A review of design specifications of opening in the web for simply supported RC beams

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Gladys Mills
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1 Journal o Civil Engineering and Conruion Tehnolog Vol. (4, pp. 8-89, April 011 Availale online a hp:// SSN Aadei Journal Full Lengh Reearh Paper A review o deign peiiaion o opening in he we or ipl uppored RC ea Sorouh Airi*, Reza aoudnia and ohaad Ain Aeri Deparen o Civil and Sruural Engineering, Faul o Engineering and Buil Environen, Univerii Keangaan alaia, Selangor, alaia. Aeped 5 April, 011 The preen ud review he deign peiiaion o opening in he we or ipl uppored reinored onree (RC ea and reangular onree ea ondued previou reearher. A nuer o paper have een ound o handle he reinored onree ea onaining a erie or iolaed we opening. The ee o he ize and loaion o he opening on he ehavior o uh ea are exained and he rengh o hee opening are inveigaed a well. Thi paper, hereore, diue and derie he previou reearhe whih are relaed o he opening in he we o reinored onree (RC ea. Ke word: We opening, deign proedure, reinored onree ea. NTRODUCTON n order o ave headroo in uilding, and opiize he required ore heigh in uilding, ea are provided wih opening in he we or he paage o ervie du. Beaue o he liied deph o he RC ea, inroduing he opening in hee ea i ver igniian hereore; hi ud i going o review he work ha ha een done oher reearher, ine ver liied daa have een repored on deign peiiaion o onree ea wih we opening. OVERVEW OF THE RESEARCH On he ai o oe experienal udie, everal deign equaion or noral and lighweigh onree deep ea wih we opening were inrodued Kong and Sharp (1977 and Kong e al. (1970, 1973, The uliae hear rengh equaion or reinored onree deep ea are: or olid deep ea, and x Q 1 D a in D D α1 or olid deep ea, and *Correponding auhor. E-ail: orouh.airi@ahoo.o. Tel: (1 k x Q 1 λ in D k D + a α1 k D or deep ea wih we opening Where; 1 Epirial oeiien (1.40 or noral rengh onree, 1.35 or ligh weigh onree; widh o he ea; D Overall deph; Clinder-pliing enile rengh o he onree; x Clear-hear-pan diane; Epirial oeiien (300 N/ or deored eel ar, 130 N/ or plain eel ar; Deph a whih a pial ar inere he poenial riial diagonal rak in olid deep ea, whih i approxiael a he line joining he loading and reaion poin and; An epirial oeiien, equal o 1.5 or we ar and1.0 or ain ar. Oher geoeri noaion are deried in Figure 1. The ir er on he righ ide o he eond equaion how he load apai o ru. The ir er alo onider he lower load pah when an opening i in he naural loading pah. The eond er on he righ ide o he equaion ariulae he onriuion o reinoreen in deep ea. i worhwhile enioning ha hee equaion are onl appliale or he onree rengh le han 46 Pa. Sih and Vanioi (198 arried ou everal laoraor e over deep ea o reognize he onriuion (

2 Airi e al. 83 Figure 1. Noaion or ize and loaion o opening (Kong e al., o we reinoreen upon hanging he a/d raio. The onluded ha he iniu reinoreen raio hould e greaer han 0.18 and 0.3 or verial and horizonal reinoreen repeivel, and he onriuion o we 4 d reinoreen anno exeed. However, he lear pan o deph raio o he eed ea wa eween 0.77 and 1.34 whih were uh le han he raio uggeed AS (The Auralian Sandard. anur e al. (199 exained he deleion o reinored onree ea wih we opening. The inended o develop a iple ehod or prediing he ervie load deleion o reinored onree ea ha onain a large opening in he we. Conidering hi a ha he poin o onralexure our a id-pan o he hord eer during he proe o loading, deleion aued a uni load or ox ruure i given he a elow: le 1E( 3 + n whih and are he oen o ineria or op and oo hord, repeivel. The orreponding deleion aued hearing deoraion o he unior oninuou ediu i: le ( GA eq The GA paraeer o he equivalen oninuou ediu i hen oained ro Equaion 3 and 4 a: (3 (4 ( GA eq 1E( l e + FACLTATON OF SELECTNG THE SZE AND LOCATON OF THE WEB OPENNGS Kiang-Hwee and anur (1996 propoed a iple deign proedure or reinored onree ea wih large we opening. The opening hould e provided o ha hord have enough onree area o develop he uliae opreion lok in lexure and uiien deph o provide eiien hear reinoreen. The hould no e deeper han one-hal he ea deph and hould e loaed no loer han one-hal he ea deph ro uppor or onenraed load. n oninuou ea ha generall our in praie, reduion in ine due o he proviion o opening hrough we aue a rediriuion o inernal ore and oen, he aoun o whih need o e evaluaed eore a deign an proeed. Baed on he review o lieraure on he ehavior and rengh o he ea wih we opening, he ollowing guideline an e inrodued o ailiae he eleion o he ize and loaion o he we opening (Figure. For T-ea, opening hould preeral e poiioned luh wih he lange or eae in onruion. n he eae o reangular ea, opening are generall poiioned a id-deph o he eion; however, he a alo e plaed eenriall wih repe o deph. The uiien onree over hould e provided or he reinoreen o he hord eer aove and elow he opening. The opreion hord hould alo have enough onree area o develop he uliae opreion lok (5

