Strengthening of web opening in non-compact steel girders

Transcription

1 IOSR Jurnal f Mechanical and Civil Engineering (IOSR-JMCE) e-issn: ,p-ISSN: X, Vlume 12, Issue 5 Ver. II (Sep. - Oc. 2015), PP Srenghening f web pening in nn-cmpac seel girders Fauh M. F. Shaker 1 and Mahmud Shaha 2 1 Assisan Prfessr, Civil Eng. Deparmen, Faculy f Eng. Maaria, Helwan Universiy, Cair. 2 Graduae suden, Civil Eng. Deparmen, Faculy f Eng. Maaria, Helwan Universiy, Cair. Absrac: The use f web penings pass he uiliies f srucures hrugh seel beams can help in minimizing buildings heigh and hence decreasing perainal and mainenance css. Hwever, web penings can significanly reduce he shear and bending srengh capaciy f he seel beams. The las researches fcused n he sudy f perfraed beams wih cmpac seel webs exclude he effec f lcal buckling. Therefre, he bjecive f his paper is sudy he effec f web penings n he capaciy f beams having nn-cmpac secins in rder deermine he criical psiins f web penings. Thus, suppsing he suiable echnique fr web srenghening accrding shape, size and lcain f he pening wih respec beam lengh. The sudy is fcused n he nn-cmpac and slender web beams due is ecnmical and cmmn uses. The sudy als invesigaed he efficiency f differen ypes f siffeners welded a he pening regins in rder increase he beams ulimae lad carrying capaciy. The bained resuls shwed ha he lngiudinal siffeners is he bes srenghening sysem. The analyical invesigain uilizes nnlinear finie elemen mdeling echniques using ANSYS prgram, cnsidering bh gemeric and maerial nnlineariies. The resuls f he finie elemen mdels were verified wih he resuls f experimenal ess fund in lieraure. Keywrds: Nn-Linear Analysis, Seel Srucures, Web Openings, Perfraed Seel Girder, Vierendeel Mechanism, Web Reinfrcemen, Nn-cmpac Web and Finie Elemen Mehd. I. Inrducin Passing f uiliies and services such as venilain ducs, air cndiin ducs, elecrical and daa cmmunicain sysems, fire precin sysems, heaing and cling sysems and insrumenain cables may be needed increasing he flr heigh. This leads addiinal cs, beside i is unaccepable chice frm he archiecural view, where here is a sric requiremen n he sry heigh f many buildings especially in mdern mulisry buildings. Therefre, penings shuld be prvided in he web f seel girders permi passing he uiliies wihin he cnsrucinal deph f he flr which resul minimizing he flr heigh give a gd archiecural emphasis. Hwever, he exisence f web penings may have a significan passive effec, where he beam may be weakened in he viciniy f he pening due he reducin in he beam srengh which will ccur. The mehd f using he shear-mmen ineracin curves was widely used in he pas, bu he mehdlgy is nw enhanced by a cmprehensive finie elemen sudy. Many researchers have surveyed he behavir, srengh, and esablish a design mehdlgy fr designing beams wihu r wih reinfrced web penings. Recenly, researchers end sudy he behavir and deermine he lad capaciy fr differen ypes f perfraed cmpac seel beams under disribued and cncenraed lads. Cngdn and Redwd [1] carried u ess n a beam wih a cmpac web having a single reinfrced recangular pening esimae he srengh f beams wih reinfrced recangular hles assuming perfecly plasic behavir. Mrever, hey esimaed he required area f reinfrcemen in rder achieve he maximum shear carrying capaciy f he secin. Cper and Snell [2] cnduced an experimenal invesigain n sixeen simply suppred beams f A36 seel W12x45 shapes. They carried u he ess by subjecing he beams a single cncenraed lad a mid span under varius mmen--shear rai bain he elasic sresses in he viciniy f web penings. They fund ha he basis f vierendeel mehd f analysis calculae he nrmal sresses a he perfraed secin was in gd agreemen wih he measured experimenal nrmal sresses. The hriznal shear sresses calculaed by he vierendeel mehd did n mach well wih he measured shear sresses. Lupien and Redwd [3] cnduced an experimenal invesigain n six simply suppred beams wih mid deph recangular web penings. The penings were reinfrced hriznally frm ne side f he beam web which was cnsidered as slender. They esed he beams under varius mmen--shear rais sudy he efficiency and effec f ne sided reinfrcemen fr he pening gain frm is ecnmy in welding and handling. They fund ha here are sme siuains where he reinfrcemen placed n ne side f he web pening culd be used. Als, hey fund ha he necessary anchrage lengh f he reinfrcemen will nrmally be greaer han fr he same area symmerically placed. Darwin [4] is prepared a guide fr he design f seel and cmpsie beams wih web penings due he recmmendains f he cmmiee f research f he American Insiue f Seel Cnsrucin. This is par f a series f publicains n special pics relaed fabricaed-srucural seel beams. Is purpse is serve as a supplemenal reference he AISC manual f Seel Cnsrucin assis pracicing engineers engaged in building design [5]. This design guide presens a unified apprach he design f DOI:.9790/ Page

