AlllOO TmTSfl

NBSIR 81-2366

Method for Assessing Costs of

Noise Control Requirements in

Multifamily Residential and

Educational Buildings

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Building Technology

Building Economics and Regulatory Technology Division

and Environmental Design Research Division

Washington, DC 20234

li|:: NBS

PUBLICATIONS

December 1 981

Prepared for :^QCc:===

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31-2366

1981

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^ronmentai Protection Agency

ce of Noise Abatement and Control

national BOTUU.O or 8TANDAIIMI

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NBSIR 81-2366

METHOD FOR ASSESSING COSTS OF

NOISE CONTROL REQUIREMENTS IN

MULTIFAMILY RESIDENTIAL AND

EDUCATIONAL BUILDINGS

JAN 8 1982

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Stephen F. Weber

Fred F. Rudder, Jr. Michael J. Boehm

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Building Technology

Building Economics and Regulatory Technology Division

and Environmental Design Research Division

Washington, DC 20234

December 1981

Prepared for Environmental Protection Agency

Office of Noise Abatement and Control

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige. Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler. Director
- V I..
ABSTRACT

This report presents a methodology developed to measure the cost impacts of

acoustical performance requirements for new buildings. The methodology can

be applied to a wide range of noise control requirements. The cost items

addressed by this methodology are expected changes in construction costs,

the cost of acoustical testing to certify levels of performance, code administration costs, and energy savings due to modifications of the building

envelope. The building components considered, which are those most commonly

affected by noise control requirements, are doors, windows, interior walls,

exterior walls, and floor/ceiling assemblies. The basic cost assessment

method consists of linear cost estimation equations for most component designs

commonly used in educational and multifamily residential buildings. Each

equation relates the acoustical performance of the design to its construction

cost so that construction costs associated with alternate levels of acoustical

performance can be compared. The methodology also includes a cost minimization

model useful for selecting the least-cost design for a particular level of

acoustical performance.

Keywords: acoustical design; acoustics; architectural daslga; building codes;

building economics; construction costs; cost minimization; economic

impact; economics; energy; model code; noise control.

iii
PREFACE

The rf?search leading to this report was conducted by the Applied Economics

Group and the Building and Community Acoustics Group in the Center for

Building Technology, National Engineering Laboratory, at the National Bur- eau of Standards. The effort was sponsored by the U.S. Environmental Protection Agency, Office of Noise Abatement and Control (ONAC) under the

Interagency Agreement, "Method for Assessing Impacts of a Model Noise Control

Code," dated August 9, 1979.

The authors are grateful to Casey Caccavari, Joseph Montgomery, and Frank Pesce

of ONAC for the encouragement and suggestions thej^ provided throughout the

research effort. The authors have benefited also from the many helpful comments

made by the NBS reviewers of the report; William Danner, James Gross,

Harold Marshall, Heinz Trechsel, and Simone Yaniv. Special credit is due to

Anne Hillstrom for verifying the numerical examples and editing several drafts

of the report. The authors are also grateful to the staff of the Word Processing

Center for the many hours of typing needed to bring the report to camera-ready

form.

iv
TABLE OF CONTENTS

Page

1. INTRODUCTION 1

1.1 Purpose and Scope 1 1.2 Organization 2

2. MODEL NOISE CONTROL CODE PROVISIONS 4

2.1 Outdoor Noise Isolation and Acoustical Privacy 4

2.2 Impact Noise Isolation and Mechanical Equipment Noise 6

3. ANALYTICAL APPROACH 8

3.1 Relationship between Construction Cost and Sound

Transmission Class 8

3.1.1 Establishing Component Design Categories 8

3.1.2 Architectural Design Variations 9

3.1.3 Derivation of Cost Estimating Equations 10

3 .2 Design Assumptions 16

3.2.1 Doors 16

3.2.2 Windows and Sliding Glass Doors 16

3.2.3 Exterior Walls 16

3.2.4 Interior Walls 17

3.2.5 Floor/Celling Assemblies 17

4. APPLICATION OF COST EQUATIONS TO BUILDING COMPONENTS 18

4.1 Single Component Applications 18

4.2 Multi-Component Applications 20

4.2.1 Data Required to Determine the Minimum Constructon Cost

Design 21

4.2.2 The Design Equations 21

4.2.3 Example Design Calculations 21

4.2.4 A Few Words of Caution 27

5. ENERGY SAVINGS AND NON-CONSTRUCTION COSTS 30

5.1 Energy Savings 30

5.2 Code Administration Costs 32

5.2.1 Overview of Administrative Requirements 32

5.2.2 Specialized Skills 32

5.2.3 Specialized Documentation 35

5.2.4 The Experience of San Diego 36

V
TABLE OF CONTENTS (Continued)

Page

5.3 Acoustical Testing Costs for Acceptance 37

6 . CONCLUSION 41

REFERENCES ........................... 42

Appendix A: COST ESTIMATING EQUATIONS FOR BUILDING COMPONENTS A-1

Appendix B: ADJUSTING FOR REGIONAL CONSTRUCTION COST DIFFERENCES B-1

Appendix C: DESIGN OF MINIMUM COST MULTI-COMPONENT WALLS TO ACHIEVE A

SPECIFIED LEVEL OF NOISE INSULATION C-1

vi
LIST OF TABLES

Page

Table 2.1 Model Noise Control Provisions Developed by Bolt,

Beranek, and Newman, Inc 5

Table 2.2 Model Noise Control Code Specifications (Decibels) for

Outdoor Noise Isolation and Acoustical Privacy 5

Table 2.3 Major Building Components Affected by the Outdoor Noise

Isolation and Acoustical Privacy Provisions of the MNCC 7

Table 3.1 Acoustical Performance and Cost Data Used in the Regression

Analysis for Doors 11

Table 3.2 Estimated Regression Coefficients and Relevant Cost and

STC Ranges for each Component Design Category 14

Table 4.1 Minimum Cost Equations for a Two Component Wall Design 22

Table 4.2 Minimum Cost Equations for a Three Component Wall Design .... 22

Table 5.1 Code Administration Functions Required for Analysis, Plan

Review, and Acceptance According to the Model Noise

Control Code 33

Table 5.2 Model Noise Control Code Acceptance Testing Requirements for

Occupancy Permit, by Building Type 38

Table B.l Regional Cost Adjustment Factors (RCAF) for Major

U.S. Cities B-2

Table C.l Detailed Calculation Results for Design No. 1 C-19

Table C.2 Calculations for Example Problem for Minimum Cost STC

Design Range C-25

Table C.3 Calculations for Example Problem for Varying Door STC

Rating C-25

vii
LIST OF FIGURES

Page

Figure 3.1 Scatter Plot of Data Points and Least Squares Linear

Regression for Doors 13

Figure 4.1 Selection of Specific Designs Relative to the Optimum

Design Point (R*, C*) 29

Figure C.l Example Calculation Using Equation (C.25) to Illustrate the

Effect of Varying Glazing Area C-21

Figure C.2 Example Calculation Using Equation (C.29) to Illustrate Minimum Cost Design with a Single Fixed Component C-26

viil
CONVERSION FACTORS FROM CUSTOMARY TO METRIC (SI) UNITS

Quantity To Convert From To Multiply By

length linear foot (f) meter 3.048 X 10-1

area square foot (sf) square meter 9.290 X 10-2

energy therm joule 1 .055 X 108

U-value Btu/hr/sf/A°F watt/m2/A°C 5.678

price dollars /square foot dollars/ square

meter

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1. INTRODUCTION

1.1 PURPOSE AND SCOPE

The purpose of this report is to present a standard methodology for measuring

selected economic impacts of acoustical performance requirements for new educational and multifamily residential buildings. The primary economic impacts

address'd by this assessment method are those related to costs. The most

important costs are the additional construction costs estimated to result from

complying with new acoustical performance requirements of proposed code provisions. Two other cost items are discussed in general terms: the costs for

acoustical testing to certify compliance, and the administrative costs

attributable to acoustical performance provisions.

The majo’* benefit expected from acoustical performance provisions, namely an

improved acoustical environment in multifamily residences and educational

facilities, is not addressed by the assessment method presented in this report.

Efforts to relate changes in property values or rental rates to improved

acoustical performance in residences are recommended for future research.

There is some discussion of one important benefit that under certain circumstances could result from new acoustical performance provisions: the value of

energy savings due to modifications in the exterior envelope of the building.

In order to illustrate the cost assessment method, a particular sound transmission control code, called the Model Noise Control Code (MNCC),^ is used.

This proposed model code was developed by the acoustical consulting firm of

Bolt, Beranek, and Newman, Inc. (BBN) under the sponsorship of the Environmental Protection Agency. ^ Unique to the MNCC are variable performance

requirements based on expected noise levels surrounding the buildings in

question. In contrast, current building noise control provisions in the

Appendix of the Uniform Building Code ,^ have fixed performance requirements

regardless of the amount of noise in the building's environment. As described

in the BBN reports, the MNCC could be substituted for the current building

noise control provisions contained in the Appendix, Chapter 35, "Sound Transmission Control," of the Uniform Building Code. The performance requirements

^ The selection of the MNCC to illustrate the Impact assessment method should

not be construed as an endorsement by NBS or the authors. One code was needed for an example code in order to show how the methodology works.

The MNCC is general enough for all aspects of the methodology to apply to

it, and specific enough to show how the methodology can be applied to a particular code.

^ The Model Noise Control Code (MNCC) developed by Bolt, Beranek, and Newman Inc.

(BBN) is presented in two reports: Noise Control for Building Codes: Model

Noise Control Provisions (No. 3759), and Implementation Manual (No. 3837)

(Cambridge, Mass., Bolt, Beranek, and Newman, Inc., 1978).

^ International Conference of Building Officials, Uniform Building Code (Whittier, CA: International Conference of Building Officials, 1979), Appendix,

Chapter 35, "Sound Transmission Control," pp . 668-669.

I
of the MNCC are restricted to residential multifamily and educational building

applications

.

The methodology presented here consists of the application of linear cost

functions which were estimated for the designs most commonly used for the

door, window, wall, and deck assemblies of residential and educational buildings.

Each cost function relates the acoustical performance of each assembly design

to its corresponding construction cost. Moreover, each function explicitly

presents an estimate of the extra construction cost required for a unit Increase

in the acoustical performance of a design. Thus these cost functions provide

a method to estimate and compare the construction costs of a design under two

alternative levels of acoustical performance: (1) that called for by existing

requirements or current construction practice; and (2) whatever alternative

acoustical performance level is being proposed. The linear cost functions

that are presented in this report cover only the most commonly used designs

and materials for which reliable acoustical performance and cost data were available at the time the analysis was conducted. To apply the methodology to

other designs, specific cost estimating functions need to be developed.

In addition to the analysis of the building code provisions governing sound

transmission control, the methodology presented here has two other useful

applications. First, the methodology is general enough to assess the costs

of changing the acoustical performance levels of building components regardless of whether the specifications being analyzed are contained in a building

code. This is because a wide range of acoustical performance values and

their corresponding construction costs were obtained and used as the data base

in estimating the cost functions for those designs analyzed here. The ranges

of acoustical performance values used for the designs are sufficiently broad

to cover both current construction practice as well as most Increases in

recommended acoustical performance levels likely to occur in the near term.

Moreover, for designs not covered by the cost functions presented here, the

basic methodology can be used to derive the appropriate cost functions.

The other useful application of the methodology is that it can provide architects and builders with valuable information about the cost consequences of

designing buildings to alternative levels of acoustical performance. Indeed,

a special cost minimization model is presented which guides architects to

select the least-cost combination of levels of component acoustical performance

when a single performance criterion addresses more than one building component.

This least-cost solution can be found for any specific acoustical performance

criterion using a hand calculator.

1.2 ORGANIZATION

Section 2 of this report begins with an overview of the specific provisions

of the acoustical performance code used to illustrate this methodology, the

MNCC, and identifies the types of buildings affected by each provision. The

detailed acoustical performance requirements specified in the MNCC provisions

are presented in tabular form and interpreted. Then the major building

envelope components affected by the MNCC provisions are identified.

2
Section 3 contains a description of the analytical procedure used to develop

the cost assessment methodology. First, the underlying assumptions are explained for categorizing the component designs used in developing the cost

functions. Next, the procedure used to derive the cost functions is presented

in detail along with a discussion of the statistical measures used to describe

the underlying regression results. The assumptions needed to assure appropriate

usage of the cost functions are also explained. The section concludes with a detailed description of each of the five major building components addressed by

this methodology.

Section 4 describes how the cost equations are to be applied in estimating the

additional construction costs due to increases in the acoustical performance

requirements of a building. The first subsection deals with the simple case of an acoustical performance requirement which affects the design and construction

of a single homogeneous building component. The second subsection treats the

complex case of a performance requirement simultaneously affecting more than

one building component.

Section 5 discusses non-construction related costs and the value of energy

savings that may result from certain acoustical performance provisions. A

technique is presented for estimating the possible energy saving benefits from

acoustical improvements in window designs. The non-construction related costs

are of two categories: one for the costs of acoustical testing of a completed

building, and the other for the costs of administering the code. These cost

items are treated separately to allow the measures to be applied only when

appropriate to the particular noise control code being evaluated.

There are three appendixes to this report, the first two of which provide data

needed to apply the methodology. Appendix A contains the technical specifications for each assembly design, the estimated linear cost equations, and statistical measures of how well the equations represent the relationship between cost

and acoustical performance. Appendix B presents a table of regional cost adjustment factors and illustrates how to apply these factors to account for regional

construction cost differences. Appendix C provides a detailed derivation and

formulation of the cost-minimizing model for multi-component designs.

3
2. MODEL NOISE CONTROL CODE PROVISIONS

This section reviews the provisions of the MNCC used to illustrate the cost

assessment method and identifies the building types and major building envelope

components affected by those provisions. Our purpose here is to provide the

reader with a brief description of the MNCC sections which are specifically

addressed by the methodology. For more elaborate details on these MNCC provisions, the BBN reports prepared for the Environmental Protection Agency

should be consulted.

2.1 OUTDOOR NOISE ISOLATION AND ACOUSTICAL PRIVACY

Table 2.1 presents the titles of the four MNCC provisions and indicates the

building types affected by each. The first two provisions. Outdoor Noise Isolation and Acoustical Privacy, both govern the transmission of airborne noise

into and within buildings. It is expected that these provisions would account

for most of the increased cost resulting from widespread adoption of the MNCC.

The acoustical provisions contained in building codes today are generally

presented in terms of a fixed acoustical performance requirement .2 In contrast,

the airborne noise requirements of the MNCC vary as a function of the outdoor

acoustical environment. This acoustical environment is measured in decibels

of outdoor Day-Night Sound Level (DNL) which is defined as "...the equivalent

A-weighted sound level during a 24-hour period with 10 decibels added to the

equivalent A-weighted sound level during the nighttime hours (10:00 p.m. to

7:00 a.m.)."^

The Outdoor Noise Isolation provision (section 3507) imposes outdoor noise

isolation requirements on the exterior shell of the building. It affects both

multifamily residential and educational buildings exposed to outdoor DNL values

greater than 60 dB. As indicated in table 2.2, the outdoor noise isolation

requirements vary directly with changes in the DNL ranges.

The Acoustical Privacy provision (section 3504) imposes performance requirements

for airborne noise transmission reductions for multifamily residential and

educational buildings. These noise transmission reduction requirements distinguish two types of acoustical privacy provided by building separations (e.g.,

floors/ceilings or interior walls): (1) Interior Private to Private dwelling

1 Bolt, Beranek, and Newman, Inc., Reports 3759 and 3837.

2 For an overview of various noise control codes currently in effect, see Bolt,

Beranek, and Newman, Inc. Interim Report 3547, task 1: Development of Noise

Control Requirements for Model Building Cod e (Cambridge: Bolt, Beranek, and

Newman, Inc., 1977), pp. 15-20.

^ Bolt, Beranek, and Newman, Inc., Report No. 3759, p. 27. A-weightlng is a system of weights which gives relative importance to each frequency range

in accordance with human hearing.

4
Table 2.1 Model Noise Control Provisions Developed by Bolt, Beranek, and Newman, Inc.

Provision Buildings Affected^

Outdoor Noise Isolation (sec. 3507) R E

Acoustical Privacy (sec. 3504) R E

Impact Noise Isolation (sec. 3505) R

Mechanical Equipment Noise (sec. 3506) R E

a Key: R = E =

Table 2.2

Multifamily high-rise, low-rise, and townhouse buildings.

All educational buildings.

Model Noise Control Code Specifications (Decibels) for Outdoor Noise

Isolation and Acoustical Privacy

If Outdoor Outdoor Noise Acoustical Privacy

Day-Night

Sound Level

Isolation

(sec. 3507)

(sec. 3504)

> < Outside to Inside^ Public To

Private^

Private To

Private^

50 - 55 60

50 55 - 50 55

55 60 - 45 50

60 65 20 40 45

65 70 25 40 45

70 75 30 40 45

75 80 35 40 45

80 *****C0NSTRUCTI0N PROHIBITED********************

^ The difference, in decibels, between the outdoor equivalent A-weighted sound

level and the corresponding equivalent A-weighted sound level in the receiving

space.

b The Normalized Sound Level Difference as defined in Bolt, Beranek, and Newman,

Inc., Report No. 3759, p. 29. The MNCC recommends that these values be

Increased 5 dB when using STC as the design requirement.

5
unit separations (party walls); and (2) Interior Public to private dwelling

unit separations.

These requirements vary inversely with changes in the outdoor DNL within a range from 60 dB and lower. These requirements, however, become constant above

60 dB.

The predominant construction cost impacts of the performance requirements for

Outdoor Noise Isolation and Acoustical Privacy given in table 2.2 affect five

different building components.^ Table 2.3 lists these components and indicates

which provisions affect each component. The exterior walls are affected by

the Outdoor Noise Isolation provision. Windows and doors are affected by both

provisions. Interior walls and floor/ceiling assemblies are affected only by

the Acoustical Privacy provision.

2.2 IMPACT NOISE ISOLATION AND MECHANICAL EQUIPMENT NOISE

The other two provisions listed on table 2.1 are Impact Noise Isolation and

Mechanical Equipment Noise. The Impact Noise Isolation provision (section 3505)

calls for prescriptive compliance with a Construction Handbook of approved

designs for impact noise reduction. ^ This provision could not be addressed by

the methodology presented in this report because the proposed Construction

Handbook of acceptable designs has not yet been prepared. If this provision

were Implemented it would primarily affect multifamily residential buildings.

The fourth provision addresses Mechanical Equipment Noise (section 3506).

This provision requires that both multifamily residential and educational

buildings control the noise transmission of various building machinery and

appliances

.

The Mechanical Equipment Noise provision specifies that the A-weighted sound

levels produced by the operation of mechanical equipment be no greater than

45 dB in any dwelling unit or guest room. It also specifies that operation of

appliances produce an A-welghted sound level no more than 70 dB and food waste

disposals no more than 88 dB.

^ The Outdoor Noise Isolation requirement may also affect the construction cost

of roofs. This component is not included in the analysis since its impact on the entire cost of a high-rise building is likely to be minimal.

2 For justification of the use of prescriptive rather than performance

requirements for Impact Noise Isolation see Bolt, Beranek, and Newman Inc.,

Report 3759, p.45.

6
Table 2.3 Major Building Components Affected by the Outdoor Noise Isolation

and Acoustical Privacy Provisions of the MNCC.

Building Component

Outdoor Noise

Isolation Provision

Acoustical

Privacy Provis

Exterior Walls X

Windows X X

Doors X X

Interior Walls (Partitions) X

Floor/Ceiling Assemblies X

7
3. ANALYTICAL APPROACH

This section describes the approach used to determine the functional

relationship between construction cost and acoustical performance and presents

the limitations that should be noted when these equations are applied to assess economic impacts. The first subsection covers the basic approach and data sources used in estimating construction costs and acoustical performance levels

of building component designs. The approach includes a procedure for categorizing designs and regressing construction cost on acoustical performance for

each design assembly. The second part of this section discusses how to use the

derived cost equations to assess impacts of noise control provisions on the

affected building components.

3.1 RELATIONSHIP BETWEEN CONSTRUCTION COST AND SOUND TRANSMISSION CLASS

This subsection is based on the premise that a direct relationship exists

between the construction cost and acoustical performance levels of the building

components affected by noise requirements. It explains how the categories for

design assemblies were established, how individual designs were varied within

each category, and how the cost equations were derived for each category.

The measure of acoustical performance for building components used in this

methodology is the Sound Transmission Class (STC). This measure is defined as "...a single-number rating of the airborne sound insulation of a specific

partition (party wall or floor/ceiling construction), derived from sound transmission loss values in accordance with procedures of ASTM E413-73, 'Determination

of Sound Transmission Class.' STC is a laboratory measurement taken under

ideal conditions. The application of these measured values to field conditions

requires the assumption that the quality of workmanship is controlled at the

construction site.