3 84 J. Civ. Eng. Conr. Tehnol. Figure. Guideline or loaion o he we opening (Kiang-Hwee and anur, in lexure and uiien deph o provide eiien hear reinoreen. Opening hould no e poiioned loer han one-hal he ea deph D o he uppor in order o avoid he riial region or hear ailure and reinoreen ongeion. oreover, poiioning o an opening loer han 0.5 D o an onenraed load hould e avoided. Deph o he opening hould e liied o 50% o he overall ea deph. When uliple opening are ued, he po eparaing wo adjaen opening hould no e le han 0.5 D o inure ha eah opening ehave independenl. DESGN SPECFCATON OF BEAS WTH SALL OPENNGS n heir ook eniled Conree ea wih opening, anur and Kiang-Hwee (1999 repreened he ollowing proedure o oain he uliae oen apai o olid ea and ea wih opening. The opening ha are irular, quare, or nearl quare in hape a e onidered a all opening provided ha he deph (or diaeer o he opening i le han 40% o he overall ea deph. Hene, he anali and deign o a ea wih all opening a ollow he oure o aion iilar o ha o a olid ea. Fir, a olid ea ha i uje o pure ending i aued. Finall, he ea will exhii a well-developed paern o rak, a hown in Figure 3(a. Aording o he uual lexural rengh heor, he rain and re diriuion aro a eion a uliae ae are hown in Figure 3(. The enile re reulan, T, and he opreive re reulan, C, or a ouple exal equal o he applied oen a ollape. he ea eion hown in Figure 3( i aued o e under-reinored, ha i, he eel reinoreen ield a ailure, and i he aual opreive re lok a noinal ending rengh i replaed Whine equivalen reangular re lok, hen T and C a e oained a ollow: T A (6 C 0.85 a (7 Where: A area o enile reinoreen, ield rengh o enile reinoreen, linder opreive rengh o onree, widh o he eion, and a deph o reangular opreive re lok. The horizonal equiliriu, ha i, C T give a A 0.85 The noinal lexural rengh, n i hen oained ro oen equiliriu a: n A a ( d (8 (9 Whih on uiuing Equaion (8, redue o n A A d 0.59 ( (10

4 Airi e al. 85 ( Condiion a uliae ae Figure 3. Bea ujeed o pure ending (anur and Kiang-Hwee, Now, a hown in Figure 4(a, onider ha a ranvere opening o an hape i inrodued in he ae ea. i worhwhile enioning ha he proviion o opening doe no hange he load-arring ehani a long a he opening and he uliae rengh o he ea will no e inluened he preene o he opening. Following he preeding diuion, here will e no reduion in he uliae oen apai o he ea i he iniu deph o he opreion hord, h, i greaer han or equal o he deph o opreive re lok, a, ha i, when h A 0.85 (11 Bea are uuall uje o oined ending and hear. Figure 5(a how a ipl-uppored, reinored onree ea wih an opening, uje o a onenraed load a a diane x ro he uppor on he ae ide o he opening. The ree-od diagra a he ea opening an e repreened a in Figure 5(, and he ree-od diagra o he hord eer aove and elow he opening a in Figure 5(. i oerved ha he unknown aion ee a he ener o he opening are he axial ore (N and N, he ending oen ( and, and he hear ore (V and V in he hord eer. There are hree equiliriu equaion relaing hee ix unknown. The are: V + V V (14 n whih and V are he applied oen and hear ore, repeivel, a he ener o he opening. Thu, he ea i aiall indeerinae o he hird degree. DESGN SPECFCATON OF BEAS WTH LARGE OPENNGS Kiang-Hwee and anur (1996 alo propoed a iple deign proedure or reinored onree ea wih large we opening a hown uequenl. Deign olid egen The olid egen o he ea an e deigned in uual anner i he ending oen and hear ore envelope are onidered. Conien wih he e reul, onra lexure poin are onidered a id-pan o he hord eer or whih he axial load i oained dividing he ea oen a he ener o he opening he diane eween he plai enroid o he hord eer. Deign hord eer + + NZ N + N 0 (1 (13 Fore and oen in hord eer: A i i hown in Figure 6, he deerine he uliae deign ending oen and hear ore V a he iddle o he opening egen ro ending oen and hear ore envelope, and alulae axial ore N and N (poiive

