Bridge Besrgn C o d e . Part H i ' , Pretoria, S u l h Alnca. 1981)
... clions ..... ...... .. .. ,. General ............................ ....... .... ..... Ultimate limit stales ..............................
~. .~ .... .. .. ... .. ...... ~...... ... .. ..... ........,...... . ~ ...... . ............... ................................ , ~ " .
..................... ............ ...,. . . , * . . . . ..... ~~. .. tion ............... .... ....
...*........'.
.. ... ..
. " ..... ~ ~ . ~* . ~ ~ " . Materials ...................................... .*.... .,,,....-....." ~......~ .. . . . ..a . . , f~ "..................,..*.........,.,....................... * . ... , ~ ~ eneral .................................. ............ . . . . . . . . . . . . . . . . . . . . . . . . . . . ............ . . . . . I . L . . . . . . , . . . . . . . , . ~ ~ . ~ . . * ~ .......................... alues of .-".".
tructures
..... ....
. ..
..
..
.~
.. ....
.. eneral . . . . . . . . ~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , . L . . . . . . . . . . . . . ; I . . . ..........." ..,........ ltimate limit stat _,....... " . . . , ~. . . I . . . . I . . I ............. ._ . . , . . . I . . . . . . . . . . .... ..... .. ~. .. .. .. ... .... limit states ... ..... ....... ... .. .L
..L....I_.I.
eflection .............. ....................
... ..... ....
....
. ...".""........ . ~ ."".......
..........,....
tS
eneral ............................
nalysis
"..,~
~'....,.......
. ~ .~..."..." . ~ ~. .~ . "....*- ~ ~ ~ ....... ~ . ........"...'..". ures .............................. . " ~. ...*.... .... ..... ...-....~ . " . . ..... ... .. .. ......... ~. ~.. ~ ~ . , ., of sections ....... .. .. .. ".".,*.a
C R E T E ................... ..~ " , ~ .
. " I I . . . . . " " . . . . ~ " . . " I " L . . I r . , O . " I I I , . O . . , . . ~ . . . . " * " " . . / . . " . ' * " O I . . * I . 1 "
~~"..~~*~*.~.~..~"
..................................
" ~ . I I " 1 ' . . ~ , , L . r l . . * . r O I . . 1 _ " . " . . I . . . I 1 . ' . . " _ 1 . . I " ~ I . . . . , , " * * f . . t . s . 1 . . I
......
. . , , _ *
itudinal shear ...................~.*, ction in beams ............. ....... Crack control in beams ..... ..,.......... s
~
"
~
'
.
,
"
*
,.",....,-.......,,
o
~
s
.,...
...
....
. . / j . . . i l . , . - i_.....
...I
.l.,..I.
. . l O . . L . .
"
.
...", . . " ~ . *
~
~-.*"~~.-.~.,"*-..
..", " ~ ". . .. ~ ~ ~ . ~
~ ......... ~ ~ ~ .... ~. ~ ...,..~~....... - .~ .. " ~~ ~ .. ... ~~" . . *. .., "~. . . . ............................ ......., ~ . * ~ ... . ~ ~ ~ . ~ oments an shear forces in slabs ..,..,............. .... ab
~
. . I " I ' . . " ", . . . .
. Y . l . "
l..,l.
. . I j j , . . . , I" I . I "." ...I)
..
~
.
.
,
...i.. ........... '..,." .,.. "..'"......-...... " I * . " . * . . _ . I l..l..ll
,, ' ~ . ~ ~ . . . " ~ ..... "..,.~.." . ' .~"".... . ~ ..... . ~ "~~, . , . ~ , ~ . " . . ~ < " " " ~ " . . . . ....... .. ...< . . . . ~ . . . . " " ~ . " " . * . . " . ~ . ~.., r . . . " ..... . . . . . a .
...'._.. . " " " " " .. . I ." .......... ..
I.. ..
Columns General ............................
. ~
"
...9
. . . . . . I
.....I
".
..
.."" " ~ " . .. .....* ~ ~ . . ~.............~ - ~ . ~ . ~."-... .~~ . ~ " " ~ * ~ . . > ~ . ~ ~"~
........**..... .....,
. . ~ . . ~
. .
, . . . . " ~
. . ' n
D _
~
. I . . '
. . ~
. . , . . _
. . . . I
. ~
. . , . .
. I " .
. . . . . . . . . . I
. . . I . ~
. I . . .
. . ~
. ~
~
cross-section ............... * . " . . . " " ~.... ~~..~~ ................................*..~*9.. ...... '...".." . . . . . . . . . . . . . . ..
rectangular
or circular
. . S .
. I . . . I
eneral ...................
. O . . . , . , . . . I
,.
. . . . . . I . . .
~ . .... " .'..... . ..'.. , ~ .~ "....."". ~. ~ ~.........
aEls ...........................................-..'..*.". . ""..... .-.,.. ....* ~
. concrete wails ....................................
.....
mosraerats
axial forces ............................ .......... ,. ........" ....... .*.....~ . . .................... wails .,..... ...... ... ~. . . I . . . . . . . . . . . . I . i . . " .... ........ ....._........ ,.* .*... ... ..... .............................. ........... ...... ".*.."*.,.' "
.
*
I
.
.
"
. . l . . L I . . , I .
I
"."*
S) ...,~
.
.
"
.
.
.
