Experimental and analytical progressive collapse assessment of a steel frame building

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Experimental and analytical progressive collapse assessment of a steel

frame building

Brian I. Song a, Halil Sezen b,⇑

a URS Corporation, Warrenville, IL, USAb Department of Civil and Environmental Engineering and Geodetic Science, The Ohio State University, Columbus, OH, USA

a r t i c l e i n f o

Article history:

Received 19 August 2011

Revised 19 June 2012

Accepted 31 May 2013

Available online 2 July 2013

Keywords:

Progressive collapse

Steel buildings

Column failure

Load redistribution

Collapse experiment

a b s t r a c t

A field experiment and numerical simulations were performed to investigate the progressive collapse

potential of an existing steel frame building. Four first-story columns were physically removed from

the building to understand the subsequent load redistribution within the building. Experimental data

from the field tests were used to compare and verify the computational models and simulations. Due

to the scarcity of data from full-scale tests, the experimental data produced during this research is a valu-

able addition to the state of knowledge on progressive collapse of buildings. The progressive collapse

design guidelines typically recommend simplified analysis procedures involving instantaneous removal

of specified critical columns in a building. This paper investigates the effectiveness of such commonly

used progressive collapse evaluation and design methodologies through numerical simulation and exper-

imental data.

2013 Elsevier Ltd. All rights reserved.

1. Introduction

Progressive collapse is generally defined as small or local struc-

tural failure resulting in damage and failure of the adjoining mem-

bers and, in turn, causing total collapse of the building or a

disproportionately large part of it. Progressive collapse of building

structures is initiated by loss of one or more vertical load carrying

members, usually columns. After one or more columns fail, an

alternative load path is needed to transfer the load to other struc-

tural elements. If the neighboring elements are not designed to re-

sist the redistributed loads, failure will happen with further load

redistribution until equilibrium is reached, resulting in partial or

total collapse of the structure.

Progressive collapse is triggered by abnormal loading that

causes local failure of one or more columns if the building lacks

sufficient ductility, continuity and/or redundancy. The local orcomplete collapse may cause significant casualties and damage

disproportionate to the initial failure. A notable example is partial

collapse of the Ronan Point apartment building in London. An acci-

dental gas explosion in a corner kitchen on the 18th floor initiated

progressive collapse of the 24-story building in 1968. This event

triggered extensive progressive collapse research and led to devel-

opment of design guidelines for the prevention of progressive

collapse [13].

The World Trade Center 7 (WTC 7) in New York City was a 47-

story office building adjacent to the WTC towers (WTC 1 and 2)that collapsed following the terrorist attacks of September 11,

2001. WTC 7 collapsed several hours after the collapse of twin

WTC towers. The NIST report [11] concluded that: ‘‘An initial local

failure occurred at the lower floors (below floor 13) of the building

due to fire and/or debris induced structural damage of a critical

column (the initiating event) which supported a large span floor

bay with an area of about 2000 square feet. Vertical progression

of the initial local failure occurred up to the east penthouse, as

the large floor bays were unable to redistribute the loads, bringing

down the interior structure below the east penthouse. Horizontal

progression of the failure across the lower floors triggered by

damage due to the vertical failure, resulting in a disproportionate

collapse of the entire structure.’’ The FEMA 403 [6] study empha-

sized the significance of fires on the collapse. This is a good exam-ple of disproportionate collapse caused by debris and/or fire

induced failure of a column or columns in a tall steel building. In

this research, several columns were sequentially removed from a

building, which can resemble the initial debris damage and gradual

and intensifying fire damage or a various other loads.

Failure of one or more columns in a building and the resulting

progressive collapse may be a result of a variety of events with dif-

ferent loading rates, pressures or magnitudes. The magnitude and

probability of natural and man-made hazards are usually difficult

to predict. Therefore, most of the current progressive collapse

design guidelines are threat-independent and do not intend to

prevent such local damage, e.g., ACI 318 [1]. Rather, their purpose

0141-0296/$ - see front matter 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.engstruct.2013.05.050

⇑ Corresponding author. Tel.: +1 614 292 1338.

E-mail addresses: [email protected] (B.I. Song), [email protected] (H. Sezen).

