Flexural Behaviour of Precast, Prestressed Ribbed RPC Bottom Panels

Transcription

1 Send Orders for Reprins o reprins@benhamsiene.ae 98 The Open Civil Engineering Journal Open Aess Flexural Behaviour of Preas Presressed Ribbed RPC Boom Panels Zheng Wenzhong* Lu Xueyuan and Wang Ying Key Lab of Sruures Dynami Behavior and Conrol of he Minisry Eduaion Harbin Insiue of Tehnology Harbin P.R. China Absra: This sudy inrodues a new ype of preas presressed reaive powder onree (RPC) boom panel for a large-span omposie slab. The boom panels whih have one or wo invered ribs wih openings a as formwork during he onsruion sage. The paper experimenally invesigaed he rak haraerisis defleion and normal seion bearing apaiy of four preas presressed ribbed RPC boom panels under flexural load. The resuls indiaed ha he RPC ulimae srain under non-uniform ompression is and he plasi influene oeffiien of he seion modulus is linear wih he longiudinal reinforemen raio. The ensile sress of RPC a he raked seion should be onsidered while alulaing he flexural siffness; he equaion used o deermine he nominal ensile sress of RPC as a major variable for alulaing he rak widh a he boom of panels was proposed. The boom panels generally exhibi an over-reinfored failure mode behaviour wihou he omposie layer; he alulaion mehod of he normal seion bearing apaiy of his mode was esablished. Keywords: Crak widh flexural siffness normal seion bearing apaiy preas presressed ribbed RPC boom panel reaive powder onree. 1. INTRODUCTION The omposie slab is a semi-fabriaed sysem ha onsiss of a preas boom panel and a omposie layer. The preas boom panel as as formwork during he onsruion sage and hen forms an inegral par of he omposie layer afer he solidifiaion of as-in-plae onree. Compared wih as-in-plae slabs omposie slabs have he advanages of low os rapid onsruion and improved qualiy onrol whih have led o is widespread appliaion hroughou he world [1 ]. To improve he inegriy of he wo layers a preas boom panel wih rough surfaes [2 3] or wih laie seel russ projes a he op [4-6] an be used. Preas boom panels wih a rough surfae are easy o produe bu have small spans. Preas boom panels wih laie seel russ projes a he op have beer inegriy and larger spans; however seel russes are expensive if hey are applied in large spans. To overome hese problems Jiang Qingqing [7] proposed a preas boom slab wih an invered rib ha has beer flexural siffness and bearing apaiy whih an be applied in larger spans and an redue os. To produe wo-way omposie slabs and furher improve he inegriy of he wo layers Wu Fangbo [8 9] and Zhou Youxiang [10] proposed he use of solid and hollow omposie slabs wih preas presressed ribbed boom panels respeively. The preas boom panels and heir omposie slabs are shown in Fig. (1). A row of invered ribs on whih reangular openings are se is loaed in he middle of he preas boom panel of a solid omposie slab (Fig. (1). *Address orrespondene o his auhor a he Key Lab of Sruures Dynami Behavior and Conrol of he Minisry Eduaion Harbin Insiue of Tehnology Harbin P.R. China; Tel: ; Fax: ; lv_xueyuan@126.om (a1)). Following he assembly of he boom panel ransverse reinforemens an be arranged in he reangular openings and a wo-way solid omposie slab ha has good inegriy is formed afer he as-in-plae onree is poured and hardened (Fig. (1). (a2)). A double-rib preas boom panel is applied in hollow omposie slabs (Fig. (1). (b1)). Eah side of he boom panel onains a row of invered ribs wih reangular openings. Lighweigh maerials an be plaed beween he wo rows of