~~
. ~ " " ~ " . ..... ~ . ~ . .~. . ~~. .' " ~ .~~ . . . ~' ~ *. ..." . "~~....'. ..~ .~~ ~
...................... ......................................... .... ... in bases .. ....... ......... ~~ " ~ .. . . ~ ~ ~ ." . .. .."*,."...".,. .,.........r..l.l_,,... I I ; ~ I ' . , ' " 1 . " * " . ~ ~ . . l . I " . r . . . 1 , j . . . " . " " . " " ~ ~ f ' , ~ . . " . " . . . . l . . t . ~ " . . ~ . l .
.................,.~.~.a..*.,,.
......."" ....
'..~
. " . " . . . . , . " . - . .~~~~ a-
..... ".... ~ " ~ . . ~ . erations affecting Desige-a Details ................... ........ .... "..." _j.I,l.I..I. "..'...... . I . . . . . oncrete cover I,.," . . _ . ~ " . ...,, rations ........................... ~.~.. ~ ~ ~ . . . ~ ~ . . ......., scenleni in members .., .... .... . . ..... ~. ~. of reinforcement in frrembers .. .... earing stress ................... rage reinforcernerrt .... .... ...... ....,. . * ~ . * " ~" .., ~ " ~ . ....-.
.lI"..."j.Ir.jr*
'
C . . ~ r . _ I I . . . . "
I.l,II
_ L . _ . . l . I L I _
......~.
,
.
9
9
9
9
9
9
9
9
9
9
9
.
9
9
9
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9
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9
9
.
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9
.
.
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.
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...........................................................................
........................................................................................................... ...........................................................................
........................................................................... ............................................................................. ams .......................... ....... ..
........................................................................... ...........................................................................
...........................................................................
........................................................................... and laps ....................... ...............................
...........................................................................
PRESTRESSED CONCRETE, CRETE .................................................. .............................................................................. .............................................................................. .. concrete ...................................... ..............................................................................
............................................................................. at Frames .................................................................
res ..................................................................................... nts ................................................................#............. ry moments ..................................................................
...................................................................................................
............................................................................ xure ....................................................................
............................................................................ ............................................................................
ts ............................................................................ ............................................................................... ther than friction losses .................... ....................... ...................................................
er ............................ ......... ...................................................................................................... erations affecting D esi Details ..................... .............................. neral ...........................................................................................................
...................................................................... ............................................................. .............................................*.............................
rat .................... uction ...............................%.
......................
tructural Connection eneral ..................... Continuity of reinforc Connections usin Other types of co
..............................................*..................... .
........
.......................................................... een U % $ S
........................................................................... .........................................................................
....
11
15
ser-ts ......................................................
.......................
..................................... 120
.......................................................... ................................................................ utmenis
......................... .........
...........
utmeilt ............................................
or abln"ln?ents .....................S................... ................................................................. .............................................................
........................ .............. uamerits ....................... ... ......... effects .................... ..............a. states ............................... ........
FO
COMF3LiANCE WITH ....................................................... 30
....
...................
.D
viii
12
TENDONS
iN
.................... 13
DLIGTS FOR
..................................................................
Bridge Design Code. TMH7. Pretoria South
Africa.
"1
........................................................
imil stat ...................................... acteristic stress for
..........................................................
in beams ..............................................................
............................................................................... stress .....................................................................
36
umns ...................................................................... ............................................................................ ment under particular conditions of exposure ...... ....................................................................... tresses ................................................................. 73 e perimete r of a grou p of bars ............................ 73 shear stress, in concrete beam s containing low-density ....................................................................................................... Maximum value of shear stresses in concrete beam s containing low-densit ............................
........................... ...........................
..........................
nventional) ....... ...................... ........ .................
87
87
....................
.........................
..........................
91
age
curve for concret
normal derlsiey
...........
steel reinforcement ..................
2'
Paw-relaxation steel .................
................................ $01 as-dra
21
steel wife ...................................................................... alues
.................. ....,...
3"
...........................
...............................
bearing ...............................
..........
bearirlg ........................
efinitiow of dimer?sioi~ at
.....S.......... 35 ....
.....................a......
.................
37
.........................................................
tinn of csbrnpressiva Forces .......... salid section .....................
ararneters fo shear in salid sHabs under concea\$rated oads ............................. .............
43
...................
........................
49
.................................................................. ...................................................... .................................................................
......................
..........................
tions) for creep at
41'7
...............
"636
time of ic~ading]............................
oncrete) ................................................... " 1 3 8 fo creep ...............................................
oefficieni k, variation as
function of time) ..............................................
aefFicient k, (environmental co ditiansj for shrinkage ................................. 14
hickness) to shrir~kage .................... Relaxation coefficient, oefficient Coefficient
oefficier~t
...............................................................
......................
(a)R aJ
........ .............
...................................................................
40) ...........................................................................
5) ...........................
............
145
recast concrete members.
eo
Effective thickness Thickness of Thickness of
Il
yed orneult diagram
Bridge Dosrgn Code, TMH7* P:e!cria,
,%uEh
Al nc~ , 98
Prestressed concrete: Prestressed
lassification requirements.
restress:
tensile stress
prestres s: tensile stresses
r the tensile fac e.