Engineering Structures 56 (2013) 664–672

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is to provide a level of resistance against disproportionate collapse

and to increase the overall structural integrity. Design guidelines

typically require minimum level of redundancy, strength, ductility

and element continuity. The codes typically prescribe simplified

analysis procedures requiring instantaneous removal of certain

critical columns in a building, e.g., GSA [8]. In this paper, effective-

ness of such commonly used progressive collapse evaluation and

design methodologies is investigated through numerical simula-

tions and experimental testing of the building.

A large number of numerical studies have been conducted to

evaluate the effectiveness and consistency of the current progres-

sive collapse design guidelines. However, very limited experimen-

tal research has been performed to validate the results of these

computational studies and to verify the methodologies prescribed

in the guidelines. This is mainly because it is difficult to construct

and test full-scale building specimens and such large-scale testing

is discouragingly expensive. In this study, an existing steel frame

building, Ohio Union building, was tested by physically removing

four first-story columns. The building was instrumented and the

experiment was conducted prior to its scheduled demolition. The

building was also modeled and analyzed using the computer pro-

gram, SAP 2000 [15], following the requirements of the current

progressive collapse evaluation and design guidelines. The results

from static and dynamic analysis of the building were compared

with the experimental data.

2. Progressive collapse guidelines

American Society of Civil Engineers (ASCE 7, [3]), General Ser-

vices Administration [8], Department of Defense (Unified Facilities

Criteria, [4], and National Institute of Standards and Technology

[12] have developed criteria and guidelines to evaluate, design

and improve structural integrity and progressive collapse resis-

tance of existing and new buildings. ASCE 7 [3] provides design

load combinations including abnormal loads and associated

probabilities. It also presents general direct and indirect design ap-proaches to ensure structural integrity following local damage to a

primary load-carrying member. In this paper, the collapse resis-

tance of the test building is evaluated using the load combinations

recommended by the ASCE 7 standard and GSA guidelines [8].

General Services Administration [8] provides guidelines for

evaluation of existing buildings and design of new buildings

against progressive collapse. A simplified threat independent

methodology is recommended for buildings with fairly regular

plans and up to ten stories above ground. A linear elastic static

analysis of the building is required after the instantaneous removal

of a first story column located near the middle of longitudinal and

transverse perimeter frame or at the corner of the building. Pro-

gressive collapse and possible subsequent failure of elements are

investigated using the calculated demand-to-capacity ratio (DCR)

for each structural element. DCR is defined as the ratio of the force

(moment, shear, or axial force) calculated after the instantaneous

loss of a column and the corresponding capacity of the member.

In this study, the test building was analyzed using the load combi-

nations specified by the GSA and the corresponding DCRs were cal-

culated. The acceptance criteria provided by the GSAwas then used

to assess the potential for progressive collapse.

3. Building experiment

The Ohio Union building, shown in Fig. 1, was located on the

Ohio State University campus. The four-story moment frame build-

ing was constructed in 1950. The building included a rectangular

floor plan with three columns on each transverse axis and ninecolumns along the longitudinal axes. Column and beam section

properties and the longitudinal test frame geometry are shown

in Table 1 and Fig. 2, respectively. In Table 1, the first and last num-

bers are the depth (in inch units) and nominal weight (lb/ft) of the

columns or beams, respectively (1 in. = 25.4 mm, 1 ft = 305 mm,

and 1 lb = 4.448 N). The letters WF and B are wide-flange (WF)

shaped I-beam and light I-beam, respectively, which were com-

monly used in the 1950s [2].

Before the building’s demolition, four first-story columns were

removed in the following order: (1) two columns near the middle

of the longitudinal perimeter frame, (2) column in the building cor-

ner, and (3) column next to the corner column. As shown in Figs. 1

and 3, four of the nine exterior columns were first torched near the

top and bottom. Only a small portion of the flange was left intact

when the cross sections were cut. The middle column segment be-

tween the torched sections was then pulled out by a bulldozer

using a steel cable (Fig. 3).

