蘇鵬++李恒++丑佳璇++彭暉
摘要:表層嵌貼預(yù)應(yīng)力FRP板條加固鋼筋混凝土結(jié)構(gòu)技術(shù)可充分發(fā)揮FRP材料強(qiáng)度,且不需設(shè)置永久錨具,具有較大的潛力。以試驗(yàn)得到的嵌貼FRP混凝土粘結(jié)滑移關(guān)系為基礎(chǔ),建立了嵌貼預(yù)應(yīng)力CFRP板條與混凝土的粘結(jié)應(yīng)力微分方程,并根據(jù)邊界條件推導(dǎo)了方程的解析解,得到了嵌貼預(yù)應(yīng)力CFRP板條放張后界面粘結(jié)應(yīng)力、CFRP拉伸應(yīng)力的分析模型。與試驗(yàn)結(jié)果的比較表明,該模型得出的界面粘結(jié)應(yīng)力及CFRP拉伸應(yīng)力與試驗(yàn)結(jié)果吻合較好。在此基礎(chǔ)上,考慮放張后CFRP混凝土界面不出現(xiàn)剝離的條件,分析了粘結(jié)界面能抵抗的最大容許預(yù)應(yīng)力。
關(guān)鍵詞:表層嵌貼;CFRP板條;預(yù)應(yīng)力;粘結(jié)滑移關(guān)系;應(yīng)力傳遞
中圖分類號(hào):TU378.2文獻(xiàn)標(biāo)志碼:A文章編號(hào):16744764(2017)01006809
收稿日期:20160304
基金項(xiàng)目:國(guó)家自然科學(xué)基金(51578078);國(guó)家重點(diǎn)基礎(chǔ)研究發(fā)展計(jì)劃(973)(2015CB057701);湖南省科技計(jì)劃(2014FJ4176);湖南省教育廳科學(xué)研究重點(diǎn)項(xiàng)目(14A005);長(zhǎng)沙市科技計(jì)劃(K150802031)
作者簡(jiǎn)介:蘇鵬(1991),男,主要從事橋梁結(jié)構(gòu)耐久性能研究,(Email)1027833712@qq.com。
彭暉(通信作者),男,教授,博士,博士生導(dǎo)師,(Email)anchor1210@126.com。
Received:20160304
Foundation item:National Natural Science Foundation of China (No. 51578078);National Program on Key Basic Research Project of China (973 Program)(No. 2014FJ4176);Scientific Research Key Project in Hunan Province Department of Education(No.14A005);Science and Technology Plan of Changsha(No.K150802031)
Author brief:Su Peng(1991), main research interest: bridge structure durability performance,(Email)1027833712@qq.com.
Peng Hui(corresponding author),professor,PhD,doctorial supervisor,(Email) anchor1210@126.com.Stress transfer of reinforced concrete beam strengthened with
nearsurface mounted prestressed CFRP strips
Su Penga ,Li Henga , Chou Jiaxuana ,Peng Huia,b
(a. School of Civil Engineering and Architecture; b. NationalLocal Joint Engineering Laboratory of
Technique for Longterm Performance Enhancement of Bridges in Southern District,
Changsha University of Science & Technology, Changsha 410114,P.R.China)
Abstract:Due to the advantages of making full use of high strength of FRP and saving the cost of premature anchorages for prestressed FRP, the technique of strengthening with prestressed nearsurface mounted (NSM) FRP was considered as a potential technique for strengthening of reinforced concrete structures. The bond behavior of the NSM CFRP strip in the stress transfer length after releasing the prestress was studied. Based on the bond slip constitutive relationship obtained from experimental research, the differential equation of the bond stress at the NSM FRPconcrete interface was established. Then the analytical solution of the differential equation was acquired according to the boundary conditions, and the equations of distribution of the bond stress at the bonded interface and the tensile stress of CFRP were presented. The theoretical results were in good agreement with the test results, which indicated that the equations could be used to predict the distribution of bond stress at the NSM FRPconcrete interface after prestressing force release. Moreover, the maximum allowable prestress was obtained by considering no debonding at the bonded joint to be induced due to pretension release.
