Analysis Procedures 

For 

Progressive Collapse of Buildings 

by 

H. S. Lew 1

1

 Building and Fire Research Laboratory, National Institute of Standards and Technology, Gaithersburg, 

Maryland, U.S.A 20899-8611 

ABSTRACT 

This paper presents simple analytical approaches 

for evaluating progressive collapse potential of 

low- and mid-rise buildings that could be used in 

routine design by design professionals. 

Although nonlinear time history analysis would 

be more realistic in representing progressive 

collapse phenomenon, high fidelity structural 

models to represent nonlinear structural behavior 

are required to produce accurate results. In 

routine design of low- and mid-rise buildings, 

simple static procedures with appropriate 

acceptance criteria would be more suitable for 

evaluating progressive collapse potential. 

KEYWORDS: analysis; buildings; collapse; 

failure; linear; nonlinear; progressive collapse; 

static procedures. 

1. INTRODUCTION

In recent years, there has been heightened 

awareness among building owners and U.S. 

government agencies of collapse of buildings in 

a “progressive” manner. Because buildings that 

collapse in a progressive way could lead to a 

catastrophic event, a large number of deaths and 

injuries and loss of properties, many owners of 

high-rise buildings and government agencies are 

interested in evaluating the progressive potential 

of existing buildings and in designing new 

buildings to resist progressive collapse. The 

National Institute of Standards and Technology 

(NIST) is working with design professionals, 

researchers, building owners, building regulators, 

and building code and standard developing 

organizations to develop guidelines for 

analyzing buildings to resist progressive 

collapse. 

Progressive collapse is defined as the spread of 

an initial failure from element to element, 

eventually resulting in the collapse of an entire 

structure or a disproportionately large part of it 

[ASCE 2002]. When local failure of primary 

structural members propagate to failure of 

adjoining members, progressive collapse will 

ensue unless adjoining structural members arrest 

further progression of failure. For example, if a 

column in a multi-story framed building is 

destroyed due to explosion, structural members 

above the failed column will sustain large 

displacements instantaneously, and also will fail 

unless the beams that are framed to the column 

develop a catenary response to arrest collapse of 

the floor area that was supported by the failed 

column. 

Progressive collapse is a dynamic and nonlinear 

event, as it takes place in a very short time frame 

and structural members undergo nonlinear 

deformation before failure. To analyze 

rigorously progressive collapse potential of a 

structure, nonlinear dynamic analysis should be 

performed to account for energy dissipation, 

large inelastic deformations, materials yielding, 

cracking and fracture. However, the nonlinear 

dynamic analysis requires step-by-step 

integration which is very time consuming. 

Furthermore, because of the general lack of 

structural behavior data especially related to 

beam to column connections of both steel and 

NIST Special Publication 1025

This publication is available free of charge from:

http://dx.doi.org/10.6028/NIST.SP.1025
concrete, it is difficult to evaluate the results of 

the analysis. As a result of these reasons,

nonlinear dynamic analysis is not used in routine

design and analysis of low- and mid-rise 

buildings, which account for nearly 93 percent 

of buildings in the U.S. 

For buildings of 10 stories or less in height with 

relatively simple layouts, both the U.S. General 

Services Administration [GSA 2003] and the 

Interagency Security Committee [ISC 2001]

recommend the alternate load path method be 

used to assess the vulnerability of new and 

existing buildings to progressive collapse. This 

prescriptive method requires a check of the

capability of the structural system to resist

removal of a specific critical structural member.

Analytical procedures that could be used for the 

alternate load method are presented in this paper. 

2. Analysis Procedures 

2.1 Linear Static Analysis 

The response of a structure to redistributed loads 

following the sudden loss of a critical loadcarrying member is dynamic and nonlinear. 

