(

TAKAAN TSANG

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Ministry of Public Works and Electric Power.

Directorate General of Housing,Building,Pianning and Urban Development B U I L D I N G R E S E A R C H I N S T I T U T E. RHC

REPRINT

NOTASI INTERNASIONAL UNTUK KONSTRUKSI BETON

Oleh lr. Wiratman Wangsadinata

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SYMPOSIUM PEMBANGUNAN GEDUNG2 01 INDONESIA

Bandung, 28 - 30 September 1972 • .

/ •

NOTASI INTE~~ATIONAL UNTUK KONSTRUKSI BETON -·-·-- ---------------

Pengantar

Oleh

I r. 'tl i ratman Wang sad i nata.

Salah satu kesul itan yang telah dialaml bertahun-t&hun oleh balk

pembaca maupun penul Is dari karye-kar~ teknik ialah tidak adanya suatu

~tentuan notssl y~ seregam di I ingkungan lnternasional. Dalam menya­

jlkan hasi 1-hasi I penel itian telah menjadi kebiasaan untuk menggunakan

notasi yang dlpakai dalam peretureo-per~turan dan standar-standar nasi­

on&-1. dan bertwbung pGOelitlan sering kal i menceT\Js-k.an koosepsi-kon5€psl

baru yang memerlukan lambang-lambang tambahan, berbagai-bagai cara te­

lah ditempuh dalam penentuannya, sehingga dalam I lngkungan nasional pun

serlng terjadl ketidak seragaman. Dengan demikian sangat dirasakan per­

lu adanye ketentuap-ketentuan dan cor~-cara penentuan notasl yang dapat

dJterfma umum di kalangan lnternaslonal.

Dalam bidang konstruksi Beton beberapa buah panitia penti~~ te­

lah menyusun konsep-konsep rekomendasi mengenai notasi dalam bGberapa

tahun berselang ini, misalnya Commission VI I (Notations, terminology)

dari Comlte European du Beton, Committee 104 (NQtations) dari American

Concrete Institute dan British Standards Institution (BLCP/80) dan ten­

tunya panitia-panitia nasional di berbagai-bagai negara lain. Dalam si­

dang plena ke-13 darl CEB di Scheveningen dalam tahun 1969 berbagai-ba­

gal pembicara telah menekankan perlu adanya keseragaman lnternasional

dalam notasl Konstruksi Beton. Setelah diskusl yang panjang tercapai lah

persesualan faham mengenai prinslp-prinsip umum. Pertemuan-pertemuan

terplsah kemudian diadakan antara CEB dan ACI. Suatu kelompok kerja ga­

bungan telah bersldang di Madrid dalam bulan Maret 1971 yang telah me­

nyusun suatu rekomendasi mengenai notasi yang sudah terperincl, untuk

diajukan ke sidang pleno ke-14 dari CEB di Copenhagen bulan Mel 1971.

Rekomendasi tersebut telah diterima oleh sidang, balk prinslp-prinsip­

nya maupun detall-detailnya. Dengan demikian pertama kal i dalam sejarah

konstruksl beton telah tercapai persesuaian faham lnternasional menge­

nai notasi ini. Notasi tersebut selanjutnya telah dipakai dalam ACI Bu­

Ilding Code 1971, Rekomendasi-rekomendasi FIP-CEB dan dalam peraturan-

D itc~r inid trji 19 J/- /tt/H/T-/-1::

N. I. : /96/ '7t.f-N.K.: Obl-3 ~ <!5L Oll,$l.J /~Y»;fl.

I

peraturan naslonaf negara2 anggauta. Yang terpentlng ialah bahwa reko ..

mendasi notasi t9rsebut telah diajukan kepada lnternasional Standard

Organization melalui ISO/TC 71 (Concrete and reinforced concrete), yang

ternyata menerlmanye untuk dijcdlkan usul ISO yang baru.

