Bridge Besrgn Code. Part 3 Hi ' , Pretoria, S u l h Alnca. 1981)

clions ..... ....... ... ... .... ... . . . . . ..... . . ,. . . . . .. .. . , ~ " . .. . . .. . ... . .. . ~ . . . . ~. . ~ .~ ..... . . - ~ .... .. .. . . .. . ~

General ............................ ........ ~ .... ..... . . "...... ~ ~ . ~ . ....... " . . . . ...... . ... ... ..... ~ ........,...... Ultimate limit stales .............................. .. ................ ................................

S ..................... .. ............. ... ...,. ~ ..,*.... ~ ..... " . . ~ ....*........'. ' "

tion .......... ..... . . . .... . .. .. . . .... . .. .. . . . .. . ~ . ~. ~~. . . .. ". . .. . ... .... .. ~ " . ..

Materials ...................................... ~ .*.... ".,,,....-....." ~~.~ ...... ~ . . ~ ~ ~ . . . . . .a . . , f . " ~~ ..... ~ . * . ~ ~ " . eneral .................................. "..................,..*.........,.,.. ~~ ..................... ~ * . , ~ ~ ....

............ . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............ I . . . . . I . L . . . . . . , . . . . . . . , . ~ ~ . ~ . . * ~ alues of y,. .......................... .......,..... .-".".

tructures . . . . . .. .. . ..... .. ..... .... . ... . . . . . .. . . .. , . . .. . .~ ." ." . .~ .. . *. .. . . .... ,. . ~ . . , eneral . . .. ... .. .. . . . .L . . . . . . . .~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , .L . . . . . . . . . . . . . ; I . . . ~ ..........." ...,........ ~ . . ltimate limit stat I _,....... . ...L....I_.I. " . . . ,~ . . . . I . . . . I . . I ............. .._ . . . , . . . I . . . . . . . . . . ~ .... ~ .....

limit states ... ..... ........ . ... ... . .. . . . .. .. .... .. . . . ... , . . .... . . . . " . $ . .. . ~. .. ~ ~. . " , ,

eflection .............. ..................... ... .... ,..... ~ .... " , ~ ".., ~ . . ~ "...".""........ . . ~ "."".......

- CtS ............................ . ...........,.... ~'....,.......

eneral ............................ .... ........ ~ . . ~ "........"...'..". ~.~ "..."..." ~ . ~ . ~ " ~ ,".. ~ . . - ~ ~ .. "....*- ures .............................. ".".,*.a ~ ...*.... " .... ~ ..... " ...-.... ~."..." ...... ~.

nalysis of sections ....... . . . ... . . . .. .. ... ... .. ......... ... ... . . . . ., . . ~ .. . ~ . .. ~. , " ~ . . . . . ~. . . ~ ~ . , ~ " ~ .

CRETE ................... ...~ " , ~ .

. I . " . " I I . . . . . " " . . . . ~ " . . " I " L . . I r . , O . " I I I , . O . . , . . ~ . . . . " * " " . . / . . " . ' * " O I . . * I . 1 "

S .................................. "....'..b.. ~ ~ " . . ~ ~ * ~ * . ~ . ~ . . ~ " ~ . " " ~ . I I " 1 ' . . ~ , , L . r l . . * . r O I . . 1 _ " . " . . I . . . I 1 . ' . . " _ 1 . . I " ~ I . . . . , , " * * f . . t . s . 1 . . I

...... ~ . . , , _ * . . l O . . L . . , . . l . , . . I . . . . I r D " . . / j . . . i l . , . - " " i_.... .

itudinal shear ...................~.*, ~ s ~ " ~ ' . , " * o s ~ ,.",. ~ ...,-.......,, ~~ ~ " . ~ ~ ~ ...", ~ . . " ~ . *

ction in beams ............. . . ....... ...... ... .... ....., ~ .,... ~ ~ - . * " ~ ~ . - . ~ . , " * - . . ~ ~ . ~ . " . . ~ . Crack control in beams ..... , ,..,.......... ..................... ..", ~ " ~ . . ~ ~ ~ . ~ ,"...

abs ............................ .... .......... ~ ~ ~ . . ~ ~ ~ . . ~ .... ~ . ~ - ~ ,..,.. ~ ....... ~ . " ~ ~ . . ~ . . . ~ ....~"..*.,".... ~ . . oments and shear forces in slabs ..,..,............. .. ..... .. ........, ~ . * ~ . . ~ ~ ~ . ~ ... ~ ~ . . ,

. . I " I ' . . " " ,,.... " . Y . l . " l . . , l . " . " . . " . . . ... . . r . - - ........... l l . . l . . l l . . . i . .

. . I j j , . . . , I "I.I"" ,. . . . I ) '..,." ..,.. "..'".. .....-...... ) " I * . " . * . . _ . I

"..,.~.." .,,. ' ~ . ~ ~ . . . " ~ . . ' . " . ~ . ~ " ~ ..... ~" .... ~ ..... ~ , . , .~ ,~ . " . .~<" " "~" . . . . . . . " " ~ . " " . * . . " . ~ . ~ , r . . . " .... ". , . ."~ ...... + .....a. I ....... I... .... <....~.

I . . . . ,...'._.. " . " " " " " . . I " . . . I . .......... . .... . I . . . r . . . . . . I . . .9 ......I "..

Columns " " ~ * ~ . . > ~ . ~ ... ~"~ .."" ~ " ~ " . . General ............................ ... .........**..... ~ ....., ".." ~ .....* ~ ~ . . ~ - ~ . ~ . ~ . ~ -............. ~ . ~ . ~ ."-...

. ~ " . . ~ . . ~ . . , . . . . " ~ . . ' n D _ ~ . I . . ' . . ~ . . , . . _ . . . . I . ~ . . , . . . I " . . . . . . . . . . . I . . . I . ~ . I . . . . . ~ . ~ ~

a u h rectangular or circular cross-section ............... S ................................*..~*9.. a . . ~ . . S . * . " . . . " " ~ ~ ~ . . ~ ~ ..... . . . . . . I . . . I . . ' . . O . . . , . , . . . I '...".." I . . . . . . . . . . . . . . -.., . . . . . . . I . . . f " ...... ",..

aEls ...........................................-..'..*.". ~ . . " .... ~ .'..... eneral ................... .. ............. ~ ~ . , ~ . ~ ~ ~ ,"".... ~ ..-.,.. ~~ ....* ~ . . , ~ ~ ~ ...'.. ~ . " . ~ ~ ......"". ~ .........

concrete wails .................................... ..... mosraerats and axial forces ............................