2 2H Srenghening f web pening in nn-cmpac seel girders srucural seel members wih reinfrced r unreinfrced web penings. Redwd and Ch SH. [6] develped a general mehd f analysis fr he design f seel and cmpsie beams wih web penings. They invesigaed he behavir f seel and cmpsie beams wih web penings and summarized a mehd predic he ulimae srengh and relaed i he available design aids. Prakash, e al. [7] carried u a finie elemen analysis using ANSYS sfware fr seel and cmpsie beams wih unreinfrced and reinfrced cenrally single recangular web penings. The scpe f heir sudy deals wih he aspec rai fr he penings, defrmain characerisics, lad carrying capaciies and vierendeel mechanisms. They bserved ha he web pening in lw shear and high mmen regin ends perfrm beer han he web pening in high shear and lw mmen regin. Als, hey bserved a cnsiderable reducin in he sresses and deflecins by increasing he amun f srenghening f he web pening. Akwasi [8] sudied he behavir f seel beams wih web penings and he variain f sresses in differen crss secins f seel beams. The web pening was cnsidered recangular wih and wihu reinfrcemen. Fur FEA mdels were analyzed. The mdels were wide flange beams wih slid webs, w mdels wih web pening wihu reinfrcemen and her w mdels wih reinfrced web penings. The aim f his research is sudy he effec f web penings n he capaciy f differen beams having nn-cmpac secins deermine he criical psiins f web penings which need srenghening. Then, he bes srenghening echnique fr each case f web pening fr beams having nn-cmpac secins is presened. Differen parameers are cnsidered such as pening heigh--beam deph rai, pening shape, aspec rai f pening, lcain f pening alng he beam lengh and varius reinfrcemen echniques arund he web pening. II. Finie Elemen Analysis The ms cmprehensive versin f ANSYS [9] prvides many new funcins ha can simulae and analyze he mechanical behaviur f beams having web penings. Afer defining ladings and carrying u analyses, resuls can be viewed as numerical and graphical. Acually, he capaciy f beam having web pening is affeced by many parameers such as pening shape, dimensins, lcain, ec. Sme f hese parameers were n cnsidered in his sudy such as; welds, imperfecins (i.e. residual sresses), and represenain f he envirnmen (i.e., emperaure). The finie elemen mdel deails are described in he fllwing subsecins. 2.1 Mdelling f seel pars Fur-nde shell elemen SHELL181 is used mdel all he seel elemens. This includes he p and bm flanges, webs, and seel reinfrcemens. I has bh bending and membrane capabiliies. The elemen has six degrees f freedm a each nde; hree ranslains in he ndal x, y, and z direcins and hree rains abu he ndal x, y, and z-axes. The generain f elemen is dne aking in cnsiderain he pening psiin, as he mesh is fine near he pening and denser away frm i. S, he mesh size is varied ensure he cnsisen behavir f he mdel. The cnsidered size f mesh is equal d/20 (d: is he web deph) arund he pening beam, and d/15 fr cnnecin beween web and flange f he seel beam, and a he zne near he supprs. Als, he size f mesh is aken equal d/ fr he res f he beam. The meshing can be achieved by using he sep f au meshing which ffers a large scale fr meshing beween fines carse mesh. The cmpressin flange was prvided by laeral resrain preven laeral rsinal buckling. Fig. 1 shws a ypical finie elemen mesh f perfraed seel beam. 2.2 Maerial prperies The sress srain relainship fr he seel maerial was aken as elasically perfec plasic wih a mdulus f elasiciy (E) equal 2.1E+08 kn/m² and Pissn s rai f 0.3. e b h d w L 2a L q SECTION (A-A) Fig. 1. Typical finie elemen mesh f perfraed seel beam Fig. 2.Deail f beams used in verificain by Lupien and Redwd [3] DOI:.9790/ Page

3 Beam Srenghening f web pening in nn-cmpac seel girders Table 1: Crss secin dimensins f beams esed by Lupien and Redwd [3] d (in) b (in) (in) w (in) h (in) q (in) e (in) 2a (in) 2H (in) L (in) RL RL Table 2: Maerial prperies f beams which were esed by Lupien and Redwd [3] Beam Yield sress f y (kip/in²) Flanges Web Reinfrcemen RL RL III. Verificain f The Finie Elemen Mdel The reliabiliy f he prpsed finie elemen mdels is checked by verifying heir resuls wih he previus experimenal resuls which were prepared by Lupien and Redwd [3]. They esed w simply suppred seel beams RL2 and RL3 wih mid deph recangular web penings as shwn in Fig. 2. The penings were reinfrced hriznally frm ne side f beam web, abve and belw he pening. The dimensins and maerial prperies f he esed beams are presened in Table 1 and Table 2 respecively. The cener f pening was lcalized a he middle and he firs ne hird f he beam span fr beams RL2 and RL3 respecively. The applied cncenraed lads ac a he end f ne hird and a he end f las hird f he beam span fr beam RL2, I aced a he mid f span fr beam RL3. The w esed beams were mdelled by using FEA as shwn in Fig. 3. Figures 4 and 5 shw he cmparisns beween he lad-deflecin curves resuling frm he FEA by he auhrs and he crrespnding experimenal esed beams by Lupien and Redwd [3]. I can be bserved frm he figures ha he resuls bained by he prpsed finie elemen mdel have a fair agreemen wih hse bained by Lupien and Redwd [3] wih lerances less han 2% which validaes he effeciveness f he adped numerical mdel. a) Beam RL2 b) Beam RL3 Fig. 3. Typical finie elemen mdel by auhrs fr beams used in verificain frm Lupien and Redwd [3] Experimenal by Lupien and Redwd Experimenal by Lupien and Redwd Fig. 4 (Lad- deflecin) curve fr beam RL2 Fig. 5 (Lad- deflecin) curve fr beam RL3 DOI:.9790/ Page

