NBSIR 76-1106

Design to Reduce the Risk of

Progressive Collapse

Edgar V. Leyendecker and Bruce R. Ellingwood

Center for Building Technology

Institute for Applied Technology

National Bureau of Standards

Washington, D. C. 20234

January 1 977

Final Report

Prepared for:

Division of Energy, Building Technology, and Standards

Office of Policy Development and Research

Department of Housing and Urban Development

Washington, D. C. 20410

NBSIR 76-1106

DESIGN TO REDUCE THE RISK OF

PROGRESSIVE COLLAPSE

Edgar V. Leyendecker and Bruce R. Ellingwood

Center for Building Technology

Institute for Applied Technology

National Bureau of Standards

Washington, D. C. 20234

January 1977

Final Report

Prepared for Division of Energy, Building Technology, and Standards

Office of Policy Development and Research

Department of Housing and Urban Development

Washington, D. C. 20410

U.S. DEPARTMENT OF COMMERCE, Elliot L. Richardson, Secretary

Edward O. Vetter, Under Secretary

Dr. Betsy Ancker-Johnson. Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler. Acting Director

or r ,*l“

,cv
.
NOTATION

The following is a list of the symbols mO'St frequently employed in this

report and its Appendix:

AB = abnormal load event;

D, L^sj, W

A|\j 5 i = Dead load, and live load and wind loads according to

ANSI A 5 8 . 1 -1 97 2 [2], respectively;

F = failure event;

UST , W" = mean short-term live load and wind load, respectively;

N = normal load event;

P(Ej) = probability of occurrence of event E^;

P(E

1

1

2

) = probability of occurrence of E^ on the condition that event

E

2 occurs;

P,M = axial thrust and moment on bearing wall element;

p^= probability of failure;

P

v

, p^, p^

= vent pressure, magnitude of first and second explosion pressure

peak (figure 18), respectively;

q P

, q^ B = resistance to gas explosion, gas explosion pressure, respectively;

R‘, R" = nominal and mean resistance, respectively;

S^b> S^g = nominal and mean abnormal load, respectively;

T = time;

= safety index, defined in section 4.2;

y . , y . = load factors for load i to be applied to the nominal and mean load

value, respectively;

6 r

, = coefficients of variation in resistance and load i, respectively;
X = mean rate of occurrence of abnormal load;

$ ,

<j> -1

= standard normal probability distribution function and

respecti vely

<J>

,

<JT = resistance factors to be applied to the nominal and mean

respecti vely

its inverse,

resistance,

V

= vent ratio, defined in the Appendix.
CONTENTS

Page

/ NOTATION ill

ABSTRACT 1 1. INTRODUCTION 3

1 . 1 Background 3 1.2 ObjectiveandScope 6 2. PROGRESSIVE COLLAPSE AND ABNORMAL LOADS 7 2.1 BasicConcepts 7 2.2 Abnormal Loading Events 10

2.3 Concepts for Control by Design 18

3. PROBABILITY OF STRUCTURAL FAILURE UNDER ABNORMAL LOADS —

A CASE STUDY 21 4. DIRECT DESIGN STRATEGIES 36

4.1 Introduction 36

4.2 Specific Local Resistance Method 36

4.3 Alternate Path Method 42

4.4 Design Applications in the United States 46

5. CONCLUSIONS AND RECOMMENDATIONS 47

5 . 1 Summary 47

5.2 Conclusions and Recommendations 47

6. ACKNOWLEDGMENTS 50

7. REFERENCES 51 APPENDIX. GAS EXPLOSION PRESSURES 56

v

DESIGN TO REDUCE THE

RISK OF PROGRESSIVE COLLAPSE

by

* * Edgar V. Leyendecker and Bruce R. Ellingwood

ABSTRACT

A progressive collapse is described as a chain reaction of failures

following damage to a relatively small portion of a structure. The damage

which results characteristically is out of proportion to the damage which

initiated the collapse. The basic concepts associated with progressive

collapse are described and the background leading to the concepts is summarized.

Possible causes of progressive collapse are discussed, with concentration

on abnormal events which have a low probability of occurrence but may have

catastrophic consequences. A case study of the probability of structural

failure as a consequence of one type of abnormal load (a gas explosion)

shows that these probabilities exceed levels generally considered acceptable

to engineers.

Direct design strategies for reducing progressive collapse are described

as (1) the Alternate Path Method and (2) the Specific Local Resistance

Method. Equations for load combinations, including appropriate load factors,

are presented for each design method. The advantages and disadvantages of

each approach are described and it is concluded that the alternate path

method affords the designer more flexibility. Although the design strategies

are applicable to any type of structure at any time in its life cycle, this

report provides detailed recommendations for completed buildings.

Key words : Abnormal loading; alternate path; building code; design criteria;

probability; progressive collapse; reliability; structural engineering;

uncertainty.

Dr. Leyendecker and Dr. Ellingwood are Research Structural Engineers in the

Structures Section of the Structures, Materials, and Safety Division of the

National Bureau of Standards' Center for Building Technology.

1
Figure 1 Ron an Point Apartment Building After the Collapse, with a Second

Identical Building in the Background. (Courtesy of London

Express News and Feature Services).

2
1. INTRODUCTION

1 . 1 Background

In 1968 the newly occupied Ronan Point apartment building, located in

London, England, underwent a partial "house of cards" collapse (figure 1).

The building consisted of 22 stories of apartments built using precast concrete

panels which rested on a cast- in-place podium containing garages and a car deck [25]1. The collapse followed a gas explosion in the kitchen of an apartment on the 18th floor which blew out an exterior wall panel. The resulting

loss of support caused a chain reaction of collapse upwards to the roof. The

collapse also progressed almost to the ground as debris from above fell on successive floors below. This type of chain reaction or propagation of failure following damage to a relatively small portion of a structure has been

termed "progressive collapse." Since the gas explosion which initiated the

collapse was a loading event not usually considered in building design, it was termed an abnormal loading.

The subsequent report [25] of the Commission of Inquiry concluded, among

other findings, that although the concrete panel structure met applicable

building regulations it was not "an acceptable building." The Commission

focussed on the lack of load redistribution capability, or what it termed

"alternate paths," in the building. In general, the Commission expressed its

belief that rei nf orced-concrete and steel-framed structures possessed such

redundancy, as demonstrated by their behavior during World War II bombings

(figure 2). On the other hand the Commission pointed out that it was not neces sarily a natural concomitant that panel structures should lack alternate paths

which could provide protection against progressive collapse. This point was illustrated by the behavior of a concrete panel building in Algeria shown in

figure 3 which lost several panels due to a bomb explosion but did not

collapse.

Subsequent to the report on the Ronan Point collapse, the Ministry of

Housing and Local Government issued Circular 62/68 entitled "Flats Constructed

with Precast Concrete Panels. Appraisal and Strengthening of Existing Blocks:

Design of New Blocks [18]." In addition to other items, the circular required

that multistory buildings be designed to provide either an alternate load path

in the event of the loss of a single critical member or sufficient local resist

ance to withstand the effects of a 5 psi (34 kN/m 2

) pressure. The specified

pressure was based on a gas-type explosion, although this was not stated in the

document. The intent of the 5 psi (34 kN/m 2

) design pressure was to prevent

the initial failure needed to trigger a progressive collapse, while the

intent of the alternate path approach was to allow the initial failure but

confine its effects to prevent progressive collapse. An amendment

^Numbers in brackets refer to references listed at the end of the report.

3
Figure 2 Detail of a Seven-Story-Steel -Framed

Building After a Wartime (World War II)

Bomb .

4
to the British building regulations was later proposed [47] which was similar to Circular 62/68 [18] and was finally adopted as the "Fifth Amendment"

[55] totheregulations.

In the United Kingdom (U.K.) the Ronan Point collapse aroused widespread

concern as a social problem involving life safety [6]. However, the "Fifth

Amendment" received considerable criticism not only in the U.K. but elsewhere.

As a matter of philosophy, it was claimed that since a collapse was a collapse,

a progressive type of failure should not be singled out for attention in the

building regulations [6]. Proponents of this position argued that a safe building was achieved not by a set of restrictive building regulations, but only

when an engineer, architect, and builder unite to make it safe [6,7], The

local resistance approach was criticized on the basis of the lack of information

about the dynamic effect of an abnormal load on a structure and, due to this

insufficient knowledge, specification of a static pressure of 5 psi (34 kN/m 2

) was considered unjustified [4,7,31,32]. Moreover, it was argued that the

required pressure would not necessarily protect against other abnormal events

such as vehicular collisions [29]. The alternate path approach was thought to

be too complex [31,32] as well as illogical, since more than one critical loadcarrying member could be removed by an abnormal event such as an explosion [29],

Finally the regulations were criticized for being implemented without knowing

the effect on the cost of building construction [6,38].

Despeyroux [14] pointed out that the 1967 Comite European du Beton (CEB)

Recommendations [49] addressed the possibility that panel structures might

behave as a "house of cards" as is indicated in the following translation [25].

'General Organisation of the Structure

One can hardly over -emphasise the absolute necessity of

effectively joining the various components of the structure

together in order to obviate any possible tendency for it to

behave lihe a 'house of cards’ and of organising the structure

accordingly . In this respect it would appear to be of major

importance to install mechanically continuous steel ties interconnecting opposite walls or facades and providing safeguards

for all the vertical panels'.

Both Despeyroux [14] and Saillard [52] regretted that the official Ronan Point

report did not specifically point out that the collaps.ed building violated these

CEB principles. Saillard further observed that the Algerian building cited in

the Ronan Point report and shown in figure 3 in fact met the CEB requirements

and survived a severe explosion. Like some of their British counterparts,

they also thought the 5 psi (34 kN/m ) pressure was too high and the alternate

path approach was too complex. Robinson [50] also suggested that the alternate

5
path approach was too severe a requirement since engineers have long

designed statically determinate structures that have no alternate path.

Firnkas [20] expressed the opinion that the Ronan Point Structure

would not have been acceptable in the United States since the design of

concrete panel structures in the U.S. was considerably more conservative at

that time than in the U.K. Later, Popoff [45,46] argued for the adoption

of design principles similar to those used in earthquake design rather than

the adoption of rules such as contained in the "Fifth Amendment." This

approach would consist primarily of good detailing as well as minimum

strength and continuity provisions.

Despite the above objections, the Ronan Point incident has affected

the building regulations of many countries. Burnett [10] has documented

and compared the non -U.S. regulations. In North America the Canadian Code

has incorporated a progressive collapse design requirement [41,42]. However,

there is limited guidance in current U.S. codes and standards with regard

to progressive collapse. The 1972 American National Standards Institute's

Standard (ANSI) A58.1 [2] contains merely a warning on the hazards associated

with progressive collapse. The City of New York amended its building code

in 1973 [51] to require that progressive collapse resistance be provided by

either the local resistance or the alternate path method.

Currently the subject of progressive collapse is under study by committees

of the American Concrete Institute and the Prestressed Concrete Institute. It

is anticipated that the ANSI A58.1 committee will soon appoint a group to study

possible standard provisions. The Department of Housing and Urban Development

(HUD) has also expressed concern with progressive collapse, and this concern

has resulted in both sponsored research at the National Bureau of Standards

and the Portland Cement Association and a draft document [57] for guidance in

design.

