Plate Element Concrete Reinforcement Analysis

Size: px

Start display at page:

Download "Plate Element Concrete Reinforcement Analysis"

Vincent Blair
6 years ago
Views:

Strand7 Rlas.4 Faturs Plat Elmnt oncrt Rinorcmnt Analsis Introduction oncrt is a widl usd construction matrial with high comprssiv t low tnsil strngths.

1 Strand7 Rlas.4 Faturs Plat Elmnt oncrt Rinorcmnt Analsis Introduction oncrt is a widl usd construction matrial with high comprssiv t low tnsil strngths. Its poor prormanc in tnsion must thror b addrssd b incorporating stl rinorcmnt in th ara whr tnsil strngth has to b nhancd; comprssion rinorcmnt is also somtims ndd to provid additional strngth and stinss. Strand7 provids a dsign modul to modl and anals rinorcd concrt structurs o custom gomtr and proprtis. An ovrviw o th rinorcmnt modul and an ampl ar includd hr. Ovrviw oncrt Rinorcmnt Laout (Proprt Stup hoos Proprt/Plat R. Th dialog bo that dins th rinorcmnt laout opns up. Thr can b up to 4 lars o rinorcmnt bars includd and dind or analss. Lar o stl bars is alwas paralll to Lar 3; Lar is alwas paralll to Lar 4. Lars and ar dind to b nar th surac o th plat lmnt, and Lars 3 and 4 nar to th + surac. Lars and (or 3 and 4 do not nd to b at right angls; th angl btwn thm can b dind during th application o th rinorcmnt attribut to th plat lmnts. Prsntd b Strand7 Pt Limitd 83

Strand7 Rlas.4 Faturs Gomtr Tab Laout Smmtric option spciis that Lar is closr to th surac than Lar. Anti-Smmtric option is whr Lar is closr to th surac.

Bar diamtrs Ths din th cross sctional diamtrs or stl bars rom Lar to Lar 4, illustratd as d to d4 in th dialog bo igur.

2 Strand7 Rlas.4 Faturs Gomtr Tab Laout Smmtric option spciis that Lar is closr to th surac than Lar. Anti-Smmtric option is whr Lar is closr to th surac. ovr Anti-Smmtric Smmtric c and c din th dpth (covr o th closst lar o stl bars to th or + surac o th concrt matrial rspctivl. Ths must b ntrd to din th dimnsions o th concrt or dsign purpos. Bar diamtrs Ths din th cross sctional diamtrs or stl bars rom Lar to Lar 4, illustratd as d to d4 in th dialog bo igur. Bar diamtrs automaticall bcom inactiv i not rquird b th intndd rsults calculations. Bar spacings Ths din th spacings btwn stl bars in ach individual lar, illustratd as s in th dialog bo igur. Bar spacings automaticall bcom inactiv i not rquird b th intndd rsults calculations. olours Stl bar dirctions will b displad on th plat lmnts with th colours dind. Each colour rprsnts lars in th sam orintation. oncrt Tab E Th modulus o lasticit o th concrt matrial or dsign purpos. ot that this valu is indpndnt on th modulus dind in Plat Proprtis. ε Th maimum allowabl outr ibr comprssiv strain on concrt with a tpical valu o in most oncrt 84 Prsntd b Strand7 Pt Limitd

Strand7 Rlas.4 Faturs ods (AI, BS80, AS3600, or 0.0035 in Eurocod, as illustratd in th dialog bo igur. c Th tru pa strss on th strss-strain curv o th concrt in comprssion; i.

