NBSIR 78-1440

A Literature Review of Fire and

Live Load Surveys in Residences

Lionel A. Issen

Center for Fire Research

National Engineering Laboratory

National Bureau of Standards

Washington, D C. 20234

May 1978

Final Report

Sponsored in part by:

Office of Policy Development and Research

Department of Housing and Urban Development

Washington, D.C. 20410

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

NBSIR 78-1440

A LITERATURE REVIEW OF FIRE AND

LIVE LOAD SURVEYS IN RESIDENCES

Lionel A. Issen

Center for Fire Research

National Engineering Laboratory

National Bureau of Standards

Washington, D C. 20234

May 1978

Final Report

Sponsored in part by:

Office of Policy Development and Research

Department of Housing and Urban Development

Washington, D.C. 20410

U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Dr. Sidney Harman, Under Secretary

Jordan J. Baruch, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

CONTENTS

Page

LIST OF TABLES

LIST OF FIGURES

Abstract 1

1. INTRODUCTION 1

2. APPLICATION OF SURVEY DATA 2 2.1 Classification of Loads 2 2.2 Statistical Weaknesses of Load Survey Data 2

3. INGBERG'S RESIDENTIAL FIRE LOAD SURVEY 3

4. RECENT LOAD SURVEYS 6

4.1 Karman's Survey 6

4.2 Sentler's Survey 8

4.2.1 Method for Estimating Effect of Load Changes ... 9

4.3 Williams and Dannenf eldt ' s Survey 10

5. METHODS FOR ESTIMATING SAMPLE SIZE 12

5.1 Method 1 - Size of Sample Based on Sample Mean 12

5.1.1 Examples of Sample Size Estimates, Method 1. . . . 13

5.1.2 Ingberg's Data 13

5.1.3 Williams and Dannenf eldt ' s Data 15

5.2 Method 2 - Size of Sample Based on Precision of the

Standard Deviation 16

5.2.1 Example of Sample Size Estimates, Method 2 ... . 17

5.3 Limitations on Sample Size Selection Methods 17

6. SURVEY GUIDES 17

6.1 Literature Guides 17

6.2 Survey Costs 18

7. SUMMARY 19

8. REFERENCES 21

iii
LIST OF TABLES

Page

Table 1. Summary Data for Apartments and Residences 4

Table 2. Summary of Karman's Survey Furnishing .Loads 7

Table 3. Summary of Sentler's Survey 8

Table 4. Expected Changes in Largest Average Load after

Changes in Occupants - Sentler's Survey, Built after

1940 10

Table 5. Williams and Dannenfeldt Survey - Contents Fire Load . . 11

Table 6. Estimate of Sample Size Based on Entire ApartmentIngberg's Data 14

Table 7. Estimated Sample Size Based on Individual Ingberg's

Data 14

Table 8. Estimated Sample Size Based on Residence Data

Williams & Dannenfeldt Data 15

LIST OF FIGURES

Page

Figure 1. Number of degrees of freedom required to estimate

the standard deviation within P% of its true value

with confidence coefficient y 16

iv
A LITERATURE REVIEW OF FIRE AND LIVE LOAD SURVEYS IN RESIDENCES

Lionel A. Issen

Abstract

A search of the literature shows that most load surveys

have been concerned with commercial and industrial occupancies

and only a few have dealt with residences. Many surveys have

been inadequately reported from a statistical viewpoint, and

the data have been misapplied. A common error has been to assume that the largest observed load is the largest expected

load. The statistics of extremes should be used to determine

reasonable design values. Methods for estimating the sampling

size (for a prescribed accuracy) are given and illustrated

with examples.

Key words: Design loads; fire; fire loads; household

surveys; live loads; residential surveys; statistics of

extremes

.

1 . INTRODUCTION

Load surveys have always interested structural engineers and their

predecessors, the master builders. An examination of older structures

and documents indicates that . the master builders of the past must have

understood, even if only intuitively or empirically, the connection

between loads, forces in members, and structural sizes. This kind of

understanding implies a knowledge of the loads produced by different

furnishings and other load items.

The main source for historical data was Heaney's thesis [1]\ A

second source for information on load surveys and related literature was

the bibliography in the paper by Culver and Kushner [2], The oldest

reported load survey that Heaney [1] uncovered was carried out by Stoney

in 1869 . It was concerned principally with the maximum load produced by

people in assembly areas. The oldest residential survey found was made

by Aus in New York in 1904.

Heaney [1] lists 59 published load surveys. Only eight of these were classed as "domestic dwellings." Of these eight, only Ingberg's

survey [3] considered fire loads. The others were only concerned with

the live loads. This report provides a guide to the literature on residential load surveys and discusses (1) their planning and conduct,

Numbers in brackets refer to the literature references listed at the

end of this paper.

1
(2) the limitations on the use of the data, and (3) newer methods of

analysis

.

2. APPLICATION OF SURVEY DATA

2.1 Classification of Loads

In the past it appears that load survey data have been misapplied by

misunderstanding both the data from the load survey and the effect of all

the load producing actions on the structure. The main errors are the

assumption that the maximum observed load is the same as the maximum

expected load, and that the average or some cumulative percentile of the

observed loads may be directly extrapolated to a design load. The former

is in error because the maximum observed load may differ significantly

from the maximum expected load [1,3] and the latter ignores impact,

tolerable levels of vibration, long term deflections and short term

heavy loads.