4 d h f Srenghening f web pening in nn-cmpac seel girders IV. Parameric Sudy An exensive parameric sudy using he finie elemen mdel described earlier is cnduced. The variains in values f lad capaciies were bained fr nn-cmpac beams befre and afer he srenghening f web pening by using differen ypes f reinfrcemen. Tw differen cases f lading were sudied, unifrm disribued lad and cncenraed lad acing a mid f beam span in rder invesigae he beam under varius rais beween he mmen and shear frce a he cenreline f he web pening. Fry nine finie elemen mdels (B1 B49) wih varius gemeric parameers were mdelled. These mdels were classified in hree caegries. The firs, beam B1 was mdelled as a seel beam wihu pening. I was used as a guide deermine he percen f reducin in he value f he beam lad capaciy due web pening. The her ypes were beams wih web penings having recangular shapes (B2 B37) and circular shapes (B38 B49). Fig. 6 shws he beam cnfigurain and Table 3 presens he beam secin prperies which were used in his sudy. Sme assumpins were cnsidered in he mdelling such as, n laeral buckling fr beams; where all mdels were fully laerally resrained. Als, n sress cncenrain arund supprs, where duble bearing siffener plae wih dimensins 500 x 80 x mm were prvided a each suppr. One suppr was cnsidered as a hinged suppr while he her suppr was simulaed as a rller suppr. Finally, all penings were cenered verically wih he beams web dephs. There are many parameers cnsidered invesigae heir effecs n he capaciy f perfraed beams such as he pening shape, he pening heigh (h ), he pening widh (a ) and he psiin f he pening frm he beam end suppr. The shape f pening is cnsidered as a square, recangular r circular. The pening heigh (h ) beam deph (d) rai was aken equal 0.25, 0.50, and The pening widh (a ) was cnsidered equal ne, w, and hree imes he pening heigh (h ), where, he cenre f pening assumed a disance (D) frm lef suppr as shwn in Fig. 6. Fur lcains f he pening were cnsidered, a (D) equal %, 20%, 35%, and 50% frm he beam span, whereas he rai beween he mmen and shear frce a hese psiins is varied. Tables 4 7 illusrae he variable parameers fr he sudied beams wih differen pening shapes (square, recangular and circular). Finally, he effec f five differen reinfrcemen ypes as shwn in Fig. 7 was sudied. The relain beween he failure lad and he pening psiin (as a percenage frm beam span) has been represened in he frm f ables and curves. Bearing siffener Bearing siffener 2 PL. 500X80X 2 PL. 500X80X b a r w 50 mm D L=7500mm f s s L s = d s h h L s = h h h L s = h L s = d h 50 mm Fig. 6 Layu cnfigurain f he sudied beam s L s =1.5 a a a s s a s = a L s L s =1.5 a a L s = a a s s Type (A) Type (B) Type (C) Type (D) Type (E) d (mm) b (mm) Fig. 7 Differen ypes f web pening reinfrcemen20 Table 3: Secin prperies f he sudied beam w (mm) f (mm) L (mm) r (mm) b s (mm) s (mm) F y (N/mm²) DOI:.9790/ Page

