NBSIR 74-526

Analysis of Non-Reinforced Masonry

Building Response to Abnormal

Loading and Resistance to Progressive

Collapse

W. McGuire and E. V. Leyendecker

Center for Building Technology

Institute for Applied Technology

National Bureau of Standards

Washington, D. C. 20234

November 1974

Final Report

Prepared for Office of Policy Development and Research

Department of Housing and Urban Development

Washington. D. C. 20410

NBSIR 74-526

ANALYSIS OF NON-REINFORCED MASONRY

BUILDING RESPONSE TO ABNORMAL

LOADING AND RESISTANCE TO PROGRESSIVE

COLLAPSE

W. McGuire and E. V. Leyendecker

Center for Building Technology

Institute for Applied Technology

National Bureau of Standards

Washington, D. C. 20234

November 1974

Final Report

Prepared for Office of Policy Development and Research

Department of Housing and Urban Development

Washington, D. C. 20410

U. S. DEPARTMENT OF COMMERCE. Frederick B. Dent. Secretary

NATIONAL BUREAU OF STANDARDS, Richard W. Roberts. Director

SI Conversion Units

In view of present accepted practice in this technological area, U.S.

customary units of measurement have been used throughout this report. It

should be noted that the U.S. is a signatory to the General Conference on Weights and Measures which gave official status to the metric SI system of

units in 1960. Readers interested in making use of the coherent system of SI

units will find conversion factors in ASTM Standard Metric Practice Guide,

ASTM Designation E 380-72 (available from American Society for Testing and

Materials, 1916 Race Street, Philadelphia, Pennsylvania 19103). Conversion

factors for units used in this paper are:

Length

Area

1 in = 0.0254* meter

1 ft = 0.3048* meter

2 -4 2 1 in = 6.4516* x 10 meter

1 ft^ = 9.2903 X 10"^ meter^

Force

1 lb (Ibf) = 4.44 8 newton

1 kip = 4448 newton

Pressure , Stress

1 psi = 6895 pascal (N/m^)

1 psf = 47.8 8 pascal (N/m^)

Moment

1 Ibf-ft = 1.3558 newton-meter

*Exact value

i
TABLE OF CONTENTS

. . . , Page

SI Conversion Units i

1. Introduction 1

2. Case Study Approach 2 2.1 Building Information 2 2.2 Problem Statement 2

3. The "Adams" Building 3 3.1 Description 3 3.2 Structural Response 3 3.2.1 Critical Element 3 3.2.2 Loading Function 4 3.2.3 Resistance Interaction Relationship 4 3.2.4 Analysis 5 3.3 Conclusions for "Adams" Building 7

4. The "Baker" Building 7 4.1 Description 7 4.2 Structural Response. . . 7 4.2.1 Critical Element. 7 4.2.2 Loading Function. 8 4.2.3 Resistance Interaction Relationship 8 4.2.4 Analysis 8 4.3 Conclusions for "Baker" Building 10

5. The "Carter" Building

........

11

5.1 Description, 11

5.2 Structural Response 11

5.2.1 Critical Element 11

5.2.2 Loading Function 11

5.2.3 Resistance Interaction Relationship 11

5.2.4 Analysis. . 11

5.3 Conclusions for "Carter" Building 12

6. The "Drake" Building 13

6.1 Description .13

6.2 Structural Response. 13

6.2.1 Critical Element 13

6.2.2 Loading Function. 13

6.2.3 Resistance Interaction Relationship 13

6.2.4 Analysis 13

6.3 Conclusions for "Drake" Building 14

7. The "Edwards" Building 14

7.1 Description 14

7.2 Structural Response 14

7.2.1 Critical Element 14

7.2.2 Loading Function 14

7.2 3 Resistance Interaction Relationship 14

7.2.4 Analysis .15

7.3 Conclusions for "Edwards" Building 15

8. Conclusions - Progressive Collapse 15

ii
TABLE OF CONTENTS (continued)

Page

9. Recommendations for Study and Research. 15

9.1 Design Against Progressive Collapse 15

9.2 Engineered Masonry Construction - State of the Art 16

9.3 Suggested Studies and Research 16

10. Acknowledgements 18

11. References 18

iii

ANALYSIS OF NON-REINFORCED MASONRY BUILDING

RESPONSE TO ABNORMAL LOADING AND

RESISTANCE TO PROGRESSIVE COLLAPSE

by

William McGuire* and Edgar V. Leyendecker**

Structures Section

Structures, Materials, and Life Safety Division

Center for Building Technology

ABSTRACT

Five case studies of susaeiptibility to progressive aollapse

were made of non-reinforced masonry bearing wall buildings . All

were assumed to comply with governing building codes. Based on the assumed failure mechanisms , analysis indicated that two of

the structures had excellent resistance to progressive collapse

,

one was marginal , and two had little resistance to progressive

collapse . Analytical approaches used are illustrated and areas of needed re search are identified.

Key Words: Abnormal loading; Building; Gas explosion; Load-bearing

masonry; Load-bearing walls; Masonry; Masonry research;

Progressive collapse.

1. Introduction

Some multistory buildings may collapse progressively following local

failure caused by abnormal loading. A history of this phenomenon and

examples of its occurrence have been described by Somes [9].i/ The National

Bureau of Standards, sponsored by the Department of Housing and Urban

Development, is conducting research to provide information needed in the

development of rational criteria for the prevention of progressive collapse.

As part of this research, analytical studies are being made of the response

of actual buildings to abnormal loads.

This paper is a report on the findings of case studies of non-reinforced

masonry structures. It also contains recommendations for further research.

The case studies have a three-fold purpose:

1. The assessment of susceptibility to progressive collapse of some common types of contemporary building construction.

2. The illustration of some analytical approaches that can be used

to determine susceptibility to progressive collapse.

3. The identification of specific subjects of research, the results

of which are needed before comprehensive and rigorous design

criteria can be developed for specific materials.

*Professor McGuire was a Visiting Researcher from Cornell University, Ithaca,

New York, October 1972 to March 1973.

**Dr. Leyendecker is a Structural Research Engineer at the Center for

Building Technology.

—^Figures in brackets designate references listed at the end of the report.

1
It is patently impossible to investigate all the possibilities for abnormal

loading, all the ways in which structures are being built, and all the

ways in which they resist, or fail to resist, abnormal loading. But, even within the limited scope of the case studies, it is believed the

above three objectives can be achieved.

2. Case Study Approach

2.1 Building Information

In order that the case studies would be realistic, drawings and specifications for several masonry bearing-wall buildings were reviewed. It is

assumed that all designs provided the required margins of safety with respect

to failure under the required building code design loads. Five case studies

typical of those reviewed were chosen. These ranged from six to ten stories

tall and were of non-reinforced masonry construction. Portions judged

potentially sensitive to progressive collapse were then studied analytically.

Based on the assumed failure mechanisms, it can be shown that the progressive collapse resistance of one of the cases studied is relatively low.

The probability of progressive collapse in a particular building is very

small even though the probability of encountering at least one progressive

collapse in a class of buildings (such as non-reinforced masonry) susceptible

to such failure may be high. The reasonable and proper conclusion to draw

from a finding of susceptibility to progressive collapse in one or more of

the five cases studied is that the problem could be prevalent in this type

of construction and should be investigated at greater depth.

2.2 Problem Statement

The first question posed in each study is whether, under any feasible

abnormal load, a primary structural element would fail. If the building

proves invulnerable to such local collapse then of course the investigation

stops right there; there would be no problem. If, however, local failure

is indicated, the next question studied is whether the failure could spread

progressively to a substantial portion of the building or whether there

exist alternate paths which would enable the structure to bridge the failure

with only local distortion and damage.

Studies of this sort obviously involve judgement and selectivity.

One cannot study every member of a large building without spending an unreasonable amount of time. In each case the building plans were inspected

and a primary structural element was selected for analysis. This was

a member which seemed, on the basis of engineering judgement, to be vulnerabl

to local failure under abnormal loading, and to present possibilities

for the initiation of a progressive failure. In all cases exterior elements

were analyzed; however, in each building there appear to be interior elements

which have about the same degree of resistance (or lack of resistance)

as the one studied. It was not considered necessary to analyze all possibili

ties of progressive collapse since the objectives of this report could be

achievecr by the analysis of a few selected elements.

To analyze a structure, an abnormal loading function must be postulated.

Experience has showji that there is a relatively high probability of a natural

gas explosion in one apartment. Although further research on the pressuretime histories of gas explosions is desirable, sufficient information

exists to develop plausible loading functions [3,6,8]. Since the analysis
of resistance to such loading functions yields the type of information

desired in these studies, they were employed as a basis for analysis.

The details of their use will be illustrated in the case studies.

Definitions of effective alternate structural paths mus't also be

left to the case studies. The alternate path method is a general approach.

Its application involves an examination of the structure that remains

after loss of a primary element to determine whether stable equilibrium--

of at least a temporary nature (such as for evacuation of occupants)

is possible through arching, cantilever, catenary, or similar action.

It may require consideration of the resistance of elements whose load

bearing capabilities were disregarded in the original design.