Keywords:nearsurface mounted(NSM); CFRP strips; prestressed; bondslip relationship; stress transfer
纖維增強(qiáng)復(fù)合材料(Fiber Reinforced Polymer, FRP)作為一種新型加固材料,由于其質(zhì)量輕、力學(xué)性能強(qiáng)、易于成型和耐久性能好等優(yōu)點(diǎn),已在土木工程結(jié)構(gòu)特別是混凝土橋梁加固中得到了廣泛應(yīng)用。傳統(tǒng)的外貼(Externally Bonded, EB)FRP加固技術(shù)由于其工藝簡(jiǎn)單、方便,廣受工程界歡迎。但EB FRP 難以充分發(fā)揮FRP 的高強(qiáng)材料性能[1],并且EB FRP混凝土界面易剝離。為了充分發(fā)揮FRP的高強(qiáng)性能,對(duì)FRP預(yù)先施加預(yù)應(yīng)力,這樣預(yù)應(yīng)力外貼FRP技術(shù)就得到了開(kāi)發(fā)和利用[23]。另一方面,為了解決EB FRP與混凝土界面易剝離的問(wèn)題,并更好保護(hù)FRP,表層嵌貼(NearSurfaceMounted, NSM)FRP技術(shù)得到了開(kāi)發(fā)和利用[46]。這項(xiàng)技術(shù)將FRP筋或板條嵌入預(yù)制的混凝土槽中并填入環(huán)氧樹(shù)脂膠用來(lái)粘結(jié)FRP與混凝土,通過(guò)擴(kuò)大FRP混凝土之間的粘結(jié)面積來(lái)增強(qiáng)兩者間的粘結(jié)能力,但也沒(méi)能很好地發(fā)揮FRP 的高強(qiáng)性能。最近出現(xiàn)的預(yù)應(yīng)力NSM FRP 技術(shù)通過(guò)對(duì)嵌貼的 FRP預(yù)先施加預(yù)應(yīng)力實(shí)現(xiàn)了對(duì)FRP 強(qiáng)度的充分利用,并更顯著地提高了結(jié)構(gòu)的受力性能,同時(shí)NSM FRP混凝土的粘結(jié)能力可為預(yù)應(yīng)力提供錨固,從而節(jié)省預(yù)應(yīng)力加固技術(shù)中所需要的機(jī)械錨具費(fèi)用,具有較顯著的技術(shù)經(jīng)濟(jì)優(yōu)勢(shì)和廣闊的應(yīng)用前景[78]。
與傳統(tǒng)的預(yù)應(yīng)力混凝土結(jié)構(gòu)不同,預(yù)應(yīng)力NSM加固是將FRP嵌貼在混凝土保護(hù)層中,F(xiàn)RP中的預(yù)應(yīng)力通過(guò)FRP混凝土間的粘結(jié)傳遞至被加固結(jié)構(gòu)。因此,F(xiàn)RP混凝土間的粘結(jié)能力決定了放張預(yù)應(yīng)力后FRP與混凝土之間的應(yīng)力傳遞行為,這種應(yīng)力傳遞又對(duì)預(yù)應(yīng)力NSM FRP加固結(jié)構(gòu)的性能有著重要影響。預(yù)應(yīng)力過(guò)大時(shí),F(xiàn)RP混凝土之間的粘結(jié)可能無(wú)法抵抗應(yīng)力傳遞所產(chǎn)生的過(guò)大剪應(yīng)力,發(fā)生粘結(jié)剝離甚至破壞;預(yù)應(yīng)力過(guò)小,則無(wú)法充分發(fā)揮FRP的高強(qiáng)性能,造成技術(shù)經(jīng)濟(jì)上的低效和浪費(fèi)。因此,研究放張后FRP混凝土間的應(yīng)力傳遞行為并確定粘結(jié)界面所能承受的預(yù)應(yīng)力容許水平,對(duì)于應(yīng)用和推廣預(yù)應(yīng)力NSM FRP加固技術(shù)至關(guān)重要。