1.2 Objective and Scope

The objectives of this report are to describe general approaches to

designing structures to resist progressive collapse. Data which support the

recommendations are included in the report.

The design recommendations contained herein are considered applicable to

all types of construction but are intended for a structure in the completed

state as opposed to one under construction. Although certain portions of

the report should be useful in deriving similar guidelines for buildings

under construction, the development of such guidelines was considered to be

outside the scope of this study.

6
2. PROGRESSIVE COLLAPSE AND ABNORMAL LOADS

2.1 BasicConcepts

The progressive type of collapse consists of (1) an event which results in

(2) failure of one or more primary structural elements followed by (3) a chain

reaction of failures. The second and third stages of this process are shown

schematically in figures 4a and 4b (modified after Dragosavic [15]), respectively, for the Ronan Point collapse.

The sequence of events that occurs during a collapse (progressive or otherwise) is shown in figure 5. This diagram will be discussed using several

exampl es

(a) Ronan Point - Following the initial wall panel failure, the loads

redistributed. However, since adjacent members lacked continuity

and strength, additional members failed. Since the building had

not totally collapsed, the loads redistributed again. The cycle

continued until the failure zone isolated itself. This chain

reaction of failures was considered out of proportion to the

initial failure caused by the gas explosion and was termed a "progressive collapse."

(b) Algeria (figure 3) - Following the initial local failures, the

load redistributed. Since, this building had both sufficient

strength and continuity that the redistributed loads could be

supported by surrounding elements, the collapse was contained.

(c) Hypothetical examples - Consider a building supported by one column at the ground story. A loading event that causes failure

of that column results in the collapse of the entire structure.

Since there is no chain reaction of failures, the collapse is

not termed a progressive collapse.

If a building is supported by four columns, the destruction of two

(or more) of these columns will cause redistribution of loads. The

surrounding elements probably will be unable to carry the redistributed loads because the destroyed elements constitute such a large

portion of the support system, and a chain reaction of failures

will occur. However, this failure is termed a general rather than

a progressive collapse because the initial damage is more than a small portion of the structure.

7
Figure 4 Schematic of the Ronan Point Collapse, Modified After

Dragosavic (15).

8
Progressive collapse

Figure 5 Sequence of Events During Structural Collapse.

g
The preceding discussion demonstrates the definition of progressive collapse, namely:

a chain reaction or propagation of failures following damage to

a relatively small portion of a structure

This is a qualitative definition since the meaning of "a relatively small

portion of a structure "requires judgement and depends on the damage level

society is willing to accept.

In order to determine how serious a problem progressive collapses might

be, Allen and Schriever [1] conducted a survey to determine their frequency of occurrence. They used two news sources — the Engineering News Record (ENR)

from 1968 to 1972 and newspaper clippings from Canadian newspapers from 1962

to 1972. The results of the Allen and Schriever survey are shown in figure 6. Based upon the ENR data, an estimate of 5-1/2 progressive collapses per year

was obtained. This is about 20 percent of the total of 110 collapses recorded

by ENR during the four-year survey period. The newspaper survey over a tenyear period resulted in a slightly larger annual estimate of progressive collapses, 7-1/2 per year, constituting about 15 percent of the total number of

collapses. It may be concluded that progressive collapse is a serious enough

problem to warrant consideration in design.

2.2 Abnormal Loading Events

Buildings are routinely designed for dead, live, snow, wind, and earthquake

loads. However, there are those loads which, although they may have a low probability of occurrence relative to common structural design loads, may precipitate catastrophic structural failure if they occur. These are termed abnormal

loading events.

Somes [53] has attempted to classify the various abnormal loadings as follows:

A. Violent Change in Air Pressure

B . Acc i denta 1 Impact

C. Faulty Practice

D . Foundati on Failure

Burnett [9] has developed a more extensive classification system.

There have been a number of efforts to gather data on abnormal events

subsequent to the Ronan Point Collapse [1,9,22,24,34,35,53,60]. The report

by Leyendecker and Burnett [34] contains data on the following types of abnormal events in the United States:

o Gas-Related Explosions

o Bomb Explosions

o Motor Vehicle Collision with Buildings
500

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ADJACENT

EXCAVATION
o Sonic Boom

o Aircraft Collision with Buildings

o Explosion of Hazardous Materials

These loads fall in Somes' category A and B. The purpose of their study was

to assess the risk of such loadings in completed residential buildings. The

list of loadings was not considered exhaustive; however, based on earlier work

by Allen and Schriever [1] and Ligtenberg [35] these loads were considered as plausible sources of the initial failure which might lead to progressive

collapse.

It was concluded [34] that, of the abnormal loads listed above, only the

gas explosion, bomb explosion, and vehicular collision constitute a problem

for buildings. The annual data for these loads are summarized in figure 7. Both the total number of incidents and the annual frequency per million

dwelling units (based on a 1970 total of 67.7 million dwelling units) are shown.

The damage levels described in the figure are based on the following definitions

(1) Total incidents - All incidents involving a particular abnormal

load.

(2) Intermediate damage - Damage between $1000 and $10,000 for gas

explosions: $1000 and $5000 vehicular collision, or described as intermediate for bomb explosions. This level implies fairly

extensive damage such as walls blown down.

(3) Severe damage - Damage in excess of $10,000 for gas explosions;

$5000 for vehicular collision; or described as severe for bomb

explosions. This level implies extensive structural damage,

such as dwelling unit destroyed.

These definitions, which involve some arbitrary judgements, were adopted

because of the limitations on the available data. For example, the number of

incidents causing damage in excess of a prescribed lev vel (as measured in

dollars) or a brief description of damage is all that is usually provided.

There is rarely complete information on the type or number of structures

affected or an adequate description of their damage. There are also no available U.S. data which provide a correlation between a prescribed damage level

and a corresponding damage loss in dollars. Finally, there are no data on the

load characteristics of the actual events. However, it is interesting to note

that Taylor and Alexander [60] collected data in which some 122 gas explosions

caused damage judged as significant (similar to the category of severe used in

this report) with an estimated total loss of repa i r £ 500 , 000 . This is an average of £4100 per incident or about $10,200 (at an exchange rate of $2.50)

in terms of the 1971 - 1972 collection period. Although circumstances differ

12
ANNUAL

FREQUENCY

OF

OCCURRENCE

PER

MILLION

DWELLING

UNITS,

LOG

SCALE

1000

100

0.1

JJ TOTAL INCIDENTS

600

" V7A INCIDENTS WITH INTERMEDIATE

- 1223 OR SEVERE DAMAGE

jH INCIDENTS WITH SEVERE DAMAGE

o

o

ino

GAS BOMB VEHICULAR

EXPLOSIONS EXPLOSIONS COLLISIONS

Figure 7 Summary of Annual Probabilities of Abnormal Loadings for 1970

13

530
considerably, this lends further substance to the judgments made above which

correlate damage to dollar amounts.

The data for the gas explosion, bomb explosion, and vehicular collision

may be discussed in terms of probability theory. The probability of structural

failure due to abnormal loads, P(F)

A

g-, may be stated as

P(F) ab = P ( F

| AB ) x P(AB) (1)

where

P ( F

| A B ) = Probability of failure given an abnormal load event;

P(AB) = Probability of occurrence of an abnormal load event.

The probability of occurrence of an abnormal load event, P(AB), is independent of any particular type of building construction or procedure used in

design but may depend on the occupancy. On the other hand, the probability

of failure given an event, P ( F | A B ) , is a function of building type as well

as the particular codes and standards used in its design and construction.

Equation 1 assists in the interpretation of the annual frequencies shown

in figure 7. The probability of occurrence, P ( AB ) , is readily obtained from

the data in the figure. Since data on P ( F | A B ) and P ( F

) A B are not available,

data have been presented instead in a form resulting in the probability of

damage above a prescribed level, P(D) ,

P(D)

p =

P ( Dp | AB ) x P ( AB )

where

P ( D

p

| AB ) = Probability of damage above a prescribed

abnormal load event;

level, given an

P ( AB ) = Probability of occurrence of an abnormal load event

P

= Subscript indicating the prescribed damage level, e.g.

intermediate or severe.

The terms P ( D

) p and P ( AB ) are obtainable from the data in figure 7 and

P ( Dp

| AB ) may be computed using equation 2 rewritten as

P ( D

)

P(DlAB) = EL P P ( AB

)

(2a )

14
Using this equation, values for P ( D

^

] AB ) were computed and are shown in table 1.

Table 1 Calculated Estimates of P(D

P

i AB >

P(D)

P Cal cul ated P(D

p |AB)

Abnormal

Loading P ( AB

)

Based on Intermediate

Damage

Based on Severe Damage

Based on Intermedi ate

Damage

Based On

Severe Damage

Gas . Expl

1 8x1

0" 6 2 . 5x 1 0” 6

1 . 6x1 O' 6 0.14 0.089

Bomb Expl

2 . 1 x 1 0" 6 0. 34x1

0" 6 0. 22x1

0’ 6 0.16 0.11

Veh . Coll. 600x 1 0" 6 86. 0x1

0" 6 7 . 8x10” 6 0.1 4 0. 01 3

NOTE: The probabilities listed are per dwelling unit.

Based on the data in figure 7 and table 1, the following conclusions were made

1. Gas explosions occur with an annual frequency of 18 events per

million dwelling units. Among all construction types there is an annual frequency of 1.6 events per million dwelling units causing

severe damage. Based upon the assumption that severe damage is

equivalent to structural failure there is a 9 percent probability

of element failure, given that the event occurs.

2. Bomb explosions occur with an annual frequency of 2.1 events per

million dwelling units. Among all construction types there is an annual frequency of 0.22 events per million dwelling units causing

severe damage. Based on the assumption that severe damage is

equivalent to structural failure, there is an 11 percent probability

of element failure given that the event occurs.

3. Vehicular collisions with buildings occur with an annual frequency of

600 events per million dwelling units. Among all construction types

there is an annual frequency of 7.8 events per million dwelling

units causing severe damage. Based on the assumption that severe damage is equivalent to structural failure, there is a 1 percent

probability of element failure, given that the event occurs.

Since abnormal loads are quite rare and reasonably uniformly distributed

in time, it may be assumed that their occurrence is a Poisson process. If

N(T) is the number of abnormal loads occurring in time interval T, then

( AT

)

n

e

" ' T

n ! P[N(T) = n] (3)
where A is the mean rate of occurrence of abnormal loads; for small values of

A, A = P(AB). Denoting p

f = P(F|AB), the number of failed elements Np in T

is also a Poisson process with the same probability law as equation 3,

replacing A with Ap

f

. The probability of one or more structural elements

failing from gas explosions is then P[Np(T) > 0] =p f AT. With lifetime T typically about 60 years, A = 18 x 10 6

, and assuminq that p ( D severe

lAB) »

P ( F

| A B ) « 0.1 from table 1, the probability of failure due to abnormal load

during the life of the structure is about 1.1 x 10~ 4

. This compares

unfavorably with the probability of failure under normal loads, which is of

the order of 1 0

‘ 5 or less [17]. It should be noted that the statistics do

not differentiate between building types or the regulations used in their

design.