3 Strand7 Rlas.4 Faturs ods (AI, BS80, AS3600, or in Eurocod, as illustratd in th dialog bo igur. c Th tru pa strss on th strss-strain curv o th concrt in comprssion; i.. usuall th strss valu at 0.00 ε comprssiv. φ Th total strngth rduction actor applid to c to ta account o th cts o long-trm loading on maimum comprssiv strss, illustratd as Φ in th dialog bo igur. This valu is spciid b th appropriat dsign oncrt ods,.g in Eurocod, or 0.6~0.8 in AS3600. (ot: additional actor ma b applicabl,.g. i Rctangular Strss Bloc is usd, an additional actor o 0.85 is rquird b th AS3600. Th partial sat actor or concrt with a tpical valu o.5 spciid b Eurocod, illustratd as in th dialog bo igur. c ot: th quotint is th ctiv dsign concrt pa strss, which is th charactristic comprssiv clindrical strngth at 8 das, c, in AS3600. Stl Tab E Th modulus o lasticit o th rinorcmnt stl matrial or dsign purpos. Th tru ild strss or th stl bars. Elastic-Prctl Plastic rlationship is assumd or th stl. Th partial sat actor or rinorcmnt with a tpical valu o.5 spciid b Eurocod, illustratd as S in th dialog bo igur. As_b (bas Th stl rinorcmnt is rprsntd as a uniorm lar o a constant thicnss, sandwichd btwn concrt lars. Th minimum cross sctional ara o th rinorcmnt pr unit lngth o th slab, usuall spciid b various concrt cods, is thror dind as th ratio o quivalnt thicnss o stl bars t S to concrt slab thicnss t, as shown in th igur on th right. ts t As _ b ( bas ts t ot: Th ctiv dsign stl strss s is tan as S. Prsntd b Strand7 Pt Limitd 85

considrs onl omnts as shown in dialog bo igur; It considrs onl th tnsiond stl bars locatd in th tnsil part o th concrt sction.

4 Strand7 Rlas.4 Faturs 86 Prsntd b Strand7 Pt Limitd Rsults Tab Rsults Tab Rsults Tab Rsults Tab thod Simpliid (bnding onl consists o 3 basic aturs: It considrs onl omnts as shown in dialog bo igur; It considrs onl th tnsiond stl bars locatd in th tnsil part o th concrt sction. It uss a rctangular strss bloc in th comprssiv concrt rgion. alculation procdurs ar as ollows: d F F A F F S S S S φ d d φ φ φ φ Th ollowing quadratic is solvd or : 0 + d φ φ Various rsults can thn b drivd,.g. amount o stl rquird i bar spacings ar givn. Rctangular Strss Bloc

5 Strand7 Rlas.4 Faturs Prsntd b Strand7 Pt Limitd 87 I th rctangular strss bloc is not dsird, and/or mmbran orcs ar to b considrd, and/or th comprssion stl bars ar to b considrd, thn th ollowing mthod can b slctd. Elasto-plastic itration rplacs th rctangular strss bloc with a bilinar lastic-plastic strss-strain curv or th concrt, dtrmind rom th valus E and ε ntrd in th oncrt Tab. Although Eurocod rcommnds th us o parabolic-rctangular shap strss bloc, th us o lastic-plastic and rctangular strss blocs ar also allowd as dirncs ar usuall not vr signiicant. A similar bilinar lastic-plastic strss-strain curv is usd or th stl. Itrativ Solution o Rinorcd oncrt Th nonlinar matrial bhaviour o a stl rinorcd concrt slab, whr th stl is rprsntd as a uniorm lar o a constant thicnss, can b dtrmind b using a lard approach, similarl to th laminatd composit matrial. For th rinorcd concrt analsis, th slab is dividd into a numbr o thin lars with ach lar bing ithr concrt or stl, dpnding on th rinorcmnt laout. This approach allows us to considr both mmbran and bnding loads on th composit. Th constitutiv quation or th slab and concrt composit can b dscribd b κ ε D B B m whr h h h h d d / / ( ( ( τ σ σ τ σ σ is th rsultant orc vctor, which has units o orc pr unit lngth, and h h h h d d / / ( ( ( τ σ σ τ σ σ is th rsultant momnt vctor, which has units o momnt pr unit lngth. and ar obtaind rom th init structural lmnt solution as strss and momnt rsultants on th plat lmnt. is th tnsional stinss matri (mmbran lasticit matri dind b ( h h Q D is th bnding stinss matri dind b ( h h Q D and B is th tnsional/bnding coupling matri dind b ( h h Q B whr Q is th lasticit matri or lar (which ma b ithr concrt or stl, and th matrics, D and B ar all smmtric. m ε is th mid-plan mmbran strain vctor and κ is th plat curvatur vctor. In th cas o nonlinar matrial bhaviour (both concrt and stl, Q is a unction o th strain in th lar,

Strand7 Rlas.4 Faturs lading to a st o nonlinar quations which ma b solvd using standard wton-raphson itration.