3.1.1 Establishing Component Design Categories

When the cost and STC values of all documentable architectural designs for a given component are displayed in a single scatter diagram, the relationship

between the two variables remains unclear. When the diverse designs are grouped into more closely defined homogeneous categories, however, the direct

effect of acoustical performance on cost becomes quite apparent. These groups

of homogeneous designs are called Component Design Categories (CDC) and are formed by limiting the range of variation of key design characterstics such as general aesthetic appearance, and structural loading performance. In this way

the statistical analysis within each CDC is allowed to focus on the central

question addressed by the cost assessment methodology; the effect of varying

STC on construction cost. Because of the grouping procedure, the cost assess- ment method cannot be used to make acoustical performance/cost trade-offs

between two different CDC's, but rather is limited to analyzing such trade-offs

only within a single CDC.

^ Bolt, Beranek, and Newman, Inc., Report 3759, p. 30.

8
3.1.2 Architectural Design Variations

Within each established CDC, specific currently available designs were selected

to represent a broad range of STC values. For each of these architectural designs, data on construction cost per unit area and STC were gathered from a number of published sources. The cost data for floor/ceiling assemblies and exterior and interior walls were taken from the Design Cost Flle .^ The cost data for

doors and windows were taken from the Eastern Edition of both of these sources,

which means they are based on construction costs in Philadelphia. To find costs

in other cities, the regional cost indexing system provided by the Building Cost

File is presented in Appendix C of this report. This cost indexing can be used

to adjust the Philadelphia-based costs of acoustical performance reported in

Appendix A to the equivalent cost in any one of 122 U.S. cities.

The STC data were collected from various sources. Exterior and Interior wall

data are from the Design Cost File . The STC data on doors are from three

sources: a National Bureau of Standards publication entitled. Acoustical and

Thermal Performance of Exterior Residential Walls, Doors, and Windows ; the

Building Cost File ; and a National Institute for Occupational Safety and Health

Report entitled Compendium of Materials for Noise Control .^ STC values for

windows are based on an estimating procedure using separate equations for

single pane and for double pane glazing.

Single pane: STC = 38.3 + 10.5 log^Q (h) , for 3/32 < h < 1 .0 (3.1)

Double pane:^ STC = 42.4 + 10.93 log,Q (H) + 10.77 log.Q (d), (3.2)

for 9/32 < H < 1/2 and 3/4 < d < 6.0

1 McKee-Berger-Mansueto , Inc., Design Cost File (New York: Von Nostrand

Reinhold Company, 1979), pp. 129-218.

2 McKee-Berger-Mansueto, Inc., Building Cost File (New York: Von Nostrand

Reinhold Company 1978), pp. 5-186. The cost per unit area of each building

component is derived on the basis of the published unit costs for the

elements of each component. To assure comparability, these 1978 data were adjusted to 1979 dollars using the method of adjusting for construction

cost changes that is discussed and illustrated in subsection 4.1, below.

3 H. J. Sabine e^ al^. , Acoustical and Thermal Performance of Exterior

Residential Walls, Doors, and Windows , Building Science Series 77

(Washington, D.C.: National Bureau of Standards, 1975), pp. 122-147; and

Robert A. Hedeen, Compendium of Materials for Noise Control , DREW (NIOSH)

Report 80-116 (Washington, D.C.: Department of Health, Education, and

Welfare, National Institute of Occupational Safety and Health, May 1980),

p . 81

.

^ The data on which this estimating procedure for double glazing is based was taken from J. D. Quirt, Measurement of Sound Transmission Loss of Windows , Building Research Note No. 172 (Ottawa, Canada: National Research Council

of Canada, 1981).

9
where

h = pane thickness (inches);

H = total pane thickness of the two panes (inches); and

d = air space thickness (inches).

STC data for floor/ceiling assemblies were estimated with the use of an itemized list of basic design materials found in the Design Cost File and some basic architectural designs found in A Guide to Airborne, Impact, and Structure

Borne Noise-Control in Multifamily Dwellings .^ The basic deck designs are varied slightly with different materials in order to achieve sufficient variation in STC levels to establish a relationship between cost and acoustical

performance.

3.1.3 Derivation of Cost Estimating Equations

This subsection presents the analysis of the relationship between construction

cost and STC for the five major building components expected to be affected by

noise control requirements. The components analyzed are; (1) doors;

(2) windows and sliding glass doors; (3) exterior walls; (4) interior walls;

and (5) floor/ceiling assemblies. The relationships presented here are expressed as linear equations; with construction cost being a linear function

of the STC level. These equations are to be used to develop an estimate of

the cost Impact of a given change in the STC level required for a particular

building component. Each equation represents one particular CDC.

For each individual design within a particular CDC, the construction costs and

the STC values were established based on the data sources discussed above in

subsection 3.1.2. Using this data on cost and STC, a least squares regression

line was calculated for each CDC according to the following format:

Cost = A + B . STC, (3.3)

where A = the intercept of the equation; and

B = the slope of the equation.

To illustrate how this was done, consider the regression for doors. Table 3.1

shows the acoustical performance levels and construction costs for the nine

doors used in the regression. Both wood and metal doors were used, either

hollow or solid, all with steel frames and weatherstripping, all with the same 3x7 foot dimensions and some with added soundproofing. When the least squares

regression was calculated, the following equation for the regression line

resulted

Cost = 0.77 + 0.462 . STC (3.4)

1 R. D. Berendt , G. E. Winzer and C. B. Burroughs, A Guide to Airborne, Impact , and Structure Borne Noise-Control in Multifamily Dwellings (Washington, D.C.:

National Bureau of Standards, 1967), ch. 6., p.7.

10
Table 3.1 Acoustical Performance and

Analysis for Doors

Cost Data Used in the Regression

— Acoustical

Door Description^ Performance (STC)^ Unit Cost ($/sf)^

(1) Interior, hollow core wood door

with rotary natural birch veneer

20 11.47

(2) Interior, solid core wood door

with rotary natural birch veneer

27 13.56

(3) Hollow, 18 gauge metal door 33 15.29

(4) Hollow, 16 gauge metal door 35 15.79

(5) Interior, solid core door

rotary natural birch veneer and

soundproof ing

36 18.97

(6) Hollow, 14 gauge metal door 37 16.62

(7) Hollow, 12 gauge metal door 41 17 .14

(8) Interior, solid core door with

rotary natural birch veneer and

soundproofing

42 19.79

(9) Interior, solid core door with

rotary natural birch veneer and

soundproofing

51 26.94

^ Each door is 3' x 7* or 21 sf with a hollow metal door frame, an aluminum

threshold with interlocking weatherstripping, and 17 ft of zinc weatherstripping. Doors (1) through (8) are all 13/4 inches thick, while door

(9) is 2 1/4 Inches thick. The density of the core material in doors

(5) and (8) is the only factor that distinguishes the two from each

other.

^ The STC values for doors (1) and (2) are from H. J. Sabine, et ^. , pp. 127-147.

The STC values for doors (3), (4), (6) and (7) are from equation 49 .A in

Robert A. Hedeen, p. 81. The STC values for the remaining doors are from

Building Cost File , p. 91.

^ All cost data are estimated from Building Cost File, pp. 88-101.

11
Figure 3.1 shows graphically the data points and resulting regression line.

Each point represents the construction cost and STC level of a particular door.

The slope of the line, B = 0.4625 measures the rate of change in cost per unit

change in STC and is interpreted as the marginal construction cost of a oneunit increase in the STC level. This equation (3.4) would be used to determine

cost increases resulting from a noise control code provision by multiplying a provision's required STC Improvement by B. Thus, for example, if an MNCC

provision required an STC improvement for doors of 5, then the additional

construction cost would be 5 x 0.462 or $2.31 per square foot of door.

The results of the regression analyses for all of the CDCs are summarized in

table 3.2. For each CDC name, the intercept, the slope, and the ranges of

relevant values covered by each regression in terms of STC and Cost are given.

For example, CDC 3.2 (Stud Frame Walls with Stucco Exterior) would be estimated

to cost $4.08/sf if STC of 40 were required. ^ Moreover, if a new noise control

code called for improving the acoustical performance of the same wall from an

STC of 40 to an STC of 45, the additional construction cost would be estimated

to be about $0.26/sf.2

In Appendix A, results of the regression analysis are presented in detail.

For each CDC a description is provided of all the variations in materials

specifications and construction techniques used to establish a range of STC

values. The number of distinct STC design values analyzed and the range of

STC values covered by those designs are also reported for each CDC. In addition

to the estimated coefficients of the least squares regression line, two other

statistics are reported which Indicate the validity and reliability of the

relationship. The t-statistic for the slope of each regression equation is

presented in parentheses directly below the slope coefficient. This statistic

is the ratio of the slope to its own standard error and provides a measure of

whether the estimated slope value is significantly different from zero. [Note that a zero slope would imply that there is no relationship between

construction cost and STC values.] The degree of confidence to be placed on

the significance of the slope coefficient is indicated by the asterisk(s)

following the parentheses. A single asterisk means 95 percent level while a double asterisk means a 99 percent level of confidence. Of all the equations

presented in this report 84 percent have 99 percent confidence levels and the

rest have 95 percent levels.

In addition to the test for significance on the slope coefficient, the

adjusted (multiple correlation coefficient) is also presented for each CDC.

This statistic is a measure of the goodness of fit of the regression line to

the data, adjusted for the number of specific designs analyzed in the regression. The direct interpretation of R^ is the proportion of variation in con- struction cost explained by the STC values. Thus an R^ of 0.9 would indicate

that 90 percent of the variation in cost among these designs is accounted for

by STC values. All but one of the equations reported in Appendix A have

1 2.00 + 0.052 (40) = 4.08.

2 0.052 (5) = 0.26.

12
15 20 25 30 35 40 45 50 55

DOOR STC RATING

Figure 3.1 Scatter Plot of Data Points and Least Squares Linear

Regression for Doors.

13
Table 3.2 Estimating Regression Coefficients and Relevant Cost and STC Ranges

for each Component Design Category. (Continued)

Component Design Category Intercept Slope Range: Range: Cost

($/sf) ($/sf/STC) STC ($/sf)

Doors

1.1 Wood or Metal Doors 0.77 0.462 20-51 10.01-24.33

2.1

Windows

Aluminum Frame Fixed Sheet or Plate

Glass -13.10 0.940 29-47 14.16-31 .08

2.2 Aluminum Frame Fixed Tempered Glass -6.44 0.811 31-47 18.70-31.68

2.3 Steel Frame Fixed Sheet or Plate

Glass -13.48 0.788 29-47 9.37-23.56

2.4 Steel Frame Fixed Tempered Glass -8.13 0.717 31-47 14.10-25.57

2.5 Aluminum Frame Pivoting Casement

Sheet or Plate Glass -12.74 0.945 29-47 14.67-31.68

2.6 Aluminum Frame Pivoting Casement

Tempered Glass -7.97 0.881 31-47 19.34-33,44

2.7 Steel Frame Pivoting Casement

Sheet or Plate Glass -13.51 0.787 29-47 9.31-23.48

2.8 Steel Frame Pivoting Casement

Tempered Glass -12.34 0.848 31-47 13.95-27.52

2.9 Aluminum Frame Double Hung Sheet

or Plate Glass -12.66 0.938 29-47 14.54-31.43

2.10 Aluminum Frame Double Hung

Tempered Glass “7.85 0.874 31-47 19.24-33.23

2.11 Steel Frame Double Hung Sheet or Plate Glass -13.74 0.804 29-47 9.58-24.05

2.12 Steel Frame Double Hung Tempered

Glass -8,18 0.724 31-47 14,26-25.85

2.13 Aluminum Frame Horizontal Sliding

Sheet or Plate Glass -12.46 0.878 29-47 13,00-28.81

CM Aluminum Frame Horizontal Sliding

Tempered Glass -7.09 0.802 31-47 17.77-30.60

Exterior Walls

3.1 Stud Frame with Wood Siding Exterior 1,14 0.072 37-48 3.80- 4.57

3.2 Stud Frame with Stucco Exterior 2.00 0.052 37-47 3.92- 4.44

3.3 Stud Frame with Aluminum Siding -0.63 0.110 37-50 3.44- 4.87

3.4 Stud Frame with 22 Gauge Metal Siding

Exterior 4.45 0.072 37-48 7.11- 7.91

3.5 Stud Frame with Brick Veneer 2.07 0.079 48-65 5.86- 7.21

3,6 Cast in Place Concrete 0.22 0.171 47-60 8.26-10.48

3.7 Concrete Wall with Brick Veneer -44.46 1.094 53-56 13.52-16.80

3.8 Concrete Block -6.13 0.245 44-80^ 4.65-13.48

3.9 Concrete Block without Parge

Coat, with Brick Veneer -23.25 0.609 50-55 7.20-10.25

3.10 Concrete Block with Parge Coat & Brick Veneer -8.50 0.273 58-63 7.33- 8.70

14
Table 3.2 (Concluded)

Component Design Category Intercept

($/sf)

Slope

($/sf/STC)

Range

:

STC

Range : Cost

($/sf)

3.11 Concrete Block with Granite Veneer 3.46 0.408 50-61 23.87- 28.36

3.12 Concrete Block with Marble Veneer 4.01 0.386 50-61 23.31-27.56

3.13 Concrete Block with Limestone Veneer 1.54 0.299 50-61 16.49- 19.78

3.14 Precast Concrete 2.00 0.268 40-61 12.72-18.35

4.1

Interior Walls

Wood Stud Frame Plaster 0.90 0.063 32-45 2.92- 3.74

4.2 Metal Stud Frame Plaster with Gpysum

Lath -0.05 0.076 38-52 2.84- 3.90

4.3 Metal Shaft Frame Drywall 1.62 0.048 25-59 2.82- 4.45

4.4 Wood Stud Frame Drywall -1.36 0.108 32-47 2.10- 3.72

4.5 Metal Stud Frame Drywall -0.69 0.074 38-55 2.12- 3.38

4.6 Cast in Place Concrete 1.32 0.144 46-62 7.94-10.25

4.7 Brick -22.66 0.554 47-67 3.37-14.46

4.8 Lightweight Concrete Block -1.61 0.098 32-53 1.53- 3.58

4.9 Heavyweight Concrete Block 0.80 0.079 35-58 3.57- 5.38

4.10 Structural Clay Tile -5.24 0.190 35-43 1.41- 2.93

5.1

Floor/Ceiling Decks

Wood Joists with Dr3n«7all Ceiling 1.30 0.034 34-60 2.46- 3.34

5.2 Wood Joists with Plaster Celling on Gypsum Lath 0.01 0.051 48-58 2.46- 2.97

5.3 Wood Joists with Plaster Celling on Metal Lath 0.68 0.056 41-58 2.98- 3.93

5.4 Drop Celling Panels Added to

Floor Structural System -0.08 0.044 25-40 1.02- 1.68

5.5 Dry Wall Ceiling Added to

Concrete Slab^ 0.59 0.039 8-22 0.90- 1.45

5.6 Steel Joists & Drjrwall Celling Added

to Floor Structural System^ 0.54 0.045 8-27 0.90- 1.76

^ The upper STC extreme for this concrete block CDC is estimated for a double wall of solid

block construction of high quality construction.

^ Values of cost and STC for the floor structural system are not included in these

estimating equations.

^ A concrete slab is the only floor structural system compatible with the design

specifications used to develop this CDC estimating equation. The values of cost and

STC for the concrete slab, however, are not Included in this estimating equation.

15
adjusted r2 values greater than 0.5; indeed 49 percent have r2 statistics

in3.2 excess of 0.9 and 69 percent exceed 0.8.

DESIGN ASSUMPTIONS

This subsection describes in some detail the design assumptions underlying the

CDC cost equations. These assumptions must be taken into account whenever the

methodology is applied to assess economic impacts. Each of the five major

envelope components of dwelling units and classrooms is discussed in turn.

3.2.1 Doors

Doors typically found in educational buildings and residential dwelling unit

main entrances were considered similar enough to be grouped into a single CDC.

The corresponding cost estimating equation for doers in Appendix A.l and illustrated in the example above represents both wood and metal doors. The cost

data were calculated in terms of a 3 x 7 foot door and converted to a square

foot basis by dividing the entire cost of the door by 21. This particular door

size was assumed to be reasonable in light of current building firecode exit

requirements and current standard practice.^ It is also assumed that the doors are weatherstripped since this is standard practice. Moreover, acoustical test

results on doors without weatherstripping tend to be inconsistent .2 This is

because test results are dominated by varying crack widths around the perimeter

of doors as a result of different installation procedures.

3.2.2 Windows and Sliding Glass Doors

The cost equations for windows and sliding glass doors in Appendix A. 2 are categorized by window glazing and frame type. Aluminum and steel are the only

frame types analyzed because together they accounted for 93 percent of the windows Installed in new multifamily residential buildings in 1980, the most recent

year for which statistics are available.^ Each of the seven metal frame types

is assumed to have weatherstripping. Four glazing types are presented for each

each frame type; (1) sheet and plate glass; (2) tempered glass; (3) insulating

glass; and (4) laminated glass. The first two are presented as least squares

linear equations, and the last two are handled as discrete points due to the

lack of sufficient data points to conduct regression analysis.

3.2.3 Exterior Walls

The exterior wall cost equations presented in Appendix A. 3 permit one to

calculate cost per square foot of exterior wall surface area at any specific

^ The firecode exit requirements assumed here are those given by International

Conference of Building Officials, Uniform Building Code (Whittier, CA: International Conference of Building Officials, 1979), pp. 501-502.

2 H. J. Sabine, ^ al.

3 Architectural Aluminum Manufacturers Association, Architectural Aluminum

Industry Statistical Review; 198C (Chicago; Architectural Aluminum Manufacturers Association, 1981), table 14, p. 20.

f

L

16
STC level within the stated range. Extrapolations of these cost equations

beyond the stated range would require further cost estimating and acoustical

testing of alternative interior finishes for each exterior wall CDC. Throughout

the entire range of CDCs listed, it is assumed that quality construction methods

and materials are employed.

3.2.4 Interior Walls

The cost equations for the Interior Wall CDCs presented in Appendix A. 4 are to

be used to establish the cost per square foot of wall area. Special care must

be taken in using these costs, because the entire cost per square foot of wall area is not attributable to each dwelling unit. For party walls between dwelling units, each should be charged half the cost of common partitions. This is

not the case, however, for walls classified as publlc-to-prlvate separations.

The total cost of each unit’s public-to-private wall surface area is to be

charged to that unit in the cost assessment.

One frequently used method of increasing STC is to design partitions with

greater density. One drawback to this approach is the consequent increase in

dead load on the building elements with the added cost of increasing the structural strength. The cost equations reported in Appendix A. 4 do not include

these possible increased structural costs because the CDCs employed here do not

have greatly varied densities. Instead, an alternative method of greatly

increasing the STC of a wall, double-wall construction, was used. However, the

possible economic Impact of lost floor area is not included in this methodology.

As indicated by Berendt, Winzer, and Burroughs, "Double walls have substantially

greater sound insulation than a single wall of the same weight."^ It is also

assumed that acoustical flanking paths around walls have been sealed in

conformity with code requirements.^

3.2.5 Floor/Ceiling Assemblies

The cost estimating equations for floor/ceiling assemblies are presented in

Appendix A. 5. These equations are to be used to estimate construction cost

per square foot as a function of STC level. Note that exterior roofs are not

included among these equations. For three of the six CDC designs, the cost

and STC values of the floor structural system are meant to be combined with

these estimating equations. That is, values for cost and STC of the floor

structural system should be combined with the total cost and STC values derived

form using equations (5.4), (5.5), and (5.6) of table 3.2.

^ Raymond D. Berendt, George E. Winzer, and Courtney B. Burroughs, A Guide to

Airborne, Impact, and Structure Borne Noise-Control in Multifamily Dwellings

Federal Housing Administration Publication 750 (Washington, D.C.: U. S. Department of Housing and Urban Development, September 1967), ch. 6, p. 7.

2 For a detailed description of the design requirements of a firewall, see the

International Conference of Building Officials, Uniform Building Code

(Whittier, CA: International Conference of Building Officials, 1979),

pp. 102-119.

17
A. APPLICATION OF COST EQUATIONS TO BUILDING COMPONENTS

This section Illustrates how the cost estimating equations presented in

Appendix A are to be applied to determine how much additional cost is expected

to result from noise control provisions. Subsection 4.1 deals with the case

of a single homogeneous building component governed by a particular provision.

The example used is that of a party wall separating two apartment units. Such

party walls are governed by the private-to-private acoustical privacy provision

of the MNCC. Subsection 4.2 deals with the more complex case of two or more building components that are simultaneously governed by the same provision.

Two examples are used to illustrate this multi-component case. The first deals

with two components governed by the MNCC publlc-to-prlvate acoustical privacy

provision: a basic interior wall structure, and a door leading to the main

hallway. The second example concerns three distinct building components governed by the MNCC outdoor noise provision: a basic exterior wall structure, a window, and a door.

4.1 SINGLE COMPONENT APPLICATIONS

The application of the cost assessment methodology to a single building component is relatively straightforward. The basic construction cost estimating

equation is found on table 3.2 above for the particular CDC being estimated.