" . * I . . " . . l . . L I . . , I . .......... ' . ." .,.. . ........." ........ " I . . " . . .

wails .,..... .. ...... .. .... ~. " " . " * ~~ .*..... ~ . . . .................... . . I . . . . . . . . . . . . I . i . . " ..... ' ........ " ....._....... ,.,.* ..*... '...

S ..... . ............................ ' .. ............ ' ...... "".*.."*.,.'

S) ..., ~ . ~ " " ~ " . . ~ . ~ . ~ ~ ' ~ ~ ~ * ~ . ~ ~ ~ ..... .... ". " . . . ~ . . " . ~ . . . ' ~ . . " ~ . . . ~ ...." .....'. S ...................... >. " . " .......................................... . .... *. . .-...... ....

in bases .. ....... .......... .......... .. ......... . . ~ ~ ~ . . . ~ " . . " " . ~ ~ ".."*,."...".,. . , . . . . . . . . . r . . l . l_ , , . . . r I I ; ~ I ' . , ' " 1 . " * " . ~ ~ . . l . I " . r . . . 1 , j . . . " . " " . " " ~ ~ f ' , ~ . . " . " . . . . l . . t . ~ " . . ~ . l .

S . . . . . . . . . . . . . . . . . , . ~ . ~ . a . . * . , , . " . " . " . . . . , . " . - . . a - "~~~~ ' . . ~ ~ " . ~ ........"" . . . . . . .

erations affecting Desige-a Details ................... ......... ..... .....-. ".... ~" ~ " ~ . . ~ . . l I " . . . " j . I r . j r * _ j . I , l . I . . I . s C . . ~ r . _ I I . . . . " ........ .... "..." ..l. " ' < ~ ~ ~ . "

oncrete cover I . l , I I ...,, I _ L . _ . . l . I L I _ I , . , " . . _ . ~ " . "..'...... I . I . . . . . rations ........................... ., ......., ~.~ .... ~ ~ ~ . . . ~ ~ . .

scenleni in members .., .. . .... .. .... . . ..... ... . ..... . .......~. . ~ " . .. of reinforcement in frrembers .. ..... . . . . . .. .. . ' * , ~ * ~ . ~, ~. " e ~ * . " " ~. .

earing stress ................... ... . . 9 9 9 9 9 9 9 9 9 9 9 . 9 9 9 9 , . 9 9 9 . 9 . . ~ ~ ~

rage of reinforcernerrt .... .. ..... .. ...... .. . . ....,. . * ~ . * " ~ . ~ ~ . . . ".,"

........................................................................... ...........................................................................................................

...........................................................................

........................................................................... ............................................................................. S

ams .......................... .. ........ ......-. .. ........................................................................... ........................................................................... ........................................................................... ........................................................................... and laps ....................... .. ................................

...........................................................................

G : PRESTRESSED CONCRETE, I CRETE ..................................................

..............................................................................

.............................................................................. concrete ...................................... ..~,.. ..

..............................................................................

.............................................................................

at Frames ................................................................. res .....................................................................................

nts ................................................................#............. ry moments ..................................................................

................................................................................................... ............................................................................ xure .................................................................... ............................................................................ ............................................................................

ts ............................................................................ ...............................................................................

ther than friction losses .................... .. ........................ ................................................... ers ............................ ... ..........

......................................................................................................

erations affecting Desi n Details ..................... ,. ............................... ........................................................................................................... eneral

...................................................................... 11 1

............................................................. ams 1 .............................................*............................. 1

rat .................... ............ ..............................................*..................... 1 uction ...............................%. ..a............... 1

n ...................... ........ ........ .. . . 1$2

.......................................................... Structural Connection een U%$S 117 ..................... General ........................................................................... 157

Continuity of reinforc ......................................................................... Connections usin ser-ts ...................................................... Other types of co ....................... .... ...................................... 120

.......................................................... 1 ................................................................ 12

......................... ........... butmenis ......... 12 ............................................ butmeilt 1

or abln"ln?ents .....................S................... 1 ................................................................. I

1 .............................................................. ....... ......................... . . . . . . . . . . . . . .

uamerits ....................... ... .... .......... 12 ma\ effects .................... .. ...............a. 1

............................... ........ i t states .. 1

FOR COMF3LiANCE WITH ....................................................... 130

................... .................... ETE .... 134

.D TENDONS iN DLIGTS FOR "1 47 ...................................................................

viii Bridge Design Code. P m 3

TMH7. Pretoria . South Africa. !

........................................................ 11

imil state ...................................... .. I

acteristic stress for ..........................................................

c . in beams .............................................................. 35 ............................................................................... 36

stress ..................................................................... 43 umns ...................................................................... 5

............................................................................ 56 ment under particular conditions of exposure ...... 6 S ....................................................................... -7 tresses ................................................................. 73

e perimeter of a group of bars ............................ 73 shear stress, vc, in concrete beams containing low-density

....................................................................................................... te W1

Maximum value of shear stresses in concrete beams containing low-density 81 .............................

........................... 82

........................... 85 86 ...........................

....... onventional) 87 ...................... nd 87

r 87 ......... ................. .................... tes 8

9 ..........................

.......................... 91

age

curve for concret of normal derlsiey ........... 20

.................. cume for steel reinforcement ..... 2'1

Paw-relaxation steel ................................ ................. 21

curve $01 'as-dra t3" steel wife and 22 .......................................................................

alues of kV .................. .....,... ........................... .. ................................ 34

bearing ............................... .. . . . . . . . . . . . 34

efinitiow of dimer?sioi~ av at a flexible bearirlg ........................ .....S.......... 35

........ 37 ......................a...... .................

411 ..........................................................

tinn of csbrnpressiva Forces .......... 4.1

B salid section ..................... ................ 43

ararneters for shear in salid sHabs under concea\$rated toads ................... ... 48

............................. ............. . . . . . . . . . . . . . . . . . . . . . . . . 49

55 ...................................................................

gy ...................................................... 63

................................................................. 41'7

.. 122 ....................... ..........................

