2001-2002 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

Lu, ZT

Teng, JG

Wong, YL

Zhang, JW

2001-2002 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishedVoR allowe

PolyU Institutional Repository

???????????????????????张继文　　滕锦光　　吕志涛　　黄玉龙　 (????)　 (??????)　 (????)　 (??????)?　?　?????????? (CFRP)????????????????????????。??? , ?????????????????? , ?????????。??????????????????????? , ??????????。?? , ????????????????????????????:???? ,?? , ??????????????????????????。???????? , ????????????????。???　??　?????　???　??　?????????:TU375.202　　　?????:A????:1000-131X (2002)02-0020-061　?　　????????????????? , ????(?? , GFRP ?? CFRP ?)???? , ???? ,???????? , ????? , ????? , ??????????????????????? 。??? , ??????????????????????????????? , ??????????????????? , ????????? , ?????????????????? , ?????????[ 1] , ????? FRP ?? , ???????????????? 。????????????????????????? , ???????????????。????????????????????? (?:?????????? , ?????????)。?? ,????????????????????????????????????????????????????? 。???????????????????????? , ??????????。2　????2.1　?????????????????????????????:2001-04-22?????????????? (G-S567), ?????????。? , ??????????? (1800×1800×70),??????? (C25)???? (???????500???????  6.5@150 , ??), ??????? 1。????? SB1? SB5 , ??? SB1 ????? , ????? , ???????????? 1?2mm??????。??????????:???? b×b (3?)??? t (2?)。?SB2?SB3?????????? (500×500), ????? , ??? 1mm ? 2mm 。? SB4????????? (850×850), ??1mm 。?SB5??1mm???? (1400×1400)。????????????? 5mm , ?? ,??????? 1700mm×1700mm 。????????????????????????????8.65%, 25%? 67.8%。?????????????? ET???? , ??????????????? , ????????????????? 4mm ?????????。? 1　????????????? ?　　?????(MPa)????(MPa)????(MPa)?　????(MPa)??? 1800×1800×70(mm) — 26.4 — —?　? ??? 6.5@150mm (??) — — 340 431?　? ??? — — 335 417??? ET???? 5960 94 — 11?????????? , ???????????。?? , ??????????? , ?????????????? , ???? 2mm , ???????　? 35?? 2 ? ?　?　?　?　?　? Vol.35　No.2　2 0 0 2 ? 4 ? CHINA CIVIL ENGINEERING JOURNAL Apr. 　2002DOI :10.15951/j.tmgcxb.2002.02.003??????? , ?????????? 。???? , ??????????????? , ????????。?? , ??????????????????????????? 。?? , ??????????????????? , ???????????????????????。?? , ???????????????? 3?????。2.2　?????????????? 1??。?????????? , ???????????????????????? , ????????? 。????????150×150?????????????? 。(a)???(b)A-A???? 1　?????????????????:(1)???? , ??????????? , ???????????;(2)?????? , ??????????;(3)???? ,??????????????????;(4)?????????? , ???????????????。??????????? 0.3kN 。??????? , ????????。3　???????3.1　????????????????????????????????????????。??????????????????? 。???????? , ?????????????????? , ?? , ???? , ?? , ??????????。???????? , ??????????? , ????????? , ????????。???????????????????2。? 2　????????????????????(mm)?????????(%)????P cr(kN)??? SB1?????γcr(%)?????? Pe(kN)??? SB1????γe(%)??????(????)P u , min(kN)?????????P u , minPeSB1(???) ??? 21(0.00) 55.0(0.00) 36.1 0.66SB2500×500×1(8.65) 40(90.5) 67.5(22.7) 46.1 0.68SB3500×500×2(8.65) 40(90.5) 65.0(18.2) 46.1 0.71SB4850×850×1(25.0) 60(186) 85.0(54.5) 64.0 0.75SB51400×1400×1(67.8) 100 (376) 165 (200) 176.7 1.07?? 2????????????????? ,?????????? ,?????????????????????? 。?? ,? SB4 ?????1mm??? ,????????? 25%,???????????? SB1? 2.86? ,?????????1.54?。????????????????????????? ,?????????????????????????????。?????????????????? ,????????? 。?? ,???? ,??????????????? ,?????????????????????。3.2　?????????????????????????? ,???????? SB4????? 2。(a)???·21·　? 35?　? 2 ? ????·???????????????????????(b)???? 2　???????????????? , ?????????????????? , ?????????????????????。?? , ?????????????????4? 5?????????? , ???????? , ?????????????????????????????????????。3.3　???3?? 5???????-?????? , ????????? SB1????? , ??????????? 