5 Tables 4 7: Summary f differen parameers cnsidered in he sudy f beams wih square, recangular r circular penings Table 4 : Beams wih square r recangular pening and h /d =0.25 Beam N. B2 B3 20 B B5 50 B6 B7 20 B B9 50 B B11 20 B B13 50 Table5 : Beams wih square r recangular pening and h /d =0.50 Beam N. B14 B15 20 B B17 50 B18 B19 20 B B21 50 B22 B23 20 B B25 50 Table 6 : Beams wih square r recangular pening h /d =0.70 Beam N. B26 B27 20 B B29 50 B30 B31 20 B B33 50 B34 B35 20 B B37 50 Table 7 : Beams having circular pening (wih diameer =h 0) Beam N. B 38 B B B B 42 B B B B 46 B B B The value f failure lad fr each mdel frm he afremenined mdels was deermined wih cnsidering he web pening wihu reinfrcemen. Afer ha i is cmpared wih he failure lad fr unperfraed beam (B1). All affeced mdels due he web pening were srenghened by using ne ype frm five differen siffeners mehds, as shwn in Figure (7). The siffeners are classified five ypes A, B, C, D and E. Where ypes A, B and C refer exended hriznal siffener abve and belw he pening, exended verical siffener lef and righ he pening and hriznal and verical siffener arund he pening wihu exensin (sleeve reinfrcemen) respecively. while, ypes D and E refer hriznal siffener abve and belw he pening in addiin un-exended verical siffener lef and righ he pening and exended verical siffener lef and righ he pening in addiin un-exended hriznal siffener abve and belw he pening respecively. All siffeners have he same dimensins (usand dimensins, b s =80mm and hickness, s =8mm). The effec f each ype frm he mainained siffeners ypes is sudied deermine he bes echnique srenghen he nn-cmpac perfraed beams. V. Resuls And Discussins Firs, he maximum lad capaciy f nn-cmpac unperfraed beam (B1) under he effec f differen w cases f lading, unifrm disribued lad and cncenraed lad a mid f he beam span is fund equal 40.73kN/m and 157.0kN respecively. The maximum lad capaciies fr nncmpac perfraed beams (B2) (B49) are bained frm he FEA and are pled as percen frm he crrespnding lad capaciy fr he unperfraed beam (B1) as shwn in Figs (11) (17). Secnd, hese resuls are sudied demnsrae he effec f he web pening in reducing and minimizing he lad capaciy fr each perfraed beam accrding he pening shape and lcain. Third, he beams affeced due he web pening are deermined. They are acked in cnsiderain sudy he effec f he differen ypes f reinfrcemens fr each case deermine he bes reinfrcemen sysem ha can be used resre he lss frm he beam capaciy. 5.1 Perfraed beams wihu reinfrcemen under unifrm disribued lad As illusraed in Figures (11) and (14), i is shwn ha he lad capaciy f he perfraed beam is n affeced by he pening shape (square, recangular r circular) if he pening heigh-beam deph rai (h /d) equals 0.25 when he pening is lcaed a any psiin frm he beam span unless a mid f he beam span. The same phenmenn can be niced fr h /d =0. 50 bu nly fr square r circular pening, as shwn in Figure (12). While, a significan reducin in he beam lad capaciy is ccurred fr recangular pening lcaed a criical shear zne (near end suppr) wih h /d =0.50. This can be explained by he mmen-shear ineracin equain (EQ.1) which cnsiss f he summain f rais beween he acual sraining acins (mmen and shear) and he DOI:.9790/ Page

6 crrespnding crss secin srengh (bending and shear capaciies). Therefre, he decrease f crss secin srengh agains bending r shear minimizes he abiliy resis a crrespnding sraining acin (mmen r shear) and he al capaciy f beam is decreased as such: Where: = R 3 where [R 1.0] (EQ.1) M u : he facred bending mmen a pening cenreline V u : he facred shear a pening cenreline M m : he maximum nminal bending capaciy a he lcain f pening cenreline under pure bending; i ccurs when V u = 0. V m : he maximum nminal shear capaciy a he lcain f an pening cenreline under pure shear; i ccurs when M u = 0. Ø: he resisance facr, equal 0.90 fr seel beams. Fig. 8 Perfraed secin frce disribuin [] Cnsequenly, he lad capaciy f beam is n affeced by he pening wih square r circular shape when he rai beween pening heigh--beam deph (h/d) up 0.50 when i is lcaed a any psiin frm he beam span unless abu mid f span. This is because he remaining par frm he web area afer pening as shwn in Figure (8) is enugh resis he applied shear wihu any reducin in he secin capaciy. Hwever, he siffness f he beam secin decreased by he assciain f he crss secins alng he beam lengh especially when he pening is lcaed a mid span. Over and abve, he increase f he pening widh decreases he verall capaciy f he perfraed beam especially, when he pening is lcaed near he criical shear zne because, he increase in pening widh prduces an addiinal mmen (vierendeel mmen) which is induced due shear ransfer alng pening widh, as shwn in Figure 8. Therefre, failure f seel beams wih web penings are frequenly gverned by Vierendeel cllapse mechanism ha ccurs due a change rae in he bending mmen disribuin (and cnsequenly, he shear frce) alng he pening []. This increase in he bending mmen is usually resised by upper and lwer Tees hrugh heir respecive lcal bending srenghs, Figure 8 []. The web f he beam is hick and is n prne buckling in shear under he acin f he lads, he cllapse is likely be iniiaed by he frmain f fur plasic hinges, near he fur crners f he hle in he web abve and belw he penings due addiinal virendeel mmen as shwn in Figure (9). Hwever, when he edges f he penings are un-siffened, he nn-cmpac r slender secins are suscepible lcal buckling f he web-flange secin (T secin) a he hriznal edge ha is in cmpressin due he glbal bending acin as shwn in Figure. The pening in such cases may be siffened r nly he elasic capaciy f he web-flange secin may be used. I is necessary check fr he cmpressin zne sabiliy f he large recangular penings in high mmen regins. This is carried u by reaing i as an axially laded clumn wih effecive lengh equal ha f he lengh f he pening (a ) []. Fig.9.Deails f 4-Plasic hinges frmed in web Fig. lcal buckling f unsiffened web a he pening DOI:.9790/ Page