Bridge Design C d e , H7, Pretoria, South Alnca, 1989
Interior surfaces of erstructures or cellular ents or piers on nsation is unlike1 oncrete permanently under water
deck
soffits
arts of structures
an
in
I_-.--
in extreme environments
limitations are su mm arized in
ssed concrete "Ihan Lower values of stress are given for ole concrete c r o s s - s e c t ~ o n norm of excessive cre
values
ay
Des~gn Africa, TM1.47. PrePwia,
1080
fo the servicea
Interpolate between and 0,38
sections of approximately those uniform breadth
ssion
Not
applicabie
.a$
fo limiting flexural stresses in joints fo post-tension
ate an
feu
he characteristic values of acti tions) ar given in statistical data. the lack
combinations
to
shoui
cor-2sjderecl.
ivsn in 2.1.2.
erial.
nsaty may be
nalysis
loading,
structures: Ts determine th appropriate value
taken from
trans~en: permanent tr?zr, dalerrnine the deflectians, or th calculation ha grven in Table an l;i?if ihaevatiie
eater than Pt-iai ~ I V ~ E le 34 Appendix B) anaiysir; iscarrred termediate betflser~ dl-ie
th
effec~r
an a p p w haif that valide as
O ~ S ,
ng
ects
half
that %he ffect "ake values given
creep
' I
under short-term loadin
dvltegicanlate
between
Interpolate
eEween an
,3
1.67
flanges) rrifsrrn
Tension
or
near-uniform
1,33
ot
applicable
1,25
retensigned terrsloned
stic
the values of
re su
le to the cha racteristi rcernent and prestr
fo reinforcement is
applicable
to
th
1,OO.
istribution of forces
ars,
th
effectiv
aclie=tiss or
the klCti~nats
be refined,
esul ts
or specialist literature
0,6"i"takes mto account th ratio e W e e n th characterrslic cube strength strength in fiexural member.
be
taken
khe bendceq
Vi Lh
CC: i-
GPO
F
9
TENDONS
CO M P L YI N G
WITH
5 8 9 6 ( 1 9 8 0 1 , R E FE R
SPECIFICA LLY TO SECTION S W S S EC T I OP d I A ND T F i B L U 4 , %HIGH APPLY O STE EL WIRE, SECTIOPI WIRE STFE L STRAW
CoLD W O R K E D HiGil T E N S I L E 175 GP 4486 R L L O Y S T E E L B C R S COMPLYING WlTH ( 1 9 6 9 ) A N D F 3 R T R E A T E D I S+ -W IR E S T E E L S T R A N D COMPL.YING W I T H 4 7 5 7 (1971 SFGTION
ol analysis
lexural stiffness ers itnit widt
ntire crass-section of he n?ember kc~srcreH"ese~fi&~n:Tl~e
Me! t r a n s f o i a ~ ~ c edr:Cigun: Th area the cross-section $ha$ trr cornpression, ther with th tensile rernforcemanl transformed the basts sf t-nodrda;
approach shoui re Axial, wrsio
th dIfPsrs17r
w o w s of th various parts ~ s t a n t s , hen required qe Design C o d e , P,WI 1-MM7, Preruria. 9 u t h Afnca, 1989
box beams,
se the effects of the most severe analysis of th structure. For uthoritative technical liter
he requirements of
DeSign Prsloria.
1989
TMt-7,
Pretoria.
1989
the ultimate and serviceabililry limit states. esign of reinfo rced c limitations on cra rnit state given in
the tiitirnate
verrred
licabie, stresses at
lastic method or redistr the ultimate limit stat subjected to th "extrem e" or "very e governed the serviceabili
forcement that shoul
iven on the miraimum cover to reinensure durabili
make rec-
effects, including the effects of Pap% th bsltirn actions" or 'biiitimate loads"
the "ultimate actions" or "ultima'ce lo
"sewice a c t ~ ~ t l s " 2
7ii
this
As above
ructural Frames
with
the
re
rlgoroid.; elastic mom ents abtatnecf rricd mrt, providcd It-le follswirlg
be made to rasknre thaf there is m?omerr%s reduced, r ~ ~ a k i n g sence
ss than
0,
special Er~vestigation, c12 plastic ro"aaQisn apa city
r n x e !haat
Q,O"I
he
hos e calculated either rnbers or elements considere roportionally reduc ess appropriate te
ed or continuous smaller, restraints whe re d
is the effective de pth rweasured from th the extreme com pression fibre
For cantilevers with lateral restraint prtrvided snfy face from the end the cantilever to th 100bz/d, whichever is the sm aller.
(a) Plane sections are ass u concrete in com pression or compression is being
centr
th
lane when the str the strains reinforceme
(b) The stresses in the concrete in eornpressron ca strain curve in Figure with ym
The tensile strength o f the concrete The stresses in the reinlorc mei% can igure with ym Alternative procedures m ay b a d o p t e d , namely either
(i) The ultimate morne resistance is concrete strai utermosi: the ul'r~ma temame resistance is the section shouid the tenslie reirrirrrce
ether in tensior?
rectangular section the neu tral axis li
trains in the concrete com pression fibre
the reinforcem ent the appiicaThe calculat in at the oute rconcrete shou ld not excee
of the tensile re inforce me nt is not less than
except where the requirements for the calculated strain in the concrete, e to the ap plication o times the ultimate loads, can be satisfied. ltima te force m ay be ignore
f the force doe s not exc ee
are define :h ratio of less for continuous bea ms or 2 for simply s uppo rte sum ption that plane se cti ing does not hold for dee this Code are not accurate. transition -to-de pth ratios is gradual an hods of calculating the non -lin in distributions, and for adequa te deta iling of the rein force loads is significant, especially with large
charts that form Parts
tensile reinforcement. the elastic ultimate
Equation
1"he uktrmate
Icuiated From
taker? th rhlcianess of
lesser a!