This equation is used to calculate the basic construction cost under both cur- rent acoustical practice and the new noise control provisions. The difference

between these two cost figures represents the expected increase in the basic

construction cost. Then this basic construction cost figure is adjusted to

account for the general contractor’s mark-up and the architectural and engineering design fees. Finally, adjustments are made to account for regional

construction cost differences and the effects of inflation over time. These

adjustments are accomplished by applying a multiplication factor to the basic

construction cost.

The building component used to illustrate this single component application of

the methodology is that of a metal stud frame dr3n»7all partition. The CDC

construction cost estimating equation for such a partition is:^

Cost/sf = -0.69 + 0.074(STC).

A current design STC level of 50 is assumed in this case based on the Sound

Transmission Control provision found in the Appendix of the Uniform Building

Code Assuming an outdoor day-night sound level of between 55 and 60 dB

and assuming the partition is a private-to-private separation, the MNCC design

1 The intercept and slope values of this cost estimating equation are taken

from CDC 4.5 of table 3.2.

2 International Conference of Building Officials, Uniform Building Code , Appendix, p. 668.

18
requirement is an STC rating of 55. ^ Using the above equation and the current

and expected STC requirements, current and expected cost estimates can be

calculated:

Current Cost/sf = -0.69 + 0.074(STC)

= -0.69 + 0.074(50)

= $3.01.

Expected Cost/sf = -0.69 + 0.074(55)

= $3.38.

The change in cost/sf is calculated by subtracting the Current Cost/sf from the

Expected Cost/sf;

Cost Change/sf = $3.38 - $3.01

= $0.37.

It should be noted that the Cost Change/sf can also be calculated by multiplying the marginal cost factor (i.e., the slope of the cost estimating

equation) by the change in required STC;

Cost Change/sf = 0 .074(STC2"STCi)

= 0.074(55-50)

= $0.37.

These cost estimates are for basic construction costs. There are, however,

other cost components which must still be accounted for by multiplying the

change in cost/sf by certain factors. Two such factors are the general con- tractor’s mark-up percentage (CMP) and the architectural and engineering

design fee percentages (DFP) . Median values for these percentages have been

estimated to be 5.5 percent for CMP^ and 6.4 percent for DFP. 3 These two

percentages are additive because they are both applied to the same basic

construction cost estimates derived from the CDC equations. Thus, the proper

calculation procedure to account for these adjustments is as follows:

^ See table 2.2 of this report.

^ Building Cost File; Eastern Edition , p. 1.

^ Boeckh, Inc., "Architectural Fees," in Boeckh Building Valuation Manual , 2nd

Edition (Milwaukee: Boeckh Publications - A Division of American Appraisal

Associates, Inc., 1979), pp. C37-38.

19
Adjusted Cost Change = Basic Construction Cost Change x [1 + CMP + DFP

j

^ 100

= 0.37 X r i + 5.5 + 6.4 ]

,

100

= 0.41 ($/sf).

Additional adjustments must be made to this figure in order to account for

regional construction cost differences and for inflation over time. The cost

data used to develop the cost estimating equations are relevant for the base

city of the Eastern Edition of the Building Cost File , namely Philadelphia.

If the construction project being evaluated were in Sacramento, for example, one would find the Regional Cost Adjustment Factor (RCAF) for Sacramento in

Appendix C and multiply it times the construction cost figure adjusted for

mark-up and design fee. For the case example above, the calculation would be

as follows:

Cost Change in Sacramento = Cost Change in Philadelphia x RCAF

= $0.41/sf X $1,106

= $0,45/sf.

To adjust the cost figure for inflation, one must note that the cost data on

which the cost estimating equations were based refer to construction costs in

Midyear 1979. One of the Boeckh Indexes for construction costs published by

the American Appraisal Company^ is designed for apartments, hotels, and office

buildings and should serve fairly well for both educational and multifamily

residential buildings. This index gives 169.3 for May-June 1979 and 197.1 for

March-Aprll 1981. Thus, to update the above cost figure for Sacramento from

its midyear 1979 basis to March-April 1981 dollars one would multiply by the

ratio 197.1/169.3 as follows:

197.1

$0.45/sf X (— ) = $0.52/sf.

169.3

4.2 MULTI-COMPONENT APPLICATIONS

The model noise control provisions discussed in section 2 specify noise

isolation performance requirements for both interior building partitions and

exterior walls. In either case, the construction cost of a single component

continuous partition or exterior wall may be directly estimated using the CDC

cost equation for the particular construction. If the construction comprises

two or more components, however, the possibility arises of trading off noise

1 This construction cost index series is published bimonthly in the U.S.

Department of Commerce, Construction Review.

20
insulation in one component for that in another component to find the leastcost combined solution. This section describes a method for conducting such

trade off studies. In particular, the method utilizes the CDC cost equations

discussed in section 3.2 and allows the user to determine the noise Insulation

specification for each component that will minimize the total construction cost

of the combined design while still satisfying the given noise control provision.

Details concerning the assumptions and the derivation of the design selection

method a^re presented in Appendix C. The method is mathematically exact and is

easily used to obtain design results. However, the user must always remember

that the linear relationship assumed to exist between construction cost and

component noise isolation is only an approximation.

4.2.1 Data Required to Determine the Minimum Construction Cost Design

To determine the minimum cost dei-ign for a multi-component wall, it is necessary to know details concerning the design. Specifically, the required data are the percentages of total surface area of each component and the component

construction. Hence, the basic parameters defining the noise insulation of a composite or multi-component wall are the component surface areas and the

component construction or noise insulation characteristics. The Component

Design Categories or CDCs are used to define the cost/noise Insulation characteristics of the component construction for this design method.

4.2.2 The Design Equations

The method allows the user to calculate the noise insulation requirements for

each component of a multi-component wall using a pocket calculator. The con- struction cost of the design is minimized for all designs meeting the noise

insulation specification. The user must always remember that a "design," as used here, is a combination of component areas and component materials (CDC

cost equations). Changing either the distribution of surface areas among the

components or changing the component materials defines a new design and will

result in a different minimum cost solution.

Appendix C presents the general equation for calculating the noise insulation

required of each component to define the minimum cost design. In this section,

specialized equations are presented for two and three component designs. These

two cases encompass almost all building noise Insulation situations of practical

interest. Table 4.1 presents the design equations and nomenclature for a two

component wall design, while table 4.2 does the same for a three component

wall design. Example calculations illustrate the use of the design equations

to estimate both the component noise Insulation requirements and the minimum

construction cost for achieving a specified noise control provision.

4.2.3 Example Design Calculations

Two example design calculations are presented. The first example problem

is an partition with a door separating a public space from a private space. The

second example calculation is for an exterior wall design.

21
Table 4.1 - Minimum Cost Equations for a Two Component Wall Design

The Two Component Wall Must provide a Design Noise Insulation of R^,.

-The Noise Insulation Required for Each of the Two Components is:

Component 1: R^ = R^, - 10 log^Q [Bl/(ki + \H 2 B2 )], and

Component 2; R2 = Rq ~ 10 loglO [®2/(^l ®1 ^2 ®2)]*

-The Minimum Construction Cost per Unit Area of the Two Component Wall

is Calculated Using;

Cost per unit area = kj [A^ + R^] + k2 [A2 + B2 R2 ]

•

-The Definitions of the Above Terms are as Follows:

Component Cost: C^ = A^ + Bj_ Rj^; i = 1, 2 (See table 3.2 or Appendix A)

Fraction of Total Area: k^^; i = 1, 2 (Note: k^ + k2 = 1)

Design Noise Insulations R^,.

See Appendix C, equation (C.28) for limitations on R^

Table 4.2 - Minimum Cost Equations for a Three Component Wall Design

-The Three Component Partition Must Provide a Design Noise Insulation of R(,

.

-The Noise Insulation Required For Each of the Three Components is:

Component 1: R]^ = R^ - 10 logj^Q [B2 /(k2

B]^ + k2 B2 + k3 B3 )],

Component 2; R2 = R^ “ 10 loglO [®2/(^l ®1 ^2 ®2 "* ^3 ®3)]>

Component 3: R3 = R^. - 10 log^Q [B3 /(k3 B3 + k2 B2 + k3 B3 )].

-The Minimum Construction Cost per Unit Area of the Three Component Wall

is Calculated Usings

Cost per unit area = kj [Aj^ + R^] + k2 [A2 + B2 R2 ] + ^*31^3 + B3 R3

].

-The Definitions of the Above Terms are as Follows

s

Component Cost s Cj^ = A^ + B^ Rj_; i = 1, 2, 3

(See table 3.2 or Appendix A)

Fraction of Total Area: kj^; 1 = 1, 2, 3 (Note: k^ + k2 + k3 = 1)

Design Noise Insulation: R^.. See Appendix C, equation (C.30) for limitations on Rp

22
Example No. 1, Two Component Interior Wall ^

For this example, the partition separating a public space from a private space

is comprised of a basic wall and a door. The total surface area is 96 square

feet. The wall is metal stud frame drywall partition. The door dimensions are 3x7 feet. The outdoor day-night sound level is estimated to be 58 dB. It

is required to calculate the noise insulation requirements for the wall and

the door and to estimat' the construction cost for this interior partition in

order to meet the MNCC provisions.

Since this is a two component partition, the minimization equations are listed

in table 4.1. First, we denote the wall as component 1 and use a subscript

"1" on all data related to the wall. The door data are then denoted by the

subscript 2.

The fractional area of each component is;

wall, ki = (75/96) = 0.781

door, k2 = (21/96) = 0.219

check: k]^ + k2 = 1.000

From table 3.2, the CDC cost equation for a metal stud frame drywall

partition is:

Cl = -0.69 + 0.074 Ri

38 ^ Rl ^ 55 (STC units).

From table 3.2, the CDC cost equation for wood or metal doors is:

C2 = 0.77 + 0.462 R2

20 1 R2 1 51 (STC units).

Then, in terms of the parameters required for the design equations in table

4.1, the constants describing the component costs are:

Component 1 (Wall) Ai = -0.6S; Bi = 0.074

Component 2 (Door) A2 = 0.77; B2 = 0.462

Then, from table 4.1, the noise insulation rating for the wall (component 1)

required to meet the MNCC provisions, R^,, is:

1 In these example problems, numerical results are presented to several decimal

places so that the reader can closely follow the calculations. Costs should

be rounded to the nearest cent and dB to the nearest whole number in practice.

23
Rl = Rc - 10 logio [0.074/((0.781) (0.074) + (0.219)(0.462))]

= Rc - 10 logio [0.074/0.159]

= + 3.3; STC units.

For the door, the noise insulation rating required to meet the MNCC Provision,

Rc, is:

R2 = Rc - 10 logio [0.462/0.159]

= R(, - 4.6; STC units.

From table 35-A of the MNCC, the noise isolation requirements are a normalized

level difference of 40 dB corresponding to a noise insulation requirement of

STC 45 at the building design stage. From table no. 35-B of the MNCC, these

requirements must be increased 5 dB for an outdoor environmental day-night

sound level between 55 and 60 dB.^ That is, for our example problem, the MNCC

requirements are a normalized level difference of 45 dB or an STC rating of 50

for the composite wall. Since of the CDC cost equations are expressed in terms

of the STC rating of the components, we select R^. = 50 for use in the

minimization equations.

Hence, for our example problem, the minimum construction cost design (utilizing

a door with metal stud frame drywall construction and the door comprising 21.9

percent of the total partition area) is:

Rl = 50 + 3.3 = 53.3 Wall STC Rating

R2 = 50 - 4.6 = 45.4 Door STC Rating.

We compare these values with the limits of the cost equations to check that the

component STC ratings are physically possible. (See Appendix C.3.3).

From table 4.1 and the data for the example problem, the estimated minimum

construction cost per unit area is:

C = (0.781) [-0.69 + 0.074(53.3)] + (0.219) [0.77 + 0.462(45.4)]

min

= (0.781) (3.25) + (0.219) (21.74) = $7.30/sf.

The above results provide the minimum cost design. That is, a metal stud frame

drywall partition with an STC rating of 53 costing $3.25/sf and a door with an STC rating of 45 costing $21.74/sf will provide a composite STC rating of 50

at an average cost of $7.30/sf. We note that in absolute costs, the estimated

construction cost for the wall is $243.75 and the door cost is $456.54.

^Table 2.2 of this report summarizes tables 35-A and 35-B of the MNCC provisions.

24
To Illustrate that the above result is a minimum cost, we note that if both the

wall and the door have STC ratings of 50 then the total structure will have an

STC rating of 50. Substituting these values into the above cost equation, the

average cost per unit area is estimated to be $7.58/sf for this "obvious"

design requiring an STC 50 wall and door.

The comparison between the cost of the "obvious" design and the estimated

minimum cost design does not prove that the estimated minimum cost is an absolute minimum. One should read Appendix C to understand that the method does

gtiarantee a minimum total cost assuming that the component cost is a linear

function of the component STC rating. Section 4.2.4, below, discusses practical limitations of this design method.

Example No. 2: Three Component Exterior Wall

This example problem Illustrates the use of the minimum cost design method to

determine the noise insulation performance of exterior wall components in order

to meet the MNCC provisions. The basic steps required to conduct the calculations are identical to the first example problem. However, for the exterior

wall problem, it is necessary to adjust the A-welghted outdoor- to-lndoor sound

isolation requirements of the MNCC provisions so that the design criteria for

the calculation scheme is expressed in the STC units of the CDC cost equations.

For this example problem, the total surface area of the exterior wall between

the outside and the interior living space is 240 sf. The exterior wall components are 60 sf of glazing, one door (3x7 feet), and the basic wall.

The construction utilizes a frame structure with a stucco exterior finish and

aluminum frame double hung windows with either sheet or plate glass. The outdoor

day-night sound level to which this construction will be exposed is estimated

to be in the range of 75 to 80 dB. The problem is to determine the component

noise insulation requirements to achieve the A-weighted sound level reduction

of 35 dB required by table 35-C jf the MNCC. (See table 2.2 of this report.)

First, to use the minimum cost design method for an exterior wall it is

necessary to adjust the A-welghted sound level reduction of the MNCC provisions

to obtain the design criterion in STC units. ^ The required adjustments (See

Appendix C.2) are of the form;

STC = + adjustment

where aLa is the A-welghted sound level reduction in table 35-C of the MNCC.

The adjustment required depends upon the predominant environmental noise source outside the building (i.e., highway traffic, aircraft, or railway noise) and

the interior room furnishings. For a typically furnished i*oom, an average

^ The reader will note that for partitions (table 35-A of the MNCC), the noise

Isolation criterion is specified as a normalized A-welghted sound level difference with the design requirement specified in STC units. For the interior

partitions, the MNCC applies a 5 dB adjustment.

25
adjustment of +3 dB appears appropriate for any of the above listed noise

sources. For sites exposed predominately to highway and/or railway noise, a +2 dB adjustment may be used. For sites exposed predominately to aircraft

noise, a +4 dB adjustment may be used. The explicit adjustment selected is a judgment best determined by the architect or acoustical consultant.

For our example problem, the +3 dB correction is selected so that the STC

design criterion as determined by the outdoor day-night sound level and the

MNCC provision is:

Rc = 35 + 3 = 38.

From table 3.2 or Appendix A, the cost equations for the particular Component

Design Categories of this example are:

Component 1; Stud Frame Wall with Stucco Exterior:

Cl = 2.00 + 0.052.R1, 37 < Ri < 47

Component 2; Doors:

C2 = 0.77 + 0.462.R2, 20 < R2 < 51

Component 3; Double Hung Aluminum Frame Sheet and Plate Glass:

C 3 = -12.66 + O. 938 .R3 , 29 < R3 £

47.

The ratios of component surface areas to total surface area for this example

are

:

ki = 159/240 = 0.6625

k2 = 21/240 = 0.0875

k3 = 60/240 = 0.2500.

The design equations for the three component partition are listed in table 4.2.

To best use these equations, one first calculates the weighted marginal cost

of the total construction as follows:

ki Bi + k2 B2 + k3 B3 = (0.6625) (0.052)

+ (0.0875) (0.462)

+ (0.2500) (0.938) = 0.3094.

From table 4.2, the STC design values for each component are calculated as follows:

26
Exterior Wall: Rj^ = Rq - 10 logj^Q [0.052/0.3094]

R(, + 7.8

Door

:

R2 = Rc - 10 logio [0.462/0.3094]

Rc - 1.7

Windows

:

R3 = Rc - 10 logio [0.938/0.3094]

Rc - 4.8

For the composite wall STC design value of Rc = 38, the following component STC

design values are determined:

Exterior Wall STC = Rj^ = 38 + 7.8 = 45.8 or 46

which are physically possible values (See Appendix C.3.3). Hence, the estimated

minimum construction cost per square foot for the exterior wall of this example

problem is:

Cmln = (0.6625) [2.00 + 0.052(45.8)]

+ (0.0875) [0.77 + 0.462(36.3)]

+ (0.2500) [-12.66 + 0.938(33.2)]

= $9.06/sf.

Another possible design satisfying the MNCC provisions would be the design

requiring that each component independently meet the provisions. That is the

design specifying R]^ = R2 = R3 = 38 , for this example problem. This is the

"obvious" design. Using the CDC cost equations for this example, the cost per

square foot for the obvious design is $9.98/sf. Hence, the minimum cost

design is estimated to be $0.92/sf less than the "obvious" design. For the

240 square foot structure of this example, the minimum cost design represents

a cost savings of $220.80 per living unit over the "obvious" design.

4.2.4 A Few Words of Caution

The calculation method described in this section allows judgements to be

made — based on construction cost — concerning component specifications that

achieve a composite performance requirement. The method does not provide absolute ansvrers to a specific problem. However, the method does provide a starting

point at which the architect and designer may refine a design to meet the MNCC

provisions without incurring excessive construction costs . To place the method

in perspective, a few words of caution concerning the use and interpretation of

results are provided.

Door STC = R2 = 38 - 1.7 = 36.3 or 36

Window STC = R3 = 38 - 4.8 = 33.2 or 33

27
First, the cost equations for each component design category are only average

results. The equations are developed from a tabulation of designs in each

category with each design represented as a "point" when plotted as component

cost versus the STC rating. Figure 3.1 Illustrates the concept using the door

CDC. Each point in figure 3.1 represents a specific design within the componen

design category. As indicated in figure 3.1, few of the specific designs are points on the straight line of the component cost equation.

To Illustrate the significance of the linear cost equations, a small region of

the data scatter of cost and STC is illustrated in figure 4.1. The STC value

R* represents the component STC rating predicted using the minimum cost design

method. The component cost per unit area, C*, is calculated using the CDC cost

equation and the STC value R*. It is not likely that the predicted design

point (R*, C*) for the minimum cost design will exactly correspond to any

specific design used to determine the CDC cost equation. However, one should

recognize the advantages of the model rather than emphasize the limitations.

The basic advantage of the method is that the design point (R*, C*) for a component is obtained using simple calculations that require a few minutes and

a pocket calculator. Alternatively, a computer program could be developed that

sorted through all specific designs of each CDC selected for the structure.

The result would then be a listing of specific designs that provided the true

minimum cost structure based upon the data files used. It was felt that this

approach might prove too cumbersome in that the user must have access to a computer and must continually use the program for each problem encountered.

Further, the computerized approach would not allow for a convenient parameter

study afforded by the manual method described here. An example of such a parameter study is presented in Appendix C.4.

Figure 4.1 Illustrates the flexibility of the manual method for refining the

estimated minimum cost design. In figure 4.1, the specific design selected

for each component would be determined relative to the design point (R*, C*)

depending upon the architectural requirements. For example, the architect

would select specific design points (Ri, Cj^) in a neighborhood of the design

point (R*, C*). As indicated in figure 4.1, the specific design points (R^,

and (R5, C5) represent an increase in the component noise insulation and

a decrease in component cost relative to (R*, C*). Using these design points,

the architect would increase the ?'oise insulation of the total design and

decrease the total construction cost. The design point (R3 , C 3 ) represents a design that has decreased noise insulation and Increased cost relative to (R*,

C*). The result is that the architect can either make a decision based on

one of the available designs or create a new design using (R*, C*) as the

design objective.

A limitation of the design method described here is that the user must always

check the results to Insure that the optimum noise insulation value, R*, for

each component is within the range of values for which the component cost equation is defined. For the two examples presented in section 4.2.3, the calculated optimum STC values for each component are all included in the STC range

for the component's cost equation. Using the method, it is possible for the

noise control code provision, R^, to be such a magnitude that the optimum com- ponent STC value is outside the range of the cost equation. In this case, the

optimum design is found by following the procedure described in Appendix C.3.4.

28
COMPONENT

COST,

C,

$/sf

Figure 4.1 Selection of Specific Designs Relative to the

Optimum Design Point (R*, C*)

.

29
5. ENERGY SAVINGS AND NON-CONSTRUCTION COSTS

This section deals with three types of economic impacts other than the

construction-related expenditures. The first subsection treats the energy

savings that may result from increasing the acoustical performance of exterior

glazing. The second subsection deals with the code administration costs likely

to result from a noise control code. The experience of the City of San Diego

is reviewed as a basis for the latter discussion. The final subsection concerns

the costs of acoustical testing required by a noise control code for building

occupancy certification.

5 . 1 ENERGY SAVINGS

One special economic effect of improved acoustical performance of the exterior

envelope concerns possible energy savings. This subsection provides an illustration of how energy savings for one building component might be calculated.