ribs during onsruion. Following assembly ransverse reinforemens an be arranged in he openings and a wo-way hollow omposie slab ha has good inegriy is formed afer solidifiaion of he as-in-plae onree (Fig. (1). (b2)). The appliable spans of boh omposie slabs menioned above are generally less han 8 m. One reason for he limied span is ha he presressing wires in preas boom panels provide mos of he reinforemen of a omposie slab; as a resul as he span of a omposie slab inreases he amoun of presressing in he boom panel mus be inreased whih leads o he exessive elasi ompression and reeping loss of he presress. Anoher reason is ha he flexural rak srain of an ordinary onree is relaively low so he rak widh and defleion mos likely anno saisfy he servieabiliy requiremens. To avoid hese problems we proposed using reaive powder onree (RPC) insead of ordinary onree o manufaure he preas presressed ribbed boom panels menioned above. RPC is a relaively new emen marix omposie ha was invened in he 1990 s [11 12]; RPC has ulra-high mehanial properies (he ompressive srengh is generally in he range of MPa) and superior durabiliy [13 14] and i an be used as an exellen building maerial. Currenly RPC is used in many ypes of onsruion inluding / Benham Open

2 Flexural Behaviour of Preas Presressed Ribbed RPC Boom Panels The Open Civil Engineering Journal 2015 Volume 9 99 (a1) Single-rib preas boom panel (b1) Double-rib preas boom panel (a2) Solid omposie slab Fig. (1). Preas ribbed boom panels and omposie slabs. (b2) Hollow omposie slab Table 1. Speimen parameers. Speimens Number of Presressing Wires Calulaion Span/mm b/mm b 1/mm h 1/mm h/mm B B B B Table 2. Speimen parameers. Cemen SF GBFS Quarz sand Superplasiizer W/B Seel fibre (by Volume) bridges [15] faory buildings [16] oean engineering and rehabiliaion [17]. A he servieabiliy limi sae and he ulimae limi sae he sress of he RPC in he ension zone of he flexural members should no be negleed [18]. Therefore i is neessary o sudy he flexural behaviour of hese members inluding he disribuion and developmen of raks he developmen of he alulaion mehods of he raking momen he flexural siffness and he normal seion bearing apaiy. 2. EXPERIMENTAL DETAIL 2.1. Speimen Design Four preas presressed ribbed RPC boom panels were designed and fabriaed of whih B1 and B2 were single-rib preas boom panels and B3 and B4 were double-rib preas boom panels. Eah of he speimens had a lengh of 2600 mm and he widh and hikness of he preas boom panel s flange was 500 mm and 40 mm respeively. The size of eah of he reangular openings in he invered ribs was 75 mm 25 mm and he spaing was 125 mm. Preensioned ehnology was used o produe he preas boom panel and he presressing wires were loaed a he middle of he preas boom panel s flange. The he parameers are presened in Table 1 and deails of speimens are shown in Fig. (2) Maerials The emeniious maerials used in his paper are as follows: P O 42.5 Porland emen (Chinese ode sandard ompressive > 42.5 MPa a he age of 28 days). The silia fume (SF) SiO 2 onen exeeds 92% and has a speifi surfae area of m 2 /kg. The granulaed blas furnae slag (GBFS) has a speifi surfae area of 475 m 2 /kg. Quarz sand: pariles of fineness of 70 holes and 140 holes were mixed in a raio of 1:1. Superplasiizer: polyarboxylae was used as a superplasiizer in he RPC mixes. Copperized seel fibres ha were 13 mm in lengh and 0.22 mm in diameer were used. The speimens remained in he formwork for 24 h and were auolaved a C for 12 h o aelerae he uring afer demoulding as presened in Table 2.