lange
where
is
ue
to ultimate loads
the m inim um breadth of the secti ithin the effective depth d) d bea m, should be take inirnurn rib bread th. f ontains bars with diameters 9, reater than b/8, should is the effective depth to tension reinfo rcem en t. of links, or links comb ined with bent-u th the followin
minimum reinforcement re uirernents, it is assume
link or a com posite
for v ultimate shear stress,
5,vc to
within
distarn
u s e d , th main reii2torceme ort
pravid
adequately resist
ompvessive forces
ec%ion onsider
shear stress,
in
able
derive
from
foilowtny relatrunsirip
ttdinal t e n s ~ o n einf r c e m e n l l h a t nc equal tu th reinfoicem contrallexkire mated with th
eriding mamenrs shoriid be considered
used, th area of additional effectivcty rovided in th tensile z o n e * (additlanal axial zerisde lorcesj should be
re
defined above
charactsrrstic str-engkih of greater not be taken
tP
longitudirsal relirforceiner7t whici"~ Ak
for special cases,
in
particular
shear reinforcement, not m ore tension me mbers of ny bar should b ear resistance at Id be taken a s the sum of the vertical corn on ents th n forces at the section, which is equivalent usin tion values. B ars should b e checked for bearing stress (see
lion. axial com load factors corresp member subjecte
reater than series axial tensil partial ioad factors correspondi
vc shall
bs
zero.
.1
th determination al' th th d e p t h , "the carTlpsnerlts
parallel to the shear
ts:siwnai resrstarlce sections (box-sections) re ta
hers th
c c w n t however,
srbffness ot
ns of m em bers, torsional design m ay be carried out as a ch eck, after the esign. This is particularly relev nt to some mem bers in which the maximum torsionat mom ent does no t occur under the same loading as the ma xim um flexural mornent. In such circums tances, reinforcement in excess of that required for flexure r forces may b ed as part of the torsion reinforcement, if r m o m en ts c the restraint of angu ar ro ta ti timate limit state are no t necessary for equilibrium, may be neglecte experience or analysis has show n that torsion will play
shear stress sho uld be cal The lollow ing stress limits must com ply wi h the requirem ents of 3.3.4.6 for combine iona l shear stress, v provided. In no in Table is defin
lygonal links effectively I. The clos ed links
that the closed links and
Bridge Design C o d e . PMW7. Prstwia. South Africa,
1989
y,
cot2 0,
crass-sectisr-i area of
where
section
S+
y,
10
resist torsion
is the spacing
th
larger
. . ................
le
......... .. .....
(" 2)
closed link provided ar
!inks
centre-line
d~mensisn
links
TX4l-i
Bridge 6asgt-7 Go&, Parf
Pretoria, %u%hAlnca, 1989
TlON
COMPRESSIVE
FORCES
reater t h a n 450
ilcioseti
eross-s
or ualions I ai is actually requ
reinforcement d e r w e sections may, however', E q u a t ~ ~ r a s an
here
v,
where
cj,o
tor
perimeter
of
dstaiiing req~iiremen"iof
shoiil still
c o m b ~ n e d ffects of
3
of
than-wailed box
varies linearly from
to
Th
th
"coilon
be
arid
observed
shear
flarl
bax-beams
divrded into gies ca with an etfectrve wall tl~ickgless
where
sections efficiently cannot treated equrvalent hallow sections
es%ircle that
IS
car?
canbained ithin U,
mean polygonal pzrlrneter which defined ian Iincs of the eEective wails and encloses crosspkssit~o Lsrialtudinai re~nfarcemeiat haft each corner at tnl9rsection of th median lines, erinleter of the cross-seclioi~al A p f l provided thal mintinurn cover closed lrnks maintained the length
th
PERIMETER
nd .12a
Ultimate
apply where
torsional shear stress
B r ~ d g e esign C od e, P TMW7. Pretoria, % u f h Africa.
1989
rectangular sections,
fa other sections, remains ~ j n c h a n g e
where the
g s o m e t r j of th cr n, the percentlocation steel, suall)~ess than trnkss reliable data skippofling taken higher val~ie re available
in
conc rete
v m a x in shear reinforcem ded together the ments of Equation need apply only to the ultimate, torsional and shear re sistan ces of the con cret fo th relevant sectional properties and th allowed shear stresses v," a n d v m a x e sp e definitions.) 3.1.3
dinal shear resistance in
accordant
provisions of Section
Pretoria,
&uth
A f r ~ c a .1989
ultimate resis be m ade for th
erse means of
voided slabs, the stresse transverse sh ear effects (eg an analysis base Vierendeel frame).
orcement due pr-opriate analysis ectisn acts
t ~ o n in-plane
required Forces in "r?ed i r e c t i o f ~ s re~nfearcemenf, can be ma de by calculatrng that adequate strength is provided all d ~ r e c ~ i o n s
shear stress,
is the shear force
to ijltrmate
ioa
~indei is the effectiv o shear reinforcemen
re
strength may be allowed fa
less than <.;vc, ~$dher'e when %he tress, is o b t a ~ n e drm Table 7. eni-u:.,sncement shear of rsns within d~stance ,d 2d from solid slab bess than The si-searstress,
Brldqe Design Code, Pxii 'i-Uiii-7, S o u t h Africa. 1949
maximum shea r stress, ,75 Pa , whichever is th !s
calculating shear stresses in slabs, any breadth be ing considered shoul lues due to lateral spreading of conce ntrated or non -uniform loads m ay be accou nt, provided the assclmptions mad e are suppo rted by theoretical erirnental test results. Ths dispersal of wheel tak en only to the to surface of the co ncrete sla
of the loade d area, as show in Figure case e dep ths t th axural rensile reinforcem ent in cantilever sla
re of equal area. shear force,
Bridge Design C d e , TMH7. Pretoria. South Africa.