Impact and vibrating loads which may be produced by wind gusts,

moving furniture, running children, passing vehicles, etc., may cause unpleasant vibrations to the occupants of a residence.

Long term loads, such as those produced by heavier items (semipermanent partitions, heavy furniture, pianos, fish tanks, water beds,

heavy appliances) may produce excessive long term permanent deflections

in the structure.

Short term heavy loads may be produced in residences when the house

is being redecorated and the furnishings from several rooms are stored

in one room or when parties or meetings are held.

Thus, any recommendations for design loads which may be imbedded

in codes and design manuals should include impact, long term deflections,

and short term overloading. Analogous considerations should also be

applied to fire loads.

2.2 Statistical Weaknesses of Load Survey Data

A great weakness of most load surveys, particularly those made prior

to 1960 is that they did not make adequate use of statistical analysis.

This is not to suggest that very sophisticated statistical analyses are always necessary. However, mean, standard deviation, confidence limits,

estimates of required sample size to achieve desired levels of accuracy,

probability distribution functions of the observed loadings, and analysis

of the probability of extreme loads would improve the value and usefulness

of the surveys. Hasofer [4] has stated, "The published results of past

surveys are unfortunately not given in a suitable form (for analysis).

The main methodological mistake was the statistical misconception that one can obtain a reasonable picture of possible maxima of loads by looking

2
at the observed maxima of the survey. The statistical theory of extreme

values has shown that this is an unreliable and inefficient method of

analysis."

3. INGBERG'S RESIDENTIAL FIRE LOAD SURVEY

Ingberg's survey [3] had been preceded by a series of burnout tests

of office type occupancies that extended over a decade. From these tests

Inberg [5] had developed a method for relating the actual temperatures

measured in a fire produced by a known fire load to an equivalent standard

ASTM E-119 [6] fire test exposure. This method which was extended in

1939 to include burnouts of residential occupancies [7] was based on comparing equivalent areas under the temperature-time curve for the

experimental fire with that from a standard ASTM E-119 test.

Ingberg surveyed 13 residential occupancies (apartments and singlefamily homes), which included 1 basement, 10 bathrooms, 18 bedrooms and

closets combined, 3 dining rooms, 12 hallways, 11 kitchens, 1 library,

13 living rooms, 6 storerooms (in apartments), 1 vestibule. These

data are shown in table 1. The survey provided information on fire loads

which could be used to estimate the fire endurance that should be

provided by the compartment walls and f loor/ceiling.

The data in BMS 92 [3] and a subsequent publication BMS 149 [8]

represented the first effort to describe the fire load in a variety of

occupancies. Though the data in BMS 92 from a statistical viewpoint

constitutes a small sample, they have continued to be of interest to

design engineers and regulatory officials. In 1976 BMS 92 was reissued

to meet the continued demand for it. At this time we know that it is

not adequate to use a single method to relate fire load^ and required

fire resistance^. Other factors such as the interior finish, the nature

of the materials and the ventilation are also important in determining

the equivalent fire exposure. Harmathy and Lie [9] and others have

pointed out that it is inadequate to estimate equivalent fire exposure

times by equating equivalent areas under a time temperature curve as Ingberg did in developing his equivalent fire load concept [5,7].

Harmathy and Lie have also shown that the maximum temperature as well as duration of temperature controls the structural behavior of assemblies

in a fire.

Notwithstanding these modern developments and limitations, Ingberg's

approach has been used for many years for estimating required fire

endurances. It should be noted that Ingberg [5] clearly understood the

approximations involved in his equivalent fire load concept.

Fire load is usually defined as the unit floor load of combustibles in

terms of a standard material, usually wood.

Fire resistance is the time that a building element withstands the

ASTM E-119 test usually expressed in hours.

3
Table 1. Summary Data for Apartments and Residences

(Ingberg's Sujrvey) [3]

Combustible Contents

Survey

No

.

Floor

area Movable

prop- erty

Floor Exposed

woodwork

other

than

floor

Total

Entire apartment or residence

ft 2 lb/ft2 lb/ft5 lb/ft 2 lb/ft

A-l 695 3.1 3 3.6 9.7

A- 2 670.5 2.5 3 2.8 8.2

A- 3 544 2.4 2.7 3.4 8.5

A- 4 604.5 2.7 3 2.6 8.2 A-6 519 3.4 3 2.9 9.3

A- 7 647 4.0 3 2.7 9.7 A- 8 431 3.4 3 3.6 10

A- 9 514 3.5 3 2.9 9.4 A-10 734 3.7 1.9 2.9 8.5 A-l 1 734 2.9 1.9 2.8 7.6 A-l 2 748 4.9 0 2.7 7.6 A-13 529 4.6 3 1.5 9.1

A- 17 796 3.1 3 2.2 8.3

Average .

.

