ISO 3898:2013
(Main)Bases for design of structures — Names and symbols of physical quantities and generic quantities
Bases for design of structures — Names and symbols of physical quantities and generic quantities
ISO 3898:2013 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.
Bases du calcul des constructions — Noms et symboles des grandeurs physiques et grandeurs génériques
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Standards Content (Sample)
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
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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), obs(erved), i, j (ordinal numbers), etc.;
index iv): subscripts/indices related to the Basic variables and the Performance functionals. The
preferred order is: first the indices ‘S’, ‘s’ and ‘R’, ‘r’, then the other indices iv).
EXAMPLES
Basic variables:
F: f (Action in general, Loadcase), a(ccidental), g (permanent), sn(ow),etc.;
GE: ge (Geometry of structure in general);
M: m (Material property in general), el(asticity), cr(eepiness), etc.;
Performance functionals:
S: s (Response of structure, Sequel or Effect of action(s), Action-effect), dyn(amical), sli(ding),
etc.;
NOTE Sometimes deviating from S, the symbol E is used, e.g. in a number of Eurocodes,
and erroneously in ISO 22111:2007.
R: r (Resistance of structure, Capacity), frac(tional), fat(igue), etc.
index v): subscripts/indices related to (1) place, then to (2) direction;
EXAMPLES 1 (joint, knot, point, foundation) A, B, C, ., a, b, c, ., 1, 2, 3, ., etc.;
EXAMPLES 2 x, y, z, //, etc.
index vi): subscripts/indices related to types of material;
EXAMPLES c(oncrete), ma(sonry), etc.
3.2.2.7 If, by applying the subscripts/indices i to vi (or superscripts), the dimension of the original
physical quantity does not change, so < K > = < K > , such subscripts/indices are called descriptive
index
subscripts/indices (or superscripts).
3.2.2.8 A (compound) symbol is written without a final full stop (except for normal punctuation).
EXAMPLES
physical quantities with names with one term symbol
area A
thickness t
force F
strength f
factor μ
physical quantities with names as a combination of terms symbol
maximum area A
max
nominal thickness of a flange t
fl;nom
design (value of a) force F
d
admissible (value of the) strength of wood in direction x f
ti;xx;adm
friction factor μ
fric
NOTE For the equivalent rules in the case of generic quantities reference here is made to A.4.3.
3.3 Rules for forming and writing names and symbols of units
NOTE This International Standard adopts (the rules of) the International System of units (SI).
4 © ISO 2013 – All rights reserved
3.3.1 Names
All names are given in ISO 80000-1. The names are written in Latin lower case letter.
EXAMPLES
(7) base units: metre, kilogram, second, ampere, kelvin, mole and candela;
(18+3) derived units: newton, pascal, radian, etc.;
(20 prefixes for) multiples of units: (multiple:) megapascal, etc.; (sub-multiple:) millimetre, etc.;
compound units: newton metre, metre per second, etc.
3.3.2 Symbols
The symbol of a unit is only (a kernel of) one or more successive separate (mostly) Latin lower and/or upper
case letter symbols, written in Roman (upright) type (irrespective of the type used in the rest of the text).
EXAMPLES m, K, kg, s, N, Pa, rad, MPa, mm, etc.
No subscripts (and superscripts) are allowed.
The symbol of a compound unit: a multiplication is indicated by one space or a half-high dot and a division
can be indicated by a solidus (/).
−1
EXAMPLES N·m or N m, m/s or m s , etc.
A (compound) symbol is written without a final full stop (except for normal punctuation) and shall be
placed after the numerical value, leaving a space between that value and the unit symbol.
EXAMPLE F = 10,8 kN, etc.
3.4 Additional rules for forming of symbols
3.4.1 Symbols of physical quantities
3.4.1.1 Subscripts/indices
In most cases a subscript/index may be selected from the Tables 5 to 11. If other subscripts/indices (or
superscripts) are used a clear definition of their meaning shall be given.