目前,部分研究人員對(duì)EB預(yù)應(yīng)力CFRP放張端部的粘結(jié)應(yīng)力分布進(jìn)行了研究,并提出了不設(shè)置永久錨具條件下EB CFRP的最大容許預(yù)應(yīng)力水平[910]。但由于外貼CFRP與混凝土間的粘結(jié)能力有限,實(shí)際工程結(jié)構(gòu)采用外貼預(yù)應(yīng)力CFRP加固時(shí)多設(shè)置了永久錨具。如前所述,F(xiàn)RP板條的預(yù)應(yīng)力由嵌貼FRP混凝土間的粘結(jié)能力實(shí)現(xiàn)錨固,在不考慮槽壁混凝土破壞的條件下,F(xiàn)RP與混凝土間的粘結(jié)性能決定了可錨固的預(yù)應(yīng)力最大值。關(guān)于NSM FRP與混凝土的粘結(jié)性能目前已經(jīng)開(kāi)展了一定的研究[11],學(xué)者們分別調(diào)查和分析了開(kāi)槽構(gòu)造[1213]、槽邊距[1415]等因素對(duì)NSM FRP混凝土粘結(jié)性能的影響,建立了多個(gè)局部粘結(jié)強(qiáng)度模型[1617]。另外,Badawi等[18]研究了不同表面形式、不同應(yīng)力水平的預(yù)應(yīng)力NSM FRP筋放張后的傳遞長(zhǎng)度,但針對(duì)預(yù)應(yīng)力NSM FRP放張后,F(xiàn)RP混凝土界面粘結(jié)應(yīng)力分布及應(yīng)力傳遞行為的研究工作尚未見(jiàn)報(bào)道。
本文在通過(guò)試驗(yàn)研究考察嵌貼CFRP板條與混凝土間的粘結(jié)滑移行為的基礎(chǔ)上,獲得了考慮殘余摩擦力的三線性粘結(jié)滑移本構(gòu)關(guān)系,建立了預(yù)應(yīng)力放張后嵌貼FRP板條與混凝土界面的粘結(jié)應(yīng)力分布模型,并分析了粘結(jié)界面所能抵抗的最大預(yù)應(yīng)力,為表層嵌貼預(yù)應(yīng)力CFRP加固技術(shù)的應(yīng)用和發(fā)展提供了理論依據(jù)和指導(dǎo)。
1嵌貼FRP混凝土粘結(jié)滑移關(guān)系及
加固梁模型通過(guò)拔出試驗(yàn),考察了嵌貼CFRP板條與混凝土間的粘結(jié)行為 [19],共進(jìn)行了33個(gè)表層嵌貼CFRP加固混凝土試件的單剪試驗(yàn),試件設(shè)計(jì)及試驗(yàn)裝置如圖1、2所示。試件由素混凝土棱柱體和嵌貼的CFRP板條組成,混凝土棱柱規(guī)格及強(qiáng)度如表1所示,棱柱體表面均制作了30 mm深度的預(yù)制槽用于嵌貼FRP。試件加固采用美國(guó)Aslan公司生產(chǎn)的500型CFRP板條,截面尺寸分別為16 mm×2.0 mm和16 mm×4.5 mm;粘結(jié)樹(shù)脂采用瑞士Sika公司生產(chǎn)的Sikadur30型樹(shù)脂,廠商提供的各種加固材料力學(xué)性能指標(biāo)如表2所示。通過(guò)分析試驗(yàn)結(jié)果發(fā)現(xiàn),粘結(jié)破壞后界面還存在一定的殘余粘結(jié)承載力,這是由于在表層嵌貼FRP混凝土界面剝離后,由于存在混凝土與樹(shù)脂膠的粘結(jié)約束,在剝離界面上仍然存在一定的殘余摩擦力(圖3)。據(jù)此,在應(yīng)力傳遞長(zhǎng)度內(nèi)的粘結(jié)應(yīng)力分布分析中采用了如圖4所示的考慮殘余摩擦力的簡(jiǎn)化三線性粘結(jié)滑移模型。在此基礎(chǔ)上,基于張珂等[10]提出的外貼預(yù)應(yīng)力FRP放張后粘結(jié)行為假設(shè)與分析方法,構(gòu)建考慮殘余摩擦力的嵌貼預(yù)應(yīng)力FRP放張后的粘結(jié)應(yīng)力分布分析模型。
圖1試件尺寸
Fig.1The Dimension of specimens圖2試驗(yàn)平面圖
Fig. 2Plan view of test表1混凝土棱柱體規(guī)格