Depending upon the type of abnormal loading event, the probability of an event occurring in a building is likely to increase with the building size. In the case of the gas or bomb explosion the statistics summarized in figure 7 are independent of the location of a unit in a building. Thus the probability of occurrence for either such event increases in proportion with the number of

units in a building. In the case of the vehicular collision, it is assumed

that only the ground story is accessible to a vehicle and hence the probability

of collision is proportional only to the number of units at ground level.

The variation of the probability with building size for the category

of severe abnormal loading events is shown in figure 8. The effect of

building size on the probability of an event is shown by plotting probability

versus the number of dwelling units (the p ro ba b i 1 i t i e s were obtained by

multiplying the appropriate data in figure 7 by the number of residential

units). Auxiliary axes are provided to indicate the number of stories when

there are 5, 10, 15 or 20 dwelling units per story. Since the data for

vehicular collisions were taken proportional to the number of units at the

ground level rather than the number of units in the building, comparisons

can only be made at discrete points. Thus, the horizontal lines shown in

figure 8 which indicate probability of severe collision, are maximums for

buildings with the number of units per story shown encircled in the figure.

For instance, assuming 10 units/story and reading the appropriate axis, it

may be seen that the probability for a gas explosion exceeds a vehicular

collision for buildings greater than about 5 stories in height, assuming a constant number of units per story. It can be shown by reading the appropriate

axis that this height of 5 stories is independent of the number of units

per story. Similarly bomb explosions exceed vehicular collisions for

buildings over 35 stories in height, assuming a constant number of units per

story. This height is also independent of the number of units per story.

A data point for an explosion in a building the size of Ronan Point (see

section 1) is shown based on an annual frequency of 2.2 severe gas-related

explosions per million dwelling units (Great Britain data, see reference [34])

16
ANNUAL

PROBABILITY

OF

OCCURRENCE

IN

RESIDENTIAL

BUILDINGS

(LOG

SCALE)

- IO

-

- 10

iiiiiii

800 I 10 20 30 NUMBER OF UNITS PER STORY

NUMBER

OFSTORIES

Figure 8 Variation of Probability of Severe Abnormal Loadings with

Increasing Size of Building.

1 7
and a 22-story high building with 5 dwelling units per story. Note that the

point is very close to the U.S. data for explosions causing severe damage.

The probabilities of these three abnormal loading events increase with

building size. For the case of severe damage, the gas explosion event approaches an annual probability of 1 x 1 0

3

, exceeds the bomb explosion event by an order of magnitude, and is greater than that for vehicular collisions for

buildings in excess of five stories in height. In addition, there are sufficient data available to develop a design load on a rational basis. Therefore the gas explosion would appear to be the most appropriate load to use

in situations where one normative abnormal load must be specified in order

to determine possible structural damage or needed resistance.

No data on load magnitudes were available for the U.S. statistics used in

the previous section. In all of the reports previously cited, only Taylor and

Alexander [60] reported load data. They evaluated 122 gas explosions judged as severe. Each of the incidents was investigated and a low and high estimate for

pressure was assigned based on characteristics of physical damage. Their

results are shown in figure 9. As expected, "large" peak pressures occur only rarely. In particular, the

pressure of 5 psi (34 kN/m 2

) which is mentioned frequently in progressive

collapse literature was exceeded only four times (at most) in the two years of

their survey.

2.3 Concepts for Reducing the Risk of Progressive Collapse

Conceptually the approaches for reducing the risk of a progressive or chain reaction type of failure may be categorized as (similar to Burnett [10]):

1 . Event Control , 2. Direct Design, or

3. Indirect Design.

Event Control refers to reducing the risk of progressive collapse by

such means as (a) eliminating the event, e . g . , avoiding the use of gas in a building , (b) protecting against the event, e.g., erecting a barrier around

a column to prevent vehicular collision, or (c) reducing the effect of the

event, e.g., provide explosion venting to reduce pressure buildup. This

approach does not increase the resistance of a structure to progressive

collapse. For instance, the Ronan Point building was susceptible to progressive collapse since the structure was built much like a house of cards [25].

The lack of inherent resistance to such collapse would have been unchanged

even if gas service had not been supplied to the building. This approach is

also dependent on factors that are outside the control of the designer and

thus is not considered a practical means of reducing the risk of progressive

col 1 apse . 0
Figure 9

PEAK PRESSURE (psi)

Frequency-Sever i ty Curve for the Significant Events i and Alexander's Survey.

1 9

e

n Tay 1 or
The remaining two approaches are within the control of a designer.

These approaches should satisfy the following performance requirement:

Structures should be designed so that if local damage occurs , there is a reasonable probability that the structure as a whole will not be damaged to an extent disproportionate to

the original cause of the local damage.

The requirement expresses the need for structures to be inherently capable

of limiting the spread of local damage regardless of the cause. This does

not mean an initial failure should necessarily be prevented but rather the

structure should be capable of absorbing the damage, regardless of the reason

for the initiating event. The statement applies equally to all construction,

regardless of materials. Although some materials may require more care than

others, it should be noted that progressive failures have been documented

[24,59] in most construction materials.

Direct Design refers to explicit consideration of resistance to progressive collapse during the design process. The two basic design means are

(1) the Alternate Path Method or (2) the Specific Local Resistance Method.

The first method allows local failure to occur but seeks to provide alternate

load paths so that the damage is absorbed and major collapse is averted.

The second method seeks to provide sufficient strength to resist an event

although some damage may occur. This method may, as a consequence of

developing strength in critical elements and joints, also result in sufficient

strength and continuity to provide alternate paths. However, it cannot be

assumed that the provision of specific local resistance will result in an alternate path. It should also be noted that the two methods can be used

in conjunction with each other in a particular structure. This report

develops guidelines which may be used in the two Direct Design methods

described above.

Indirect Design refers to consideration of resistance to progressive

collapse by specifying minimum levels of strength, continuity, and ductility.

The latter approach has been advocated by many [5,19,39,45,46]. McGuire [39]

refers to this approach as General Structural Integrity. Fintel and

Schulz [19] have also used the latter phrase to describe this approach.

However, they have modified the definition by also defining General Structural

Integrity as the ability to bridge over local failure (i.e. possessing

alternate paths). This Indirect Design approach cannot always be assumed to

result in the ability to bridge over local failure since such a method

cannot be general enough to apply to every possible structural configuration.

The provision of General Structural Integrity (as defined by McGuire)

is attractive because of its simplicity and ease of use. However, the

20
development of the minimum levels of strength, continuity, and ductility

will usually require laboratory investigation and is thus outside the scope

of this report.

Application of the two design methods is illustrated in figure 10. The

performance statement contained in the general code provisions states what

is expected of the designer. The Direct Design method provides guidelines

for achieving the required performance. For simplicity it is desirable that

requirements for General Structural Integrity be included in the specific

materials portion of the code (in general these requirements are yet to be

determined). These provisions would be deemed to satisfy the performance

statement unless the building is unusual. The designer would then use the

Direct Design method to satisfy the performance requirement.

The definition of an unusual structure is not precise. The meaning

implied here is a structure which does not have a history of performance,

contains new materials or structural concepts or, in short, a structure

departing from the type envisioned in formulating the specific material

oriented design requirements.

By virtue of the normal design process, a certain amount of strength

and continuity is provided which is also available to resist the abnormal

load. Thus, normal design may , at the same time, provide protection against

abnormal events, and indeed this has been demonstrated in the past on a number of occasions (figures 2 and 3). However, since codes, standards, and

building materials, as well as construction techniques change with time, it

cannot be assumed that this protection will always be provided in the future.

Therefore it is considered necessary that progressive collapse provisions be

included in general design requirements.

3. PROBABILITY OF STRUCTURAL FAILURE UNDER ABNORMAL LOADS —

A CASE STUDY

As discussed previously, vulnerability to abnormal loads is a special

problem in structures in which limited continuity between structural elements

exists [53]. In such instances special precautions must be taken at the

planning stages of design to insure that in the unlikely event of an abnormal

load occurrence, the resulting structural damage will remain localized. As

the abnormal load as well as factors governing the element resistance are random in nature, specific design criteria for the above purpose should have

a probabilistic basis.

In this section initial failure risks for an existing structural design

subjected to a gas explosion are evaluated. This is done both to compare such

risks with others tacitly dealt with by the engineering profession

and society in general, and to aid in establishing target reliability levels

21
Figure 10 Design Procedure.

22
upon which abnormal load design criteria can be based. An eight-story non- reinforced brick masonry residential building has been selected for this case study because it is typical of a structure where limited continuity may exist

even when properly designed according to current building codes, and because

such structures represent a significant proportion of the building population

in the United States. This building was also considered by McGuire and

Leyendecker [40] in a previous deterministic study.

Figure 11 is an elevation view and half section of the building studied.

The walls and piers are lettered for identification. In the part investigated,

the brick cross wall spacing is 92 ft (28.0 m). Floor construction is of

8-in (20.3 cm) deep, one-way, prestressed, precast concrete planks. They

bear on the corridor walls and on the exterior walls, piers, and lintels.

There are no longitudinal ties (floor reinforcement parallel to the planes

of the walls) between the ends of the planks. The brick walls and piers

are reinforced only at the f 1 oor-to-wal 1 connections.

The structural element selected for analysis of vulnerability to local

failure is a one-story section of Pier B. Pier B is also located wholly

within one apartment and thus is subject to the full initial effect of an explosion within a single living unit. Pier B is 3-ft (0.91 m) wide and

nominally 8-in (20.3 cm) thick solid brick construction. Loss of one story

of Pier B would result in loss of support for a 15-ft (4.57 m) length of

floor (3 ft (0.91 m) of pier, one 4-ft (1.22 m) spandrel, and one 8-ft (2.44 m)

spandrel). There is no apparent potential for post-failure arching over

such a damaged section.

The axial thrust F^ and moment in the eighth, fifth, and first story

elements (figure 12) which arise from normal gravity load and live loads [40] are summarized in table 2. The dead load is the weight of the elements themselves, as well as the roof and floor slabs tributary to the elements. The

live load of interest is the one actually acting at the time the abnormal load occurs. Although limited data are available to determine this [30] it would be

expected to be somewhat less than the survey live loads found in offices [37],

which have been observed to be 11-13 psf (527-622 kN/m 2 ). The range of 5

-

10 psf (239-479 kN/m 2

) was therefore assumed in this analysis; the risk

estimates were found to be insensitive to the actual live load because the

live load-dead load ratio in masonry structures is very low. Wind loads

have been neglected, assuming the probability of a joint occurrence of

extreme wind and gas explosion to be negligible. In a statistical sense,

the loads thus selected for the analysis would be the mean loads acting on the structure at an arbitrary time instant.

The gas explosion pressure q^g is assumed to be applied uniformly to

the interior face of the element, inducing axial force c

p q^g anc* bending moment

c q» D in the column, where c and c are influence coefficients,

m AB p m

23
JCu

19•

00 \o

0M

e

‘Cow

CO

8tf> Boor

5tto floor

1st floor

//'vv> * Li

// r'/gw'Avu///v*

6"-*" 26- 2

*

///xv

^_6*

Partial elevation "E" Partial section

Figure 11 Partial Elevation and Section

Figure 12 Load-Bearing Brick

Masonry Element.

24
Table 2 . Forces in Masonry Elements under Normal Loads

Story No.

Axial Thrust F^ (kips) Bending Moment M

^ (in-kips)

Live Load 5 psf 10 psf 5 psf 10 psf

8 11.5 11.5 4.8 4.5

5 45.7 47 .