............... .................. itions) for creep ... "636

............................ y j at the time of ic~ading] 137

................................................... concrete) " 1 3 8

) for creep ............................................... 738

.............................................. Goefficieni k, (variation as a function of time) "i 40

................................. CaefFicient k, (environmental co ditiansj for shrinkage 141

........ ..................... thickness) tor shrir~kage ........ 142

Relaxation coefficient, q ............................................................... .. ... . . . . . . . . . . . 1 4 3

................................................................... ....................... Coefficient Q, .. 144

Coefficient $, (a)R - 8 , 40) ........................................................................... 145

oefficier~t 4, (aJh - 0, 45) ........................... ............ ................................... 145

recast concrete members.

con

eo

Effective thickness Thickness of Ils Thickness of

yed orneult diagram

Bridge Dosrgn Code, P m 3 TMH7* P:e!cria, ,%uEh A l n c ~ , 1989

(b ) Prestressed concrete: Prestressed c

lassification requirements.

restress: no tensile stress

prestress: tensile stresses

r the tensile face.

Bridge Design C d e , P m 3 H7, Pretoria, South Alnca, 1989

Interior surfaces of

erstructures or cellular ents or piers on nsation is unlike1

oncrete permanently under water

e deck soffits and

arts of structures in

I_-.-- h -1 in extreme environments o

limitations are summarized in I

Lower values of stress are given for ssed concrete "Ihan ole concrete cross-sect~on is norm of excessive cre

r values may be

e Des~gn CO&, P u t 3 TM1.47. PrePwia, W t h Africa, 1080

T ns for the servicea

Interpolate ate between n 0 5 0 f C u

and and 0,38 f c U 0 3 0 feu

sections of approximately uniform breadth to those

ssion

Not e applicabie

.a$ for limiting flexural stresses in joints for post-tension

The characteristic values of acti tions) are given in the lack of statistical data.

combinations 1 to 3 shoui e cor-2sjderecl.

ivsn in 2.1.2. hod

t erial.

nsaty may be taken from

nalysis o f structures: Ts determine t f permanent and trans~en: loading, use the appropriate value t tr?zr, to dalerrnine the

or the calculation of deflectians, m hat grven in Table 3 and l;i?if ihaevatiie

eater than Pt-iai ~ I V ~ E ' I

le 34 Appendix 3 B) e anaiysir; iscarrred

termediate betflser~

s dl-ie to the e f fec~r O ~ S , US@ an appw-

haif that valide as

that %he effect of ng half "ake values given E i t

ects of creep

under short-term loadin

f

1 l I

dvltegicanlate Interpolate between eEween

t25 and l ,33 1.67

flanges)

rrifsrrn or near-uniform 1,33

Tension Not 1,25 applicable retensigned

terrsloned

stic

the values of y, are sum

le to the characteristic rcernent and prestre

f y, applicable to the for reinforcement is 1,OO.

istribution of forces

ars, the effectiv P

X

aclie=tiss for the klCti~nats ese may be refined, and

esul ts or specialist literature

" 0,6"i"takes mto account the ratio eWeen the characterrslic cube strength and khe bendceq strength in a fiexural member.

n a y be taken as

Vi W' Lhl CC: i- m

2 0 0 G P O F 0 9 T E N D O N S C O M P L Y I N G W I T H

$ S 5 8 9 6 ( 1 9 8 0 1 , R E F E R S P E C I F I C A L L Y T O S E C T I O N 2 , S W S S E C T I O P d I 3 ( b ) A N D T F i B L U 4 , % H I G H A P P L Y TO S T E E L W I R E , AND SECTIOPI 3 TO 7 - W I R E S T F E L S T R A W D

1 7 5 GPe F O R CoLD W O R K E D H i G i l T E N S I L E R L L O Y S T E E L B C R S COMPLYING W l T H BS 4 4 8 6 ( 1 9 6 9 ) A N D F 3 R T R E A T E D I S + - W I R E S T E E L S T R A N D C O M P L . Y I N G W I T H B S 4757 (1971 1 , S F G T I O N 3

ol analysis s h lexural stiffness ers sr itnit widt

kc~srcreH"ese~fi&~n:Tl~e entire crass-section of the n?ember i

(c) Me! transfoia~~cd ser:Cigun: The area of the cross-section $ha$ is trr cornpression, ther with the tensile rernforcemanl transformed on the basts sf t-nodrda;

nt approach shoui the dIfPsrs17r bsh wows of the various parts re. Axial, wrsio ~stants, when required by

qe Design Code, P,WI 5 1-MM7, Preruria. 9 u t h Afnca, 1989

box beams, if

se the effects of the most severe analysis of th structure. For uthoritative technical liter

he requirements of

B! DeSign C 3 7 . Prsloria. ca. 1989

TMt-7, Pretoria. W t h 1989

the ultimate and serviceabililry limit states.

esign of reinforced c verrred by the tiitirnate e limitations on crac licabie, stresses at "re

rnit state given in

lastic method or redistr t the ultimate limit stat

subjected to the "extreme" or "very e governed by the serviceabili

iven on the miraimum cover to rein- forcement that shoul ensure durabili

not make rec-

ad effects, including the effects of of Pap% l) far the bsltirn

actions" or 'biiitimate loads" and

f the "ultimate actions" or "ultima'ce loa "sewice ac t~~ t l s " or rt 2 and 2 2 07ii this

As above

ructural Frames

ccaadanee with the rec

moments abtatnecf h y rlgoroid.; elastic a rricd mrt, providcd It-le follswirlg cm

st be made to rasknre thaf there is a ere m?omerr%s e reduced, r ~ ~ a k i n g

sence OF a special Er~vestigation, "c12 plastic ro"aaQisn capacity may he

ss than 0,0 or r nxe !haat Q,O"I 5

hose calculated either

rnbers or elements considere roportionally reduc ess appropriate te

een t h

ed or continuous

smaller,

Y restraints

where d is the effective depth rweasured from the centr the extreme compression fibre

For cantilevers with lateral restraint prtrvided snfy at the s from the end of the cantilever to the face OF the sup 100bz/d, whichever is the smaller.