The columns were removed within a very short time period

representing an instantaneous column removal as recommended

in the design guidelines. As shown in Fig. 4, 15 strain gauges were

installed on the columns and beams closely linked to the removed

columns to monitor the redistribution of gravity loads using the

change in strains measured during the removal of columns. During

the column removal process, a portable data acquisition system

and a scanner connected to a laptop computer recorded the strains.

No significant visible damage was observed in the building even

after the four columns were removed. Detailed description of the

test building, instrumentation, experimental procedure and re-

corded data can be found in Song [16].

During the field experiment, strains in members neighboring

the removed columns were measured as each column was torched

and removed. In this study, universal general purpose strain

gauges with a resistance of 120 ± 0.3% Ohms were used. All strain

values dropped to negative values after each column was torched

or removed, and then stabilized after a certain amount of time.

These negative strain values indicate that the structural members

contracted and compressed when the neighboring columns were

torched. Most of the measured strain values dropped more whenthe columns were torched than when they were removed during

the experiment. The largest drop of strain values was observed

when the last column was torched.

4. Analysis procedures and results

Numerical simulations of the test building were performed

using the computer program SAP2000 [15] to investigate the

progressive collapse performance of the building. At the time of

testing, the frames carried only dead loads due to weight of walls,

slabs, beams, and columns. In the linear static analysis, the dead

loads were multiplied by 2.0 as recommended in the GSA guide-

lines [8]. The live load was assumed to be zero in all analysesbecause the test building was not occupied, and most of the parti-

tions, furniture and other non-structural loads were removed from

the building. To calculate the dead load of the walls, densities of

glass and brick were assumed to be 2579 kg/m3 and 1920 kg/m3,

respectively. Properties of frame members were obtained from

the original structural drawings and design notes. Yield strength

of all frame members of the Ohio Union building was assumed to

be 345 MPa (50 ksi), as specified in the original design drawings.

Details of the modeling and analysis assumptions and results are

reported in Song [16] and Song et al. [17,18].

Two-dimensional (2-D) as well as three-dimensional (3-D)

models of the building were developed to analyze and compare

the progressive collapse response. Fig. 5 shows 2-D and 3-D

SAP2000 models of the Ohio Union building with frame membernumbers. As in the actual building experiment, four circled

B.I. Song, H. Sezen/ Engineering Structures 56 (2013) 664–672 665

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columns were sequentially removed in the following order: col-

umns 27, 22, 2, and 7.

Linear static, nonlinear static, linear dynamic, and nonlinear

dynamic analysis methods, in order of increasing complexity, can

be used to analyze a structure to investigate its structural behavior.

Researchers investigated the advantage and disadvantage of eachof these procedures for progressive collapse analysis [14]. A com-

plex analysis is desired to obtain more realistic results represent-

ing the actual nonlinear and dynamic response of the structure

during the progressive collapse. However, both GSA and DOD

guidelines recommend the simplest method, linear static, for the

progressive collapse analysis since this method is cost-effective

and easy to perform. One of the objectives of this paper is to

Fig. 1. (a) Building before demolition, (b) four first-story columns exposed, (c) columns removed, and (d) building during the gradual demolition process.

Table 1

Column and beam sections of the Ohio Union building.

Column section Beam section

Column number Column type Beam number Beam type

C1 10 WF 72 B1 24 B 76

C2 12 WF 133 B2 21 B 68

C3 12 WF 120 B3 16 B 58

C4 10 WF 100 B4 21 WF 62

C5 10 WF 89 B5 18 WF 50

C6 10 WF 54 B6 14 B 17.2

C7 10 WF 112 B7 14 B 22

C8 10 WF 60 B8 24 WF 76

C9 10 WF 33 B9 18 WF 45

Fig. 2. Longitudinal frame elevation including beam and columns sections (see Table 1).

666 B.I. Song, H. Sezen / Engineering Structures 56 (2013) 664–672


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compare the simplest and most complicated analysis procedures

(i.e., linear static and nonlinear dynamic procedures) for the eval-uation of progressive collapse potential of the test building.

4.1. 2-D linear static analysis

Linear static analysis is a simple and commonly used method to

investigate progressive collapse potential of a building [3], and [8].