I Includ mmbran orcs is activ, thn th Forc illustratd in th dialog bo igur will b considrd in th itrativ procss togthr with th omnt.

$reo (c...at or matrial libraris and.bsl or bam sction libraris and should b locatd in th...\data oldr o th installd Strand7 dirctor.$ Proprt Application (Attributs Stup hoos Attributs/Plats/oncrt Rinorcmnt. Slct th appropriat Rinorcmnt Laout dind in proprt rom th dropdown mnu.

Proprt Application (Attributs Stup hoos Attributs/Plats/oncrt Rinorcmnt. Slct th appropriat Rinorcmnt Laout dind in proprt rom th dropdown mnu.

6 Strand7 Rlas.4 Faturs lading to a st o nonlinar quations which ma b solvd using standard wton-raphson itration. ot that although ach pl in th rinorcd concrt composit ma hibit nonlinar strss-strain bhaviour, th assumption o linar gross strain variation through th slab thicnss is mad. I Includ mmbran orcs is activ, thn th Forc illustratd in th dialog bo igur will b considrd in th itrativ procss togthr with th omnt. Allow comprssion rinorcmnt mans that comprssiv stl bars will also b includd whr rquird to shar th comprssiv loads. Rinorcmnt Librar Similar to th Strand7 matrial and sction libraris, rinorcmnt laouts can b rad rom and stord to a rinorcmnt databas or as o accss in othr modls. Th rinorcmnt libraris hav th tnsion.reo (c...at or matrial libraris and.bsl or bam sction libraris and should b locatd in th...\data oldr o th installd Strand7 dirctor. Proprt Application (Attributs Stup hoos Attributs/Plats/oncrt Rinorcmnt. Slct th appropriat Rinorcmnt Laout dind in proprt rom th dropdown mnu. Th orintation angl o Lars is an angl in dgrs, btwn th plat lmnt s local -ais and th dirction o th rinorcmnt on lars. Lars, 4 Lars, 3 Aligning Rinorcmnts Th rinorcmnt dirctions can b modiid b changing th lmnt s local ais dirction, or b stting dirnt angls in th attribut dialog bo. Th rinorcmnt alignmnt tool is vr usul or th aligmnt o rinorcmnt dirctions on larg modls. hoos Tools/Align/Plat Rinorcmnt Dirction to opn dialog bo or aligning tool. This tool allows th orintations o th rinorcmnts to b modiid according to an dsird coordinat sstm. ot that a coordinat sstm must b dind bor th alignmnt can b mad. 88 Prsntd b Strand7 Pt Limitd

7 Strand7 Rlas.4 Faturs Lars, 3 Lars, 4 Aligning Etracting Rsults ontours Thr ar various rsults options availabl or th rinorcd concrt modul. hoos Rsults/Rsults Sttings and slct ontour undr Draw as, and R undr Quantit. Thr is also a usul Unit button, which allows th slction o prrrd units to b displad in th rinorcmnt contour. Prsntd b Strand7 Pt Limitd 89