3.4.1.2 Precautions
In preventing confusion the following precautions shall be taken:
— where there is a possibility of confusing 1 (numeral) with l (letter symbol), the letter symbol L or ℓ
shall be used in place of the letter symbol l;
— the Latin upper case letter symbol O shall not be used as a main letter symbol owing to the possibility
of confusion with the numeral 0 (zero). The Latin lower case letter symbol o may, however, be used
as a subscript/index with the same meaning as the numeral 0 (zero);
— the Greek lower case letter symbols iota (ι), omicron (ο) and upsilon (υ) shall not be used owing to the
possibility of confusing them with various Latin letter symbols. For the same reason, it is recommended
to avoid, as far as possible, the use of the Greek lower case letter symbols kappa (κ) and chi (χ). If the
Greek lower case letter symbols eta (η), mu (μ) and omega (ω) are used, care must be taken in writing
these letter symbols to avoid confusion with the Latin lower case letter symbols n, u and w.
3.4.2 Kernel-extending-subscripts/indices
In contrast with a descriptive subscript/index by applying a so-called ‘kernel-extending-subscript/index’
(k-e-index), the dimension of the (original) physical quantity will be changed (slightly). The order of
both types of subscripts/indices is as follows (the graphical symbol ‘ | ‘ separates the descriptive indices
from the kernel-extending-indices):
K
k-e-index|descriptive indices
or
K
k-e-index|vi;v;iv;iii;ii;i
A kernel-extending-subscript/index can be one of the types vi to i and if more than one k-e-index is
necessary the order of these subscripts/indices shall conform to 3.2.2.6.
EXAMPLE By applying descriptive subscripts/indices the dimension of the original physical quantity X does
not change, so < X > = < X > . But in particular cases the dimension of < X > will be (slightly) altered,
|vi;. ;i index|
so < X > ≠ < X > .
vi; . ;i|
Compare the following physical quantities, viz. the original physical quantity X versus the particular
physical quantity X :
index
‘force’ (X) versus ‘force per area’ (X ) or ‘number’ (X) versus ‘number per year’ (X ), etc.
index index
In some cases, for the symbol of the particular physical quantity, this International Standard gives
another, new kernel, e.g.:
symbol of the physical quantity ‘force’: F with [F] = N versus the symbol of the physical quantity
‘force per area’:
p with [p] = N/m .
But in other cases the original kernel will only be changed/extended by a so-called ‘kernel-
extending-subscript/index’, e.g.:
symbol of the physical quantity ‘number’: n with [n] = 1 versus the symbol of the physical quantity
‘number per year’: n with [n ] = 1/year.
a| a|
In this last example the subscript/index ‘a’ is mentioned a ‘kernel-extending-subscript/index’ or the
compound symbol ‘n ’ can be considered as a new kernel.
a
3.5 Tables
3.5.1 Format of the tables in this International Standard
3.5.1.1 Table 1 General use in the design of structures of types of alphabets
Table 1 in this International Standard is arranged so that it consists of three columns. The first column
(from the left) gives the types of alphabets (in combination with upper case respectively lower case
letter symbols), the second column gives dimensions and the third column gives common examples and
recommendations of physical quantities having that dimension.
3.5.1.2 Tables 2 to 4 of physical quantities
The tables of physical quantities and units in this International Standard (Tables 2 to 4) are - in
accordance with ISO 80000 arranged so that the physical quantities are presented in the first 5 columns
6 © ISO 2013 – All rights reserved
and the units in columns 6 to 8. The quantities and corresponding symbols and units are in accordance
with ISO 80000-3 and ISO 80000-4.
NOTE In the ISO 80000 series this layout is presented on two opposite pages.
All units between two full lines on the right-half belong to the physical quantities between the
corresponding full lines on the left-half of the pages.
In each table the symbols of the physical quantities (so the rows of a table) are arranged in alphabetical
order with respect tot the alphabet involved.
With respect to the numbering of the items, the first digit of the number corresponds with the number
of the table.
3.5.1.3 Tables 5 to 10 of indices
The tables of indices in this International Standard (Tables 5 to 7, 9 and 10) are arranged so that every
table consists of two columns: the left column gives the symbol (mostly one or more successive separate
letter symbols) and the right column gives the meaning of the index involved.
Table 8 of this International Standard is arranged so that it consists of three columns: the first column
(from the left) gives the upper case (of one or more successive) letter symbols, the second column gives
the lower case letter symbols and the third column gives the meaning of the index involved.
