Reinforcement Design Algorithm For Concrete Shells

Transcription

1 Te 1 s Regionl onferene of Eng. Si. UEJ Spil ISSUE vol.11o pp Reinforemen Design Algorim For onree Sells Dr. Hni. Fmi Professor ivil Engineering Deprmen ollege of Engineering rin Universi Dr. il. Ali Leurer ivil Engineering Deprmen ollege of Engineering rin Universi AsrT Te sene of universll eped soluions in e sruurl onree odes for e design of reinforemen in sells gives rise o e prolem of luling e required reinforemen in ese sruures. Te onsn developmen of e ompuer s performne sorge pi oed wi e powerful numeril meods revel e need for srd proedure o design sells sujeed o memrne fleurl fores. In is pper e soluion for e design of e required reinforemen in onree sells is presened sed on omplee ierive ompuionl lgorim o design sell elemens sujeed o oed memrne fores ending momens. In e design equions e reinforemen will onriue o ension e onree ompression srus prllel o e rk direion will onriue o ompression. Te reinforemen is ssumed o ve wo orogonl lers pled in e op oom surfes wi pproprie overs. E reinforemen ler s reinforing rs pled orogonll. For e onree ompression srus e sress is ssumed o e uniforml disriued in e dep of Wine s sress lok. Tis design lgorim is ieved developing design ode (DRSH) sed on omplee ierive ompuionl lgorim. Tis progrm n e used s s-lone version o deere e lod rring pi of riil poins in reinfored onree pnels ples sells; o verif e design ode on e elemen level five eperimenl models re designed. Te designed elemens give luled ulime srengs from 7 o 18% iger n es resuls vlues eep one model wi onfirms e dequ of e design lgorim e developed design ode. Ke words: Finie elemen sells onree sruure sress nlsis 1. Overview of Design eods for Reinfored onree Sells: A n poin in e sell s sown in Fig. (1) wo differen pes of inernl fores m our simulneousl; ose ssoied wi memrne ion ( ) ose ssoied wi ending of e sell ( ). Even oug sells resis e pplied fores primril roug in-plne memrne ion ending is sill indued on e sell. Terefore more rionl ppro o e design proess is o simulneousl inlude oed memrne fores ending momens. UEJ vol.11 o.3008 Reinforemen Design Algorim 38

2 Figure (1) Applied fores momens on n elemen urrenl designers firs perform e design wi memrne fores onl ler provide e reinforemen for ending in priulr loions su s ner oundries or ner sruurl disoninuiies. Design of reinforemen in sells for oed memrne ending se of sress is omple prolem ill now e omplee soluion for is prolem s no een presened in e inernionl odes does no inlude n dvne in is priulr field. Te AI-ode (AI ) [1] onins per on sells folded ples wiou n ler design lgorim u onl menions n meod of design wi ssures suffiien sreng wi equilirium is onsidered pplile. Te odel ode 90 ( EB-FIP 1993) [ 3] suggess e use of ree-ler model e ple m e modeled s omprig ree lers. Te ouer ler provides resisne o e in-plne effes of o e ending e in-plne loding wile e inner ler provides ser rnsfer eween e ouer lers. Te proposed model is onl pproime s i does no model e differen lever rms for onree seel fores. In ddiion i does no give n proedure o design e elemen i onl ses n e deerion of e lever rm vlues for e inernl fores is omple m require ierion e e depend on e levels of reinforemen on e ikness of e onree lers. Te Euro ode ( Design 1991) [3] suggess differen meod ug e usul epressions for ples sujeed o inplne loding sls o ending does no inlude n provisions for sells. Tese simplified epressions of generl use re no sfe e re inonsisen s sown Gup [4]. A generl soluion owever s sred o evolve in 1986 Gup [4]. Gup developed n ierive ril--error design meod ug e priniple of imum resisne dividing e sell ino wo imginr onree lers wiin e orogonll pled reinforing ler. He onl onsidered e se in wi reinforemen is needed in o ouer lers; us e meod is inpproprie for n oer se. Wi respe o e need of reinforemen four differen ses mus e nlzed reed seprel: reinforemen needed onl in e oom ler; reinforemen needed onl in e op ler; no reinforemen needed. Also e sowed few smple design prolems on e elemen level. In 1993 Loureno Figueirs [3] presened n uomed design of reinfored onree ples sells in ordne wi e odel ode 90. Te uors ssumed iniil lever rm d 0. 8 referring n ierive proedure mig e doped o lule e lever rms u no ddiionl provisions is given. Te implemened e design equions on ompuer progrm performed severl design emples ompring e resuls wi opimizion module ple of imizing e sum of e ensile fores ene e required reinforemen. Te found e resuls nged e reinforemen deresed ( %). UEJ vol.11 o.3008 Fmi Ali 383

