AN IMPROVED CREEP AND SHRINKAGE BASED MODEL FOR DEFLECTIONS OF COMPOSITE MEMBERS REINFORCED WITH CARBON FIBER REINFORCED BARS
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1 N MPROVED CREEP ND SHRNKGE BSED MODEL FOR DEFLECTONS OF COMPOSTE MEMBERS RENFORCED WTH CRBON FBER RENFORCED BRS M.. Fruqi, S. Bhdr D. Sun, nd J. Si Deprmen o Civil nd rhieurl Engineering, Tex & M Univeriy, Kingville, US E-Mil: m-ruqi@muk.edu BSTRCT Corroion o eel nd reuling degrdion o onree everely e he erviebiliy nd ey o uure. Million o dollr re pen every yer or he repir nd rehbiliion o uh uure. Crbon iber reinored polymer (CFRP provide exellen hoie o rei orroion. n hi pper n improved nlyil model o predi he reep nd hrinkge bed deleion o CFRP reinored onree lexurl member i preened. Deleion vlue re ompred wih experimenl d rom lierure nd ommonly ued model. Our reul how h he propoed model orrele well wih he experimenl reul nd provide muh beer prediion hn he merin Conree niue (C proedure nd ommon lierure model. Keyword: model, uure, eel, onree, CFRP reinoremen, lexurl member, reep, hrinkge, deleion.. NTRODUCTON Reinored onree uure, expoed o mophere re uepible o orroion o reinoring eel. Thi ubequenly e he erviebiliy nd ey o uure. Expoure o evere nd hrh limi ondiion ggrve he iuion. Reoiing meure or he rehbiliion o uure n inur huge o. Fiber Reinored Polymer (FRP provide exellen reine o orroion. Long erm deleion nd urvure re governed by reep nd hrinkge. Someime hee ime-dependen deormion n be o lrge h i ould poe evere hre o he erviebiliy o he uure. n hi pper, n improved nlyil model o predi he reep nd hrinkge bed deleion o CFRP reinored onree lexurl member i preened. Deleion vlue re eed wih experimenl d rom lierure, ommonly ued lierure model, nd C proedure.. PROPOSED PPROCH Experimenl d [] on deleion nd ommon nlyil pprohe [, ] or prediing he ime dependen behvior o CFRP reinored onree bem hve been ued omprion in hi reerh. The pplibiliy o hee ommon model i limied due o heir inbiliy o oun or relive humidiy. Thi bi reerh oni o wo pr. Fir pr involve he developmen o propoed nlyil model nd he eond pr ompre he model vlue wih he experimenl d nd oher model.. Propoed model Symbol ued in he model re lied in he nomenlure eion. Tol deleion ny priulr ime i he um o innneou nd ime dependen deleion. The innneou deleion i ompued by eli nlyi. Time dependen urvure nd deleion hve been deermined uing reep nd hrinkge oeiien. Seion properie hve been deermined uing ge djued eli modulu mehod. Men urvure he end o loding period i: ( + λ [] ( λ M.75 λ M pplied rked For rked nd unrked eion M E M E eeive Prboli vriion i umed or innneou enl deleion. The pproxime innneou mximum deleion ener i provided by: ( L i [] 5 Men urvure ime i provided by: ( λ ( + + λ ( + [] λ (.5 M M rked pplied Chnge o urvure i provided by: [, ε (, y r ] + [4] α ϕ( 74
2 [ ϕ, ε (, y r ] + [5] α ( ge djued eion properie re: α [6] r eeive r b + ( d + ( d [7] vlue re obined by eing he ollowing equion o zero: b + ( d ( d { (, } η η(, η (, E CFRP E (, 57 E (, ( ( (8 + { (4.85 } y ; r ; b eeive r r ( M M + Creep lulion re ollow: ϕ (, ϕβ (, ϕ ϕ β ( m β ( [ ( M r M ] r {(.46( h } ϕ [9] + e h [8] he g u β ( m 5. ( m mo.5 {. (. } β ( + [{( }{ + ( }]. β (, β H 8 [ + (. ]( h β 5 h H Shrinkge lulion re ollow: (, (, ε ε β o ε ε ( m o ε β β β e 6 (.[ 6 + ( 9 ] β [] m m mo 5 or ype Ι emen [ ( ].55 Long erm deleion mid-pn i provided by: ( L + ( ( l ln. []. COMPRSON OF DEFLECTON VLUES Figure- nd Tble- ummrize he reul o bem B, while Figure- nd Tble- ummrize he reul o bem B. To ommode ommon humidiy rnge in hi re, lower nd upper vlue o 5% nd 8% were onidered. For bem B, he propoed rio rnge rom. o.6 ompred o.66 o 5.97 or ommon model. n he e o bem B, he propoed rio rnge rom.98 o.9 ompred o.6 o 7.55 rnge or oher model. Figure nd how imilr onluion. Figure-. Grphil omprion o deleion vlue or bem B. 75