Indonesia (melalui JDNI) adalah anggota dari ISO, sehlngga sela­

yaknyalah apabi Ia kita segera mengikutl langkah yang telah ditempuh di

kalangan lnternasional dalam penggunaan notasi2 tersebut. Hat inl sebe­

narnya telah dicoba oleh Panitia Peraturan Beton Bertulang Indonesia

1971, akan tetapi berhubung sempitnya waktu, panitia tidak berhasil un­

tuk sudah memasukkan notasi-notasi lnternasional ini ke dalam PBI 1971.

Hal ini te:lah diberitahukan dalam kata pengantar dari PBI 1971.

Walaupun di dalam PBI 1971 bel urn digunakan notasi 2 lnternaslonal,

namun dalam penul !san karya2 teknik dalam publ ikasi2 selanjutnya, sela­

yaknya telah sudah diikuti notasi2 tersebut. Untuk memperkenalkan notasi

lnternasional ini kepada dunia teknik pembangunan Indonesia, berikut

disajikan kutipan langsung dari sebuah uralar\ dalam majalah "CONCRETE",

Vo I • 6 No. I b u I an Jan u a r i I 9 72 •

Tul isan inl sengaja tidak disadur kedalam bahasa Indonesia untuk mence­

gah salah penafsiran atau terjemahan.

An international notation for concrete

Introduction The possibility of arriving at a common international notation for concrete has been considered for many years by the Comite European du Beton (Recom­mendations lnternationales CEB, 1963), the American Concrete Institute and others, but agreement appeared unlikely until the thirteenth biennial meeting of the CEB, held at Scheveningen, Holland, in September 1969 when a common CEB-ACI standard for notations was discussed.

At this meeting the point was repeatedly made in the General Assembly that several major codes, induding those of the CEB, the ACt, Scandinavia, the UK and others, were soon to appear in new editions and that the Scheveningen meeting represented perhaps the last chance to arrive at a common standard for decades. During the discussions numerous compromises were therefore made and agreement was finally reached on the Common Principles CEB-FIP-ACI described in this report.

Following this agreement, work was undertaken within the various associations to prepare a detailed list of notations. Commission CEB VII met in Madrid in September 1970 and ACt Comrr:;ttee 1 04 pursued its work and hallotted on the proposals in early 1971. In addition, to hasten matters, a small workir.g group met in Madrid at the end of March 1971 to improve the detailed list, taking advantage of lesson3 learned from some of the difficulties encountered in the praceeding months. This group consisted of Prof. Rusch (CEB), Messrs. Reese and Gerstle (ACI), Mr Spratt (UK) and Messrs Kordina and Meseguer (CEB).

In May 1971 Commission VII presented its proposals to the fourteenth biennial meeting of the CEB in Copenhagen. Following a discussion of the proposals and subject only to minor amendment the General Assembly voted unanimously in favour of their adoption. Further, as a result of this agreement ISO/TC 71 agreed to put it forward as a new ISO proposal.

The following notes have been extracted from a a report prepared by Mr B. H. Spratt (Cement and Concrete Association).

Preparation of notations

1.1 :Construction of symbols The preparation of a symbol to represent a given quantity or term shall be as follows.

i. The leading or main letter of the symbol shall be selected from Tables, 2, 3, 4 or 5 based on consideration of dimensions and usage as given in Table 1.

ii. Descriptive subscripts may be selected as desired. Where subscripts other than those

appearing in Tables 6, 7 and 8 are used, a clear definition of their meaning shall be given.

iii. As a guide in the construction of symbols, the first subscripts should indicate the location and the following subscripts identify the cause (nature, location, etc.). •

iv. When there is no likelihood of confusion some or all of the descriptive subscripts can be omitted.

v. If desired, numerical figures may be used as subscripts.

vi. A prime (') representing compression shall be added to symbols representing geometrical quantities, if required.

vii. The sign of a computed stress is given by positive ( +) for tension and negative (-) for compression.