1989
where ZA,,
th th characteristicsnrer t4 greater
Values
for
stress sh~wlcd
away f r c m Ihe critical
ea
ulated
reinforcement
perimete
factor
SECTION
Bridp
Desrqn Code,
TMtQ', Pretoria. S o u t h Wfnsa. 1389
ance
ed in
with th
provisiens
of Secti
accordarice with 3.
assumptions, fo columns with circular shapes The methods rowided th effective height case being considered surate accuracy.
generally conservative th aaa"ysis may These rnetho fiirda rne ni~ l r nc refined by usmg more ccurale ~ n e t h o based effects to relevant act~ ons refii?en7enisw o u k l in th case columns that r10"icompiy wiEh il th assurnpiions of these clauses, ti;lrq~!17y nor;the case of c o l ~ ~ m n sit neat-r-syrnmclr1~3Eross-secbuns rismatic) shapes.
here
is th
The effective height, is the clear height be le 10 are base
in
assump tions
rotational restraint is at least (El), being the flex odu cls of the equivalent modul he moment of inertia of the rotationa l rigidity of elastometric be arin mo re accurat evaluation of th effective h ffnessvalues are le from first principles. here
movements und tcuiation ch ose n f for the columns using engineeri s, arliculation system s,
Bridge Design Code. Part
TMH7. Pretoria, South Africa.
19
IDEALIZED
BUCKLING
CQLUMN
RESTRAINTS
MODE
---p FOSI TION
-v----
FULL
-L"
TO
FULL
----pidLL
FiJLi
"JLL
-----p NONE
OTTOM
FULL
h0ME
BOTTOM
FULL
----pNONE
£38
SSLIME0
VALUE
IJL
kONE
NONE
FULL
FLICL"
fo
he
ultimate limit stat
lumn cross-section to de-
in
ssumed to remain plane the strain distri compression an the compressive an tensile strains in
above assumptions,
TMM7. Pretotia. S o u t h
Africa, 1989
the
cl
ad
characteristic cube strength of the concrete
is th
epth
assume minimum vaiu the
concrete in corn ression, subject to
th area ef c o r n p r e s s i o r i r e i i ~ f s r c e r n e f ~ t compressed face
more i i i g l ~ l y
th stress in th inforcement the other tace, derived Figure and taken negative if lerisile
is th ji)
eross-sectional area of reir~forr:e!r?ent in th e u r r s ~ d e r e d being in
other face
compression
th resultant eccei;"ricity of inacl irucreases
from
"irorn
to
decreases
2d
rs the depth
the
th from
section in
s u r f a c e to highly compressed face the
plane of bending Ihe
rernfor-ceme~t
the
more
PLANE
BENDING
AXIS
BENDING
CROSS-SECTION
ltant eccentrici ot exceed 0,45fcub se 3.8.4.1 for minimum pro
re as defin vide resistant
Bridge Dsag C o d e , TMH7, Pretwm. S o u t h Africa,
1989
2e), only nom inal reinforceion of longitudinal reinforce-
of tension reinforcement ent must
nd
are th
axis
MLIx
where
ffcU
YC
of concrete
ther caiumn sections, des
Bridge Design C o d e , P a - i TMI-4Sq Preawia, S m d i Afrtca, 1989
lender column of con signed for its ultimate
is the initial moment due to ultimate loads, but may not be less than esponding to the n ominal allowance for construc tion tolerances given
h% s the overall epth of the cross-section in the piane of bending effective height either in the plane of ben ding or in the p lane at right hichever is greater. ends where transverse loads occur may be reduced to:
is the smaller initial en
te loads (assum ed to be in double cuw ature) ultimate loads (assume
In
ke n as less th
hen the o verall de hx slender column bent ltimate axial load,
Bridge Design C o d e . Part T M H 7 , Pretoria. S a u t h Africa. 1989
where
is th
esltiiriate a x i a l
average value in th
o ultimate loads sho ate shear stress, vc,
cross-se ctional eccen tricity o an (decompression) at an fo rectangular co is the ec centricity of th
Bridge Design C o d e , Par( 'TMQI7, Pretoria, S o u t h Africa, 1989
ntire concre te secti column that results in ze
ultimate lrzla
ss
beam
fo th
the purpcsse
axis
oferat:k
vertical near-veflical) load dirncns~en rnore "ran four l i m e s reinforcement taken into account
bearing concrete mernbe ifs lesser lateral
counted-inrts, sr with In oeher
cantilevers sup ported cases, th clauses rven below apply
reinforced wall Rernlorcement must cornply with conditions given in slender Simiidrly to columns, a wall considered either should here th ratio its effecrive height constant lhrckn ess m ay be cor-isidere d o e s not exceed thewise considered slender For w a l k with lit. shoui necessary reach ore fa~ndamental
slenderness ralio ralih; of th effective height th wall to thickness. The effective height should restrained in posr'r~on b3tk ends From Table her? tn wall sm?uIci ;Iend?iness reinforcemen t c3mpliei; with th requirerneri;; not exceed 40, unless I-are 'ban slenderness ratio may be not restrained in the wall ti should nor exceed 30 The
TM117,
Bricigi3 Design Code, Part aru Frs?ori;e, South A E n a , 1989
me nts induc ed by deflection axial and horizontal forces along a rmine d by analysis and thei ation of the bearings. For by elastic analysis. mo me nt per unit length in the direction about an axis ere nw is the e plane of a wall) should be taken a w?timate xial load pe r unit length and is the thickness of the wall. Mo ents in the all (ie about an axis normal to a wall) shoul be calculated for the m ost relevant loads. is non-uniform, consider effects" and the be necessary to consider the maximum and minimum ratios load in designing reinforcement areas a nd concret