。?????????????? , ?????? SB2 , SB3?????? SB4????????? , ????? , ??????????? , ?????? SB5???????。?? , ???????? , ????????? , ?? , SB5 ????SB2? 2.5? 。? 3　?????-????3.4　???????????????(? 3)?? ,??????????????????? 。?????? ,??????????? ,??????????????????? 。???????? , ? SB2 ?SB4????????????????????????????????????????? ,?????????? ,??????????????? ,????????????????????。?????? ,?SB2? SB4?????????? ,?SB2? SB3?????? ,? SB4????????? ,?? ,??????????????(? 2a)。???????? SB5?? , ????? , ?????????????? , ????????????? (?????????? , ???????),?? , ?????????????????。?? , ???????????? (?????)????? , ??????????? 。??????? , ?????? , ????????????? , ???????????????????????????????? 。?????????? , ???????? , ??????????????。3.5　?????????SB2?SB3????SB4?????????? , ??????????? , ????????? , ????????? , ?? , ????????????????????? , ??????? , ??????????????????? (????????????????????????????????????)。??????????????????????????。3.6　?????????SB2?SB3?? , ???????????????? , ?????????????????????。??? , ?? 1mm ??? SB2?????????? 2mm ??? SB3?? 。??????????????????????????????????????????????????。?? , ????????? , ??????????????????????? 。?? , ??? , ?????????????????????????。????????????????? , ???????????????????????????? , ???????????????。?4???????????????????????????? 。??????? SB2 ? SB3 ,?????????????? , ????????SB4? SB5 , ???????????????。???????? , ?? 1mm ???? SB2 , SB4 ?SB5 , ???????????????????。?? , ????????????? SB2? SB3 , ??????? , ???????????? 。???·22· ?　?　?　?　?　? 2002 ?? , ???????????? , ????????????????。? 4　???????????4　???????????????????????????????????? , ?????????????。????? Jo-hansen[ 2 ～ 4]? 1943?????????????????????????????????? 。????:1.??????????????????????????? , ??????????????;2.?????? , ??????????????????????? 。???????????????????????? 。?????????????????? , ??????????。????????????????????????? 。?????????????????? , ???????????????????????? ,??????????????????? , ?????????? , ?????? 5a , 5b? 5c 。???????????:???????????????? ,????? mp? θ;???? ,??m′p? θ′。?? , m p , m′p ????????????????????? 。?????? , mp=m′p 。4.1　???????????? 5b?????? , ??????????????? , ???? Pu ??????? Ee ????????????????????? E i ????????:Ee =Pu ×1 =Pu (1)E i =8m p 1 -k 1 -k 2 +2k21(1 -k1 -k2)(1 -k 2) (2)?? , k 1= sa ??????????????? , k2=ba?????????? ,???????????。? E e=E i ?????????????Pu ?:Pu =8mp 1-k1 -k2 +2k21(1-k1 -k2)(1 -k2) (3)?? (3)?????? k1????? , ?:dPudk 1=16 mp k1(2 -k1 -2k2)(1 -k 1 -k 2)2(1 -k 2) (4)?dPudk 1=0 , ???? , ? k1=0? , ?? 5a?????? , Pu ???? Pu ,min , ?:Pu ,min =8mp 11 -k2 (5)???? Pu , min??????????? 。?? , ????????????????????????? (SB1), ???????????????????????? k3=ca (????????????)??? (3)? (5)?? k2 ??? ,???? (6)、 ? (7)??:Pu =8mp 1-k1 -k3 +2k21(1-k1 -k3)(1 -k3) (6)Pu ,min =8mp 11 -k3 (7)4.2　???????5c???????????????????????????????? (????????????????), ??????????????? , ??????? , ???????????????。???????????????????????? , ???????????????:P u =8mp 1 -2k11-k 2 +8tan φ4 (8)?? , φ=arcsin k12u,u = 1 -k 222 + 1-k22-k 12 ·?? (8)???? k1?? , ??:dP udk 1=8mp - 21-k2 +2sec2 φ4 dφdk 1 (9)?????? , ?????? Pu???? k 1??? , ?? k1 ? , ?????????????(8)?? , ???????2??3。??? (9)???? , ???????? k 1 ???? , ?? , ??????????????? k1??? 。·23·　? 35?　? 2 ? ????·???????????????????????? 5　?????????????5　??????????????????????? P u ??? (8)????? 、? (3)?? (6)???????? (5)?? (7)??????????????????? 6 , ?? , ?? k 1 ???? [ 0 , k 1 ,max] ????? ,k 1 ,max =1-k 22 ?????SB1 , k1 , max=1-k32 , ???? 5c?????????????? 2φ≤π2。????? k 1 ,max??? 3。? 3　????????????????????????k2(k3)k1 , maxP e(kN)????k1 ???P u ,min(kN)??(%)?????(????)k1 ???Pu ,min(kN)??