3 In 004 in [5] developed omplee ierive ompuionl lgorim urel lules e inernl lever rms o design ple or sell elemen sujeed o oed memrne fores ending momens in wi e sell elemen is nlzed gloll no s wo memrne ouer lers in e ree-ler model. Te lgorim is developed on e sis of Gup s derivion (1986). Gup oined e design equions prl for e se of reinforemen required in e op oom lers simulneousl. Tree more ses re developed for e reinforemen required onl in e oom ler for reinforemen required onl in e op ler for no reinforemen required. in in is pper presened e omplee design lgorim for e wo ses: reinforemen required in o op oom lers reinforemen required in e oom ler e oer wo ses (reinforemen required in e op ler no reinforemens required) re derived presened in e presen work in similr w on e sis of Gup s in s derivion o re e im o provide omplee ler design lgorim for reinfored onree sells. Finll e design ode (DRSH) is used o design severl eperimenl emples o ompre e presen design lgorim wi ose for oer design ems (i.e. Gup Loureno Figueirs in) Formulion of Design Equions: A pil sell elemen sujeed simulneousl o memrne fores ending wig momens per uni leng is sown in Fig. (1). In e ulime se e pplied fores ve o e in equilirium wi e ensile fores in e reinforemen e ompressive fores in e onree ompression sru ve o e prllel wi e rk direion. In is limi se onree sress in ompression is ssumed o e disriued uniforml in e dep of Wine s sress lok. Te ensile sreng of onree ws ignored s in e urren design pilosop (AI ) [1]. Figure () sows sell elemen wi reinforemen represened s smered lers. A rigid-plsi evior is ssumed for e reinforemen. I is ssumed e reinforemen onsiss of wo orogonl lers pled e op e oom surfes wi pproprie overs e orogonl reinforemen ler s reinforing rs in e - -direions respeivel. Te pi of ese reinforemens n e designed s were susrips designe e direions s for e op oom lers respeivel. A e limi se veril plne of rk wose norml mkes n ngle wi e -is in e -plne peneres e op oom surfes Fig. (3). Te onree is in ompression prllel o is rk; i is ssumed e dep of Wine s sress lok is respeivel. UEJ vol.11 o.3008 Reinforemen Design Algorim 384

4 Figure () Four reinforemen lers (wo for op wo for oom) [5] Figure (3) rk direions [5].1Reinforemen required in op oom lers: Te ol fores momens resised e reinforemen in e - -direions re given Te verge ompressive sress prllel o e rk direion in e onree lok is f e fore momen resulns of e op oom onree loks re 1 f 3 f 4 were; is e ol ikness of e sell elemen ( ) ( ) re e deps of sress loks Te resig fores momens given Eqs. (1-4) sould e in equilirium wi e pplied fores momens. Terefore e equilirium equions for uni rked elemen in e - -direions re UEJ vol.11 o.3008 Fmi Ali 385

5 os os os os os os 5 6 in wi 1 os os Terefore e ssem of si equions Eqs. (5) (6) onin eig unknowns: four reinforemen piies ; rk direions ; e deps of ompressive sress lok. Idell ese quniies sould e seleed so e ol pi of reinforemen is s imum s possile. As disussed Gup [4] Loureno Figueirs [] e iniil vlues of give sisfor 4 resul wi = = 0.. Tese vlues re o e djused n ierive proedure unil e equilirium ondiions re sisfied. From Eqs. (3) o (6) e op oom onree lok resulns n e wrien s ( ( were; ) ) ( ) Te reinforemen piies of op oom lers in e - -orogonl direions re given Eqs. (1)-(7) s n n 8 n n 9 o o 10 o o 11 7 were Te ompressive fores in onree n e oined Eqs. (.7) (1) re given Wen e vlues of or re ver smll en e ompressive fores in Eq. (14) will e ver lrge e ierive numeril meod will eome unsle. Loureno Figueirs [] used 10 ( ) 80 rierion for e purpose of voiding numeril insili. in [5] found ll e elemens onverge wiin e mimum rnge of ( ) 5 5. Terefore e se ) 0 ( ) 5 In e ses of or Eq. (14) n epressed s ( wen o void numeril insili. re se o zero en re equl o zero respeivel UEJ vol.11 o.3008 Reinforemen Design Algorim 386