3 100 The Open Civil Engineering Journal 2015 Volume 9 Wenzhong e al. (a) Single-rib preas boom panel Fig. (2). Deails of he speimens. (b) Double-rib preas boom panel Table 3. Mehanial haraerisis of RPC in speimens. Speimen B1 B2 B3 B4 Compressive srengh /MPa Axial ensile srengh /MPa Noe: he RPC elasi modulus was 41.2 GPa and he RPC ompressive srain orresponding o he peak sress was Fig. (3). RPC dumbbell-shaped speimen. The speimens used for he ompression ess were 70.7 mm 70.7 mm 228 mm prisms and dumbbell-shaped (shown in Fig. (3) speimens were used for he axial ensile ess. The mehanial haraerisis of he RPC used in he speimens is presened in Table 3. The equaion of he ompressive sress-srain relaionship is given by Equaion (1):

4 Flexural Behaviour of Preas Presressed Ribbed RPC Boom Panels The Open Civil Engineering Journal 2015 Volume P/2 LVDT P/2 LVDT Blok LVDT Fig. (4). Experimenal devie. Fig. (5). Measuremen of he effeive presress. * 1.55 " #1.2 " 4 $ ' $ " & 0 %" ) " ' & 0 ( %" ) 0 ( "! f = + " 0 $ 6 & " 2 ' #1 %" ) + " - 0 ( " 0 where! is he ompressive sress of he RPC prism; f is he ompressive srengh of he RPC prism;! is he ompressive srain of he RPC prism; and! 0 is he ompressive srain orresponding o he peak sress of RPC. The reinforemen in he speimens onsised of low relaxaion spiral ribbed wires wih an elasi modulus of 193 GPa a srengh of 1588 MPa and a yield srengh of 1451 MPa. The onrolled sress for he srehing was 1020 MPa Experimenal Devie Speimens were simply suppored and esed under woonenraed line loads applied a he middle-hird of he slabs. To onvenienly observe he raks he boom faes of he speimens were oriened upward. To avoid he shear lag effe [19] rigidiy bloks were used o level he ribs and flange of eah of he speimens. The mid-span defleion was moniored using linear variable differenial ransformers (LVDTs). Resisane srain gauges were oninuously aahed a he op of ribs and he boom surfae of speimens of he pure bending seion; he experimenal devie is shown in Fig. (4). A eah level of load he widh of eah rak a he inerseion poins wih presressing wires were moniored using a rak-widh measuremen insrumen (0.002 mm) and he new raks were marked. 5 (1) 2.4. Measuremen of he Effeive Presress To auraely deermine he effeive presress of he presressing wires in he speimens he booms of he ribbed RPC boom panels (whih were fabriaed under he same ondiions) were grooved o expose he presressing wires and resisane srain gauges were aahed as shown in Fig. (5). The hanges in srain were measured by a srain olleion sysem and hen he effeive presress in he presressing wires was alulaed. 3. STRUCTURAL RESPONSE The raking momens of B1 B2 B3 and B4 were 7.67 kn m kn m kn m and kn m respeively. The firs rak of eah of he speimens appeared a he seion wih he opening. The raks exended and widened wih loading and some of he raks exended o he upper fae of he flange of eah speimen; however no rak was found on he ribs. Craks disappeared afer exending aross some disane and hen randomly appeared again a a nearby loaion and oninued o exend in he same direion. The raks on he boom fae of he flange of eah speimen were fine dense and disoninuous and no onsisen rak spaing was observed. The rak widh was obviously narrower han ha of an ordinary onree flexural member: a he mid-span momen of 0.95 imes he ulimae bending momen (M u ) he observed maximum rak widh was 0.2 mm. New raks were onsanly emerging unil he ulimae bending momen; he rak paerns of he pure bending seion on he boom fae of speimens are shown in Fig. (6). The mid-span load-defleion urves of all of he speimens are shown in Fig. (7). The mid-span defleions were approximaely linear wih he load before raking and beame larger gradually afer raking. When he load ex-

