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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