Fig. 6 shows the elastic moment diagrams after the removal of each

column from the Ohio Union building. When the first two columns

were removed, the largest bending moments were localized and

typically occurred in the members above or immediately next to

the removed columns. The maximum moments significantly in-

creased and spread within the frame when three and four columns

were removed.

Demand-to-capacity ratios (DCR) were calculated for eachframe member, and the building response was evaluated by

comparing the calculated DCR values based on the recommenda-

tions of GSA guidelines. DCR for moment is defined as the ratioof the maximum moment demand M max of the beam or column

calculated from linear elastic analysis to its expected ultimate

moment capacity M p, which is calculated as the product of plastic

section modulus and yield strength. In M p calculations for columns,

the effect of the axial load is neglected because the column axial

loads were relatively small and did not significantly affect the

moment capacity of the cross section.

DCR ¼ M maxM p

ð1Þ

Fig. 7 shows the moment diagram and the corresponding

maximum DCR values at the end of each beam and top of each

column after four columns were removed from the frame. The

columns in the top story had higher DCR values, indicating thatafter removal of columns additional loads were transferred

Fig. 3. Before and after removal of middle part of a column.

Fig. 4. Plan view of strain gauge placement in Ohio Union building with columns and beam labeled (15 strain gauges are shown in the circles).


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upward as well as to the adjacent spans. Smaller cross section

used in the top story columns is another reason for the higher

DCR values observed in the top story. As shown in Fig. 7, the

maximum DCR value of 2.83 was calculated in Column 10 in

the top story. The maximum calculated beam DCR value was0.94 in beam 63 in the third floor level.

Fig. 8 shows DCR values for each frame member for all column

removal cases. Frame member numbers up to 45 are columns, and

beams are numbered from 46 to 85 (Fig. 5a). After the first column

was removed, DCR values for all columns and beams were below

0.5. The DCR values after the loss of second column was similarto those of third column loss, all of which were less than 1.5. The

Fig. 5. (a) Two-dimensional SAP2000 model with frame member numbers and (b) three-dimensional SAP2000 model of the Ohio Union building (circled columns are

removed in the order shown).

Fig. 6. Moment diagrams: (a) after one column was removed, (b) after two columns were removed, (c) after three columns were removed, and (d) after four columns were

removed.



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DCR values for columns were remarkably increased after the fourth

column was lost. Columns were impacted more than beams when

all four columns were removed from the frame. As acceptance cri-

teria, the maximum DCR limits specified in GSA [8] are 2.0 and 3.0

for columns and beams for the test building, respectively. After all

four columns were removed, no beams and five columns (i.e., col-

umns 8, 9, 10, 20 and 25) exceeded the DCR criteria. The change in

DCR values for beams was not significant compared with that of

columns. The DCR values of beams were always less than 1.0. This

is probably due to potential redistribution of loads to the adjacent

beams in the analyzed frame.

After four columns were removed, the building was more

susceptible to progressive collapse. This was also reflected in the

maximum displacements calculated from linear static analysis.

As columns were sequentially removed, the maximum vertical dis-

placements were calculated as 11.40, 11.54, 30.73, and 17.93 cm at

the joints immediate above the first (column 27), second (column

22), third (column 2) and forth (column 7) removed columns,

respectively.

4.2. 2-D nonlinear dynamic analysis

Progressive collapse is a dynamic event involving vibration of

building elements and resulting in internal dynamic forces affected

by inertia and damping. Progressive collapse is inherently a

nonlinear event in which structural elements are stressed beyond

their elastic limit to failure. Nonlinear dynamic procedure reflectsthe dynamic and nonlinear aspects of the progressive collapse

phenomenon and therefore nonlinear dynamic analysis is more

realistic and accurate than linear static analysis.

In nonlinear dynamic analysis, a major load bearing structural

element is removed dynamically and the structural material is al-lowed to undergo nonlinear behavior. Fig. 9 illustrates the replace-

ment of a removed column by equivalent loads in nonlinear

dynamic analysis. First, the building is modeled with its dead load

assigned. After the internal (equivalent) forces in a given column

are determined from static analysis, the column is replaced with

its equivalent forces to simulate the instantaneous removal of

the column. As shown in Fig. 10, the equivalent load is first as-

signed with a uniform time history function. This corresponds to

the initial case where the column is still in place and carrying

the dead load. Then the column is suddenly removed using a step

function. The sum of a uniform time history function and the col-

umn loss function represents the column loss. This is referred to

as a time-history analysis where the response of the structure is

calculated during and after the removal of column(s) as a functionof time.

