Wai-Fah Chen.The Civil Engineering Handbook

Подождите немного. Документ загружается.

66-28 The Civil Engineering Handbook, Second Edition

on the assumption of steady-state work requirements from one year to the next, as embodied in the

quantity standards. Whereas pavement and bridge programming systems may employ a decision-making

procedure that balances the costs of a project against its beneﬁts, MMSs make no attempt to quantify

the beneﬁts of the work performed. Also, PMSs analyze long-term alternatives in pavement actions and

recommend not only the appropriate capital rehabilitation and reconstruction projects and their timing

and location but also the appropriate level of routine and periodic maintenance. These recommendations

could be included into the MMSs as planning and budgeting guidelines. One key change to MMSs that

will allow for better integration is incorporating the ability to consider speciﬁc road segments in planning

and scheduling. Another is to base maintenance work planning on an expended set of information,

including condition ratings, trafﬁc and accident levels, treatment histories, and planned construction

project status.

Decentralization and the Use of Technology

Data processing and reporting methods in current MMSs are time consuming for ﬁeld personnel and

unable to produce sufﬁcient timely reporting of results for effective management use. There is a need to

shift planning and management responsibility to levels closer to the subdistricts where the work is

accomplished. Many states have done so, but there is also the need to provide interactive computerized

tools to assist maintenance personnel in the subdistricts to carry out their tasks more efﬁciently.

Flexibility

Effective linkages among budgets, work plans, and work accomplishments in the existing MMSs are vital.

With time, however, there is a need to allow for possible replanning of work and for granting greater

freedom to maintenance managers to reschedule activities or shift resources across categories of activities.

Such increased ﬂexibility would also allow for easier coordination with nonmaintenance activities in

highway asset management.

Sophistication

Feature inventories should be expended to include additional information such as condition ratings,

types of damages, trafﬁc conditions, congestion levels, accident histories, and past treatments that affect

maintenance decision making. Currently, MMS performance standards in most states represent average

conditions and need to be reﬁned to take into account different work circumstances, as reﬂected in an

expended feature inventory. In addition to engineering and managerial tools now being used, improved

operational planning and scheduling methods and economic analysis need to be introduced to the MMS.

The details are discussed below:

Maintenance capital tradeoffs: The tradeoffs between maintenance expenditure and the level or fre-

quency of capital improvement of pavements and bridges need to be explored by life cycle cost

analysis.

Level-of-service tradeoffs: The advantages and disadvantages of maintenance expenditure on nonphys-

ical assets such as ditch cleaning and deicing should be addressed by analytical procedures such

as utility analysis and conjoint analysis for assessing level-of-service tradeoffs.

Agency and user cost analysis: Agency costs may be estimated on the basis of historical data and expert

judgment. User costs are important for assessing delays associated with maintenance work zones

and for calculating beneﬁts of road and bridge improvements.

Optimal resource allocation: Methods for determining the best set of maintenance and improvement

actions over time, given a budget constraint, can provide estimates of optimal future spending.

Additional problems such as short-term scheduling of labor, materials and equipment for daily

maintenance operations, and the optimal level of service for various maintenance activities, given

a budget constraint, can also be addressed.

Maintenance management systems play a useful role in overall highway asset management. This is

because the operational functions associated with this management system have far-reaching implications

on other management systems, including risk management.

Highway Asset Management 66-29

Congestion Management System

Tr afﬁc congestion has become a major concern on existing highways, and the situation is deteriorating

at an alarming rate. Detrimental consequences of trafﬁc congestion include longer travel time, higher

fuel consumption, and increased air pollution and are associated with annual congestion costs exceeding

$70 billion [TTI, 1998]. Obviously, highway asset management needs to include the management of

congestion; otherwise, many system objectives of asset management will not be realized. Many states

have established congestion management systems to combat the problem of trafﬁc congestion. A CMS

is deﬁned as “a systematic process that provides information on transportation system performance and

alternative strategies to alleviate congestion and enhance mobility of persons and goods” [NARA, 1993].