12.3 13.2

1 79.8 83.4 12.3 13.2

1 psf = 47.88 N/m 2

The strength of the masonry wall element in combined bending and thrust

is given by Yokel, Dikkers and Mathey [61] in the form of the interaction

diagram shown in figure 13. Three expressions are required to describe the

capacity, depending on whether the section cracks prior to failure. Conceptually, the margin of safety M is defined along the direction of the resultant

applied load for normal loads and (S^+S^g) when an abnormal load acts,

as shown in figure 13. The mode of failure may be affected by the occurrence

of the abnormal load, since its effect is to reduce the axial thrust while

increasing the moment. The applied thrust and moment components of

under the combination of normal and abnormal loads are

P F N + c

p q AB

M = M

N + c m

q AB

The resistance of the element may be defined as the explosion pressure, q D , at incipient failure. This definition is simply to make q D and q „ D dimensionally consistent, which is required in the subsequent reliability analysis.

Let e cr

= M cr

/ p cr

> the eccentricity ratio where failure and cracking

occur simultaneously. If M/P> e

c ^

, cracking occurs prior to failure, and

q

R may be obtained by substituting P and M from equation 4 into the interaction

equations [61], yielding

q R = max (q , q ) K i 2

where

q

i

q

2

t/6 (sP

q +F

n

) - M n+

e

c m

- c

p t/6

^-B + ^B 2 -4AC

^

/ 2 A

(5a)

(5b)

25
AXIAL

LOAD

P

Figure 13 Interaction D i a g r a in for Brick Masonry Section.

2b
in which

A - Ac 2

' (5c) op

B = 2c

p

fl oF N + c m

- V/2

C = M

N

- F

N t/2 + V/ - e

A

o “

2 1 a - 2s

3P

o (a - s) 2

In equations 5, the following notation is employed

A

o

== Area of net section

a Flexural compressive strength coefficient

f m

= Compressive strength of masonry

f

i Tensile strength of masonry

P 0 Short wall axial load capacity (f^ A)

s = Ratio of tensile strength to axial compressive strength of

masonry (fj./f^)

t Thickness of wall

If e = e cr

’ failure occurs prior to cracking, and

q R

=

( aP

0

' F N^ t/6 ' V e (5d)

c m

+ c

p t/6

The term e in equations 5b, 5c, and 5d is a random variable with zero mean which denotes the variability in moment capacity exhibited by the experimental data about the interaction strength equation when all the parameters

in equations 5 are precisely known. This may be obtained by comparing controlled

27
laboratory test data [61] to analysis, wherein the standard deviation o

£ appears to be about 5 in-kips (0.565 kN-m) for the size of bearing wall

element considered here. In addition, f m>

f ^ , F^, M^ and q AB are also

random variables which contribute additional statistical variability to the

resistance and thus affect the design risk.

Conceptually, the probability of failure of the bearing wall element

under normal and abnormal load may be computed as

p (q R

< qAB ] F (x) f (x) dx

q R

qAB

( 6 )

where q

R and q A g are resistance and load effects, and F q (x) and f

q A B

( x ) are probability distribution and density functions, respectively, of q R and

q AB

. Since the member capacity is described by an interactive relationship

and the direction of the load vector as well as its magnitude is a random

variable (see figure 13), the identification of the appropriate probability

distributions and the computation of the failure probability is a formidable

task. To perform this computation, the Monte-Carlo simulation procedure

summarized in figure 14 is employed. With this approach values of f m

, f

t

,

F

n

, M

n

, and e are selected using a random number generator, and the resistance

q R is calculated according to equation 5. An abnormal load q Ag

is then

randomly selected and if q

R

< q AB

a failure is recorded. The process is

repeated a sufficient number of times that the probability of failure can

be estimated as the number of failures divided by number of trials.

For illustrative purposes, it has been assumed that the log normal probability law governs f , f

t

, F ^ and q Ag , while c is normally distributed.

The means and statistical uncertainties (coefficients of variation) used in

the simulation are summarized in table 3.

Table 3. Statistics used in Simulation

Parameter Mean Uncerta i nty

f m 2900 psi 0.15

f

t 175 psi 0.20

f n (Table 2) 0.12

m

n (Table 2) 0.12

q AB Va r i e s 0.36

1 psi = 6.895 k N / m

2

28
Figure 14 Summary of Monte-Carlo Simulation.

29
The material uncertainties are typical for average workmanship and quality

control of masonry. The load variabilities reflect the uncertainty in the sum of dead and live loads. Since in typical residential masonry construction

the live load-dead load ratio is quite small, this uncertainty is considerably

less than that obtained from live load survey data [13,37]. The qas explosion

pressure uncertainty was obtained from data reported by Dragosavic [16];

these data are analyzed and discussed in some detail in the Appendix. It might

be noted that the risk analysis and conclusions were found to be insensitive

to small variations in the statistics in table 3.

The simulated probability of failure of the bearing wall element is

shown in figure 15 as a function of the mean gas explosions pressure q^g, the

story, and the mean live load. One thousand trials were made for each point.

The live load magnitude appears to have little effect; this is because the

live load-dead load ratio is very small in masonry structures. Abnormal

load pressures of 2 to 3 psi (14 to 21 kN/m 2

) would not be at all unusual

[16,40,48,56,60]. The net structural effect of the explosion is to reduce

the axial thrust and increase the applied moment on the masonry element.

The loss of the beneficial moderate compression (see figure 13) in the

element in concert with a sudden increase in flexure is likely to precipitate

failure, particularly in the upper story elements where the normal load

thrust is small. This is reflected in figure 15 where if q ^ ^

= 2 psi (14 kN/m 2

) the failure probability for the eighth story element is 0.83 while for the

first story element it is 0.003.

To place these numbers in some perspective, risks associated with

currently acceptable reinforced concrete designs subjected to normal loads

have been found to be of the order 10” 5 for flexure and shear [17] and

less for compression. When a gas explosion occurs, failure probabilities of

the order of 0.01 would be required in order to achieve a similar reliability

over the life of the structure (this is discussed further in section 4).

The risk associated with the eighth story element therefore is clearly

unacceptable from a structural reliability standpoint. Moreover, an eighth story failure could easily propagate down through the rest of the

unreinforced masonry structure, resulting in a progressive collapse [40].

Specific design provisions to lessen this risk would thus appear to be

warranted

It is apparent from figure 13 that the failure mode, i.e. cracked or uncracked section, will depend on the magnitude of the abnormal load vector

Sab w ^ c ^ is related to the magnitude of q^g. The failure probability may be

expressed as

P (F ) = P (F I Cr) • P (Cr ) + P (F | NCr )

’ P (NCr ) (7)

30
GO

0.01

0.0001

O Live load = 5 psf ( .24 k N/m2

) a Live load = 10 psf (.48k N/m2

)

2 3 4 5 6 psi

H

1

I

' T

8 1 1 T“ —*1 —

—1 10 15 20 25 30 35 40 kN/m2

MEAN 6AS PRESSURE

Figure 15 Probability of Failure of Unreinforced Brick Masonry Bearing

Wall Under Abnormal Load.

31
where P(F|Cr) and P(F|NCr) are probabilities of failure on the condition that

the section is cracked and uncracked, respectively, and P(Cr) and P(NCr) are,

respectively, the probabilities that the appropriate failure mode is the

cracked or uncracked section. P(F|Cr) and P ( F

| N C r ) would depend on the

relative colinear magnitudes of S and M (figure 13) in the appropriate direction, while P(Cr) would be equivalent to P(e

app

e cr>

In figure 16, P ( F | C r ) and P(Cr) are shown for the fifth story element

along with the P(F) from figure 15. As expected, a large q Ag increases the

likelihood of a post-cracking type failure, since a large q^ B induces a large moment while reducing the axial thrust. It is interesting that P ( F

| C r

)

appears to furnish a conservative upper bound to the total probability of

failure under abnormal load. The relative margin of safety is so great for

sections failing prior to cracking, i.e. e < e . that P(F|NCr)~0; this

app c r is not especially surprising, since masonry elements have great compressive

but relatively little tensile strength. Therefore, in developing criteria

for designing masonry structural elements against gas explosions (or other

abnormal loads) it would be a conservative but simplifying assumption to assume that member section cracking occurs prior to failure.

Confidence intervals on the statistical estimates obtained from a numerical experiment are helpful in establishing the usefulness of such

estimates. The confidence limits depend on the number of Monte-Carlo

trials. If the true probability of failure is 0.01, then the 95 percent

confidence limits on the Monte-Carlo estimate are approximately 0.005 and

0.02 if 1000 trials are made [26]. Monte-Carlo simulation may also be used to

determine the mean and uncertainty in q

R in equation 6. This requires

fewer trials than the calculation of small probabilities. With q" n and 6,

i R Or available, P(F|Cr) may be estimated by prescribing lognormal distributions

for q R and q

ftB [3], whence

p (F | Cr

)

1 - <t>

1x1 (q R^qAB )

V'

6 a

2 +

6

2 qR q AB

(8)

where <t>(.) is the standard normal probability distribution. Herein, it was found that for the fifth story 6 Qr = 0.15, while q

R = 3.4 psi (23 kN/m 2 ).

Using these values, equation 8 is also plotted in figure 16, where it is

shown to provide a conservative approximation to the probability estimate

obtained by the Monte-Carlo procedure. Equation 8 can also be employed to

extrapolate the risk analysis into the low probability region, where the

required number of Monte-Carlo trials might become prohibitively large.

32
Figure 16 Modal Dependence of Failure Probability - 5th Story.

psi

kN/ m

2

33
Since there is a good chance of local failure, given the abnormal load,

the question of whether the failure will progress or be contained must also

be answered. If a one-story section of Pier B collapses, the two adjacent

spandrels deriving support from that section will fall with it (see figures

11 and 17). The presence of windows on each side of the pier in each story

precludes the possibility of effective arching in the plane of the exterior

face. An explosion which removes a story-height section of Pier B will

also render the drywall partitions of at least the focal apartment incapable

of resisting any direct vertical load.

Exactly what would happen during and following the progressive loss of a full Pier B is difficult to analyze quantitatively. It seems clear that the

ends of the planks which derive their support from Pier B would deflect a foot

or more and that a number of them would pull away from the sagging reinforcing

bars that tie the planks together. The restraint at the inner corridor

wall ends would not prevent this. An optimistic appraisal of the possibilities

is that floor failure would progress upward several stories from the focal

point until the cumulative effect of the interior partitions, acting in the

fashion of a crumpled egg crate structure, would be sufficient to shore up

the remaining floors. A more pessimistic appraisal is that the partitions

in the story immediately above the initial failure story would be incapable

of resisting collapse of their ceiling planks and that these dry wall

partitions would be completely ineffective under the combination of load

from above and loss of support from below (the failed ceiling of the apartment

with the initial failure). The complete story-by-story failure of this

tier of apartments would then progress to the roof. In addition, the

falling debris could cause failure to the ground. Inward and lateral

spread is a further possibility because of overloading (in both axial force

and bending) of the corridor wall and the exterior piers and walls adjacent

to the collapsed Pier B. Regardless of whether one is optimistic or pessimistic in speculating

on the consequences of blowing out a one-story section of Pier B, one conclusion is clear: failure would be extensive and fall well within any

definition of progressive collapse.