(a) Plane sections are assu lane when the str concrete in compression the strains !n the reinforceme ether in tensior? or compression is being

(b) The stresses in the concrete in eornpressron can strain curve in Figure 1 with ym = 1,s

(c) The tensile strength of the concrete can

(d) The stresses in the reinlorc mei% can be igure 2 with ym = 1 , f 5.

Alternative procedures may be adopted, namely

either (i) The ultimate morne f resistance is concrete strain at t utermosi: cam the ul'r~mate mame resistance is

the section shouid b the tenslie reirrirrrce

f rectangular section the neutral axis li

trains in the concrete the reinforcement c y the appiica- V

. The calculat in at the outer- l: compression fibre concrete should not excee tion, the section sho proporlioned such that the

of the tensile reinforcement is not less than f

except where the requirements for the calculated strain in the concrete, e to the application of 1 . l 5 times the ultimate loads, can be satisfied.

f a cross-section of a beam that has to resist a small axial thrust, ltimate force may be ignore if the force does not excee

ms are define !:h ratio of less 3 for continuous beams or 2 for simply supporte

sumption that plane sectio ing does not hold for dee this Code are not accurate. The transition -to-depth ratios is gradual an hods of calculating the non-lin

in distributions, and for adequate detailing of the reinforce- loads is significant, especially with large

charts that form Parts 2 an

tensile reinforcement.

f the elastic ultimate

Equation l , may Icuiated From @

1"he uktrmate m e taker? as the lesser a!' re by is the rhlcianess of "re flange

where V is th ue to ultimate loads

the minimum breadth of the secti ithin the effective depth d) d beam, should be take inirnurn rib breadth. If t ontains bars with diameters 9, greater than b/8, b should be

is the effective depth to tension reinforcement.

m of links, or links combined with bent-u th the followin

minimum reinforcement re uirernents, it is assume

S M link or a composite

for v 5 5,vc to

ultimate shear stress,

within a distarn

used, the main reii2torceme ec%ion consider ort and be pravid can adequately resist the ompvessive forces

e shear stress, wc, in

- 1 able 8 is derive from the foilowtny relatrunsirip

ttdinal tens~on reinf rcemenl lhat nce equal tu the

on reinfoicem f contrallexkire mated with the

eriding mamenrs shoriid be considered

used, the area of additional effectivcty rovided in the tensile zone* (additlanal

and axial zerisde lorcesj should be

Gy are as defined above

charactsrrstic str-engkih of tPe longitudirsal relirforceiner7t whici"~ not be taken ;S greater t n m 450 !Aka

for special cases, in particular

r shear reinforcement, not more

tension members of o

ny bar should be t ear resistance at Id be taken as the sum of the vertical corn onents of the n forces at the section, which is equivalent to usin

tion values. Bars should be checked for bearing stress (see 3.

lion.

The axial com load factors corresp

For a member subjecte F vc shall bs zero.

reater than 0.1 2 q U or cm a series The axial tensil

partial ioad factors correspondi

For the determination al' the e depth, "the carTlpsnerlts oE the

parallel to the shear sh c c w n t however,

hers the ts:siwnai resrstarlce c: srbffness ot sections (box-sections) are ta

ns of members, torsional design may be carried out as a check, after the esign. This is particularly relev nt to some members in which the maximum

torsionat moment does not occur under the same loading as the maximum flexural mornent. In such circumstances, reinforcement in excess of that required for flexure

r forces may b ed as part of the torsion reinforcement, if r moments c a m the restraint of angular rotat i~n are not necessary for equilibrium, may be neglecte timate limit state

t experience or analysis has shown that torsion will play

shear stress should be calc The lollowing stress limits must comply wi:h the requirements of 3.3.4.6 for combined

ional shear stress, v,, e provided. In no cas

ven in Table 9 and B, is defin

lygonal links effectively I. The closed links

that the closed links and

Bridge Design Code. P PMW7. Prstwia. South Africa, 1989

( X , + y, ) cot2 0, . . . . ................ ' ......... .. . . . . . . . . . . . . ("l 2)

where AS, is the crass-sectisr-i l area of one leg of a closed link provided ar section 10 resist torsion

S+ is the spacing of ahe ! inks

y, cs the larger centre-line d~mensisn of the links

Bridge 6asgt-7 Go&, Parf 3 TX4l-i 7 , Pretoria, %u%h Alnca, 1989

TlON OF COMPRESSIVE FORCES

reater than 450

IS t h e eross-s ilcioseti by the m

The reinforcement derwe ualions I I and 12 for i than-wailed box sections may, however', ai is actually requ Equat~~ras 1 l an

here kv, varies linearly from I ,

to cj,o tor ve 1

where klo = perimeter of Ao.

The dstaiiing req~iiremen"i of 3 3 4 5 shoiil still be observed

See 3 3 4 6 for &he comb~ned effects of "coilon arid shear m flarl

of bax-beams

sections %h& cannot be efficiently divrded into cam gies can be treated as equrvalent hallow sections with an etfectrve wall tl~ickgless

where de, IS the es% circle that car? be canbained within U,,

Ue, is the length 01 the mean polygonal pzrlrneter which is defined by ian Iincs of the eEective wails and encloses a cross-

Lsrialtudinai %) re~nfarcemeiat shaft be pkssit~o each corner at the tnl9rsection of the median lines, on

erinleter of the cross-seclioi~al area Apf l provided thal mintinurn cover of closed lrnks 1s maintained

" a f I , V E A N P E R I M E T E R U e f

nd .12a apply where

Ultimate torsional shear stress A

Br~dge Design Code, P m 3. TMW7. Pretoria, %ufh Africa. 1989

for rectangular sections, OP

far other sections, remains ~jnchange

where the ex n $he gsometrj of the cr n, the percent- location of $he steel, ai suall)~ less than 2 but

taken as i trnkss reliable data skippofling higher val~ie are available

fin

concrete on1

, C v 5 vmax sin

shear reinforcem ded together the

ments of Equation 13 need apply only to the ultimate, torsional and shear resistances of the concret for the relevant sectional properties and th allowed shear stresses v," and vmax respe 3.1.3 for definitions.)

dinal shear resistance d in accordant

provisions of Section 2

1 M W . Pretoria, &uth Afr~ca. 1989

The ultimate resis

be made for the f

In voided slabs, the stresse erse flexural r orcement due da transverse shear effects s h by means of a pr-opriate analysis (eg an analysis base ectisn acts as a Vierendeel frame).