Congestion management implies a direct customer orientation to planning and investment and can be

tailored to provide a mechanism to measure the economic and environmental consequences of current

system performance and proposed future investments.

A CMS is generally composed of nine elements:

1. identiﬁcation of targeted CMS locations or networks

2. deﬁnition of congestion performance measures

3. selection of performance objectives and standards

4. system monitoring and evaluation

5. identiﬁcation of system deﬁciencies

6. selection and evaluation of appropriate congestion mitigation strategies

7. implementation of selected strategies

8. effectiveness evaluation of implemented strategies

9. establishment of a process to periodically update a CMS

CMS is often described as a unique management system because it provides a direct formal link to

planning required under the 1990 Clean Air Act amendments.

Possible congestion mitigation measures related to physical assets may include road or lane widening,

high-occupancy vehicle (HOV) facilities, trafﬁc signals and related devices, and Intelligent Transportation

Systems technologies, including detectors, sensors, and trafﬁc control centers. Choocharukul and Sinha

[2000] provide a congestion management system geared to physical assets. As changes in roadway facilities

can affect the level of service and vice versa, there is a direct connection between CMS and other

management systems.

Safety Management System

High rates of highway crashes make it necessary to identify highway facility problem areas so that

necessary remedial safety-enhancing investments can be carried out. Regulation of highway use through

policy formulation and implementation is another way to enhance highway safety but is of less relevance

to highway asset management than investments made on physical facilities. Also, SMS integrates vehicle,

driver, and roadway elements into a comprehensive approach to solving highway safety problems. How-

ever, the role of roadway elements is of particular relevance to highway asset management. Many states

have developed safety management systems to address the issue of highway safety. An example is the

highway safety management system developed for the state of Indiana [Farooq et al., 1995].

An SMS is deﬁned as a systematic process that has the goal of reducing the number and severity of

trafﬁc crashes by ensuring that all opportunities to improve highway safety are identiﬁed, considered,

implemented as appropriate, and evaluated in all phases of highway planning, design, construction,

maintenance, and operation, and by providing information for selecting and implementing effective

highway safety strategies and projects [NARA, 1993].

SMSs typically seek to promote widespread collaboration around highway safety issues and broaden

the range of organizations involved in such efforts by including public health, emergency medical services

(EMS), and law enforcement agencies in the development and implementation of the systems. A safety

management system generally consists of the following elements: deﬁnition of safety performance measures

66-30 The Civil Engineering Handbook, Second Edition

and standards, identiﬁcation of existing and potential safety problems, identiﬁcation and evaluation of

safety-enhancing measures, evaluation of the effectiveness of implemented measures, and review of the

SMS on a continuing basis.

From the operational function dimension of asset management (Fig. 66.1), activities carried out on

highway facilities with the objective of enhancing safety include the construction or repair of road signs

and guardrails, the laying of new pavement surfaces to improve friction, and pothole repair. Safety

management systems provide not only decision support tools for policy makers to allocate resources to

solve safety-related highway problems but also data that enable the conduction of tradeoff analyses

between investments in highway safety on one hand and investments in highway facility condition or

other areas of highway usage on the other. Furthermore, costs and occurrence levels of various highway

crash types are monitored using SMS databases to determine the extent to which asset management

system objectives, such as highway safety, are being achieved.

Closely related to highway safety management is risk management. A risk management system is a

collection of operational procedures to minimize loss due to tort liability. Risk management systems have

been developed to address the rapid upsurge in tort claims following the loss of sovereign immunity [Yu

and Demetsky, 1992; Gittings, 1989]. Risk management operational procedures include facility improve-

ment, legal measures, and highway policy implementation. Of these procedures, facility improvement is

linked directly to highway asset management.