5 102 The Open Civil Engineering Journal 2015 Volume 9 Wenzhong e al. (a) B1 (b) B2 () B3 Fig. (6). Crak paerns on he boom fae of he speimens. eeded 0.8 M u he mid-span load-defleion urves ended o be horizonal and failure ourred due o he rushing of he RPC on he op of rib while he presressing wires did no yield. The ulimae bending momens of B1 B2 B3 and B4 were kn m kn m kn m and kn m respeively. The rushed area of he RPC was limied o he seion of he reangular opening for B1; however no relaionship wih he seion of reangular openings was found for he oher speimens. Only one of he ribs failed for speimens B3 and B4. The RPC ompressive srain on he op of he rib was found o inrease approximaely linearly wih loading before raking and o inrease gradually afer raking and he RPC ompressive srain was found o inrease subsanially while approahing failure. The RPC ompressive srain on he op of he rib was approximaely a he momen before failure ourred whih is onsisen wih he resul of he RPC beam [20]. All of he speimens exhibied he over-reinfored failure mode behaviour. In he ype of boom panel onsidered here he presressing wires are he major reinforemen of he omposie slabs in praial engineering. When suh a boom panel is a he ulimae limi sae he ompressive area of onree is muh greaer han ha of he RPC rib; herefore his ype of boom panel wihou omposie onree layer generally exhibis over-reinfored failure mode behaviour. 4. RESULTS AND DISCUSSION The seion wih openings was hosen as he alulaing seion in his paper beause i is he weakes seion of a preas presressed ribbed RPC boom panel. (d) B4 Fig. (7). Mid-span load-defleion urves Effeive Sress in he Presressing Wires The experimenal resuls indiaed ha he average effeive presress in he presressing wires of B1 B2 B3 and B4 under no-load ondiions were MPa MPa MPa and MPa respeively. The alulaions in he elasi analysis deermined ha he RPC ompressive sress on he op of he ribs for B1 B2 B3 and B4 were 6.13 MPa 9.46 MPa 9.79 MPa and MPa respeively and he sress levels (! p f R ) for B1 B2 B3 and B4 were and respeively.

6 Flexural Behaviour of Preas Presressed Ribbed RPC Boom Panels The Open Civil Engineering Journal 2015 Volume Fig. (8). Sress and srain disribuions a he raked seion Craking Momen The flexural raking ensile srains of B1 B2 B3 and B4 were and respeively whih were muh greaer han he srain orresponding o he RPC peak ensile sress [21]. Under he raking momens of he speimens he ompressive srains of RPC on he op of ribs are relaively small and in he elasi region bu he par of he RPC in he ension zone beame plasi. To alulae he raking momen of speimen he plasi influene oeffiien of he seion modulus! was inrodued. Aording o referene [22]! an be alulaed as follows:! = M r "# W p 0 f R (2) where M r is he raking momen and W 0 is he ransformed elasi seion modulus a he exreme ension fibre (he elasi modulus raio of presressing wires o RPC is α E =E p /E R =193000/41200=4.68). Based on he experimenal daa! of B1 B2 B3 and B4 was and 1.51 respeively. The bond beween presressing wires and RPC an inhibi raking; herefore! inreased wih he inrease of presressing wire amoun. Fiing he resuls generaed Equaion (3).! = 24.75" e (3) where! e is he raio of he area of he presressing wires o he area of he preas presressed ribbed RPC boom panels flange. The mean raio of fied values o experimenal derived values of! is 1.01 and he oeffiien of variaion is Defleion Calulaion The flexural siffness of all speimens dereased wih he inrease of he mid-span momen. Under he raking momen he flexural siffness values of B1 B2 B3 and B4 were 0.84E R I 0.84E R I 0.85E R I and 0.88E R I respeively whih were onsisen wih ha of an ordinary onree flexural member [22]. To simplify he alulaion 0.85E R I was aken as he flexural siffness of he speimens before raking ourred. In he pos-raking sage based on plane ross-seion assumpion he heigh of he neural axis an be alulaed aording o he daa measured by resisane srain gauges aahed