5 86 J. Civ. Eng. Conr. Tehnol. ( Condiion hrough he opening a uliae ae Figure 4. Bea wih opening under pure ending (anur and Kiang-Hwee, or opreion aing, repeivel, in he op and oo hord. N Z (15 3 wl 8 vl 0 vl + 0 (0 (1 N N (16 Where, z i he diane eween he plai enroid o he op and oo hord. Diriue he applied hear eween he op and oo hord a: V V V V ( ( g g g + g + g g (17 (18 g and g are he gro oen o ineria o op and oo hord, repeivel. Calulae oen a he end o hord eer ro ai (Figure 6. 1 wl 8 vl 0 (19 4 vl 0 ( Deign o reinoreen or hord Deign o longiudinal reinoreen or hord eer The longiudinal reinoreen in he op and oo o he olid eion adjaen o he opening hould e oninued hroughou he opening egen. Addiional reinoreen i required o rei he oined oen, and axial ore in eah hord eer i deigned a well. A a rial, eah hord i eriall reinored in uh a iuaion. Deign o hear reinoreen or hord eer The hear reinore arried he op and oo hord are given Equaion 17 and 18, repeivel. Conidering hee ore, he required aoun o reinoreen an e deigned in a anner iilar o he reinored onree ea and la.

6 Airi e al. 87 Figure 5. Bea wih an opening under ending and hear: (a The ea, ( Free-od diagra a opening; ( Free-od diagra o he hord (anur and Kiang-Hwee, Deign o po eween he opening The po hould e deigned a a olid egen o arr he oal applied hear. The onriuion o he orner reinoreen a he wo adjaen opening hould e ignored. SERVCABLTY RESTRCTONS FOR CHECKNG THE DESGN 0.5( η. v Av φ. v (3 n whih V,, and v are he deign hear, apai reduion aor and ield re o irrup, repeivel. The verial irrup hould e plaed a loe o he edge o he opening a peried he required onree over. The required area o diagonal reinoreen A d i given a: Two iporan requireen hould e e or deigning he ervieaili. The are raking and deleion. 0.75( η. v A d φ..inφ d (4 Craking Conidering hi a ha rak onrol requireen o he olid egen are provided eiher proper reinoreen deailing or phial alulaion, he ollowing rak onrol proviion are reoended or riial eion a orner o he opening. A eah verial edge o he opening, a oinaion o verial irrup and diagonal ar will e ued wih a hear onenraion aor o. For eah ide o he opening, he required area o verial irrup A v i given : Where d i he ield re and i he angle o inlinaion o diagonal ar o he ea axi. The ae aoun o diagonal reinoreen hould e provided oh a he op and oo orner o he opening in order o avoid onuion during onruion and o aoun or an poile load reveral. Deleion The indire wa o aiing he ervieaili