The windows used in this illustration are originally designed to be 1/4 inch

plate glass in fixed aluminum frames with a coefficient of thermal transmission

(U value) of 1.09 Btu/hr/sf

/

a°F.

The total window area is 80 sf, and the

STC rating of this window is 31. The windows being analyzed are part of a building which consumes natural gas fuel at a cost of $0.64/therm with a heating

efficiency of 75 percent. The building is located in a climate with 4000 heating degree days per year; for this illustration the savings are based only

on heating requirements. The possible savings from a reduced cooling load are

not included.

Consider the effect of a noise control requirement that calls for an STC

rating of 36. It is assumed that this requirement is met by changing the glass

in the windows to 1 inch insulating glass, which has a U value of 0.57.^ In

order to calculate life-cycle energy savings of such a change, the following

assumptions are made:

1. The life of the windows is 25 years.

2. The salvage value of the windows is zero.

1 American Society of Heating, Refrigerating and Air-Conditioning Engineers,

Inc. (ASHRAE), ASHRAE Handbook of Fundamentals (New York, 1972), table 8,

p. 370.

2 Ibid.

30
3. The real discount rate is 10 percent.

4. The annual fuel price escalation rate is 2 percent.^

The annual energy savings are calculated as follows:

Energy consumption = (Thermal transmittance) x (hrs/day) x (degree days/year)

X (window area) /(heating effficlency)

Current energy consumption = (1.09 Btu/hr/sf /a°F) x (24 hr/day)

X (4000 degree days/year) x (80 sf)/(.75)

= 111.6 Therms/year

Expected energy consumption = (0.57 Btu/hr/sf /a°F) x (24 hr/day)

X (4000 degree days/year) x (80 sf)/(.75)

= 58.4 Therms /year

Annual energy savings = (Current energy consumption - Expected energy

consumption) x (cost of fuel)

= (111.6 Therms/year - 58.4 Therms/year) x ( $0 .64/Therm)

= $34. 05/year.

Under the given assumptions, the formula for life-cycle energy savings is:

Life-cycle energy savings = A(2;_jL_£)[l ~ ],

1 - e 1 + 1

where A = Annual energy savings, i = real discount rate, e = fuel price

escalation rate, and n = assumed life of windows.^ Using this formula we find:

25

Life-cycle energy savings = ($34 .05) ( ) [1 - ( 1 *02

^

i .10 - .02 1 + .10

= ($34. 05)(12.75)(. 84858)

= $368.40.

1 This projected fuel price escalation rate for natural gas is taken from

Federal Register Department of Energy, Office of Conservation and Solar

Energy. Vol. 45, No. 16 (Washington, D.C.: U.S. Government Printing Office,

1980), p. 5646.

2 Rosalie T. Ruegg ^ ad . , Life-Cycle Costing: A Guide for Selecting Energy

Conservation Projects for Public Buildings , National Bureau of Standards,

Building Science Series 113 (Washington, D.C.: U.S. Government Printing Office,

1978), p. 9.

31
Thus, the present value of the heating energy savings due to the assumed noise

control requirement change would be $368. 40

5.2 CODE ADMINISTRATION COSTS

Generally, a jurisdiction adopting any code can expect to incur operating

costs above those presently experienced for building code administration. For

the MNCC it is difficult to formulate a quantitative estimate of these costs,

since many of the specialized requirements of the MNCC may already be met by

current activities of the jurisdiction’s present code administration. It is

appropriate, however, to describe the specialized administrative requirements

of the MNCC provisions. Basically, these specialized requirements include personnel skills, and documentation necessary to administer the MNCC provisions.

Details of the considerations discussed here are described in the Implementation

Manual developed by BBN as supporting documentation for the Model Noise Control

Code.^ An overview of the experience of the City of San Diego, California is

presented to illustrate one jurisdiction’s approach to implementing a noise

control ordinance.^ Code administration costs are not a specific element of

this cost assessment method but these costs must be recognized by the local

jurisdiction as a potential cost factor.

5.2.1 Overview of Administrative Requirements

The MNCC provisions require of a code jurisdiction certain specialized personnel

skills and documentation necessary to administer the noise control code. Table

5.1 presents an overview of these MNCC requirements related to administration.

Specific tasks are defined by the MNCC for Issuing the construction permit and

for Issuing the occcupancy permit. Table 5.1 indicates these tasks by the

sections of the MNCC. Basically, these tasks encompass document review and

evaluation of analyses and test data submitted by the builder. The necessary

skills and documentation required for tasks leading to issue of the construction permit are described in this section. Costs associated with acoustical

acceptance testing are discussed in the following section.

5.2.2 Specialized Skills

The MNCC provisions require a basic level of skill in environmental noise

prediction and noise control in buildings. The noise isolation performance of

interior walls and decks (section 3504) and the exterior building shell (section

^ The total energy savings would equal the heating plus cooling energy saving.

The cooling energy saving calculation method can be found in ASHRAE, "Cooling

and Heating Load Calculation Manual," New York, New York: American Society of

Heating, Refrigerating, and Air-Conditioning Engineers, Inc., 1979, p. 7-11.

^ Bolt, Beranek, and Newman, Inc., Report No. 3837.

^ San Diego, California: Case History of a Municipal Noise Control Program:

(Washington, D.C.: U.S. Environmental Protection Agency, Office of Noise

Abatement and Control; 1978).

32
Code

Administration

Functions

Required

for

Analysis,

Plan

Review,

and

Acceptance

According

to

the

Model

Noise

Control

Code

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33

Sometimes

required
3507) is based upon the present and the future outdoor noise environment

expected at the building site. Since these performance requirements are based

upon predictions of the outdoor day-night sound level, the building code official must verify the designer’s prediction when reviewing documents prior to

issuing the construction permit. Hence, the building code official reviewing

these estimates must possess basic technical skills related to environmental

noise prediction. The necessary level of these technical skills will depend

upon the documentation available to building code officials concerning environmental noise within their jurisdiction as described below. These skills may be

initiated and maintained either by training of existing staff or hiring staff

with the required technical background. The specific approach taken can only

be assessed at the local level.

Documentation review prior to issuing the construction permit requires the

evaluation of acoustical analyses of mechanical equipment noise (section 3506)

and airborne noise isolation of the Interior walls (section 3504) and the

exterior building shell (section 3507). These skills may be classified within

the technical area of building noise control and are consistent with the technical skills in the area of environmental noise prediction described above.

The basic technical skills for building noise control may also be initiated and

maintained either by training existing staff or hiring staff with the required

technical background.

Prior to occupancy, the MNCC provisions require the building owner to conduct

acoustical acceptance tests of the finished building to certify that both the

construction and operation of mechanical equipment meet the applicable performance requirements. If the acceptance test report(s) Indicate that the performance requirements are not satisfied, the building owner must complete remedial

action — including additional testing — to certify compliance. The building

code official must possess the skills necessary to review the acceptance test

reports, to evaluate their accuracy and to require remedial action as appropriate. These requirements are described in section 3508 of the MNCC. The staff

trained in reviewing the documents for issuing building permits can be expected

to possess also the necessary skills required for evaluation of the acoustical

acceptance test reports.

In summary, the MNCC provisions define technical skills that may not be available within a jurisdiction’s current staff. The necessary skills may be realized either by training existing staff or by hiring additional staff with the

appropriate technical background. Training may be obtained, for example, by

staff attending short courses on environmental noise and building noise control.

Once the nucleus of technical skills is established within a jurisdiction these

skills may be maintained and expanded at a level appropriate to the local

requirements. This may include instructing building inspectors in common con- struction defects that result in degradation of noise isolation performance.

The staff size required to administer the MNCC provisions also depends upon the

local requirements as described in the Implementation Manual .^ The resulting

^ Bolt, Beranek, and Newman, Inc., Report No. 3837, p. 24-30.

34
administration costs for staff may be defrayed by appropriate adjustments to

the building permit fees.

5.2.3 Specialized Documentation

The MNCC provisions require the availability of specialized documentation to

support the administration of the various sections of the code. This documentation must be available to the building owner prior to application for the

construction permit. First, an accepted technique for predicting the environmental noise expected at the site during the building's useful life must be

available. The Implementation Manual includes such a prediction method that

encompasses the noise generated by major sources of transportation noise.

Second, the impact noise isolation provision (section 3505) is a prescriptive

requirement wherein the builder will consruct f loor/ceiling assemblies in

compliance with a Construction Handbook . Section 3507 of the MNCC also refers

to the Construction Handbook for examples of exterior building shell configurations that will satisfy the outdoor noise isolation provisions. Because the

Construction Handbook that must accompany the MNCC provisions has not been

prepared, the adopting jurisdiction would have to develop and/or provide the

equivalent documentation.

Additional specialized documentation is required to ease the administrative

work associated with enforcing the MNCC provisions. This documentation is

concerned with the prediction of the outdoor day-night sound levels within the

jurisdiction and with establishing a portfolio of noise insulation data of

building construction configurations. The data necessary to estimate both

present and future outdoor day-night sound levels must be based upon local

conditions. As described in the Implementation Manual , most of the necessary

data may be obtained from other local, state, and Federal Government agencies.

These data may even be available in the form of noise level contours or "noise

maps" for areas within the jursidictlon.

The effort required to establish a portfolio of noise Isolation data for building construction is rather minor because a number of useful sources already

exist. For example, the State of California has published an extensive catalog

of STC and IIC ratings for wall and floor/celling assemblies.^ Additionally,

publications are available that describe practical design methods for implementing building noise control.^ Due to the availability of data relative to the

the building construction requirements to achieve a design level of noise

isolation, a local jurisdiction should readily be able to establish a comprehensive portfolio of acceptable designs. These data, would be used by the

^ Catalog of STC and IIC Ratings for Wall and Floor/Ceiling Assemblies , (Berkeley: California Department of Health Services, Office of Noise

Control, 1980).

^ Quieting in the Home : (Washington, D.C.: U.S. Environmental Protection

Agency, Office of Noise Abatement and Control, 1978).

35
building code official during his review of the building plans prior to issuing

the construction permit.

5.2.4 The Experience of San Diego

Given the above discussion, it can be appreciated that a quantitative estimate

of code administration costs can only be based upon the requirements of the

local jurisdiction. However, a brief overview of the experience of the City of

San Diego, California, provides some useful Insights. This overview is based

upon a case history study^ of San Diego’s municipal noise control program and

the implementation of building noise isolation standards within the framework

of the San Diego Noise Control Ordinance.

In 1973, the San Diego City Council adopted Article 9.5, Noise Abatement and

Control, of the San Diego Municipal Code. This Article does not contain a section covering building noise isolation. However, the San Diego Noise Ordinance does establish the Noise Abatement and Control Administration within the

City Building Inspection Department. In 1978, the San Diego Noise Abatement

and Control Administration employed five staff members; an administrator, an assistant administrator (professional), a field inspector (nonprofessional),

a stenographer (secretary), and a clerk typist. This staff represents 4 to 5 percent of the total department staff and is responsible for the administration

of the San Diego Noise Control Ordinance. In addition to these responsibilities, the staff also assists other departments within the City government in

administration of California noise control ordinances. For example, the staff

assisted the Building Inspection Department in reviewing 600 building plans

for compliance with the California Noise Insulation Standards^ during 1977.

From an administrative standpoint, the basic tasks performed by the San Diego

Noise Abatement and Control staff in assisting the Building Inspection Department parallel the administrative requirements of the MNCC. As part of their

responsibilities, the San Diego staff must maintain an official record of noise

levels in the city called the ”°San Diego City Noise Map." This documentation

serves as the basis for determining the noise insulation from outdoor sources

that is required by the California Noise Insulation Standards. Hence, the

San Diego staff has an estimate of the outdoor noise environment readily available for use in reviewing building plans. The MNCC requires a similar activity

^ San Diego, California; Case History of a Municipal Noise Control Program

(Washington, D.C., U.S. Environmental Protection Agency, Office of Noise

Control, 1978.)

^ "California Noise Insulation Standards", California Administrative Code , Title 25, Chapter 1, Subchapter 1, Article 4, February, 1974.

36
to establish the noise insulation requirements for the building.^ Both the

California Noise Insulation Standards and the MNCC require the building code

official to verify that the proposed construction satisfies the appropriate

noise insulation standards.

The MNCC provisions require the building owner to certify by a defined set of

field tests that the finished construction satisfies the design standards. The

California Noise Insulation Standards require field testing only if, in the

judgment of the building code official, such testing is necessary. This judgment is based upon field inspection to determine whether the construction is in

accordance with the approved plans. The approach taken by the City of

San Diego in requiring acceptance testing — and the costs of the testing —

are described in the next section.

Hence, as part of the administration of the MNCC provisions, the adopting

jurisdiction may decide to incorporate construction inspection for designed

noise control features as a duty of the building inspector. As described above,

staff administering the MNCC provisions may readily train building inspectors

to recognize construction faults that degrade noise insulation of the approved

design. Using this approach, the likelihood of expensive remedial construction

and testing (section 3508 of MNCC) is remote. The Implementation Manual details

the recommended inspections as part of the code administration.^

5.3 ACOUSTICAL TESTING COSTS FOR ACCEPTANCE

A noise control code usually requires acceptance tests, which further increase

costs. As indicated in table 5.1, the MNCC provisions require acceptance testing

for airborne noise Isolation (sections 3504 and 3507) and for noise generated by

the operation of mechanical equipment (section 3506). The costs of conducting

the acceptance testing are paid by the building owner. Table 5.2 further illustrates the acceptance testing requirements by indicating the building categories

included in each section of the MNCC provisions. As emphasized in the annotation to the Model Noise Control Code, the only certain means by which one can verify that the MNCC provisions are met is a final measurement in the completed

building.^ The MNCC provisions require that the acceptance testing be conducted

by a qualified acoustical engineer/consultant as defined in section 3503.

^ The California Noise Insulation Standard specifies constant noise insulation

requirements for interior walls and floor/ceiling assemblies both for airborne

noise and impact noise.

o^ Bolt, Beranek, and Newman, Inc., Report No. 3837, p. 37.

^ Bolt, Beranek, and Newman, Report No. 3759.

37
Model

Noise

Control

Code

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38

Key:

R*=

Multifamily

high-rise,

low-rise,

and

townhouse

buildings. E=

All

educational

buildings.

R=

All

residential

buildings.

N/A=

Not

applicable.
As noted in the comment column of table 5.2, the airborne noise isolation

acceptance tests are based upon standard test methods. Section 3504 requires

acceptance testing using the ASTM 597-77T recommended practice.^ Section 3507

requires acceptance testing using the procedures of International Standard ISO

140/V^ and A-weighted sound level measurements. The consulting firm of Bolt,

Beranek and Newman estimates that the cost in 1978 of conducting the performance

testing to be approximately $25 to $40 per test (one test denotes a building

component)

The total costs of conducting acceptance testing can be estimated on the basis

of a unit or component cost and the number of tests required by the MNCC provisions. Section 3504(c) of the MNCC provisions specifies the number of tests

required for acceptance. This number depends upon two categories of space-tospace utilization for walls and floor-ceiling assemblies and on the possible

variation of construction type within the building or project. Hence, the

number of tests required and the related testing cost can only be estimated

for each specific building design or project. These total costs can be

expected to vary significantly from building to building or project to project.

Compared to the airborne noise isolation tests required in section 3504 and

3507, the acceptance testing for mechanical equipment noise under section

3506 is easily conducted. The number of tests required is also dependent

upon the specific building design as in the case of airborne noise isolation

tests. It is difficult, therefore, to estimate an average total cost per

building.

The above discussion focuses on the direct testing cost to certify the final

building for occupancy. However, the adopting jurisdiction should be aware of

possible additional costs that may arise as a result of the acceptance testing.

First, the ASTM 597-77T test standard recommends minimum aging periods for the

finished construction before testing can be conducted. These aging periods

range from 28 days for masonry to 12 hours for wall board construction using

typical joint and finishing compounds. Hence, the aging period represents a potential time delay between completion of construction and acceptance testing.

The costs of this time delay, if any, can only be determined for the specific

building construction and would be borne by the building owner. Second, the

acceptance testing required under section 3507 of the MNCC provisions applies

to all residential and educational buildings and implies that all facades are

to be tested using the ISO 140/V procedure. Two considerations arise concerning these testing costs. The first consideration is the total cost if every

^ American Society for Testing and Materials, Annual Book of ASTM Standards

(PhiladelpViia, PA).

2 International Organization for Standardization, Acoustics - Measurement of

Sound Insulation in Buildings and of Building Elements - Part V; Field

Measurements of Airborne Sound Insulation of Facade Elements and Facades

ISO 140/V-1978(E), (Geneva, 1978).

^ Bolt, Beranek, and Newman, Report 3759.

39
exterior facade element is included in the test. For example, testing every

exterior facade element (vertical wall separating an interior space from the

outside) of a single dwelling unit could potentially increase the final sales

cost several hundred dollars. Second, the ISO 140/V procedure requires the

positioning of a microphone on the facade exterior. This requirement presents

practical difficulties for facade elemments located over two stories above the

ground elevation. Hence, the placement of an exterior microphone for conducting an acceptance test may become a technical challenge in itself. As a result,

additional test costs can be estimated only on the basis of the specific building design.

An alternate approach to acceptance testing is taken by the San Diego Noise

Abatement and Control Administration. As described in section 5.2, the

San Diego staff assists the Building Inspection Department in administration

of the California Noise Insulation Standards. During construction, building

inspectors verify that the approved design is constructed and that common construction faults degrading noise isolation are avoided. The requirement to

conduct acoustical performance tests is left to the judgment of the building

code official. Additionally, the California Noise Insulation Standard

recognizes a complaint by an occupant as one basis for requiring field testing.

In this case, the complainant posts a bond or sufficient funds in an escrow

account for the cost of the required tests. If the field tests indicate

compliance with the standards, the testing costs are chargeable to the

complainant. If the tests show noncompliance, the testing costs are borne by

the building owner or builder. This approach avoids continuous testing of

every building by insuring quality construction per the approved design.

Hence, testing costs are incurred only if the building code official either

detects faulty construction or receives a complaint from the occupant.

40
6 . CONCLUSION

This research on the cost impacts of noise control requirements for multifamily residential and educational buildings has led to two major accomplishments. First, a general methodology has been developed to estimate the cost

impacts of a wide range of noise insulation requirements applied to a single

building component. The methodology is composed of five basic steps: (1)

identifying the affected building component; (2) selecting the category of

designs to be applied to the component (Component Design Category); (3) obtaining reliable construction cost and STC data on a range of specific designs

within the selected Component Design Category; (4) applying these data to

develop a cost estimating equation that defines construction cost as a function

of STC level; and (5) using this equation to estimate the cost of constructing

the component both with and without the noise control requirement being analyzed.

In this report, the general methodology was applied to 45 commonly used Component

Design Categories for five building components: doors, windows, interior

walls, exterior walls, and floor/ceiling assemblies.

The second major accomplishment of this research is a special cost minimization

method for the acoustical design of a multi-component wall. When used with appropriate cost estimating equations, this method provides the theoretical leastcost STC values for the constituent components of a wall which satisfy given com- posite noise control requirements within a reasonable range. The method also

determines the minimum construction cost. For a fixed set of Component Design

Categories and a fixed area distribution among components, a plot of minimum

construction cost versus composite noise control requirement can be derived.

The cost minimization method has several applications. First, the theoretical

STC values determined by the method provide a basis for a designer to select

the specific values of each component STC. The designer can use the theoretical

values to establish detailed component specifications and obtain refined con- struction cost estimates based on these designs and local economic conditions.

Secondly, for a given area distribution of a particular set of Component Design

Categories, the designer can use the method to estimate the change in construction cost for different composite noise control requirements. The plot of

minimum construction cost versus the composite requirement provides the basis

for this application. Thirdly, the method can be used to evaluate the cost

implications of alternative designs. For a given composite noise control

requirement, one can determine the effect on minimum construction cost of

changing the component area distribution for a given set of Component Design

Categories. Similarly, the designer can use the method to measure the cost

consequences of changing the Component Design Categories for a particular

component area distribution and composite noise control requirement.

The primary focus of this report concerns the estimation of construction-related

costs necessary to achieve alternative noise control specifications. The report

also discusses other costs related to implementation of a model noise control code.

Although a cost estimation model for quantifying these implementation costs is

not developed here, the general overview of the relevant cost considerations

provided in section 5 serves as an aid to establishing such cost estimates

for the specific conditions of a local jurisdiction.

41
REFERENCES

1. American Society of Heating, Refrigerating, and Air-Conditioning Engineers,

Inc., ASHRAE Handbook of Fundamentals , New York, 1972.

2. American Society of Testing and Materials, "Standard Classification for

Determination of Sound Transmission Class," ASTM Standard No. E413-73,

Annual Book of ASTM Standard , Philadelphia, 1973.

3. American Society of Testing and Materials, "Tentative Recommended Practice

for Determining a Single-Number Rating of Airborne Sound Isolation in

Multiunit Building Specifications," ASTM Standard No. E 597-77T, Annual

Book of ASTM Standards , Philadelphia, 1977,

4. Architectural Aluminum Manufacturers Association, Architectural Aluminum

Industry Statistical Review; 1980 , Chicago, 1981.

