AVERAGE STRESS-STRAIN RELATIONSHIP OF STEEL BARS EMBEDDED IN CONCRETE

Transcription

1 1 th World Conerene on Earthquake Engineering Vanouver, B.C., Canada Augut 1-6, 4 Paper No. 9 AVERAGE STRESS-STRAIN RELATIONSHIP OF STEEL BARS EMBEDDED IN CONCRETE Shaohua CHEN 1 and Tohimi KABEYASAWA SUMMARY In reent ear, material propert aed modeling method o reinored onrete memer are popularl adopted or nonlinear and dnami rame anale o truture, uh a multipring model, ier model and rame-element model or olumn and eam, alo the panel model (maro-fem) or hear wall. In thee maro-model, onrete and teel ar are idealized a uniorm and ontinuit material, average tre-train relation o onrete and teel ar hould e ued. The average tre-train relationhip o onrete or reinored onrete have een propoed in oten ompreion urve and tiening tenile urve. B axial tenion anali o reinored onrete ar with ond-lip relationhip etween teel ar and onrete, thi tud propoe an average tre-train relationhip o teel ar emedded in onrete. Alo a i-linear ond-lip model i propoed, the analtial approahe are tated. Uing the average tre-train relationhip o teel ar or rame model o eam or olumn, a good orrepondene etween analtial and experimental reult i otained. INTRODUCTION Man average tre-train relation model o teel ar emedded in onrete are propoed aed on experimental method and analtial method. In thi paper, we propoe an average tre-train relation model analtial method with a i-linear ond-lip model etween teel ar and onrete. Uing the propoed i-linear ond-lip model, reinored onrete ar under tenion loading are analzed and good orrepondene i got. Bae on tatitial anali o analtial reult, the average tre-train relation model i propoed. And we alo propoed the relation in ompreion region onidering the ulking o teel ar. Uing the propoed tre-train model, we did anali or rame-element model or eam, good preiion i got. 1 Diater Prevention Reearh Diviion, National Reearh Intitute or Earth Siene and Diater Prevention, Tukua, Iaraki, Japan h_hen@oai.go.jp Earthquake Reearh Intitute, The Univerit o Toko, Toko, Japan kae@eri.u-toko.a.jp

2 AVERAGE STRESS-STRAIN RELATION FOR CONCRETE Average Stre-train Relation o Conrete Without uing htereti model aed on ore-diplaement relation, material propertie aed maroelement model are popularl propoed in reent tudie or reinored onrete memer. In our tud, average tre-train relation o onrete hown in Figure.1 i adopted. σ σ t = t (ε t /ε).4 t εtmax βεtmax α ε α 1 ε E α ε 1 α 4 σmax ε 1 ε εun (εmax, σmax) ζ Figure.1: Average Stre-train Relation o Conrete Conidering ond eet etween teel ar and onrete, tenion tiening model i adopted or tenion envelope [Izumo, Shima and Okamura, 1989]. But or plain onrete, tenion trength i ater raked like roken line. Under plane tre tatu or panel model o hear wall, tre otening model are adopted or ompreion envelope [Vehio and Collin, 198]. Bond Stre-lip Relation etween Steel Bar and Conrete In order to anali reinored onrete ar under tenion loading, a i-linear model i propoed or ond tre-lip relation (Figure.1).The ond trength (τ u ) an e alulated with next ormula (1) propoed [Fujii and Morita, 198], τ mean the ond trength without tirrup ar, τ t tand or the eet o tirrup ar. But in ielding region o teel ar, the ond trength i redued to.τ u. τ = τ τ τ u t + τ t = (.7 = 49kA i t + 4.7) ND (1)

3 Where, i i deided plitting pattern hown in Figure. (a), () and (), take the minimum value o next vi, i and i alulated ormula (). A t tand or the um o area o tirrup ar and mean the pith o tirrup ar. The other parameter are hown in Figure.. vi i i = = (min [( + ) D + 1] = ND 1, k = 1 D + 1), k = 1, k = () τu τ Ater Yielding o teel ar (a) ( vi +1)D () ( i +1)ND () min O K Su.τu S D D D ( i +1)D Figure.: Bond Stre-lip Relation etween Conrete and Steel Bar The initial tine K an e hown a ormula () [Iwata, Li and Ohno, 1998]. ( 4) ( 1 D) ( KN ) K = 116 m () Uing the tenion keleton o onrete and ond-lip relation, the tenion keleton ure o teel ar i derived at next paragraph. THE AVERAGE STRESS-STRAIN RELATION FOR STEEL BAR Tenion keleton urve The keleton urve o are ar i oten impliied O-A-B-C, ut the keleton urve o ar emedded in onrete an e impliied a a i-linear model like O-A -C (Figure.). Here, ε h =.15, E p =.5E. σ.5 Bare Bar C C A B Ep Ep * A A * Steel Bar Emedded in Conrete O ε E εh.5 Figure.: tre-train relation o Steel Bar ε