7 88 J. Civ. Eng. Conr. Tehnol. Figure 6. Free-od diagra o opening egen (Kiang-Hwee and anur, requireen o deleion liiing he pan- eeive deph raio i no valid or a ea wih opening. Thereore, an eiae o he aual ervie load deleion i neear. DESGN SPECFCATON OF HGH STRENGTH CONCRETE DEEP BEAS Tan e al. (1995, 1997, 003 and Leong and Tan (003 explored he ee o high rengh, hear pan o deph raio and we reinoreen raio o he ea eploing oh experienal progra and nuerial anale. The deign orula or high rengh onree deep ea i: v n 1 in θ + A A Where: r inθ + 1 in w w A Aw w + A A d And an θ inθ ( h l a a θ in( θ + θ d l inθ (5 (6 (7 in whih; angle eween he longiudinal enion reinoreen and he diagonal ru, oined enile rengh o reinoreen and onree, A area o onree eion, A r ro-eional area o diagonal ru, ield rengh o longiudinal eel reinoreen, A w area o we reinoreen, w ield rengh o we reinoreen, w angle eween he we reinoreen and he axi o ea a he inereion o he reinoreen and diagonal ru, d w diane ro he ea op o he inereion o he we reinoreen wih he line onneing he uppor enre and he load enre, d eeive deph, enile rengh o onree, h overall heigh o deep ea, l a heigh o oo node, l widh o uppor earing plae, and a hear pan eaured eween onenraed load and uppor poin. RESULTS AND DSCUSSON For inveigaing he veriiaion o exiing Equaion 16 ea were exained Yoo e al. (003 ha een eleed hen experienal reul are opared o reul oained orreponding orula, he proporion o oparion and deail are hown in Tale 1. A i i ovioul een in he Tale 1, none o equaion have reaonale aura in prediing o uliae load or orreponding ea. For exaple he raio relae o Equaion ( wih ean o 0.8, undereiae earing apai o ea. i aued er ha, hi er i onerned wih he poiion and ize o he we opening. Sine he opening ize inreae and approahe o he ae o he ea, hi er will produe negaive value. Finall, proporion relaed o veriiaion o Equaion 5

8 Airi e al. 89 Tale 1. Coparion he experienal and equaion reul. Speien Calulaion Equaion ( Reul (Kn Equaion (5 Experien Equaion ( Equaion (5 RO RO RO RO RO RO RO are ore han 1 whih guee overeiae ailure load whih ould e due o he a ha he equaion doe no onider he ee o onree o uh a high rengh. Conluion Several analial reearhe arried ou previou reearher on onree ee wih all and large opening, deep ea and reangular onree ea wih we opening were reviewed in hi paper; however, ore evaluaion o ehavior or onree ea wih we opening i needed o gain ore eiien and reaonale ehod or deigning and onruion. The analzed reearh udie provided everal praial reul. oreover, an equaion were repreened o deign and analze he RC ea wih all and large opening. REFERENCES Kong FK, Sharp GR (1973. Shear Srengh o Ligh-weigh Reinored Conree Deep Bea wih We Opening. Sru. Eng., 51: Kong FK, Sharp GR (1977. Sruural dealizaion or Deep Bea wih We Opening. ag. Conree Re., 9: Kong FK, Roin PJ, Cole DF (1970. We Reinoreen Ee on Deep Bea. AC J., 67: Kong FK, Sharp GR, Appleon SC, Beauon CJ, Kuik LA. (1978. Sruural dealizaion or Deep Bea wih We Opening: Furher Evidene. ag. Conree Re., 30: anur A, Tan KH (1996. Deign Proedure or Reinored Conree Bea wih Large We Opening. AC Sru. J., 93(4: Leong CL, Tan KH (003. Propoed Reviion on CRA Deign Equaion or Noral and High Srengh Conree Deep Bea. ag. Conree Re., 55: anur A, Kiang-Hwee T (1999, Conree ea wih opening anal and deign. CRC Pre, pp anur A, Huang L, Tan KH, Lee SL (199. Deleion o Reinored Conree Bea wih We Opening. AC Sru. J., 89(4: anur A, Huang L, Tan KH, Lee SL (199. Deleion o reinored onree ea wih we opening. AC Sru. J., 89(4: anur A, Lee YF, Tan KH, Lee SL (1991. Te on RC oninuou ea wih opening. J. Sru. Eng., 117(6: Sih KN, Vanioi AS (198. Shear Srengh o Deep Bea. AC J., 79: Tan KH, Teng S, Kong FK, Lu HY (1997. ain Tenion Seel in High Srengh Conree Deep and Shor Bea. AC Sru. J., 94: Tan KH, Tong K, Tang CY (003. Conien Sru-and-Tie odeling o Deep Bea wih We Opening. ag. Conree Re., 55: Tan KH, Kong FK, Teng S, Guan L. (1995. High-Srengh Conree Deep Bea wih Eeive Span and Shear Span Variaion. AC Sru. J., 9: Yoo T, Doh JH, Guan H (003. Experienal work on reinored and prereed onree deep ea wih variou we opening. Vioria Univ., Auralia, 1:

Analysis of Members with Axial Loads and Moments. (Length effects Disregarded, Short Column )

Analysis of Members with Axial Loads and Moments. (Length effects Disregarded, Short Column ) Analyi o emer wih Axial Loa an omen (Lengh ee Diregare, Shor Column ) A. Reaing Aignmen Chaper 9 o ex Chaper 10 o ACI B. reenaion o he INTERACTION DIAGRA or FAILURE ENVELO We have een ha a given eion an