66.5 General Requirements of Highway Asset

Management System

The primary function of a highway asset management system is to serve as a decision-making tool for

highway agencies. Toward this end, the system must satisfy the following criteria [Sinha and Fwa, 1989;

FHWA and AASHTO, 1996]:

Comprehensiveness: A highway asset management system must address all major issues affecting the

performance of highways. Elements from each dimension of the asset management matrix struc-

ture should be considered. Because of the multiobjective nature of the system, solutions developed

for individual subsystems or for a single objective are unlikely to be globally optimal for the total

highway asset management system.

Flexibility: The management system must be ﬂexible to accommodate variations in different regions of

a highway network. Such variations include highway functional class, unit costs of highway activities,

priorities among system objectives, preferences over different highway functional activities, differ-

ences in climatic and environmental conditions, and so on. Management system needs also change

with time as responsibilities shift, infrastructure elements change, organization and budget compo-

sitions are restructured, and new technologies are developed. A management system should therefore

be capable to the type of agency it is intended to serve and ﬂexible to changing requirements.

Sensitivity: To be a good strategic decision-making aid, the highway asset management system must

be capable of analyzing the impacts of changing macroeconomic factors such as inﬂation, energy

price and availability, changes in automobile and truck characteristics, and changes in type and

intensity of trafﬁc loadings. It should also be capable of analyzing the implications of different

highway policy decisions.

Coordination: Most state highway agencies currently operate management systems that could provide

valuable information for highway asset management. These systems are intended to cyclically

monitor the condition, measure real-life performance, predict future trends, recommend candidate

projects and preservation treatments, and monitor the implications of investments (or lack

thereof) on system objectives, such as safety and congestion.

In a primer for asset management [FHWA, 1999], it is stated that asset management should be guided

by principles of customer focus, system orientation, long-term planning, and ﬂexibility, among others.

Highway Asset Management 66-31

Conclusion

Highway asset management combines the various management systems into a single integrated system,

thus enabling the evaluation of impacts of operational function decisions made in one system on

performance measures in another system. For instance, it makes possible the determination of system-

wide increases in crash rates if annual expenditure on roadside safety–enhancing facilities is decreased

in favor of pavement repair. Highway asset management systems provide decision-making tools to

improve highway transportation services with limited resources. As transportation needs and facilities

of communities differ vastly, so do the management systems of their highway agencies. Important factors

inﬂuencing the type and scope of management systems are the nature of the facilities to be provided and

maintained and the available funds, equipment, and manpower. Highway asset management is an evo-

lutionary process that is expected to be responsive to the needs of road users and highway agencies.

Operational functions such as data collection, analysis, optimization, and strategy selection should be

pursued continuously, and tools and technologies used in asset management need to be regularly updated

and improved. The component management systems of asset management need to be updated as needed,

such as improvements in data quality and relationships to other management systems. It is important

that highway asset management systems are ﬂexible, keeping abreast of the changing needs of highway

transportation, yet robust enough to be applicable in a wide variety of areas related to asset management.

Deﬁning Terms

Asset valuation — The use of depreciation or other approaches to determine the value of a highway

asset at a given point in time.

Bayesian estimates — A statistical technique used to update estimates when new data become available.

Cash ﬂow — The sequence of beneﬁts and costs over time, associated with an alternative (not all of

which need to involve monetary transactions).

Distress — Deterioration in the condition of a physical highway asset, such as cracking or rutting of a

highway pavement.

Dynamic programming — The technique used to formulate and solve optimization problems by recur-

sively solving subproblems.

Geographic Information Systems — A database with capabilities to manipulate, analyze, and display

spatial data.

Global Positioning System — Te c hnology developed by the military that uses satellites to determine

the latitude and longitude of a position anywhere in the world.

Heuristic optimization — Te c hniques used to ﬁnd satisfactory, not necessarily optimal, solutions to

optimization problems. Some heuristic techniques provide solutions with values that differ

from the optimal solution value by not more than a provable bound.

Linear programming — The techniques used to formulate and solve optimization problems in which

the decision variables are continuous and the objective function and constraints are linear.