5. Beranek, L.L., ed.. Noise and Vibration Control , New York: McGraw-Hill

Book Company, 1971,

6. Berendt, R.D., Winzer, G.E., and Burroughs, C.B., A Guide to Airborne

,

Impact and Structureborne Noise-Control in Multifamily Dwellings , Fede ra

1

Housing Administration Publication 750, Washington, D.C., Department of

Housing and Urban Development, September 1967,

7. Boeckh, Inc,, "Architectural Fees", Boeckh Building Valuation Manual , 2nd

ed., Milwaukee, Wise., 1979.

8. Bolt, Beranek, and Newman, Inc., Development of Noise Control Requirements

for Model Building Code , Interim Report No. 3547, Cambridge, Mass., 1977.

9. Bolt, Beranek, and Newman, Inc., Noise Control for Building Codes:

Implementation Manual , Report No. 3837, Cambridge, Mass., 1978.

10. Bolt, Beranek, and Newman, Inc., Noise Control for Building Codes: Noise

Control Provisions , Report No. 3759, Cambridge, Mass., 1978.

11. U.S. Department of Commerce, Construction Review , Washington, D.C.

Published bimonthly.

12. U.S. Department of Energy, Office of Conservation and Solar Energy,

Federal Register , Vol. 45, No. 16 (1980), p, 5644.

13. Fukiniski, T., and Yamamoto, T., "Field Measurement of Sound Insulation of

Houses by the Integral of Sound Energy," Proceedings Inter-Noise 75 , Sandai, Japan: Inter-Noise 75, 1975, pp. 351-354.

14. Gilbert, P., An Investigation of the Protection of Dwellings from External

Noise through Facade Walls , Paris; Centre Scientiflque et Technique du

Batiment, Translated in National Bureau of Standards, Technical Note

710-2, Washington, D.C., March 1972.

42
15. Hedeen, R.A., Compendium of Materials for Noise Control , Washington, D.C.,

Department of Health, Education and Welfare, National Institute of

Occupational Safety and Health, Report DHEW (NIOSH) 80-116, May 1980.

16. Hildebrand, F.B., Methods of Applied Mathematics , New York: Prentice-Hall,

Inc., 1952.

17. International Conference of Building Officials, Uniform Building Code , 1979 ed., Whittier, California, 1979.

18. International Organization for Standardization, "Field Measurements of

Airborne Sound Insulation of Facade Elements and Facades," International

Standard ISO 140/V-1978(E) , Acoustics-Measurement of Sound Insulation in

Buildings and of Building Elements , 1978-07-15, 1st ed., Geneva, 1978,

Part V.

19. Lewis, P.T., "A Method for Field Measurement of the Transmission Loss of

Building Facades," Journal of Sound and Vibration , Vol. 33, No. 2 (1974),

pp. 127-141.

20. Ljunggren, S., Sound Insulation of Windows with Respect to Traffic Noise , Report No. H-3065-A, Gothenburg, Sweden; Ingemanssons Ingenjbrsbyra AB,

February 1972.

21. Mange, G.E., Skale, S.R., and Sutherland, L.C., Background Report on Outdoor-Indoor Noise Reduction Calculation Procedures Employing the Exterior

Wall Noise Rating (EWNR) Method , Report No. FHWA-TS-77-220 , Washington,

D.C., U.S. Department of Transportation, Federal Highway Administration,

March 1978.

22. McKee-Berger-Mansueto, Inc., Building Cost File; Eastern Edition , New

York: Von Nostrand Reinhold Company, 1978.

23. McKee-Berger-Mansueto, Inc., Design Cost File , New York; Von Nostrand

Relnhold Company, 1979.

24. Pallett, D.S. e^ a^. , Design Guide ^or Reducing Transportation Noise in

and Around Buildings , National Bureau of Standards, Building Science

Series 84, Washington, D.C., 1978.

25. Quirt, J.D., Measurement of Sound Transmission Loss of Windows , Building

Research Note No. 172, National Research Council of Canada, Ottawa, 1981.

26. Ruegg, R. T. et al. , Life-Cycle Costing; A Guide for Selecting Energy

Conservation Projects for Public Buildings , National Bureau of Standards,

Building Science Series 113, Washington, D.C., September 1978.

27. Sabine, H. J. et al.. Acoustical and Thermal Performance of Exterior Walls,

Doors, and Windows , Washington, D.C.: U.S. Department of Commerce, National

Bureau of Standards, 1975.

43
28. Sharp, B.H., Kasper, P.K., and Montrol, M.L., Sound Transmission through

Building S true tures-Review and Recommendations for Research , National

Bureau of Standards, Report No. GCR-80-250, Washington, D.C., July 1980.

29. Ungar, E.E., Structureborne Sound in Buildings; Needed Practical Research

in Light of the Current State-of-the-Art , National Bureau of Standards,

Report No. GCR~80~250, Washington, D.C., June 1980.

44
APPENDIX A. COST ESTIMATING EQUATIONS FOR BUILDING COMPONENTS

This appendix contains cost estimating equations for most commonly used designs

in multifamily residential and educational buildings. These equations are to

be used in estimating changes in basic construction costs resulting from noise

control requirements. The estlmaited costs are all expressed in $/sf. The

estimating equations are grouped according to the five major building components

likely to be affected by noise control requirements; (1) Doors; (2) Windows

and Sliding Glass Doors; (3) Exterior Walls; (4) Interior Walls; and (5)

Floor/Ceiling Assemblies. Within each building component group there is an estimating equation for each CDC, as explained in section 3. For each CDC

there is a list of specifications which describe the architectural design for

the equation. The cost estimating equation is reported along with the

t-statistic indicating the significance of the estimated coefficient of STC.

The adjusted r2, the range of STC values, and the number of individual designs

used in the regression are also reported for each CDC. The data listed in

table 3.2 are obtained by rounding the data presented in this appendix.

NOTE:

The value of the t-statistlc is enclosed in parenthesis below the STC

coefficient. The following notation is used:

(Value)* denotes a 95 percent level of confidence; and

(Value)** denotes a 99 percent level of confidence.
APPENDIX A. 1. DOORS

CDC Headings

A. 1.1 Wood or Metal Doors
A. 1.1 Wood or Metal Doors

Cost = 0.769 + 0.4616 STC

(6.6114)**

Adjusted = .84224

STC Range Covered; 20-51

Number of Designs: 9

Description:

1. 3'x7' Door; Metal or Wood; Unfinished

2. Assumed Constant Frame; Weatherstripped Continuously

3. Hardware Assumed Constant
APPENDIX A. 2. WINDOWS AND SLIDING GLASS DOORS

GDC Headings

A. 2.1 Aluminum Frame Fixed Sheet or Plate Glass

A,2,2 Aluminum Frame Fixed Tempered Glass

A. 2.

3

Steel Frame Fixed Sheet or Plate Glass

A. 2.4 Steel Frame Fixed Tempered Glass

A. 2.

5

Aluminum Frame Pivoting Casement Sheet or Plate Glass

A. 2.

6

Aluminum Frame Pivoting Casement Tempered Glass

A.2.7 Steel Frame Pivoting Casement Sheet or Plate Glass

A. 2.8 Steel Frame Pivoting Casement Tempered Glass

A. 2.

9

Aluminum Frame Double Hung Sheet or Plate Glass

A.2.10 Aluminum Frame Double Hung Tempered Glass

A. 2. 11 Steel Frame Double Hung Sheet or Plate Glass

A. 2. 12 Steel Frame Double Hung Tempered Glass

A.2.13 Aluminum Frame Horizontal Sliding Sheet or Plate Glass

A. 2. 14 Aluminum Frame Horizontal Sliding Tempered Glass

A.2.15 Sliding Glass Door

A-4
Aluminum Frame Fixed Glass Window

A. 2.1 Sheet or Plate Glass

Cost = -13.099 + 0.9401 STC

(14.8576)**

Adjusted = .956474

STC Range Covered: 29-47

Number of Designs: 11

1

27.30

36

Insulating Glass

Thickness(in) 1/2 5/8

Cost 24.35 25.87

STC 32 34

A. 2. 2 Tempered Glass

Cost = -6.4391 + 0.8113 STC

(5.35736)**

Adjusted R^ = .798279

STC Range Covered: 31-47

Number of Designs: 8

Laminated Glass

3/4

28.20

43

A-5

Thickness (in)

Cost

STC

5/16 1/2

21.37 23.31

36 40

i
Steel Frame Fixed Glass Window

A. 2. 3 Sheet or Plate Glass

Cost = -13.476 + 0.7880 STC

(10.6121)**

Adjusted = .917774

STC Range Covered; 29-47

Number of Designs; 11

Insulating Glass

Thickness (in) 1/2 5/8 1

Cost 21.29 21.77 22.25

STC 32 34 36

A. 2. 4 Tempered Glass

Cost = -8.128 + 0.7171 STC

(9.40619)**

Adjusted R^ = .925907

STC Range Covered; 31-47

Number of Designs; 8

Laminated Glass

Thickness(in) 5/16 1/2 3/4

Cost 15.27 18.21 23.10

STC 36 40 43

A-6
Aluminum Frame Pivoting Casement Window

A. 2. 5 Sheet or Plate Glass

Cost = + 0.9446 STC

(14.8948)**

Adjusted r2 = .956683

STC Range Covered: 29-47

Number of Designs: 11

Insulating Glass

Thickness(in) 1/2

Cost 24.93

STC 32

5/8 1

26.50 27 .83

34 36

A. 2. 6 Tempered Glass

Cost = -7.966 + 0.8813 STC

(11.1561)**

Adjusted r2 = .946343

STC Range Covered: 31-47

Number of Designs: 8

Laminated Glass

Thickness( in) 5/16 1/2 3/4

Cost 20.88 23.82 28.71

STC 36 40 43

A-7
Steel Frame Pivoting Casement Window

A. 2.7 Sheet or Plate Glass

Cost = -13.508 + 0.7869 STC

(10.6103)**

Adjusted = .917749

STC Range Covered: 29-47

Number of Designs: 11

Insulating Glass

Thickness (in) 1/2 5/8 1

Cost 18.96 20.95 22.15

STC 32 34 36

A. 2. 8 Tempered Glass

Cost = -12.340 + 0.8483 STC

(5,07651)**

Adjusted R^ = .779673

STC Range Covered: 31-47

Number of Designs: 8

Laminated Glass

Thickness (in) 5/16 1/2 3/4

Cost 15.20 18.14 23.03

STC 36 40 43

A-8
Aluminum Frame Double Hung Window

A. 2. 9 Sheet or Plate Glass

Cost = -12.659 + 0.9382 STC

(14.8353)**

Adjusted = .956348

STC Range Covered: 29-47

Number of Designs: 11

Insulating Glass

Thickness(in) 1/2

Cost 24.53

STC 32

5/8 1

26.33 27.70

34 36

A. 2. 10 Tempered Glass

Cost = -7.850 + 0.8741 STC

(11.1259)**

Adjusted R^ = .946065

STC Range Covered: 31-47

Number of Designs: 8

Laminated Glass

Thlckness( in) 5/16 1/2 3/4

Cost 20.75 23.69 28.58

STC 36 40 43
Steel Frame Double Hung Window

A. 2. 11 Sheet or Plate Glass

Cost = -13.743 + 0.8043 STC

(10.6796)**

Adjusted = .918735

STC Range Covered: 29-47

Number of Designs: 11

Insulating Glass

Thickness ( in) 1/2 5/8 1

Cost 19.32 26.06 22.15

STC 32 34 36

A. 2. 12 Tempered Glass

Cost = -8.183 + 0.7244 STC

(7.89161)**

Adjusted R^ = .897477

STC Range Covered: 31-47

Number of Designs: 8

Laminated Glass

Thickness( in) 5/16 1/2 3/4

Cost 15.54 18.48 23.37

STC 36 40 43

A- 10
Aluminum Frame Horizontal Sliding Window

A. 2. 13 Sheet or Plate Glass

Cost = -12.458 + 0.8781 STC

(13.643)**

Adjusted = .948752

STC Range Covered: 29-47

Number of Designs; 11

Insulating Glass

Thickness( in) 1/2 5/8 1

Cost 22.80 23.52 23.97

STC 32 34 36

A. 2. 14 Tempered Glass

Cost = -7.087 + 0.8024 STC

(9.9424)**

Adjusted R^ = .933239

STC Range Covered: 31-47

Number of Designs; 8

Laminated Glass

Thickness(in) 5/16 1/2 3/4

Cost 19.02 21.96 26.85

STC 36 40 43

A-11
A. 2. 15 Sliding Glass Doors

Glass Type Plate Insulating Insulating

Thickness (In) 1/4 5/8 1

Cost 22.89 27.47 30.19

STC 31 34 36

A-12
APPENDIX A. 3. EXTERIOR WALLS

GDC Headings

A.3.1 Stud Frame Wall with Wood Siding Exterior

A. 3.

2

Stud Frame Wall with Stucco Exterior

A. 3.

3

Stud Frame Wall with Aluminum Siding Exterior

A. 3.

4

Stud Frame Wall with Metal Siding 22 Ga. Exterior

A. 3.

5

Stud Frame Wall with Brick Veneer

A. 3.

6

Cast In Place Concrete Wall

A. 3.

7

Concrete Wall with Brick Veneer

A. 3.

8

Concrete Block Wall

A.3.9 Concrete Block Wall: Without Parge Coat, With Brick Veneer

A. 3. 10 Concrete Block Wall: With Parge Coat and Brick Veneer

A.3.11 Granite Veneer

A.3.12 Marble Veneer

A. 3. 13 Limestone Veneer

A.3.14 Precast Concrete Walls

A-13
A. 3.1 Stud Frame Walls with Wood Siding Exterior

Cost = 1.144 + 0.0715 STC

(3.74847)*

Adjusted = .723008

STC Range Covered: 37-48

Number of Designs: 6

Description:

1. Steel or Wood Frame; Thickness 3 l/4"-6"

2. 1/2" Firecode Drywall; Taped and Spackled

3. 2 1/2" Fiberglass Insulation

4. 5/8" Gypsum Sheathing; Felt and Foil Backed

5. Stained Siding: Textured Plywood, Clapboard, Redwood, or Hardwood

A. 3.2 Stud Frame Walls with Stucco Exterior

Cost = 2.001 + 0.0516 STC

(3.24024)*

Adjusted R^ = .655153

STC Range Covered: 37-47

Number of Designs: 6

Description:

1. Steel or Wood Frame; Thickness 3 l/4"-6"

2. 1/2" Firecode Drywall; Taped and Spackled

3. 2 1/2" Fiberglass Insulation

4. 5/8" Gypsum Sheathing; Felt and Foil Backed

5. 3/4" Stucco on Self Firr Lath

A-14
A. 3,3 Stud Frame Walls with Aluminum Siding Exterior

Cost = -0.628 + 0.1103 STC

(3.34714)*

Adjusted = .629706

STC Range Covered: 37-50

Number of Designs: 7

Description:

1. Steel or Wood Frame; Thickness 3 l/4"-6"

2. 1/2" Firecode Drywall; Taped and Spackled

3. 2 1/2" Fiberglass Insulation

4. 5/8" Gypsum Sheathing; Felt and Foil Backed

5. Siding; Insulated and Non-Insulated Aluminum

A. 3.4 Stud Frame Walls with Metal Siding 22 Ga. Exterior

Cost = 4.454 + 0.0715 STC

(3.74847)*

Adjusted R^ = .723008

STC Range Covered: 37-48

Number of Designs: 6

Description:

1. Steel or Wood Frame; Thickness 3 l/4"-6"

2. 1/2" Firecode Drywall; Taped and Spackled

3. 2 1/2" Fiberglass Insulation

4. 5/8" Gypsum Sheathing; Felt and Foil Backed

5. Siding; 22 Ga. Metal; Porcelain Enameled

A-15
A. 3. 5 Stud Frame Wall with Brick Veneer

Cost = 2.068 + 0.0791 STC

(6.83657)**

Adjusted = .91958

STC Range Covered: 48-65

Number of Designs: 5

Description:

1. Wood and Metal Framing

2. Standard Face Brick; Tooled Finish

3. Wall Ties

4. Varied With and Without 4" Batt Insulation

5. Flashed and Dampproofed

A-16
A«3,6 Cast In Place Concrete Wall

Cost = 0.218 + 0.177 STC

(8.27719)**

Adjusted = .882371

STC Range Covered: 47-60

Number of Designs: 10

Description:

1. Concrete; 3000 psi. Rebars; Thickness 6"-15"

2. Varied With and Without 1" Rigid Insulation

3. Dampproofed

A. 3. 7 Concrete Wall with Brick Veneer

Cost = -44.463 + 1.0940 STC

(30.0886)**

Adjusted R^ = .996694

STC Range Covered: 53-56

Number of Designs: 4

Description:

1. Cast In Place Concrete; 3000 psi; Thickness 6"-12"

2. Standard Face Brick; Tooled Finish

3. Wall Ties and Shelf Angles

4. Varied With and Without 1” Rigid Insulation

5. Flashed and Dampproofed

A-17
A. 3. 8 Concrete Block Wall

Cost = -6.133 + 0.2A52 STC

(17.2591)**

Adjusted = .899962

STC Range Covered: 44-80

Number of Designs: 34

Description:

1. Concrete Block; Heavyweight; Split and Smooth Face; Tooled Finish;

2 Coats of Silicone Dampproofing

2. Durowall Every 2nd Course

3. Flashed and Asphalt Dampproofing

4. Varied With and Without 1" Rigid Insulation

5. The upper STC limit is based upon an estimate for a double wall of

solid concrete block separated by an airspace.

A. 3. 9 Concrete Block Wall: Without Parge Coat, With Brick Veneer

Cost = -23.250 + 0.609 STC

(83.3679)**

Adjusted R^ = .999281

STC Range Covered: 50-55

Number of Designs: 6

Description:

1 . Standard Face Brick; Tooled Finish

2. Concrete Block; Light and Heavyweight; 3000 psi; Joints Struck Smooth;

Reinforced; Thickness 4"-8"

3. Wall Ties

4. Varied With and Without 1" Rigid Insulation

5. Flashed and Dampproofed

A-18
A. 3. 10 Concrete Block Wall; With Parge Coat and Brick Veneer

Cost = -8.504 + 0.2734 STC

(7.25868)**

Adjusted = .911799

STC Range Covered: 58-63

Number of Designs; 6

Description;

1. Concrete Block; Light and Heavyweight; Joints Struck Smooth

Thickness 4"-8”

2. Standard Face Brick; Tool Finish

3. Wall Ties

4. Varied With and Without 1" Rigid Insulation

5. Flashed and Dampproofed

A. 3. 11 Granite Veneer

Cost = 3.464 + 0.4079 STC

(11.3246)**

Adjusted R^ = .947857

STC Range Covered: 50-61

Number of Designs: 8

Description:

1. Finished Granite; Median Quality; Thickness 2" or 3”

2. Concrete Block; Heavyweight; Joints Struck Smooth; 6"-12"

3. Varied With and Without 1" Rigid Insulation

4. Steel Shelf Angle and Stone Anchor

5. Flashed and Dampproofed

A-19
A. 3. 12 Marble Veneer

Cost = 4.010 + 0.3864 STC

(6.7044)**

Adjusted = .862608

STC Range Covered; 50-61

Number of Designs: 8

Description:

1. Finished Marble, Median Quality 1 l/2"-2 1/4"

2. Concrete Block; Heavyweight; Joints Struck Smooth; 6"-12"

3. Varied With and Without 1" Rigid Insulation

4. Steel Shelf Angle and Stone Anchor

5. Flashed and Dampproofed

A. 3. 13 Limestone Veneer

Cost = 1.536 + 0.2989 STC

(11.7394)**

Adjusted R^ = .951326

STC Range Covered: 50-61

Number of Designs: 8

Description:

1. Limestone Panels; Light Texture 2"-4"

2. Concrete Block; Joints Struck Smooth; 6"-12

3. Varied With and Without 1" Rigid Insulation

4. Steel Shelf Angle and Stone Anchor

5. Flashed and Dampproofed

A-20
A. 3. 14 Precast Concrete Walls

Cost = 1.997 + 0.2683 STC

(21.6376)**

Adjusted = .970905

STC Range Covered: 40-61

Number of Designs: 15

Description:

1. Precast Concrete; Self Anchored and Masonry Anchored;

Thickness 4"-6"

2. Varied Rigid Insulation 1", 1 1/2", and None

3. Masonry Block; Joints Struck Smooth; Thickness 8"-12"

4. Stone Anchor

5. Dampproofed

A-21
APPENDIX A. 4. INTERIOR WALLS

CDC Headings

A.4.1 Wood Stud Frame Plaster Partition

k,h,l Metal Stud Frame Plaster Partition With Gypsum Lath

A. 4.

3

Shaft Stud Frame Drywall Partition

A.4.4 Wood Stud Frame Drywall Partition

A. 4.

5

Metal Stud Frame Drywall Partition

A. 4.

6

Concrete Partition Cast In Place

A. 4.

7

Brick Partition

A. 4.

8

Block Partition Lightweight Concrete Block

A. 4.

9

Heavyweight Concrete Block Partition

A.4.10 Structural Clay Tile Partition

A-22
A. 4.1 Wood Stud Frame Plaster Partition

Cost = 0.904 + 0.0633 STC

(3.48883)**

Adjusted = .503878

STC Range Covered: 32-45

Number of Designs: 12

Description:

