ISO 3898:2013

INTERNATIONAL ISO
STANDARD 3898
Fourth edition
2013-03-01
Bases for design of structures —
Names and symbols of physical
quantities and generic quantities
Bases du calcul des constructions — Noms et symboles des grandeurs
physiques et grandeurs génériques
Reference number
©
ISO 2013
© ISO 2013
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized otherwise in any form
or by any means, electronic or mechanical, including photocopying, or posting on the internet or an intranet, without prior
written permission. Permission can be requested from either ISO at the address below or ISO’s member body in the country of
the requester.
ISO copyright office
Case postale 56 • CH-1211 Geneva 20
Tel. + 41 22 749 01 11
Fax + 41 22 749 09 47
E-mail copyright@iso.org
Web www.iso.org
Published in Switzerland
ii © ISO 2013 – All rights reserved

Contents Page
Foreword .iv
0 Introduction .v
1 Scope . 1
2 Normative references . 1
3 Names and symbols for physical quantities and units . 1
3.1 General rules and method for forming and writing names and symbols . 1
3.2 Rules and method for forming and writing names and symbols of physical quantities . 1
3.3 Rules for forming and writing names and symbols of units . 4
3.4 Additional rules for forming of symbols . 5
3.5 Tables . 6
Annex A (normative) Definition and scope of generic quantities .29
Bibliography .41
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (ISO member bodies). The work of preparing International Standards is normally carried out
through ISO technical committees. Each member body interested in a subject for which a technical
committee has been established has the right to be represented on that committee. International
organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.
ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of
electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International
Standards adopted by the technical committees are circulated to the member bodies for voting.
Publication as an International Standard requires approval by at least 75 % of the member bodies
casting a vote.
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 3898 was prepared by Technical Committee ISO/TC 98, Bases for design of structures, Subcommittee
SC 1, Terminology and symbols.
This fourth edition cancels and replaces the third edition (ISO 3898:1997), which has been
technically revised.
The main reasons for this fourth edition of ISO 3898 are
— application of new techniques and methods in the analysis and design of structures, e.g. probabilistic
and partial factor methods, introduction of codes for new design situations, and more advanced
materials have increased the need for a more fundamental set of rules for the formation and
presentation of symbols, and
— revisions of the ISO Guide 31 series for the International System of Units (S.I.).
The major technical changes from the previous edition are the following:
— the normative references have been updated; particularly with regard to the ISO 80000 series;
— the so-called ‘kernel-index-method’ for forming and writing names and new (compound) symbols
is presented;
— the presentation of the (tables of) indices has been altered in accordance herewith;
— the concept of ‘generic quantities’ is introduced (Annex A).
iv © ISO 2013 – All rights reserved