Location referencing system — A system that uniquely describes the geographical location of a feature

with respect to some projection or other position referencing system.

Markov chain — A stochastic process in which the present state of the system determines the future

evolution of the process independently of the past.

Mixed-integer programming — The techniques used to formulate and solve optimization problems

in which at least some decision variables are discrete and the objective function and constraints

are linear.

Network-level analysis — The evaluation of dependent or independent alternatives for a set of highway

asset facilities.

Network-level optimization — The techniques used to formulate and solve optimization problems in

such a way that the polynomial time algorithms developed for some network problems can be

used.

66-32 The Civil Engineering Handbook, Second Edition

Ordinary least squares — A technique for calculating the regression equation that minimizes the sum

of the squares of the error terms, that is, the differences between the observed and predicted

values for the dependent variable.

Pavement proﬁle — The vertical shape of the pavement surface.

Pavement segment — A length of pavement that forms the basic unit for which data is collected, stored,

and analyzed and for which alternatives are evaluated and decisions are taken.

Programming — The determination and scheduling of activities to be performed and the resources

needed to implement the program.

Project-level analysis — The evaluation of mutually exclusive alternatives for a single physical highway

asset.

Regression analysis — The technique of mathematically estimating the parameters of functions

describing a process to ﬁt the functions to data.

Sampling technique — The method used to choose units of physical highway assets to include in the

sample, with the objective of obtaining a statistically adequate, representative sample at reason-

able costs.

Abbreviations

References

American Association of State Highway and Transportation Ofﬁcials (AASHTO), AASHTO Guidelines

for Pavement Management Systems, Washington, D.C., 1990.

Choocharukul, K. and Sinha, K.C., Development of a Congestion Management System Methodology for

Indiana, Draft Final Report, Joint Transportation Research Program, Purdue University, West

Lafayette, IN, 2000.

Denardo, E.V., Dynamic Programming: Models and Applications, Prentice Hall, Englewood Cliffs, NJ, 1981.

Dornan, D., What Is GASB34 and How Is It Related to Asset Management?, paper presented at 4th

National Asset Management Conference, Madison, WI, 2001.

AADT Annual average daily trafﬁc

AASHTO American Association of State Highway and Transportation Ofﬁcials

AHP Analytic hierarchy process

BMS Bridge management system

CMS Congestion management system

CRC Continuously reinforced concrete

DP Dynamic programming

FHWA Federal Highway Administration

GASB Governmental Accounting Standards Board

GIS Geographical Information Systems

GPS Global Positioning System

JCP Jointed concrete pavement

LCC Life cycle cost

LOS Level of service

LP Linear programming

MIP Mixed-integer programming

MMS Maintenance management system

OLS Ordinary least squares

PCC Portland cement concrete

PMS Pavement management system

RTRRM Response-type road roughness meter

SMS Safety management system

Highway Asset Management 66-33

Farooq, O. et al., Development of a Highway Safety, Management System for Indiana: Phase I, Joint

Tr ansportation Research Program, Purdue University, West Lafayette, IN, 1995.

Federal Highway Administration, Bridge Management Systems, Demonstration Project 71, U.S. Depart-

ment of Transportation, Washington, D.C., 1987.

Federal Highway Administration, Automated Pavement Condition Data Collection Equipment, U.S. Depart-

ment of Transportation, Washington, D.C., 1989.

Federal Highway Administration, Advanced Course on Pavement Management, U.S. Department of Trans-

portation, Washington, D.C., 1991.

Federal Highway Administration, Asset Management Primer, Ofﬁce of Asset Management, U.S. Depart-

ment of Transportation, Washington, D.C., 1999.

Federal Highway Administration (FHWA) and American Association of State Highway and Transporta-

tion Ofﬁcials (AASHTO), Asset Management: Advancing the State of the Art into the 21st Century

through Public-Private Dialogue, U.S. Department of Transportation and AASHTO, Washington,

D.C., 1996.