8 Strand7 Rlas.4 Faturs Wood-Armr omnts Ths ar momnts to b rsistd b ach lar o rinorcmnt calculatd according to th publishd quations, which allow dsignrs to ma allowanc or plat bnding and twisting momnts whn dsigning th rinorcmnt within a rinorcd concrt panl. Th approach assums that on dirction o rinorcmnt is alignd with th ais o th plat. Th scond dirction nd not b orthogonal to th irst. Th scond dirction o rinorcmnt (transvrs rinorcmnt is dind as bingα dgrs rom th rinorcmnt masurd anti-clocwis rom th rinorcmnt. Th quations calculat th momnt in th andα dirction that th sction nds to b dsignd to withstand. Ths trms ar dind as and. Strand7 uss th ollowing plat convntion: α F F α F F This convntion should b usd whn using th quations dind hr. and momnts ar bnding momnts. Bottom Stl: is a twisting momnt. + cotα + cotα + cot α + sinα + cotα α + sin α sinα i < 0 thn i 0 ( + cotα + + cotα + cot α and α sin α i α < 0 thn i α 0 and + cotα + cot α + ( + cotα 90 Prsntd b Strand7 Pt Limitd

9 Strand7 Rlas.4 Faturs Top Stl: α Stl (As sin + α cot α + + i > 0 thn i 0 + cot α + and α sin α i α > 0 thn i and + sin α cot α ( + cot α α 0 cot α + cot α + cot cot α sin α α ( + cotα This is a contour that givs th rquird rinorcmnt or a balancd sction supporting th calculatd momnt and mmbran orcs i spciid. Th contour can b calculatd at ach lar and can b prsntd in on o iv dirnt was. /Lngth: Th total amount o rinorcmnt stl rquird in trms o total cross sctional ara o th stl bars pr unit lngth in th dirction prpndicular to th ais o th stl bars. Spacing: Basd on th nominal bar diamtrs dind in th rinorcmnt laout, spacing btwn th stl bars is calculatd, illustratd as s in th dialog bo igur. Bar diamtr: Basd on th nominal bar spacings dind in th rinorcmnt laout, bar diamtrs or th chosn lar ar calculatd. /A_slab: Th ratio o th rinorcmnt cross-sctional ara to th cross-sctional ara o th slab. /A_bas: Th ratio o th amount o rinorcmnt to th bas amount spciid in th rinorcmnt laout. I this valu is gratr than, it indicats that th bas amount o rinorcmnt spciid b th ods is insuicint. Stl (As lss As_b This is a contour that givs th tra amount o rinorcmnt rquird in addition to th bas amount o stl spciid in th rinorcmnt laout. Th contour is th sam as Stl (As, but th valus hav th bas amount subtractd, i.. As - As_b. Stl Strss (Usr Th strss o ach lar o stl rinorcmnt ma b contourd. For this contour, th stl proprt dind in th rinorcmnt laout is usd to dtrmin th strss du to th momnts. Th rsults can also b viwd b using P, Listing and XY Plots. cot α Prsntd b Strand7 Pt Limitd 9

10 Strand7 Rlas.4 Faturs Eampls Two ampls ar includd to dmonstrat th unctionalit o th Rinorcd oncrt modul. Eampl Singl Rinorcd Rctangular Bam 300 mm This ampl shows th mthod o stting up a rinorcd bam b using a plat modl with rinorcmnt attributs assignd. Th stl strss, minimum rquirmnts o stl in trms o ara/lngth, spacings, diamtrs and ratio o aras, as wll as th ctiv dsign bnding momnts ar calculatd without od spciic constraints. 450 mm 390 mm 3 X 4 Bars Eampl Doubl Rinorcd T-Bam with Dsign Factors 60 mm 000 mm alculations ar prormd on a T-bam to dtrmin various rsults basd on od spciic dsign critria with th inclusion o both comprssiv and tnsil rinorcmnt. Du to th gomtr ost, mmbran orcs ar pctd to b gnratd in addition to th bnding momnt; hnc, th mmbran orcs ar includd in th Elasto-Plastic Itration option. 90 mm 7 X 0 Bars 6 X 8 Bars 0 mm 800 mm 300 mm 9 Prsntd b Strand7 Pt Limitd