3.4 2.6 2.8 8.8

Basement

A-l 783 0.8 0.0 0.2 1.0

Bathroom

A-l 58 1.2 3.0 1.0 5.2

A- 2 60 0.4 2.2 7.4 10.0 A-3 35 .1 0.0 1.9 2.0 A-6 42 1.2 .5 7.1 8.8

A-7 35 0.5 3.0 3.0 6.5 A-8 35 .8 3.0 3.0 6.8

A- 9 35 1.1 3.0 3.0 7.1 A-10 42 1.5 3.0 2.8 7.3

A-l 1 42 1.5 3.0 2.8 7.3 A-17 47 1.6 3.0 4.5 9.1

Average . .

,

1.0 3.7 7.0

Combustible Contents

Survey

No. Floor

area Movableprop- erty

Floor Exposed

woodwork

other

than

floor

Total

Bedroom and bedroom closets combined

ft 2 lb/ft 2 lb/ft 2 lb/ft 2 lb/ft 2

A-l 110 3.7 3.0 3.1 9.8 A-l 136 5.4 3.0 4.6 13.0

A-2a 86 3.9 3.0 1.9 8.8

A- 3 188 4.

1

3. 0 2.3 9.4 A-6 133 7.3 3.0 2.5 12.8

A- 7 128 6.5 3.0 2.2 11.7

A- 7 145 6.7 3.0 2.0 11.7

A-8fc 133 5.0 3.0 3.2 11 .

2

A- 9 138 6.2 3.0 4.0 13.2 A-10 112 4.8 3.0 2.6 10.4 A-10^ 161 3. 8 3.0 3.

1

9.9

A- 11 112 6.6 3.0 2.6 12.2

A-llfr 161 4.3 3.0 2.2 9.5 A-12 154 3.8 0.0 3.0 6.8 A-13a 144 4.4 3.0 1.6 9.0

A-13a 80 7.2 3.0 1.5 11.7 A-17 126 4.2 3.0 1.8 9.0 A-17 126 2.5 3.0 1.8 7.3

Average

.

5.0 2.6 10.4

Dining room

A- 2 132 2.9 3.0 1.9 7.8

A- 4 137.5 3.6 3.0 0.7 7.3 A-12 224 3.0 0.0 3.5 6.5

Average

.

3.2 . 2.0 7.2

No closets.

b Two closets.

Note: 1 lb/ft 2 - 4.88 kg/m2

4
Table 1. Summary Data for Apartments and Residences, Continued

(Ingberg's Survey) [3]

Combustible Contents

Survey

No. Floor

area Movable

prop- erty

Floor Exposed

woodwork

other

than

floor

Total

Combustible Contents

Survey

No. Floor

area Movable

property

Floor Exposed

woodwork

other

than floor

Total

Hallway

ft 2 lb/ft 2 lb/ft 2 lb/ft 2 lb/ft 2

A-l 21 2.6 3.0 6.5 12.1

A-l 11 1.0 3.0 9.7 13. 7 A- 2 86 2.1 3.0 2.4 7.5 A- 3 25 1.0 3.0 7.4 11.4

A- 4 81 5.4 3.0 0.6 9.0

52 0.0 3.0 6.8 9.8

A- 7 67 .0 3.0 5.8 8.8

A- 8 42 .0 3.0 8.1 11.1

A-9 28 .0 3.0 5.5 8.5

A- 10 27 .0 3.0 7.7 10.7

A-ll 27 .0 3.0 7.7 10.7

A-17 20 .0 3.0 9.5 12.5

Average

.

1.0 6.5 10.5

Kitchen

A-l 109 1.6 3.0 6.1 10.7

A- 2 152 0.7 3.0 2.4 6.1 A-3 47.5 .2 0.5 4.0 4.7 A- 4 148.5 . 7 3.0 4.2 7.9

96 1.0 3.0 2.6 6.6

A- 7 90 2.1 3.0 3.2 8.3

A-9 137 0.5 3.0 3.0 6.5 A-10 171 .5 1.0 1.4 2.9 A-ll 171 1.8 1.0 1.7 4.5

A- 13 103 3.8 3.0 1.4 8.2 A-17 87 0.7 3.0 4.5 8.2

1.2 3.1 6.8

Library

Living room

ft 2 lb/ft 2 lb/ ft 2 lb/ft 2 lb/ft 2

A-l 250 3.3 3.0 1.9 8.2 A- 2 132 4.8 3.0 2.6 10.4 A-3 233 3.3 3.0 2.0 8.3 A-4 237.5 4.3 3.0 1.3 8.6

A- 6 175 3.5 3.0 0.6 7.1 A- 7 167 3.0 3.0 .7 6.7

A- 8 213 3.6 3.0 1.9 8.5 A-9 167 4.6 3.0 1.1 8.7 A-10 217 6.8 0.0 3.5 10.3

A-ll 217 1.4 .9 3.4 5.7 A-12 224 4.4 .0 2.1 6.5 A-13 202.5 4.3 3.0 1.6 8.9 A-17 283 3.9 3.0 0.9 7.5

Average 3.9 1.8 8.1

Storeroom (apartment house)

A- 5 264 6.2 0.0 0.0 6.2

A- 5 301 2.4 .0 .0 2.4 A-14 432 8.8 .0 .2 9. 0 A-l 5 1,221 8.0 . 0 .0 8.0 A-16 1,446 10.0 .0 .0 10.0 A-17 98 2.8 3.0 1.3 7.6

Average 6.4 0.3 7.2

Vestibule

A- 2 22.5 2.2 3.0 4.4 9.6

A-12 146 10.6 2.4

5
Ingberg's survey may be criticized on the statistical grounds that

the sample size was too small, that there was no weighting of the data

in terms of statistical significance or variation, and the data were

not presented in a form that lent themselves to further analysis.