However, as in seismic design, one simple

approach is to use an equivalent static elastic

analysis if buildings have relatively simple 

layouts and do not fall in the following 

categories: 

a) Buildings that utilize a combination of 

frames and walls in the structural 

systems, 

b) Buildings with vertical discontinuities in

columns and walls, which utilize 

transfer girders, 

c) Buildings that have a large variance in 

structural bay size, 

d) Buildings that have plan irregularities, 

and 

e) Buildings that have closely spaced 

columns, which can lead to uncertainty 

in the application of a simplified

analysis. 

A more sophisticated analysis, such as nonlinear dynamic analysis, is required for buildings

that have the above structural characteristics, (a) 

through (e). 

When performing a static analysis, the 

characteristic loads to be applied to the structure

are: 

Load = 2 (DL + 0.25 LL) (1) 

where 

DL = dead load 

 LL = live load. 

For the load combination in Eq. 1, only 25

percent of the live load is used since the

probability of that full live load being present 

during a progressive collapse event is small. An

amplification factor of 2 is applied to the load 

combination to account for dynamic effects. 

After the static analysis, a demand-capacity ratio 

(DCR) is computed for each of the structural 

members in the building. 

DCR = 

CE

UD

Q

Q

where 

QUD = force (bending moment, axial force, 

shear force) determined in a component 

or connection from the analysis 

QCE = expected ultimate, unfactored capacity 

(bending moment, axial force, shear

force) of the component or connection. 

In the analysis, design material strength may be 

increased by a strength-increase factor to

account for expected actual strength of materials. 

For reinforced concrete members, this factor

could be taken as 1.5. For steel members this 

factor may vary from 1.05 to 1.10, depending on

types and age of steel. 

Using the DCR criteria, structural members and

connections that have DCR values greater than 

2.0 are considered to be severely damaged or 

collapsed [GSA 2003]. In the case of shear 

forces, failure is imminent when the DCR value 

exceeds 1.0. 

Once the DCRs have been computed, the extent 

of damage or collapse can be determined. GSA 

specifies that the maximum allowable area of
collapse resulting from the instantaneous 

removal of an exterior column (or wall ) shall be 

smaller of the following two areas: (1) the 

structural bay directly associated with the 

removed column or (2) 170 m2

 (1830 ft2) at the 

floor level directly above the removed column. 

Similar limits are given areas based on the 

removal of an interior column. 

An interim design guide for buildings to resist 

progressive collapse proposed by the 

Department of Defense [UFC 2004] also 

considers the characteristic loads for the 

equivalent static load analysis. 

 Load = 1.0 DL + 0.5 LL + 0.2 WL (2) 

where 

WL = wind load per ASCE 7-02. 

Equation 2 does not include the dynamic 

amplification factor but includes 20 percent of 

the wind load. 

Instead of calculating the demand capacity ratio 

DCR, the Uniform Facility Criteria (UFC) 

requires iterative analyses for linear elastic static 

methods. For example, when a structural 

member that cannot sustain a constant moment, 

that member is removed if the internal moment 

exceeds the flexural design strength. The loads 

associated with the member are doubled and 

redistributed to the member below, and analysis 

is repeated. This corresponds to the sequential 

removal of members when their ultimate 

moment capacities are exceeded and replacing 

them with fixed moments equal in magnitude to 

their ultimate moment capacity, then reanalyzing 

the remaining structure. At the conclusion of 

analysis, the extent of damage is quantified, 

which is similar to the GSA requirements. For 

removal of a column on the exterior envelope of 

the building, the local damaged area of the floor 

directly above or below the removed member 

must be les the 70 m2

 (750 ft2) or 15 percent of 

the floor area, whichever is smaller. 

While the linear static analysis is relatively 

simple, it approximates to the behavior of the 

actual building performance and may sometimes 

mask hazardous dynamic effects. The linear 

static analysis cannot account for the 

redistribution of forces, nonlinear material 

properties, and the development of membrane 

modes of resistance. Thus, this approach, in 

general, would produce conservative designs. 