0 Introduction
0.1  The concept of a ‘physical quantity’
The concept of a ‘physical quantity’ is, according to ISO/IEC Guide 99, defined by the following descriptive
statement: an attribute of a phenomenon, body or substance that can be distinguished qualitatively and
determined quantitatively.
The concept ‘physical quantity’ is designated by a name [ = a verbal designation of an individual concept
(see 3.4.2 of ISO 1087-1:2000)] and a corresponding symbol.
A physical quantity is characterized by its unique dimension. The dimension of a physical quantity is
expressed in units (of measurement).
NOTE 1 According to the ISO/IEC Directives, Part 2 for drafting International Standards, SI units are applied.
NOTE 2 Physical quantities can be dimensionless, e.g. often the case with factors. In that case their dimension
is noted as 1.
The names and symbols of the most important physical quantities (according ISO/IEC Guide 99: physical
quantities in a general sense) - and their characterizing units - within the field of physical sciences and
technology are given in ISO 80000-1. However, this is a limited set of names and symbols.
0.2  General method for forming and writing names and symbols of physical quantities
The names and symbols of the most important physical quantities (and their units) within the field of
the design of structures are given in this document: see the Tables 2 to 4 of this International Standard
(but necessarily there will/must be some overlap with ISO 80000-1).
This set of names and symbols is also limited, but with the help of the method given in this International
Standard (kernel-index-method) the user will be able to form/compose new and unique (compound) symbols
for a wide variety of physical quantities (according ISO/IEC Guide 99: particular physical quantities).
Adapted ‘reading’ of the compound symbols moreover enables the user to designate and particularize
the corresponding unique names of the physical quantities (see examples in 3.2.2.5 and 3.2.2.8).
The method itself is presented/worked-out in 3.1 of this International Standard, the kernel of a compound
symbol is given in or has to be chosen from the above mentioned Tables 2 to 4 and the indices forming
that unique (compound) symbol (mostly subscripts) are given in or have to be chosen from Tables 5 to 10.
INTERNATIONAL STANDARD ISO 3898:2013(E)
Bases for design of structures — Names and symbols of
physical quantities and generic quantities
1 Scope
This International Standard covers physical quantities in a general sense. The kernel-index-method
enables to form (compound) symbols of physical quantities related to a particular material and/or a
particular technical field of design of structures.
It also gives the main names, symbols, and units for physical quantities within the field of design of structures.
Annex A in a general sense covers ‘generic quantities’ which are genuine to this field. The kernel-index-
method can likewise be applied.
2 Normative references
The following documents, in whole or in part, are normatively referenced in this document and are
indispensable for its application. For dated references, only the edition cited applies. For undated
references, the latest edition of the referenced document (including any amendments) applies.
ISO 80000-1, Quantities and units — Part 1: General
ISO 80000-2, Quantities and units — Part 2: Mathematical signs and symbols to be used in the natural
sciences and technology
ISO 80000-3, Quantities and units — Part 3: Space and time
ISO 80000-4, Quantities and units — Part 4: Mechanics
3 Names and symbols for physical quantities and units
3.1 General rules and method for forming and writing names and symbols
The kernel of a (compound) symbol can be chosen from Tables 2, 3 and 4 and indices (mostly subscripts)
forming that unique (compound) symbol can be chosen from Tables 5 to 10.
NOTE 1 The rules are mainly adopted from the ISO 80000 series. In 3.2 the ‘kernel-index-method’ (KIM) has
been formulated for the first time in an ISO International Standard. The method stems from the mathematical
disciplines: Riemannian geometry and Affinor/Tensor analysis (Second half of nineteenth century).
NOTE 2 ISO 10241 can be used as a basis for formulating the correct name and definition of terms and quantities.
3.2 Rules and method for forming and writing names and symbols of physical quantities
3.2.1 Names
The name (in general) of a general physical quantity is (mostly) one term, being a noun, written in Latin
lower case letter symbols in Roman (upright) type.
For several systems of physical quantities the names (and the symbols) of some physical quantities in
a general sense are given in the ISO 80000 series. For the design of structures the system of physical
quantities in a general sense is given in the Tables 2, 3 and 4 of this International Standard.
In case of the name of a new or a particular physical quantity a new name/term can be chosen/composed,
for instance, by combining the name of an already existing physical quantity with all kinds of other terms.
For some terms like: coefficient, factor, parameter, number, ratio, level and constant, some guidance for
applying them is given in ISO 80000-1.
EXAMPLE 1 One term of a physical quantity: area, thickness, force, strength, factor, etc.
EXAMPLE 2 A combination of (one of the above mentioned terms with other) terms:
— maximum area, nominal thickness of a flange, design value of a force,
— admissible (value of the) strength of timber in direction x, friction factor, etc.
3.2.2 Symbols
The following applies to the forming and notation of symbols:
3.2.2.1 The symbol of a physical quantity is a one-letter symbol, the kernel, written in italic type.
NOTE There is one exception: a characteristic number has two letter symbols, see ISO 80000-11.
3.2.2.2 A letter symbol for a kernel can be a lower case or an upper case letter symbol of the Latin or
the Greek alphabet (see Tables 2, 3 and 4). In most cases the choice for a kernel of a physical quantity
shall be based on considerations of dimension or the main usage, as given in Table 1 of this International
Standard. A dimension or a main usage of a physical quantity not included in Table 1 shall comply the
nearest appropriate category listed.
3.2.2.3 The kernel may be modified by applying one or more subscripts/indices (and sometimes
superscripts), a so-called: compound symbol.
3.2.2.4 Subscripts/indices may be formed from letter symbols, digits and graphical symbols: they are
written in Roman (upright) type. If the kernel of a physical quantity is used as a subscript/index it is
written in italic type. Several kinds of subscripts/indices are given in the Tables 5 to 10.
3.2.2.5 A subscript/index is placed at the bottom right position of the kernel. By applying more than
one subscript/index (sometimes superscript) the distinct indices should preferably be separated by a
semi-colon (;). In the case of simple and clear, distinctive index symbols also a space or comma (,) is
allowed. For simply two or three of these index symbols no separation at all may be appropriate.
NOTE Other positions, e.g. at the upper right, are possible too. However, in general these positions are
reserved for other applications.
2 © ISO 2013 – All rights reserved

EXAMPLES
F external force;
ext
K nominal (value of) external couple;
nom
N , V , V normal and shear forces in a cross-section of a beam;
x y z
M , M , T bending and torsional moments in a cross-section of a beam;
y z x
m , m , m internal bending and torsional moments per length in a plate or shell;
xx yy xy
w serviceability limit (state) of deflection;
ser
f ultimate limit (state) of strength;
u
ε , 1/2γ , ε two-dimensional normal and shear strains in general;
x z y
γ partial factor for the transfer of material properties, geometry of structure and
R
actions into resistance of structure;
γ partial factor for the transfer of actions, geometry of structure and material prop-
S
erties into response of structure;
v humidity per volume at saturation.
sat
3.2.2.6 By applying more than one subscript/index, the order of the subscripts/indices is from right to
left as follows (if necessary/relevant the same rules can be applied for superscripts):
General format (K: kernel of a physical quantity, vi to i: indices):
K
vi;v;iv;iii;ii;i
index i): subscripts/indices related to probabilistic and partial factor methods of analysis and design;
EXAMPLES rep(resentative), nom(inal), k (characteristic), d(esign), etc.;
index ii): subscripts/indices related to types of limit state;
EXAMPLES u(ltimate), ser(viceability), fat(igue), fi(re), etc.;
index iii): subscripts/indices related to various aspects;
EXAMPLES g(uaranteed), max(imum),
...