The index symbols (so the rows of the table) in each of the five subdivisions of the columns (three Basic
variables and two Performance functionals) of the table are arranged in alphabetical order.
3.5.1.4 Table 11 of mathematical signs and graphical symbols for use in the analysis and design
of structures
The table of mathematical signs and graphical symbols in this International Standard (Table 11) is
arranged so that the table consists of two columns: the left column gives the mathematical sign or
graphical symbol and the right column gives a description of the sign/symbol with a short explanation.
3.5.2 Descriptive contents of the tables in this International Standard
3.5.2.1 Table 1 General use in the design of structures of types of alphabets
This table gives general guide-lines for the use of types of alphabets/scripts in combination with upper case
and lower case letter symbols for forming symbols for physical quantities in general: common and new.
3.5.2.2 Tables 2 to 4 of physical quantities
The names (only in English) of the most important physical quantities in a general sense within the field
of the design of structures are given together with their symbols and - in some cases - definitions. These
names and symbols are recommendations. The definitions are given for identification of the physical
quantities involved.
The scalar or vector character of the physical quantities is pointed out, especially, when this is needed
for definitions.
In most cases one name but always one symbol for the physical quantity is given. If two or more names
are given for one physical quantity and no special distinction is made, they are equivalent.
With respect to the system of units only the International System of Units (SI) is applied (see ISO 80000-1).
(In some cases non-SI units are given, but this is explicitly mentioned in the column ‘Remarks’.) Only the
names (in English) and the international SI-symbols for the corresponding physical quantities are given
and some remarks.
3.5.2.3 Tables 5 to 10 of indices
The meanings (only in English) of the most important indices (mostly subscripts) are given together
with their corresponding symbols. The meanings and symbols are recommendations. The meaning is
the ‘verbal designation of a general concept in a specific subject field’ (see 3.4.3 in ISO 1087-1:2000), a
definition of the concept is not given and is not necessary because (in most cases) it speaks for itself.
3.5.2.4 Table 11 of mathematical signs and graphical symbols for use in the analysis and design
of structures
Most of the mathematical signs and symbols for use in the physical sciences and technology are given in
ISO 80000-2. The mathematical signs and graphical symbols given in Table 11 are more or less specific
for their use in the analysis and design of structures and they are a subset of or an additional set with
respect to the set, given in ISO 80000-2.
3.5.3 Specific contents of the tables in this International Standard
Tables 1 to 11 inclusive.
Table 1 — General use in the design of structures of types of alphabets/scripts in combination
with upper case and lower case letter symbols for forming symbols of physical quantities
Types of alphabets/scripts in com- Dimension Main usages: examples of physical
bination with upper case and lower quantities (p.q.s)
case letter symbols
Latin script 1 force 1 external and internal forces
upper case letter symbols
2 force times length 2 external and internal moments
3 length to a power other than one 3 area, volume, section modulus, first
and second (axial/polar) moments of
area
4 temperature 4 temperature
‘exceptions’
5 length 5 span
6 force per area, force times area per 6 p.q.s with respect to the elasticity of
length materials
7 time 7 period, vibration time
Latin script 1 length 1 linear dimensions (length, distance,
lower case letter symbols displacement, etc.)