Due to the possibility of confusion, some letters in the Roman and Greek alphabets should not be used except in special circumstances. In the tables these letters are marked (void) or otherwise noted for the following reasons:

The Roman upper- and lower-case 0 should not be used as a leading letter due to the possibility of confusion. The lower-case may however be used as asubscr:m with the same meaningasO (numeral). The Greek lower-case letters 'iota' (t), 'kappa'(~~:, x), 'omicron' (o), 'upsilon' (u) and 'chi' (X) should not be used, due to the possibility of confusing them with ;arious Roman letters. On the other hand, Roman lower-case p should not be used due to the possibility of confusion with the Greek lower-case 'rho' (p). It should be noted that when Greek lower-case fetters 'eta' (11} and 'omega' (("} are used, care must be taken in writing the lettsr to avoid confusion with Roman lower-case letters nand w. The possibility of confusing 1 (numeral} with I (letter) in some typewritten work is acc;:epted and it has been agreed that L shall be used in place of I (letter} where ambiguity would otherwise arise in typewritten work.

1.2: Examples 1. Notation for the descriptive term ·Area of concrete'.

As the quantity is an area it is apparent from the dimensions and usage columns of Table 1 that a Roman upper-case letter is required. From Table 2 therefore the letter A-meaning area-is selected as the leading letter.

To define the word 'concrete' a subscript is chosen from those given in Tables 6, 7 or 8, the nearest in this case being cfrom Table 6.

Thus. Ac = area of concrete.

•where necessary to avoid confusion it is recommended rhat a comma be used betweel'l the two categories of subscripts.

An International notation for concrete

2. Notation for the descriptive term 'Depth to com­pression reinforcement'.

As the term is a linear dimension it is apparent from the dimensions and usage columns of Table 1 that a Roman lower-case letter is required. From Table 3 therefore the letter d-meaning effecting depth-is selected as the leading letter.

To define the word 'compression' a prime ' may be added as it is to be used with a geometrical quantity.

Thus, d' = depth to compression reinforcement.

3. Notation for the descriptive term 'Concrete shrinkage strain'.

As the term is dimensionless it is apparent from tlie dimensions and usage columns of Table 1 that a Greek lower-case letter is required. From

Table 4 therefore the letter £-meaning strain­is selected as the leading letter.

To define the words 'concrete shrinkage' a subscript is chosen from those given in Tables 6, 7 or 8, the nearest in this case being cs from Table7.

Thus. £ .. = concrete shrinkage strain. (Or ECii if confusion is possible, see note to

Table7.)

Table 1 Letter guide fo1 the constluction of 1ymbol1.

Type of letter I Dimensions

Roman Force, force times upper-case length, area tO a (Table 2) power, temperature

I Usage

1 . Moments, shears. nornu;! forces. concentrated loads, total loads

2. Area, first and second moments of area

3. Strain moduli (exception to dimensions)

4. Temperature

Roman Length. length per 1 . Unit moments. shears. normal lower-case time to a power, forces. loads (Table 3) force per unit length 2. Linear dimensions (length,

or area except whera width, thickness. etc.) used assubscripts 3. Strengths (or stresses) •

Greek upper-caee

Greek Dimensionless lower-case (Table4)

Notes:

4. Velocity, acceleration. frequency

6. Descriptive letters (subscripts)

Raserved for mathematics

1 . Coefficients and dimensionless ratios

2. Strains 3. Angles 4. Specific gravity (ratio of

densities) 5. Stresses• (exception to

dimensions)

•some countries use lower-case Roman letters for stresses, but

TablaZ Uppe1-caseRomanlettels

Letter Meaning

A area 8 C torsional moment of inertia D E strain modulus' F action (loads and imposed deformations) 1

G modulus of shear; dead load H I moment of inertia J K any coefficient with proper dimensions L a M bending moment N normal force 0 (void) P prestressing force 0 liveload R S first moment of an area; action effect• (internal M.

N. V. T) ; snow load T torsional moment; temperature u V shearing force W windload X reactions or forces in general, parallel to axis x Y reactions or forces in general, parallel to axis y Z reactions or forces in general, parallel to axis z

Notes: 1 . When necessary for clarity a subscript should be uaed (e.g. Eo to define strain modulus at origin).