4. RECENT LOAD SURVEYS

The most recent residential loads survey for which reports were

available are those of Karman [10,11] (Hungary), Sentler [12] (Sweden),

and Williams and Dannenfeldt [13] (South Africa).

Sentler and Karman both estimated the maximum live loads to be

expected in an apartment by assuming a number of changes (rearrangements

of furnishings or changes in tenancy) during the life of the structure.

Though Williams and Dannenfeldt considered fire loads, they had only a small sample of 6 houses and 2 apartments. This small a sample should

be used only for getting a feel for the magnitude of fire and live loads

and for estimating the approximate size of the sample for a comprehensive

load survey.

4 . 1 Karman* s Survey

Karman's [10,11] survey which was carried out in Hungary in the

early 1960's appears to be the first residential load survey in which

a serious effort was made to analyze the data from a statistical viewpoint.

The data were summarized into histograms, and the statistics of

extremes was used to estimate the effects of changes of loads due to

changes of tenants or rearrangements of furniture during the life of the

residential unit.

Karman [10,11] surveyed 183 apartments distributed in Budapest, in

suburban Budapest, in a provincial city and in a small village. The

"apartments" included 88 single family-houses and 95 apartments in

apartment buildings. His objective was to determine design loads for

specification purposes.

The actual loads per room were analyzed under three different

criteria: equivalent average room load, equivalent load for average

moment, and equivalent load for average shear. He found that there was only a slight difference between these three methods, and so he recom- mended the use of the average room load as it is the easiest to use.

It should be noted that this procedure may be inadequate and may be

criticized on probabilistic grounds [4]. A better procedure would be

to use influence surfaces for moment and shear [14], but this requires

a very detailed analysis.

6
Karman attempted to describe distributions based on an estimated

number of changes of occupants during the life of the structure. Though

his analysis was based on the statistics of extremes, it was limited

because he did not attempt to fit a probability distribution function to

his data, which would aid in estimating the mean and the distribution of

the tail, that is of the maximum loads.

Karman proposed a load reduction formula for large room sizes, but

this does not seem to be justified. Note that Sentler [12] found no correlation of floor load and room size. The data from Karman' s survey

are summarized in table 2.

Table 2. Summary of Karman 's Survey Furnishing

Loads [10,11]

Room

Type

Number of

Rooms

Average Load

Kp/m2 psf

Anteroom 155 21.8 4.5

Kitchen 175 36.3 7.4

* Rooms 500 38.6 7.9

kk

Apartment 183 36.5 7.5

kkk

Largest 183 84.2 17.2

not otherwise identified

kk

whole apartment

kkk

all the movable furnishings in the largest room in

each apartment

Note: 1 Kp/m2 = 1 kg/m 2

1 psf = 4.882 Kp/m2

Karman notes that design loads should include the effects of long term

loading, of varying loads, and of short term heavy loads. He also uses

the terms "static and dynamic fatigue" [10] to include all these effects.

7
4.2 Sentler’s Survey

Sentler [12] applied an analysis, similar to that of Karman, using

the theory of statistics of extremes. The survey included 120 apartment

units which were located inside Stockholm and in the neighboring suburbs.

The material on which Sentler’s [12] paper is based was originally

gathered as part of a fire load survey for the Swedish Institute of

National Defense which was reported by Sjolin in 1969 [15]. Nilsson [16]

also analyzed this survey data, but his summaries were presented in a form that are unsuitable for comparison with other analyses. A summary

of the results of this survey is given in table 3.

Table 3. Summary of Sentler’s Survey [12]

Number Mean Std. Dev. Mean Std. Dev.

Observed (N/m 2

) (N/m 2) (psf) (psf)

Prior to 1940

Sitting Rooms 65 317.9 124.2 6 .

6

2.6

Bedrooms 73 264.0 112.2 5.5 2.3

Hallways 14 201.7 88.2 4.2 1.8

All Rooms 152 289 121 6.0 2.5

Post 1940

Sitting Rooms 67 265.8 95.7 5.6 2.0

Bedrooms 89 198.4 79.4 4.1 1.7

Hallways 33 86.1 88.5 1.8 1.8

All Rooms 189 227 93 4.7 1.9

1 psf = 47.880 N/m 2

Sentler notes that his results are lower than Karman’s [10]. He

attributes this to differences in life styles in Hungary and Sweden. He

also concludes:

1. The live load for sitting rooms and bedrooms is independent

of size.

2. There is no justification for reducing the allowable live

load for larger rooms.

3. In terms of numbers of rooms in each dwelling unit, apartments

with a greater number of rooms tend to have a lower maximum

live load than those with fewer rooms.

8
4 . Design loads should include the effect of short term heavy

loads'^

.

Sentler fitted two different continuous probability distribution functions

to his data; following this he estimated the expected effect on the live

load of subsequent changes of tenants by using the statistics of extremes

[17,18,19]. Sentler suggested that if a more conservative, i.e., a higher

upper bound, estimate is desired the log-normal distribution should be

fitted to the data, otherwise he suggested that the gamma distribution be

used because it appears to fit the original data better [20]. He feels

that both these distributions provide a good fit to residential load

survey data.