11 Strand7 Rlas.4 Faturs Eampl : Singl Rinorcd Rctangular Bam Th rinorcd rctangular sction on th right contains thr 4 (450 mm bars or bottom rinorcmnt. A positiv bnding momnt o 0 5.mm is applid and comprssion rinorcmnt is not mplod. Find: a Th Stl Strss basd on th coniguration shown on right; b Ectiv Dsign omnt to rsist b th rinorcmnts; c inimum rinorcmnt Spacings i 4 bars ar usd; d inimum rinorcmnt bar Diamtr i spacings o 00 mm ar usd; inimum ara o rinorcmnt pr lngth. inimum ara ratio o rinorcmnt and concrt. 450 mm 390 mm 300 mm 0 5.mm 3 X 4 Bars atrial proprtis ar: 3 Pa, E 3000 Pa, E S Pa, SY 500 Pa. To p th modl simpl, a singl Quad8 plat lmnt is adquat. odl Prparation hoos Fil/w. hoos Global/Units and st mm. hoos rat/od: od : (0,0,0 od : (300,0,0 hoos rat/elmnt and crat a bam lmnt conncting nod and. hoos Tools/Etrud/b Incrmnt and trud th bam lmnt into a plat lmnt, with Incrmnts Y st as 300, and Sourc st as Eras. hoos Viw/Entit Displa and chc Draw As and slct Orintation undr Draw As in th Plat tab. hoos Attributs/od/Rstraint and i all dgrs o rdom o nod and nod 3. hoos Tools/Subdivid, st Quad8 as th Targts Plat and Divisions A and B to, thn applis to th onl plat lmnt in th modl. hoos rat/lin, slct Rigid rom th drop down mnu, and crat XYZ rigid lins to nod, nod 7, and nod 4. hoos Attributs/od/omnt, appl a 8.mm o Y omnt to nod 7. hoos Proprt/Plat, choos atrials.. and slct AS3600 (994 oncrt - omprssiv Strngth 'c 3 pa rom th matrial librar, and ntr 0 or th Poisson s Ratio to clud th Poisson s ct. Entr a mbran Thicnss o 450 mm in th Gomtr tab. Prsntd b Strand7 Pt Limitd 93

Strand7 Rlas.4 Faturs Th modl can b solvd; choos Solvr/Linar Static and clic Solv. Basd on this, th rinorcmnt concrt modul prorms urthr calculations to produc th rinorcmnt rsults.

12 Strand7 Rlas.4 Faturs Th modl can b solvd; choos Solvr/Linar Static and clic Solv. Basd on this, th rinorcmnt concrt modul prorms urthr calculations to produc th rinorcmnt rsults. Rinorcmnt Application hoos Proprt/Plat R and crat a rinorcmnt laout with th dault nam, thn ntr th ollowings into thir rspctiv clls undr th Gomtr tab (not th laout is spciid in th plat local ais sstm: Bar diamtr : sqrt(4504/pi Bar spacing : 300/3 ovr c : Undr th oncrt tab, th dsign paramtrs ar adjustd as ollows, sinc w ar onl intrstd in th unscald stl strsss: E : 3000 ε : 0 c : 3 φ : : 94 Prsntd b Strand7 Pt Limitd

Strand7 Rlas.4 Faturs Undr th Stl tab, th dsign actors ar not considrd or this ampl: E : 00000 : 500 : As_b (bas : 0 Undr th Rsults tab, Slct Simpliid (bnding onl sinc th comprssiv rinorcmnt is absnt.

hoos Attributs/Plat/oncrt Rinorcmnt, slct : Rinorcmnt Laout rom th dropdown mnu and assign this laout to th plat lmnt.