S-sections of the various port priate ultimate axial load a d in accord ance ith 3.6.2. Th e assurnpt (see 3.3.2.1) apply and ar bending only in the plane jected to significant ben ding both in the p lane of the wall ngles to it, consideration should be iven first to bending the plane o r to establish a distribution of tens ion and com ress ion along the leng th of the ension and com ion should then be combined ultimate axial loa
Bridge Besign Code, Part Pretoria, S o u t h Africa, 1989
is
rack width should
moments
accurate m ethods, by an elastic analysis of pi principles of soil mechanics, th faliowi made:
is axially Io be uniformly distributed
ions
by th
lamifs
th
a caEcuEated
application
oltirnate is
be assume (b) when base is eccentr~cali oaded, th reactions F o r c o ! i ~ m r ~ s wails res"rrair?ed linearly across the as base shou the mlamen"rtransfer move ment at the ba from 3.5. e n tisolated b a s e The cr ~t ica l ection n the desrgn of th bottom r ~ ~ i l f ~ ~ c e r r e an mension of rhe ceiur-nn wall, e taken as bemg t a d ~stan ce f 0,15imes ek endicularly inwards From of % h $ > C O I U ~ F I oi" wall
moment at any verlicat sectioi-1 taken as that
ing ccsalpieteiy across
b a s e should reactions on an
be
-CONCRETE
S T ?U T
REINFCRCEVENT TIE
rea, in wPi;cll case th The s hear strength of escribed below.
th more sever
Shear along an flexura l reinfor where av is th section is the effective
the column eri is ion reinforcement, ee
th lace o f t h e colid
apply. revisions
rnent in bases. Th e crit ica l secticasls for local boisding are. (a) those des cr~b (b) sections
which the depth c h a r g e s
any reinforcemei~"rstops, nd
the of in reinforh;ement ieqkired to resist the pile reaction should be continued pile centre line an provided with an anchorage the centre line of 30 ba diameters. in
bu:: the eefects The deflection of bases need n o " i k i e eonside:e c%ifferentir?i in part shall settlement on the structure whole taken rnlo ac-sisna
appropriate, dependrr.19on
type a!
over to reinforcement ould also be governed under the envisaged conditions of exposure. Table den se natural-aggregate natural-aggregate concrete whic shoula i n c l u d ~ n ginks, ginks, when using the indicated grade of c tions expos ure, but subject subject also to the a may be necess necessar aryy to to s pe c~ fyhe fyhe concret required durability, such as specifying concrete subject to to sulpha te attack. attack. For factory-ma factory-ma de precas t components, the cover dimensio be reduced redu ced by mm , but should not not be less than 20 wh ere the cover sho uld not be less than 30 For compo or footings cast dry in con tactw ith soil, the the cove r dimension dimension be increased by ey are cast und ater against against ca if they are cast unde r cover of in situ components cast in contac here a surface treatment such as bush hammerir! concrete, the expected depth of the treatment should cover.
the
nominal
at different p oints , wit the ends at least for bundles stop dle of three, three, but t mo re than four
imes
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
ars: Subject to the reduction in arranged as pairs in in contact or in bund les of hree or or four in contact. .l
Bars in a bundle sh the bar size apart, one bar at time cros s-se ction ther les les shc~ uld ot
reinforcement (gr
hould be taken as th
the gross section, cement. For other sl
less than that
etion in specific specific case s in uantities uantities of reinforc numbe r of of longitudinal bars provide in a column should be four in lar columns columns a nd ix in circular circular colum ns, an d their size or diam ete than 12 The total cross-sectionzl cross-sectionzl area of these these bars sh ver is the less er, of the the cro ss-section of the colu e ultimate axial lo
of
is
than ,4
n reinforced reinforced concrete concrete walls the verlical reinforcem ent may be in on on the forces acting on the wa ll.
rticular eondi!ions
Surfaces sl-&leered agalnsh
alternate
45
ie slab suffiis, beam sides and softits w h i c ! ~ ondensat!on
and sea-spray. sea-spray. by vwater.pruofing vwater.pruofing or permanent formwork that will not weather or corrode; interior surfaces pedestrian
piers an colidmm whi which ch condensac ondensation is unlikely.
surfaces p e r m a n e n t l y satuby water with Concrete
nently tindei water
negligible
aggressiveness*" concrete.
Concrete
Al e x t e m a l
grade permitted
surfaces nor
rain or aitemate drying an w e l t i r g
sheltered
negligible aggres-
bridge-deck soffits interr'rhl
water With
siveness"* to concrete.
prc!ec
led
Pw
ain,
surfaces on iwkrich condensation likely.
50
exposure
30
25
Buried parts of structure or surfaces in contact with backfill. Concrete permanently under flowin ater, ie abutment alls and foundations and submerged piers in rivers.
oncrete parapets, alls, all exposed surfaces of superstructures and sub-
Concrete grade not permi
arts of structures contact with ter, industrially
Con crete
terrain.