The case studies are summarized in the following sections. The first

two of the five buildings were studied extensively and the other three

superficially. Recommendations for further studies . and research conclude

the report.

3. The "Adams" Building

3.1 Description

The "Adams" Building is an eight-story brick-masonry, bearing-wall

apartment house. Figure 3.1 is an elevation view and half section of

the building portion studied. The walls and piers are lettered for identification. A plan of a typical floor in the portion studied, is shown in

figure 3.2 and the layout of a single-bedroom apartment is shown on figure

3.3. In the part investigated, the brick cross wall spacing is 92 ft.

Floor construction is of 8-in deep, one-way, prestressed, precast

concrete planks. They bear on the corridor walls and on the exterior

walls, piers, and lintels (figure 3.1). There are no longitudinal ties

(floor reinforcement parallel to the planes of the walls) between the

ends of the planks. There are ties at the one-third points of the floor

span which will be discussed later (figure 3.14).

The brick walls and piers are reinforced only at the floor-to-wall

connections as shown in figure 3.4 (the plank reinforcement is not shown

on the drawing) . The double-angle lintels have a 6-in minimum width of

bearing on the exterior walls and piers.

3 . 2 Structural Response

3.2.1 Critical Element

The structural element selected for analysis of vulnerability to

local failure is a one-story section of Pier B (see figure 3.1). Pier

B is 3-ft wide and 8-in thick of solid brick, single-wythe construction.

Loss of one story of Pier B would result in loss of support for a 15-ft

length of floor (3 ft of pier, one 4-ft spandrel, and one 8-ft spandrel).

There is no apparent potential for post-failure arching over such a damaged

section. Pier B is also located wholly within one apartment (see figure

3.3) and thus subject to the full initial effect of an explosion within

a single living unit.

3
3.2.2 Loading Function

The most useful information on natural-gas explosions currently available

is the work of Rasbash [6], Stretch [8] and Mainstone [3,4]. Rasbash has

presented the ft)llowing empirical equation for estimating the peak pressure:

. p = 1.5 p + 0.4K (Eq. 1)

where

p^ = peak pressure, psi

p^ = pressure at which vents open, psi

K = venting ratio

= (minimum cross-section area of room) /(vent area)

In cases such as the "Adams" Building in which venting is supplied

by the breaking of window glass, Rasbash and Stretch suggest using p^

= 1 psi in Equation 1. However, Mainstone has prepared empirical charts

and suggestions for estimating a range of breaking pressures (p^) for

windows of different sizes and types [3].

A natural gas explosion is a relatively slow deflagration. Mainstone

suggests that the pressure rise time is of the order of 0.1 second and

the decay period lasts about 0.2 seconds [4].

These recommendations of Rasbash, Stretch, and Mainstone are applied

in figure 3.5 with the resulting range of maximum pressures as shown.

Recognizing the approximate nature of pressure and time calculations,

and allowing for the scatter to be expected, it is reasonable to conclude

that a 3-psi peak pressure is highly feasible and that resistance to anything

less than 3.5 psi would indicate questionable structural integrity in

the event of a natural gas explosion. Variations in rise time and duration

are not included because, as shall be seen, structural response is insensitive

to changes in these parameters for such a relatively slow pulse.

This estimation of the loading function assumes that a natural gasair mixture covers the living/dining room and the bedroom prior to detonation

and also that partitions separating rooms remain essentially in place

until after the windows break and the pressure reaches its peak intensity.

3.2.3 Resistance Interaction Relationship

Pier B will be analyzed as an unreinforced , one-story element subjected

to axial force and bending. The most reliable current information on

the resistance of masonry members subjected to this loading combination is

contained in the papers of Yokel, Mathey, and Dikkers [12,13,14,15]. They

propose the following interaction equations for the combined axial force

and bending resistance of sections which crack at or before the ultimate

load [15]

:

M = - (s P + P) (Eq. 2)

6 °

4
or M = ^

(1 - 1.33 I ^-J) (Eq. 3)

whichever is greater. In the equations,

A = Area of net section

a = Flexural compressive strength coefficient

f^ = Compressive strength of masonry

f^ = Tensile strength of masonry

M = Cracking moment

c

= Maximum moment capacity, computed using linear stress gradients

P = Applied vertical compressive load

P = Short wall axial load capacity (f' A) o m

s = Ratio of tensile strength to axial compressive strength of masonry

t m

t = Thickness of wall

Equation 2 controls for cases in which failure occurs immediately upon

first cracking of the section. Equation 3 controls for cases in which tests

have demonstrated that there is post-cracking resistance. Equations 2 and 3 are plotted on figure 3.6 for values of the Pier B parameters. The parameters fin and f^ are based on data in "Recommended Practice for Engineered

Brick Masonry [7]". The value of was obtained from table 2 based on an assumed brick compressive strength of 10,000 psi and Type S mortar. The

value of = 175 psi was obtained from table 5.7 for a wall thickness of

7.5 in using a single-wythe brick. The compressive strength coefficient

"a" of 1.6 was based on the work of Yokel and Dikkers [13].

Separate calculations, which are not included herein, have shown that

neither shearing resistance nor flexural instability control the resistance

of Pier B.

3.2.4 Analysis

Under loads of short duration, a dynamic analysis may be required

in order to obtain accurate results. In the present case, the natural

period of the pier is approximately one-fourth of the rise time of the

explosion (figure 3.7). Because of this difference, a static analysis

of the pier's response would appear to give a satisfactory indication

of true behavior. Further investigation based upon the triangular pulse

shape, shown in figure 3.5, following procedures in Biggs [1] and Jacobsen

and Ayre [2] , indicate that use of the peak pressure in a static analysis

is justified. The problem will therefore be treated as a static one. To study differences in behavior following an explosion in the upper,

middle, and lower regions of the building, the 8th-story, 5th-story, and

Ist-story elements of Pier B are analyzed. Figure 3.8 describes the vertical

loads used in each analysis. It is assumed that internal pressure in

the outer quarter of the apartment where the explosion occurs-, causes tension

5
in Pier B. The vertical forces in the analyzed elements are tabulated

on Figure 3.9 and the bending moments due to floor load eccentricity

on figure 3.10.

Figure 3.11 indicates that if a blast having a peak intensity of

1.4 psi occurred in an eighth-story apartment, the section of Pier B contiguous to that apartment would collapse. A trial and error solution of the

interaction equation was used, with only the successful trial being shown.

Although the interaction equation applies to the resistance of a cross section of the element, failure of the midheight section will precipitate

collapse of the entire member.

In lower stories. Pier B may enjoy some joint continuity because

of dead and live load compression which is not counterbalanced by blast

uplift. Assuming continuity, a frame analysis (not reproduced) indicated

the end and midheight bending moments due to blast to be approximately

equal. They have, therefore, been assumed equal in the analysis of the

first story and fifth-story.

Figure 3.12 shows that a blast pressure intensity of about 3.4 psi

in a fifth-story apartment would cause failure of the top, middle, and

bottom sections of the contiguous Pier B, that is, collapse of the element.

A pressure of 5.4 psi would be required for a similar occurrence in the

first-story, as indicated on figure 3.13. The increase in resistance

as one goes down the building is a result of the increasingly beneficial

effect of the dead and live load compression. Note that the live load used

herein was a reduced live load of 5 psf.

Comparing these results with the postulated loading function (figure

3.5), the conclusion is that a natural gas explosion in the upper three

stories would almost certainly cause failure of a Pier B in that story.

An explosion in the next two stories would probably cause such local failure

of Pier B and an explosion in the lower three stories would probably not.

Since there is a good chance of local failure, the question of whether the

failure will progress or be contained must 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 3.1

and 3.4). 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 removed a story-height section of Pier B will

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

resisting any direct vertical load.

The shear keys between adjacent planks cannot provide effective flexural

resistance in the direction transverse to the plank span. There are, however,

two lines of bridging buried in the floor as shown on figure 3.14. The

intended function of this reinforcement was to improve the diaphragm action

of the floors in transmitting wind loads to the cross walls. It is conceivable

that in the event of loss of a section of Pier B below a particular floor,

the bridging in that floor would serve as a catenary to span the resulting

15-ft gap. Making the generous assumption that the bars would not pull

out of their concrete encasement, the slab is analyzed approximately on figure 3.15. This analysis shows that the bars would yield and permit

the exterior ends of the floor planks to deflect approximately 15 in.

This is more than sufficient to cause loss of support for the section

of Pier B in the story above, resulting in its collapse. This chain of

events can progress to the top of the building.
3.3 Conclusions for "Adams" Building

Exactly what would happen during and following the progressive loss of

a full Pier B is impossible 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

bridging. 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

accumulative 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 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 a Pier B, one conclusion is clear: failure would be extensive and fall well within

any definition of progressive collapse.

4. The "Baker" Building

4.1 Description

The "Baker" Building is an eight-story brick-masonry, bearing-wall

apartment house. Figure 4.1 is an elevation view and half section of the

building portion studied. A plan of a typical three-bedroom corner apartment

is shown on figure 4.2. There are no interior brick cross walls normal to

the wall shown in elevation "E".