In this study, both geometric and material nonlinear behaviors

were considered in the nonlinear dynamic analysis. Material prop-

erties such as yield strength, ultimate strength, and ductility were

important parameters to design a building model. P -Delta effect

was considered as a geometric nonlinearity. Also, several dynamic

and nonlinear parameters including time step, damping ratio, and

plastic hinges was defined before performing nonlinear time his-

tory analysis.

The vertical displacements of the joints above each removed

column were calculated during and after removal of each column

in the first story. Fig. 11 shows the vertical displacement history

of Joint 1, 2, 3, and 4 above the first (column 27), second (column

22), third (column 2), and fourth (column7) removed columns,

respectively (Fig. 5a) after the removal of fourth column. The col-

umns were removed at time of 0 s and negative values indicate

0.32

0.38

0.34

2.25

2.14

2.83

1.21

1.56

2.38

0.22

0.45

0.89

1.10

0.16

1.54

1.44

2.24

0.63

0.41

0.45

0.17

0.35

0.37

0.07

0.45

0.44

0.86

0.11

0.14

0.12

0.17

0.03

0.47

0.40

0.39

0.21

0.91

0.82

0.77

0.51

0.58

0.56

0.49

0.24

0.94

0.83

0.80

0.91

0.07

0.00

0.15

0.09

0.48

0.42

0.32

0.40

0.56

0.55

0.42

0.41

0.34

0.26

0.27

0.18

Fig. 7. Moment diagram and corresponding DCR values after the loss of four columns in the Ohio Union building.

Fig. 8. Change in DCR values of each frame member for all cases.

Fig. 9. Column removal load representation for nonlinear dynamic analysis.


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downward displacements. As shown in Fig. 11, the joints above the

four removed columns settled at the permanent displacements of

6.05, 6.12, 17.93, and 9.98 cm, respectively. The maximum

transient vertical displacements calculated from 2-D nonlinear dy-

namic analysis were 7.11, 7.24, 20.47, and 11.33 cm at Joint 1, 2, 3,

and 4, respectively.

4.3. Comparison of results from 2-D and 3-D analyses

A 3-D model of the Ohio Union building was developed, and

progressive collapse analysis was performed using this model.

Fig. 12 shows a comparison of DCR values for moments determined

from 2-D and 3-D models after four columns were removed. In 2-D

linear static analysis, columns were more impacted than beams.Five columns exceeded the DCR criteria of 2.0 [8], but none for

the beams after four columns were removed. The DCR values of

all beams were less than 1.0, and the maximum DCR value ob-

served in beams was 0.94. However, DCR values calculated from

3-D linear static analysis showed an opposite trend compared to

2-D results. Beams were more influenced by the column loss. The

maximum DCR value of beams was 1.49 while that of columns

was 0.96. The reason that beams had higher DCR values than

columns in the 3-D linear static analysis was possibly due to the

larger deformation and participation of beams in the transverse

direction. It was found that beams, especially in the top story, were

significantly deformed in the transverse direction after each col-

umn removal. 2-D linear static analysis may lead to limited and

underestimated demands for beams.

More interestingly, it was observed that DCR values calculated

from the 3-D linear static analysis were smaller than those from

2-D linear static analysis for columns and most beams. As shown

in Fig. 12, all members had DCR values of less than 1.5, and satis-

fied GSA acceptance criteria of 2.0 for columns and 3.0 for beams.This could be mainly due to contribution of transverse beams. The

transverse beams can distribute loads to the connected columns

and beams in the transverse direction, leading to a decrease of

force demands in structural members.