To summarize the significant results of this section:

0) If a gas explosion pressure of 2 psi (14 k N / m

2

) occurs, the

probability of brick masonry element failure ranges from 0.003 in

the lower story to 0.83 in the top story.

(2) It is conservative to assume that section cracking occurs prior to

failure.

34
Figure 17 Bridging Mechanism After Brick Masonry Pier Failure.

35
In view of the first conclusion, it is disturbing to find that in some proposed

design procedures [28,33,58], no special precautions are taken for abnormal

loadings in the top stories although they are in the lower stories. The present

analysis reveals that the top story elements are most likely to fail in the

event of a gas explosion. Therefore, special attention should be paid to

insure that either these elements do not fail or that if they do, the

failure will be localized. It would be more difficult to support the debris

load resulting from their failure than to design to localize the failure.

In this particular design the alternate load paths could not be achieved.

Frequently the provision of appropriate floor plan will greatly simplify the

development of alternate paths. Other masonry buildings analyzed by McGuire

and Leyendecker [40] showed this to be the case.

4. DIRECT DESIGN STRATEGIES

4.1 Introduction

Direct design strategies to minimize the effects of progressive collapse

have been discussed in section 2.3 and consist of (1) the Specific Local

Resistance Method and/or (2) the Alternate Path Method. These two approaches

are discussed in the following sections.

4.2 Specific Local Resistance Method

The method of specific local resistance or reserve load capacity to

withstand abnormal events may be implemented in a number of ways. Perhaps

the easiest is simply to increase the load factors applied to the normal

loads and allow the additional conservatism to protect against abnormal

loads. However, as shown in figure 13 the abnormal load may cause the

failure mode to change (due to a stress reversal) so that the benefits of

increasing safety factors in one limit state only to have the structural

element fail in another are marginal. It therefore is apparent that

this approach requires a specific abnormal load be identified, so that reserve capacity can be referenced to a specific limit state. Subsequent

to the development of specific design criteria, some of the shortcomings of

this approach will be identified. It should be emphasized at the outset

that these criteria are directed toward those structural elements whose

loss would endanger the performance of the remaining structure.

Design criteria which incorporate the effects of uncertainties arising

from statistical variability and imperfect information in the parameters

should have a probabilistic basis. When the (generalized) structural

resistance R and (generalized) applied load effect S are random variables,

the relevant indicator of structural safety is the probability of failure.

36
as given in equation 6. Symbolically, may be expressed as,

p f = p f

{y ' 5 r'

6 s

} (9a)

where y is a set of load and resistance factors while 6 R and 6

^ are statistical uncertainties in resistance and load effects. When available information

is only sufficient to define the means and uncertainties in R and S, the

reliability of a design may be defined alternatively by the safety index 8^

S f = B f (y, 6 r

, s s

) (9b)

may be thought of as the distance (measured in standard deviation units)

from a point in design space (R,S), represented by a particular design y,

to the failure surface defined by the specific Limit state. Thus, larger

values of B f imply higher reliability. It is important to realize that if

the probability distributions for R and S are known, then 8 ^ and p f are uniquely related; for example, if R and S are mutually independent normal

random variables, and the limit state is a linear function of them, B^ =

$

” 1

( 1 - p ^ ) , where $

~ 1 ( • ) is the percent point function of the standard

normal probability distribution function tabulated in statistical texts.

Even when probability distributions for R and S are unknown, however,

Sf may be related to general risk levels in an approximate sense; if 8^ = 2.3,

p

f = 1

- 2

, while if 8^ = 3, Pf

1® 10~ 3

. This is important in cases, such as the design for abnormal loads, where no prior information may exist to evaluate an appropriate 8^ through calibration. In any event, when either p^ or 8^

is prescribed, a correspond i ng y may be extracted from equations 9a or 9b.

These safety factors should account for the fact that the abnormal load

is not only random in magnitude, but in occurrence. It will subsequently be

shown that this permits a reduction in the magnitude of the load factors

applied to the normal loads when abnormal loads are included in the design

equation. Let

F = structural failure event

N = normal load event

AB = abnormal load event . Using the theorem of total probability, and recognizing that P(N) a 1.0,

P(F) = P(F|N) + P ( F | AB )• P ( AB ) (10)

If is the normal long-term load effect, the first term is simply P ( F | N ) = P(R<S^y), which is typically 10~ or less, as discussed earlier. The second

term P ( F

| A B ) = P(R<Sj) is analogous to the risk found from the Monte-Carlo

simulation, being the instantaneous normal plus abnormal load. P(AB) is

the probability of occurrence of the abnormal load, which has been discussed

in section 2.2. 37
It is important that these two terms be identified separately. P ( AB

)

will remain independent of any structural strategy taken to increase safety,

and may be changed only by limiting or controlling the usage of gas.

Existing data (section 2 ) suggest that P ( A B ) = 18 x 10” 6 /residential

unit/year for gas explosions. On the other hand, P ( F

| A B ) may be reduced to

acceptable limits independently of P ( A B ) by increasing the load factors.

Equation 10 emphasizes that building safety can be controlled by limiting

the risk of abnormal loads (small P(AB)), by increasing the capacity of key

elements or zones (small P(F|AB)), or by a combination of both approaches.

Structural failures resulting from abnormal loads can be controlled in a reasonable way by requiring that the probability of failure of a structural

element due to an abnormal load should be less over the life, T, of the

structure than its probability of failure under maximum normal loads. Since

the lifetime probability of failure from abnormal load has been found in

section 2.2 to be p f P(AB)T the above-mentioned design criterion becomes

Pf = p < R<s

i> < TPl/hry p ‘ f I n > ( 11 )

With P ( F| N ) typically about 10" , T ^60 yr, and P(AB) = 18 x 10" , an appropriate p^ for abnormal load design would appear to be less than

0.01. An appropriate set y can thus be obtained from equation 9a using

Pf = 0.01, or from equation 9b using

8f

= 2.3. It might be recalled that

Monte-Carlo simulation revealed that when normally designed non-re inforced

brick masonry bearing walls are subjected to moderate gas explosion pressures,

this conditional failure probability may exceed 50 percent.

The design equation takes the form

<f> R y d

d r L

LST y ab sab ( 12 )

in which R, L ^ ^ , and S A B are the mean resistance, instantaneous live load,

and abnormal load, respectively. Wind load effects have been ignored,

reflecting the negligible probability of a joint occurrence of strong wind

and abnormal load. Equation 12 may also be written in terms of nominal

resistance R

' and live load L A ^ ^ which designers are more familiar with

(e.g. American National Standard, ANSI A 58. 1 - 1 972 [2]), viz.

4> R

' y

D

D + y L L AN S I + y AB

S AB ( 13 )

in which 4> R/R', Y

l - Y

l

L st

/L ansi and y ab y ab S AB /S AB'

38
The live load ratio is determined by comparing mean load survey values

[ 37 ] with those specified in ANSI A58.1 A 2]. It is assumed that the load ratio

L ST /L ANSI is the same for residences and offices; thus, using Mitchell's

data [37], L ^ ^ 5 j = 26 percent for areas of about 1 50-200 ft 2 (13.94-

18.58 m

2 ). Eastern European data reported by Karmen [30] tend to support

this.

Empirical equations for the abnormal load have been developed from

an experimental program [16] which is discussed in the Appendix of this

report. As an upper bound equation, Dragosavic recommended that (in kN/m 2 units)

s

1 bAB

= max 3 +

2 Pv

+ 0.04

'P 2

3 + P, (14a)

which is an equivalent static gas pressure dependent on venting pressure p and vent area ratio ip = (vent area)/(Room volume). A statistical analysis

(Appendix) of these data revealed that, based on a 25 percent probability

of exceedance, an appropriate static design pressure would be (in kN/m 2 units)

s

1 AB max 2 + 1.2 pj, 1.2 + 0 . 6 p 0.05 (14b)

A somewhat different expression was proposed by Rasbash [48] and

Stretch [56] on the basis of limited test data on pressures generated by

gas explosions,

S^

B = 1.5 p v + 2.8 K (kN/m 2

) (14c)

for design, where K is the rato of the minimum bounding surface area to the

unit area.

A comparison of the pressures obtained from equations 14a, 14b and 14c

for a typical kitchen 10 ft (3.05 m) square by 8 ft (2.44 m ) in height

with various glazing is shown in table 4. Equation 14a has been divided by

0.8 to make its comparison with equation 14b consistant (refer to appendix)

39
Table 4. Abnormal Load Design Pressures

Glazing Design

psi

Pressures

,

( kN/m 2

) No . of

Panes

Size Ratio Equation

(Glass Area/ 14a [16]

(Floor Area

)

Equation

1 4b

Equation

14c [48, 56]

2 2

1 x 4' x 3/32" 0.16 2.40 (16.6) 2.02 (13.9) 2.5 (17.2)

1 4

1 x 4’ x 3/16" 0.16 2.61 (18.0) 2.23 (15.4) 3.0 (20.7)

2 3- 3/8'x6-3/4'xl/4" 0.23 1.51 (10.4) 1 .22 (8.40) 1.87(12.9)

1 *

2

- 1/2'x4'x3/32" 0.10 5.00 (34.5) 4 . 63 (31.9) 3.6 (24.8)

*HUD-MPS requires a minimum of 10 percent of floor area.

It may be observed that in no case does the design pressure exceed the 5 psi (34 kN/m 2

) required in the Fifth Amendment [55] and CP 110 [12]. However,

it should be noted that due to increasing requirements for energy conservation,

smaller window areas could lead to increases in design pressures. Where the

glazing is a large percentage of floor area, the use of equation 14b also

results in additional design economies over either equations 14a or 14c.

Using equation 14b for the abnormal load design pressure results in

S

/\B — ^ • 3 S A

for those p

v and ip of interest in design.

Finally, the specific load and resistance factors in equation 13 are determined from equation 9b, using an iterative procedure for calculating

<j), y

l and y AB from 6 R

, 6 D

, 6 L and 65^

described by Paloheimo and Hannus [44].

6 ^ is quite small, say 0.06. Live load survey data for offices [13,37]

and residences [30] show that 6 L « 0.60 for short-term loads. Data for gas

explosion pressures generated under nominally identical conditions (same room volume, venting, gas-air mixture) imply that 6 ,- « 0.40 (See Appendix);

b AB

the above uncertainties include contributions due to modeling and imperfect

information [3,23]. For 99 percent reliability (6 * 2.3) and assuming

that the mean abnormal load effect conceivably could exceed the mean gravity

load effect by a factor of two, equation 9b yields y

D

= 1.01, y,

= 1.37, and y AB = 1.65 in equation 12 for average quality and workmanship.

The load factors in equation 13 thus become y

L = 1.37 x 0.26 = 0.36 and

Yab - 1 - 65 / 1 - 3 = 1-28; rounding off, the design equation would be,

ip R

1 _> D + 0.4 L ANSI + 1 . 3 S AB (15a)

40
when the gravity and abnormal load effects superpose. When the gravity and

abnormal loads have opposite sense, then.