4 The real ield trength o teel ar emedded in onrete an e alulated next ormula (4) [Hu, 199]. * 1.5 n t = (4) ρ Where, ρ tand or reinorement ratio, n tand or rate o E /E. In order to deide the look ield trength and harden tine E p, reinored onrete ar will e analzed under inrement tenion loading (Figure.4). The ditriution o tre and train are hown a Figure.4. In the anali, next uppoition are made. (1) Crak have uniorm ditriution and ame width. () Stre in onrete etion ha uniorm ditriution. A oon a the tre ome to the tenion trength o onrete, rak our. () Conrete etween rak i elati. (4) Stre and train o onrete near rak are. (5) Bond tre ditriution i mmetr etween two loe rak. (6) There i no lip at the middle etween two loe rak. The lip etween teel ar and onrete an e alulated next ormula (5). S( x) = x ( ε ε ) dx Balane o onrete an e repreented ormula (7) or (7 ). (5) P Balane o teel ar an e hown a ormula (6) or (6 ). τ πd dx = E dε πd / 4 (6) Figure.4 Bond Stre Ditriution Or dε E D 4 ε ε τ = C C = dx Ep D 4 ε > ε h (6 ) σ σ w σ (x) σ (x) ε w ε (x) ε (x) S=W/ τ u X x a ε ε σ S=W/ P (a) Stre Ditriution () Strain Ditriution () Bond Stre Ditriution τ πd dx = E Or τ = dε dx dε A C C = ED 4 p (7) (7 ) The oundar ondition an e hown a ormula (8).

5 dε dx x= dε, =, ε x= a / dx x= = ± = (8) Uing aove ormula (5) (8) and numerial method, average tre-train relation o reinored onrete ar an e olved. Figure.5 i a ample, the etion i 15x15mm and the teel ar i deormed ar (D16). The anali reult (heav line) reprodued experiment reult (dotted line) with good preiion; even the numer o rak had a good orrepondene. Average tre (1Mpa) 平均応力 ( 1 kg/ m ) m Anali p=1.7% Experiment Firt Crak Bare ar 1 4 Average 平均ひずみ train ( (.1) 1 - ) Figure.5 Average tre-train relation o reinored onrete ar Cut out the tenion ontriution o onrete onidered in tenion tiening model rom the anali reult o reinored onrete ar, average tre-train relation o teel ar an e got. The let graph o Figure.6 how the variation parameter o reinorement ratio p, and the right graph how the variation parameter o onrete trength. In Figure.7, the inluene o ield trength o teel ar i hown. Average tre (1Mpa) 平均応力 σ m ( 1 kg/ m ) Bare Bar From ottom to top: p=.75, 1.5, 1.5,.,.5,.% =Mpa =Mpa Average 平均ひずみ train ε(.1) m Parameter: reinorement ratio p Average tre (1Mpa) 平均応力 σ m ( 1 kg/ m ) Figure.6 Average tre-train relation o teel ar 4. Bare Bar From ottom to top: =6, 5, 1. 4,, 1Mpa p=1.%.5 =Mpa Average 平均ひずみ train ε(.1) m Parameter: onrete trength