Floor construction is of 8-in deep, one-way prestressed, precast

hollow-core concrete planks which bear on the interior concrete masonry

walls and on the exterior brick walls, piers, and lintels (figure 4.1).

The brick walls and piers are reinforced only at the floor-to-wall

connections (figure 4.3). The plank reinforcement is not shown on the

sketch. There are no longitudinal ties (floor reinforcement parrallel to

the wall portion analyzed) between the planks. The triple angle lintels

have 8-in bearing on the exterior walls and piers.

4.2 Structural Response

4.2.1 Critical Element

The structural element selected for analysis is the 14 ft-6 in long

segment of the wall which extends from the side of the window in bedroom

1 to the face of the 12-in by 16-in pier in bedroom 2 (see figure 4.2).

It is assumed that the 13 ft-0 in wall in bedroom 1, the spandrels above

and below the window in bedroom 1, and the 12 in by 16 in pier, will all

survive the initial blast even if the wall segment under consideration

is blown out. The wall segment is located wholly within one apartment

and thus subject to the full initial effect of an explosion within the

living unit.

7
The above assumptions as to remaining elements are considered generous

and there may be other, more vulnerable elements in this building. But one of the purposes of this study is to investigate the behavior of different

types of structural members. The wall segment selected for analysis provides

a good basis for study of the blast and progressive collapse resistance

of planar elements of brick masonry such as post-failure in-plane arching

over a damaged wall segment.

4.2.2 Loading Function

Peak pressures are calculated from Equation 1, the Rasbash fromula

(figure 4.4). The pressures are somewhat higher than in the previous

study because of the smaller amount of venting. In the present case,

a 3 psi peak pressure is highly feasible and resistance to anything less

than 4 psi would indicate questionable structural integrity.

4.2.3 Resistance Interaction Relationship

A one-foot wide vertical strip of the wall is analyzed for blast

resistance. The Yokel, Mathey , and Dikkers formulas. Equations 2 and

3, for this strip are plotted on figure 4.5. The parameters f^ and f^ are based on data in "Recommended Practice for Engineered Brick Masonry

[7]". The value of fj^ was obtained from table 2 based on an assumed brick

compressive strength of 10,000 psi and Type S mortar. The value of f^ = 140 psi was obtained from table 5.7 for a multi-wythe brick wall of 7 ft8 in thickness. The compressive strength coefficient "a" of 1.6 was based

on the work of Yokel and Dikkers [13]

.

4.2.4 Analysis ' -,

'

,

a) . General

The possibility of wall failure in the eighth, fourth, or first story

is investigated in figures 4.6 through 4.8. The analysis of the one-foot

wide strip of wall proceeds just as in the previous study. The intensity

of direct stress on the wall is less than that on Pier B of the "Adams"

Building. Since there is less beneficial compression, the calculated

failure pressures are somewhat smaller in this case than in the previous

one. This, combined with the higher possible blast pressures, results

in a more critical situation regarding the probability of failure of a one-story element in the lower portions of the building. In this structure

it may be concluded that a natural gas explosion in the upper three stories

would almost certainly cause failure of a wall segment and that an explosion

in the lower five stories would probably cause failure.

The question of whether failure will progress is more difficult to answer in this case than in the "Adams" Building. There are no internal

ties between floor planks which might develop catenary action and permit

the floor to bridge over a damaged area. The possibility that the planks

may hang from the exterior wall above and that this wall may successfully

arch over the blasted apartment must be investigated. It will be assumed

that the bent bars which connect the floor to the wall (figure 4.3) function

as proper hangers, although they appear rather short.

An attempt was first made to assess the ultimate arching capability

of the exterior wall. Various failure mechanisms in the wall panel above

a removed segment were assumed and analyzed. However, the problem of

in-plane failure of a brick wall is not as well documented as the ultimate

8
resistance of steel and concrete frames, therefore firm conclusions could

not be reached from simple mechanism analysis. Also, even though failure

in certain modes appeared possible, displacement following such theoretical

failure would bring segments of the wall into contact with other elements

which would probably offer sufficient resistance to prevent complete collapse,

at least for a time sufficient to permit evacuation of the building. So

many assumptions were necessary to permit analysis of these post-failure

conditions as to make the results meaningless hence, they are not reported

herein

.

The approach finally adopted was to analyze the wall above a failed

segment as an elastic body using the SAP plane stress, finite element

program [11] . If anarlysis shows that all of the principal tensile stresses

in the wall are tolerably small and that the required reactions can be

developed by the portions of the structure which remain after an explosion,

it is a convincing demonstration that collapse will not be progressive.

The converse does not necessarily hold. Large tensile stresses may simply

signify failure of another small section of wall with arching over this

region. Repeated analysis with succeeding sections of wall removed may

enable one to conclude whether the process stops with a sufficient portion

of structure left to ensure overall stability, or whether collapse will

progress. In the present case successive iterations were not necessary

since, as will be shown, the stresses and reactions obtained in the first

set of analyses were small enough to justify the conclusion that the wall

will arch above the failed story provided, of course, that the basic and

rather generous assumptions regarding the integrity of the pier and remaining

walls in the apartment with the initial failure are realized (section 4,2.1).

This analysis should be viewed more as a demonstration of an approach

than as a refined tool. Further research is needed before designers can interpret with certainty the results of analyses such as these. For example,

the magnitude of tensile stress which indicates a given probability of

cracking has not been defined. The significance of local stress concentration

needs codification. The limits of treating a combination of bricks and

mortar as an homogenous, isotropic medium are not clear nor is it certain

whether, if these limits are serious, they can be overcome in a practical

way. Suggestions for some of this research will be presented later. The

approach looks promising. If it can be refined, it should be of general

use to designers of masonry structures.

b) . Plane Stress Analysis and Results

Two stories of the wall above a failed segment were idealized as shown on figure 4.9. The wall was treated as a plane stress member with

the thicknesses indicated. The 12-in by 16-in pier at the left side of the

wall in figure 4.9 was considered to be an edge beam as was an 8 -in by 16-in

strip of the wall perpendicular to the right side of the wall shown in

figure 4.9, To study the effect of variations in the resistance offered by

the three floors, three sets of boundary conditions were assumed as indicated

in figure 4.9. The full weight of the wall and edge beams was included in

all analyses. For each set of boundary conditions, three floor loading

conditions were used, making a total of nine analyses. At each loaded

floor, the dead and reduced live load on the outer half of the floor span were applied to the wall. Changing the number of floors loaded gave some indication of whether loads on upper floors are transmitted to the side

supports through arching rather than flexural action.

The reactions for all analyses are shown on figure 4.10. Figures

4.11, 4.12, and 4.13 are plots of principal stresses in the planar elements

for the second set of boundary conditions (horizontal restraint at each

9
floor and vertical support at the bottom only) . It is believed that these

are the most realistic support conditions. Figure 4.14 contains a principal

stress plot for an additional analysis —one made using one story only

and a finer mesh. Distributions of horizontal stress are shown on figure

4.15, for one loading and two boundary conditions.

Observation of the reactions (figure 4.10) indicates that in all cases

they could probably be supplied by adjacent portions of the building without

overstressing. There is a question of whether the 2.12 kip horizontal

reaction at the base of the wall in the case of all floors loaded (figure

4 , 10-Boundary Set B) could be realized. Since there are no ties in the

floor, this force would have to be developed through a combination of

bending resistance of the end wall and shearing resistance of the

small segment of wall remaining in the story below. They seem to

be capable of providing such resistance. As seen from figure 4.10, some other calculated reactions are larger than this one. However, they occur

either in regions removed from the damaged area, e.g., the 3.32 kip reaction

at the floor above, or they require only the readily mobilized compressive

resistance of the building, e.g., the 19.07 kip reaction at the lower,

left corner. The maximum calculated tensile stress in the two-story analyses which

are reproduced is 82.6 psi. It occurs below a corner of the lower window

(figure 4.13). Since the mesh used is rather coarse and there is a stress

gradient in this area, the peak stress at the corner will actually be

higher than this (compare with figure 4.14). There would probably be

localized cracking in this region, but it is doubtful that it would be

serious. Over most of the structure analyzed, both tensile and compressive

stresses are tolerably small.

The principal stress directions in figures 4.11 through 4.13 illustrate

the way forces arch around window openings and in the direction of supports.

However, the study is inconclusive as to the full extent and character

of the cracking that might occur in a multistory wall of a large number

of tiers. For example, it can be seen that the increase in maximum principal

stress along the bottom of the wall is approximately proportional to the

magnitudes of the distributed floor loads added successively to the upper

stories (compare figures 4.11, 4.12, and 4.13). Additional studies would

be needed to determine the level above which most of a superimposed load

is transmitted to the side supports rather than affecting the midspan

horizontal stress at the bottom of the wall.

4.3 Conclusions for "Baker" Building .

In spite of the above indication that the analysis is not complete,

it may still be concluded that this wall would not collapse progressively

if the assumptions as to the elements remaining in the apartment containing

the explosion are valid (section 4.2.1). As stated earlier, however, there

may be other more vulnerable elements that were not investigated because of

a desire to focus on wall behavior.