2 length per time to a power 2 velocity, acceleration
3 force per length, force per area, force 3 internal and external forces per
per volume length, per area or per volume, pres-
sure, strength
4 force times length per length 4 internal moments per length
5 mass 5 mass
6 force per mass 6 acceleration, e.g. due to gravity
7 time 7 duration
8 time to the power minus one 8 frequency
9 certain dimensions 9 geometric parameters, coefficients
(in general), other spring constants,
statistical quantities
‘exceptions’
10 dimensionless 10 factor (in general), number
Greek script - reserved for mathematics and physics
upper case letter symbols
8 © ISO 2013 – All rights reserved
Table 1 (continued)
Types of alphabets/scripts in com- Dimension Main usages: examples of physical
bination with upper case and lower quantities (p.q.s)
case letter symbols
Greek script 1 dimensionless 1 (change of) angle, ratio, reliability
lower case letter symbols index, (various) factors, strain, relative
length coordinates, slenderness, rela-
tive (air) humidity
‘exceptions’
2 certain dimensions 2 angular acceleration, linear expan-
sion coefficient, weight and mass
density; (change of) curvature, statisti-
cal quantities, stress, angular velocity,
circular frequency
10 © ISO 2013 – All rights reserved
Table 2 — Physical quantities - names - symbols, formed by one separate Latin upper case letter symbol in italic type
[Roman type symbols represent specific collections of physical quantities (See Annex A)]
Physical quantities Units
Item No. Name Symbol Definition Remarks Name SI-symbol Remarks
2.1.1 Accidental action A several dimensions
2.1.2 Earthquake action A (Q )
eq, eq
2.2 area A A = ∫∫ dx dy dA (= dx·dy): square metre m
A
where area of a surface ele-
x and y are cartesian ment
coordinates
- (vacant) B
2.3 (empirical) constant C name of [C] [C]
2.4 flexural rigidity per length D newton metre N·m
2.5 damage index/ratio of fatigue D one 1
n
i
D = Γ
N
i
where
n : number of applied load
i
cycles with stress range
level S
i
N : number of load cycles
i
at failure for stress range
level S
i
2.6 modulus of elasticity E pascal Pa 1 Pa = 1 N/m
2.7 expectation E(X) E(X)= ∫ xf(x) dx X: continuous sto- name of [E(X)] [E(X)]
chastic variable
2.8 (external) force in general F newton N
2.9.1 Action in general, Loadcase F several dimensions
2.9.2 Permanent action G
2.9.3 Self-weight (action) G
sw
2.10 Geometry (of structure) GE
2.11 modulus of rigidity, G pascal Pa
shear modulus
- (vacant) H
a
See note in 3.2.2.6, Performance functionals.
Table 2 (continued)
Physical quantities Units
Item No. Name Symbol Definition Remarks Name SI-symbol Remarks
2 4
2.12 second or quadratic axial moment I I = ∫∫ r dA r , see ISO 80000-4 metre to the power four m
A Q Q
of area
- (vacant) J
2.13 modulus of compression, bulk K pascal Pa
modulus
2.14 (external) moment of a couple K newton metre N·m
2.15 length, span L metre m
2.16.1 (bending) moment in general M,(M ) newton metre N·m
m
2.16.2 (internal) moment, M
s
due to actions
2.16.3 (internal) moment, M
r
by resistance
2.16.4 (internal) bending moment, due M
s;m
to actions
2.16.5 (internal) bending moment, by M
r;m
resistance
2.17 Material property in general M several dimensions
2.18.1 normal force in general N newton N
2.18.2 normal force, N
s
due to actions
2.18.3 normal force, N
r
by resistance
- (vacant) O
2.19 probability P(A) 0 ≤ P(A) ≤ 1 A: event A one 1
2.20 prestressing force P newton N
a
See note in 3.2.2.6, Performance functionals.
12 © ISO 2013 – All rights reserved
Table 2 (continued)
Physical quantities Units
Item No. Name Symbol Definition Remarks Name SI-symbol Remarks
2.21.1 Variable action Q several dimensions
2.21.2 Snow action Q
sn
2.21.3 Wind action Q
w
2.22 Resistance, Capacity R
a
2.23 Response , Sequel or Effect of S
action(s), Action-effect (or Sol-
licitation)
2.24 linear (axial) moment of area S S =∫∫ r dA r , see ISO 80000-4 cubic metre m
A Q Q
(static moment)
2.25 period T duration of one cycle second s
2.26 reference period T chosen duration of a life- year a non-SI unit:
ref
cycle of a structure a = 32·10 s
2.27 temperature T kelvin K
2.28.1 torsional/twisting moment in T,(M ) newton metre N·m
t
general
2.28.2 (internal) torsional T,(M )
s;t
or twisting moment,
due to actions
2.28.3 (internal) torsional T,(M )
r,t
or twisting moment,
by resistance
- (vacant) U
2.29.1 shear force in general V newton N
2.29.2 shear force, V
s
due to actions
2.29.3 shear force, V
r
by resistance
2.30 volume V V = ∫∫∫ dx dy dz where cubic metre m
V
x, y and z are cartesian
coordinates
2.31 factor of variation V one 1
a
See note in 3.2.2.6, Performance functionals.