Garcia-Diaz, A. and Liebman, J.S., Optimal strategies for bridge replacement, Transp. Eng. J. ASCE, 109, 1983.

Gittings, G.L., Attacking tort liability through an improved risk management process: a state perspective,

Transp. Q., 43, 1989.

Governmental Accounting Standards Board (GASB), GASB Statement No. 34: Basic Financial Statements

and Management’s Discussion and Analysis for State and Local Governments, Norwalk, CT, 1999.

Haas, R., Hudson, W.R., and Zaniewski, J., Modern Pavement Management, Krieger Publishing, Malabar,

FL, 1994.

Jiang, Y. and Sinha, K.C., The Development of Optimal Strategy for Maintenance, Rehabilitation and

Replacement of Highway Bridges, Final Report Volume 6: Performance and Optimization, Joint

Tr ansportation Research Program, Purdue University, West Lafayette, IN, 1990.

Kleywegt, A.J. and Sinha, K.C., Tools for Bridge Management Data Analysis, Transportation Research

Circular 423 (Characteristics of Bridge Management Systems), Transportation Research Board,

National Research Council, Washington, D.C., 1994.

Labi, S., Impact Evaluation of Highway Pavement Maintenance Activities, Ph.D. dissertation, Purdue

University, West Lafayette, IN, 2001.

Mahoney, J.P. and Lytton, R.L., Measurement of Pavement Performance Using Statistical Sampling Tech-

niques, Research Report 207-2, Texas Transportation Institute, Texas A&M University, College

Station, TX, 1978.

Markow, M.J. et al., Role of Highway Maintenance in Integrated Management Systems, NCHRP Report

363, National Academy Press, Washington, D.C., 1994.

Maze, T.H., Valuing Transportation Assets: What Are the Possible Approaches?, paper presented at 4th

National Asset Management Conference, Madison, WI, 2001.

National Archives and Records Administration (NARA), Interim Final Rule, Federal Register, Vol. 58,

No. 229, Washington, D.C., December 1, 1993.

Reno, A.T., Shaw, and Hyman, W.A., NCHRP Synthesis of Highway Practice 366: Guidelines for Effective

Maintenance Budgeting Strategies, Tr ansportation Research Board, National Research Council,

Washington, D.C., 1994.

Saaty, T.L., A scaling method for priorities in hierarchical structures, J. Math. Psychol., 15, 1977.

Sherali, H.D., Jarvis, J.J., and Bazaraa, M.S., Linear Programming and Network Flows, John Wiley & Sons,

Inc., New York, 1992.

Strategic Highway Research Program (SHRP), Distress Identiﬁcation Manual for the Long-Term Pavement

Performance Studies, National Research Council, Washington, D.C., 1993.

Sinha, K.C. and Fwa, T.F., On the Concept of Total Highway Management, Transportation Research

Record 1229, Transportation Research Board, National Research Council, Washington, D.C., 1989.

Sinha, K.C. et al., The Development of Optimal Strategy for Maintenance, Rehabilitation and Replace-

ment of Highway Bridges, Final Report Volume 1: The Elements of the Indiana Bridge Management

System, Joint Transportation Research Program, Purdue University, West Lafayette, IN, 1991.

66-34 The Civil Engineering Handbook, Second Edition

Steuer, R., Multiple Criteria Optimization: Theory, Computation, and Application, John Wiley & Sons,

Inc., New York, 1986.

Te xas Transportation Institute, Urban Roadway Congestion Annual Report 1998, College Station, TX,

1998.

Yu, K. and Demetsky, M.J., A Framework for Evaluation of Risk Management Programs in State Depart-

ments of Transportation: Risk Management Systems Volume III, Transportation Research Record

1345, Transportation Research Board, National Research Council, Washington, D.C., 1992.