Table 2 shows the comparison of maximum vertical displace-

ments calculated from 2-D and 3-D analyses. 3-D models showed

lower maximum displacements than 2-D models for both linear

static and nonlinear dynamic analysis. Similar to the DCR results,

the transverse beams connected to the interior columns and the

beams increased the overall resistance of structure, leading to

smaller deformations in the 3-D model. As shown in Table 2, Linear

static analysis resulted in higher maximum vertical displacements

than nonlinear dynamic analysis in both 2-D and 3-D models. For

example, the maximum vertical displacement calculated from2-D linear static analysis was 30.73 cm at Joint 3 while that from

Fig. 10. Time history function for column loss simulation.

Fig. 11. Displacement of joints above each removed column after all columns wereremoved.

Fig. 12. Comparison of DCR values determined from 2-D and 3-D linear static

analysis after removal of four columns.



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the 2-D nonlinear dynamic analysis was 20.47 cm. It seems that

the impact factor of 2 (i.e., dead loads multiplied by 2) in linear sta-tic analysis led to very conservative results. Marjanishvili reported

that a more complicated analysis method such as nonlinear dy-

namic analysis may result in less severe structural response, due

to more accurate estimates of load distribution and less stringent

evaluation criteria.

Table 3 shows plastic hinge rotations at the location where

columns were removed after four columns removal. Plastic hinge

rotation was chosen as acceptance criteria for the nonlinear

dynamic analysis [8], which also possibly evaluates whether the

moment connection of the frame is strong enough to survive the

excessive moment rotation of the joints. Plastic hinge rotation

angle for beam members on each side of the removed column

can be measuredbetween horizontal line and tangent to maximum

deflected shape, which is defined by Eq. (2).

h ¼ tan1 dmax

L

ð2Þ

where h is the maximum hinge rotation, dn the maximum displace-

ment of columns at the location where the column is removed, and

L is thebeamlength or column spacing in the longitudinal direction.

As shown in Table 3, hinge rotations calculated from the 3-D

model were smaller than those from the 2-D model, because of

lower maximum displacement values in 3-D nonlinear dynamic

analysis. The maximum plastic hinge rotation was only 1.80 at

the hinge above third removed column (Column 2) in linear static

analysis. For both 2-D and 3-D nonlinear dynamic procedure, the

values of plastic hinge rotation were much smaller than 12 of GSA [8] criteria, indicating that the Ohio Union building was not

susceptible to progressive collapse. Considering that no significant

deformations were observed during field testing, GSA criteria for

plastic deformations or hinge rotations may be more realistic than

the GSA criteria for force demands or DCR values.

4.4. Comparison of calculated and measured strains

Table 4 shows changes in strain (De) obtained from the field

test, compared with those calculated from 2-D and 3-D models.

During the field test, strain values changed as each column was

torched and removed. De (Field Test) reported in Table 4 are the

changes in strain values recorded by the strain gauges in the field

after the last column torching. De (Computational Model) is the

changes in strain values after the last column removal. De is calcu-

lated by considering the combined effect of axial load and a bend-

ing moment, both of which were determined from the SAP2000

analysis. Details of calculations and assumptions are reported in

Song [16].Total of fifteen (15) strain gauges were used in this experiment

(see Fig. 4). Table 4 compares selected strain measurements and

analytical model results. Six strain gauges were selected since

strain gauges 1, 3, 7, 10 and 12 are attached to the same columns

of the selected gauges 2, 4, 8, 9 and 11, respectively, and strain

gauges 5, 6, 13 and 14 were attached above the removed columns.

The strain gauges on the same column showed very similar strain

measurements. The strain gauge 15, attached on Beam 67, was

selected from the experimental study to compare the results from

2-D and 3-D models because it was the only strain gauge left in the

perimeter frame in the 2-D model after the four columns were

removed (location of strain gauges are shown in Fig. 4). Strain

gauges 2, 4, 8, 9 and 11 were attached on the interior columns.

As shown in Table 4, for strain gauge 15 attached on Beam 67,De calculated from the 3-D model was closer to the experimental

result than that from the 2-D model. 3-D model can account for

redistribution of the building’s weight to both exterior and interior

Table 2

Comparison of vertical displacement (cm) after all columns removal.