Looking at the results as a semi-quantitative demonstration of an approach, there are several things to be said. The comparative stress

distributions on figure 4.15 illustrate the beneficial effects of horizontal

constraint at each floor. The refined mesh (see figure 4.14) gives a good

idea of the magnitude of stress concentration around windows and points

of support or constraint. Treatment of the wall as an elastic medium

appears reasonable in view of the brittle nature of bricks and mortar.

With the computer programs currently available, a finite element analysis

is not difficult or expensive. Input is straightforward, running times

10
of even moderately large all-purpose programs seem reasonable, and output

presentation is clear. If it is possible to conclude successfully the

research needed to quantify the effects of non-homogeneity, to establish

permissible (or failure) stresses on a realistic (probably probabilistic)

basis, and to guide engineers in ways of reducing real walls to realistic

analytical models, the use of modern methods of plate and shell analysis

can become practical design office tools.

5. The "Carter" Building

5.1 Description

The "Carter" Building is also an eight-story brick masonry, bearingwall apartment house. Figure 5.1 is an elevation view and section of

the building portion studied. A plan of a typical apartment in this

region is shown on figure 5.2. In the part investigated, the brick cross wall spacing is 65 feet.

Floor construction is of 14-in deep steel bar joists with a 2 1/2-in

cast-in-place concrete deck. The concrete is placed on corrugated slab

form reinforced with 6 x 6-10/10 welded wire fabric. The joists bear

on the exterior walls (figure 5.3) . The brick walls are not reinforced except that over each window there

are three horizontal layers of prefabricated joint reinforcement spaced

8 in o.c. vertically and extending 2 ft beyond the window opening on each

side. The double-angle lintels shown in figure 3.5 have 5-inch bearing.

5.2 Structural Response

5.2.1 Critical Element

Detailed calculations were not made for this building. There are sufficient similarities between it and the previous two buildings to permit

reasonable qualitative analysis of its resistance. The behavior of the

5ft-7in wide section of wall between bedrooms 1 and 2 will be discussed

(figures 5.1 and 5.2) in the following sections.

5.2.2 Loading Function

Application of the Rasbash formula yields peak gas explosion pressures

of 2.7 and 4.2 psi in bedrooms 1 and 2 respectively. The difference is

a result of the different venting in the two rooms. Just as in the "Baker"

Building, an average peak pressure of 3 psi is highly feasible and resistance

to anything less than 4 psi would indicate questionable structural integrity.

5.2.3 Resistance Interaction Relationship

The resistance of a one-foot wide vertical strip of the wall is essentially

the same as that of the "Baker" Building (figure 4.5)

.

5.2.4 Analysis

The steel bar joist floors are somewhat lighter than the concrete plank

floors in the "Baker" Building. On the other hand, the wall in the "Carter"

Building is subjected to the vertical reactions from the spandrels on each

11
side at each floor. In the "Baker" Building, the spandrel reactions

affect only a small region at one end of the wall segment. For practical

purposes, the net effects of the vertical load in the two buildings

are about the same. Thus, the possibility of failure of a one-story

section of the exterior wall considered is about the same as in the

"Baker" Building. Therefore, it may be concluded that a natural gas

explosion in the upper three stories of the "Carter" Building would

almost certainly cause failure of a one-story section of the wall and

that there would be a high probability of failure of such a section

should an explosion occur in one of the lower stories.

In considering what might happen after a one-story section of wall

is removed, it is useful to observe that the general wall layout is, in

terms of structural behavior, intermediate between that of the "Adams" Building

and the "Baker" Building (compare figures 5.1, 3 . 1 , and 4.1). In the "Adams"

Building resistance is in discrete piers without any arching potential.

In the "Baker" Building, the in-plane arching capability of the solid

wall is considerable. In the present case, the wall above an apartment

containing an explosion is punctured by window openings, but there are still continuous expanses of masonry which may have some potential for

bridging over a gap through in-plane redistribution of forces. A finite

element analysis would be of use in evaluating this possibility. One

was not made because, for the purpose of this report, that approach was adequately demonstrated in the study of the "Baker" Building. In lieu

of an analysis, the results of the earlier studies will be used as a guide

to a discussion of what would probably happen in the stories immediately

above the apartment containing an explosion.

If a 5 ft-7 in wide section of bedroom wall is blown out in one apartment,

the spandrels which it supports will go with it. There is no vertical

reinforcement in the brick above the adjacent windows and flashing at

the floor level interrupts the masonry bond. The 2-1/2 in concrete

floor above will attempt to span the 14 ft-4 in gap created by the loss

of the wall segment and the lintels supported on the wall. Assuming that

the floor mesh acts as a catenary and making an analysis similiar to that

on figures 3.14 and 3.15, it can be shown that the maximum deflection

of the floor deck will be about 6 in. The wall above will lose support

and, since it has no reinforcement, it will crack under its own weight.

Whether it will fall out and permit sequential failure up to the roof

is impossible to determine without a more thorough analysis. Adjacent

spandrels would resist the large order displacements and rotations required

to permit a clean drop of any substantial height of the wall strip which

has been considered to be the critical element. It is probable that failure

will be arrested after several stories of sagging and realignment of walls,

spandrels, floors, and interior partitions.

5.3 Conclusions for "Carter" Building

It is quite clear that it is possible to lose a one-story section

of the critical wall through a gas explosion. The analysis has not been

carried far enough to support definite conclusions whether the collapse

would be progressive. Based largely on an interpretation of the results

of the two earlier studies, it is believed that there would be significant

damage and at least partial collapse extending several stories above

the source of the explosion.

12
6. The "Drake" Building

6.1 Description

The "Drake" Building is a six-story, brick and concrete block, bearingwall apartment house. Figure 6.1 is a partial elevation and section of the

building portions studied. A plan of a typical apartment in this region

is shown on figure 6.2. The masonry cross-wall spacing is approximately

150 feet.

Floor construction is of 16-in deep steel bar joists with a 2 1/2-

in cast-in-place concrete deck. The concrete is placed on corrugated

slab form and reinforced with 6x6- 8/8 welded wire fabric. The joists

bear on reinforced masonry tie beams at the exterior walls. These 12-in

thick walls are constructed with 4-in thick brick and 8-in thick concrete

block (figure 6.3). The brick and block are bonded with prefabricated

joint reinforcement in each block bed joint (B-in vertical spacing) ,

6.2 Structural Response

6.2.1 Critical Element

Detailed calculations were not made for this building. The behavior

of the 4 ft-8 in wide section of wall between bedrooms 1 and 2 (figures

6.1 and 6.2) will be discussed. The similarities and the differences

between this and the previous building will be featured.

6.2.2 Loading Function

The peak gas explosion pressures (Equation 1) are 2.8 psi in bedrooms

1 and 2. Resistance to anything less then 3 psi would indicate questionable

structural integrity.

6.2.3 Resistance Interaction Relationship

If the assumption is made that the exterior wall acts as a solid, monolithic wall of 12-inch thickness, the resisting function (Equation 2 and 3) are as shown on figure 6.4. If, at the other extreme, composite action is

completely disregarded and the wall is assumed to act as an 8 in thick,

unreinforced wall, the resisting function is essentially the same as that of

the "Baker" Building (figure 4.5). True behavior is somewhere between these

extremes. No attempt was made to develoe a more accurate measure of resistance in this exploratory study. The curves on figures 4.5 and 6.4 will be

considered as lower and upper bounds in discussing performance . 2/

6.2.4 Analysis

Loading conditions on the actual element are about the same as those

on the element studied in the "Carter" Building. The internal pressure

needed to blow out a one-story gtrip on the top floor will be between

1.6 psi (figure 4.8) and 3.3 psi (figure 6.4). The indication is that

if the explosion occurred in the upper two stories of the building there

would be a good possibility that the wall would blow out, but if it occurred

in the lower half, it is doubtful that failure would occur.

Reference 15 contains information on the behavior of cavity and composite

walls. None of the data presented corresponds directly to the walls of the

"Carter" Building, but the findings generally confirm the lower and upper

bound approach used here.

13
If failure of a one story section did occur, the presence of the

tie beam at each floor (figure 6.3) would cause subsequent behavior to

be quite different from that of the otherwise similar "Carter" Building.

The tie beam is capable of spanning the 12 ft-8 in gap caused by the loss

of a wall and two adjacent spandrels, without excessive deflection. It

will provide some vertical support for the wall above and, probably more

important, it should serve as a tie in enabling the wall to develop its

in-plane arching capability.

6.3 Conclusions for "Drake" Building

Although this study has been cursory, there is good reason to conclude

--based on the previous, more detailed analyses—that in this case, even

jLf a one-story section of wall were blown out, collapse would not be progressive .

7. The "Edwards" Building

7.1 Description

The Edwards Building is a ten-story, brick and concrete block, bearingwall apartment house. Figure 7.1 is a partial elevation and section of the

building portion studied. A plan of a typical corner apartment is shown on figure 7.2.

Floor construction is of 8-in deep, one-way, prestressed precast concrete planks. They bear on the cross walls (figure 7.3). The interior

concrete masonry cross walls are reinforced by vertical bars placed in

grout filled cells. The amount of reinforcement varies with height, being

greatest in the bottom story. Brick and block in the exterior wall are bonded with prefabricated joint reinforcement in every second bed joint, i.e.,

16 in on center.