<p R' > 1 . 4S 1 AB - D (15b)

A summary of other load factors and the approximate risks they correspond to

is given in table 5

Table 5. Load Factor Design for Specific Local Resistance

6 f y

l y ab p f

1 . 6 0.3 1 . 1 .05

2.3 0.4 1 . 3 .01

o

co 0.4 1 . 4 .001

Specific ^-factors have not been given because it was considered undesirable to tie the design equation to a specific material. However, for a number of materials, a simple calculation reveals that for the 3^ values of

interest here, ij> ’R ~ R

1 and thus in order to simplify, equation 15 could be

written without the ^-factor. Moreover, it was found that for a wide range

of 6 R (say 0.10 £ 6 R

<_ 0.25) which cover numerous materials common to con- struction, the above load factors were quite insensitive to 6 R

. This implies

that the load side of equation 13 is virtually material-independent, and could

be included in the "Loads and General Design" section of a model building code.

Equation 15 is similar in form to the abnormal load criteria of the UK [55]

Swedish [21] and Dutch [43] building codes, with the exception that it was con- sidered unnecessary to include the wind load term in equation 15. In all these

criteria, the live (and wind) load factors are less than unity. Despite the

presence of y^g, equation 15 may not be as penalizing as the British or Swedish

design criteria which require S ^ g

= 5 psi (34 kN/m 2

) and 5.8 psi (40 kN/m 2

) respectively; in contrast, equation 14b may result in S^g less than 1 psi

(6.9 kN/m 2 ), depending on the vent ratio. Moreover, the European criteria do

not have a reliability basis, and were derived subjectively.

The necessity of identifying a specific abnormal load (here taken to be

a gas explosion) is admittedly a drawback, because of the paucity of

abnormal load data with which to develop specifications. It is re-emphasized

41
that only elements whose loss would endanger subsequent structural performance

need satisfy the abnormal load criteria given above; moreover, these criteria

are applicable for all buildings in which specific local resistance must be

provided.

It might also be observed that event control may be used to some advantage in reducing the effect of the abnormal load; note, for instance that

venting which is a form of event control is included in the gas pressure

equation.

4.3 Alternate Path Method

In contrast to the specific local resistance approach discussed in the

previous section, the concept of providing alternate paths directs attention

toward the behavior of the structure after some elements are lost, regardless of cause. This is attractive not only from a philosophical point of view, as the

limit state considered is directly relevant to the overall structural performance in the event of an accidental overload, but also because abnormal loads

need not be specifically identified in the design equation. It should be

emphasized, however, that this by no means obviates the need to understand the

characteristics and magnitudes of abnormal load events since such knowledge is

generally required in order to predict how much of the structure is actually

damaged. For instance the design pressures given by equation 14b provide some basis for estimating the amount of damage that might occur as the result of a gas explosion and hence for applying alternate load path concepts to a specific

design situation. However, in situations where gas may not be present, other

abnormal load events still are not precluded. Under these circumstances and

in the absence of any current reliable data on abnormal load magnitudes it is

necessary to specify a priori those damage levels that the structure must

tolerate before the alternate path design concepts can be applied.

In the final analysis, the primary objective of designing damage tolerance

into structures is to minimize the loss of life that might otherwise occur in

the event of an abnormal load, and to permit the safe egress of the occupants

from the damaged structure. Naturally, the specification of such tolerable

damage limits is largely subjective, and involves technical and social judgment to a significant degree. Because the point is often ignored by engineers

and not realized by society in general, it seems worthwhile to note that a balance always exists between safety and economy in design. Obviously, structures could be built which would withstand practically any abnormal load;

however, these would be prohibitively costly and, at the same time, would

not constitute an optimal utilization of resources from the viewpoint of

society at large.

The determination of this optimal point of balance between safety and

cost involves a scaling of social values, and an assessment of the willingness

on the part of individuals in society to incur risks. One must differentiate

42
between risks which are incurred voluntarily (sportcar racing) with those

which are incurred involuntarily (occupying a dwelling). Acceptable risks

for involuntary activities tend to be two to three orders of magnitude less

than for voluntary activities [54] and allowable damage provisions must

recognize that exposure to the structural consequences of abnormal loads

is involuntary in nature. Finally, it is noted that in developing a standard,

widespread use will almost certainly occur before its social and economic

impact can be evaluated.

In terms of the safety of occupying structures vis £ vis other activities,

it may be assumed that these social values have stabilized. Therefore,

current tolerable risks associated with other involuntary activities,

whether explicitly or implicitly realized, are appropriate as a basis for

developing a criterion for acceptable damage following an abnormal load.

With these points in mind, it is suggested that the damage be considered

tolerable if it is confined to the stories immediately adjacent to the

origin of the incident causing damage. Damage resulting from the loss of the

primary elements may extend into the story above and below the unit assumed

to be the focal point of the abnormal loading event. In any one of the

stories, damage should not extend outside an area greater than 750 sq. ft

(69.7 m

2

) or 15 percent of the floor area. It is felt that this requirement

will limit fatalities to an average of less than one per incident, which

should limit the total average number of annual fatalities to something

less than the mortality associated with fires and two orders of magnitude

less than that associated with automobile accidents. The damaged zone may

be isolated (or contained) within these limits by zoning a structure through

the use of expansion joints. This approach appears most appropriate for

low-rise structures.

Compliance may be determined by assuming that the primary structural

elements are incapable of carrying load, one element at a time, and evaluating the resulting structural behavior. The following definitions of primary

structural elements are similar to those used in the U.K. [55] as well as

a HUD draft document [57]:

(1) major load carrying beams

(2) floor slabs between supports

( 3 ) columns

(4) bearing wall panels

These recommendations are similar to those used in Denmark [11] as well

as those used in the U.K. [55]. Sweden [21] controls the damage by specifying

a volume of tolerable damage rather than an area. When a primary structural element is removed, the remaining structure

must continue to carry its existing loads for a sufficient time at least to

43
safely evacuate the structure and inspect the extent of damage. In identifying the appropriate design loads to use in applying the alternate path concept,

their duration and frequency relative to those design requirements is of primary interest. It might be recalled, for example, that wind loads were neglected in the specific local resistance approach, because the probability of the

joint occurrence of an abnormal load and high wind were deemed negligible.

However, since the damaged structure may be expected to function for an extended

time, at a reduced level of safety, this assumption may no longer be justified.

For these reasons, the effects of short-term wind loads should be included in

the design equation used to evaluate the residual strength of a damaged

structure. An appropriate load combination thus would be,

Dead + Short-Term Live + Monthly Maximum Wind (16)

Load factors for use in the design equation are derived using the same procedure as that used to arrive at equation 15. For short-term load

effects, 6^ = 0.6C as before. The uncertainty in the monthly maximum

wind load effect is estimated as 6 W

= 0.40, although this may vary from site

to site and is based in part on judgment. (It is entirely coincidental that

6,, is the same as 6 C .) In order to write the design equation in terms of

W b AB

familiar ANSI A58.1 loads, note that

W/W ANSI

26 percent as before, and

10-20 percent if W is the mean monthly maximum wind speed. For a reliability of 99 percent for the damaged structure (B^ = 2.3), with L/D <_ 0. 5 and W/D < 0. 25 , y. 1.90 and y

W 1.20 in equation 12 from equation

9b; the design equation for applying the alternate path concepts thus becomes.

f R ' i D * 0- 5 L

flfJS I + °- 2 “ansi <’7a)

when gravity and wind load effects have the same sense. When they oppose

one another,

<J>R' 1 D - 0.3 W ANSI (17b)

the dead load factor being rounded to unity in both cases. Specific <j> factors

have not been given so as not to limit equation 17 to one particular material.

As before, the load side of equation 17 is insensitive to small variations

in 6^, implying its applicability to different construction materials.

Numerous factors may be considered when designing a structure to

bridge over a damaged zone. These factors include:

(1) Floor plan — The selection of a proper floor plan layout of

walls and columns is possibly the most important aspect of

44
designing a building which will possess alternate load paths.

While it is difficult to give, all possible features of a good

floor plan, desirable features include longitudinal spine walls

(walls perpendicular to cross walls) which serve to enhance

both the stability of the cross walls and limit the amount of

wall damaged in an abnormal loading event. Other stabilizing

features might include stair wells or elevator shafts.

(2) Short returns on walls — A return is a short length of wall

usually at right angles to another wall.

(3) Redistribution of floor slab load — A slab which has lost its

support along one edge should be able to change span directions

and transmit load to other supports.

(4) Internal partitions — The strength of partitions normally neglected in design may be utilized.

(5) Catenary action — Slab span may increase as the result of loss

of an intermediate support. Loads may be carried by catenary

action with accompanying large deflections.

(6) Beam action of walls — If a bearing wall is damaged, the load

may be distributed into the stories above by beam action of

walls. That is, the walls may be considered to act as webs

of deep beams with floor slabs as flanges. However, walls and

slabs must be adequately tied together.

(7) Arching action — In-plane arching of walls may serve to bridge

over a damage zone in masonry construction.

Design examples using these principles have been discussed by Taylor [59]

and Haseltine and Thomas [27,28]. These authors point out that the concepts

are relatively easy to apply if incorporated at the design stage. McGuire

and Leyendecker [40] have shown that it is relatively easy to check the

resistence of a building to progressive collapse by rather simple analysis.

It should be pointed out that in the event an alternate path cannot be

developed, it may be necessary to design strong points into a structure using

the method of specific local resistance. Therefore, the two design concepts

discussed in sections 4.2 and 4.3 are not entirely mutually exclusive, and in some instances may be used to complement each other.

Use of the alternate path concept will result in a structure with the

coherence to limit the spread of collapse. Use of the method represents a feasible means of determining minimum requirements for strength and continuity

which can result in buildings said to possess structural integrity.

The provision in a code of specified mini mums for strength and continuity

is attractive for the typical structure if the requirements are sufficient to develop an alternate path. However, unless the reasons for the minimums are

45
apparent in the code, a designer of an unusual structure may overlook the

need for considering progressive collapse. Such minimum requirements would

have to be established for different types of construction and would have to be carefully updated as construction practices change. Nonetheless the concept

is useful since, if the provisions are adequate, then design for progressive

collapse might require nothing more than a final check after the usual design

is completed. It should be noted that the Department of Housing and Urban

Development is currently sponsoring research on large panel construction

at the Portland Cement Assocation. One aspect of the research concerns establishing levels of minimum strength and continuity required to achieve structural integrity for that particular type of construction.

4.4 Design Applications in the United States

In 1969 the Department of Housing and Urban Development (HUD) initiated

Operation BREAKTHROUGH, a program designed to encourage the development and

introduction of industrialization into the housing industry in the United

States. The National Bureau of Standards, on behalf of HUD, drafted criteria

[8] which were used to guide the development and subsequent evaluation of these

housing systems. These "Guide Criteria" contained a recommendation against

progressive collapse under catastrophic loading which was similar in concept

to the "Fifth Amendment." Cost data for incorporating these progressive

collapse provisions in design are not meaningful since, for the most part,

the systems requiring provisions were adaptations of existing designs which

were subsequently modified to meet the criterion. The solutions used in

five of the systems were documented in detail by Yokel, Pielert, and Schwab

[62], They concluded that:

1. The systems with clear spans between transverse bearing walls

greater than 19 ft (5.79 m) had to use "strong" transverse bearing

walls at least for the end walls and the transverse walls next to

the end walls. In all cases, special provisions had to be made

to provide lateral support to the end walls.

2. The systems with clear spans of 12 ft (3.66 m) or less relied

principally on alternate paths of load support.