Table 2 (continued)
Physical quantities Units
Item No. Name Symbol Definition Remarks Name SI-symbol Remarks
2.32 section modulus W W = I / r cubic metre m
2.33 physical quantity X X = {X}·[X] name of [X] [X]
in general
2.34 Basic variable or Performance X several dimensions
functional in general
- (vacant) Y
- (vacant) Z
a
See note in 3.2.2.6, Performance functionals.
14 © ISO 2013 – All rights reserved
Table 3 — Physical quantities - names - symbols, formed by one separate Latin lower case letter symbol in italic type
Physical quantities Units
Item No. Name Symbol Definition Remarks Name SI-symbol Remarks
3.1 acceleration a,(a) a = dv ⁄ dt metre per square m/s
second
3.2 distance a metre m
3.3 geometrical parameter a name of [a] [a]
3.4 breadth, width b metre m
- (vacant) c
3.5.1 depth d metre m
3.5.2 diameter d
3.5.3 eccentricity e
3.6 force per volume f f = dF ⁄ dV newton per cubic metre N/m
3.7 frequency f f = 1 ⁄ T hertz Hz 1 Hz = 1/s
3.8.1 strength f newton per square N/m
metre
3.8.2 distributed permanent load g e.g. g
sw
self-weight
a 2
3.9 (local) acceleration of free fall g standard acceleration metre per square m/s
of free fall: second
g = 9,80665 m/s
n
3.10 gravitational field strength g g = G·m ⁄ r G (gravitational con- newton per kilogram N/kg
γ γ
stant) =
−11
6,6742 (10)·10
2 2
N·m /kg
3.11.1 height h metre m
3.11.2 thickness h see 3.26.2
3.11.3 radius of gyration i i = √(l ⁄ A)
3.12 number of days j one 1
3.13 coefficient k name of [k] [k] ≠ 1
3.14 factor k one 1
3.15 bedding spring coefficient k newton per cubic metre N/m
a
Unfortunately in much literature the name of ‘acceleration due to gravity’ is used.
b
Can be replaced by L or by ℓ to avoid confusion with the numeral 1.
Table 3 (continued)
Physical quantities Units
Item No. Name Symbol Definition Remarks Name SI-symbol Remarks
b
3.16 length, span l see text 3.4.1.2 metre m
3.17 mass m kilogram kg
3.18 internal moment per length m in plates and shells: newton metre per N·m/m
(bending and torsional moment) m , m , m metre
xx xy yy
3.19 (arithmetic) mean of a sample m,(x) name of [m] [m]
3.20 number n one 1
3.21 internal force per length (normal n in plates and shells: newton per metre N/m
and shear force) n , n , n
xx xy yy
- (vacant) o
3.22.1 force per area p p= dF ⁄ dA newton per square N/m
metre = pascal
3.22.2 pressure p
3.22.3 distributed variable load q e.g. q
w
wind load
3.23 force per length q q = dF ⁄ ds newton per metre N/m
3.24 radius r,(r) r = (x,y,z) metre m
3.25 standard deviation of a sample s name of [s] [s]
3.26.1 spacing, length of path s metre m
3.26.2 thickness (of thin layers) t of plates and shells
3.27 time t second s
3.28 duration ∆ t name of [t] min, h, d, non-SI units:
a (annum) 1 min = 60 s
1 h = 3600 s
1 d = 86400 s
3.29.1 perimeter u metre m
3.29.2 (horizontal) displacement u,(u) u = (u , u , u )
x y z
(of a point), sway
3.29.3 translation of a rigid body u
3.30 velocity v,(v) v = du ⁄ dt = dw ⁄ dt metre per second m/s
a
Unfortunately in much literature the name of ‘acceleration due to gravity’ is used.
b
Can be replaced by L or by ℓ to avoid confusion with the numeral 1.
16 © ISO 2013 – All rights reserved
Table 3 (continued)
Physical quantities Units
Item No. Name Symbol Definition Remarks Name SI-symbol Remarks
3.31.1 (vertical) displacement w,(w) w = (w ,w ,w ) metre m
x y z
(of a point), deflection
3.31.2 length coordinates, x, y, z
cartesian coordinates
3.31.3 lever arm z,( y)
a
Unfortunately in much literature the name of ‘acceleration due to gravity’ is used.
b
Can be replaced by L or by ℓ to avoid confusion with the numeral 1.