t~on 04' in-plane

can be made by calculatrng the required Forces in "r?e directiof~s of re~nfearcemenf, so that adequate strength is provided in all d~rec~ ions

rap The shear stress, v, a$ any

is the shear force ue to ijltrmate ioa

~ i n d e i consideration

d is the effectiv

o shear reinforcement is re d when %he stress, v, ss less than <.;vc, ~$dher'e has is obta~ned frmn Table 7. rr eni-u:.,sncement Ew shear

strength may be allowed fa rsns within a d~stance a,d 2d from $he face of ,-I j The si-sear stress, v , in a solid slab bess than 20

Brldqe Design Code, Pxii 3 'i-Uiii-7, PI mm, South Africa. 1949

maximum shear stress, ,75 MPa, whichever is th

!st calculating shear stresses in slabs, any breadth being considered should lues due to lateral spreading of concentrated or non-uniform loads may be account, provided the assclmptions made are supported by a theoretical

erirnental test results. Ths dispersal of wheel taken only to the to surface of the concrete sla

of the loaded area, as shown in Figure 1 3, case axural rensile reinforcement in ve depths to the f l u

a cantilever sla

re of equal area.

shear force,

Bridge Design C d e , P m 3 TMH7. Pretoria. South Africa. 1989

where ZA,, IS the

f is the characteristicsnrer ear reinforcement Y V

t4 as not greater $ha

Values for sh r stress sh~wlcd be c ulated on perimete away f r c m Ihe critical perimeter an

factor

S E C T I O N

Br idp Desrqn Code, Part 3 TMtQ', Pretoria. South Wfnsa. 1389

ance with the provisiens of Secti

ed in accordarice with 3.

S

assumptions, for a columns with sym circular shapes The methods m case being considered rowided the effective height isd surate accuracy.

These rnetho S are generally conservative s n d the aaa"ysis may be refined by usmg more ccurale ~netho based on f i i rdarneni~l princ

I I relevant act~ons an effects into ac r ~ t Sum refii?en7enis woukl in the case of columns that da r10"icompiy wiEh ail the assurnpiions of these clauses, and In the case of c o l ~ ~ m n s with neat-r-syrnmclr1~3E cross-secbuns or ti;lrq~!17y (nor;-

rismatic) shapes.

here I, is th

: The effective height, L e , in a is the clear height be

le 10 are base assumptions

rotational restraint is at least 4( , (El), being the flex oducls of the equivalent modul he moment of inertia of the

rotational rigidity of elastometric bearin

here a more accurat evaluation of the effective h ffness values are le

from first principles.

movements und tcuiation chosen fo

for the columns using engineeri

s, arliculation systems,

Bridge Design Code. Part 3 TMH7. Pretoria, South Africa. 19

I D E A L I Z E D C Q L U M N B R 0 B U C K L I N G MODE

R E S T R A I N T S ---p

F O S I T I O N -v----

F U L L

-- -

F U 1- L"

FULL

----p-

i d L L

-

F i J L i

-

" J L L

-----p

N O N E

F lJ L L.

h 0 M E

FULL

N O N E

----p-

F IJL i..

k O N E

F U L L

-

TOP

F U L L " BOTTOM

T 6 P

--

B O T T O M

T 0 P

£38 l- TOM F U L I.. *

N O N E

FLICL"

+' A S S L I M E 0 V A L U E i S E E 3 . 5 L . 2

ed for the ultimate limit stat

lumn cross-section to de-

ssumed to remain plane hen the strain distri te in compression and the compressive an tensile strains in the

the above assumptions, m

TMM7. Pretotia. South Africa, 1989

f C cl is the characteristic cube strength of the concrete

adC is the assume epth of concrete in corn ression, subject to a minimum vaiu

is the area ef cornpressiori rei i~fsrcernef~t in the more i i ig l~ ly compressed face

is the stress in the r inforcement t r r the other tace, derived "irorn Figure 2 and taken as negative if lerisile

is the eross-sectional area of reir~forr:e!r?ent in the other face be eurrs~dered as being

ji) in compression

s the resultant eccei;"ricity of inacl irucreases and dc decreases from h to 2d"

h rs the depth of the section in ths plane of bending

d" th from the surface to Ihe rernfor-ceme~t in the more highly compressed face

1 , PLANE OF BENDING

1 -

A X I S OF .- BENDING

CROSS-SECTION 0

ltant eccentrici ot exceed 0,45fcub (h - 2e), only nominal reinforce-

see 3.8.4.1 for minimum pro ion of longitudinal reinforce-

are as defin of tension reinforcement vide resistant ent must be re

Bridge Dsagn Code, P TMH7, Pretwm. South Africa, 1989

nd My are the

MLIx and MYY apr x-x axis and

where ffcU and % YC

A a of concrete

ASC

ther caiumn sections, desi

Bridge Design Code, Pa-i 3 TMI-4Sq Preawia, Smdi Afrtca, 1989

lender column of con- signed for its ultimate

M,, is the initial moment due to ultimate loads, but may not be less than esponding to the nominal allowance for construction tolerances given

h% is the overall epth of the cross-section in the piane of bending M Y

e effective height either in the plane of bending or in the plane at right hichever is greater.

ends where no transverse loads occur may be reduced to:

M, is the smaller initial en te loads (assumed to be nt in double cuwature)

ultimate loads (assume

In $I ken as less th

hen the overall de dth hx, a slender column bent ltimate axial load,

Bridge Design Code. Part 3 T M H 7 , Pretoria. S a u t h Africa. 1989

where N is the esltiiriate axial b a d

average value in th

o ultimate loads sho ate shear stress, vc,

e cross-sectional ntire concrete secti

eccentricity of an column that results in ze (decompression) at an

for a rectangular co

is the eccentricity of the

Bridge Design Code, Par( 3 'TMQI7, Pretoria, South Africa, 1989

60 ultimate lrzla s for the X - x axis

ss a beam For the purpcsse oferat:k

t l rs a vertical (or near-veflical) load- bearing concrete mernbe l dirncns~en is rnore "ran four limes ifs lesser lateral e reinforcement is taken into account

y counted-inrts, sr as cantilevers supported ce with 3 4 In oeher cases, the clauses rven below apply

