TCVN 6203:2012 ISO 3898:1997 Basic for structural design -Notations – General Symbols

Preface

TCVN 6203:2012 replaces TCVN 6203:1995 (ISO 3898:1987)

TCVN 6203:2012 is completely equivalent to ISO 3898:1997.

TCVN 6203:2012 was converted from TCVN 6203:1995 in accordance with the provisions of Clause 1, Article 69 of the Law on Standards and Technical Regulations and Point b), Clause 1, Article 6 of the Government’s Decree No. 127/2007/ND-CP dated August 1, 2007, detailing the implementation of a number of articles of the Law on Standards and Technical Regulations.

TCVN 6203:2012 was compiled by the Institute of Architecture, Urban and Rural Planning – Ministry of Construction, proposed by the Ministry of Construction, appraised by the Directorate for Standards, Metrology and Quality, and announced by the Ministry of Science and Technology.

1. Scope

This standard specifies standard symbols used for structural design.

The standard includes common necessary terms applied in this field, except for terms related to materials or special technical areas.

This standard only represents the symbols used without affecting the exact definitions required for each term within the scope of other standards.

Table 1 provides general instructions on the use of different letter types. Tables 2, 3, and 4 specify the letters, used as main symbols, and their meanings. Table 5 specifies the list of special symbols and mathematical symbols. Table 6 specifies the letters or groups of letters when used as subscripts and their meanings.

2. References

The following referenced documents are essential for the application of this standard. For dated references, only the cited edition applies. For undated references, the latest edition of the referenced document (including any amendments) applies.

TCVN 6398-0:1998, Quantities and units – Part 0: General principles

3. Construction of symbols

The construction of a symbol to represent a given quantity or term shall follow these steps:

3.1. The main letter of the symbol shall be chosen from Tables 2, 3, 4, or 5 on the basis of considering the main use as stated in Table 1.

3.2. The subscript letters for description may be chosen according to Table 6. When using other subscript letters, they shall be clearly defined.

3.3. Numerals may be used as subscripts.

3.4. When there are multiple subscripts used with the main symbol, they shall be separated by a comma or semicolon to avoid confusion.

3.5. When constructing a symbol to represent the effect of an action, the first subscript shall represent the effect of that action and subsequent subscripts represent the action.

3.6. When no confusion can occur, one or all subscripts may be omitted.

3.7. When there are no special provisions, a plus sign (+) is used to denote tensile stress and a minus sign (-) is used to denote compressive stress.

3.8. The principle of using italic letters, upright letters, or drawings shall be applied according to TCVN 6398-0:1998.

NOTE: Subscripts such as c, t (ten) can be used to avoid using the ‘ (comma) symbol.

4. Precautions

The following precautions shall be taken to avoid confusion:

a) When confusion between the numeral 1 and the letter I is possible in some typed text, L shall be used instead of I.

b) The lowercase letter o and the uppercase letter O of the Latin alphabet shall not be used as a main symbol because they can be confused with the numeral 0 (zero). However, the letter “o” can be used as a symbol with the meaning of the numeral 0 (zero).

c) The lowercase Greek letters iota (i), omicron (o), and upsilon (u) shall not be used because they can be confused with other Latin letters. Likewise, the use of kappa (k) and chi (c) should be avoided if possible. When using lowercase Greek letters such as eta (h), omega (w), and mu (m), care should be taken when writing to avoid confusion with lowercase Latin letters such as n, w, and u.

Table 1 – Guidelines for using letters to construct symbols

Type of letter	Usage
Uppercase Latin letters	– Actions, internal forces, internal moments – Area, first and second moments of area – Modulus of elasticity – Temperature
Lowercase Latin letters	– Actions, internal forces, internal moments (per unit length or area) – Distance (eccentricity, length, etc.) – Strength – Velocity, acceleration, frequency – Descriptive subscripts – Mass – Time
Uppercase Greek letters	All mathematical and physical quantities, except for geometric and mechanical quantities
Lowercase Greek letters	– Coefficients, ratios- Stress resultant – Angles – Density (mass density and weight density) – Stress
NOTE: Concepts not listed in Table 1 shall apply the closest corresponding type stated.