Table 4 — Physical quantities - names - symbols, formed by one separate Greek lower case letter symbol in italic type
[Roman type symbols represent specific collections of physical quantities (See Annex A)]
Physical quantities Units
Item No. Name Symbol Definition Remarks Name SI-symbol Definition
4.1 angle (plane) α α = s ⁄ r one or radian 1 or rad 1 rad = m/m
where = 1
s: length of the
included arc of a
circle between two
radii of the circle
r: radius of circle
4.2 angular acceleration α α = dω ⁄ dt radian per square rad ⁄ s
second
4.3 linear expansion coefficient α,(α ) α = (1 ⁄ ℓ)(dℓ ⁄ dT) kelvin to the power 1 ⁄ K
ℓ
minus one
4.4.1 ratio α one 1
4.4.2 FORM sensitivity factor, or α FORM: First Order
Separation factor Reliability Method
4.5 angle (plane) β see 4.1 one or radian 1 or rad
4.6.1 ratio β one 1
4.6.2 reliability index β see ISO 2394
4.7 (shear)angle (plane) γ see 4.1 and 4.10.2 one or radian 1 or rad
4.8 factor in reliability analysis, γ see ISO 2394 one 1
partial factor
4.9 weight per volume, γ γ = ρ ·g newton per cubic N ⁄ m
weight density metre
- (vacant) δ see Table 11
4.10.1 (linear) strain ε,(e) ε = Δl ⁄ l one 1
o
(relative elongation) where
Δl: increase in length
(elongation)
l : original length
o
18 © ISO 2013 – All rights reserved
Table 4 (continued)
Physical quantities Units
Item No. Name Symbol Definition Remarks Name SI-symbol Definition
4.10.2 strain (normal and shear) ε,(γ) 2-dimensional: one 1
ε , ε , ε
xx xy yy
or
ε , ½γ , ε
x z y
4.10.3 relative coordinate ζ ζ= (z ⁄ l)
4.10.4 ratio in general ζ e.g. damping ratio
4.10.5 volumetric strain η η = ΔV ⁄ V
o
where
ΔV: increase in vol-
ume
V : original volume
o
4.10.6 relative coordinate η η = (γ ⁄ l)
4.10.7 conversion factor η see EN 1990
4.11.1 angle (plane) θ see 4.1 one radian 1 or rad
4.11.2 change (in size) of angle ∆θ
(due to a torsional moment)
4.12 uncertainty of model(ling) θ (and θ) see ISO 2394 one 1
- (vacant) ι
−1
4.13.1 curvature κ κ = 1 ⁄ r metre to the power m
minus one
4.13.2 change of curvature ∆κ
4.14.1 slenderness λ l ⁄ i one 1
buc
4.14.2 (correction) factor μ
4.14.3 (static) factor of friction μ μ = F ⁄ F
// ⟘
4.15 (arithmetic) mean of a μ name of [μ] [μ]
population as a whole
4.16 (arithmetic) Mean of a μ several dimensions
population as a whole
4.17 Poisson’s ratio ν,(μ) one 1
Table 4 (continued)
Physical quantities Units
Item No. Name Symbol Definition Remarks Name SI-symbol Definition
4.18 humidity per volume υ kilogram per cubic kg/m
metre
4.19 relative coordinate ξ ξ = (x ⁄ l) one 1
- (vacant) ο
- (vacant) π see Table 11
4.20 (mass)density, ρ ρ = m ⁄ V kilogram per cubic kg/m
mass per volume metre
4.21 standard deviation of a σ name of [σ] [σ]
population as a whole
4.22 standard deviation of a σ several dimensions
population as a whole
4.23.1 (normal) stress σ σ = dF ⁄ dA 2-dimensional: pascal Pa 1 Pa = 1 N ⁄ m
⟘
σ , σ , σ
xx xy yy
4.23.2 (shear) stress τ,(σ)
or
σ , τ , σ
x z y
- (vacant) υ
4.24.1 angle (plane) φ see 4.1 one or radian 1 or rad
4.24.2 change (in size) of angle ∆φ
(due to a bending moment
(and shear force))
4.25 angle of (internal) friction φ numeral degrees .° non-SI unit
4.26 rotation of a rigid body φ radian rad 1 rad = m ⁄ m
= 1
- (vacant) χ
20 © ISO 2013 – All rights reserved
Table 4 (continued)
Physical quantities Units
Item No. Name Symbol Definition Remarks Name SI-symbol Definition
4.27.1 combination factor ψ see ISO 2394 one 1
of a variable action
4.27.2 frequent factor ψ
of a variable action
4.27.3 quasi-permanent factor ψ
of a variable action
4.27.4 relative humidity ψ ψ = v / v actual humidity
sat
per volume (v)
divided by humid-