Table 1The concrete specification 混凝土棱柱體尺寸混凝土強(qiáng)度等級(jí)150 mm×150 mm×300 mm
150 mm×150 mm×500 mmC15、C40、C60表2加固材料力學(xué)性能
Table 2Properties of FRP and epoxy材料類型拉伸強(qiáng)度/MPa拉伸模量/MPaAslan500型CFRP板條2 068131 000Sikadur30型樹(shù)脂24~2711 200圖3試驗(yàn)得到的表層嵌貼
CFRP與混凝土局部粘結(jié)滑移曲線
Fig.3Curves of bond stress versus slip of interface
between NSM CFRP and concrete from experimental study圖4嵌貼CFRP與混凝土界面粘結(jié)滑移本構(gòu)模型
Fig.4Bondslip relationship of interface between
NSM FRP and concrete以預(yù)應(yīng)力NSM FRP加固鋼筋混凝土梁為對(duì)象進(jìn)行分析,如圖5所示,梁支座間凈跨2L1;梁底嵌貼預(yù)應(yīng)力CFRP板條,粘結(jié)長(zhǎng)度為2L;混凝土梁寬tc,高bc;CFRP寬tCF,厚bCF;彈性模量ECF;混凝土槽寬tg,高bg,加固截面如圖6所示。CFRP板條采取兩端對(duì)稱張拉,由于跨中CFRP未發(fā)生變形,以跨中為坐標(biāo)原點(diǎn)建立坐標(biāo)系,僅對(duì)對(duì)稱結(jié)構(gòu)右側(cè)進(jìn)行分析,xx截面處CFRP變形如圖7(a)所示,虛線和實(shí)線分別表示CFRP放張前和放張后的位置,放張之前CFRP位置u1(x),放張之后CFRP發(fā)生回縮,新的位置u0(x)。微元段CFRP表面應(yīng)力狀態(tài)如圖7(b)所示。
如前所述,考慮殘余摩擦力的簡(jiǎn)化三線型模型及粘結(jié)滑移本構(gòu)關(guān)系模型分別如圖4、式(1)所示。τ(δ)=τfδδ1,0≤δ≤δ1
τ(δ)=τf-τrδf-δ1(δf-δ)+τr,δ1≤δ≤δf
τ(δ)=τr,δ≥δf (1)式中:τf為最大粘結(jié)剪應(yīng)力;τr為殘余摩擦應(yīng)力;δ1為最大粘結(jié)剪應(yīng)力對(duì)應(yīng)的粘結(jié)滑移值;δf為最大粘結(jié)滑移值。根據(jù)文獻(xiàn)[19]的試驗(yàn)研究(所用材料:混凝土強(qiáng)度C40,CFRP板條截面2 mm×16 mm,CFRP名義拉伸強(qiáng)度2 068 MPa,彈性模型131 GPa),得到局部粘結(jié)滑移曲線各特征點(diǎn)的平均值:δf=1 mm,δ1=01 mm,τf=13.6 MPa,τr=42 MPa。
圖5表層嵌貼預(yù)應(yīng)力CFRP加固梁平視圖
Fig. 5Plan view of beam strengthened with
prestressed NSM CFRP圖6CFRP加固梁橫截面
Fig.6Cross section of beam strengthened
with prestressed NSM CFRP圖7應(yīng)力傳遞長(zhǎng)度內(nèi)CFRP應(yīng)力狀態(tài)
Fig. 7Stress of CFRP in stress transfer length2端部粘結(jié)應(yīng)力分析
σp0為初始施加碳纖維FRP的預(yù)應(yīng)力,放張前CFRP應(yīng)力處處相等,均為σp0,放張后定義坐標(biāo)x處CFRP應(yīng)力降低至σ1(x),CFRP中拉應(yīng)力為N1(x),界面剪應(yīng)力為τ(x)。
