to be rigid. 

 Bottom chord is supported laterally at bridging truss Damper is not included in the model.  Metal deck is not included in the model. Camber is not included in the model.

XY

Z

40 in.

52 in.

144 in.

144 in.
Loading Loading

Gravity loading includes:

 Self-weight of structure 8 psf superimposed dead load (SDL) 13.75 psf service live load (25% of the design 

live load of 55 psf)

Thermal Loading:

 Truss: ramped from 20°C to 700°C Slab: ramped from 20°C to 700°C 

at bottom of slab, and 20°C to 300°C attop of slab, linear gradient throughthickness

1CTRUSS-07c (Gravity Load 

300

344.444

38

ELEMENTSTEMPERATURESTMIN=300TMAX=700
Truss Vertical Deflection Truss Vertical Deflection

1

MN

Y XMX

Z

CTRUSS-08c (Gravity + Temperature : Dynamic analysis) 

-34.347

-30.458

-26.569

-22.68

-18.791

-14.902

-11.012

-7.123

-3.234

.655029

APR 17 2004

02:14:42

NODAL SOLUTIONSTEP=3SUB =330TIME=1.946UZ (AVG)RSYS=0DMX =34.382SMN =-34.347SMX =.655029

Node 540

-35-30-25-20-15-10

-5

0

0 200 4

Tempera

Displacement (in)

Node 540

diagonal buckling

knuckle failure
Column Horizontal Deflection Column Horizontal Deflection

Y

XZ

Node 3908

-0.6-0.4-0.2

0.00.20.40.60.8

0 200 4

Tempera

Displacement (in)

Node 3908

diagonal buckling

knuckle failure
Axial Stress Contour at Interior End Axial Stress Contour at Interior End

Displacement magnification factor = 1.
Axial Stress Contour at Exterior End Axial Stress Contour at Exterior End

Displacement magnification factor = 1.
Total Horizontal Reaction at Exteri

Total Horizontal Reaction at Exteri

XY

Z

-80000-60000-40000-20000

0

2000040000

0 200 

Temp

Total Horizontal Reaction Force (lb)

diagonal buckling
Thermal Response

Diagonal bars start to buckle at ~340 

0

C

 Maximum vertical deflection at truss center 7 Exterior column is pushed out 0.7 in. Top chord of truss yields due to differential t

between steel and concrete.

 Truss pushes against interior and exterior se Concrete slab pushes against interior core a

Knuckles start to fail at ~400 

0

C

 Maximum vertical deflection at truss center 1 Exterior column is pushed out a maximum o Shear studs on strap fail.
Thermal Response (cont.)

Interior Seat Bolt fails at ~500 

0

C

 Maximum vertical deflection at truss center 19.2 in Exterior column push reverses direction and outwa Truss pulls at the interior seat, while concrete slab 

interior core. 

 Truss still pushes against the exterior seat and con

against the spandrel.

 Catenary truss no longer restrains column inward 

Truss “walks off” the interior seat at ~650 

0

C

 Maximum vertical deflection at truss center is 32.6  Exterior column is pulled inward 0.3 in.  Truss has no support at interior seat. Concrete sla

and vertical support against the interior core.

 Exterior seat provides vertical support for the truss
Thermal Response (cont.)

Truss support fails at exterior column at ~660 

0

 Gusset plate fails in tension at 660 

0C.

 Vertical load carrying capacity of the fillet welds 

standoffs reduce due to added bending momen

 Strap breaks at 660 

oC.

 Fillet welds at the seat standoffs fail at 660 

oC.

 Truss loses the vertical support at the exterior c Concrete slab provides vertical and horizontal s

core.
Finite Element Model Translation Finite Element Model Translation
Translator Features & Program Features Translator Features & Program Features

The model translator is written in a 

combination of Tcl/Tk and ANSYS 

APDL commands.

This allows the program to work seamlessly 

within the ANSYS Graphical User Interface.

The translator utiliz

format requiring interaction.

Translation status i

track progress.

Summary report wi
WTC SAP WTC SAP-to-ANSYS Model Conversion ANSYS Model Conversion

SAP2000 text file is used as input to the translatorSpecific models translated include:

 A Typical Truss Floor System WTC 1 or 2 simplified full building model (translation 
Validation of Converted Models Validation of Converted Models

Validation through comparison of the converted ANSYS areference models.