Rernlorcement must cornply with the conditions given in 3 reinforced wall should be considered as either sho or slender Simiidrly to columns, a wall of constant lhrckness may be cor-isidere here the ratio f its effecrive height does not exceed "1 lit. shoui thewise be considered 2s slender For wa l k with a

ore fa~ndamental reach may be necessary

ess The slenderness ralio is the ralih; of the effective height of the wall to its thickness. The effective height should he From Table 10 her? tne wall is restrained in posr'r~on at b3tk ends reinforcement c3mpliei; with the requirerneri;; OF 3 & 4, the ;Iend?iness r a m sm?uIci not exceed 40, unless I-are 'ban 1 slenderness ratio may be up 60 45 hen the wall is not restrained in

tio should nor exceed 30

Bricigi3 Design Code, Part aruj

TM117, Frs?ori;e, South A E n a , 1989

ments induced by deflection axial and horizontal forces along a

rmined by analysis and their ation of the bearings. For

by elastic analysis.

moment per unit length in the direction about an axis e plane of a wall) should be taken as ere nw is the

w?timate axial load per unit length and is the thickness of the wall. Moments in the all (ie about an axis normal to a wall) shoul be calculated for the most

relevant loads.

is non-uniform, consider effects" and the

be necessary to consider the maximum and minimum ratios I load in designing reinforcement areas and concret

S-sections of the various port priate ultimate axial load a

d in accordance ith 3.6.2. The assurnpti (see 3.3.2.1) apply and ar t bending only in the plane

jected to significant bending both in the plane of the wall ngles to it, consideration should be iven first to bending the plane of t r to establish a distribution of tension and com ression along the length of the

ension and com ion should then be combined ultimate axial loa

Bridge Besign Code, Part 3 HI, Pretoria, South Africa, 1989

is lamifs i f the

rack width should a caEcuEated in

S

bads and moments accurate methods, eg by an elastic analysis of a pi1 r by the application of

principles of soil mechanics, the faliowi made:

ase is axially Ioa ions "l oltirnate is to be uniformly distributed

(b) when the base is eccentr~caliy loaded, the reactions may be assume linearly across the ase For co ! i~mr~s an wails res"rrair?ed i movement at the ba , the mlamen"rtransfer d "i the base shou from 3.5.

The cr~tical section in the desrgn of the bottom r ~ ~ i l f ~ ~ c e r r e e n t of an isolated base may e taken as bemg at a d~stance of 0,15 times eke d mension of rhe ceiur-nn or wall,

endicularly inwards From &he face of %h$> C C O I U ~ F I oi" wall

The moment at any verlicat sectioi-1 ing ccsalpieteiy across a base should be taken as that reactions on an

-CONCRETE ST?UT

REINFCRCEVENT TIE

rea, in wPi;cll case th

The shear strength of the more sever escribed below.

(a) Shear along an

flexural reinfor

where av is the f the column or section

d is the effective eri is ion reinforcement,

een the lace o f the colid

apply.

revisions of 3 rnent in bases. The critical secticasls for local boisding are. (a) those descr~be

(b) sections at which the depth charges or any reinforcemei~"rstops, and

hose in the vicinity of piles, in reinforh;ement ieqkired to resist the pile reaction should be continued pile centre line and bo provided with an anchorage the centre line of 30 bar diameters.

The deflection of bases need no"ikie eonside:e bu:: the eefects G; c%ifferentir?i settlement on the structure as whole or in part shall hc taken rnlo ac-sisna

a

s appropriate, dependrr.19 on the type a!

.pa!pads aq lnoqs s!yl 'paJ!nbal S! sa3l24 iiu!o[ aql 40 uo!] jepads $1 .sassa~ls ~aqlo pue eays aql jo lunome anp aye4 plnoqs pue aqljo uo!pa~jp ay101 sal6ue 1q6!1 je aq Alle~aua6 plnoqs slu!o! uo!lm~lsuo=)

ua~!6 aq pjnoys uogeJ ~e~p e uo slu!o! uo!l essa3au S! t! uay

over to reinforcement S ould also be governed under the envisaged conditions of exposure. Table dense natural-aggregate concrete which shoula be p includ~ng links, when using the indicated grade of c tions of exposure, but subject also to the a it may be necessary to spec~fy the concret required durability, such as specifying t concrete subject to sulphate attack.

For factory-made precast components, the cover dimensio be reduced by 5 mm, but should not be less than 20 mm, where the cover should not be less than 30 mm. For compo or footings cast dry in contactwith soil, the cover dimension be increased by 25 mm; i f ey are cast und and if they are cast under ater against ca cover of in situ components cast in contac 40 mm.

here a surface treatment such as bush hammerir! concrete, the expected depth of the treatment should ta the nominal cover.

Special care should be exercised in conditions of extrenl concrete of low density or porous aggregates are used (see

fied otherwise in these clauses, the rec

.l ars: Subject to the reduction in arranged as pairs in contact or in bundles of hree or four in contact.

Bars in a bundle sh at different points, with the ends at least 40 times the bar size apart, for bundles stop one bar at a time i dle of three, but t cross-section ther more than four

les shc~uld not

reinforcement (gr

, should be taken as th

imum effective reiniorcemerit in F the gross section,

less than that cement. For other sl

etion in specific cases in uantities of reinforce

number of longitudinal bars provide in a column should be four in lar columns and six in circular columns, and their size or diamete S than 12 mm. The total cross-sectionzl area of these bars shod % of the cross-section of the colu ver is the lesser,

e ultimate axial loa

efinition a wall cannot be consider as a reinforce concrete wall i entage of vertical reinforcement provi is less than 0,4 % of the gross concret

SS-sectional area, in which case it sha considered to be a plain concrete wa S). In reinforced concrete walls the verlical reinforcement may be in on

on the forces acting on the wall.

rticular eondi!ions of exposure

agalnsh alternate

and sea-spray.

Surfaces sl-&leered 50 45 40 30 25

ie slab suffiis, beam sides and softits 017 whic!~ condensat!on

by vwater.pruofing or permanent formwork that will not weather or corrode;

interior surfaces of pedestrian

piers and colidmm on which condensa- tion is unlikely.