Table 2 – Uppercase Latin letters

Letter	Meaning
A	Area
A	Accidental action
B	(Not used)
C	Fixed or nominal value
C	Coerce
D	Flexural stiffness (plate, shell)
D	Chỉ số tổn thất (mỏi)
E	Modulus of elasticity
E (hay Eq)	Seismic action
E	Effect of action
F	General action
F	Force (in general)
G	Shear modulus
G	Permanent action ¹⁾
H	Horizontal component of a force
I	Second moment of area of a plane section
J	(Not used)
K	Stiffness of a spring (frame)
L	May be used for length (see Table 3) or height of a part or a structural member
M	Moment in general
M	Bending moment
N	Normal force
O	(Avoid if possible)
P	Prestressing action
P (hay p)	Probability
Q	Variable action
R	Resultant force
R	Reaction
R	Resistance
S	First moment of area of a plane section (static moment)
S	Internal force, internal moment
S (hay S_n)	Snow action
T	Torsional moment
T	Temperature
T	Time period
U	(Not used)
V	Shear force
V	Volume
V	Vertical component of a force
V (hay v)	Conversion factor
W	Section modulus ²⁾
W	Wind load
X	Value of property (of material)
X, Y, Z	General forces (parallel to x, y, or z axes)
NOTES: 1) A subscript may be added if deemed necessary (e.g., Go – self-weight load). 2) May be used with appropriate subscript (e, or el, pl) in appropriate positions. Wpl is sometimes replaced by Z.

Table 3 – Lowercase Latin letters

Letter	Meaning
a	Spacing
a	Acceleration
a	Geometric parameterer
b	Width
c	(Not used)
d	Deflection angled
d	Depth (e.g., for foundations)
d	Diameter
e	Diameter eccentricity
f	Strength (of material)
f	Frequency
g	Permanent distributed load ¹⁾
g	Gravitational acceleration
h	Heighth
h	Thickness
i	Radius of gyration
j	Number of days
k	Coefficient
I	Length; structural member length²⁾
m	Bending moment per unit length or width
m	Mass
n	Normal force per unit length or width
n	Number of …
o	(Not used)
p	Pressure
p	Probability
q	Variable distributed loadi¹⁾
r	Radius
s	Sample standard deviation
s	Spacing
s	Distributed snow load
t	Time in general
t	Thickness of thin member
t	Torsional moment per unit length or width
u	Perimeter
u, v, w	Displacement components of a point
v	Velocity
v	Shear force per unit length or width
w	Distributed wind load
x, y, z	Coordinates
z	Lever arm
NOTES: 1) A subscript may be added if deemed necessary (e.g., g_o – distributed self-weight load). 2) L or l may be used for length, or to avoid confusion with the numeral 1.

Table 4 – Lowercase Greek letters

Letter	Symbol	Meaning
alpha	a	Angle; ratio
beta	b	ratio, factor
beta	b	Reliability index
gamma	g	Localized factor (reliability)
gamma	g	Ratio (relative stiffness)
gamma	g	Shear strain¹⁾
gamma	g	Weight per unit volume (specific weight)
delta	d	Conversion factor
epsilon	e	strain ²⁾
xi, eta, zeta	x, h, z	Relative coordinates
eta	h	Conversion factor
theta	q	Angle, angle of rotation
iota	i	(Not used)
kappa	k	(Avoid if possible)
lamđa	l	Ratio (slenderness), factor
mu	m	Coefficient, friction coefficient
mu	m	Mean value of a set
mu	m	Adjustment factor
nu	n	Poisson’s ratio
omicron	o	(Avoid if possible)
pi	p	(Only use in mathematics)
rho	r	Mass per unit volume (mass density)
sigma	s	Normal stress
sigma	s	Standard deviation of a set
tau	t	Shear stress³⁾
upsilon	u	(Not used)
phi	j (Φ)	Angle of friction (e.g., for soil)
phi	j (Φ)	Angle, reduction factor
chi	c	(Avoid if possible)
psi	y	Relative humidity
psi	y	Reduction factor
omega	w	Angular velocity
omega	w	Moisture content
NOTES: 1) For shear strain, e may be used with non-symmetric subscript. E.g., e₂₃ or e_yz. 2) E.g., e_{e, max}, e_{0, 02,} , e_u. 3) For shear strain, s may also be used with non-symmetric subscript. E.g., s₂₃ or s_yz.

