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CFRP网格-聚合物水泥砂浆加固RC梁抗剪承载力计算方法

王博 王媛媛 王征鹏 张军雷 王天松

王博, 王媛媛, 王征鹏, 等. CFRP网格-聚合物水泥砂浆加固RC梁抗剪承载力计算方法[J]. 复合材料学报, 2023, 40(2): 990-1003. doi: 10.13801/j.cnki.fhclxb.20220419.004
引用本文: 王博, 王媛媛, 王征鹏, 等. CFRP网格-聚合物水泥砂浆加固RC梁抗剪承载力计算方法[J]. 复合材料学报, 2023, 40(2): 990-1003. doi: 10.13801/j.cnki.fhclxb.20220419.004
WANG Bo, WANG Yuanyuan, WANG Zhengpeng, et al. Study on calculation method of RC beam's shear bearing capacity of CFRP grid-polymer cement mortar[J]. Acta Materiae Compositae Sinica, 2023, 40(2): 990-1003. doi: 10.13801/j.cnki.fhclxb.20220419.004
Citation: WANG Bo, WANG Yuanyuan, WANG Zhengpeng, et al. Study on calculation method of RC beam's shear bearing capacity of CFRP grid-polymer cement mortar[J]. Acta Materiae Compositae Sinica, 2023, 40(2): 990-1003. doi: 10.13801/j.cnki.fhclxb.20220419.004

CFRP网格-聚合物水泥砂浆加固RC梁抗剪承载力计算方法

doi: 10.13801/j.cnki.fhclxb.20220419.004
基金项目: 陕西省青年科技新星项目(2021KJXX-17)
详细信息
    通讯作者:

    王博,博士,教授,博士生导师,研究方向为工程抗震与韧性提升 E-mail: chnwangbo@chd.edu.cn

  • 中图分类号: TU

Study on calculation method of RC beam's shear bearing capacity of CFRP grid-polymer cement mortar

Funds: Shaanxi Province Youth Science and Technology Nova Project (2021KJXX-17)
  • 摘要: 为揭示碳纤维增强树脂复合材料(Carbon fiber reinforced polymer,CFRP)网格-聚合物水泥砂浆(Polymer cement mortar,PCM)抗剪加固钢筋混凝土(RC)梁的受剪机制并建立其承载力计算方法,对RC梁进行了四点弯曲试验和有限元模拟,重点分析了CFRP网格对RC加固梁的抗剪贡献,建立了基于改进的桁架拱模型的抗剪承载力计算方法。结果表明:RC梁侧粘贴CFRP网格-PCM加固层不仅可以抑制斜裂缝的发展,而且还提高了抗剪承载力;CFRP网格与钢筋之间具有良好的协同工作性能,其中,横向CFRP网格筋分担了约16%的箍筋应变;回归分析指出纵向CFRP网格筋的应变约为横向CFRP网格筋应变的0.29倍;综合考虑纵向CFRP网格的销栓作用和横向CFRP网格分担的箍筋应变,提出了基于改进桁架-拱模型的承载力计算方法,具有更好的适用性和准确性,能够满足设计要求。

     

  • 图  1  试件尺寸及配筋图

    Figure  1.  Drawing of specimen size and reinforcement

    P—Load

    图  2  试验加载示意图

    Figure  2.  Schematic diagram of experimental loading

    图  3  位移计和应变片布置位置

    C-1-C-6—Surface strain gauge of specimen; D1-D8—Displacement sensor; S-1-S-7—Reinforcement strain gauge of BS and BGS

    Figure  3.  Position of displacement gauge and strain gauge

    图  4  CFRP网格-PCM加固钢筋混凝土(RC)梁有限元模型

    RP—Reinforced polymer

    Figure  4.  CFRP grid-PCM reinforced concrete (RC) beam finite element model

    图  5  试验梁BGS剪切破坏裂缝分布

    Figure  5.  Distribution of shear failure cracks in BGS specimen

    图  6  CFRP网格-PCM加固RC梁试验与有限元模拟破坏形态对比

    Figure  6.  Comparison of failure modes between the test of CFRP grid-PCM shear-reinforced RC beams and finite element simulation