6 ( ) os 15 f 1 9 ( ) os Wen e luled vlues of Eqs. (8) o (11) re negive en no reinforemen is required in direion. One n se e reinforemen pi in direion o zero relule e vlues of or. in in is sud implemened e imum reinforemen re ( A ) of AI s [1] for limiing rk wid sping under e servie lod ondiion. In e direion e imum pi n e oined A s f were f is e ield sress of reinforemen. Terefore in Eq. (8) wen en se lule new vlue s n 1 ( n ) were; is ol ikness of e sell elemen ( ) Te oom ler onree fores re in e - -direions respeivel e ser fores e equilirium equions eome in wi os os os os. Ten os 1 0 Similrl from Eqs. (9)-(11) if re smller n en = respeivel oin or vlues ordingl..reinforemen required onl in op ler: Reinforemen is required onl for e op lers; us e ol fores momens resised e reinforemen in e - - direions n e epressed s 18 Te fore momen resulns of e op onree lok re Terefore e ssem of si equions Eqs. (0) (1) onins eig unknowns: wo reinforemen piies rk direion sress loks onree fores deps of ompressive oom ler.from Eqs. (19) (1) e op onree lok resuln n e wrien s ( ) 3 Te prinipl fore of e oom ler e dep of e ompressive sress lok n e epressed respeivel s UEJ vol.11 o.3008 Fmi Ali 387

7 1 f 4 From Eq. (5) if en s n is smller n = is luled 1 (1 D) 1 8 As efore e imum reinforemen re ( A ) of AI [1] ws s implemened. Terefore wi e imum reinforemen pi in e oom ler ug Eqs. (18) (3) e ensile seel fores developed e op ler n e given s Similrl wen en s n 1 = (1 is smller n D is luled ) 9 in wi D 1 n o 1 D D D 5 6 Te design equions for e reinforemen required onl in e oom no reinforemen required re omied ere e omplee design lgorims for e four ses re presened in deils in Ref. [6] 3 Verifiion Emples Te design lgorims re implemened in design ode DRSH (g for: Design of Reinforemen in onree SHell) developed in e presen work o verif e design ode on e elemen level severl design eperimenl emples re designed ompred wi ose of oer design ems s sown in e ne seions. Also seing 0 wen 5 void numeril insili en 0 is epressed s 7 o Design emples: Gup s design prolem: Gup [4] sowed design emple prolem in e se of reinforemen required in e op oom lers simulneousl. Te design vriles of Gup s emple (wi re e onl inpu d required for DRSH) re given in Tle (1). UEJ vol.11 o.3008 Reinforemen Design Algorim 388

8 Tle (1) Design vriles of Gup s emple. = k/ m (-000 l/ in.); = k/ m. (1700 l/ in.); (1000 l/ in.) = k.m/ m ( l-in/in.); = k.m/ m (700 l-in/in.); k.m/ m (00 l-in/in.) f =6.895 P(1000psi) ; Iniill ssume m. = f = P (60000 psi) ; = 0.54m (10 in) = k/ m. =0. = m. = = 45 = As sown in Tle () e presened design ode produe pproimel e sme ol reinforemen pi of Gup s resul for imum reinforemen rio ( =0.0) wi ver smll imum reinforemen rio e ol reinforemen pi is inresed onl.419% wi respe o Gup s resuls. Tle () omprison of e designs wi wiou seing imum reinforemen rios e Gup s resul Gup s Resul Presen Sud =0.0 = k/m o. of 6 6 ierions (m) 0.054(1.0in) (m) 0.076(3.0in) ( ) ( ) (k/m) (k/m) (k/m) (k/m) Sum of Tensile Fores 9.179(1309l/ in) (959l/ in) (174l/ in) (354l/ in) Loureno Figueirs s design prolem: Loureno Figueirs [] sowed wo design emples one for se of e reinforemen required in op oom lers simulneousl e oer one for se of reinforemen required onl in e op ler. Ten e resuling reinforemens in is work ve een ompred wi ose oined Loureno Figueirs [] wi eir opimizion module [] ple of UEJ vol.11 o.3008 Fmi Ali 389

9 imizing e sum of ensile fores ene e required reinforemen. Te design vriles of e firs design se (wo ensile lers) re given in Tle (3) Tle (3) Design vriles of Loureno Figueirs s firs design prolem = -00 k/ m.; =-60 k m/ m. ; f =7.34 P ; Iniill ssume =300k/ m.; = 40 k m/ m.; f = 348 P ; = 0. m = =75 k/ m. =-00 k m/ m. =0. = 0.04 m. = = m. A omprison of e design for is se Loureno Figueirs [] eir opimizion module wi e presen design ode DRSH is given in Tle (4) sows e presen design ode provides ensile fores in e reinforemen less n ose oined Loureno Figueirs ver lose o e reinforemen fores provided e opimizion module. Tle (4) omprison wi e designs resuls of Loureno Figueirs s firs design prolem Loureno Figueirs s Presen sud Design resuls Opimizion module o. of ierions - 7 (m) (m) ( ) ( ) (k/m) (k/m) (k/m) (k/m) Te design vriles of e seond design se(ompression in op ler) re given in Tle(5) UEJ vol.11 o.3008 Reinforemen Design Algorim 390