a he op of ribs and he boom of he speimens. For he mid-span momen beween M r -0.8 M u he heighs of he neural axis of he speimens remain approximaely onsan. The mean heighs of he neural axis of B1 B2 B3 and B4 were 34.8 mm 65.9 mm 53.7 mm and 62.3 mm respeively. The formula o alulae he mean heigh of he neural axis in pos-raking sage (M r -0.8 M u ) was deermined by fiing o be he following: x 91.2 Ar = + A 22.1 (4) f where A r is he ross-seional area of ribs wihou opening and A f is he ross-seional area of he flange of he speimen. The mean raio of he fied values o he experimenally derived values of he heigh of he neural axis is 1.0 and he oeffiien of variaion is To onsider he ensile sress of RPC a a raked seion he RPC ensile sress of he preas boom panel flange is assumed o be uniformly disribued he reduion oeffiien of he RPC elasi modulus ( k! ) is inrodued and he RPC ensile sress on he ribs is assumed o be negligible. The pos-raking flexural siffness model of he speimens is shown in Fig. (8). When he neural axis passes hrough he openings and above he openings he momens of ineria ( I r ) a he raked seions an be alulaed using Equaions (5-1). and (5-2). I r = ( ) b r x 3! x" # E A p x k" bh f x I r = b r x3 3 +! E A p x k" bh f x (5-1) (5-2) where x! is he disane from he neural axis o he op of he openings. The effeive momen of ineria an be alulaed using Equaion (6).

7 104 The Open Civil Engineering Journal 2015 Volume 9 Wenzhong e al.! I e = # " M r M 3 $ (! & I g + * 1' # % * ) " where I g =0.85I. M r M 3 $ + - & % - I r (6) On he basis of mehanis knowledge he pos-raking defleion of mid-span an be alulaed as follows: 23pl 3! = (7) 1296E R I e Aording o he analysis i an be deermined ha k! = The alulaed flexural siffness (! ) agreed well wih he experimenally derived flexural siffness (! ) (M r M u )!! is shown in Fig. (9) for whih he mean value is 1.02 and he oeffiien of variaion is Fig. (9). Raio of he fied value o he experimenally derived value of he mid-span defleion Crak Widh Calulaion Reinforing seel sress is used as he major variable in mos equaions [22-24] used for alulaing he rak widhs in he flexural members. However he differene beween he disane from he neural axis o he presressing wires and he disane from he neural axis o he boom fae was relaively large; herefore he reinforing seel sress a he raked seion anno auraely predi he rak widh. In his paper he ross-seions of speimens were assumed o be elasi hus enabling he nominal ensile sress (! R ) a boom fae o be alulaed. The reinforemen raio should also be onsidered for he bond beween presressing wires o enable he RPC o inhibi he rak widh. For mid-span momen values of M r -0.8 M u he rak widh was found o be linear wih loading; he fiing resul in Equaion (8). ( ) w m = $ % 2.52! R " # f R & ' (10"3 (8) The experimenal and alulaed resuls of he rak widh are shown in Fig. (10). The mean value of he alulaed rak widh o he measured raked widh was 1.02 and he oeffiien of variaion was Fig. (10). Measured and alulaed values of he average rak widh. The maximum rak widh an be obained by Equaion (8). muliplied by an amplifiaion oeffiien! s : w =! w (9) max s m The amplifiaion oeffiien! s an be deermined using he probabiliy disribuion of he rak widhs. Saisial analysis indiaed ha for he mid-span momen values in he range of M r -0.8 M u wi w m follows he lognormal disribuion wih a mean ( µ ) and sandard deviaion (! ) of and respeively ( w i is he rak widh a a erain load level w m is he average rak widh a he load level). The frequeny disribuion and probabiliy densiy urve of wi w m are shown in Fig. (11). The alulaions indiaed ha he amplifiaion oeffiien (! s ) of he rak widh wih 95% onfidene is 1.9. As a resul he maximum rak widh wih 95% onfidene an be alulaion using Equaion (10). w # 3 (! " f ) = $ ' 4.78 # % ( & 10 (10) m R R Fig. (11). Crak widh frequeny disribuion Normal Seion Bearing Capaiy In onras wih an ordinary onree flexural member he effe of RPC ensile sress should be onsidered a he