1. Wood Studs With Blocking; Thickness 3"-6" Nominal

2. Gypsum Plaster; Varied 1-3 Coats; Sanded

3. Varied; Gypsum Lath 3/8"-l/2'*; Metal Lath 3.4 lb.; Drywall l/2"-l 1/4

With and Without 1 1/2" Soundproof Glass Fiber Insulation

A. 4. 2 Metal Stud Frame Plaster Partition With Gypsum Lath

Cost = -0.048 + 0.0755 STC

(3.91263)**

Adjusted R^ = .565366

STC Range Covered: 38-52

Number of Designs: 12

Description:

1. Metal Studs With Runners and Bracing; Thickness 1 5/8"-3 1/4"

2. Gypsum Lath; Perforated; Thickness 3/8" and 1/2"

3. Gypsum Plaster; 2 Coats; Sanded; Thickness 3/8" and 1/2"

4. Varied With and Without Resilient Clips

5. Varied With and Without 1 1/2" Soundproof Glass Fiber Insulation

A-23
A. 4. 3 Metal Shaft Frame Drywall Partition

Cost = 1.619 + 0.0475 STC

(8.08837)**

Adjusted = .697041

STC Range Covered: 25-59

Number of Designs; 29

Description:

1. Shaft Studs 1 l/2"-4”

2. Firecode Drywall; Taped and Spackled; Thickness l/2"-l 1/4"

3. Coreboard; Thickness 1" or 2"

4. Varied With and Without Resilient Channels

5. Varied With and Without 1 1/2" Soundproof Glass Fiber Insulation

A. 4. 4 Wood Stud Frame Drywall Partition

Cost = -1.363 + 0.1080 STC

(4.19982)**

Adjusted R^ = .648965

STC Range Covered: 32-47

Number of Designs: 10

Description:

1. Wood Stud With Blocking; Thickness 3"-6" Nominal

2. Firecode Drywall; Taped and Spackled; Thickness 1/2" and 5/8"

3. Varied With and Without Resilient Clips

4. Varied With and Without 1 1/2" Soundproof Glass Fiber Insulation

A-24
A. 4. 5 Metal Stud Frame Drywall Partition

Cost = -0.692 + 0.0740 STC

(10.5884)**

Adjusted = .874129

STC Range Covered: 38-55

Number of Designs: 17

Description:

1. Metal Studs With Runners and Bracing; Thickness 1 5/8"-3 1/4"

2. Firecode Drywall; Taped and Spackled; Thickness 1/2" and 5/8"

3. Varied With and Without Resilient Clips

4. Varied With and Without 1 1/2" Soundproof Glass Fiber Insulation

A. 4. 6 Concrete Partition Cast In Place

Cost = 1.323 + 0.1440 STC

(13.9371)**

Adjusted R^ = .96024

STC Range Covered: 46-62

Number of Designs: 9

Description:

1. Concrete: Lightweight and Regular; 3000 psi

2. Spaded Clean

3. Rebars

4. Partition Thickness 6"-16"

A-25
A. 4, 7 Brick Partition

Cost = -22.660 + 0.5538 STC

(19.8403)**

Adjusted = .987426

STC Range Covered: 47-67

Number of Designs: 6

Description:

1. Common Face Brick

2. Common Brick

3. Tooled Joints

A. 4. 8 Block Partition Lightweight Concrete Block

Cost = -1.608 + 0.0983 STC

(11.384)**

Adjusted R^ = .89554

STC Range Covered: 32-53

Number of Designs: 16

Description:

1. Lightweight Concrete Block: Solid and Hollow Core

2. Joints Struck Smooth

3. Durowall Reinforcing Every 2nd Course

4. Partition Thickness 3"-12"

A-26
A. 4. 9 Heavyweight Concrete Block Partition

Cost = 0.804 + 0.0792 STC

(6.89108)**

Adjusted = .756046

STC Range Covered; 35-58

Number of Designs: 16

Description;

1. Heavyweight Concrete Block; Joints Struck Smooth

2. Durowall Reinforcing Every 2nd Concrete

A. 4. 10 Structural Clay Tile Partition

Cost = -5.238 + 0.1899 STC

(7.10287)**

Adjusted R^ = .722428

STC Range Covered: 35-43

Number of Designs; 20

Description:

1. Structural Clay Tile; Hollow Core; Joints Struck Smooth; Rough and Smooth

Surface

2. Durowall Reinforced Every 2nd Course

A-27
APPENDIX A. 5. FLOOR/CEILING ASSEMBLIES

CDC Headings

A. 5.1 Wood Joists With Drywall Ceiling

A. 5. 2 Wood Joists With Plaster Ceiling on Gypsum Lath

A. 5. 3 Wood Joists With Plaster Ceiling on Metal Lath

A. 5. 4 Drop Ceiling Panels Added to Floor Structural System

A. 5.5 Drywall Ceiling Added to Concrete Slab

A. 5.6 Steel Joists & Drywall Ceiling Added to Floor Structural System

A-28
A. 5.1 Wood Joists With Drywall Celling

Cost = 1.302 + 0.0338 STC

(5.51387)**

Adjusted = .648012

STC Range Covered: 34-60

Number of Designs: 17

Description:

1. 2"x8" Wood Floor Joists

2. Bridging

3. 5/8" T&G Plywood

4. 3/8"-l 1/4" Drywall; Taped and Spackled

5. Varied With, Without and In Combination: Various Backing and Core

Boards; Resilient Clips; and l"-4" Insulation

A. 5.2 Wood Joists With Plaster Celling on Gypsum Lath

Cost = 0.013 + 0.0509 STC

(18.24373)**

Adjusted R^ = .95940

STC Range Covered: 48-58

Number of Designs: 15

Description:

1. 2"x8" Wood Floor Joists

2. Bridging

3. 5/8" T&G Plywoood

4. Gypsum Lath 3/8"-l/2" and Two Coats of Gypsum Plaster

5. Varied With, Without and In Combinations: 2"-4" of Insulation; l/4"-5/8

Gypsum Backing Board; and Resilient Clips

A-29
A. 5. 3 Wood Joists With Plaster Celling on Metal Lath

Cost = 0.684 + 0.0557 STC

(11.9017)*

Adjusted = .88641

STC Range Covered: 41-58

Number of Designs: 19

Description:

1. 2"x8" Wood Floor Joists

2. Bridging

3. 5/8" T&G Plywood

4. Metal Lath With Plaster or special acoustical plaster

5. Varied With, Without, and In Combination: Various Backing and Core

Boards; l"-4" Insulation

A. 5.

4

Drop Ceiling Panels Added to Floor Structural System

Cost = -0.075 + 0.0443 STC

(2.81656)*

Adjusted R^ = .464273

STC Range Covered: 25-40 Not Including STC for the Floor Structural System

of the Floor /Ceiling Assembly

Number of Designs: 9

Description:

1. Various Ceiling Tiles With Appropriate Mounting Material

Note: The cost and STC values for the floor structural system of the floor/

ceiling assembly are not Included in this estimating equation. Before

the floor/ceiling assembly's complete Total Cost and STC values can be

applied in this methodology, the Total Cost and STC values of the floo

structural system must be determined independently and then combined

with the corresponding values derived from the estimating equation.
A. 5. 5 Deck Drywall Celling Added to Concrete Slab

Cost = 0.588 + 0.0388 STC

(6.32012)**

Adjusted = .829584

STC Range Covered: 8-22 Not Including STC for the Floor Structural System of

the Floor/Ceiling Assembly

Number of Designs: 9

Description:

1. I"x2" Furring

2. 3/8"-5/8" Gypsum Dr3rwall; Tape and Spackle

3. Varied With and Without 1" Mineral Fiber Insulation; and Also With

and Without Resilient Clips

Note: The cost and STC values for the floor structural system of the floor/

ceiling assembly are not included in this estimating equation. Before

the floor/ceiling assembly's complete Total Cost and STC values can be

applied in this methodology, the Total Cost and STC values of the floor

structural system must be determined independently and then combined

with the corresponding values derived from the estimating equation.

In this case, a concrete slab is the only type of floor structural

system compatible with the design specifications used to develop this

CDC estimating equation.

A. 5. 6 Steel Joists With Drywall Ceiling Floor Structural System

Cost = 0.536 + 0.0446 STC

(14.5924)**

Adjusted r2 = .950659

STC Range Covered: 8-27 Not Including STC for the Floor Structural System of

the Floor /Celling Assembly

Number of Designs: 12

Description:

1. I"x2" Furring

2. 3/8'’-5/8” Gypsum Drywall; Taped and Spackled

A-31
3. Varied With, Without, and In Combinations; Various Backing and Core

Boards; l"-3" Insulation; and Resilient Clips

Note: The cost and STC values for the floor structural system of the floor/

celling assembly are not included in this estimating equation. Before

the f loor/ceiling assembly's complete Total Cost and STC values can be

applied in this methodology, the Total Cost and STC values of the floor

structural system must be determined independently and then combined

with the corresponding values derived from the estimating equation.

A-32
APPENDIX B. ADJUSTING FOR REGIONAL CONSTRUCTION COST DIFFERENCES

The cost equations presented in Appendix A are based on cost information from

the Eastern Edition of the Building Cost File . That edition uses Philadelphia

as the source of its basic cost information. In order to account for price

diffferences between cities, it is necessary to multiply the result of any

cost equation from Appendix A by a Regional Cost Adjustment Factor (RCAF)

.

Table B.l presents RCAFs for most major cities. The RCAF for a particular

city is the ratio of the acoustical treatment cost index for that city divided

by the acoustical treatment cost index for Philadelphia.

As an example of how to use the RCAF, suppose a building were to be constructed

in Bismarck, North Dakota and one had calculated the increase in construction

cost for doors to be $45.00 per door including the contractor markup and the

A&E design fee. To calculate the Increase in construction cost appropriate for

Bismarck, one would do the following:

Bismarck increase in cost = Bismarck RCAF x Base Increase in cost

= (0.824) X $45.00

= $37.08

Thus the estimated Increase in construction cost for the door in Bismarck, North

Dakota would be $37.08 per door.

B-1
Table B.l. Regional Cost Adjustment Factors (RCAF)

for Major U.S. Cities

CITY STATE RCAF

Abilene TX 0.843

Albany NY 0.942

Albuquerque NM 0.958

Amarillo TX 0.890

Anchorage AK 1.398

Atlanta GA 0.860

Baltimore MD 0.900

Bangor ME 0.904

20 City Base 0.997

Baton Rouge LA 0.877

Billings MT 0.832

Binghamton NY 0.882

Birmingham AL 0.803

Bismarck ND 0.824

Boise ID 0.909

Boston MA 1.032

Buffalo NY 1.125

Burlington VT 0.948

Camden NJ 1.007

Centralia IL 0.921

Charleston

4 WV 0.909

Charleston , SC 0.761

Charlotte NC 0.778

B-2
Table B.l. Regional Cost Adjustment Factors (RCAF)

for Major U.S. Cities (Continue)

CITY STATE RCAF

Cheyenne WY 0.924

Chicago IL 0.982

Cincinnati OH 1.200

Cleveland OH 1.138

Columbus GA 0.788

Columbus OH 1.131

Corpus Christ! TX 0.844

Council Bluffs lA 0.824

Dallas TX 0.921

Denver CO 0.962

Des Moines lA 0.862

Detroit MI 1.229

Dover DE 0.931

Dubuque lA 0.888

Duluth MN 0.901

El Paso TX 0.849

Evansville IN 0.887

Fargo ND 0.847

Fort Worth TX 0.921

Fresno CA 1.108

Grand Rapids MI 1.104

Great Falls MT 0.872

Harrisburg PA 0.882

I
Table B.l. Regional Cost Adjustment Factors (RCAF)

for Major U.S. Cities (Continue)

CITY STATE RCAF

Hartford CT 0.950

Honolulu HI 0.946

Houston TX 0.942

Indianapolis IN 1.192

Jackson MS 0.864

Jacksonville FL 0.873

Kansas City MO 0.886

Knoxville TN 0.801

Lansing MI 1.152

Las Vegas NV 1.024

Lexington KY 1.129

Little Rock AR 0.799

Los Angeles CA 1.044

Louisville KY 1.129

Madison WI 0.890

Manchester NH 0.915

Memphis TN 0.881

Miami FL 0.886

Milwaukee WI 0.959

Minneapolis MN 0.918

Mobile AL 0.911

Moline IL 0.865

B-4
Table B.l. Regional Cost Adjustment Factors (RCAF)

for Major U.S. Cities (Continue)

CITY STATE RCAF

Nashville TN 0.824

NassauSuffolk County NY 1.052

New Haven CT 0.956

New Orleans LA 0.925

New York City NY 1.068

Newark NJ 0.981

Norfolk VA 0.815

North Platte NE 0.942

Oklahoma City OK 0.903

Omaha NE 0.878

Paduka KY 0.851

Peoria IL 0.954

Philadelphia PA 1.000

Phoenix AZ 0.983

Pittsburgh PA 1.010

Portland OR 1.073

Portland ME 0.904

Providence RI 1.004

Pueblo CO 0.933

Raleigh NC 0.778

Redding CA 1.106

Reno NE 0.980

B-5
Table B.l. Regional Cost Adjustment Factors (RCAF)

for Major U.S. Cities (Continue)

CITY STATE RCAF

Richmond VA 0.815

Roanoke VA 0.797

Sacramento CA 1.106

Salt Lake City VT 0.970

San Antonio TX 0.889

San Diego CA 1.004

San Francisco CA 1.106

San Juan Puerto Rico 0.709

Savannah GA 0.812

Scranton PA 0.899

Seattle WA 1.047

Shreveport LA 0.902

Sioux Falls SD 0.852

South Bend IN 0.915

Spokane WA 1.046

Springfield MO 0.860

Springfield MA 0.989

Springfield IL 0.921

St. Louis MO 0.919

Syracuse NY 1.077

Tallahassee FL 0.760

Tampa FL 0.865

Toledo OH 1.129

B-6
Table B.l. Regional Cost Adjustment Factors (RCAF)

for Major U.S. Cities (Continue)

CITY STATE RCAF

Topeka KS 0.835

Trenton NJ 0.971

Tulsa OK 0.906

Tuscon AZ 0.983

Washington DC 0.912

Westchester

County NY 0.992

Wichita KS 0.848

Wilmington DE 0.931

Winston-Salem NC 0.778

Yakima WA 1.047

B-7

APPENDIX C

DESIGN OF MINIMUM COST MULTI-COMPONENT WALLS TO ACHIEVE A

SPECIFIED LEVEL OF NOISE INSULATION

This appendix describes a method for selecting the noise insulation values of

each component of a multi-component wall so that the noise insulation property

of the total structure meets a specified value and the total construction cost

is minimized. The method uses the cost equations presented in Appendix A. The user selects the particular Component Design Categories corresponding to each

component of the multi-component wall. Using a pocket calculator, the minimum

cost design is obtained with a few minutes effort. Examples are presented in

this appendix illustrating several uses of the method.

C.l NOISE INSULATION OF MULTI-COMPONENT WALLS

A multi-component wall is a composite structure consisting of two or more different components. For example, a basic wall structure with doors and

windows is a multi-component wall. Each component may exhibit a different

noise insulation property such as an STC rating. For the multi-component wall,

it is then necessary to determine the noise insulation value of the multicomponent wall from the noise insulation properties of each of the components.

Assuming that the acoustic power is uniformly distributed over the surface of

the multi-component wall, the noise insulation of the wall is expressed in

terms of the noise insulation properties of the N components by the

relationship :

Rj. = - 10 log { E • 10 ^

1 , dB (C.l)

i=l

where

Rq = the "composite" noise insulation property of the multi-component

wall;

R^ = the noise insulation property of the ith component;

k^ = S^/S is the fraction of the total wall area, S, of the ith

component; and

= the wall area of the ith component.

Hence, to calculate the noise insulation property of the composite wall it is

necessary to know both the noise insulation properties of the components and

the fraction (or percentage) of the total wall area comprising each component.

Concerning the "noise insulation property" of both the component and the

composite or multi-component wall, the relationship indicated by equation (C.l)

^ See L. L. Beranek, ed.. Noise and Vibration Control (New York: McGraw-Hill

Book Company, 1971) pp. 311-312.

C-1
is applicable for sound transmission loss at a given frequency and for single

number noise insulation ratings such as the Sound Transmission Class or STC

rating. Since the cost equations presented in Appendix A are developed using

the STC rating for noise insulation, the STC rating will be used for the noise

insulation property of components in the remaining discussion of this appendix.

That is, Rj[ will denote the STC rating of the ith component of a multi-component

wall and will denote the composite "STC rating" (i.e., the composite sound

insulation property) of the multi-component wall.

For a majority of configurations encountered in practice, a multi-component

wall comprising two or three elements is sufficient to characterize the structure. For example, common configurations of two component walls are a basic

wall structure such as described by the Component Design Categories presented

in Appendix A. 3 an A. 4 and either a door (Appendix A.l) or a glazing component

(Appendix A. 2). A three component wall may comprise a basic wall structure,

doors, and a single type of glazing. Hence, it is convenient to present the

general form of equation (C.l) as specialized results for both the two

component wall and the three component wall.

C.1.1 Noise Insulation of a Two Component Wall

For a two component wall, one sets N=2 in equation (C.l) to obtain:

-Ri/10 -R^/IO

R^, = -10 log

j 10 ^ + k

2 10 ^

}

. (C.2a)

Noting that + k2 = 1 , this result may be further simplified to obtain:

(R,-R,)/10

R^ = R]^ -10 log

( 1 + k2 [10

^ ^ - 1] I

. (C.2b)

For example, if component 1 is a wall structure with an STC rating of 40 and

component 2 is a door with an STC rating of 30 and the door comprises

15 percent of the total wall area, then R]^=40, R£=30 and k2=0.15 and R(.=36.3.

The multi-component wall then is estimated to have an STC rating of 36. (One

should, in general, round fractions of a dB or STC ratings to the nearest

whole integer.)

C.l.

2

Noise Insulation of a Three Component Wall

For a three component wall, one sets N=3 in equation (C.l) to obtain:

-Ri/10 -R,/10 -R./IO

R^ = -10 log

{ k^ 10 ^ + k

2 10 ^ + k

3 10 }

, (C.3)

where

ki + k2 + ks = 1

.

C-2
For example, suppose that the door in the two component wall described in

section C.1.1 is installed so that a perimeter crack exists around the door and

the perimeter crack represents 0.5 percent of the total wall area. Denoting

the crack as "component 3" with an STC rating of zero, the composite STC rating

is obtained using equation (C.3) with the data: Rj^=40, k]^=0.85, R2=30,

k2=0.l45; and R3=0, k3=0,005. The composite STC rating with the door and

the crack is R<,=22.8 or the composite STC rating is 23. Hence, the 0.5 percent

opening around the door results in a degradation of the noise insulation performance of 13 STC units. This example illustrates the importance of using

gaskets and seals around doors and windows to maintain the design integrity of

multi-component wall noise insulation.

C.2 NOISE ISOLATION OF MULTI-COMPONENT WALLS

The discussion of section C.l addresses the topic of noise insulation of

multi-component walls. For the model described in this report, the single

number noise insulation rating selected for use is the Sound Transmission Class

or STC rating. 1 Noise insulation is a property of the structure that is

determined from laboratory tests. Noise isolation is a measure of the overall

noise attenuation achieved by a building structural component or components as realized in the specific built environment. This section discusses and presents relationships between noise insulation performance of a design and noise

isolation performance of the constructed building. This relationship is

necessary in order to understand the performance requirements for building

structure noise isolation as used in noise control codes,

Basically, the noise isolation of a building component is measured as the

difference between the sound level on the source side of the component and the

sound level on the receiver side of the component. The noise insulation of the

building component is defined in terms of the acoustic sound power incident

upon the component on the source side and the sound power transmitted by the

component to the receiving space. Hence, the relationship between the noise

insulation property of the building component and the noise isolation performance of the component in the built environment involves the relationship

between sound power and sound pressure on both the source side and the receiver

side of the component. As might be expected, the relationship is different for

components separating interior building spaces and for components separating an

^ See American Society of Testing and Materials, "Standard Classification for

Determination of Sound Transmission Class," ASTM E413-73, Annual Book of ASTM

Standards , 1973.

2 The discussion here will not attempt to consider flanking sound transmission.

The Interested reader should see B. H. Sharp, P, K. Kasper, and M. L, Montrol,

Sound Transmission through Building Structures-Review and Recommendations for

Research , National Bureau of Standards Report No. GCR-80-250 (Washington, D.C.

U.S. Department of Commerce, 1980) and E. E. Ungar, Structureborne Sound in

Buildings: Needed Practical Research in Light of the Current State-of-the-Art

National Bureau of Standards Report No. GCR-80-248 (Washington, D.C.: U.S.