4.2.1 Method for Estimating Effect of Load Changes

The theory behind Sentler’ s method has been published elsewhere

[17,18,19]. The procedure is to first plot the survey data as a histogram.

Next fit a suitable probability distribution function (pdf) to the data.

Sentler used both log-normal and gamma distributions. The gamma distribution is to be preferred because the upper tail has an exponential form,

and there are indications that it fits load survey data better than the

log-normal distribution [20].

From the selected pdf calculate the cumulative probability function

(cpf ) . The pdf, after a number of changes of occupancy of the maximum

of the n changes, is given by:

-l 1/ f R

(x) = n*[F

x

(x)] n * f x(x)

where f (x) n pdf after n changes evaluated at a load x

n

Fx(x)

number of changes of occupants (loading) in life of

structure

cpf from survey data evaluated at a load x

fx

(X) pdf from survey data evaluated at a load x

If we substitute on the right-hand side of the equation the probability

values for the maximum expected load, or the maximum load that may occur with a probability of P (which may be some value like 95%, 99.9 % etc.), we will get the probability of the occurrence of the maximum load due

to a specified number of changes of occupants or loadings during the

life structure. Table 4 shows that the value of the largest average

load after only five changes increases to over 150% of the original

value

.

These might be produced by large gatherings of people and during

renovation when the furniture from several rooms might be placed in one room. Detailed derivation of this equation are given in references [10] and

[ 12 ].

9
Table 4. Expected Changes in Largest Average Load after Changes

in Occupants - Sentler's [12] Survey, Built after 1940

Type of

Distribution

No. of

Occupant

Changes

Mean Ratio to

Original

(N/m Data

2

) (psf)

Original Value 1 227 4.7 1

Log-normal Distribution 5 358 7.5 1.58

10 416 8.7 1.83

15 451 9.4 1.99

Gamma Distribution 5 343 7.2 1.51

10 398 8.1 1.72

15 415 8.7 1.83

Note: 1 psf = 47.880 N/m2

4.3 Williams and Dannenf eldt ' s Survey

Williams and Dannenf eldt [13] carried out a survey of six dwellings

and two flats (apartments), in the Union of South Africa in 1974. The

objective was to develop criteria for the fire resistance required for

fire barriers in residential occupancies.

Initially a catalog of furnishings was assembled for use by the

surveyors. The catalog entries had previously been analyzed for weight,

size, and materials. The householder was to identify the furnishings by

the appropriate catalog entry. This turned out to be impractical because

of the normal changes in furniture styles and the large variety of

furniture types. The procedure was then changed to having surveyors

weigh all the furnishing items and identify them with the closest

furnishing item in the catalog.

The observed fire loads (see table 5) , were within the range reported

in BMS 92 [3]; however, the authors' assumption that these surveys are representative of the fire loads in all residences in the Union of

South Africa is questionable. This will be discussed below.

10
Table

5.

Williams

and

Dannenf

eldt

's

Survey

-

Contents

Fire

Load

[13]

* Q

<3O CN X s x \ CO 3 W oo cx 00

pi Pi 3 M 3

p-i oX

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01 x

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3 5 0 x a; oi in m

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CJ I—I CO

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c o

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x

3

PP

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cn o i-'~oo r^. O x <t OO'CT cn cn H CN CO H CnCN H CN vO X vO >—

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x <r x

<r <r <tx <r <r -d- <r

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x <r vo x

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02

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nX

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a)

i—

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oo32

a

03B

o

0

01

11

ually

described

as

"lounge/dining

room
5. METHODS FOR ESTIMATING SAMPLE SIZE

There are a number of methods for estimating the sample size required

for a survey. The method or methods that may be used will depend on

(1) the nature of the data, that is, how much information we have

a priori, about the population that we are sampling; (2) the statistic

that we wish to control, such as mean or standard deviation; and (3)

the level of accuracy that is acceptable. Most of the methods are sensitive to the level of accuracy; that is, for a higher level of

precision or certainty a larger sample size is required. Some methods

are relatively independent of population size provided the population

exceeds a "small population" size [21]. These will not be discussed

here as they do not appear to be appropriate for a loads survey. Two

methods of estimating sample size will be described. These methods of

sample size determination are for simple random samples. Because of the

difficulties in conducting a load survey, advanced survey design methods

do not appear justified at this time even though they could lead to

smaller sample sizes. The first is based on the sample mean; the second

is based on the sample standard deviation. Both are from Natrella's

Handbook [22].

5.1 Method 1 - Size of Sample Based on Sample Mean

This method uses either Student's t distribution or the normal

distribution. Student's t distribution is used if we have an estimate

of the population standard deviation based on a known sample size. The

normal distribution is used if we know the population standard deviation

or we can assume some value for it.

We wish to know the sample size required to estimate the mean m

of a population. We are willing to take a risk that our estimate is off

by d or more. There is available an estimate s of the population standard

deviation a based on q degrees of freedom, where q is usually one less

than the sample size.

1. Choose d, the allowable margin of error, and a, the risk

that our estimate of m will be off by d or more.

2 . Look up ^ or ^ degrees freedom in a table of

Student's t distribution.