PPENDIX

Mathematics, Symbols,

and Physical Constants

Greek Alphabet

International System of Units (SI)

eﬁnitions of SI Base Units

•

ames and Symbols for the SI Base Units

•

SI D

erived Units

with Special Names and Symbols

•

nits in Use Together with the SI

Conversion Constants and Multipliers

ecommended Decimal Multiples and Submultiples

•

Conversion Factors — Metric to

English

•

onversion Factors — English to Metric

•

onversion Factors — General

•

emperature Factors

•

onversion of Temperatures

Physical Constants

neral

•

onstants

•

onstants Involving

•

umerical Constants

Symbols and Terminology for Physical and Chemical Quantities

Elementary Algebra and Geometry

undamental Properties (Real Numbers)

•

xponents

•

ractional Exponents

•

rrational

Exponents

•

ogarithms

•

actorials

•

inomial Theorem

•

actors and Expansion

•

rogression

•

omplex Numbers

•

olar Form

•

ermutations

•

ombinations

•

Algebraic

Equations

•

ometry

Determinants, Matrices, and Linear Systems of Equations

eterminants

•

valuation by Cofactors

•

roperties of Determinants

•

atrices

•

perations

•

roperties

•

ranspose

•

dentity Matrix

•

Adjoint

•

nverse Matrix

•

ystems of Linear

Equations

•

atrix Solution

Trigonometry

riangles

•

rigonometric Functions of an Angle

•

nverse Trigonometric Functions

Analytic Geometry

ectangular Coordinates

•

istance between Two Points; Slope

•

quations of Straight Lines

•

istance from a Point to a Line

•

ircle

•

arabola

•

lipse

•

yperbola (

> 1)

•

hange of Axes

Series

ernoulli and Euler Numbers

•

eries of Functions

•

ror Function

•

eries Expansion

Differential Calculus

otation

•

lope of a Curve

•

Angle of Intersection of Two Curves

•

adius of Curvature

•

elative Maxima and Minima

•

oints of Inﬂection of a Curve

•

aylor’s Formula

•

ndeterminant Forms

• Numerical Methods • Functions of Two Variables • Partial Derivatives

Integral Calculus

Indeﬁnite Integral • Deﬁnite Integral • Properties • Common Applications of the Deﬁnite

Integral

• Cylindrical and Spherical Coordinates • Double Integration • Surface Area and

Vo lume by Double Integration

• Centroid

Vector Analysis

Vectors • Ve c t o r D ifferentiation • Divergence Theorem (Gauss) • Stokes’ Theorem • Planar

Motion in Polar Coordinates

Special Functions

Hyperbolic Functions • Laplace Transforms • z-Transform • Trigonometric Identities • Fourier

Series

• Functions with Period Other Than 2π • Bessel Functions • Legendre Polynomials •

Laguerre Polynomials • Hermite Polynomials • Orthogonality

Statistics

Arithmetic Mean • Median • Mode • Geometric Mean • Harmonic Mean • Var iance • Standard

Deviation

• Coefﬁcient of Variation • Probability • Binomial Distribution • Mean of Binomially

Distributed Variable

• Normal Distribution • Poisson Distribution

Tables of Probability and Statistics

Areas under the Standard Normal Curve • Poisson Distribution • t-Distribution •

Distribution • Va riance Ratio

Tables of Derivatives

Integrals

Elementary Forms • Forms Containing (a + bx)

The Fourier Transforms

Fourier Transforms • Finite Sine Transforms • Finite Cosine Transforms • Fourier Sine

Tr ansforms

• Fourier Cosine Transforms • Fourier Transforms

Numerical Methods

Solution of Equations by Iteration • Finite Differences • Interpolation

Probability

Deﬁnitions • Deﬁnition of Probability • Marginal and Conditional Probability • Probability

Theorems

• Random Variable • Probability Function (Discrete Case) • Cumulative

Distribution Function (Discrete Case)

• Probability Density (Continuous Case) • Cumulative

Distribution Function (Continuous Case)