7 Fr he same reasn, he reducin in lad capaciy was even mre prnunced fr all perfraed beams wih differen web pening shapes and wih h /d =0.70, as shwn in Figure (13). I is bserved ha a a big rai f widh--heigh f pening, he lss in unifrm lad capaciy f he beam is sharply decreased when he pening is lcaed near suppr, i.e. a high shear zne (a D/L=% and 20%) due he increase in he addiinal mmen (vierendeel mmen) as discussed befre. When prviding he same pening arund mid-span, i.e. a high bending mmen zne (a D/L=35% and 50%) leads sligh lss in he unifrm lad capaciy. This bservain supprs he recmmendains f several researchers prvide he web pening arund he middle f beam span fr beams subjeced unifrm lad, where he lss in he unifrm lad capaciy will be less han he her lcains. Frm Figures (12) (14), i is illusraed ha when he pening a high shear zne (D/L = %) and has circular shape wih (h/d) equal 0.50 and 0.70 he reducin in he unifrm lad capaciy f beam is less abu nly 1%. Fr square pening wih he same dimensins and gemeric cndiins, he reducin is abu 20-40%. The same hing can be illusraed when he pening a high mmen zne (D/L=50%) bu wih lile differences. This cnfirms ha he beams wih circular penings are presening higher ulimae lads han he her invesigaed pening gemeries especially, a high shear zne. Figures illusrae an evluin f he Vn Mises sress disribuin fr specimens B30, B42 and B46. I is bserved ha he fur plasic hinges were frmed in he web abu pening, fr any pening shape. 5.2 Perfraed beams wihu reinfrcemen under cncenraed lad a mid span f beam Accrding he naure f his case f lading, he disribuin f shear frce is cnsan alng he beam span bu he bending mmen increases gradually a maximum a mid span f beam. Therefre, he addiinal mmen (vierendeel mmen) which resuled due shear ransfer alng pening widh, will n be differen due he variain f he pening psiins. Therefre, as expeced, he beams wih recangular penings prduce he smaller ulimae lads, i.e. abu 30% less han he equivalen beams wih square r circular penings as shwn in Figures (15) (18). In hese beams, he Vierendeel cllapse mechanism was bserved in all he beams wih recangular penings independen f he beam pening psiin alng he span. I shuld als be pined u ha he beams wih recangular penings lcaed a a disance 0.50 L frm he supprs reached ulimae lads less han heir equivalen beams wih recangular penings lcaed a a disance 0.1 L frm he supprs. This issue is easily explained by he fac ha he Vierendeel mechanism frmain is inimaely assciaed he shear frce magniude a he pening, i.e. increasing he shear frce magniude a he pening reduces he beam cllapse lad. Figures (15) and (18) bserved ha he value f beam ulimae lad is n affeced due web pening wih square r circular shape when he rai beween heigh f pening and beam deph (h/d) up 0.50 a any psiin alng he beam span excep a mid span. The ulimae lad a his pin reduces beween 7% and 17 % fr square pening as well as by 4 % and 16 % fr circular pening wih (h/d) rai equals 0.25 and 0.50 respecively. S, i is recmmended ha he pening mus n carry u a he psiins f lad cncenrains alng he beam span. I can be bserved frm Figure (17) ha he beam wih square pening and (h/d) equal 0.70 presens a cllapse mde cmbining he Vierendeel cllapse mechanism wih a lad applicain pin bending cllapse. Fr hese beams, penings lcaed a a pin disancing 0.50 L (where L represens he beam span) frm he supprs prduced ulimae lads less han beams wih penings a 0. L frm he supprs. This fac indicaes ha he bending sresses begin play a significan in heses beam ulimae lads. Beams wih circular penings presened w disinc cllapse mdes. The beams wih penings lcaed a a disance 0. L frm he supprs had heir cllapse assciaed a Vierendeel mechanism cllapse. The Vierendeel mmen is minimum in case f circular pening where he ranslain f shear n bh sides f he pening is very smh. Therefre he circular gemery enables he beams susain higher ulimae lads, similar he ulimae lads f beams wihu penings. And he pening did n influence he beam cllapse lad. Beams wih circular penings lcaed a 0.50 L frm he supprs had heir cllapse as an ineracin f Vierendeel mechanism and lad applicain pin bending cllapse. Figure 18 presens he variain f he ulimae lad a he web pening cener. Mrever, i is illusraed ha if he perfraed beam has a recangular pening wih varius recangulariy rais (1:2 r 1:3) and he pening heigh--beam deph rai (h/d) up 0.70; hen he lad capaciy decreased by abu 60% 80% frm he beam capaciy. Als i is bserved ha he psiin f pening alng he beam span des n affec he beam capaciy as shwn in Figure (17) because he addiinal vierendeel mmen in his case is high and seady alng he beam span due he cnsancy f he shear disribuin alng he beam span. DOI:.9790/ Page