    图  7  CFRP网格-PCM加固RC梁荷载-位移曲线对比

    Figure  7.  Comparison of load-displacement curves of CFRP grid-PCM shear-reinforced RC beams

    图  8  试件BS和BGS的荷载-钢筋应变曲线

    Figure  8.  Load-steel strain curves of BS and BGS specimens

    图  9  荷载-CFRP网格应变曲线

    G1, G2, G11, G13, G18, G20, G21, G24, G28, G29, G36, G40—Strain gauges

    Figure  9.  Load-CFRP grids strain curves

    图  10  纵向和横向CFRP网格与箍筋之间的相互作用

    Figure  10.  Interactions between the vertical and horizontal CFRP grids and the stirrups

    图  11  纵向和横向CFRP网格筋应变的关系曲线

    λ—Shear span ratio; fc—Compressive strength of the concrete; ρg—CFRP grid reinforcement rate; Eg—Elastic modulus of the CFRP grid; εu—Effective strain of the FRP grid bars

    Figure  11.  Strain curves of CFRP grid in horizontal and vertical directions

    图  12  改进的桁架拱模型

    Figure  12.  Improved truss arch model

    图  13  基于不同FRP网格抗剪加固RC梁承载力计算方法的计算结果比较

    Figure  13.  Comparison of calculation results of calculation methods for the bearing capacity of RC beams strengthened with different FRP grids

    表  1  试件设计

    Table  1.   Specimen design

    SpecimenExisting steel barsFRP gridShear
    span λ
    PCM thickness/
    mm
    Existing vertical reinforcement ratio/%Anti-shear reinforcement ratio/%
    Tensile reinforcementHandling reinforcementStirrup
    BSD32-SD345D10-SD345D10-SD345@2002.635.80.36
    BGD32-SD345CR8-100×100205.60.22
    BGSD32-SD345D10-SD345D6-SD345@200CR8-100×100205.80.35
    Notes: B—Reinforced concrete beam; S—Beam is equipped with stirrup; G—Stick carbon fiber reinforced polymer (CFRP) grid-polymer cement mortar (PCM) reinforcement layer on both sides; BS—Reinforced concrete beams provided with stirrups; BG—Reinforced concrete beam with only CFRP-PCM reinforced layer without stirrup; BGS—Reinforced concrete beams with stirrups and CFRP-PCM reinforcement layer; D—Diameter; SD—Reinforcement strength grade; CR8—CFRP grid of 8 mm in diameter; FRP—Fiber reinforced polymer.
    下载: 导出CSV

    表  2  混凝土配合比

    Table  2.   Concrete mix proportion

    Maximum
    grain size/mm
    Colony/
    mm
    Water cement
    ratio/%
    Air ratio/%Measurement unit/(kg·m–3)
    WaterCementFine aggregateCoarse aggregateAdmixture
    2012055.64.515828479211261.3
    下载: 导出CSV

    表  3  混凝土和聚合物水泥砂浆(PCM)材料性能

    Table  3.   Properties of concrete and polymer cement mortar (PCM) materials

    MaterialCompression strength/MPaTensile strength/MPaModulus of elasticity/GPa
    Concrete34.12.9231.9
    PCM36.72.8730.1
    下载: 导出CSV

    表  4  钢筋与碳纤维增强树脂复合材料(CFRP)网格的力学性能

    Table  4.   Mechanical properties of steel and carbon fiber reinforced polymer (CFRP) grids

    MaterialTypeCross-sectional area/mm2Yield strength
    /MPa
    Modulus of elasticity/GPaTensile strength
    /MPa
    Concrete ironD32794.2389200 587
    D10 71.3413200 561
    D6 31.7417200 570
    CFRP gridCR8 26.41001400
    下载: 导出CSV