 Reactions due to gravity load, Deformations due to gravity load,  Deformations due to arbitrary lateral load, and Natural frequencies and mode shapes.

0.695

(-3.2%)

Maximum Slab 0.718Displacement (in.)

2210.85

(-0.09%)

2212.8

1

Total Reaction (kip)

ANSYS

SAP (BEAM 188)

4.43

(+2.5%)

Dominant Natural Frequency 4.32of Floor (Hz)

5447.7

(-0.018%)

Total Mass (lb-sec2/in.) 5448.7

ANSYS

SAP (BEAM 188)
Full Floor Finite Element Model Full Floor Finite Element Model
Full Floor Model for Nonlinear Analysis Full Floor Model for Nonlinear Analysis

Double-to-Single TrussBeam Elements for ColumnsNonlinear MaterialsShell Modeling of Spandrel & Local Column VicinityBreak Elements

 Knuckles Truss Connections Interior and Exterior Truss

Seats

 Slab-to-Spandrel Connection
Full Floor Model for Nonlinear Analysis Full Floor Model for Nonlinear Analysis
Full Floor Model for Nonlinear Analysis Full Floor Model for Nonlinear Analysis
Full Floor Model for Nonlinear Analysis Full Floor Model for Nonlinear Analysis
Full Floor Model for Nonlinear Analysis Full Floor Model for Nonlinear Analysis
Long Span Truss in Full Floor Model with

Long Span Truss in Full Floor Model with

1

ELEMENTSTYPE NUM
Exterior Wall Finite Element Model Exterior Wall Finite Element Model
Exterior Wall Analysis Exterior Wall Analysis

Goals:

 Capture the potential failure modes and failu

the exterior columns under gravity loads and due to fires.

 Develop a simplified representation for globa

Failure Modes: 

 Column collapse due to large lateral deflecti Column buckling due to loss of lateral bracin Failure of column splice bolts and spandrel s

Analysis: 

 Nonlinear, inelastic analysis (ANSYS) under 

thermal load.
Exterior Wall Model Exterior Wall Model

1

Y XZ

SWALL-02 

ELEMENTSSEC NUMUROTACEL

Floor 91

150 158

Floor 99

Y

Z

X
Exterior Wall Model Exterior Wall Model

1SWALL-02 

ELEMENTSSEC NUM

BEAM189 elements for columns

SHELL181 elements for spandrels

10 elements

4 elements each side of splice
Column Splice Column Splice

• Exterior columns have column splices at every third floor.• Each splice consists of a butt plate on each column with (typ

connect the two plates.

• In the area of interest (floors 92 to 100) the butt plates are 1-

7/8” diameter A325 bolts. 

View of Splice in 

Detailed FEM

Outside

Inside Face

14”

Spandrel (at floor locations)

B(a

Column Cross Sectio

Not to Scale
Simplified Model of Column Splice Simplified Model of Column Splice

A simplified model of the column splice was developed to 

splice properties to be added to the line-element colu

 Tensile bolt flexibility. Rotational flexibility. Failure in rotation and axial tension due to bolt ten Temperature dependent bolt strength. Bolt shear failure is not modeled. Bolt pretension is not modeled as it plays only a m

stiffness.

Bolt tensile response is based on bolt tests.
Exterior Wall Model Loading Exterior Wall Model Loading

Gravity loads

Self-weight.Superimposed dead and live loads from fColumn loads from structure above mode

Transverse loads

Loads from thermal expansion of floors.

Loads from sagging floors.

Temperature loads

Thermal-time history distributions for vari

scenarios, including ASTM standard E11

Different levels of fireproofing considered

damaged fireproofing (bare steel).
Exterior Wall Analysis Exterior Wall Analysis

Analyses are in progress to determine failu

and sequences:

Under various fire scenarios, andFor various conditions of fireproofing

Results will be used to refine simplified wa

for global collapse analyses.
Task 3... Task 3...Results to date provide:

 Understanding of truss behavior (including c

elevated temperatures.

By the end of the month:

 Behavior and capacity of exterior columns u

scenarios.

 Behavior and capacity of floor system unde

Work has started on Task 3 to:

 Include damage estimates (from Project 2). Identify specific load redistribution paths for 

impact and various fireproofing conditions.

 Determine the contribution of local and subs

to aircraft impact and fire growth to the detestability.