Department of Commerce, 1980),

C-3
interior space from intruding exterior noise. The performance requirements of

the MNCC recognize these differences. The noise isolation requirements for

interior walls are a distinct consideration from the noise isolation

requirements for exterior walls.

C.2.1 Noise Isolation of Interior Walls

The airborne noise isolation requirements of interior walls are presented in

tables 35~A and 35-B of the Model Noise Control Code. The requirements are specified in terms of the normalized sound level difference between adjacent

interior spaces within the building. This quantity is determined by conducting

field tests using the procedures of ASTM E597-77T, "Tentative Recommended

Practice for Determining a Single-Number Rating of Airborne Sound Isolation in

Multiunit Building Specifications." The definition used in that report for

the normalized sound level difference is;

Dn = Lg - Lj. + 10 log(Sfji/Ar), (C.4)

where

^ is the normalized sound level difference

Ls is the average (A-weighted) sound level in the source room

L|- is the average (A-weighted) sound level in the receiving room

Sf^ is the floor area in the receiving room

Aj. is the amount of sound absorption in the receiving room.

The relationship indicated in equation (C.4) is the form used to present test

results based upon ASTM E597-77T. The MNCC provisions in table 35-A indicate

that the design value for the interior partition, in terms of the STC rating,

should be selected 5 units above the required normalized sound level difference.

This 5 unit adjustment is a design margin recommended by the MNCC provisions.

The cost model developed in this appendix allows the designer to estimate the

cost of incorporating this design margin so that a value may be placed upon

this particular design approach.

C.2.2 Noise Isolation of Exterior Walls

The airborne noise isolation requirements of exterior walls are presented in

table 35-C of the Model Noise Control Code. The requirements are specified as the "sound level reduction provided by the exterior shell." As defined by the

MNCC, the sound level reduction is the difference, in decibels, between the outdoor equivalent A-welghted sound level, Lgq, and the corresponding equivalent Aweighted sound level inside the building. The exterior level is to be measured

at a distance of 2 meters from the outside surface of the wall. In order to

utilize the cost minimization model described in the next section of this

appendix, it is necessary to develop a relationship between the A-weighted

sound level reduction required by the MNCC provisions (table 35-C) and the

composite STC rating, Rg, of the exterior wall as given by equation (C.l).

The form of the relationship developed in this section is as follows;

Rc = AL^ + 10 log (S/A) + constant, (C.5)

C-4
where

R(, is the composite STC rating for the multi-component exterior wall

given by equation (C.l)

= (Leq)2m “ (Leq)^nterior A-weighted sound level reduction

required by the MNCC provisions of table 35-C

S is the total surface area of the exterior wall transmitting

exterior sound into the interior receiving space

A is the total sound absorption in the receiving space (average for

the 500 Hz to 1 kHz bands).

In equation (C.5), the parameters 3 and A must be expressed in consistent units

(l.e., both in m^ or sf). The following discussion focuses upon the determination of the "constant" appearing in equation (C.5).

Any relationship between a single number noise insulation rating, such as STC,

of a composite exterior wall and the sound reduction achieved in the built

environment is an approximation. For the purpose of formulating a building

code provision and providing design guidance, differences between noise sources used in laboratory measurements and the environmental noise sources to which

the building is exposed must be recognized. Specifically, the relationship must

include the following considerations;

® Reflection of sound from the building exterior wall surface

° Non-diffuse sound fields generated by environmental noise sources

° Spectral characteristics of environmental noise sources.

The MNCC provisions require that the field noise isolation performance of the

structure be verified using the procedures of ISO 140/V (1978), "AcousticsMeasurement of Sound Insulation in Buildings and of Building Elements, Part V.

Field Measurements of Airborne Sound Insulation of Facade Elements and Facades."

The testing, however, is to be performed using only A-weighted sound level data

with the exterior measurement location being 2 meters from the facade exterior

surface. This location is specified to relate field measured noise source sound levels to the corresponding source room sound level measured in the

laboratory since in either case the measured levels are approximately 3dB less

than levels measured at the surface of the wall.

This observation would suggest that a measurement location on the exterior wall

surface could be as easily justified as a location 2 meters from the exterior

surface. There are practical considerations that favor either location^;

^ For discussion of these considerations, see P. T. Lewis, "A Method for Field

Measurement of the Transmission Loss of Building Facades," Journal of Sound

and Vibration , 33(2), 1974, pp. 127-141.

C-5
however, the 2 meter location is used as the basis for the development in this

appendix since it is the location required for the MNCC provisions.

First, it is necessary to quantify the effect of reflections of the incident

sound from the exterior surface. To do this, a few terms must be defined.

The sound level at a location on the exterior surface of the facade is denoted

as ( Lgq) surface . The sound level at a location 2 meters from this exterior

surface location is denoted as (Leq)2m'’ Both of these sound levels include

the incident and the reflected components of the sound pressure. The sound

level at this location on the exterior surface but in the physical absence of

the surface is denoted as (Leq)fj-ee“ (^eq)free sound level is a measure

of only the incident sound pressure at the location of the facade since there

is no physical surface present from which the incident sound can be reflected.

For example, (Leq)free ®ight be measured at a site before the building is

constructed or might be predicted for locations on the exterior building

surface.^ All of these sound levels will vary with location over the building

surface

.

Assuming perfect reflection of incident sound waves from the building exterior

surface, the sound levels (Lgq ) ace

,

(^eq )2m> (Beq) free related as follows;

(^eq)2m “ (^eq) surface - 3 dB (C.6a)

(^eq)2m ~ (^eq)free + 3 dB (C.6b)

(^eq)surface “ (^eq)free + 6 dB. (C.6c)

The assumption of perfect reflection of the Incident sound waves applies to a smooth and acoustically hard exterior surface. It is recognized that this

condition is rarely encountered in practice. However, experimental data

describing effects of both irregular exterior surfaces and absorptive exterior

surfaces are available for more refined estimates.

2

The MNCC provisions require a specified A-weighted Sound Level Difference,

depending upon the predicted outdoor day-night sound level at the

building site. Expressed in terms of the equivalent sound levels defined

above, the required sound level reduction is expressed as;

A^A = (^eq)2m “ (^eq^lnterlor, (C.7)

where the term (Leq)£j^|-gj.j^Qj- is measured in the interior receiving space of the

building according to the test provisions in ISO 140/V (1978).

^ The measurement and/or predictions in the free environment must Include any

shielding of the facade by the building.

2 One source of this data is P. Gilbert, An Investigation of the Protection of

Dwellings from External Noise through Facade Walls , Centre Scientifique et

Technique du Batiraent, Paris, France, translated in NBS Technical Note 710-2,

(Washington, D.C.; U.S. Department of Commerce, 1978).

C-6
The result of equation (C.7) bases the sound level reduction on an exterior

mesurement at the 2 meter location including both incident and reflected

components of the sound pressure* For subsequent use in the development of

equation (C.5), it is necessary to express the sound level reduction in terms

of (Leq)free rather than (Leq)2m* Substituting equation (C.6b) into equation

(C.7), the sound level difference required by the MNCC provisions is expressed

as

:

ALa = (Leq)fj-gg - (l>eq) j^nterior *" 3 = SLR + 3 (C.8)

This expression for the sound level reduction represents the effect of sound

pressure reflections from the exterior surface of the structure as used in this

development

.

To incorporate the effect of non-diffuse exterior sound fields, it is necessary

only to state that the requirement to use and equivalent or time-averaged sound

level metric, such as Lgq, also accounts directly for this effect. Research on noise isolation of buildings from exterior environmental noise sources generally

supports this statement.^ Hence, no additional adjustment is required, in this

developement , to account non-diffuse exterior sound fields for typical environmental noise sources.

It is, however, necessary to incorporate the effect of noise source spectra for

different basic environmental noise sources such as highways, railways, and

aircraft. Fortunately, extensive numerical studies have been conducted to

determine empirically this type of adjustment.^ The form of these empirical

results relates the A-weighted sound level difference, as given by equation

(C.8), to the sound level reduction calculated using the STC ratings of each

component of the mut 11-component exterior wall. This result is;

SLRsxc = SLR + C = ALa + C - 3 (C.9)

The term SLRgxc the sound level reduction calculated using the STC ratings

of each component of the multi-component wall. The term C is an empirical

parameter dependent upon the type of environmental noise source.

^ For descriptions of some research, see S. Ljunggren, Sound Insulation of

Windows with Respect to Traffic Noises , Report No. H-3065-A, (Gothenburg,

Sweden; Ingemanssons Ingenjorsbyra AB, 1972) and T. Fukinski and T. Yamamoto,

"Field Measurement of Sound Insulation of Houses by the Integral of Sound

Energy," Proceedings Inter-noise 75 (Sandai, Japan: 1975).

2 For descriptions of some studies, see D. S. Pallett, ^ al . , Design Guide for

Reducing Transportation Noises in and Around Buildings , National Bureau of

Standards Building Science Series 84 (Washington, D.C.: U.S. Department of

Commerce, 1978) and G. E. Mange, S. R. Skale, and L. C. Sutherland, Background

Report on Outdoor-Indoor (EVfNR) Method , Federal Highway Administration Report

No. TS-77-220 (Washington, D.C.: Department of Transportation, 1978).

C-7
The sound level reduction calculation based upon the component STC rating is:

SLRstc = Rc “ 10 log(S/A)-6,

where

(C.IO)

is given by equation (C.l)

S & A are defined in equation (C«5).

Based upon the numerical studies the following average values of the parameter

C may be used for design guidance ;1

C = +2 (+ 2.8) dB For either highway or railway

environmental noise spectra (C.lla)

C = +4 (+ 3.9) dB For aircraft noise spectra

C = +3 (+ 3.6) dB For a composite of highway, railway, and

aircraft noise spectra.

(C.llb)

(C.llc)

The numercial values in parentheses are the 90 percent confidence limits for

each of the mean values of the parameter C.

The final relationship between the A-weighted sound level difference, a^A»

the MNCC provisions and the composite STC rating, R^,, of the multi-component

exterior wall is obtained by substituting equation (C.9) into equation (C.IO)

and solving for R^..

The final result, to be used for design guidance, is

Rc = aLa + 10 log(S/A) + 3 + C, STC, (C.12)

where

AL^ Is the A-welghted sound level reduction required for the MNCC

provisions

S is the surface area of the exterior wall transmitting exterior

sound into the interior receiving space

A is the total sound absorption in the receiving space (average value

for 500 Hz to 1 kHz bands)

C is the adjustment for the environmental noise source spectra (see

equation (C.ll)).

For average outdoor environmental noise conditions, the value C = +3 dB may be

used to simplify the above result. A further slmplication may also be made by

1 See G. E. Mange, S. R. Skale, and L. C. Sutherland, Report No. TS-77-220.

C-8
noting that an average value of the + 10 log(S/A) term is -3 dB.^ Hence, the

adjustment for noise source spectrum is on the order of, but opposite to, the

adjustment for interior space sound absorption. With these approximations,

the multi-component wall STC rating is related to the A-weighted sound level

reduction required by MNCC as:

Rc = ALa + 3, STC. (C.13)

It is emphasized that the results of either equation (C.12) or equation (C.13)

do not include a design margin for either flanking sound transmission or faulty

construction. These considerations are judgments that must be made by the

architect or acoustical consultant. For exterior walls, flanking sound transmission should not be a major problem for well designed structures.^ Further,

the numerical studies used to determine the empirical constant, C, exhibit

significant variation. For example, the data of D, S. Pallett, et . al. , Report

No. BSS-84 (table B-1, page 153) would lead one to the conclusion that -1 is an appropriate adjustment for equation (C.13) rather than the +3 adjustment quoted.

The lengthy discussion of this subsection is presented so that the reader may

understand the considerations required to relate an STC rating to an A-weighted

sound level reduction. The next section uses the results of this section to

determine the minimum construction cost of a multi-component wall that will

achieve the MNCC provisions.

C.3 DESIGN OF MINIMUM COST MULTI-COMPONENT WALLS

The design method described in this section provides for an explicit calculation

of the noise insulation required of each component of a multi-component wall

such that the multi-component wall achieves a specified noise insulation value

and the total construction cost of the wall is a minimum. The minimization

(or optimization) technique used to achieve the final result is the Lagrange

multiplier method.^ First, the total construction cost is expressed in terms

of the component areas and the average cost per unit area (as a function of the

noise insulation) of the components. The component cost functions used are the

GDC cost equations described in Appendix A. The noise insulation required of

each component is determined by minimizing the total construction cost subject

to the constraint that the complete assembly of components must achieve the

specified value of noise insulation.

The final results obtained are explicit expressions for the required component

noise insulation. To use these results, one requires only the GDC cost equations of appendix A. It is not necessary to solve a system of equations to

determine the solution, and calculations may be performed using a pocket

calculator.

^ See B. H. Sharp, P. K. Kasper, and M. L. Montrol, Report No. GGR-80-250.

^ See F. H. Hildebrand, Methods of Applied Mathematics (Prentice Hall, Inc.,

1952).

G-9
C.3.1 Component Cost Equations and the Total Construction Cost

Appendix A presents the cost equations developed for several Component Design

Categories (CDC) typical of U.S. building construction practice. Each of the

CDC cost equations expresses the average cost per unit area of the component^

as a linear function of the component’s STC rating. Denoting the parameters

related to each component by a subscript "i", the average cost per unit area

for the ith component is:

Cj^ = A^ + cost per unit area, (C.14)

where

Aj^ is the intercept and is the slope of a least squares curves fit

of cost estimates and STC rating points for the ith component (Bj^

is always positive),

Rj; is the STC rating for the component.

As noted in Appendix A, each CDC cost equation is defined for a limited range

of STC ratings such that

^iL ^ ^i ^ *^iUs (C.15)

where

Rj^L is the lower limit for Rj^ for which the cost equation (C.14) is

valid,

Rj^U is the upper limit for R^ for which the cost equation (C.14) is

valid

.

The inequality (C.15) simply states that it is physically possible to select

only values of the component STC rating, Rj^, within the range of values for

which the component cost equation is defined. The practical importance of this

restriction is discussed in section C.3.3.

The multi-component wall comprises N district components each defined by a CDC

cost equation. It is assumed that the total construction cost is the sum of the

construction costs for each of the components. Denoting the average construction cost per unit area of the multi-component wall by C, the total construction

cost is given by the expression^

N

S»C = Y, ^i^i ~ E ^i(^i ®i^i)> cost units. (C.16)

1=1

1 The term "component" refers to one of the CDCs listed in Appendix A.

2 Unless otherwise noted all sums, 2> are over the range i=l,...,N.

C-10
Solving for the average construction cost per unit area, C, one obtains:

C = 2 (Aj[ + cost per unit area, (C.17)

where

S is the total wall area: S = 2 Sj^

is the wall area of the ith component

= Sj^/S is the fraction of the total wall area of the 1th

component

.

It is important to note that the parameter k^ satisfies the following

relationships

:

0 < kjL < 1 and Z ki = 1. (C.18)

Equation (C.16) expresses the total construction cost in terms of the component

construction costs. Equation (C.17) expresses the average construction cost

per unit area in terms of the average component construction cost per unit area weighted by the fractional area of each component. Since the component STC

ratings, are the only variables in equations (C.16) and (C.17), a minimum

total construction cost is also a minimum average construction cost per unit area.

C.3.2 Noise Insulation for Minimum Cost

The noise Insulation of a multi-component wall is determined using equation

(C.l) and the average construction cost of the wall is determined using equation (C.17). Using these two results, the problem of estimating the minimum

construction cost to achieve a specified noise insulation rating is completely

defined. However, it is convenient first to transform the equations so that

the variable is the sound transmission coefficient, rather than the

component STC rating, R^.

The component STC rating, Rj^, and the component sound transmission coefficient,

are related by the definition

Ri = -10 log (t^) = -10 log(e) Zn(Ti), (C.19)

where

log ( ) = logio ( ) Zn ( ) = loge ( ) e = 2.718282.

Using the definition of equation (C.19), the average construction cost per unit area given by equation (C.17) becomes:^

1 Unless otherwise noted all sums. Z, are over the range i=l

,

. . .N.

C-11
C = 2 ki [A^-b^ An (C.20a)

and the composite noise insulation of the multi-component wall given by

equation (C.l) becomes;

Tc = 2 k^T (C.20b)

where

and are the intercept and slope of the CDC cost equation for

the ith component (see equation (C.14))

bj^ = 10 log(e) = 4.34295 Bj^

kj^ = S^/S (see equation (C.l) or (C.17))

“R / 10 = 10 c' is the composite sound transmission coefficient.

The problem is to determine the sound transmission coefficients, (i=l,...,

N), so that the average construction cost is minimized and the composite sound

transmission coefficient, x^,, has a specified value.

The Lagrange multiplier method is used to obtain the equations in the variable

Xj^ that must be solved to define the minimum cost design. Using the Lagrange

multiplier method, one forms of the objective function, F(xj^, X), and the

constraint function, <j>(T£), using equations (C.20). The parameter X is called

the Lagrange multiplier.

The objective function is;

F(Xi, X) = Z ki [Ai-biAn(Xi)] + X<j)(Xi). (C.21a)

The objective function is subject to the constraint;

<|)(Xi) = Z kiXi - Xc = 0. (C.21b)

The possible extrema in construction cost (maximum cost or minimum cost) are given by equations (C.16) and (C.17) for the set of numbers Xj^ (i=l,...,N)

obtained by solving the system of equations;

= -k.b./x. + k.X = 0 i=l,...N (C.22a)

9x^ 1X1 1

4)(Xj^) = Z kj^Xj^ - X (, = 0. (C.22b)

A more convenient form of the equations is obtained by expressing the Lagrange

multiplier, X, in terms of b]^ and X][ and substituting this result into each of

the N equations (C.22a). Doing this, one obtains the system of linear

equations

;

C-12
(C.23)

ki k2 k3 ... kjg 'n' ^c

—b2 b]^ 0 ... 0 0

—b3 0 b]^ ... 0

• • • •

• • •

<

•

•

• • • • 0 0 • • •

• ^0 _

The solution to this system of equations is^;

Ti = biXc/(2 k^b^) 1=1,. ..,N. (C.24)

In terms of the component STC rating, R^, one uses the relationship of

equation (C.19) to obtain;

Ri = Rc - 10 log [Bi/(2 kj.Br)] 1=1,..., N. (C.25)

Equation (C.25) is the final result. The required component STC rating, Rj[,

is expressed in terms of the specified composite STC rating, R(,, of the multicomponent wall; the marginal cost of each component, Bj^; and the fraction of

the total area for each component, k^. By substituting the N values of the

component STC ratings, R^, given by equation (C.25) into equation (C.l), it

is seen that the composite STC rating for the v/all, R^,, is obtained.

The estimated minimum construction cost is obtained by substituting the N

values of R^^ from equation (C.25) into the cost equations (C.16) or (C.17).

C.3.3 Range of Application and Discussion of Assumptions

The assumptions used to develop the component STC ratings given in equation

(C.25) are as follows:

(1) Each component comprises on constant percentage of the total surface

area of the multi-component wall,

(2) Each component is defined by its cost equation which is a linear function

of the component noise insulation (STC) rating,^

(3) The total construction cost of the multi-component wall is the sum of the

construction costs of each component.

^ The sum, Z, in equations (C.24) and (C.25) is for the subscript r=l,...,N.

2 See section 4.2.4 in the main text of this report for a discussion of the

practical implications of this assumption to design.

C-13
Assumptions (1) and (2) above define the "design configuration" so that the

only variables are the component noise insulation ratings, Rj^. Changing either

the fractional areas, kj^, or the components as defined by their cost equations,

defines a new "design configuration".

Assumption (2) also requires that the component cost equation must be a linear

function of the component noise Insulation as described by equation (C.14).

This assumption allows the problem to be formulated so that linear equations

result from the use of the Lagrange multiplier method. These linear eqxiations are solved explicitly so that numerical results can be obtained using a pocket

calculator.

Assumption (3) requires that each component cost equation must be independent

of the other component cost equations. For example, this assumption Implies

that the cost of installing a door does not depend upon the type of wall

construction used. Hence, the CDC cost equations for doors and glazing include

an average installation cost that is constant for all wall designs.

Physically, a restriction must be placed upon the range of composite noise

insulation values, R^, for which a minimum cost design can be realized. The

method used to obtain, at the building design stage, the component noise insulation ratings, Rj[, given in equations (C.25) assumes that all component cost

equations are defined for any required value of Rj relative to the composite

noise insulation rating, R^,. However, each component cost equation is defined

over a limited range of noise insulation values as indicated by equation (C.15).

Hence, the minimum cost design is obtained only for a limited range of composite

noise insulation ratings, R^,, that depends upon the particular components

selected for the design.

This restriction may be quantified by combining the results of equations (C.15)

and (C.25). First, the component noise insulation rating, Rj^, is expressed in

terms of the composite noise insulation rating, R^,, as;

Ri = Rc + A±» (C.26)

where

Ai = - 10 log [Bi/(E kj-Bj.)] .