3 Tble-. Comprion o deleion rio or bem B. Dy C Exp Model [] Exp Prop [5%] Exp Prop [8%] Exp Figure-. Grphil omprion o deleion vlue or bem B. Tble-. Comprion o deleion rio or bem B. Dy C Exp Model [] Exp Prop [5%] Exp Prop [8%] Exp CONCLUSONS ND FUTURE WORK n hi pper n improved nlyil model o predi he reep nd hrinkge bed deleion o CFRP reinored lexurl onree member i preened. Deleion vlue re eed wih experimenl d rom lierure, ommonly ued lierure model nd C proedure. Bed on hi udy, he ollowing onluion n be drwn: Comprion o nlyil prediion wih he experimenl d nd oher model how h he propoed model orrele beer wih he experimenl vlue. The re o inree o deleion i higher in he iniil loding period nd end o redue wih repe o longerm. n improved nlyil model o predi he reep nd hrinkge bed deleion o CFRP reinored onree member i inodued. Good greemen i ob erved beween nlyil prediion nd experimenl reul. Thi model n be ued deign ool o predi he long erm deleion o CFRP reinored onree member. However, more experimenl nd nlyil work i needed o urher vlide hi pproh. Fuure reerh my inlude: Ue o mbien mopheri emperure nd hpe oeiien or dieren iber reinored polymer in he model. 76
4 Nomenlure L Lengh o bem M pplied bending momen pplied M rked Crking momen 8 dy (uring period o he CFRP reinored onree bem Number o dy er he uring period i over dy E Modulu o eliiy o onree E Modulu o eliiy o CFRP CF RP E(, ge djued modulu o eliiy o onree C y Neul xi deph o he ge djued rked eion Hl o he neul xi deph o he ge djued rked eion r Rdiu o gyrion o he ge djued rked eion Gro momen o ineri o he eion r Momen o ineri o he ge djued rked eion Eeive momen o ineri o he ge djued eeive rked eion b Widh o he eion d Deph o he enion reinoremen rom he op o he eion d u g h λ λ ( Deph o he ompreion reinoremen rom he op o he eion Gro re o he ro eion Perimeer o he ro eion re o enion CFRP reinoremen re o ompreion CFRP reinoremen Trnormed re o he equivlen enion CFRP reinoremen Trnormed re o he equivlen ompreion CFRP reinoremen re o onree in ompreion Prmeer h ke ino oun ro-eionl dimenion Coeiien o innneou urvure Coeiien o long ime urvure nnneou urvure o bending Men urvure ime ( Curvure o he member ime nnneou urvure or rked eion nnneou urvure or n unrked eion Time dependen hnge in urvure due o reep nd hrinkge Chnge in urvure or rked eion Chnge in urvure or n unrked eion ϕ Time dependen reep oeiien (, ε (, Time dependen hrinkge oeiien η ge djued modulr rio (, (, ge djued men ompreive engh o onree ε Shrinkge in or priulr onree o engh nd relive humidiy ε ( m Coeiien h oun or 8 dy onree ompreive engh β Coeiien h oun or 8 dy ( m onree ompreive engh β (, Coeiien h oun or hrinkge β (, Coeiien h oun or reep β H Coeiien h ke ino oun he ee o relive humidiy or reep β Coeiien h ke ino oun he ee o relive humidiy or hrinkge β Coeiien h oun or emen ype β ( Coeiien h oun or ime m Men ompreive engh o onree 8 dy mo MP (onn vlue h, h e Prmeer h ke ino oun roeionl dimenion ϕ Bi reep oeiien ϕ Relive humidiy oeiien α Curvure reduion or Relive humidiy i nnneou deleion L Long erm deleion % relive humidiy 77
5 REFERENCES [] M. rokimy, S. Chidmbrm,. mer nd M. Shhwy.. Time-dependen deormion o onree bem reinored wih CFRP br. Compoie: Pr B. : [] 8. merin Conree niue, Commiee 9, Deoi, M. 78
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