Joints above removed columns 2-D model 3-D model

Linear static analysis Nonlinear dynamic analysis Linear static analysis Nonlinear dynamic analysis

Maximum Permanent Maximum Permanent

Joint 1 11.40 7.11 6.05 7.85 4.22 3.66

Joint 2 11.53 7.24 6.12 7.95 4.27 3.71

Joint 3 30.73 20.47 17.93 10.03 5.64 5.08 Joint 4 17.93 11.33 9.98 7.37 3.68 3.38

Table 3

Plastic hinge rotations (h, degree) at the location where each column was removed after all columns removal.

Removed columns 2-D nonlinear dynamic analysis () 3-D nonlinear dynamic analysis ()

Joint 1 0.53 0.31

Joint 2 0.54 0.32

Joint 3 1.80 0.50

Table 4

Comparison of change in strain (De) obtained from the field test after last column torching with that calculated from 2-D and 3-D analyses after all columns removal (% difference

was indicated in parentheses).

Strain gauge Field test 2-D model 3-D model

Linear static analysis Nonlinear dynamic analysis Linear static analysis Nonlinear dynamic analysis

2 (Column) 55 106 – – 165 106 (200%) 32 106 (42%)

4 (Column) 37 106 – – 121 106 (227%) 17 106 (54%)

8 (Column) 29 106 – – 34 106 (17%) 4 106 (86%)

9 (Column) 28 106 – – 104 106 (271%) 20 106 (29%)

11 (Column) 33 106 – – 49 106 (48%) 7 106 (79%)

15 (Beam) 37 106 118 106 (219%) 64 106 (73%) 53 106 (43%) 46 106 (24%)


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columns and beams while only exterior members were considered

in the 2-D model. All of De values calculated from the 3-D models

were very comparable to the measured strains.

Fig. 13 compares strain values (De) measured in the field and

calculated from linear static and nonlinear dynamic analyses after

all columns were removed. For the interior columns (i.e., Strain

gauge 4) and the beam (i.e., Strain gauge 15), the measured strains

were closer to the De values calculated from the nonlinear dy-

namic analysis. The strain increments (De) calculated from the lin-

ear static analysis were much larger than the measured values. It

should be noted that the linear static analysis was performed by

amplifying the gravity (dead) loads by a factor of 2.0 following

the recommendations of GSA [8] while the unfactored dead load

was used in dynamic analysis. If the unfactored dead loads wereused in the linear static analysis, the calculated strain would be re-

duced by half to approximately 0.00006, which is still larger than

the maximum measured strain.

5. Conclusions

Progressive collapse performance of an existing steel frame

building was evaluated by physically removing four first-story col-

umns from the building and by performing linear static and nonlin-

ear dynamic analysis of the building. The following conclusions

were reached during this study based on the evaluation of experi-

mental data and structural analysis of the test building.

The measured strain data compared relatively well with the

analysis results. In particular, 3-D model was more accurate than

the 2-D model, because 3-D models can avoid overly conservative

solutions as well as account for 3-D effects such as contribution of

transverse beams to overall resistance of the frame. The 3-D model

had lower DCR values and vertical displacements than 2-D model,

which was possibly due to inclusion of transverse beams in the 3-D

model. The 3-D model is believed to be more realistic than 2-D

model for the progressive collapse analysis.

The strain values calculated from the nonlinear dynamic analy-

sis were smaller than those from the linear static analysis, and

were closer to the measured strains. Also, linear static analysis

showed higher DCR values and vertical displacements than nonlin-

ear dynamic analysis for both 2-D and 3-D models. The amplifica-

tion factor of 2 required for the dead load in linear static analysis

may lead to very conservative analysis results.

For future research, it would be better to consider the actual

material properties and connections of the building in the analyt-

ical models in order to obtain more reliable results.

Acknowledgements

This research was partially funded by the National Science

Foundation (CMMI 0745140), American Institute of Steel Construc-

tion, and URS Corporation; this is gratefully acknowledged. The

authors would like to thank SMOOT Construction, Loewendick

Demolishing Contractors, and the Ohio State University for provid-

ing access to the test building and help with the experiment.

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Fig. 13. Comparison of calculated strains and strain measured by (a) Strain Gauge 4

and (b) Strain Gauge 15 after all columns were removed.


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Experimental and analytical progressive collapse assessment of a steel frame building