3. Compute

d

2

12
where n the sample size required

t

s =* estimate of population standard deviation

d * permissible error in estimate of the mean

a = level of risk that an error has made i.e., probability

that the population mean will lie outside the interval

ra + d

The data from Ingberg's [3] survey and from Williams and Dannenfeldt'

survey [13] will be used to estimate the required survey sample size

using Method 1.

Ingberg's data, which is shown in table 1, will be used to estimate

the sample size required. The calculations in each case are made using

unweighted data.

Case 1 uses the data from the entire apartment.

The method will be illustrated with examples.

5.1.1 Examples of Sample Size Estimates, Method 1

5.1.2 Ingberg's Data

Sample mean 3.4 psf

sample standard deviation = 0.76 psf

estimate of population

standard deviation 0.73 psf

a 0.05 (95% certain that we will not be

in error)

T., = 2.179 with 12 degrees of freedom

l-a/2

n =

where n sample size required

d = permissible error in the estimate

of the mean

s estimate of population's standard

deviation

13
Let d = 5%, 10%, 20% of the sample mean; the results of the analysis

are shown in table 6.

Table 6. Estimate of Sample Size Based on Entire Apartment-Ingberg ' s Data [3]

d d n

% of Mean psf No. of Apts

5 0.17 88

10 0.34 22

20 0.68 6

Another way of using the data to estimate the number of dwelling units

would be to look at the individual room data.

For 75 rooms we have the following data:

Average number of

per apartment

rooms

5.77 rooms /apt

sample mean = 3.17 psf

sample standard deviation = 2.54 psf

estimate of population

standard deviation 2.52 psf

t 1.990 for 74 degrees of freedom

let d = 5%, 10%, 20% of the sample mean, the

results of the

table 7. analysis are shown in

Table 7. Estimated Sample Size Based on Individual

Ingberg '

s

Data [3]

d d n Equiv.

% of Mean psf No. of rooms No. of apts.

5 0.16 982 171

10 0.32 246 43

20 0.63 64 11

14
In both cases the required sample size goes up sharply with the desired

accuracy. The difference between the sample size produced by the two

sets of calculations is that the entire apartment load represent an average or smoothing of the data; that is, it shows less variability than

the individual room data. Weighting the data according to room size

indicates additional variability in the data and so shows larger

required sample sizes.

5.1.3 Williams and Dannenfeldt ' s Data

The data of Williams and Dannenfeldt will be tested using the

individual residence room contents.

number of residences = 6

number of rooms

average number of rooms

per residence

sample mean

sample standard deviation

estimate of population standard

deviation

let d = 5%, 10%, 20% of the sample mean

a = 0.05

t = 2.571 for 5 degrees of freedom

The results of this analysis are shown in table 8.

= 45

= 7.5

= 15.4 kg/m2

= 9.0 kg/m2

= 8.9 kg/m2

Table 8. Estimated

Williams

Sample Size

& Dannenfeldt

Based

Data

on Residence Data

[13]

d d n Equivalent

% of

Mean kg/m2 No. of rooms No . of Residences

5 0.77 884 118

10 1.54 221 30

20 3.08 55 8

As before the data were unweighted.

15
5.2 Method 2 - Size of Sample Based on Precision of

the Standard Deviation

We may wish to know the size of sample required to estimate the

standard deviation with a certain precision. If we can express this

precision as a percentage of the true (unknown) standard deviation, we

can use the curves in figure 1.

Figure 1. Number of degrees of freedom required

to estimate the standard deviation within

P/ of its true value with confidence

coefficient y. [22]^

This figure is reproduced thru courtesy of the Journal of the American

Statistical Association, Vol. 45 (1950), p. 258 from an article

entitled "Sample Size Required for Estimating the Standard Deviation

as a Percent of its True Value" by J. A. Greenwood and M. M. Sandomire

It also appeared in "Experimental Statistics" by Mary G. Natrella [22]

16
5.2.1 Example of Sample Size Estimates, Method 2

For example, let us say that we wish to know how many samples we

should have in order to estimate the standard deviation within 10% of its

true value with a confidence of .95. Referring to figure 1 and going

vertically from P = 10% to the curve y = 0.95, we find that the degrees

of freedom, that is the sample size minus one, is approximately 190.

5.3 Limitations on Sample Size Selection Methods

The limitations on this and other methods of selecting sample size

are that they assume that the data is from the same population, or the same strata of the population. Among residences additional variables

are number of rooms per unit, size of unit, value of unit, room type,

socio-economic class of resident, geographical region, etc.

A priori we may have little or no information on the effect of these

and other variables on loading. One way of proceeding would be to select

an initial survey size. The actual sample or the results should be

stratified, with the stratifications being based on factors relating to

the differences between units. The strata should then be examined for

differences and based on the sample mean and standard deviation a new

sample size is determined with the desired level of confidence. If the new calculated sample size is less than the number surveyed in each

strata, then no further sampling is necessary. If the new calculated

sample size is more than the number surveyed in any strata, it is

necessary to survey only enough additional units to make up the required

totals

.

6. SURVEY GUIDES

6.1 Literature Guides

In addition to residential load surveys and statistical methods,

the following three sources of general information on the conduct and

evaluation of surveys were felt to be of value to the manager and project

leader concerned with surveys.