7.2 Structural Response

7.2.1 Critical Element . The behavior of the north wall in the region of the kitchen will

be discussed, without the aid of calculations.

7.2.2 Loading Function

If a natural gas explosion occurs in the living/dining room area,

the peak gas explosion pressure (Equation 1) is approximately 2.7 psi

.

Resistance to anything less than 3 psi would indicate questionable structural

integrity

.

7.2.3 Resistance Interaction Relationship

The resistance of a vertical strip of the north wall will be approximately

the same as that of a wall strip of the "Drake" Building if the wall is

unreinforced. Everything that was said in the previous study regarding

upper and lower bounds of resistance applies here as well. If the wall

is reinforced, the resistance is of course considerably greater.

14
7.2.4 Analysis

Even without reinforcement, the resistance of this wall is greater

than that of the "Baker" Building. A gas explosion in one of the upper

three stories might blow out a section of wall but, below this, it is

probable that the wall would not be breached. With reinforcement, effective

resistance to local damage is probable in all but the top story.

Since the wall is not pierced by windows, its arching and corbeling

capabilities appear excellent. A finite element analysis would be useful

to confirm or disprove this supposition. Even without such an analysis,

previous studies indicate that failure of this wall would be localized

and not affect more than two or three stories at most.

7.3 Conclusions for "Edwards" Building

Of the five buildings studied, the progressive collapse resistance

of the Edwards Building appears to be the best. Floor ties at the ends

of the precast planks would improve the integrity without adding substantially

to the cost but, even without these, there does not appear to be much

chance of progressive collapse.

8. Conclusions - Progressive Collapse

Five typical non-reinforced masonry buildings were studied, two in detail

and three superficially. Progressive collapse following a natural gas explosion is a serious possibility in one (the Adams Building) and also very

probable in a second (the Carter Building) . One (the Baker Building) appears

marginal if it is recognized that the assumption made regarding the integrity

of the 12 -in x-16 in pier (section 4.2.1 and figure 4.2) was very liberal.

In the remaining two, reasoning indicates that failure would be arrested

before there were serious consequences in regions removed from the source of

the explosion.

The probability of progressive collapse in a particular building is very

small even though the probability of encountering at least one progressive

collapse in a class of buildings (such as non-reinforced masonry) susceptible

to such failure may be high. However, the substantial danger of progressive

collapse in almost half of the buildings of the small sample studied in this

report is considered sufficiently great to warrant further research in the

resistance of non-reinforced masonry structures. The research needs that

have become apparent in the course of these studies are outlined in the

following section.

9. Recommendations for Study and Research

9.1 Design Against Progressive Collapse

Three measures used in dealing with progressive collapse were identified

in early British response to the Ronan Point collapse [see reference 9 for a review]

:

a) . General Structural Integrity—provision of sufficient redundancy

to give the structure a good chance of suffering only local failure under

unpredictable abnormal loading. This is accomplished through joint continuity

and inter-member ties. Experience has shown that general structural integrity

is inherent in most conventional steel and concrete structures. It has

not, as yet, been demonstrated that the same is true for the newer forms

of masonry construction and industrialized construction.

15
b) . Specific Local Resistance —design of members to resist failure under

a presumably realistic, predictable, abnormal loading. Provision of "5

psi resistance" is an example of this approach.

c) . Alternate Paths —provision of ability to span temporarily the gap

left by the destruction of a member not capable of resisting the predictable

abnormal loading. Conceptual removal of a member incapable of resisting

5 psi and verifying alternate paths in the remainder of the structure

is an example of the use of this measure.

It appears that all three measures will continue to be used in combating

progressive collapse. It is reasonable to try to provide in all buildings

structural integrity comparable to that found in conventional steel and

concrete construction. In many structures there will be members whose

loss under a reasonable abnormal loading cannot be tolerated. Such members

should be designed for specific local resistance. In general, however,

local failure under abnormal loading should be acceptable provided alternate

paths exist to prevent immediate progressive collapse.

Objections to the earlier British progressive collapse criteria centered

not on these three measures, as such, but rather on details of the ways

in which their implementation was prescribed. American criteria should

retain the measures but try to avoid the pitfalls in the early U.K.

standards. The research suggested in section 9.3 should help to do this, at

least in the formulation of specifications for the prevention of progressive

collapse in masonry structures.

9.2 Engineered Masonry Construction - State of the Art

There are paradoxes in masonry construction. It is often thought

of as being conventional, yet some of the newest masonry structures are,

in fact, very unconventional. It is the oldest way of building large

structures yet, in a number of respects, its technology lags behind that

of newer forms. In spite of its age, much of masonry's great versatility

and amenability to innovation are just beginning to be exploited.

To put masonry technology on a level of sophistication comparable

to that in steel and concrete, construction control has to be improved,

structural analyses appropriate to the medium have to be introduced,

codes must be rationalized and modernized, and the research needed to

support these developments must be conducted. It is inevitable, therefore,

that in suggesting research on progressive collapse in masonry one must

extend the scope to include subjects relating not only to the progressive

collapse problem, but to masonry design and construction in general.

9.3 Suggested Studies and Research

The following ideas stem from the work done in the case studies reported

above

:

a) . Joint Behavior'—General structural integrity and ability to provide

alternate paths depend upon the behavior of connections between the floor

elements (concrete or steel) and the masonry walls. There seems to be

little research on this subject. There is need for large, comprehensive

testing programs of typical existing connections as well as of designs

that might emerge from the research. The programs should be designed

so as to have statistical significance. Some of the specific topics to

be investigated are:

16
/

1) . The effective rigidity of joints. Moment-rotation diagrams.

The development of resisting moments in masonry walls supporting

loaded floors.

2) . Distribution of contact pressure under slabs supported by walls.

(This has been the subject of several investigations)

3) . Local contact stresses and crushing under bends or hooks in

reinforcing bars embedded in masonry. Tear-out of such bends or hooks.

4) . Effectiveness of bond and anchorage of reinforcing bars embedded

in shear keys in floors, floor topping, and several courses of masonry

(see figure 3.4 and 4.3).

b) . Bond Between Reinforcement and Masonry —This is related to the connection

problem. Allowable bond stresses have been established for masonry but

the evidence on which they are based is rather sparse and rather old.

Further, it is not clear how well these data apply to the common case

in which reinforcing bars run vertically through a number of courses of

masonry (see figures 3.4 and 4.3). Statistically significant series of

pull-out tests should be run to study the roles of the various parameters:

bars, mortar, masonry unit, and workmanship.

c) . In-Plane Behavior of Walls —Masonry is often used as a planar structural

element. Experience has shown that it has ability to arch, corbel, or otherwise distribute forces around openings, re-entrant corners, and zones

of tensile stress. But there seems to have been no effort to develop

rational methods for analyzing this capability. Research applying finite

element techniques to typical situations should be undertaken. The effects

of cracking, orthotropy, and non-homogeneity should be included. Tests

of walls would also be necessary to confirm the analytical methods or

to help in modifying them (See section 4.2.4).

d) . Dynamic Response^—The above suggestions deal with static behavior.

Numerous studies have been made of the response of walls to conventional

explosions. There seem to have been few quantitative studies of the resistance

of walls and connections to the slower dynamic loading encountered in

gaseous deflagrations. In the area of response to slow explosions specific

topics to consider are

:

1) . The comparison of theoretical and measured vibration characteristics

of walls and piers. Refinement of methods for calculating frequencies

of masonry elements.

2) . Non-destructive experimental studies of response of masonry

walls to pulses of various durations and peak pressures. Verification

of conditions under which a static analysis is valid.

3) . Destructive experimental studies to check the validity of analytical

failure mechanisms and loadi-deformation relationships (moment-rotation

and stress-strain diagrams) used in applying these mechanisms. One

of the difficult problems in applying past test results to wall analysis

is the assessment of whether the boundary conditions present in

the tests match those in the actual structure. Constraint against

in-plane movement can substantially alter resistance to lateral pressure.

Wall tests should attempt to simulate the translational and rotational

restraint conditions present in actual structures.

17
4) . Following investigation of the static behavior of joints (Item

(a) above) , comparative tests of response to slow explosions would

- be important in verifying the applicability of the static tests to

the abnormal loading problem.

e) . Stress-Strain Properties of Masonry—This is the first item recommended

for research in reference 15. In that reference it is advised that, "this

study should include a thorough investigation of the relationship between

compression strength in one-dimensional compression and in flexure and

investigation of the stress distribution corresponding to linear strain

gradients." This recommendation is strongly seconded as probably the

most important piece of research needed to improve basic understanding

of masonry behavior. Until the apparent increase in material strength

with strain gradient is more thoroughly understood, any analytical method

for calculating resistance to flexure or combined flexure and direct force

is open to the criticism of being weakly founded and of uncertain generality.