Concrete surfaces permanent ly satu-

by water with negligible aggressiveness*" to concrete.

nently tindei water

rain or aitemate drying and weltirg by water With negligible aggres- siveness"* to concrete.

All extemal Concrete 50 45 4 1 35 surfaces nor grade r w l sheltered cr permitted prc!ec led Pwn i ain,

bridge-deck soffits and interr'rhl surfaces on iwkrich condensation is likely.

Buried parts of structure or sur- faces in contact with backfill.

l

Concrete perma- nently under flowin

ater, ie abutment alls and founda-

tions and sub- merged piers in rivers.

oncrete parapets, Concrete 5 alls, all exposed grade not

surfaces of super- permi structures and sub-

-

arts of structures Concrete 6 5 contact with se ter, industrially

terrain.

ESridge Design Code. P IMW7, Pretoria, South Africa, 19

In beams or slabs where the depth of the side face excee reinforcement having an area of at least 0,05 of b,d should be provide face, with a spacing not exceeding 300 mm. However, in flat need not exceed 0,05 O/O of d2.

In a voided slab, the amount of transverse reinforcement sh of the following:

(a) in the bottom, or predominantly tensile, flange, either 1 500 rnrrr?/rn the minimum flange section;

(b) in the top, or predominantly compressive, flange, e~ther 1 000 mm2/m or of the minimum flange section.

The above-mentioned minimum flange ections required far calculatin verse secondary reinforcement shall be taken to the webs.

dditional reinforcement may be required in earns, slabs an shrinkage an thermal crackin

links: When, in a beam or column, part or all OF the main reinforcement resists compression, links or ties at least one-quarter of th of the largest compression bars should be provided at a maximum spacing times the size of the smallest compression bar. Links should be so arrange every corner and every alternate bar or group of bars in an outer layer of reinlorce- ment is supported by a link passing around the bar and having an included an not more than 135". All other bars or groups within a compression zone sho within 150 mm of a tied bar. For circular columns, where the longitudinal rei ment is located around the periphery of a circle, adequate lateral support is p by a circular tie passing around the bars or groups.

hen the designed percentage of reinforcement in the compression face of lab exceeds 1 %, links of at least 6 mm or one-quarter of the size of the I

compression bar, whichever is the greater, should be provided through the thi of the member. The spacing f these links should not exce thickness in either of the

ers reinforcemen

of the gross cros

vertical reinforcement should not exceed e concr'ete.

isted bar or a plain chamfered square ter than 18 times the nominal size of the bar.

r with transverse ribs at a substantial1 uniform spacing not greater continuous helical ribs where present). The bar shall have a

of ribs (per unit length) beyond its core (they are b ected on a plane rmal to the axis of the bar) of not less than 0 , I w mm2/

inal diameter) of the bar. The included angle of t the bar shall be at least 45".

be classified as the results of erformance tests. the test is to S rs, claimed to e equal to those

the classification, will possess the specified characteristic strength in a st. The criterion of comparison is that the free-end slip of the equivalent bar

an that of the geometrically defined bar. Tests shall be conducte h SABS 920, Section 6.5.

considered du

s e ent increases numerically in t s the effective

Stress $1

e considered to

manufacturer of the bar.

Ultimate anchora e bond stresses

( e ) any other met

bars lapped.

The length of of the smaller the size of th

s section as it is inten eber;

( i i ) the clear 150 mm;

ws (ij and jiiij occur, t

ss should the radius of any ben nteed by the manu cturer of the bar and, in

ient to ensure th the bearing stress at th

ntre-to-centre distance behve the plane of the bend; for a ba

) i f the shear capaci

ich the reinfor

ne or more of these con m load considered.

of the following:

the centre line of

tive anchorag

S: These recom related to bar sizes, but when a bar exceeds the maximum s

by more than 5 mm, a clear spacing smaller than th e avoided. A pair of bars in contact or a bundle of th

ontact should be considered as a single bar of equivalent area wh

The spacing of bars should be suitable for the proper compaction of n internal vibrator is likely to be used, sufficient S ce should be le

reinforcement to enable the vibrator to be inserted. nimum reinforc is best determined by experience or proper work titsts but, in the ab information, the following recommendations may be used as a guide.

) individual bars: Except where bars form art of a pair or below), the clear distance between bar hould be not where hagg is the maximum size of the coarse aggregate. or more rows:

(i) the gaps between corres ars in each ro e in a h e and

(ii) the clear distance except for recast members

B Design Code. P m 3 TMHY. Pretoria. South Afrim, i 489

s forming the pair are place be not less than happ + 5 mm.

(c) en rows of b

ere the depth of the side face t shall be provide

shall be distributed in 00 mm. Likewise, in the flanges f the main tensio ffective flange w

rectangular sections, the webs of without re-entrant angles, the design crack width a bers in tension (or, where the cover to the oute

on a surface at a distance cnom fr d from the foll wing equation:

is the distance from the poin the nearest longitudinal bar

norn is the required nominal cover to the tensile reinforcemen 12 (where the cover shown on the drawing i iven in Table 12, the latter value ma

here E, is the cal

is the breadth steel

9 is the moment at th toads

E, is the calcul stiffening effect of th

Mg is the moment a service loads

%ile reinforce-

is the cross-sectis irection

a, is the angle and the direction of moment.

rnt is applied in diMerent direclicsns

m is the number

Bridge D e ~ i g i i Cc&, Pan 3 TMW7, Preroa~a. *South Africa, 3989

E, is obtaine

al and local effects are calculate obtained by algebraic addition

The design crack width should then e calculated in accord may, in the case of a deck slab, where a global compression i

ith a local moment, be obtaine using (a), calculating cal moment on1

nsverse bars in slabs ith circular void um flange thickness.

ein e vent excessive cracking due to shrinkage and thermai movement, reinforce-

rrlenf should be provided in the direction of any restraint to such movements. For full nt, the area of reinforcement, calculated as a ercentage of the

section at right an irection of each restraint, should be not less than 0,5 O/O

50) reinforcement, or ,6 O h for Type

e minimum percentages of reinforcement are caiculated for cross-sections irnensions exceeding 500 mm in both directions, half the area of the core of the

ion more than 250 mm away from all concrete surfaces should be d. In slabs and walls, the reinforcement should be placed near the urface in both directions wi adequate concrete cover, or distributed

een the two surfaces as require Reinforcement that is present for other into account for the purpose of this clause.

partial, the reinforcement may be reduced accordingly, but shall comply other minimum einforcement requirements an ill be subject to the approval

the responsible idge authority. rrnanent bending moments use eccentric stress distributions temperature reinforcement

distributed uniformly arou not more than 300 mm.