(%)SB1 0.0882 0.456 55 0.110 36.1 -34.4 0.0 37.0 -32.7SB2 0.294 0.353 67.5 0.122 46.1 -31.7 0.0 47.8 -29.2SB3 0.294 0.353 65 0.122 46.1 -29.1 0.0 47.8 -26.5SB4 0.5 0.250 85 0.128 64.0 -24.7 0.0 67.5 -20.6SB5 0.824 0.088 165 0.088＊ 176.7 7.09 0.0 191.8 16.2　　＊SB5???????? k1 ???? 0.112 , ?? k1 ,max , ???? , ?? 0.088。?? 6???????? Pu? k 1??????? , ???????????? k1 =0? , Pu ????;??????? , Pu?????? k 1=0 , ???? , k1 ???????? 。??????????????????????? Pu ,min???? k 1???????? 3? , ?????????????? Pu , min??????????。?? k1=0? , ?????????????????? , ??? 6???????????????? Y ????。???? , ?????????????????? 。???????? , ?????????????? , ?? , ????????????????????????????? , ????????????? Pu ,min , ??? 3。?6　??????? Pu? k 1∈ [ 0 , k1 ,max]?????????? 3 ?????????????????Pu ,min??????? P e?????。?3????? 7????????????????????????????????????? (????)?????????。? k 2?? 0.7??? , ?????????? (????)??????????? , ?? k 2 ???????? , ?? , ??????????? 。????????????????????????????? , ????????? k 2?? 0.7????????????? , ?????????Χ????????。??? 3?? 7??????????????? Χs ?????? (?????)? Χt:Χs =1.53k32 -1.15k 22 +0.45k2 +0.62 (10)Χt =1.63k32 -1.15k 22 +0.48k2 +0.64 (11)?? , ???????????? Pud????·24· ?　?　?　?　?　? 2002 ?? 7　?????????? (????)???????:P ud = Pu ,minΧ (12)?? , Pu ,min????????? , ??? (8)??;??????? (????)??? , ????(5)??。6　?　　?????????????? , ???????????????????????? 。??????????????? , ???????????。?????????????? , ????????????????????????? 。?? , ???????? , ??????????????????????? , ???:???????? , ???????100 ～ 400mm?????? , ??????????? 50 ～ 100mm。???????? , ?????????????????????? , ??????????????? , ?? , ????????????? , ??????????????????????????? (??)????????。?? , ??????????? , ????????? , ????????? , ?????????????????????????。?? , ????????????????????? , ??????????????????????。??????????????????????:????????????????????? 。????????????????????? , ??? , ???????????? Pu , ????????????????? mp 。?　?　?　?[ 1] 　Erki M A , Hefferman P J.Reinforced concrete slabs externallystrengthened with fibre-reinforced plastic materials.Non-Metal-lic (FRP) Reinforcement for Concrete Structures , L Taerweed , E &FN Spon , 1995:509 ～ 516[ 2] 　 Johansen K W.Brudlinieteorier.I kommission hos TekniskForlag , Copenhagen , 1952 , Originally a doctors thesis[ 3] 　Johansen K W.Yield Line Theory.English Translation pub-lished by Cement and Concrete Association , London , 1962[ 4] 　Jones L L , Wood R H.Yield Line Analysis of Slabs.Firstpublished in USA by American Publishing Company , Inc.,1967THE BEHAVIOR OF TWO-WAY REINFOCED CONCRETE SLABS EXTERNALLYSTRENGTHENED WITH STEEL PLATE TO SUBJECT PATCH LOADZhang Jiwen Teng Jinguang(Southeast University) (The Hong Kong Polytechnic University)LǜZhitao Huang Yulong(Southeast University) (The Hong Kong Polytechnic University)AbstractThe behavior of two-way slabs externally strengthened with a steel plate to subject a patch load is studied in the paper , itis a simply supported reinforced concrete slab.It is focused to study the deformation , the crack resistance , the failure mode ,and the bearing capacity of the strengthened slabs.At same time , a test of five pieces of reinforced concrete square slabsbonded with steel plate is carried out.Based on the yield-line method , a practical method to predict the ultimate load ofstrengthened slabs is proposed.It is found that the results of proposed method are in good agreement with the minimum of up-per bond value.Key words:strengthening , reinforced concrete , two-way slab , bonding , yield-line method(??? 47?)·25·　? 35?　? 2 ? ????·???????????????????????

The behavior of two-way reinfoced concrete slabs externally strengthened with steel plate to subject patch load

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