Table 5 – Mathematical and special symbols

Symbol	Meaning
S	Sum
D	Difference, increment
Φ	Diameter (e.g., of reinforcement, rivets, etc.)
‘ (dấu phẩy)	Enhancement (especially for geometry and positioning)¹⁾
e	Base of natural logarithms: 2.71828…
p	Ratio of circumference to diameter: 3.14159…
n	Number of…
II hoặc //	Parallel
^	Perpendicular, normal
NOTE: 1) Subscripts such as ac, t (ten) can be used to avoid using the ‘ (comma) symbol.

Table 6 – Subscripts – Lowercase Latin letters ¹⁾

Letter²⁾	Meaning
	Genera	Material	Actions, internal forces and moments, strength⁶⁾
a (ac)			Accidental action
a (sa)		Structural steel
abs	Absolute
act, pas	Active, passive
add	Additional
adm	Admissible (allowed)
al		Aluminum
b		Brick (e.g., masonry)
c (con)		Concrete
c			Compression in general
cal	Calculated ³⁾
cr (crit)	Critical
d (des)	Design
dir, ind			Direct, indirect
dyn			Dynamic
e (el)	Elastic	Elastic limit⁴⁾
eff	Effective
eq			Seismic action
eqv	Equivalent

Table 6 (Continued)

Letter	Meaning
Letter	General	Material	Actions, internal forces and moments, strength⁵⁾
est	Estimated
exe	Execution
exp	Experimental ⁵⁾
ext	External
f			Action, force (in general)
f (fl)		Flange
f (fr)			Friction
fat	Fatigue
g			Permanent actiong
g (ga)		Guaranteed
h (hg)⁸⁾	High, higher
h (hor)	Horizontal
inf	Inferior
i (ini)	Initial (time)
i (int)	Integer
i	Number of…
j	Number of days
k	Characteristic

Table 6 (Continued)

Letter	Meaning
Letter	General	Material	Actions, internal forces and moments, strength⁵⁾
I (lon)	Longitudinal⁷⁾
I (lw)⁸⁾	Low, lower⁷⁾
lat	Lateral
Igt, sht	Long-term, short-term
lim	Limit
m			Bending in general
m (mv)	Mean value
ma	Built
max, min	Maximum, minimum
mor		Mortar
n			Normal force
n (net)	Net
n (nom)	Nominal
nor	Standard/normal
o	Zero
o	At origin
obs	Observed
p			Prestressing action
p (hoặc sp)		Prestressed steel

Table 6 (Continued)

Letter	Meaning
Letter	General	Material	Actions, internal forces and moments, strength⁵⁾
par	Parallel
per	Perpendicular
pl		Plastic
pro	Provisional
q			Variable action
r			Resistance
red	Reduced
ref	Reference
rep	Representative
req	Required
res	Residual
s			Internal force, moment
s		Reinforcing steel
s (sn)			Snow actions
s (sol)			Ground action
ser	Serviceability
shr		Shrinkage
sit			Situated (load)
st (stat)			Static

Table 6 (Continued)

Letter	Meaning
Letter	General	Material	Actions, internal forces and moments, strength⁵⁾
stab, dest			Stable, unstable
sup	Superior
t (tem)	Temperature		Thermal
t (ten)			Tension in general
th (theo)	Theoretical
t (tor)			Torsion in general
t (tra)	Transverse
tim		Timber
tot	Total
u (ult)		Ultimate (only used for materials)
v	Vertical
v			Shear force
var			Varvariable
w (wat)			Water action
w (wi)			Wind action
w		Woven/ web
x, y, z	Coordinat
y (yi)		Yield

Table 6 (End)

Letter	Meaning
Letter	General	Material	Actions, internal forces and moments, strength⁵⁾
0, 1, 2, v.v.	Particular values
¥	Asymptotic value
NOTES: 1) Abbreviations not included in this table may be taken from common English words of Latin origin. In case no confusion can occur, one or two subscripts may be reduced. 2) Letters in parentheses: to be used when a single letter could lead to confusion. If confusion is still possible, use the whole word (in English or French). 3) To be used in contrast with “observed”. 4) If necessary, an appropriate subscript may be added to the given subscript when defining the elastic limit more precisely. E.g., 0,2. 5) To be used in contrast with “theoretical”. 6) When clarification is needed, uppercase Latin letters may be used to denote actions, internal forces, internal moments, and strength. E.g., gF, gSd, gRd, s_TF. 7) L or I may also be substituted to avoid confusion with the number 1. 8) In case “sup” or “inf” cannot be used.