"The Household Survey Manual - 1969" [23] outlines Federal

Government policy on household surveys and describes some

of the difficulties of carrying out surveys. This manual

is oriented towards sociological or demographic types of

surveys. It contains useful information on the design of

questions and questionnaires, which may be helpful when

planning other kinds of surveys.

17
"An Introduction to Sample Surveys for Government Managers"

[24] complements the "Household Survey Manual." It is oriented

towards the nitty gritty of the objectives, conduct and costs

of surveys. It is very concise and reads easily.

"Evaluation Research" [25] discusses methods of assessing program

effectiveness and survey effectiveness. Both references [24]

and [25] are non-mathematical and are written for non- statisticians .

These last three references suggest that surveys are frequently difficult

and expensive to carry out. The survey should be designed and pretested

on small samples before embarking on a full size survey. The planning,

conduct methodology, and pretesting of the survey should be completed

before beginning the larger survey.

6.2 Survey Costs

The cost of the actual field survey is small compared to that of the

planning, computer programming, logistics and supervision.

The following list of eleven cost elements is from Weiss and Hatry

[24].

Cost Elements in Sample Surveys by Function

1. Overall survey planning, design, and direction.

2. Listing the units (blocks, households, individuals, businesses)

to be sampled.

3. Selecting the sample, preparing maps, instructions, and assignment

schedules

.

4. Developing the interview questionnaire and schedule (including

pretest costs for interviewing and travel)

.

5. Printing questionnaires, training materials, instruction manuals.

6. Interviewing.

a. Recruiting and selecting interviewers.

b. Interviewer training (trainer, training materials, plus

interviewer time)

.

18
c. Contacting and interviewing, calling back, locating missing

respondents

.

d. Field supervision.

e. Travel (time and expenses).

7. Editing, coding, keypunching, tabulating, computing, and if used,

computer time.

8. Telephoning, especially if a survey is by telephone or if

interviews are validated by telephone.

9. Mailing, particularly if a survey is by mail, or when explanations,

introductions, and appointments are made by mail.

10. Analyzing data and report writing.

11. Reproducing the report.

7 . SUMMARY

During the course of the literature search only four residential

load surveys were uncovered for which reports were available and for

which the data was presented in a form suitable for comparison. These

were by Ingberg [3], Karman [10,11], Sentler [12], and Williams and

Dannenfeldt [13]. The first and fourth were concerned with fire loads,

while the other two were concerned with live loads. Ingberg [3] used a sample of 13 residential units; Karman used a sample of 183 units;

Sentler used 341 units. Williams and Dannenfeldt 1 s survey used too small

a sample and their results were inadequately summarized from a statistical

viewpoint. Karman and Sentler extensively analyzed their data and used

the statistics of extremes to estimate the maximum expected loads.

A common error in load surveys is to assume that the maximum

observed load is the maximum expected load and is suitable as a design

load [1]. The maximum expected load can be estimated using the methods

of statistics of extremes. Both Karman [10,11] and Sentler [12] state

that the effects of dynamic loads, long term loads and short term heavy

loads should be included in any code or design specification. Similar

considerations apply to the effects of fire loads.

Since household furnishings are almost completely combustible, in

the absence of other information, it may be possible to estimate the fire

load from the total live load in a residence. The room finish material

may also add significantly to the total fire load [2].

19
Field surveys are generally difficult and expensive [23,24,25].

The costs of surveys can be reduced by limiting the scope of the survey,

by establishing clear objectives, by understanding the limitations of

surveys, and by small scale pretesting of the survey procedures. The

cost of the field survey is only a small part of the total expenditure.

Most of the expenses arise in the work that must be done prior to the

field survey such as planning, design and printing of forms, recruiting,

computer programming, etc., and in the work that is done after the survey

such as keypunching and analyzing the data, and report preparation and

printing.

20
8 . REFERENCES

[1] Heaney, A. C. , A Reliability Based Study Concerning Live Loads

and Structural Design, Ph.D Thesis presented to the University

of Waterloo, Waterloo, Ontario, Canada (1971).

[2] Culver C. and Kushner, J. , A Program for Survey of Fire Loads and

Live Loads in Office Buildings, NBS TN 858, National Bureau of

Standards, Washington, D.C. (1975). Available from the

Superintendent of Documents, Government Printing Office.

[3] BMS 92, Building Materials and Structures, Fire-Resistance

Classification of Building Materials, National Bureau of Standards,

Washington, D.C. (1942). (This report has been reissued as NTIS

Report No. Com 73-10974: Price $4.25.)

[4] Hasofer, A. M. , Statistical Model for Live Floor Loads, Journal

of the Structural Division, American Society of Civil Engineers,

Vol. 94, No. ST 10, 2183-2196 (October 1968). See also discussion

by C. Allin Cornell and Ross B. Corotis, and David E. Allen in

Vol. 95, No. ST 7, 1576-1583 (July 1960) and closure by A. M.

Hasofer in Vol. 96, No. ST 2, 411-413 (February 1970).

[5] Ingberg, H. , Tests of the Severity of Building Fires, Quarterly of

the NFPA, Vol. 22, No. 1, 43-61, Boston, Massachusetts (1928).