8 Flexural Behaviour of Preas Presressed Ribbed RPC Boom Panels The Open Civil Engineering Journal 2015 Volume (a) Aual sress disribuion Fig. (12). Sress disribuion on a ross seion of he speimen a he ulimae momen. (b) Equivalen sress disribuion ulimae momen [20]. The failure mode of all speimens was rushing of he RPC on he op of rib wihou he yielding of he presressing wires; herefore he normal seion bearing apaiy should be alulaed by he mehod of an over-reinfored flexural member. To deermine he normal seion bearing apaiy of a preas presressed ribbed RPC boom panel he follows assumpions are made: 1 he plane seion remains plane afer bending; 2 he ensile sress of he RPC in he boom panel flange has a reangular disribuion wih a heigh of kf R ; and 3 he ensile sress of he RPC in he rib is negleed. To simplify he alulaion he aual sress disribuion an be simplified by an equivalen reangular sress diagram (he remaining ompressive resulan fore and is applied poin onsan) as shown in Fig. (12).). Based on he RPC ompressive sress-srain relaionship he equivalen oeffiiens! and! an be deermined as 0.9 and 0.77 [20] respeively. For he srain of seion ha remains plane afer bending when he yielding of presressing wires and he failure of RPC ourred simulaneously he relaive deph of limiing ompression zone! b an be alulaed aording o following equaion: " 1! b = x b = h p # u + f py $% p0 where ( ) E s # u (11) h p is he effeive deph of he seion f py is he yield srengh of he presressing wires! is he sress in he presressing wire while he normal sress of RPC a he deph of presressing wire is equal o 0 and! u is he RPC ulimae srain under non-uniform ompressive ( ). The values of! b of B1 B2 B3 and B4 were and respeively. To simplify he alulaion and provide a margin of safey he value of! b = was hosen. Based on momen equilibrium he normal seion bearing apaiy is alulaed using Equaion (12). M u =! 1 f bh 2 R p " b ( 1# 0.5" b ) (12) p0 The alulaed value of he normal seion bearing apaiy M u and he experimenally derived value M u were found o agree well: he mean of M M is 0.99 and he oeffiien of variaion is CONCLUSION This paper inrodued preas presressed single-rib and double-rib preas RPC boom panels and invesigaed heir flexural behaviour under flexural load. Based on he resuls he following onlusions an be derived. 1) For a seel fibre mix proporion of 2% by volume he RPC ulimae srain under non-uniform ompressive is whih is greaer han ha of ordinary onree (approximaely ); he RPC bend raking ensile srain is whih is greaer han ha of ordinary onree ( ). 2) The proposed alulaion formula for raking momen onsiders he reinforemen raio when alulaing he plasi influene oeffiien of he seion modulus. 3) The raks a he boom of a preas presressed ribbed RPC boom panel were fine dense and disoninuous and no onsisen rak spaing was found. The proposed alulaion formula used he RPC nominal ensile sress as major variable and onsidered he effe of he reinforemen raio. 4) The flexural siffness gradually redued wih loading. Under he raking momen of he speimens he flexural siffness was deermined o be 0.85ER I. For values of he mid-span momen in he range of M r ~0.8 M u he effe of he RPC ensile sress should be onsidered when alulaing he flexural siffness and he RPC reduion oeffiien of he elasi modulus k! = 0.35 should be used in he alulaion. 5) In a preas presressed ribbed RPC boom panel he primary bearing reinforemens of he omposie slab he speimens exhibied over-reinfored failure mode behaviour. Based on he experimenal resuls he normal seion bearing apaiy of his mode was deermined. CONFLICT OF INTEREST The auhors onfirm ha his arile onen has no onfli of ineres. u u

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