ity per volume at
saturation (v ) at
sat
the same tem-
perature
4.28.1 angular frequency ω ω = 2π f radian per second rad ⁄ s
4.28.2 angular velocity ω ω = dφ /dt
4.29 buckling factor ω one 1
Table 5 — Index i) - indices related to probabilistic and partial factor methods of analysis
and design and formed by one or more successive separate Latin lower case letter symbols
in Roman type
Symbol Meaning
- current (or true) value of
d design value of
d-inf inferior/lower bound design value of
d-sup superior/upper bound design value of
k characteristic value of
k-inf inferior/lower bound characteristic value of
k-sup superior/upper bound characteristic value of
m mean or average value of
nom nominal value of
rep representative value of
Table 6 — Index ii) - indices related to types of limit state and formed by one or more successive
separate Latin lower case letter symbols in Roman type
a
Symbol Meaning
dur durability (DuLS)
fat fatigue (FaLS)
fi fire (FiLS)
ser serviceability (SLS)
u ultimate / structural failure (ULS)
a
The abbreviations, mentioned within brackets, are or can be used - like acronyms - in
descriptive text. The abbreviation ‘LS’ means: Limit State
Table 7 — Index iii) - (all other) indices related to various aspects and formed by one or more
successive separate Latin lower case letter symbols in Roman (and twice in italic) type
a
Symbol Meaning
indices of Roman type
abs absolute
add additional
b
adm admissible
act active
cal calculated
comp comparative
con constant, invariable
dir direct
ef, (eff) effective
eqv equivalent
est estimated
exc exceptional
a
It is recommended when determining abbreviations that are not included in this table to
start from the English term.
b
The expression ‘admissible’ in the meaning of an admissible value of . was often indicated
by placing ‘-’ above the symbol, but the index ‘adm’ is recommended, e.g. σ .
adm
Table 7 (continued)
a
Symbol Meaning
indices of Roman type
exe executional
exp experimental, exposure
fix fixed
fla flame
fl flange (of a beam)
fund fundamental
g,(gua) guaranteed, safeguarded
i,(init) initial
inc incidental
ind indirect
lg long
lgt long term
ls limit state
max maximum, peak
mea measured
min minimum
n,(net) net(to)
obs observed
ori original
pas passive
pro provisional
red reduced
ref reference
rel relative
req required
rsi residual
sh short
sht short term, brief
sit situation, site
suc suction
sur survival
tar target (value of)
th,(theo) theoretical
tot total
var variable
w, (web) web (of a beam)
indices of italic type
I, j ordinal number, number of.
a
It is recommended when determining abbreviations that are not included in this table to
start from the English term.
b
The expression ‘admissible’ in the meaning of an admissible value of . was often indicated
by placing ‘-’ above the symbol, but the index ‘adm’ is recommended, e.g. σ .
adm
22 © ISO 2013 – All rights reserved
a
Table 8 — Index iv) - indices related to the Basic variables and the Performance functionals
and formed by one or more successive separate Latin lower (and upper) case letter symbols
in Roman type
Symbol Meaning
upper case lower case
indices related to the Basic variable F
F f Action in general, Loadcase
indices related to the three types of Action in general
A a Accidental
G g Permanent
Q q Variable
indices indicating the origin of Action in general
av avalanche, snowslide
ea earth, ground/soil, (mud-current)
sw self-weight
eq earthquake, seismic activity
ex explosion
fi fire, deflagration
hur hurricane, tornado
ice ice, ice-ing
im impact, shock, coll
...
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