假定:混凝土無(wú)壓縮變形;CFRP板條截面尺寸和彈性模量在受拉過(guò)程中都不會(huì)發(fā)生改變;界面剪應(yīng)力(CFRP相對(duì)滑移(τδ)關(guān)系采用式(1)所給出的三線性關(guān)系。
放張后CFRP板條在梁端相對(duì)滑移最大,跨中橫截面相對(duì)滑移為零,剪應(yīng)力從跨中向梁端逐漸增大,其變化規(guī)律為:當(dāng)初始應(yīng)力σp0較小,端部CFRP滑移δ(L)<δ1時(shí),粘結(jié)剪應(yīng)力分布如圖8所示,從端部向跨中逐漸減小;增大σp0至放張后δ(L)=δ1時(shí),定義σp0為σp0,0,剪應(yīng)力分布如圖9所示,在端部界面剪應(yīng)力達(dá)到τ(L)=τf;σp0繼續(xù)增大,δ1<δ(L)<δf,從端部向跨中界面剪應(yīng)力先增大后減小,分布如圖10所示;σp0繼續(xù)增大,當(dāng)τ(L)=τr時(shí),剪應(yīng)力分布如圖11所示,若繼續(xù)增大σp0,CFRP將發(fā)生剝離,定義此時(shí)的σp0為σp0,max。
圖8粘結(jié)應(yīng)力彈性分布狀態(tài)
Fig. 8Elastic distribution of bond stress圖9粘結(jié)應(yīng)力彈性分布界限狀態(tài)
Fig.9Limitation of elastic distribution of bond stress圖10粘結(jié)應(yīng)力非線性分布狀態(tài)
Fig. 10Inelastic distribution of bond stress圖11界面粘結(jié)剝離狀態(tài)
Fig.11Debonding at the bonded interface2.1粘結(jié)端部滑移值δ(L)≤δ1時(shí)
在此狀態(tài),0≤δ≤δ1,0≤τ≤τf,CFRP板條、混凝土、膠層之間變形協(xié)調(diào)。當(dāng)初始預(yù)應(yīng)力σp0較小時(shí),τ(x)處于上升狀態(tài)且未達(dá)τf,如圖8所示。此時(shí)定義x=L+a時(shí),τ(x)達(dá)到理論上的τf,a為引入的虛擬參數(shù)。引入式(1)三線性剪切滑移關(guān)系τ(x)=τfδδ1=τfu0(x)-u1(x)δ1(2)兩側(cè)對(duì)x求導(dǎo),得dτ(x)dx=τfδ1[σp0ECF-σ1(x)ECF](3)兩側(cè)繼續(xù)對(duì)x求導(dǎo),得d2τ(x)dx2=-τfECFδ1dσ1(x)dx(4)由圖7(b)中力平衡可知dN1(x)=-τ(x)Lperdx(5)
dN1(x)=dσ1(x)bCFtCF(6)聯(lián)立式(5)和式(6),有dσ1(x)dx=-τ(x)LperbCFtCF(7)式中:Lper為破壞界面的周長(zhǎng),當(dāng)試件破壞在膠層與混凝土界面時(shí),有Lper=2bg+tg;試件破壞在膠層與CFRP板條界面時(shí),Lper=2bCF+2tCF。
合并式(4)和式(7),得到微分方程d2τ(x)dx2 = τfLperECFδ1tCFbCFτ(x) = λ21τ(x)(8)式中:λ1=τfLperECFδ1tCFbCF。
式(8)的解析解為[20]τ(x)=C1cosh(λ1x)+C2sinh(λ1x)(9)式中:C1、C2為待定系數(shù),邊界條件為τ(0)=0
τ(L+a)=τf
σ1(L)=0 代入式(9),得C1=0,C2=τfsinh[λ1(L+a)]
a=1λ1arcsinh[ECFλ1δ1cosh(λ1L)σp0]-L(10)代入式(3)、式(9),得τ(x)、σ1(x)表達(dá)式為τ(x)=τfsinh(λ1x)sinh[λ1(L+a)]
