## 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 length^{2)} |

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 loadi^{1)} |

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 strain^{1)} |

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 stress^{3)} |

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., e _{23} 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., s _{23} 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)}**

Letter^{2)} | Meaning | ||

| Genera | Material | Actions, internal forces and moments, strength^{6)} |

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 limit^{4)} | |

eff | Effective | ||

eq | Seismic action | ||

eqv | Equivalent |

**Table 6** *(Continued)*

Letter | Meaning | ||

General | Material | Actions, internal forces and moments, strength^{5)} | |

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 | ||

General | Material | Actions, internal forces and moments, strength^{5)} | |

I (lon) | Longitudinal^{7)} | ||

I (lw)^{8)} | Low, lower^{7)} | ||

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 | ||

General | Material | Actions, internal forces and moments, strength^{5)} | |

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 | ||

General | Material | Actions, internal forces and moments, strength^{5)} | |

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 | ||

General | Material | Actions, internal forces and moments, strength^{5)} | |

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. |