Reference 15 contains other suggestions for important research. These

should be implemented, but it is believed that the investigation of stressstrain properties deserves priority.

f) . Bond Beams —Intuitively, tie or bond beams such as illustrated on figure 6.3 appear to be effective in increasing general structural integrity

and resistance to progressive collapse. However, this intuitive impression

has not been the subject of intensive study. One might, for example,

analyze and then test the relative resistance of two masonry walls (one

with and one without a tie beam such as shown on figure 6.3) to in-plane

forces following loss of a section of wall below the one considered.

g) . Composite Walls—Considerable work, had been done on the interaction

of two types of masonry in one wall. But the resistance to gaseous deflagration

of a composite wall such as that shown in figure 6.3 is not at all clear.

Tests of walls of this type, perhaps in conjunction with some of the studies

described in Item (d) above, would be informative.

h) . Design Examples-—Detailed methods for the verification of alternate

paths will probably remain beyond codification because of the many different

situations encountered in practice. Nevertheless, a publication containing

illustrative examples drawn from actual, representative structures, would

be a useful document.

10. Acknowledgements

The authors wish to express their appreciation to the Department of

Housing and Urban Development for making this study possible. Mr. Ralph

Cooper was expecially helpful in selecting the designs which were reviewed

to establish the typical case studies. The assistance of Professor Harold

Laursen of Oregon (NBS Guest Worker) in making the finite element computer

runs was invaluable.

i 11. References

1. Biggs, J. M. , Introduction to Structural Dyman ics, McGraw-Hill Book

Company, New York, 1964.

2. Jacobsen, L. S. and Ayre , R.S., Engineering Vibrations , McGraw-Hill

Book Company, New York, 1958.

18
Mainstone, R. J., "Breakage of Glass Windows by Gas Explosions," Building

Research Station Current Paper , 26/71 , United Kingdom, 1971.

Mainstone, R.S., "Internal Blast," Committee 8 Report, Tall Buildings

Conference, Bethlehem, Pa., 1972.

Newmark, N. M. and Haltiwanger, J. D. , Airforce Design Manual, Principles

and Practices for Design of Hardened Structures," Technical- Documentary

Report AFSWC-TRD-62-138 , Kirtland Air Force Base, New Mexico, December

1962.

Rasbash, D. J., "Explosions in Domestic Structures, Part One, the Relief

of Gas and Vapour Explosions in Domestic Structures," The Structural

Engineer , October 1969.

Recommended Practice for Engineered Brick Masonry , Brick Institute of

America, McLean, Virginia 22101, November 1969.

Stretch, K. L. , "Explosions in Domestic Structures, Part Two," The

Relationship Between Containment Characteristics and Gaseous Reactions,"

The Structural Engineer , October 1969.

Somes, N. F., "Abnormal Loading on Buildings and Progressive Collapse,"

in "Building Practices for Disaster Mitigation," Building Science Series

46 , National Bureau of Standards, Washington, D.C. 20234, February 1973.

Timoshenko, S., Vibration Problems in Engineering , D. Van Nostrand, 1955.

Wilson, Edward L. , "SAP, A General Structural Analysis Program," Contract

DACW 68-67-C-004, University of California, Berkeley, Calfifornia, September, 1970.

Yokel, F. Y, , "Stability and Load Capacity of Members with No Tensile

Strength," Journal of the Structural Division , American Society of Engineers, July 1971.

Yokel, F. Y. , Dikkers, R.D., "Strength of Load-Bearing Walls," Journal

of the Structural Division , American Society of Engineers, May 1971.

Yokel, F.Y., Mathey, R. G. , and Dikkers, R. D. , "Compressive Strength of

Slender Concrete Masonry Walls," Building Science Series 33 , National

Bureau of Standards, Washington, D.C. 20234, December 1970.

Yokel, F.Y., Mathey, R.G., and Dikkers, R.D., "Strength of Masonry Walls

Under Compressive and Transverse Loads," Building Science Series 34 , National Bureau of Standards, Washington, D.C. 20234, March 1971.

19
II

li

I

I

I'
OO

X

I-GO

oro

o

_i

X

in

o

o

IHDV3„j8-8 iV S3IM0iS 8

8 d3ld

0 ti3\d

8 d3ld

V "nvM

N,

00=

O

LUCO

O

LUcn

i -co ~—;r

-CM

hi

Z

o

i

_l

LU

_J

<

cr.

o

"Li

O

&1

(-3

S

I o

llJ

UJ

UJ

_i
PRECAST DECK

'y— 2 1/2"

EXTERIOR

BEARING

SOLID ENDS IN PLANKS

NTERIOR

BEARING

SPANDREL

Figure 3.4 Floor-Wall Conneation Details, Adorns Building.
PRESSURE, p =1.5p + O.hK m V

VENT OPENING PRESSURE, pV

(a) Rasbash-Stretch , Reference 6 and 8

p =1 psi for all cases V

(b) Mainstone, Reference 3 (charts)

2

Bedroom: Window area = 0.8^4 m (single pane)

Window aspect ratio = 2.25

Limiting p^* from figure 2, reference 3

p = 1.5 X 0.^45 psi

p = 0.68 psi

V

2 Living/Dining Room: Window area = 2.8 m (single pane)

Window aspect ratio = 1.2

Limiting p_^* from figure 2, reference 3 (use

3 times 3/l6 in sheet glass values

p^ = 1.5 X 3 X 0.29 psi

p = 1.35 psi

*Mainstcne ' s "limiting p_^" is 1.5 times the "most likely'' value read from

the charts in reference 3.

VENTING RATIO, K

(a) Bedroom - Use full rolling window opening plus I'-O" depth of fixed

glass below

K= 11.5' x 8.0'/^.0' X 5.5' = ^.2

(b) Living/Dining Room - Use full sliding window opening

K = 11.5* X 8.0'/8.0' X 6.0' = 1.9

LOADING FUNCTION

Figure 3.5 Loading Function for Pier Adarr-.s Building.

T = natural period

k = pier height

(El)g^^= effective pier stiffness=0.7 El [l3

m = mass of pier

useis 96 in

(El)eff = 0.7 El = 2.69 X 10* # in*

m =0.0519 #secVin*

T= 0.025 sec

tm.O-IQ . T" 0.025"

where = rise time to maximum pressure [4

Figure 2.7 Natural Period for Pier Adonis Building.
Assumed Loading for pier B: ... • Zero live load on roof • 5psf live load on all floors • 9 feet of roof and floor vidth tributary to Pier B • 6 feet of spandrel length tributary to Pier E

O Uplift due to explosion on outer l/U of floor and ceiling

k Pm

Unit Loads

ii = 26'-2"-

r~r~r

i i 1 i i w t 7

P^=p X 9' X 26.17' X 12'

G

P^= 8500 p

G m

(P^ in lb and p in psi)

G -^m

8" Roof Deck

Roofing

Roof Dead Load

.060 ksf

.002

.062 ksf

8" Floor Deck

Partitions

.060 ksf

.005

Floor Dead Load .O65 ksf

Roof D.L. on Pier = .062x13.1x9

=7.30 kip

Floor D.L. on Pier = .065x13.1x9

= 7.65 kip/floor

Floor L.L. on Pier = .005x13.1x9

=0.59 kip/floor

Parapet Load = 3'x 9'x O.O8O =2.16 kip/pier

Spandrel: Lintel 2 x O.O8O = O.I6O

Windows 6.5 x 0.025 = O.OI6

0.176 kip/ft/spandrel

0.176 X 6 = 1.05 kip/pier/story

Pier weight = 3' x 8.71' x O.O8O = 2.10 kip/story

Figure 3.8 Vertical Loads^ Adams Building.
ITEM LOAD

Parapet

Roof Dead Load

1/2 Pier

1/2 Pier

Dead Load, 3 Floors (3x9.65)

Live Load, 3 Floors (3x0.59)

Piers, 2 stories (2x2.10)

Spandrels, 3 Floors (3x1.05)

1/2 Pier

1/2 Pier

Dead Load, 3 Floors

Live Load, 3 Floors

Piers, 2 stories (2x2.10)

Spandrels, 3 Floors (3x1.05)

1/2 Pier

1/2 Pier

(\init loads from figure 3.8)

2.16 kip

7.30

9.U6 kip 8th Story - Top

1.05

10.51 kip 8th Story - Mi dh eight

1.05

11.56 kip 8th Story - Bottom

22.90

l.TT

k.20

3.15

U3.58 kip 5th Story - lOp

1.05

hi. 63 kip 5th Story - Midheight

1.05

U5.68 kip 5th Story - Bottom

22.90

l.TT

h.20

3.15

TT.TO kip 1st Story - Top

1.05

T8.T5 kip 1st Story - Midheight

1.05

T9.80 kip 1st Story - Bottom

Figure 3.9 Pier Faroes , AdorriS Building.
2.50

1.6/-^

minimum bearing

r Roof or floor load

0.83

e= Load eccentricity= 2.98

Mq ROOF = 7.30x2.98= 21.8 in kip

Mq floor = 7.65 X 2.98 = 22.8 in k ip

Ml FLOOR = 0.59 X 2.98 = 1.8 in kip

Roof

8th floor

7th floor

6th floor

5th floor

4th floor

3rd floor

2nd floor

1st floor

rMQ=2l.8inkip ^

ML(8th story only)