8 5.3 Perfraed beams wih reinfrcemen under unifrm disribued r cncenraed lad Figures (11) (18) demnsrae ha he failure lad has a high reducin in is value due he exisence f square r recangular pening wih heigh equal d. Despie his fac, here are siuain where he use f hese penings cann be avided. Fr hese cases he use f siffeners welded a he edges f he web penings is srngly recmmended by pracice and design sandards. Aiming verify he srucural efficiency f hese siffeners, sixeen beams were simulaed wih differen siffener ypes (A, B, C, D and E). They have he same characerisics f sme f he numerical simulains perfrmed in he parameric analysis (i.e. Specimens B22 B37). The siffeners were mdelled wih he gemerical characerisics presened in Table 3, and are illusraed in Figure 7. Figures (26) (30) shw he variain in he vn Mises sresses fr perfraed beam (B30) wihu siffeners and wih siffeners ypes A, B, C and D. I indicaes ha he use f siffeners enables a beer sress redisribuin alng he web penings which leads an increase f he beams lad carrying capaciy. The relain beween he unifrm failure lads fr he srenghened beams and he psiin f he pening as a percenage frm he beam span is shwn in Figures (19) (23). Table (8) presens a cmparisn f he ulimae lads fr beams wih and wihu siffeners fr he cnfigurain relaed specimens B22 B37 subjeced cncenraed lad a mid f beam span. The ulimae lads f he siffened perfraed beams increased wih high rae especially fr beams ha have penings near he criical shear regin. Fr beams wih pening near he regin f high mmen, he ulimae lad increases bu wih a lile rae because he augmenain in lad capaciy f he srenghened beam mainly depends n he imprvemen f he shear capaciy f he perfraed secin. When, he develpmen f he shear capaciy f he perfraed secin is cncerned n shear ransfer alng he pening widh he slid crss secin f he beam a lef and righ f he pening. This leads decrease he addiinal mmen (vierendeel mmen) which resuls due shear ransfer alng he pening widh. Therefre, he funcin f he hriznal siffener is ransfer and disribue he shear sresses he slid beam secin n bh sides f he pening. S, he usage f srenghening ypes (A) and (D) imprves he capaciy f he beam wih higher rai mre han he her ypes. Regarding he failure lads shwn in Figures (19) (23) and Table (8), i is bvius ha he augmenains f ulimae lad due he use f each ype f reinfrcemens (A) r (D) are equal apprximaely. The percen f ulimae cncenraed lad f specimen B31 wihu reinfrced equals 41.56% bu i increases 88% and 92.8% fr he same beam wih reinfrcemen ype (A) r (D) respecively. S, i culd be recmmended he usage f ype (A) which refers he exended hriznal reinfrcemen because i is an effecive ype cmpensae he srengh lss f he beam a he perfraed secin and is mre ecnmic han ype (D). Meanwhile, i is clear ha ype (B), which refers exended verical siffener lef and righ f he pening is inadmissible reinfrcemen sysem fr any web pening a differen psiins. The lad capaciy f he perfraed beam having reinfrcemen ype (B) decreases han wihu reinfrcemen as shwn in Table (8).This culd be explained ha he verical siffener causes sress cncenrain a he regin arund he web pening which leads early failure as shwn in Figures (28) and (31). In general, i culd be bserved frm Figures (19) (23) ha he siffeners have high efficien cnribuin and a subsanial imprvemen f he ulimae lads f beams wih square and recangular penings wih (h/d) equals 0.50 nly. As shwn in Figure (32) he failure f beam is gverned by bending mechanism a mid span pin under cncenraed lad. Fr all beams having recangular penings wih (h/d) equal 0.70 a he criical shear zne, he use f siffeners increases he ulimae lad abu 25% frm heir maximum values as shwn in Figures (22) and (23) and Table (8) and as shwn in Figures (33) and (34) where he failure f beam (B31) wihu r wih reinfrcemen ype (D) is gverned by Vierendeel mechanism a he pening psiin. S, i is recmmended n use any recangular pening wih (h/d) higher han 0.50 a he criical shear zne. VI. Cnclusins Las searches used experimenal, numerical and analyical echniques sudy he effec f web penings n he capaciy f differen beams wih cmpac secins. A lile f hese searches cnsidered he nncmpac secins. A cmprehensive finie elemen invesigain n nn-cmpac perfraed beams wih recangular, square and circular web pening shapes was carried u. The FE mdel was validaed agains experimenal wrk fund in he lieraure and presened herein. Tw differen cases f lading were cnsidered: unifrm lad and ne cncenraed lad a mid span. Analyses f perfraed secins wih differen web pening cnfigurains shw hw he Vierendeel mechanism is affeced n nly by he size, bu als by he shape f he web pening and is lcain alng he beam span. The effecs f he criical web pening lengh and deph as DOI:.9790/ Page