1 General: ln

shear stress, vc, in concrete beams containing low-densi

ivlssr U750 in Equations 2 1,23,24 and

rage Dcild x d iap,

~d messes and lap lengths

actions" or "sewice loadsw respectively.

te actions" or "ulti

th of a section is

iven to the construction sequence an restress (but refer also to 2.2).

Bridge Design Code, Par1 3 H7, Pretoria, South

es should be used only if it has been demon the materials to be u s e

Specified characteristic strengtlls of restressing wire

&ridge Design Code, P* 3 TMHT, Pretoria, South A f n ~ a , I983

mina1 wire size

tic strengths of 7-H ---m-----

7 7 7

l

ion o S

rtical slings, type sB corlnecti

sections remain

necessary to calculate only the stresses en In Part 2 , immediately afterthe transfer0 prestress have occurred; in both cases the

oads on the strain and force in the tendons may be d tical cracking stresses given in Table 26.

ses in the concrete u n her stresses are

site construcli

T stresses in concrete for sewiceability limit states

Part 3 th Africa. 1989

lar or near-trian ion of prestress

(W ressive stresses in the concc

transfer.

nts of cracked

bel:avibur of concrete under biaxial or triaxial stress corld~ki~)i"i~ ie wl~en c017crete is subjected ro conlpres

skength 1s reduced 18 "ihe directions perpend~cular to rise

tendons.

Plane sections ar concrete in comp any additional r

all losses.

The stresses in the concr te in can~yression can be strain curve given in we 1 with ym = I ,5.

The tensile strength of the concrete can be

nal reinforcerr-re

rcernent in F i g u r ~ 2. t failure is given

either

irement for the calcul

* The neutral axis depth in these casss is too tow to provide the elongation iven in 4.3.3.1 . It is essential, therefore, that the slren rovided should exceed that prescribe

Values for f p b and X may be deriv for pretensicsned me post-tensioned members with el l provided that the effective prestress after all losses is not less

itional reinfcafscem ken using this method.

n ave additional

walysed using t h

lculations for shear are required only for the ultimate !imit

ses apply to Class 7 , Class il

ear resistance of

&idge Design C&e. P a t lj

t ten U l *I

al tensile stress,

t itiv

where

g3rovided that is taken as not less than Vd,

is %he effectwe prestress in a t e n d ~ n after all iosses h the appropriate values at (see 2 2 2) Far the 1s equation, tpe s h o ~ ! d he not greater than 0,6ipu

7 ) shoijld be taken as knc cross-sectional area of steel in !ha tension zone, irrzspective of its ci7aracteristic strengtn

is the distance from the Z C ~ ~ I ? I ~ ~ ~ S S I O I I face 10 file ceritroid ofthe steel

oment ilecessary rs praduce zero siress (decompressionj rrcrete a% the d

cteristic stren th of the tensione

f Y ~ P J i ristic strength of the untensione

C f e taken as not less than 0.1 b d c .

t is th tks as defined centre line of $he

: In post-tensioned s ltimate loads should not b

factor for the rce, to be taken as

is the horizontal corn force after all losses

deflections and/or stresse cialist literature sha

modifications.

hen prestressing steel is used sverse torsional steel, in accor Equations 1 1 and 1 1 (a), or as long in accordance with Eqknat

) , the stress assumed in desig the lesser af 450 M The compressive stress rn the concr to prestress sl? account separately in accordanc

(v + v,), for comparison with v," in Table 9, v sha

rades above 40, the value iven in Table may be increased t may not be greater than

str~rsture that is to e constructed in nal torsional steel is necessary, in

Bridge Dosign Cobe, Pan 3 TM W 4, Pr~loria, South Africa, 1989

i

I i TP as:

Design bursting tensile forces in en

, th rin

itional reinforcement for resistin

S 45" for links S V

the sum of the cross-secti S of the inclin

racteristic stren th of the incline

rcement taken into account should intersect the

face of the beams, tension face of the

PS

' h < the anchorage bond stress,

26~slsb

us is the sum of the effective perimeters of the reinforcement

ht reinforcement ond the intersecfi sured to the ben

, IhCLINE9 LINKS

ADDlT iONAL REINFORCEMENT TO RESIST HORIZONTAL FGRCES

(v) Most connections re

ring

stability of the structure

ecial materials; and

cified in full - here weld sym

urin

under the steel se

composite se

The longitudinal shea

nsit

site construction are

contact surface of the co in the precast m r i as riate.

e the concrete

surface of the precast u

cent

f," . .............................................................................. \ i

1 here is the curv

X

etlection at X .

obtained directly Iron this equation

M, + Mb p:---- -- * c -p

e n d d e f l e c t i a n n ( 3 - o l -P

6 f o o d a7 e n d K, -0,333

concrete. It is, ho

lasticity substa

nvenient to use the dynamic in an value for the static secant mo

ate concrete s of the static m is the density of

lion nor the values relatin are applicable to concret

Elastic moduli

lie

tical methods.

i t r UC@

EEP

COEF'FICBENT kL (C: ETE)

- cct f B, . ] ................................................................. c 0 ( t - t )

cct

COEFFICIENT k, (V UNCTl

d a coefficient for etric ratio of longitudinal reinf

S a function, \,

age values of k, c

concrete), the sa e c~efficients may

ef~niliora of effective "rickn

E F F I C I E N T ke (EFFEC

-- apply to pla~n (unreinfsrcedj ie membzr~ r t 3 ~

anlain~ns retnforc

m can

1 3 7 14 28 A G E AT F i4ST LOADING, j i , DAY

COEFFlClENT FOR AGE AT LOA;)ING, km

t the level of th

ue to relaxation of the steel must loss.

the relaxation th time of transfer.

The above approach assumes constant value the concrete from the time of of the same form as the c

re not reasonable, a step-by-step

restressed reinforcement shou the effects of shrinka I the non-prestress

he elastic and creep r

ep reduction coefficie

ilers or spaces ar entrats the radial