σ1(x)=σp0-ECFλ1δ1cosh(λ1x)sinh[λ1(L+a)] (11)當(dāng)a=0時(shí),剪應(yīng)力分布如圖8所示,此時(shí)τ(L)=τf,σp0,0=σp0=ECFλ1δ1tanh(λ1L),通過(guò)計(jì)算比較可知,當(dāng)式中碳纖維板條粘結(jié)長(zhǎng)度宏觀上有一定尺寸(如L>100 mm)時(shí),tanh(λ1L)趨于1,即σp0,0≈ECFλ1δ1=τfECFδ1LpertCFbCF當(dāng)tanh(2)≈0.97,即λ1L=2時(shí),可得到彈性狀態(tài)的有效粘結(jié)長(zhǎng)度為:Le,e=2λ1。
2.2粘結(jié)端部滑移值δ1<δ(L)≤δf時(shí)
當(dāng)σp0從σp0,0開(kāi)始繼續(xù)增大時(shí),剪應(yīng)力分布如圖9所示,定義τ(L-b)=τf,定義b為軟化長(zhǎng)度,與彈性狀態(tài)推導(dǎo)類似,當(dāng)0≤x≤L-b時(shí),式(9)依然成立。
對(duì)于下降段(L-b≤x≤L),由三線性粘結(jié)滑移本構(gòu)關(guān)系τ(x)=τf-τrδf-δ1(δf-δ)+τr=τfδf-τrδ1δf-δ1+
(τr-τf)δf-δ1[μ0(x)-μ1(x)](12)
d2τ(x)dx2=-τr-τf(δf-δ1)ECFdσ1(x)dx(13)將式(7)代入式(13),得d2τ(x)dx2=-τr-τf(δf-δ1)ECF(-τ(x)LpertCFbCF)=
(τr-τf)Lper(δf-δ1)ECFtCFbCFτ(x)=-λ22τ(x)(14)式中:λ2=(τf-τr)Lper(δf-δ1)ECFtCFbCF。
微分方程(14)的解為τ(x)=C3cos(λ2x)+C4sin(λ2x)(15)式中:C3,C4為待定系數(shù)。
考慮邊界條件τ(0)=0
τ(L-b)=τf(上升段)
τ(L-b)=τf(下降段)
σ1(L-b)(上升段)=σ1(L-b)(下降段)(16)代入式(9),解出C1、C2。C1=0
C2=τfsinh[λ1(L-b)] (17)將C1、C2代入τ(x)、σ1(x)表達(dá)式(11),得到式(18)。
τ(x)上升段(0≤x≤L-b)τ(x)=τf sinh(λ1x)sinh[λ1(L-b)]
σ1(x)=σp0-ECFλ1δ1cosh(λ1x)sinh[λ1(L-b)] (18)將式(16)分別代入式(15)和式(18),解得C3、C4為C3=τf cos[λ2(L-b)]+λ4sin[λ2(L-b)]
C4=τf sin[λ2(L-b)]-λ4cos[λ2(L-b)] (19)式中:λ4=λ1δ1(τf-τr)λ2(δf-δ1)tanh[λ1(L-b)]。
則有
τ(x)下降段(L-b≤x≤L)τ(x)=τf cos[λ2(L-b-x)]+
λ4sin[λ2(L-b-x)]
σ1(x)=σp0-ECFλ2(δf-δ1)τr-τf·
{τf sin[λ2(L-b-x)]-
λ4cos[λ2(L-b-x)]} (20)對(duì)軟化段長(zhǎng)度b進(jìn)行求解,考慮邊界條件σ1(L)=0(21)聯(lián)立式(20)、式(21),有σp0=ECFλ2(δf-δ1)τf-τr[τf sin(λ2b)+λ4cos(λ2b)](22)一旦軟化區(qū)域完全發(fā)展后,界面開(kāi)始出現(xiàn)剝離,此時(shí),τ(L)=τr,b=bmax,bmax為最大軟化段長(zhǎng)度,結(jié)合式(20)可得到τ(x)=τf cos(λ2b)-λ4sin(λ2b)=τr可推導(dǎo)出bmax = 1λ2 arccosτrτ2f + λ24-arccosτfτ2f + λ24 (23)將bmax代入式(20)得出σp0,maxσp0, max = ECFλ2 (δf -δ1 )τf-τrτ2f + λ24(24)3試驗(yàn)結(jié)果與分析