6 Baed on tatitial anali o analtial reult with parameter o reinorement ratio, onrete trength and teel ield trength, the look ield trength and harden tine E p o i-linear model an e hown a ormula (9). * ' E E ' p p = n ρ = t * 1.5 * = (9) Average tre (1Mpa) 平均応力 σ m ( 1 kg/ m ) Bare ar From ottom to top: =7, =Mpa 1 6, 5,4, 5, Mpa p=1.% Average 平均ひずみ train ε(.1) m Figure.7 Average tre-train relation o teel ar (Parameter: ield trength ) Compreion keleton urve In ompreion region o teel ar, ond an e negleted, o the keleton o teel ar emedded in onrete i ame a are ar. The ield train o teel ar i aout., the train at onrete ompreive trength i alo around.. Beaue o expanion and ollape o onrete loading over onrete trength, ulking o teel ar will our, o the dereae o trength i onidered ater -1.5ε. The inner rule are propoed like Figure.8. σ p (ε 5, σ 5 ) ε max β ε max E= (ε 1, σ 1 ) (ε, σ ) ε E ε p ξ p ε u ε -.E β ε min ε min (ε 4, σ 4 ) (ε, σ ) (ε, σ ) Figure.8 Hitor model o teel ar THE ANALYSIS FOR REINFOCED CONCRETE MEMBER Experiment introdution An experiment o antilever i ued to veri the propoed model, Figure.9 [Y. Kaneko, T. Kaneko and S. Otani, H. Shiohara, ]. In the experiment, onl li hear ore i applied without axial ore. The etion o memer i mm(width) x mm(height), and the hear pan i 115mm. The propertie o onrete and teel ar are hown in Tale.1.

7 Steel ar Tpe Tale.1 Propertie o material Yield Strength Tenile Strength Modulu D x1 φ x1 Conrete Age [Da] Compreive Strength Tenile Strength Modulu x x x1 φ4@8 4-D1 Shear pan 115 Figure.9 Sample o antilever P Analtial model The antilever i modeled rame-element (Figure.1). Conidering pull out o teel at ix end, length o the analtial model i 5mm longer than that o the memer. The etion i divided into ore onrete, over onrete and teel ar. Core onrete ha ame propertie o plain onrete without tenion tiening eet, over onrete look a reinored onrete onidering tenion tiening eet. Element 1 5 Element 115 Element 65 P n n1+1 4 n+17 n+18 n n 4n+175n+17 6n+177n+17 n+1 n+ n n1+n+n+1 n1+n+ n1+n+4 Y n1+n+n+ n4 X h 5n+16 6n+16 n 7n+16 8n+16 Figure.1 Analtial model o antilever Reult o anali The load-diplaement relation o tet i hown in Figure.1; the analtial reult i hown in Figure.1. In teting, diplaement i hited to negative diretion. The relation etween axial extenion and diplaement i hown in Figure.14. The axial extenion mean the train o mm region at the ixed end. Teting reult are reprodued aout initial tine, ield load and axial extenion with good aura. 9 1 n+17 n+18 n n1+ n1+ n1+ n n+17 n+18 4n d Figure.11 Cell diviion o etion Figure.1 Load-diplaement relation o tet

8 14 Load(KN) Diplaem ent(m m ) Figure.1 Load-diplaement relation o anali AxialS train(.1) Diplaem ent(m m ) RESULTS Figure.14 Axial extenion to diplaement The reult o thi paper an e onluded next point. 1. Propoed a method to olve ond-lip prolem or reinored onrete ar under tenion loading.. Propoed a ilinear model or teel ar emedded in onrete.. Analzed a antilever with the propoed model and good orrepondene wa got. REFERENCES 1. Hajime Okamura and Kohihi Maekawa, Nonlinear Anali and Contitutive Model o Reinored Conrete, Vehio, F.J. and Collin, M.P.: Repone o Reinored Conrete to In-Plane Shear and Normal Stre, Department o Civil Engineering, Puliation 8-, Univerit o Toronto, Sakae Fujii and Shiro Morita, Reearhe on Bond Strength o Deormed Steel Bar Part 1 Formula o Bond Strength, Journal o Strutural and Contrution Engineering, No.4, pp.4-, Feruar Tatumi Iwata, Zhenao Li and Yohiteru Ohno, Calulation o Long-term Deletion o Reinored Conrete Sla in Conideration o Steel Slippage at Fixed Edge, Journal o Strutural and Contrution Engineering, No.51, pp , Augut Hu, T.T.C.: Uniied Theor o Reinored Conrete, CRC Pre, USA, Hirohi Kaneko, Takahi Kaneko, Shunuke Otani and Hitohi Shiohara, Inluene o Shear Capait and Loading-Rate Eet on Dutilit o Reinored Conrete Memer, Summarie o Tehnial Paper o Annual Meeting Arhitetural Intitute o Japan, Struture IV, C-, pp.1-,