[6] Standard Methods of Fire Tests of Building Constructions and

Materials, ANSI/ASTM E119, American Society for Testing and

Materials, Philadelphia, Pennsylvania (1970).

[7] Rodak, S. and Ingberg, S. H., Full Scale Residential Occupancy

Fire Tests of 1939, NBS Report 9527, National Bureau of Standards,

Washington, D.C. (May 15, 1967), unpublished.

[8] Ingberg, S. H. , Dunham, J. W. and Thompson, J. P., Combustible

Contents in Buildings, BMS Report 149, National Bureau of

Standards, Washington, D.C. (1957). Available from the

Superintendent of Documents, Government Printing Office.

[9] Harmathy, T. Z. and Lie, T. T. , Fire Test Standard in the Light

of Fire Research, published in ASTM STP 464 Fire Test Performance,

American Society for Testing and Materials, Philadelphia,

Pennsylvania (1970).

[10]

Karman, T. , Investigations of the Useful Loads of Floor Structure

of Dwellings translated from the Scientific Reports of the

Institute of Construction Science, No. 51, Budapest, Hungary

(1965) .

21
[ 11 ] Karman, T. , Statistical Investigations on Live Loads on Floors,

International Council for Building Research, Studies and Documentation, Committee W23 on Basic Structural Engineering Requirements

for Buildings presented at the Session, Madrid, Spain (1969).

[12] Sentler, L. , A Live Load Survey in Domestic Houses, Report 47,

Division of Building Technology, Lund Institute of Technology,

Lund, Sweden (1974).

[13] Williams, E. G. and Dannenfeldt, H.~ T. H., An Investigation into

the Likely Severity of Fires in Dwellings, National Building

Research Institute, Pretoria, South Africa (1974), unpublished.

[14] McGuire, R. K. and Cornell, C. A., Live Load Effects in Office

Building, Journal of the Structural Division, American Society

of Civil Engineers, Vol. 100, No. ST 7, 1351-1366 (July 1974).

[15] Sjolin, V. , Fire in a Flat - Ignited Through Heat Radiation from

Nuclear Arms, Stockholm, Sweden (1969).

[16] Nilsson, L. , Fire Loads in Flats, Report R34:1970, National

Swedish Council for Building Research, Stockholm, Sweden (1970)

.

[17] Gumbel, E. J., Statistics of Extremes, Columbia University Press,

New York, NY (1958).

[18] Lieblein, J. , Efficient Methods of Extreme Value Methodology,

NBSIR 74-602, National Bureau of Standards, Washington, D.C.

(1974).

[19] Benjamin, J. R. and Cornell, C. A., Probability, Statistics

and Decision for Civil Engineers, McGraw-Hill Book Co., New York,

NY (1970). See particularly pages 271-286 and Appendix B.

[20] Ellingwood, B. A., National Bureau of Standards, a private

communication (1977).

[21] Hall, W. G. and Slovic, L. T. , Survey Manual for Estimating

the Incidence of Lead Paint in Housing, Appendix A., NBS TN 921,

National Bureau of Standards, Washington, D.C. (September 1976).

Available from the Superintendent of Documents, Government Printing

Office

.

[22] Natrella, M. G. , Experimental Statistics, National Bureau of

Standards Handbook No. 91, Washington, D.C. (1963). Available from

the Superintendent of Documents, Government Print Office.

[23] Anonymous, Household Survey Manual 1960, Bureau of the Budget

(now Office of Management and Budget), Washington, D.C. (1969).

Available from the Superintendent of Documents, Government Printing

Office.

22
[24] Weiss, C. H. and Hatry, H. P., An Introduction to Sample Surveys

for Government Managers, The Urban Institute, Washington, D.C.

(1971).

[25] Weiss, C. H., Evaluation Research, Prentice-Hall, Englewood, Cliffs,

NJ (1972).

23
NBS-1 14A (REV. 7-73)

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBSIR 78-1440

4. TITLE AND SUBTITLE

2. Gov’t Accession

No.

A Literature Review of Fire and Live Load

Surveys in Residences

3. Recipient’s Accession No.

5. Publication Date May 1978

6. Performing Organization Code

7. AUTHOR(S)

Lionel A. Issen 8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No. 4926679 (750)

11. Contract/Grant No.

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

Office of Policy Development and Research

Department of Housing and Urban Development

Washington, D.C. 20410

13. Type of Report it 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 search of the literature shows that most load surveys have been concerned

with commercial and industrial occupancies and only a few have dealt with

residences. Many surveys have been inadequately reported from a statistical

viewpoint, and the data have been misapplied. A common error has been to assume that the largest observed load is the largest expected load. The

statistics of extremes should be used to determine reasonable design values.

Methods for estimating the sampling size (for a prescribed accuracy) are given and illustrated with examples.

17. KEY WORDS (six to twelve entries; alphabetical order; capital

name; separated by semicolons

only the first letter of the Ural hey word unless a propat

Design loads; fire; fire loads; household surveys;

live loads; residential surveys; statistics of extremes.

18. AVAILABILITY ?Unlimited d! For Official Distribution. Do Not Release to NTIS

C

rc* er Erom Sup. of Doc., U.S. Government Printing Office Washington, D.C. 20402, SD Cat. No. CM

D ®rd

.er Erom National Technical Information Service (NTIS)

Springfield, Virginia 22151

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