10 Tle (5) Design vriles of Loureno Figueirs s seond design prolem = -00 k/ m.; = 60 k m/ m. ; f =7.34 P ; Iniill ssume =300k/ m.; =75 k/ m. = 40 k m/ m.; f = 348 P ; = 0. m = =-0 k m/ m. =0. = 0.04 m. = = m. A omprison of e design for is se Loureno Figueirs [] eir opimizion module wi e presen design ode DRSH is given in Tle (6) wi sows e presen design lgorim provides ensile fores in e reinforemen wi re in greemen wi ose oined Loureno Figueirs e opimizion module Tle (6) omprison of e designs resuls of Loureno Figueirs s seond design prolem Loureno Figueirs s Presen sud Design resuls Opimizion module - 5 o. of ierions (m) (m) ( ) ( ) (k/m) (k/m) (k/m) (k/m) Eperimenl emples: Severl eperimenl emples re designed performed wi nonliner inelsi nlsis [6] o sow e dequ of e design equions. If e luled ulime sreng is lrger n e ulime sreng oined from e es en e design meod n e onsidered sisfor Te eperimenl emples re: (1)ri e l. s [7] sl elemens L 7 L9 sujeed o orsionl momens () Polk Veio s [8] sell elemens S1 S S3 models. Tle (7) sows omprison of seel rios eween e originl esed speimen given e Loureno-Figueirs s design [3] given in s design [5] ose oined e presen design ode DRSH. As sown in Tle (7) e presen design ode provides reinforemen pi re lmos idenil o ose oined in [5]. Tle (8) sows omprison of ulime sreng oined from e es luled e nonliner inelsi nlsis [6]. Te designed elemens give luled UEJ vol.11 o.3008 Fmi Ali 391

11 ulime srengs from 7 o 18% iger n es resuls vlues eep S model euse e nonliner nlsis filed o find onvergene due o ver lrge deformion of e mode e evior of i is somew similr o norml seel sruure evior wi onfirms e dequ of e design lgorim e developed design ode. Tle (7) omprison of seel rios from originl esed speimens from design ems from presen design ode (%) odels Design ems Top ler (Seel rio) Boom l -dir. -dir. -dir. L 7 ri e l [7 ] Loureno Figueirs[3] in [5] Presen sud L 9 S 1 S ri e l [7 ] Loureno Figueirs[3] in [5] Presen sud Polk Veio [8] Loureno Figueirs[3] in [5] Presen sud Polk Veio [8] Loureno Figueirs[3] in [5] Presen sud S 3 Polk Veio [8] Loureno Figueirs[3] in [5] Presen sud UEJ vol.11 o.3008 Reinforemen Design Algorim 39

12 Tle (8) omprison of ulime sreng oined from e es luled nonliner inelsi nlsis odels Ulime omen Oined from e es (km/m) luled Ulime omen [6](km/m) Rio % [()*(1)]/100 L L S S S onlusions In is pper omplee design lgorim is ieved developing design ode (DRSH) sed on omplee ierive ompuionl lgorim. Tis progrm n e used s s-lone version o deere e lod rring pi of riil poins in reinfored onree pnels ples sells; o verif e design ode on e elemen level. Five eperimenl models re designed. Te designed elemens give luled ulime srengs from 7 o 18% iger n ose of es resuls vlues eep one model wi onfirms e dequ of e design lgorim e developed design ode. 5 Referenes 1) AI ommiee 318 Building ode requiremens for sruurl onree AI srd ; e ommenr on uilding ode requiremens for reinfored onree Amerin onree Insiue Deroi 005. ) Loureno P.B. Figueirs J.A. Auomi design of reinforemen in onree ples sells Engineering ompuion Vol pp ) Loureno P.B. Figueirs J.A. Soluion for design of reinforemen onree ples sells Journl of Sruurl Engineering ASE Vol.11 o pp ) Gup A.K. oed memrne fleurl reinforemen in ples sells Journl of Sruurl Engineering ASE Vol.11 o.3 r 1986 pp ) in.s. Design ulime evior of R ples sells uler Engineering Design Vol pp ) Hussin..A. Anlsis Opimum Reinforemen Design of onree Ples Sells PD Tesis. rin Universi Irq p. 7) ri P. Leesi P. Klif W.U. Torsion ess on reinfored onree sl elemens Journl of Sruurl Engineering ASE Vol.113 o pp ) Polk.A. Veio F.J. onliner nlsis of reinforedonree sells Journl of Sruurl Engineering ASE Vol.119 o.1 Deemer 1993 pp UEJ vol.11 o.3008 Fmi Ali 393

13 (Wine) (DRSH) UEJ vol.11 o.3008 Reinforemen Design Algorim 394

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