This is a restatement of equation (C.25). Substituting for Rj^ from equation

(C.26) into equation (C.15) one obtains;

%L < ^^c + ^i i. ^^iU i=l,...,N (C.27a)

or RiL — ^ R^ ^ ^iU ~ ^1 i=l,=..,N (C.27b)

For a design to achieve the composite noise insulation rating, Rj,, and each

component exhibit a noise insulation rating within the range R^l ^ ^^i ^ ^iU»

the value of R^, must be within the range;

|Ril - All max ^ ^c ^ {RiU ^llmins (C.28)

C-14
where

{Rj^L “ ^ilmax largest value of the set of numbers

{RiL “ » •••> N

l^^iU “ ^llmin is the smallest value of the set of numbers

{^lU “ •••» N.

The result of equation (C.28) Indicates the range of composite noise Insulation,

R^, for which equation (C.25) applies. This range of noise Insulation values

Is the range over which a minimum cost design may be achieved given the freedom

to vary the noise Insulation of each component. The next section presents the

methodology applicable to situations for which the noise Insulation value Is

specified for one or more components of the multi-component wall.

C.3.4 Noise Insulation with Specified Components

In the design of a multi-component wall to meet a specified level of noise

Insulation, s:^tuatlons may arise for which one or several of the components are specified based upon criteria other than the component's noise Insulation.

These components will exhibit a constant value of noise Insulation at a con- stant cost. If the design Includes two or more elements for which the noise

Insulation may be selected based upon cost, the methodology used to obtain

equation (C.25) Is used to obtain the minimum cost solution. An example of

such a situation Is an exterior wall containing doors and glazing with the

basic wall structure selected for architectural features and thermal Insulation

performance. The minimum cost design, In this case. Is determined by varying

only the door and glazing noise Insulation.

Suppose that an N component wall Is composed of n 2 components for which the

noise Insulation may be selected based upon cost and (N-n) components for which

the noise Insulation values and costs are constant. The multi-component wall

Is required to meet a composite noise Insulation of R(,. The minimum cost

design Is the design for which the noise Insulation of the n variable components

Is given by:

N -(Rr~ Rp)/10 ^ Rl = Rc - 10 log [1 - E • 10 "" ] - 10 log[B./ E k^B^], (C.29)

r=n+l r=l

X 1,..., n K, N,

where

Ri Is the noise Insulation for the 1th component of the minimum cost

design; 1=1,..., n < N

Rj_ Is the constant value of the noise Insulation for the 1th component:

l=n+l , n+2 , . .

.

,

N

R(2 Is the composite noise Insulation rating of the multi-component

wall

C-15
= S^/S is the fraction of the total area for the ith component:

i=l, . . . ,N

is the marginal cost for the ith component cost as a function of the

component’s noise insulation, i=l,...,N

(Bj = 0 for i=n+l , , .

, ,N)

o

In the above result, the components with variable noise insulation are denoted

by the subscripts, i=l,o..,n. The components with constant noise insulation

are denoted by the subscripts i=n+l , . .

» ,N. Equation (Cc29) is analogus to

equation (C.25).

As discussed in section C«3,3, a minimum cost design is defined over a limited

range of composite noise insulation, R^>, defined by the limits of noise insulation Rj^;L ^iU each of the components ( i=l ,

o , ,n) <. For the present

discussion, the range of R^, for which the minimum cost design is defined is

obtained by solving equation (C.29) for R^ in terms of Rj^( i=l , . .

. ,n) . The

result is;

^ _ -R./IO N -R_/10,

R^ = -10 log {[B^/ Z k^Bj.] ^ • 10 ^ + Z kj.10 }, (C.30)

r=l r=n+l

where

R^ is a variable for i=l,...,n

Rj. is a constant for r=n+l,»..,N.

The limiting values of R^ are determined by substituting the limiting values of

Rf = R^l i=l,o..,n and selecting the largest value of the

set of numbers {Rc^^iL^} smallest value of the set of numbers {Rc^^iU^l*

This is identical to procedure described in section C.3.3.

The estimated minimum average construction cost per unit area for the design is

given by;

n N

C = E ki [Ai + Bi Ri] + E kj_ A^. (C.31)

i=l i=n+l

The values of R^ in equation (C.31) are given by equation (C.29). The last sum

in equation (C.31) is, of course, a constant. The next section presents

examples illustrating the use of these results.

C.4 EXAMPLES ILLUSTRATING THE USE OF THE EQUATIONS

Two example problems are presented to illustrate the use of the design

equations presented in section C.3. In particular, the reader should note

C-16
that the method may be easily used in two ways. First, the method may be used

to determine the noise insulation required of each component to achieve a specified composite noise insulation. Second, the method may be used to

determine the total noise insulation performance range for the composite wall

and the corresponding minimum construction cost range for the composite wall.

The latter use of the method quantifies the range of noise insulation for

which the design may be used and the cost of achieving any value of noise

insulation within this range. In either case, the method is easily used and

requires only a pocket calculator.

C.4.1 Effect on Construction Cost of Varying Glazing Area

This example considers a three component wall comprised of a basic structure,

a door, and glazing. Each Component Design Category (CDC) is held constant.

Three designs are defined using these CDCs by varying only the percentage of

glazing. The example illustrates the calculation of the range of composite

noise insulation, R^,, over which a minimum cost design is defined and also

illustrates the effect on construction cost of varying the percentage of

glazing for the Component Design Categories selected.

The three CDCs selected for this example are a frame wall with aluminum siding

(component 1), a door (component 2), and glazing (component 3). The glazing is an aluminum frame with fixed sheet and plate glass. From table 3.2, the data

for the components are;

Cost Coefficients STC Limits

Component Ai Bi ^iL ^iU

No. 1, Wall - 0.63 0.110 37 50

No . 2 , Door 0.77 0.462 20 51

No . 3 , Glazing -13.10 0.940 29 47.

For the example problem, the glazing area is varied with the total area held

constant so that the three designs are defined as follows;

Component

Wall Door Glazing

Design 1 ki = 0.725 k2 = 0.175 k3 = 0.100

Design 2 kl = 0.675 k2 = 0.175 k3 = 0.150

Design 3 ki = 0.625 k2 = 0.175 k3 = 0.200.

C-17
The problem is to determine, for each of the above designs, the variation of

the minimum construction cost over the range of composite noise insulation

performance, R^,, of each design. Details of the calculations are presented for

design 1 so that the reader may follow the procedures. The results for designs

2 and 3 are presented and the complete results are summarized in a plot of

minimum construction cost versus noise Insulation, R^..

Equation (C.25) is the basis for the calculations and is, for this example:

Ri = Rc - 10 log [Bi/Z kr B,.] , i=l , 2, 3. (C.25)

Using the above data for design 1, the following results are obtained:

S kj. Bj. = (0.725) (0.110) + (0.175) (0.462)

+ (0.100) (0.940) = 0,2546,

For equation (C.25), the component STC ratings are;

Rl = Rc - 10 log [0.110/0.2546] = Rc + 3.6 (C.32a)

R2 = Rc ” 10 log [0.462/0.2546] = Rc “ 2.6 (C.32b)

R3 = Rc ~ 10 log [0.940/0,2546] = Rc " 5,7. (C.32c)

From equation (C.26), one obtains: = 3.6, A2 = -2.6, and A3 = -5.7.

The next step is to determine the range of R^, over which the minimum cost

design may be achieved. From equation (C.27b) and the STC limits for the

components one obtains:

Component 1; 37 - 3.6 ^ Rc 50 - 3.6 or 33.4 ^ R^ ^

46.4

Component 2: 20 + 2.6 ^

R(, ^51 + 2.6 or 22.6 < Rc < 53.6

Component 3: 29 + 5 .7 ^ R^, 47 + 5 .7 or 34 .7 ^ R^ ^ 52 .7

.

Selecting the largest value of the lower limit and the smallest value of the

upper limit, the composite noise insulation range for which the minimum cost

design is defined is 34.7 Rc ^6.4. This result is rounded to 35 Rc

<46. - -

For the composite noise insulation range 35 ^ R^ ^ 46, the noise insulation

values of each component, Rj^, required to achieve the composite noise insulation, Rc , are obtained from equations (C,32), The minimum construction cost

for each level, Rc, of composite noise insulation is obtained using the corre- sponding values of R^ , the cost coefficients of the components (given above)

and equation (C.17), Tlie results of these calculations are presented in table

C,1 to illustrate the relative changes in the component noise insulation. The

minimum construction cost is, of course, a linear function of the composite

noise insulation, Rc«

C-18
Table C.l. Detailed Calculation Results for Design No. 1

STC Ratings Construction Costs, $/sf

^c ^1 R

2

R

3 r ^

^1 ^2 ^3 C=Ek^C

35 38.6 32.4 29.3 3.62 15.74 14.44 6.82

36 39.6 33.4 30.3 3.73 16.21 15.38 7.08

38 41.6 35.4 32.3 3.95 17.13 17.26 7.59

40 43.6 37.4 34.3 4.17 18.05 19.14 8.10

42 45.6 39.4 36.3 4.39 18.97 21.02 8.61

44 47.6 41.4 38.3 4.61 19.90 22.90 9.12

46 49.6 43.4 40.3 4.83 20.82 24.78 9.62

^ Component 1 is the wall, Component 2 is the door, Component 3

is the glass, = 0.725, k2 = 0.175, and k3 = 0.100.

C-19
Following the same steps, the results for design 2 are:

Component 1 Rl = Rc + 4.3 9 32.7 < Rc ^ 45.7

Component 2 R2 = R(. ~ 1 .9 9 21 .9 < Rc < 52 .9

Component 3 f^3 = ^c “ 5-0 9 34.0 < Rc < 52.0

and

34 < the minimum

Rc < 46

.

cost design is defined for the range of composite STC ratings

:

The results for design 3 are:

Component 1 Rl = Rc + 4.9 9 32.1 ^ Rc < 45 .

1

Component 2 R2 = Rc - 1*4 9 21.4 < Rc < 52.4

Component 3 R3 = Rc - 4.5 9 33.5 < Rc < 51.5

and

33 < the minimum

Rc < 45.

cost design is defined for the range of composite STC ratings

:

The above results, define the minimum construction cost for the three component

wall as a linear function of the composite STC rating of the wall over a range

of the STC rating. For each design, the cost-STC functions are:

Design 1 (10 percent glazing) C = -1 .92 + 0.250

35 < Rc < 46

Design 2 (15 percent glazing) C = -2.80 + 0.296 R^,

34 < Rc j< 46

Design 3 (20 percent glazing) C = -3.49 + 0.338 R^, 33 < Rc < 45.

The minimum cost-STC functions given above are represented in figure C.l. For

this example, Increasing the percentage of glazing increases both the cost per

unit area at a constant value of Rq and the marginal cost per unit area (the

coefficient of Rc in the above results). Further, based upon the noise insulation range of the components, each of the above designs are limited on the

upper end of the Rc range by the wall component and on the lower end of the Rc

range by the glazing component. Using the method described in section C.3.4,

the minimum cost design can be extended to values of Rc both above and below

the Rc limits Indicated for each design. To extend the cost-STC functions

above the Rc limit for a design, the wall component is held constant at R]^=50

and the door and glazing STC ratings are determined using equation (C.29). To

extend the cost-STC functions below the Rc limit for a design, the glazing is

held constant at R3=29 and the door and wall STC ratings are determined using

equation (C.29). Hence, the methods presented in section C.4 allow the designer

to estimate the cost-STC function over the entire range of composite STC ratings

C-20
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C-21

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representing the complete STC performance range of all components. This type

of problem is illustrated in the next example.

Finally, it is important to note that for a constant value of each of the

above designs represent a different combination of component STC ratings

required to achieve the value of R^,. For this example and setting R^,=40, the

required component STC ratings for each design are (rounded to the nearest

integer value);

Wall Door Glazing

Design 1 Rl = 44 R2 = 37 R3 = 34

Design 2 Rx = 44 R2 = 38 R3 = 35

Design 3 Rl = 45 R2 = 39 R3 = 36

For this example, the differences in component STC ratings are not too dramatic

in that the total variation in component STC is less than 3 units between any

two of the designs. However, the marginal costs of each component, B^, are rather significant. For example, each unit change in the glazing STC rating

represents a cost of $0.94 per square foot of glazing. The method does give

the architect a technique for initially selecting the component noise insulation performance requirements so that the design may be refined to meet the

total requirements of the applicable building code.

C.4.2 Noise Insulation with Specified Components

This example illustrates the calculation procedure used if the noise insulation

of one or more components is held constant and the noise insulation ratings of

the remaining components (two or more) may be selected using the method

described in section C.3.4. The example considers a three component wall. The

basic wall structure comprises 80 percent of the total area and has an STC

rating of 39 with a construction cost of $3.42 per square foot. The doors and

the glazing each comprise 10 percent of the total wall area. The glazing is

aluminum frame double hung windows with sheet and plate glass. The problem is

to determine the estimated minimum construction cost per unit area as a function of the composite wall STC rating, Rj.

.

From the above information and the CDC cost equations in Appendix A, the data

for this example are;

Cost Coefficients STC Limits

Component Ai Bi BiL BiU ki = Si/S

. 1 , Door 0.77 0,462 20 51 0.1

1 . 2, Glazing -12.66 0.938 29 47 0.1

>. 3, Wall 3.42 R3=39 0.80

C-22
The first step in the calculation is to determine the range of R^. for which

equation (C.29) applies. To do this, equation (C.30) is used to determine the

relationship between a component's STC rating, Rj^, and the composite wall STC

rating, R^* For the door (component 1) and the above data, equation (C.30) is:

—R-l / 10 _0 Q

R^, = - 10 log [0.303 . 10 ^ + 0.8 . 10 (C.33)

Substituting the STC limits Rj^l 20 and Rj^y ~ ^1 above result,

the range for composite wall STC ratings is 25 _< R^ _< 39 .9

.

For the glazing (component 2) and the above data equation (C-30) is:

q q ~R^/10

R^ = - 10 log [0.8 . 10 + 0.149 . 10 ^ ]

. (C.34)

Substituting the STC limits R2l = 29 and R2u = for R2 in the above result,

the range for composite wall STC ratings is 35.4 ^ Rq ^ 39.8.

The above results define the STC range 35 _< R^, _< 40 as the range over which one may determine a minimum cost design. This range is established by the STC

limits of glazing (component 2).

The STC ratings for the door and the glazing are next determined using equation

(C.29). Performing the calculations indicated in equation (C.29) using the

data for this example, one obtains:

-(39-Rj/lO

R^ = R^ - 10 log [1 - 0.8 . 10 ] - 5.2

-(39-R^)/10

R

2 = Rj, - 10 log [1 - 0.8 . 10 ^ ] - 8.3,

where

35 ^ Rc < 40 .

The STC ratings, R]^ and R2 , given above represent the minimum cost design for

the range 35 ^ R^. ^ 40. The results of these calculations are presented in

table C.2.

At the upper limit of the design range (R^,=40), the minimum cost design is

defined by the component STC ratings: R]^=50, R2=47, and R3=39. At the lower

limit of the design range (R^=35), the minimum cost design is defined by the

component STC ratings: R]^=32, R2=29, and R3=39. Whereas the minimum cost

design utilizes the entire performance range of the glazing (29 < R2 < 47), the

minimum cost design utilizes door components over the range of 32 _< R]^ _< 50

.

Since the performance range of door components is 20 < R]^ < 51 , the composite

noise insulation range for the design may be Increased beyond the minimum cost

design range by varying the door STC rating. For values of R(. ^ 35, the door

STC rating would be selected in the range 20 < R]^ j< 32. For values of R^, >^40,

C-23
the door STC rating would be selected in the range 50 j< < 51. Obviously,

the variation of the door STC rating between STC 50 and STC 51 is an academic

point. However, one must generally consider the extension of the STC range

both above and below the minimum cost design range.

To develop the cost-STC values for R^, ^35, the door STC ratings are varied

over the range 20 ^ Rj^ ^ 32 with the glazing STC rating held constant at 29

and the wall STC rating held constant at 39. The composite STC rating is calculated using equation (C.l). For this example, the composite STC rating is:

R^ = - 10 log [0.1 » 10 + 0,1 ‘lO’^’^ + 0,8 • 10"3-^]

or

R^ = - 10 log [0,1 • 10 ^ + 2,266 «10 ,

where

20 £ Ri < 32 ,

The cost-STC curve for R^ £ 35 is developed by substituting values of R]^ into

the above result to calculate R^.. The construction cost is calculated using

these values of R^ and the constant costs for the glazing and the wall as indi

cated by equation (C.17). The results of these calculations for this example

problem are presented in table C,3.

The results may also be plotted as construction cost versus the composite STC

rating R^,, Figure C,2 represents such a plot. The solid line in figure C.2

represents the minimum cost or optimum design and corresponds to the results

in table C,2. The dashed line represents the extension of the optimum design

obtained by decreasing the door STC rating as described above. The points

defining the dashed curve are presented in table C.3. For completeness, one point is indicated at the upper limit of the optimum design curve that

corresponds to the design utilizing the component STC ratings R]^=51, R2=47

,

and R3=39,

Another curve is presented in figure C.2 illustrating an additional example

using a wall component with an STC rating of 51 at a construction cost of 5.85

dollars per square foot instead of the STC 39 wall described above. All other

data are identical to the example problem discussed above. In both examples,

the minimum cost or optimum design utilizes the entire noise insulation perfor

mance range of the glazing component. However, it is evident that the general

shape of the cost-STC curve is quite different for the two examples. Also, it

is evident that the minimum cost or optimum design STC range is different for

the two examples. The comparison illustrates the significance of component or CDC selection since any component will exhibit a different contribution to the

total noise Insulation depending upon the performance of all other components.

The methodology described here, however, allows the architect to evaluate

different designs and improve the productivity of the building design process.

C-24
Table C.2. Calculations for Example Problem for

Minimum Cost STC Design Range

STC Ratings Construction Costs

,

$/ sf

Rc ^1 R2 R3

P

3. ^1 C

2 C3 C = k. c.

35.4 32.1 29.0 39 15.62 14.55 3.42 5.75

36 33.0 29.9 39 16.06 15.44 3.42 5.89

37 34.9 31.8 39 16.90 17.15 3.42 6.14

38 37.2 34.1 39 17.98 19.34 3.42 6.47

39 40.8 37.7 39 19.64 22.72 3.42 6.97

39.8 50.1 46.9 39 23.88 31.34 3.42 8.28

^ Component 1 is1 the door. Component 2 is the glass. Component 3 is the

wall. ki=0.1

,

k2 =0 . 1 , and k3=0.8.

Table C.3. Calculations for Example Problem for

Varying Door STC Rating

STC Ratings Construction Cost, $/ sf

Rl R2 R3 Rc Cl^ C

2 C3 C ki Cj^

20 29 39 29.1 10.00 14.55 3.42 5.19

22 29 39 30.7 10.92 14,55 3.42 5.28

24 29 39 32.0 11.85 14.55 3.42 5.38

26 29 39 33.2 12.77 14.55 3.42 5.47

28 29 39 34.1 13.69 14.55 3.42 5.56

30 29 39 34.9 14.62 14.55 3.42 5.65

^ Component 1 is the door, Component 2 is the glass. Component 3 is the

wall, k]^=0 . 1 , k.2 =0 . 1 , and k3 =0 . 8 .

C-25
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NBS-114A (REV. 2-8C) U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

2. Performing Organ. Report No. 3. Publication Date

NBSIR 81-2366

4. TITLE AND SUBTITLE

METHOD FOR ASSESSING COSTS OF NOISE CONTROL REQUIREMENTS IN MULTIFAMILY

RESIDENTIAL AND EDUCATIONAL BUILDINGS

5. AUTHOR(S)

Stephen F. Weber, Fred F. Rudder, Jr,, and Michael J. Boehm

6. PERFORMING ORGANIZATION (If joint or other than MBS, see instructions)

national bureau of standards

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

8. Type of Report & Period Covered

Final

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State. ZIP)

Environmental Protection Agency

Office of Noise Abatement and Control

Washington, D.C. 20460

10. SUPPLEMENTARY NOTES

I I Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11. ABSTRACT (A 200~word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here) This report presents a methodology developed to measure the cost impacts of

acoustical performance requirements for new buildings. The methodology can be

applied to a wide range of noise control requirements. The cost items addressed

by this methodology are expected changes in construction costs, the cost of

acoustical testing to certify levels of performance, code administration costs,

and energy savings due to modifications of the building envelope. The building

components considered, which are those most commonly affected by noise control

requirements, are doors, windows, interior walls, exterior walls, and floor/

ceiling assemblies. The basic cost assessment method consists of linear cost

estimation equations for most component designs commonly used in educational

and multifamily residential buildings. Each equation relates the acoustical

performance of the design to its construction cost so that construction costs

associated with alternate levels of acoustical performance can be compared.

The methodology also includes a cost minimization model useful for selecting the

least-cost design for a particular level of acoustical performance.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

acoustical design; acoustics; architectural design; building codes; building

economics; construction costs; cost minimization; economic impact; economics;

energy; model code; noise control

13. AVAILABILITY

Unlimited

I I For Official Distribution. Do Not Release to NTIS

[ n Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.

' 20402.

Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

117

15. Price $ 11.00

USCOMM-DC 6043-P80