13 Strand7 Rlas.4 Faturs Undr th Stl tab, th dsign actors ar not considrd or this ampl: E : : 500 : As_b (bas : 0 Undr th Rsults tab, Slct Simpliid (bnding onl sinc th comprssiv rinorcmnt is absnt. Th Elasto-plastic itration mthod can also b chosn and th rsults ar pctd to b similar. hoos Attributs/Plat/oncrt Rinorcmnt, slct : Rinorcmnt Laout rom th dropdown mnu and assign this laout to th plat lmnt. You will onl nd to align Lar to th local -ais o th plat lmnt, which is 0 dg orintation. Etracting Rinorcmnt Rsults hoos Rsults/Opn Rsults Fil and opn th appropriat rsults il. hoos Rsults/Rsults Sttings and slct ontour, and thn slct R. Various options ar availabl and th rquird rsults can b contourd. a Stl Strss (Usr Lar : Pa b Wood-Armr omnts Lar : mm/mm (not: momnt to b rsistd b rinorcmnt in lar is 0 in this cas; t, ou should pct a small dsign momnt in lar i Poisson s ratio was st to a non-ro valu. c Stl (As Lar Spacing: mm i 4 is usd and just starts to ild undr th dsign momnt (minimum rquirmnt is approimatl.5 tims th spacing w spciid as th ild strss is roughl.5 tims th stl strss or th currnt coniguration. d Stl (As Lar Bar diamtr: mm i 00 mm spacing is usd and just starts to ild undr dsign momnt (minimum rquirmnt is approimatl (/.5 / tims th bar diamtr w spciid. Stl (As Lar /Lngth:.8395 mm /mm is th minimum ara o rinorcmnt pr unit lngth. Stl (As Lar /A_slab: is th minimum ara ratio btwn rinorcmnt and th gross concrt ara. This valu is usuall rstrictd to b at last 0.0 in th dsign od, which mans that th basic od rquirmnt is mor than nough in this cas. ot: ou can chang th displa units into a prrabl st; this can b don b clicing th Unit button, and slct th prrabl units or ara and lngth. You can also tract rsults using P, Graphs, and Listings, P rsults is shown in th ollowing: Prsntd b Strand7 Pt Limitd 95

14 Strand7 Rlas.4 Faturs Eampl : Doubl Rinorcd T-Bam with Dsign Factors Th rinorcd T sction on th right contains si 8 (60 mm bars or th bottom rinorcmnt and 7 0 (30 mm bars or th top rinorcmnt. A positiv bnding momnt o mm is applid. From th Eurocod limits onwards, invstigat th charactristics o th sction with th dcras in concrt and stl strngth. 60 mm 90 mm 7 X 0 Bars 000 mm 0 mm mm 800 mm 6 X 8 Bars 300 mm atrial proprtis ar: 3 Pa, E 3000 Pa, E S Pa, SY 500 Pa. Th Eurocod constraints ar: Φ 0.85,.5, S.5, ε , A S /A 0.0. Four Quad8 lmnts ar usd to modl th problm. W will us th Elasto-plastic Itration mthod to obtain rinorcmnt rsults du to th prsnc o comprssion rinorcmnt and th mmbran orcs. odl Prparation hoos Fil/w. hoos Global/Units and st mm. hoos rat/od: od : (0,0,0 od : (000,0,0 hoos rat/elmnt and crat a bam lmnt conncting nod and. hoos Tools/Etrud/b Incrmnt and trud th bam lmnt into a plat lmnt, with: Incrmnts Y st as 350, and Sourc st as ov; Incrmnts Y st as 300, and Sourc st as ov, Proprt Incrmnt st as ; Incrmnts Y st as 350, and Sourc st as Eras, Proprt Incrmnt st bac as 0. Du to dirnt thicnsss btwn plat lmnts, th middl plat lmnt o proprt tp shall b ost b 400 mm. hoos Attributs/Plat/Ost, ntr a valu o -400 mm and appl to th middl plat lmnt. hoos rat/elmnt, and slct Quad4 with Proprt st as, and crat a plat lmnt b joining nods 3, 4, 6, and thn 5. a sur local as o all plat lmnts ar alignd. hoos Attributs/od/Rstraint and i all dgrs o rdom o nods, 3, 5, and 7. hoos Tools/Subdivid, st Quad8 as th Targts Plat and Divisions A and B to, thn applis to all plat lmnts in th modl. hoos rat/lin, slct Rigid rom th drop down mnu, and crat XYZ rigid lins to nods,, 4, 4, 6, 7, and 8. hoos Attributs/od/omnt, appl a 4.58.mm o Y omnt to nod 4. hoos Proprt/Plat, choos atrials.. and slct AS3600 (994 oncrt - omprssiv Strngth 'c 3 pa rom th matrial librar, and ntr 0 or th Poisson s Ratio to clud th Poisson s ct or all plat proprtis. 96 Prsntd b Strand7 Pt Limitd