9 well as he web pening shape are presened hrugh a parameric FE invesigain. The invesigain f he web penings presens sme psiive resuls ha updaes he curren knwledge. Based n he FE mdel, imprvemens he assessmen f lad carrying capaciies f seel beams wih large web penings are bained by careful bservain f plasic hinge frmain a bh sides f he pening. The effec f differen pening siffener sysems is invesigaed and he bes srenghening echnique fr each case f web pening was perfrmed. The main cnclusins bained frm his research can be summarized in he fllwing: There is n variain bserved in experimenal values and finie elemen analysis resuls bained by ANSYS. The lad capaciy f he perfraed beam is n affeced by he pening shape (square, recangular r circular) if he pening heigh des n exceed 25% f beam deph and he pening is lcaed a any psiin alng he beam span unless a he mid f beam span. The same phenmenn can be cncluded fr web penings having a heigh equal half f he beam deph (h/d =0. 50) nly fr cases f square and circular pening shapes. The lad capaciy f he perfraed beam has a significan reducin, when a recangular pening wih heigh n exceeding 50% f beam deph and lcaed a he criical shear zne. Increasing he pening widh decreases he verall capaciy f he perfraed beam especially, when he pening is lcaed near he criical shear zne due he effec f addiinal mmen (Vierendeel mmen) which is induced due shear ransfer alng he pening widh. I is higher in case f recangular penings han in square nes, while i is leas fr circular penings. I is bserved ha he failure f perfraed seel beams is frequenly gverned by Vierendeel cllapse mechanism due he addiinal Vierendeel mmen which is usually resised by upper and lwer Tees hrugh heir respecive lcal bending srenghs. I is necessary check he cmpressin zne sabiliy f large recangular penings in high mmen regins. This is carried u by reaing i as an axially laded clumn wih effecive lengh equal ha f he pening lengh wih T-secin. The srengh f his clumn is gverned by is buckling behavir and he lcal buckling f is T-secin. Increasing he pening widh--heigh rai (a/h) a he firs hird f he span sharply decreases he capaciy f he perfraed secin while increasing his rai a he middle hird f he span slighly decreases he capaciy f perfraed secin. I is recmmended ha he pening mus n be dne a he psiins f lad cncenrains alng he beam span. Because he lad capaciy is sharply decreased a his secin. The lad capaciy f he perfraed beam having a recangular pening wih varius recangulariy rais (1:2 r 1:3) and pening heigh--beam deph rai (h/d) up 0.70 is decreased abu 60-80% frm is full capaciy. The beam wih circular pening presens an increase f he ulimae lad ha cann be discarded. Despie his beneficial effec, he Vierendeel mechanism is sill he cnrlling cllapse mde fr hese beams. Prviding a single circular pening wih diameer--beam deph rai (h/d) up 70% has a negligible effec n he capaciy f he beam excep a mid span when i is reduced by 8% -12 %. Therefre i is recmmended use circular penings where hey presen a higher ulimae lad fr he perfraed beam han her invesigaed pening gemeries. The usage f w exended hriznal siffeners upper and lwer he pening is he ms effecive ype f reinfrcemen cmpensae he srengh lss f he beam a he perfraed secin. Because i ransfers he shear frce alng he pening he regins besides i, herefre, Vierendeel mmen is decreased. Als i resrains he u-f-plane defrmains f he hriznal edges f he pening. Hence he buckling srengh f he reminder T-secin in he cmpressin side is increased. The usage f any ype f hriznal siffeners especially, he exended ypes A r D increases he lad capaciy f he perfraed beam wih a high rae a criical shear zne (a D/L=, 20%) han a high mmen znes (a D/L=35, 50%) Prviding an unreinfrced recangular web pening wih heigh beam deph rai (h/d) mre han 0.25 and widh--heigh rai (a/h) up 0.3 sharply decreases he shear capaciy a he perfraed secin. Reinfrcemen f he web pening wih verical siffeners has negligible effec n he capaciy f he perfraed secin; i may cause sress cncenrain arund he web pening which leads early failure. Thus, i is n recmmended use verical siffeners cmpensae he lss srengh f he beam a he perfraed secin. DOI:.9790/ Page

10 Fig. 11 max. disribued lad capaciy fr unreinfrced beams having square r recangular penings wih (h/d = 0.25) Fig. 12 max. disribued lad capaciy fr unreinfrced beams having square r recangular penings wih (h/d = 0.50) Fig. 13 max. disribued lad capaciy fr unreinfrced beams having square r recangular penings wih (h/d = 0.70) Fig. 14 max. disribued lad capaciy fr unreinfrced beams having circular penings. Fig. 15 max. cncenraed lad capaciy fr unreinfrced beams having square r recangular penings wih (h/d = 0.25) Fig. 16 max. cncenraed lad capaciy fr unreinfrced beams having square r recangular penings wih (h/d = 0.50) DOI:.9790/ Page