• Mathematical Expectation

Positional Notation

Change of Base • Examples

Credits

Associations and Societies

Ethics

Greek Alphabet

Greek

Letter

Greek

Name English Equivalent

Greek

Letter

Greek

Name

English

Equivalent

Α α Alpha a Ν ν Nu n

Β β Beta b Ξ ξ Xi x

Γ γ Gamma g Ο ο Omicron o

∆ δ Delta d Π π Pi p

Ε ε Epsilon e P ρ Rho r

Ζ ζ Zeta z Σ σ s Sigma s

Η η Eta Τ τ Tau t

Θ θ ϑ Theta th Y υ Upsilon u

Ι ι Iota i Φ φ ϕ Phi ph

Κ κ Kappa k X χ Chi ch

Λ λ Lambda l Ψ ψ Psi ps

Μ µ Mu m Ω ω Omega o

–

International System of Units (SI)

The International System of Units (SI) was adopted by the 11th General Conference on Weights and

Measures (CGPM) in 1960. It is a coherent system of units built from seven

SI base units, one for each

of the seven dimensionally independent base quantities: the meter, kilogram, second, ampere, kelvin,

mole, and candela, for the dimensions length, mass, time, electric current, thermodynamic temperature,

amount of substance, and luminous intensity, respectively. The deﬁnitions of the SI base units are given

below. The

SI derived units are expressed as products of powers of the base units, analogous to the

corresponding relations between physical quantities but with numerical factors equal to unity.

In the International System there is only one SI unit for each physical quantity. This is either the

appropriate SI base unit itself or the appropriate SI derived unit. However, any of the approved decimal

preﬁxes, called

SI preﬁxes, may be used to construct decimal multiples or submultiples of SI units.

It is recommended that only SI units be used in science and technology (with SI preﬁxes where

appropriate). Where there are special reasons for making an exception to this rule, it is recommended

always to deﬁne the units used in terms of SI units. This section is based on information supplied by

IUPAC.

Deﬁnitions of SI Base Units

Meter — The meter is the length of path traveled by light in vacuum during a time interval of 1/299

792 458 of a second (17th CGPM, 1983).

Kilogram — The kilogram is the unit of mass; it is equal to the mass of the international prototype

of the kilogram (3rd CGPM, 1901).

Second — The second is the duration of 9 192 631 770 periods of the radiation corresponding to the

transition between the two hyperﬁne levels of the ground state of the cesium-133 atom (13th CGPM,

1967).

Ampere — The ampere is that constant current which, if maintained in two straight parallel conduc-

tors of inﬁnite length, of negligible circular cross-section, and placed 1 meter apart in vacuum,

would produce between these conductors a force equal to 2

× 10

–7

newton per meter of length

(9th CGPM, 1948).

Kelvin — The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermody-

namic temperature of the triple point of water (13th CGPM, 1967).

Mole — The mole is the amount of substance of a system that contains as many elementary entities

as there are atoms in 0.012 kilogram of carbon-12. When the mole is used, the elementary entities

must be speciﬁed and may be atoms, molecules, ions, electrons, or other particles, or speciﬁed

groups of such particles (14th CGPM, 1971).

Examples of the use of the mole:

1 mol of H

contains about 6.022 × 10

molecules, or 12.044 × 10

H atoms

1 mol of HgCl has a mass of 236.04 g

1 mol of Hg

has a mass of 472.08 g

1 mol of Hg

has a mass of 401.18 g and a charge of 192.97 kC

1 mol of Fe

0.91

S has a mass of 82.88 g

1 mol of e

–

has a mass of 548.60 µg and a charge of – 96.49 kC

1 mol of photons whose frequency is 10

Hz has energy of about 39.90 kJ

Candela — The candela is the luminous intensity, in a given direction, of a source that emits

monochromatic radiation of frequency 540

× 10

hertz and that has a radiant intensity in that

direction of (1/683) watt per steradian (16th CGPM, 1979).