Ml = 0.05 in kip

{ML=o.9in k^p} ;!;yp'^°' °" '^"^ *°P°"^

bottom stories

fMD

IMl

Figure 3.10 Pier Moments due to Eaoentricity , Adams Building.
TRY Pf|,= l.4psi Assume pinned- pinned piers

1pQ+L=9.5kip Pg = 12.0 kip*

^ 1

MD+|_=2l.8inkip

96

r V (

11.6 '12.0

2.3

*Pq = 8.5 Pn, =12.0 kip (from figure 3.8)

**MG = i/8 wA*= 1/8 x(l.4x36)x(96)^ = 58.l in kip

Pd+l+g^o

'^D+L+6 = ^2.9in kip

From Eq. 2, M^. =61.5 in kip < 62.9 in kip use pm = 1-4 psi

Figure 2.12 Eighth-Story Analysis for Pier Adams Building.
TRY pm = 3.4 psi Assume equal end and midspan moments

96

PQ^^=43.eW\p Pg = 29.0 kip*

i

MQ^.|_=l2.3in kip MQ=70.6inkip

12.3 70.6

45.7 ' '29.0

*PG = 8.5pm= 29.0 kip (from figure 3.8)

**Mq= 1/16 wX^= 1/16 x{3.4x36)x(96)^= 70.6 in kip

Mq^L^q = 82.9 in kip

From Eq. 2, Mc= 1.272 x 16.7+ 61.5 =82.7 in kip « 82.9 in kip use pm=3.4psi

i

40

20

PD+L+G = '6-7kip

'^D+L+G=82.9inkip

50 100 150 M

Figure 2.12 Fifth-Story Analysis for Pier Adarr^s Building.
TRY = 5.4 psi Assume end and nriidspan moments

^D+L^'^'^'/^'^'P .PG = 46.0kip*

1 Mq^I_=I2.3 in kip MG = ll2.0inkip

96" \

\

^

^

i

I 12.3 112.0

Tpd^.l=79.8 1 460

*Pg = 8.5 Pm = 46.0 kip (from figure 3.8)

**Mg= 1/16 wA^= I/I6x(5.4x 36)x{96f = il2.0in kip

'^D+L+G = '^'^•S in kip

From Eq. 3, Me= 3.812 x33.8 [l- ^]= 124.5 in kip « 124.3 in kip

use p,^ = 5.4 psi

kip

Figure Z.IZ First-Story Analysis for Pier B, Adams Building.
APARTMENTS

'BRIDGING

\ 3 #4 bars in fill

i. )over 6" hollow

/ core ( unit

8 hollow core plank

(6" units at bridging)

-BRIDGING

15-0 gap below

(Pier B* two

spandrels)

PLAN

#4 bar .Concrete fill

•k . k

-

1

' * '

'

, . I , . .

.

'f "- *

"^e-'unit

8'

SECTION l-l

4

.1

w

o

uI 26-

2'

o

8"

Figure 3.14a Bridgingj Adonis Building.
Figure 2.14b Bridging^ Adams Building.
ASSUMPTIONS

Assume 60psf planks f 5 psf partitions + 5 psf live = 70psf

Assume plank rotates about corridor wall and derives other support from

two catenarys of equal stiffness

FLOOR DECK

L=I5'

Assume 3- #4 bars yield (steel area = 3x0.20 in^,

yield stress = 60,000 psi)

H = 3 X 0.20 X 60,000= 36,000"^

A _R2L^_ 1100(15)^12) _ . ^2 - 8H 8x36,000 ' '^'^

END DEFLECTION: ^3 = | x 10.3 = 15.5"

Figure 3.15 Alternate Path Analysis^ Adams Building.
00

O

X

00

q:

o

o

I- cx

H0V3„8-8 IV samois 9

oQ

GO

00

TYPICAL

ELEMENT

ANALYZED

T

1—

1

1 1

"9

1

"CO

1

1 1 1 1 1

LJ

n

1 1

1 1

1 1

1 1

1 1

1 1 n1 1

1 1

1 1

1 1

1 1

UJ

<

>

UJ

-J

UJ

<

a.

(0

CVJ

"cot

o

UJ

Iq:

in

o

Co

o

00

i3> &4


Pressure, p = 1.5 p + 0.4K

VENT OPENING PRESSURE, p

(a) Rasbash-Stretch, Reference 6 and 8

P = 1 psi for all cases V

(b) Mainstone, Reference 3, (charts)

2

. Window area = 0.8^* m

Aspect ratio = 1.00

Limiting p^* from figure 2, reference 3

. p^ = 1.5 X 0.7 psi

p^ = 1.05 psi, use 1.0 psi as in (a)

*Mainstone's "limiting p

" is 1.5 times the "most likely" value

read from the charts in reference 3.

• y - , , . ^ , VENTING RATIO. K

(a) Bedroom No. 1 - K = 13.0' x 8.0'/3.33' x 6.0' = 5.2

(b) Bedroom No. 2 - K = 10.33' x 8.073.33' x 6.0' = h.2

LOADING FUNCTION

Figure 4.4 Loading Function^ Baker Building.

Assumed Loading: • Zero Live on roof

• 5 psf Live Load on floor

• Uplift due to explosion on outer l/h of floor and ceiling

P^=Pj^x 12" X 2k.

5

' X 12" (refer to figure 3.8 for diagram)

P^=0.88 p

. G m

(P- in lb/ft and p in psi)

Unit Loads

:

8" Roof Deck

Roofing

.060 ksf

.002

.062 ksf

Roof D.L. on Wall=.062xl2.25=.76 k/ft

Wall weight = 8.6T'x.080=O.TO kip/story

8" Floor Deck .060 ksf

Partitions .00$

Floor Dead Load .O65 ksf

Floor D.L. on Wall=.065xl2.25=.80 kip/ft

Floor D.L. on Wall=. 005x12. 2 5=.06 kip/ft

ITEM • -

. LOAD

Roof Dead Load 0.76 kip/ft

0.76 kip/ft 8 th Story - Top

1/2 Wall .35

1.11 kip/ft 8th Story - Midheight

1/2 Wall ^ 0.35

1.1+^ kip/ft 8 th Story - Bottom

Dead Load - k Floors i+xO.,80 3.20

Live Load - k Floors 1+xO.,06 .2h

h,90 kip/ft 4th Story - Top

1/2 Wall .35

5.25 klp/ft 4th Story - Midheight

1/2 Wall .35

5.60 kip/ft 4th Story - Bottom

Dead Load - 3 Floors 3x0..80 2.k0

Live Load - 3 Floors 3x0.,06 0.18

8.18 kip/ft 1st Story - Top

1/2 Wall .35

8.53 kip/ft 1st Story - Midheight

1/2 Wall .35

8.88 kip/ft 1st Story - Bottom

Figure 4.6 Vertioal Loads and Forces^ Baker Building.
3.00 MINIMUM BEARING

2.0d| i.od -ROOF OR FLOOR LOAD

e = LOAD ECCENTRlCiTY = 3.0"

MqROOF = 0.76x3.00 =2.28 in kip/ft

Mq floor = 0.80 x 3.00 = 2.40 in kip/ft

Ml floor = 0.06x3.00 = 0.18 in kip/ft

rMD=2.28in kip/ft

/Iml=o

\^^^Mi{8\h story only) —M|_=0.05in kip/ft

ROOF

Md

Mq=0.57 in kip/ft

8th FLOOR

7th FLOOR

6th FLOOR

5th FLOOR

4th FLOOR

3rd FLOOR

2nd FLOOR

1st FLOOR

XrMD= 1. 14 in kip/ft 1 /^^^ , ...yTypicalforallbuttop

IMl= 0.09in kip/ftj ^

Figure 4. 7 Wall Moments due to Ecoentviaity, Baker Building.
8th STORY - Try Pm = '-^ psi Assume pinned-pinned piers

PD+l_ = 0.8k/ft ,Pg= I.Ik/ft* MD+L=2.3lnklp/ft

96"

1.5 Md+l=I-2

pi.i *Pg = 0.882 pm =11 k/ft (from figure 4.6)

**MG= 1/8 wh^=l/8xl2xl.3x(96f =18.0 in kip/ft

Pd+L+G = 0-4 k/ft , Mq+l+g= '8-5 in kip/ft

From Eq. 2, Mc= 0.5+ 18.0 = 18.5 in kip/ft use Prn=l.3p8i

4th STORY- Try Pm= 3.0 psi Assume equal end and midspan moments

Pd+l = 4.9 k/ft^ 'PG = 2.6k/ft* Md+l='-2 in kip/ft Mg= 20.7 In kip/ft**

\

Pd+L=

'

*Pg = 0.882 X 3.0 = 2.6 k /ft

o '2 20.7

PG = 2.6

**Mg= I/I6xl2x3.0x(96)^ = 20.7 in kip/ft

''D+L + G

= 3.0kip/ft Mq^l+g = 2l.9inkip/ft

From Eq.2, Mg = 18.0+ 4.0 = 22.0 inkip/ft« 21.9 in kip/ft use Pf„=3.0psi

96"