2. To be used as a leading letter with subscripts given in Table7.

3. Can be used for 'span; length of member' instead of I (see item 1 .1 ).

Tabla 3 Lowe1-ce•e A omen kitten

Letter Meaning

e deflection; distance b width c d e I g h

i j k I m n 0 p q I

$ t u

" w X y z

concrete cover effective depth ; diameter (see also hand Table 6) eccentricity (see also Table 5) strength (or stress)' distributed dead load ; acceleration due to gravity total depth or diameter of a cross-section;

thickness radius of gyration number of days any coefficient with proper dimensions span; length of member1

bending moment per unit length or width normal force per unit length or width (void) (void) distributed live load radius distributed snow load; standard deviation; spacing time; torsional moment per unit length or width perimeter shearing force per unit length or width" distributed wind load; crack width co-ordinate; depth to neutral axis co-ordinate; depth of rectangular stress-block co-ordinate; lever arm

Greek letters are recommended. Concepts not included above Notes : 1 . Some countries use I for normal stress. but a is should comply to the nearest appropriate categont listed. recommended.

2. Can be replaced by L where ambiguity with 1 (numeral) would otherwise arise.

3. Some countries use v for shear stress, but T is recom­mended.

T•ble 4 Lower-case Greek letters

Letter

Alpha Beta Gamma

Delta Epsilon Zeta Eta Theta Iota Kappa Lambda Mu

Nu Xi Omicron Pi Rho Sigma Tau Upsilon Phi Chi Psi Omega

Symbol Meaning

a angle; ratio (e.g. a. = Es!Ecl; coefficient f3 angle; ratio; coefficient y specific gravity; safety factor (ym for

materials and Yf for forces, actions and their effects); shear strain (angular de­formation)

6 coefficient of variation; coefficient £ strain ' coefficient 'I reduction shear coefficient IJ rotation

(void) K, x (void)

A. slenderness ratio; coefficient p. coefficient of friction; relative bending

moment v Poisson's ratio; relative normal force ~ coefficient o (void) .,. (mathematical usege only) p geometrical ratio of reinforcement u normal stress T shear stress ., (void) op creep coeffi,-: mt X (void) 1/t coefficient w mechanical ratio of reinforcement

T•blel Mathematical and special symbols

Symbol

e .,. n

Meaning

sum difference; increment diameter of reinforcing bar or tendon compression (only for geometrical or topological

pu~poses) base of Naperian logarithms 3·1416 number

T•blel Genera/subscripts.

Letter

II b c d e f g h

i k I

m n 0

Meaning

support settlement; additional bond; bar; beam concrete; compression; column design• elastic; effective forces and other actions; flange; flexure; friction dead load horizontal ; hook initial number of days characteristic • longitudinal average values; materials

numeral zero (see below)

p prestress q liveload r cracking s steel; snow;slab t torsion•: tension'; transversal u ultimate (limit state) v shear:vertical w wind; wire; web; wall x linearco-ordinate y linear co-ordinate: yield z linear co-ordinate

0, 1, 2 ... oo particular values of quantities

Notes: Italicized words correspond to international agreements; they are to be respected and to be given preference over other possibilities. 1 . Design values cover uncertainties and are obtained by

multiplying the characteristic values by appropriate coefficients (e.g. 'If for actions or their effects and 1 /ym for materials).

2. Characteristic values for loads and strengths as specified in codes should correspond to an agreed probability of their being above or below prescFibed values.

3. Where confusion may arise between tension and torsion the double subscripts tn and tr should be used.

Table 7 Subscripts for loads and other actions

Letter Meaning

g dead load (Table 6) q live load (Table 6) s snow (Table 6) w wind (Table 6) ep earth pressure eq earthquake ex explosion ; blast im impact /p liquid pressure

a support settlement (Table 6) p prestress (Table 6) cc concrete creep CS concrete shrinkage te temperature

Note: Where there is a possibility of con­fusion, a bar may be placed over a double subscript.

T•ble 8 Subscript formed from abbreviations

Abbreviation I adm cal crit exc ext ,~nft .n fat lim max min sup tot VRr

Meaning

admissible; permissible calculated critical exceptional external inferior; lower internal lateral limit maximum minimum superior; upper total variable

I. ' !

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•

I.