ESridge Design Code. IMW7, Pretoria, South Africa, 19
In beams or slabs where the depth of the side face excee reinforcement having an area at least 0,05 of should be provide face, with a spacing not exceeding 300 m m. Ho weve r, in flat d2 need not e xceed 0,05 O/
voide d slab, the amount of transverse reinforcement sh of the following: in the bottom , or predom inantly tensile, flange, either the m inimum flange section;
rnrrr?/rn
in the top, or predominantly compressive, flange, e~ th er 000 mm 2/m or of the minimum flange section. The above-m ention ed min imum 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 Wh en, in a b eam or column, part or all ma in reinforcem ent resists com press ion, links or ties at least one-quarter of th of the largest compression bars shou ld be provided at a max imum spacing times the size of the smallest compression bar. Links should be so arrange every corner a nd every alternate bar or group bars in an outer layer of reinlorcelink passing around the ba r and h aving an included an ment is supported not more than 135". All other bars or groups within a comp ressio n zone sho within 150 f a tied bar. For circular c olum ns, where the longitudinal ment is locate d around the periphery o f a circle, adequate lateral support is p by a circular tie passing around the ba rs or groups. links:
hen the designed percentage of reinforcement in the com press ion face of lab exceeds 1 % links of at least m or one-quarter of the siz of th comp ression ba r, whichever is the greater, should be provided through the th of the m emb er. The spacin these links should not exce thickness in either of th
reinforcemen of the gross cros
vertical reinforcemen t should not exceed e concr'ete.
isted bar or plain chamfered square ter than 18 times the nom inal size of
the
bar.
r with transverse ribs at a substantial1 uniform spacing not greater continuo us helical ribs where pre sen t). The bar shall have of ribs (per unit length) beyo nd its core (the y are b ecte d on plane rma l to the axis of the bar) f not less than 0 mm2/ inal diameter) of the bar. The included angle of the bar shall be at least 45". be classified as the results of erformance tests. rs, claimed to e equal o those the test is to the classification, will possess the specified characteristic strength in a The criterion of comparison is that the free-end slip of the equivalent b ar an tha t of the geom etrically de fined bar. Tests shall be conducte SABS 920, Section 6.5.
du
en
num erically in
th effective
Stress
increases
considered to
anufa cturer o th
Ultimate anchora
bar.
bond stresses
other
bars lapped. length of th smaller th size
eber; (ii)
section as
th clear 150
jiiij occur,
is
inten
ss s hould the radius of any ben nteed by the manu cturer the bar and, in ient to ensu re th the bearing stress at th
ntre-to-centre distance behve the pla ne of the bend; for
the shear capaci ic the reinfor
ne or m ore of these con load considered. of the following: the centre line of tive anchorag
These recom related to bar sizes, but when a bar exceeds the maximum s by m ore than a clear spacing smaller than th e avoided. pair of bars in contact or bundle of th ontact should be considered as a single bar of equivalent area wh The spacing of bars shou ld be suitable for the proper com paction of n internal vibrator likely to b e use d, sufficient ce should be le reinforcemen t to enab le the vibrator to be inserted. nimu m reinforc is best determ ined by experience or prope r work titsts bu t, in the ab information, the following recom men dations may be u sed as a guide. individual bars: Except
where bars form art of a pair or below), the clear distance betwee n bar hould be no where haggs the m aximum size of the coarse aggregate. or more rows: (i
the gaps between corres
(ii) the clear distance recast members
ars in each ro
na
nd
except fo
Design C o d e . Afrim,
TMHY. Pretoria. S o u t h
89
s forming the pa ir are place be not les than happ en rows of b
ere the dep th of the side face t shall be provide shall b e distributed in 00 mm . Likewise, in the flanges f the ma in tensio ffective flange w rectangular sections, the web s of without re-entrant angles, the design crack width bers in tension (or, where the cover to the o ute on a surface at a distance cnom d from the foll wing equation:
is the distance from the poin the nearest longitudinal bar norn
is the required nom inal cover to the tensile reinforce me 12 (where the cover shown on the drawing iven in Table 12, the latter value ma
here
E,
is the cal
is the brea dth steel
is th mom ent at t toads is the ca lcul stiffening effect of th moment service loads
Mg is th
%ileeinforce-
is the cross-sectis irection is the angle and the direction moment. nt is applied in diMerent direclicsns
is the number
Bridge D e ~ i g i i TMW7, Preroa~a. South Africa, 3989
is obtaine
al and local effects are c alculate obtained by algebraic addition The design crack width should then e calculated in acco rd may, in the case of deck slab, where a global compression ith a local mom ent, be obtaine using (a), calculating ca l mo me nt o nsverse bars in slabs um flange thickness.
ith circular vo id
vent excessive cracking due to shrinkage and thermai move men t, reinforcerrlenf sho uld be provide d in the direction of any restraint to su ch m ove me nts. For full nt, the a rea of reinforcem ent, calcu lated as ercentage o f the section at right an irection o f each restraint, should be not less than 0,5 for Type 50) reinforcement, or ,6 O/
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 mm away from all concrete surfaces should be d. In slabs and walls, the reinforcement should be placed near the urface in both directions adequate concrete cover, or distributed een the two surfaces as require Re inforcem ent that is prese nt for other into account for the purpose of this clause. partial, the reinforcement m ay b e redu ced accordingly, but shall comply ill be subject to the approval other minimum einforcement requirements an the responsible idge authority. rrnanent bending mom ents eccentric stress distributions tem pera ture reinforce me nt distributed uniformly arou not more than 300
General:
shear stress,
in
concrete beam s containing low-densi
ivlssr
rage
Dcild
messes
U750
Equations
ap,
la lengths
,23,24
actions" or "sewice loadsw espectively. te actions" or "ulti a section is
iven to the construction sequence an restress (b ut refer also to 2.2).