1st STORY -Try P|T^=3.5psi Assume equal end and midspan moments

PD+l_=8.2k/ft 'PG=3.lk/ft* Md+l=I 2inkip/ft Mg = 24.2 in kip/ft**

\

12 24 2

,Pg = 3.I

96'

*Pg = 0.882 X 3.5=3.1 k/ft **Mg= 1/16 x 12 x3.5x(96)^= 24.2 in kip/ft

PDtL+G=5-8 kip/ft f^D+L+G^ 25.4 in kip/ft

From Eq. 2, M(s= 18.0+ 7.7= 25.9 in kip/ft« 25.4 in kip/ft use Pf„ = 3.5psi

Figure 4.8 Story Analysis,, Baker Building.
BEAM

ELEMENTS

\} V W T H ^' V V V

PLANE STRESS ELEMENTS

if U ir w u

t

t = 8

-tt = l6

\

t=8

t=l6

V V H V V

BEAM

ELEMENTS

2a1l-0

2atr-0"

2atr-0"

2 at r=(

2at2'-d' 8'-0"

I

2 at 2-0" 8=0"

t

6 at 2'-0"

r-9"

14-6'

2atl -a

2 at 1-2"

3-4' 2-4 -H

8"

Boundary Set A - Horizontal and vertical restraint at each floor

Boundary Set B- Horizontal restraint at each floor, vertical restraint at bottom only

(as shown)

Boundary Set C - No horizontal restraint, vertical restraint at bottom only

Figure 4.9 Finite Element Idealization^ Baker Building.
OOP

I cviro^

ddd JSC J£ ^

U> —

— c\ito — m o5o oddI I JC

I

o9

a o

9 O

O t- 4> — OT5 w O o Sis

S o

o 0 =

03 _l<

0>CJN.

cvjo>p ^ -SC cog? If) (0 0000 — CM CM ^ ^

—com

^ J£ JC ro «oo^

ro 10 CM d fOtD
—ooo

odd

— eviro

lomcvj

<Mr

—— cvi ^

00 lO <x>

—

N to ^ j< lO to (VI 00 1^

tfi 00 ±

JC ^ JC 0> tr OJ CM O) 00 — cJ

J£ JC

0>

— 00

:i o o>

CVJ ^

»_

O o O H- — o o « m _i<

(D Ore

o> dd (VI ^ ^ j£

d«o oi

(3i Ks

PQ

+:> 035^o

COO

+^Oo

a,

Cu

CO
Jae J£

PO 0> —

CNi — Q

CD (D ^ Is

cJ to ^'

— itiai

<3i

RQ

T3

0) XJ o o

o

O kf- — ^ O OT iti

tr ^ — o o —

00 -l<

I

CO

o

Co

to — Jt — N ^

ro — oS

(\J ro ro
7

7

?1

/ (

X

7

+ X

10m

"s "

«»

<A iO

t> U

(A »

+

X X

\

7 a.

(35

tin
7

-/

7

y. it

"4

\

a Q. M O X

^si

X

X

X

«r

157

5a

<35
A10.7

-6.S

7 ?

X

o

X

X

m

M W

ft M E M o « U » " < _ *

5 o

' & S X

X

7

1
yf.. <- > X X —

«— — —oS ^. "^U "^S Ti ' ^"f"

'

^ ^7 S? ST

-.t- V.

?^ r;-Y, „ , y

'mm sJI?—SI"

. Q.

in p W o

g o

y ff>c« 7* toe* X

-A x

k 2

aa. < /

to I

S

+:> S

PQ

+iCO

O

CQ

o

s

•(^

Sh

+:> CO

CO

CO

to
4-1/2

l4'-6"

II . 5-4 1/2"

,

1 6-0 ^ 4 2-9 ^

Rsference axis ^

for stress

*

K

1 \^

\i

1

/

1

/ /

1

1

\

\ w

y \

\® \

KEY— Boundary Set B-AII floors loaded —^—^— Boundary Set C- All floors loaded

SCALE: I inch = 50 psi

Figure 4.16 Horizontal Stress Distribution^ Baker Building.
I
iro

o

_i

u.X

oo

if) o->

(X. <

CD

-IUl

UJtn

O

o

CD

UJ

UJ

^1III z s < o -) Z Q. O

o

O

O

V)

ic. iZ.

HDV3 „j9-6 iV S3ldOiS 9

u

CO

<35

is

o

<^ to"a

n

r

..o-.s I

in

I

o

I

I

I tf>

K) V)

OD

U

bj1

. 1

o«

pi

tin


WINDOWS>

EXHAUST

VENT

TYPICAL ELEMENT ANALYZED

SPANDREL

FLOOR LEVEL

FLOOR LEVEL T

6-0'

4-0" 4-8 4-0 10-6" 8 -0 4'-d'

< p

SECTION

PARTIAL ELEVATION "E"

X

u

<

-In

00

I

UJo

W

/AV/\\

6TH FLOOR

4TH FLOOR

STEEL BAR JOIST

1ST FLOOR

12' 22 -e

PARTIAL SECTION

Figure 6.1 Partial Elevation and Section, Drake Building.
ELEVATION "e"

Figure 6.2 Apartment Plarij Drake Building.
EXTERIOR WALL

NOMINAL

INTERIOR WALL

TRIPLE ANGLE LINTEL

SPANDREL

Figure 6.3 Floor-Wall Connection Details , Drake Building.
{d!il)d
SECTION

PARTIAL ELEVATION "e" PARTIAL SECTION

Figure 7.1 Partial Elevation and Section, Edwards Building.
12" i

SEE FIGURE 7.3 ^FOR SECTION

BEDROOM

METAL STUD AND

DRYWALL PARTITION

LIVING/DINING

ROOM

CONCRETE MASONRY

ELEMENT

ANALYZED

BRICK

27'- 4"

ELEVATION "e"

12 WALLS ARE BEARING WALLS

8 WALLS ARE NON-BEARING WALLS

Figure 7.2 Apartment Plan, Edwards Building.
12 (NOMINAL)

I » ABOVE 3R0 FLOOH

AT GROUT JOINT ABOVE 4TH FLOOR

AT GROUT JOINT BELOW 4TH FLOOR

FLOOR TOPPING

8 CONCRETE PLANK #3 BARS AT 2-0 ON CENTERS

ABOVE 3RD FLOOR

^.•:a

ur/ 13'P_aK**- -^^>^- -TTWury^ -^AJX.* a-* V?"

.will ^

b1;.f.:.-},fs

••^.1 fii^a^'

16" (NOMINAL)

I BELOW 3R0 FLOOR

-^4 BARS AT 2-0" ON CENTERS

BELOW 3RD FLOOR

(SEE FIGURE 7.2 FOR LOCATION)

Figure 7.3 Typical Bearing Wall Detail, EduJards Building.
NBS-114A (REV. 7-7J)

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. inmi.K A i ioN OK Ri;i'()K i- no. NBSIR 74-526

2. Ciov't Accession

No.

3. Kci ij^ient's Accession No.

4. i i ri.i-: ANP SI M i l I I,

1

Analysis of Non-Reinforced Masonry Building Response to

Abnormal Loading and Resistance to Progressive Collapse

5. Publication Date November 1974

6. Performing Organization ( ode

7. AT 1 IIOR(S)

Kliiiam McGuire and Edgar V. Leyendecker

8. Performing Organ. Report No. NBSIR 74-526

9. pi;ki ormin(, orcani/a i ion namk and addrkss

national bureau of standards

department of commerce

washington, d.c. 20234

10. Proiect/Task/Work Unit No. 4618488

11. Contract/Grant No.

12. Sponsoring Organization Name and ( ompletc Address (Street, City, State, ZIP)

Office of Policy Development and Research

Department of Housing and Urban Development

Washington, D. C. 20410

13. Type of ReDO/t & Period Covered Final

Nov. 1972 to March 1973

14. Sponsoring Agency Code

15. SI ppli;mI':ntary noths

16. AlfSTRACT (A 200-word or less factual summary o/ most si^iificant information. If document includes a significant

bibliography or literature survey, mention it here.) Five case studies of susceptibility to progressive collapse were made of nonreinforced masonry bearing wall buildings. All were assumed to com.ply with

governing building codes. Based on the assumed failure mechanisms, analysis

indicated that tv7o of the structures had excellent resistance to progressive

collapse, one was marginal, and two had little resistance to progressive collapse,

Analytical approaches used are illustrated and areas of needed research are identified.

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; Building; Gas explosion; Load-bearing

m.asonry; Load-bearing walls; Masonry; Masonry research; Progressive collapse.

18. AVAILABILITY [x

' Unlimited

[ For Official Distribution. Do Not Release to NTIS

[3 ' Order From Sup. of Doc, U.S. Government Printing Office Washington, D.C. 20402, SD Cat. No. CH

' X Order From Naiional Technical Information Service (NTLS)

'Springfield, Virginia 22151

19. SECURITY CLASS

(THIS REPORT)

UNCLASSIFIED

20. SECURITY CLASS

(THIS PAGE)

UNCLASSIFIED

21. NO. OF PAGES

66

22. Price

USCOMM-DC 29042-P74