3. In short-span systems using an alternate path of load support the

following joint reinforcement ties were the most critical: horizontal ties in the vertical joints between adjacent or intersecting

bearing walls; continuous vertical ties throughout the building

in the same joints; transverse horizontal ties between corridor

floor panels and adjoining floor panels; and ties between transverse

walls and corridor walls and between transverse walls and corridor

floor panels. The alternate mode of load support was also assisted

by longitudinal horizontal ties between adjoining floor panels on

46
either side of transverse bearing walls, ties between transverse

bearing walls and connecting floor panels, and vertical ties

between successive transverse bearing wall panels.

Thus, depending on the span length, the systems used either the alternate

path approach or a combination of the alternate path with strong points

provided by specific local resistance.

5. CONCLUSIONS AND RECOMMENDATIONS

5.1 Summary

This report has discussed the basic concepts underlying design procedures which reduce the risk of progressive collapse and has summarized

the background leading to the concepts. Progressive collapse was defined

as a chain reaction or propagation of failures following damage to a relatively small portion of a structure in which the resulting damage is

characteristically out of proportion to the damage which initiated the collapse.

Abnormal loading events are those events which, although they may have

a low probability of occurrence relative to traditional structural design

loads, may precipitate catastrophic structural failure if they occur. The

gas explosion, bomb explosion, and vehicular collision appear to be the

main sources of abnormal loadings on building structures. A case study of

the probability of structural failure due to a gas explosion has been made.

Strategies for reducing the risk of progressive collapse in any type

of building have been described as (1) Event Control, (2) Direct Design , and (3) Indirect Design. These strategies were discussed in detail and

finally a brief description of design applications in the U.S. was given.

This type of collapse may occur either during construction or after completion

of the structure, and although certain portions of the report should be useful

in deriving design guidelines for buildings under construction, the scope

of the report was limited to the development of guidelines for completed

buildings.

5.2 Conclusions and Recommendations

The following conclusions and recommendations are based upon supporting

data contained in this report.

5.2.1 A progressive or chain reaction type of failure may result as

a consequence of normal or abnormal load events.

5.2.2 Abnormal load events constitute an unacceptable hazard in buildings

of all types of construction and should be considered in the formulation of

building regulations.

47
5.2.3 The normal design process results in a certain amount of strength

and continuity which is also available to resist progressive collapse. This

has been demonstrated in the past on a number of occasions. However, since

codes, standards, and building materials, as well as construction techniques

change with time, it cannot be assumed that this protection will always be

provided in the future. Therefore, it is considered necessary that progressive collapse provisions be included in design requirements.

5.2.4 The three approaches for reducing the risk of a progressive or chain reaction type of failure are (1) Event Control, (2) Direct Design, and

(3) Indirect Design. Only the latter two approaches are considered practical

since Event Control is dependent on factors that are often outside the

control of the designer.

5.2.5 The Direct and Indirect Design approaches should satisfy the

following performance statement.

Structures should he designed so that there is reasonable probability

,

if local damage occurs } that the structure as a whole will not be

damaged to an extent disproportionate to the original cause of the

local damage.

5.2.6 Direct Design refers to explicit consideration of resistance

to progressive collapse during the design process. The two basic means

are (1) the Alternate Path Method and (2) the Specific Local Resistance

Method. The use of the former is preferred since it is concerned with the

stability of the building after the loading event has occurred.

5.2.7 The following procedure may be followed when using the Alternate

Path Method:

(a) Estimate the amount of damaged structure considering feasible

abnormal events. A gas explosion may be presumed in the absence of more precise information.

(b) As a minimum, damage to the following primary structural elements

should be assumed to occur, taking one element at a time:

(1) major load carrying beams

(2) floor slabs between supports

( 3 ) columns

(4) bearing wal 1 panel s .

48
(c) Following removal of the primary structural element the structure

should be designed for the following ultimate loads:

<p R' >_ D + 0.5 L ansi + 0.2 W ANSI (18a)

(?. R' > D - 0.3 W ANSI (18b)

Linder these conditions damage is to be expected but there is time for

evacuation and assessment of damage. 5.2.8

Specific local resistance should be provided when it becomes

impractical to employ the alternate path method. It should be noted that

designing to resist the loading events may, coincidentally, provide sufficient

strength and continuity to achieve alternate paths. The following procedure

may be used:

(a) In the absence of more complete data, the gas explosion may be

selected as the normative abnormal loading event since it occurs with

a frequency that is an order of magnitude greater than other such events.

2 This pressure in (kN/m units) is given as

S AB max (2 + 1 .2 p

v

) ,(1 .2 + 0.6 p

v + 0.05/,j, 2

) (19)

where pK and \p are defined in section 4.2. Additional abnormal loads

v should be included if a site study warrants them.

(b) For specific local resistance design, the gas pressure may be used

in the following equation

R' > D + 0.4 L ansi + 1.3 S' AB (20)

(c) In those instances where other abnormal loads can be identified,

their consideration in design is required.

5.2.9 The Alternate Path and Specific Local Resistance Methods may be

used in conjunction with each other in a design.

5.2.10 Minimum requirements for use in the Indirect Design approach

have not been established for specific construction types. Research should

be started in this area.

49
5.2.11 A design procedure which may eventually result in very little

additional structural design effort is shown in figure 10. An engineer would

proceed with a normal design which would incorporate specified minimum values

of strength and continuity (Indirect Design). Presuming the structure is

not judged unusual by a building official, provision of the minima would

serve as compliance for providing the required progressive collapse resistance.

An unusual building would require resorting to the general performance

requirement. The Direct Design approach could then be used to develop the

required resistance.

5.2.12 The preceding conclusions apply to all construction types;

however, it is recognized that the degree of concern and the difficulty in

developing solutions is greater for some types than for others.

6. ACKNOWLEDGMENTS

The authors would like to thank Mr. J. R. Harris, Dr. C. Culver and

Dr. F. Y. Yokel of the Center for Building Technology, National Bureau of

Standards; Mr. W. J. Werner of the Office of Policy Development and Research,

Department of Housing and Urban Development; and Dr. J. E. Breen of the

Department of Civil Engineering, the University of Texas at Austin for their

technical review of the manuscript.

50
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McGuire, W. and Leyendecker, E. V., Analysis of Non-Rei nforced Masonry

Building Response to Abnormal Loading and Resistance to Progressive

Collapse, NBSIR 74-526, National Bureau of Standards, Washington, D.C.

20234 (November 1974).

National Building Code of Canada, 1970. (NRC 11246), Associate Committee

on the National Building Code, National Research Council of Canada,

Ottawa, Ontario, Canada (1970).

National Building Code of Canada, 1975, (NRC 13982), Associate Committee

on the National Building Code, National Research Council of Canada,

Ottawa, Ontario, Canada (1975).

53
[43] Netherlands Standard NEN 3850: Technische grondslagen voor de berekening

van bouwconstructies (Regulations for the Design of Building Structures) — TGB 1972, Nederlands Normalisatie Instituut, Rijsivijk, Netherlands

(1972)

[44] Paloheimo, E. and Hannus, M., Structural Design Based on Weighted Fractiles,

Journal of the Structural Division, American Society of Civil Engineers,

V o 1 . 100, No. ST7 (July 1 974 ). [45] Popoff, A., Jr., Designing Against Progressive Collapse, PCI Design Seminar,

Tacoma, Washington (October 1972).

[46] Popoff, A., Jr., Stability of Precast Concrete Systems Buildings, ASCEIABSE International Conference on Tall Buildings, Proceedings, Vol. Ill,

Lehigh University, Bethlehem, Pennsylvania (1972) pp. 571-583.

[47] Proposed Amendments to the Buildings Regulations 1965, Ministry of Housing

and Local Government, London, England (May 30, 1969).

[48] Rasbash, D. J . , Explosions in Domestic Structures; Part 1: The Relief

of Gas and Vapour Explosions in Domestic Structures, The Structural

Engineer, Vol. 47, No. 10 (October 1969), pp. 404-408.

[49] Recommendations Internationales Unifiees Pour Le Calcul Et L'Execution

Des Constructions En Panneaux Assembles De Grand Format (International

Recommendations for the Design and Construction of Large-Panel Structures),

Comite Europeen du Beton, Bulletin No. 60, Paris, April 1967, English

translation by C. V. Amerogen, Cement and Concrete Association, No. 137,

London (July 1 968) . [50] Robinson, J. R., Observation Sur Les Conclusions Du Rapport De La Commission D'Enquete De Ronan Point (Observation on the Conclusion of the

Report of the Inquiry Commission on Ronan Point), Annales de 1 'Inst i tut

Technique du Batiment et des Travaux Publics No. 263, Paris (November

1969), pp. 1797-1799.

[51] Rules and Regulations Relating to Resistance to Progressive Collapse under

Extreme Local Loads, Housing and Development Administration, Department

of Buildings, The City Record, New York (August 2, 1973).

[52] Saillard, Y., Le Comportement De L'lmmeuble De Ronan Point En Comparaison

Des Principles De Base Des Recommendations Internationales 'Structures

En Panneaux' du Comite Europeen du Beton (Behavior of the Ronan Point

Building Compared to the Basic Principles of the International Recommendation "Panel Structures" of the Comite du Beton), Annales de I'Institut

Technique du Batiment et des Travaux Publics, No. 263, Paris (November

1969), pp. 1804-1806.

[53] Somes, N. F., Abnormal Loadings on Buildings and Progressive Collapse, a paper in Building Practices for Disaster Mitigation, National Bureau of

Standards, Building Science Series 46, U.S. Government Printing Office,

Washington, D.C. 20402, (February 1973).

54
[54] Starr, C., Social Benefit Versus Technological Risk, What is Our Society

Willing to Pay for Safety?, Science,, Washington, D.C., Vol. 165 (Septt ember 1969), pp. 1232-1238.

[55] Statutory Instrument 1970 No. 109, The Building (Fifth Amendment) Regulations, Her Majesty's Stationery Office, London, England (1970).

[56] Stretch, K. L., Explosions in Domestic Structures; Part Two: The

Relationship Between Containment Characteristics and Gaseous Reactions,

The Structural Engineer, London, Vol. 47, No. 10 (October 1969), pp. 408-

41 1 . [57] Structural Design Requirements to Increase Resistance of Buildings to

Progressive Collapse, Proposed HUD Handbook by the HUD Staff, U.S.

Department of Housing and Urban Development (November 1973).

[58] The Structural Use of Precast Concrete, British Standard Code of

Practice CP116: 1965 and Part 2: 1969, TheBritish Standards Institution,

London

[59] Taylor, D. A., Progressive Collapse, Canadian Journal of Civil Engineering,

Vol. 2, No. 4 (December 1975).

[60] Taylor, N. and Alexander, S. J., Structural Damage in Buildings Caused by

Gaseous Explosions and Other Accidental Loadings, CP 45/74, Building

Research Establishment, England (March 1974).

[61] Yokel, F. Y., Mathey, R. G., and Dikkers, R. D., Strength of Masonry Walls

Under Compressive and Transverse Loads, Building Science Series 34,

U. S. Government Printing Office, Washington, D.C. 20402 (March 1971).

[62] Yokel, F. Y., Pielert, J. H. and Schwab, A. R., The Implementation

of a Provision Against Progressive Collapse, NBSIR 75-715, National

Bureau of Standards, Washington, D.C. 20234 (August 1975).