3.1CFRP預(yù)應(yīng)力放張后的粘結(jié)應(yīng)力分布
實(shí)施了預(yù)應(yīng)力NSM CFRP加固鋼筋混凝土梁受力性能的試驗(yàn)研究(圖12、圖13),其中分別用初始應(yīng)力448和1 000 MPa的嵌貼CFRP板條對(duì)混凝土梁試件進(jìn)行加固。加固試件的參數(shù)如下:混凝土立方體抗壓強(qiáng)度f(wàn)cu=41 MPa;CFRP寬度bCF=16 mm;厚度tCF=2.0 mm;彈性模量ECF=131 GPa;開(kāi)槽深度bg=30 mm,槽寬tg=10 mm;CFRP粘結(jié)長(zhǎng)度為2 900 mm。
圖12預(yù)應(yīng)力NSM CFRP板條加固梁構(gòu)件
Fig. 12Strengthening beam with prestressed NSM CFRP圖13加固構(gòu)件靜力試驗(yàn)
Fig. 13Monotonic test of strengthened beam放張過(guò)程中CFRP板條與混凝土之間的界面應(yīng)力可以通過(guò)測(cè)量CFRP板條的受拉應(yīng)變并代入式(25)得到。τ(xi + xi + 1 2) = Ecf tf εxi + 1 -εxi xi + 1 -xi ,
i = 0,1,....,n-1(25)式中:τ(xi+xi+12)為兩測(cè)點(diǎn)之間的粘結(jié)應(yīng)力,xi和 xi+1分別為應(yīng)變片測(cè)點(diǎn) “i” 和“i+1”的橫坐標(biāo),εxiεxi+1為相對(duì)應(yīng)的CFRP板應(yīng)變值,Ecf 為CFRP板彈性模量,tf為CFRP板厚度。
圖14為初始應(yīng)力為448 MPa的CFRP板條放張后,界面粘結(jié)應(yīng)力分布的理論曲線和試驗(yàn)曲線對(duì)比,此時(shí)測(cè)點(diǎn)粘結(jié)端部的粘結(jié)應(yīng)力達(dá)到最大粘結(jié)剪應(yīng)力τf,從圖中可以看出理論曲線與試驗(yàn)曲線吻合良好,τf≈13.6 MPa。圖15初始應(yīng)力為1 000 MPa的CFRP板條放張后,界面粘結(jié)應(yīng)力分布的理論曲線與試驗(yàn)曲線對(duì)比,理論曲線與試驗(yàn)曲線吻合較好,說(shuō)明本文提出的模型可用于預(yù)測(cè)嵌貼預(yù)應(yīng)力CFRP放張后的界面粘結(jié)應(yīng)力。圖14、圖15的理論值主要計(jì)算過(guò)程分別見(jiàn)表3、表4。
圖14放張448 MPa時(shí)粘結(jié)應(yīng)力分布
Fig. 14Distribution of bond stress after releasing 448 MPa圖15放張1 000 MPa時(shí)粘結(jié)應(yīng)力分布
Fig. 15Distribution of bond stress after releasing 1 000 MPa表3放張448 MPa時(shí)理論計(jì)算值
Table 3The theoretical calculation values
after releasing 448 MPa距自由
端距離/
mm距粘結(jié)
端部距
離/mmλ1xsinh
(λ1x)sinh
[λ1(L+a)]τ(x)/
MPa03000014 283.390.00202600.680.7414 283.390.00602202.053.8314 283.390.001001803.4215.2714 283.390.011401404.7960.0314 283.390.061801006.16235.7714 283.390.22220607.52925.9814 283.390.88260208.893 636.7814 283.393.46300010.2614 283.3914 283.3913.60