2.2 Nonlinear Static Analysis 

In nonlinear static analysis, geometric 

nonlinearlity resulting from large deformations 

can be accounted for through the redistribution 

of loads as a result of the removal of a critical 

column (Fig. 1), and the structure attempts to reequilibrate to the larger spans through a change 

in behavior from a flexural response to a 

membrane response. In analysis the loads are 

applied in steps starting at zero to the total load 

level as defined by Eq. 2. At least 10 steps are 

recommended by UFC [UFC 2004]. At the end 

of the analysis, the predicted forces, moments, 

shears and deformations must be checked 

against the acceptance criteria (Table 1). 

If none of the structural members and 

connections violates the acceptance criteria, the 

analysis is complete and satisfactory resistance 

to progressive collapse has been demonstrated. 

If one or more members violate the acceptance 

criteria, the analysis is repeated with a modified 

structural model by removing failed structural 

members, and the load is applied incrementally 

again. This incremental/iterative process 

continues until the structural model stabilizes. If 

the collapse process cannot be stopped, then the 

structure must be re-designed and re-analyzed. 

If the structural model does stabilize, then the 

performance criteria of the damaged area must 

be checked. 

Nonlinear analyses depend on an accurate 

representation of material behavior to represent 

inelastic response. Of particular importance is 

the actual behavior of the joints as they undergo 

inelastic deformation. Nonlinear springs 

representing the behavior of the joints are 

required. 

Nonlinear analyses require reasonably detailed 

finite element models to represent nonlinear 

behavior of the structure, and are time 

consuming because the need for step-by-step 
increases of vertical loads until maximum loads 

are attained or until the structure collapses. 

3. Conclusion 

The potential progressive collapse analysis 

entails evaluating a structure for its vulnerability 

to the development of a partial or a total collapse 

of the structure initiated by an event that causes 

local damage. At the present time, there are no 

accepted simple analytical tools that design 

professionals could use to analyze progressive 

collapse potential of low- and mid-rise buildings. 

Although there are high-performance finite 

element analysis tools are available, they are not 

widely used due mainly to the lack of familiarity 

with the structural behavior associated with 

progressive collapse, and the lack of sufficient 

skills to develop complex structural models and 

interpret computational results. 

Until more experimental data become available 

to represent inelastic response of structural 

elements, it would be practical to use simpler 

analysis methods based on linear elastic static 

procedures, as their results could be validated by 

simpler methods such as hand calculations. 

Thus, simpler analysis methods are preferred 

from a computational point of view. 

When the results of linear elastic static 

procedures violate acceptance criteria, nonlinear 

static procedures should be attempted to account 

for the redistribution of the loads of failed 

members and the development of membrane 

action. 

4. REFERENCES 

ASCE 7-02 (2002), “Minimum Design Loads 

for Buildings and Other Structures, 2002 

edition,” American Society of Civil Engineers, 

Reston, VA 

GSA (2003), “Progressive Collapse Analysis 

and Design Guidelines for New Federal Office 

Buildings and Major Modernization Projects, 

General Services Administration, Washington, 

D.C. 

ISC (2001), “ISC Security Criteria for New 

Federal Office Buildings and Major 

Modernization Projects,” The Inter Agency 

Committee 

UFC (2004), “Unified Facility Criteria-Draft 

Design of Buildings to Resist Progressive 

Collapse,” Department of Defense 
Table 1. Acceptance Criteria and Subsequent Action 

Structural 

Behavior 

Acceptance Criteria Subsequent Action 

Flexure Flexural design strength For ductile members, insert hinge and 

apply a constant moment on both sides of 

the hinge. 

Combine axial 

and flexure 

Interaction equation Remove failed members and redistribute 

the failed member loads. 

Shear Shear design strength Remove failed members and redistribute 

the failed member loads. 

Deformation Limits defined for each 

material (FEMA 356) 

Remove failed members and redistribute 

the failed member loads. 

 Figure 1. Correct and Incorrect Approach to Removing 

 A Column