55
APPENDIX. GAS EXPLOSION PRESSURES

In the main body of this report, the load induced by a natural gas explosion was identified as the normative abnormal load for purposes of analysis

and design. This selection was made because of widespread usage of gas and

because the incidence of occurrence appears to be an order of magnitude higher

than other abnormal loads. Furthermore it would be quite uneconomical or impractical to ban the use of gas, employ automatic suppression systems on a wide scale in residences, or take nonstructural preventive measures that might

be feasible with other abnormal loads [36].

It is necessary to have some feeling for the magnitude of gas explosion

pressures regardless of which design concept is used to minimize their effect

on a structure. This pressure may be required either to design a specific

element to resist it or to identify potential damage when applying the alternate path concepts. In the following, the design pressures obtained from a recent experimental program [16] are examined, and a statistical analysis of

these data is performed.

The pressure generated by a gas explosion depends primarily on the percentage of gas in the air and the uniformity of gas-air mixture, the size and

shape of the room in which the explosion occurs, and the amount of venting or pressure relief that may occur. Natural gas can only be ignited and exploded

when the gas-air mixture contains between 6 percent and 16 percent of

gas; the optimum explosion is obtained at a well- mixed percentage of about

10.5 percent. Although in a completely closed chamber with infinitely

strong walls explosion pressures can reach as high as 100 psi (690 kN/m 2

) under optimal conditions, in practice the pressures are much lower. This

is the result of imperfect mixing and of ventinq which occurs when a wall

or portion of a boundary surface fails early in the explosion. The pressure

at which this venting occurs is termed the venting pressure p^; the pressure

relief aperture thus formed allows expansion to take place, which reduces

the pressure buildup on the remaining surfaces considerably and provides

venti lation.

Experimental programs thus have naturally tried to relate a design gas

explosion pressure to p

v and some measure of the amount of venting provided.

Rasbash [48] and Stretch [56] suggested a relation between the peak pressure

and the vent pressure and the ratio of the vent area to the smallest bounding

surface area in the room. However, this formula was developed from experiments with manuf acturered "town" gas, which is more volatile than the natural

gas used in the United States [36].

56
In more recent experimental programs reported by Dragosavic [15,16] tests were conducted with natural gas. A test structure was constructed of reinforced concrete to simulate a domestic ki'tchen and adjoining living room. In both rooms one side was left open in order to insert and test various types of

venting surfaces. Thirty -four (34) separate explosions were produced, tests 1 through 30 taking place only in the kitchen, to determine the effect of various

parameters on explosion pressures. Pressures were measured at 10 points on the wall and ceiling for each test. The first 7 tests were preliminary in

nature. Tests 8 through 19 were to show the effect of variations in strength

and area of the venting surfaces. In tests 20 through 24, the gas-air mixture

was varied. (In all other tests in the series, the gas percentage was close

to the stoichiometric optimum of 10-10.5 percent.) Tests 25 through 30 were repeats of test 19 and were conducted under nominally identical conditions

to indicate predictability. Finally, tests 31 through 34 were conducted to

show the effect of room volume and shape and to investigate the strength

of an all-brick load bearing wall. In all cases, the maximum measured

pressures were recorded. It should be remarked that these tests model an unusually severe situation, the mixture being optimum and uniformly distributed

throughout the room.

A typical pressure-time record from one of these tests is shown in

figure 18. The total duration of the load is approximately one second.

After ignition the pressure rises to the venting pressure p y at which the

venting surface fails; thereafter, there may be a small additional rise to

p

1

, after which the pressure drops off. After about 1/2 second, the pressure

again increases in a high frequency oscillatory fashion due to turbulent

afterburning of traces of gas and resonance of the mass of air between

parallel bounding surfaces. Since the frequency of these oscillations is so much higher than the natural frequency of the bounding surfaces, their

effect can be essentially ignored in comparison to the mean pressure part

p . Moreover, since the frequency of p and p is roughly 2 Hz, while the

2 1 2 resonant frequencies of masonry walls and concrete panels and floors are about 30 Hz-60 Hz, p and p may be treated effectively as static loads

1 2 for design purposes. A dynamic analysis would be considerably more involved,

and does not appear to be warrented in view of the limited data. Within

experimental limitations, it appears that p and p are attained simultaneously

1 2 in all parts of the room and the gas explosion thus may be considered to be

uniform on all bounding surfaces.

Although p and p may be considered as static loads in terms of the

1 2 dynamic response of the structure the loading rate is still sufficiently

accelerated that most structural materials would exhibit some apparent increase

in strength. This may be as high as [23] 20-30 percent over those values

specified for design. This elevation can either be accounted for by increasing

57
58

Figure

18

Typical Pressure

-Ti

me

Record.
the material strength or reducing the explosion design pressure. In Dragosavic's

study, the latter device is employed, resulting in the equivalent static

explosion pressures 0.8 p and 0.8 p to be used in conjunction with the

1 2 normal material strength. However, since this reduction is materialdependent and may not always equal 0.8, p and p are analyzed in the

1 2 unfactored form in this study.

It is apparent from figure A.l that the first pressure peak, p , i and vent vent pressure, p

v

, must be related. Dragosavic proposed the

equation

0.8 p x = 3 + pv

(kN/m2

) (A.l)

as an upper bound estimate. Correlation between p and Py was confirmed

herein by a regression analysis on data obtain e-d from tests 11 through 18 and

30, (these data correspond to figure 16 in reference 16) p on p„, resultinq

i V in the equation

p 1 = 1.19 pv

(kN/m2

) (A. 2)

The regression analysis actually estimates the mean p as a function of p.,;

i v p thus averages 19 percent above the venting pressure, as in figure 18.

The standard error is 2.98 and the correlation coefficient is 0.95.

In general, Py may be calculated from uniformly loaded plate bending

formulas [36]. In tests 11, 18 and 30, two panes of glass of unequal size

and strength comprised the vent surface. In such cases, it has been recommended

[16] that the largest Py be used. The regression analysis appears to confirm

this, as when the smaller p y is used in the regression, the correlation coefficient is 0.84 (as opposed to 0.95). However, if only test 30 is eliminated

and the regression is performed on the remaining eight (8) data, the opposite

conclusion is reached; correlation coefficients of 0.93 and 0.96 are obtained

using the large and small values of p y

, respectively. The existing test data

therefore are insufficient to determine the appropriate method for computing

Py when the venting surface consists of several panels of unequal strength. In neither case does there appear to be any significant correlation between p and

the amount of venting, however.

A design curve can be obtained by requiring that, say, only 25 percent of the

explosion pressures may exceed the design specified value. Assuming that the

distribution of pressures about the regression line is roughly normal at any Py

with standard deviation of 2.98, the 25-percent exceedance probability design

curve becomes

p, = 2 + 1.19 pv

(kN/m 2

) (A. 3)

In contrast, Dragosavic's recommended curve corresponds roughly to a 10 percent

exceedance probability.

59
The second pressure peak p is also dependent on p.. , although to a mucTi'

2

V lesser extent than is p . Since p occurs subsequent to venting, it is not

1 2 suprising that p appears to depend on the effectiveness of the vent in relieving

2 the pressure buildup within the chamber. Dragosavic proposed that where the

venting is described by ip, which is the ratio of the venting surface to the

total volume of the room, an upper bound to the peak pressures generated by the

second pulse is furnished by

0.8 p2 = 3 + 1/2 pv

+ (kN/m2

) (A. 4)

<l>

The coefficient 1/2 which is applied to p v reflects the reduced dependence

of p on p.. . However, a regression analysis of the data from tests 11 through

18 and 30 (corresponding to figure 17 in Dragosavic's report) results in the

equation

p

= 0.6 p + - 0.91 (kN/m2

) (A. 5)

with standard error of 3.19. Using this equation and making similar assumptions

as before, a 25 percent exceedance probability design curve for the second pressure

pressure pulse becomes,

p

= 1.2 + 0.6 p w + 0 . 0 5 / ip (kN/m 2

) 2 v (A. 6)

It might be noted that according to this statistical analysis, the Dragosavic

equation is unconservati vely biased when the vent area is small.

Since the maximum equivalent static pressure will govern the design, the

design pressure is given by

PD = max (p

x

, p 2

) (A. 7)

This may either be evaluated using equations A.l and A. 4 (Dragosavic's)

recommendation, or using equations A. 3 and A. 6, corresponding approximately to

a 25 percent exceedance probability.

Tests 19 and 25 through 30 were conducted under nominally identical con- ditons to provide an indication of the inherent or random variation In the

pressure. Analysis of these data revealed that p" = 16.44, 6p = 0 . 30 ,

i

i p

= 12.89, and 6 = 0.36. The latter uncertainty was useful in the

2 P 2 Monte-Carlo simulation and in deriving the specific load factors in section

4.2 of the report

60
It should be emphasized that considerable scatter was observed in all

these tests and the confidence intervals on the parameter estimates are quite

wide. It seems apparent that venting contributes significantly to this variability and more should be learned about its effect. Nevertheless, it is

believed that equations A. 2 and A. 5 provide a reasonable way to estimate the

average loads induced by gas explosions.

61
NBS-114A (REV. 7-73)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO.

• NBSIR 76-1106

2. Gov’t Accession

No.

4. TITLE AND SUBTITLE

DESIGN TO REDUCE THE RISK OF PROGRESSIVE COLLAPSE

7. AUTHOR(S)

E.V. Leyendecker and B. R. Ellinqwood

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

3. Recipient’s Accession No.

5. Publication Date January 1977

6. Performing Organization Code

8. Performing Organ. Report No.

10. Project/Task/Work Unit No. 4618488

11. Contract/Grant No.

I AA -H-37-72 Task 408

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP

)

Division of Energy, Building Technology, and Standards

Office of Policy Development and Research

Department of Housing and Urban Development

Washington, D. C. 20410

13. Type of Report & Period

Covered

Final Report

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.)

A progressive collapse is described as a chain reaction of failures following

damage to a relatively small portion of a structure. The damage which results

characteristical ly is out of proportion to the damage which initiated the collapse.

The basic concepts associated with progressive collapse are described and the background leading to the concepts is summarized. Possible causes of progressive collapse

are discussed, with concentration on abnormal events which have a low probability of

occurrence but may have catastrophic consequences. A case study of the probability

of structural failure as a consequence of one type of abnormal load (a gas explosion)

shows that these probabilities exceed levels generally considered acceptable to

engineers.

Direct design strategies for reducing progressive collapse are described as

(1) the Alternate Path Method and (2) the Specific Local Resistance Method. Equations

for load combinations, including appropriate load factors, are presented for each

design method. The advantages and disadvantages of each approach are described and

it is concluded that the alternate path method affords the designer more flexibility.

Although the design strategies are applicable to any type of structure at any time in

its life cycle, this report provides detailed recommendations for completed buildings.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons) Abnormal loading; alternate path; building code; design

criteria; probability; progressive collapse; reliability; structural engineering;

uncertainty.

18. AVAILABILITY U nl imued

For Official Distribution. Do Not Release to NTIS

T Order From Sup. of Doc., U.S. Government Printing Office Washington, D.C. 20402, SD Cat. No. Cl 3

|

1 Order From National Technical Information Service (NTIS)

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