表4放張1 000 MPa時(shí)理論計(jì)算值
Table 4The theoretical calculation values
after releasing 1 000 MPa距自由
端距離/
mm距粘結(jié)
端部距
離/mmλ1xsinh
(λ1x)sinh
[λ1(L+a)]τ(x)/
MPa0300003636.78 0 202800.68 0.74 3 636.78 0602602.05 3.83 3 636.78 0.01 1002203.42 15.27 3 636.78 0.06 1401804.79 60.03 3 636.78 0.13 1801406.16 235.77 3 636.78 0.28 2201007.52 925.98 3 636.78 2.08 260608.89 3 636.78 3 636.78 13.6 下降段計(jì)算τf cos[λ2(L-b-x)]λ4sin[λ2(L-b-x)]2802010.826 739 66-2.299 708 342 8.530008.453 895 568-2.976 642 257 5.4
3.2最大容許預(yù)應(yīng)力
如前所述,試驗(yàn)得到的粘結(jié)滑移曲線各特征點(diǎn)的平均值為: τf=13.6 MPa,τr=4.2 MPa,δ1=0.1 mm,δf=1 mm。另根據(jù)試件參數(shù)和試驗(yàn)結(jié)果,可得破壞面周長(zhǎng)Lper=36 mm;λ1=τfLperECFδ1tCFbCF=0.034 2
σp0,0≈ECFλ1δ1=447.7 MPa
λ2=(τf-τr)Lper(δf-δ1)ECFtCFbCF=0.009 47
λ4=λ1δ1(τf-τr)λ2(δf-δ1)tanh[λ1(L-a)]=3.772彈性狀態(tài)有效粘結(jié)長(zhǎng)度Le,e=2λ1=58.48 mm
最大軟化段長(zhǎng)度bmax = 1λ2 arccosτrτ2f + λ24-arccosτfτ2f + λ24 =
104.94 mm不考慮發(fā)生剝離的條件下,粘結(jié)界面可抵抗的最大容許預(yù)應(yīng)力為σp0,max = ECFλ2(δf-δ1)τf-τrτ2f + λ24 = 1 662.9 MPa4結(jié)論
基于試驗(yàn)得到的界面剝離后存在殘余摩擦的三線性粘結(jié)滑移本構(gòu)關(guān)系,提出了預(yù)應(yīng)力放張后FRP板條與混凝土界面粘結(jié)應(yīng)力的微分方程,并根據(jù)邊界條件推導(dǎo)出了方程的解析解,得到了放張后應(yīng)力傳遞長(zhǎng)度內(nèi),界面粘結(jié)應(yīng)力和FRP拉伸分布的分析模型。與試驗(yàn)結(jié)果對(duì)比分析,理論結(jié)果與試驗(yàn)結(jié)果吻合良好,表明得到的嵌貼FRP粘結(jié)應(yīng)力分布的分析模型具有一定精度,可為表層嵌貼預(yù)應(yīng)力CFRP加固技術(shù)的應(yīng)用和發(fā)展提供理論依據(jù)和設(shè)計(jì)指導(dǎo)。必須指出,本文所建立的模型是基于不考慮混凝土槽壁破壞的前提下,預(yù)應(yīng)力放張后粘結(jié)界面的應(yīng)力傳遞行為,以及CFRP混凝土界面可抵抗的最大預(yù)應(yīng)力水平。但槽壁發(fā)生破壞時(shí)不同厚度、不同強(qiáng)度的混凝土槽壁可抵抗多大的預(yù)應(yīng)力,針對(duì)槽壁破壞,可進(jìn)行有效的錨固措施及這些錨固措施對(duì)結(jié)果存在多大程度的影響,有必要針對(duì)這些因素開(kāi)展進(jìn)一步的研究。
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