11 Fig. 17 max. cncenraed lad capaciy fr unreinfrced beams having square r recangular penings wih (h/d = 0.70) Fig. 18 max. Cncenraed lad capaciy fr unreinfrced beams having circular penings. Fig. 19 max. disribued lad capaciy fr perfraed beams wih (h/d = 0.50 & a/h =2) due differen siffeners Fig. 20 max. disribued lad capaciy fr perfraed beams wih (h/d = 0.50 & a/h =3) due differen siffeners Fig. 21 max. disribued lad capaciy fr perfraed beams wih (h/d = 0.70 & a/h =1) due differen siffeners Fig. 22 max. disribued lad capaciy fr perfraed beams wih (h/d = 0.70 & a/h =2) due differen siffeners DOI:.9790/ Page

12 Fig. 23 max. disribued lad capaciy fr perfraed beams wih (h/d = 0.70 & a/h =3) due differen siffeners Fig. 24 Vn Mises sresses (kn/m2) fr beam has a circular pening wih (h/d = 0.50) wihu reinfrcemen Fig. 25 Vn Mises sresses (kn/m2) fr beam has a circular pening wih (h /d = 0.70) wihu reinfrcemen Fig.26 Vn Mises sresses (kn/m2) fr beam has a recangular pening wih (h /d = 0.70 & a /h =2) a (D/L=%) and wihu reinfrcemen Fig. 27 Vn Mises sresses (kn/m2) fr beam has a recangular pening wih (h /d = 0.70 & a /h =2) a (D/L=%) and wih reinfrcemen ype (A) Fig. 28 Vn Mises sresses (kn/m2) fr beam has a recangular pening wih (h /d = 0.70 & a /h =2) a (D/L=%) and reinfrcemen ype (B) DOI:.9790/ Page

13 Fig. 29 Vn Mises sresses (kn/m2) fr beam has a recangular pening wih (h /d = 0.70 & a /h =2) a (D/L=%) and reinfrcemen ype (C) Fig. 30 Vn Mises sresses (kn/m2) fr beam has a recangular pening wih (h /d = 0.70 & a /h =2) a (D/L=%) and reinfrcemen ype (D) Fig. 31 Vn Mises sresses (kn/m2) fr beam (B26) wih reinfrcemen Type (B) under cncenraed lad Fig. 32 Vn Mises sresses (kn/m2) fr beam (B20) wih reinfrcemen Type (D) under cncenraed lad Fig. 33 Vn Mises sresses(kn/m2) fr beam (B31) wihu reinfrcemen under cncenraed lad Fig. 34 Vn Mises sresses (kn/m2) fr beam (B31) wih reinfrcemen ype (A) under cncenraed lad DOI:.9790/ Page

14 Table 8: Percenage f failure lads fr beams B22 B37 subjeced cncenraed lad wih reinfrcemen Beam number Un-reinfrced pening % Failure lad ( % frm failure lad f unperfraed beam) pening wih differen reinfrced sysems Type (A) Type (B) Type (C) Type (D) Type (E) B B B B B B B B B B B B B B B B Acknwledgemens The auhrs acknwledge he effr presened by Prf. Dr. Abd El Mniem Amin he Prfessr f seel srucures and bridges, Civil Eng. Deparmen, Faculy f Eng. Maaria, Helwan Universiy fr his supervisin f Mahmud s maser Thesis [11] which represen he main reference f his research wrk during he perid frm 1/2012 8/2013. References [1]. Cngdn, J. G. and Redwd, R.G. Plasic behavir f beams wih reinfrced hles, Jurnal f he Srucural Divisin, ASCE, Vl. 96, N. ST9, Prc. Paper 7561, Sepember 1970, pp [2]. Cper P. B. and Snell R. R. Tess n beams wih reinfrced web penings, Jurnal f he Srucural Divisin 1972; 98- ST3: [3]. Lupien R. and Redwd R. G. Seel beams wih web penings reinfrced n ne side, The Nainal Research Cuncil f Canada, Can. J. Civ. Eng. 1978; 5: [4]. Darwin D. Seel and cmpsie beams wih web penings - American Insiue f Seel Cnsrucin Seel Design guide series 1990; N. 2, Chicag, IL. [5]. American Insiue f seel cnsrucin. Manual f seel cnsrucin: Lad and resisance facr design specificain fr srucural seel buildings. AISC-LRFD, [6]. Redwd R. G. and Ch SH. Design f seel and cmpsie beams wih web penings, J. cnsrucin seel 1993; 25: [7]. Prakash B. D., Gupa L. M., Pachpr P. D., and Deshpande N. V. Srenghening f seel beam arund recangular web penings, Inernainal Jurnal f Engineering Science and Technlgy (IJEST) 2011, ISSN: , Vl.3 N.2: [8]. Akwasi M. A. Behavir f wide flange beams wih reinfrced web penings M.Sc. Thesis, Suhern Illinis Universiy Carbndale, [9]. ANSYS, finie elemen prgram, Swansn Analysis Sysem, Inc., Release 12.1, []. Chung K. F., Liu T. C.H. and K, A.C.H., 2003 Seel beams wih large Web penings f varius shapes and sizes: an empirical design mehd using a generalized mmen-shear ineracin curve. Jurnal f Cnsrucinal Seel Research, 59, [11]. Mahmud S. M. Srenghening f web penings in seel girders M.Sc. Thesis, Helwan Universiy Cair, DOI:.9790/ Page