Bridge Design Code, Par1 H7, Pretoria, South
should th
used
materials to
only
if it
been demon
Specified characteristic strengtlls of restressing wire
&ridge D e s i g n C o d e , P* TMHT, Pretoria, South A f n ~ a , 98
mina1 wire
size
ti strengths
of 7-H
io
rtical slings, type
corlnecti
sections remain
necessary to calculate only the stresses en In Part immediately afterthe transfer0 prestress have occurred; both c a s e s th oads the strain and force in the tendons m y be tical cracking stresses given Table 26
in
stresses
Part th
Africa.
1989
in
the concrete her stresses are site construcli
concrete for sewiceability limit states
la or near-trian io of prestress
ressive stresses
(W
in th
concc
transfer.
ts
cracked
bel:avibur concrete under biaxial or triaxial stress corld~ki~)i"i~w l ~ e n 017crete subjected conlpres directions perpend~cular rise ihe skength reduced
tendons.
Plane sections ar concrete in comp any additional all losses. stresses in th concr strain curve given in tensile strength of
can~yression an with ym
in
concrete
be
reinforcerr-re
rcernent in F i g u r ~ failure given
either
irement fo the calcul
The neutral axis dep th i these ca sss essential, therefore, that the slren It
too to
provide the elongation iven rovided should exceed t h a t prescribe to
in 4.3.3.1
Values fo be deriv fo pretensicsned me post-tensioned members with provided that th effective prestress after less losses is itional reinfcafscem using this m e t h o d .
ave additional walysed using
lculations for shear required only fo th ultimate se apply to Class Class ea
!imit
resistance of
&idge Design C & e .
lj
te *I
tensile stress,
itiv
where
g3rovided that
less than
is taken
iosses ffectwe prestress in t e n d ~ n fter th appropriate values at (see Fa th equation, s h o ~ ! d no greater t h a n 0,6ipu
taken cross-sectional tension zone, irrzspective of it ci7aracteristic shoijld
area of steel
strengtn
in
!h
th distance from th
Z C ~ ~ I ? I ~ ~ ~ S S I O I I
oment ilecessary rrcrete he
file ceritroid of th steel
praduce zero siress (decompressionj
cteristic stren th of the tensione fY~PJi
ristic strength of the untensione taken as not less than
0.1b d c .
is
th
defined centre line of
post-tensioned ltimate loads should not In
factor fo is the horizontal corn
the
rce,
to
taken
force after al losses
cialist literature sh
deflections and/or stresse
modifications. prestressing steel is used sverse torsional torsional steel, in accor Equations 1 (a), or as long in accordance with Eqknat the the stress assum ed in desig th lesser af prestress The compressive stress rn th concr account sepa rately in accordanc (v
v,), for com parison with v," in Table 9,
rades above
th value greater than
iven in Table
str~rsture hat
torsional
increased
to steel
constructed
is necessary,
in
Bridge Dosign C o b e , Pan 4, r ~ l o r i a , o u t h Africa, 1989
TP
Design bursting tensile forces
in en
th
ri
itional reinforcem ent for resistin
for links the sum
the cross-secti
of the inclin
racteristic stren th of the incline rcem ent taken into account shou ld intersect the face of the beam s, tension face of the PS
26~slsb
the anchorage b ond stress,
the sum of the effective perimeters of the reinforcement ht reinforcement sured to the ben
nd the intersecfi
hCLINE9
LINKS
ADDlTiONAL
REINFORCEMENT
TO RESIST HORIZONTAL FGRCES
(v
Most connections
ring
stability of th
structure
ecial materials; and cified in full
here weld sym
urin
u n d e r th
steel se
com posite se
The lon gitudinal shea
nsit
site site co nstruction are contact surface of the co
the concrete
surface
the precas t
in the precast riate.
as
cent
..............................................................................
here
is th curv
etlection at obtained directly
Iron t h i s equation
M, p:---deflectian
n(3-ol f o o d a7
K, - 0 , 3 3 3
concrete. It is
ho
lasticity substa
nvenient to use the dynamic value for th static secant
ate concrete of the static m is th density of lion nor the values relatin are applicable to concret
Elastic moduli
li
tical methods.
EEP
COEF'FICBENT
ETE)
B, ( t - t )
................................................................
COEFFICIENT
UNCTl
k,
coefficient fo etric ratio of longitudinal reinf
function,
values of
concrete), th
c~efficients
ef~niliora f effective "rickn
EFFICIENT
ke (EFFEC
apply to p l a ~ n unreinfsrcedj
a n l a i n ~ n setnforc
i e m e m b z r ~ --
ca
AT
Fi4ST
COEFFlClENT
FOR
LOADING,
LOA;)ING,
the level of
loss.
time of transfer.
th
ue to re laxation of th steel mu st
the relax ation th
Th e above approach assume s constant value the concrete from the time o of the same form as the re no reasonable, a step-by-step restressed reinforcement shou th effects of shrinka he non-prestress
he elastic and cree p r ep reduction coefficie
or spaces ar entrats radial
ilers