15 Strand7 Rlas.4 Faturs Entr a mbran Thicnss o 0 mm and 680 mm in th Gomtr tab or plat proprt and rspctivl. hoos Solvr/Linar Static and clic Solv. Top Plats Bottom Plat As shown in th igur abov, mmbran orcs ar prsnt and ar larg nough to caus considrabl inlunc to th rinorcmnt rsults; hnc, th should b tan into account. Rinorcmnt Application hoos Proprt/Plat R and crat a rinorcmnt laout or th top plats with th ollowing stup: Bar diamtr 3 : sqrt(304/pi Bar spacing 3 : 000/7 ovr c : 60- sqrt(304/pi/ Undr th oncrt tab, th Eurocod dsign actors ar includd: E : 3000 ε : c : 3 φ : 0.85 :.5 Undr th Stl tab, th dsign actors ar also considrd: E : : 500 :.5 As_b (bas : 0.0 Undr th Rsults tab, Slct Elasto-plastic Itration mthod and st both Includ mmbran orcs and Allow comprssion rinorcmnt. hoos Proprt/Plat R and crat a nw rinorcmnt laout or th bottom plat with th sam oncrt, Stl, and Rsults stup, but with a dirnt laout pattrn: Prsntd b Strand7 Pt Limitd 97

lmnts, and assign : Bottom Rinorcmnts to th bottom plat lmnt. Etracting Rinorcmnt Rsults Th ctiv dsign paramtrs ar as ollows: Dsign oncrt omprssiv Strss 0.853/.5 8.3 Pa Dsign Stl Yild Strss 500/.

16 Strand7 Rlas.4 Faturs Bar diamtr : sqrt(604/pi Bar spacing : 300/6 ovr c : 90 - sqrt(604/pi/ hoos Attributs/Plat/oncrt Rinorcmnt, slct : Top Rinorcmnts rom th dropdown mnu and assign this laout to th top plat lmnts, and assign : Bottom Rinorcmnts to th bottom plat lmnt. Etracting Rinorcmnt Rsults Th ctiv dsign paramtrs ar as ollows: Dsign oncrt omprssiv Strss 0.853/ Pa Dsign Stl Yild Strss 500/ Pa Th oncrt omprssiv Strss without Rinorcmnt is approimatl -7 Pa as shown in th strss contour, which is considrabl lowr than th dsign concrt ild strss; hnc, lastic bhaviour o th concrt is pctd whn th partial sat actor or th concrt is st as.5. Whn th dsign concrt strngth dcrass with th partial sat actor, th amount o stl rinorcmnt is pctd to incras. 98 Prsntd b Strand7 Pt Limitd

17 Strand7 Rlas.4 Faturs Th bhaviour o th rinorcd concrt sction is summarisd in th tabl blow, with variabl partial sat actor: oncrt Partial Sat Factor Dsign Strngth (pa oncrt Strss Bloc E E E E Stl Strss (Usr omprssiv (pa Tnsil (pa inimum Rquirmnt As/Lngth (mm /m Diamtr (mm i spacing Spacing (m i diamtr As/Ac 0-6 omprssiv Tnsil omprssiv Tnsil omprssiv Tnsil omprssiv Tnsil inimum Rquirmnt As/Lngth (mm /m Diamtr (mm i spacing Spacing (m i diamtr As/Ac Dsign Strngth (pa omprssiv Tnsil omprssiv Tnsil omprssiv Tnsil omprssiv Tnsil Prsntd b Strand7 Pt Limitd 99

4.2 Design of Sections for Flexure

4.2 Design of Sections for Flexure 4. Dsign of Sctions for Flxur This sction covrs th following topics Prliminary Dsign Final Dsign for Typ 1 Mmbrs Spcial Cas Calculation of Momnt Dmand For simply supportd prstrssd bams, th maximum momnt