    表  5  混凝土塑性损伤模型参数取值

    Table  5.   Parameters of plastic damage model for concrete

    TypeExpansion angle ψOffset ε$ {\sigma _{{\text{b0}}}}/{\sigma _{{\text{c0}}}} $KcCoefficient of viscosity μ
    Value380.11.160.66670.0005
    Notes: $ {\sigma _{{\text{b0}}}}/{\sigma _{{\text{c0}}}} $—Ratio of biaxial and uniaxial compression limit strength; Kc—Ratio of stretching and the second stress invariant on the compression meridian.
    下载: 导出CSV

    表  6  CFRP网格-PCM加固RC梁试验结果汇总

    Table  6.   Summary of test results for CFRP grid-PCM shear-reinforced RC beams

    Specimen Peak load P/kN
    $ {P_{\text{t}}}/{P_{\text{c}}} $
    Cross-mid deflection D/mm
    $ {D_{\text{t}}}/{D_{\text{c}}} $
    Shear cracking load Ps/kN
    $ {P_{{\text{st}}}}/{P_{{\text{sc}}}} $
    Test value
    Pt/kN
    Simulation value
    Pc/kN
    Test value
    Dt/mm
    Simulation value
    Dc/mm
    Test value
    Pst/kN
    Simulation value
    Psc/kN
    BS6906141.128.358.071.032101721.22
    BG6176011.037.096.771.052251881.19
    BGS7577221.057.407.391.003202561.25
    下载: 导出CSV

    表  7  RGS试件参数信息

    Table  7.   Parameter information of RGS specimens

    SpecimenStirrupStirrup ratio
    /%
    Grid type-spacing: Vertical and horizontal
    /(mm×mm)
    Reinforcement ratio
    /%
    Ultimate load
    /kN
    RGS-S200D6-SD345@2000.16CR8-100×1000.22722.2
    RGS-S150D6-SD345@1500.21737.7
    RGS-S100D6-SD345@1000.32746.4
    RGS-H100 V150D6-SD345@2000.16CR8-100×1500.15711.9
    RGS-H100 V100CR8-100×1000.22722.2
    RGS-H100 V50CR8-100×500.44774.2
    Notes: RGS—Reinforced concrete (RC) beam with stirrup and CFRP-PCM reinforcement layer; S200—Stirrup spacing is 200 mm; H—Horizontal grid spacing; V—Vertical grid spacing.
    下载: 导出CSV

    表  8  CFRP网格-PCM加固RC梁试件与未加固试件参数信息

    Table  8.   Parameter information of CFRP grid-PCM shear-reinforced RC beam specimens and unreinforced specimens

    Type of specimenSpecimen numberVertical reinforcementStirrupCFRP gridPCM thickness
    /mm
    Horizontal grid ratio/%
    Tensile reinforcementCompressive reinforcement
    First groupNRS-506-D32-SD3452-D10-SD345D6-SD345@200
    RGS-50CR8@50200.44
    Second groupNRS-100
    RGS-100CR8@100200.22
    Third groupNRS-150
    RGS-150CR8@150200.15
    Notes: NRS-50—Reinforced concrete (RC) beam with no CFRP-PCM reinforcement layer but with stirrup in 50 mm spacing (NRS-100 and NRS-150 are in the same manner); RGS-50—Reinforced concrete (RC) beam with CFRP-PCM reinforcement layer and stirrup in 50 mm spacing (RGS-100 and RGS-150 are in the same manner).
    下载: 导出CSV

    表  9  纵向和横向CFRP网格应变信息汇总

    Table  9.   Summary of grid strain information for horizontal and vertical CFRP

    Specimen Shear
    span λ
    Concrete strength/MPaCFRP grid
    type
    Ratio $ {\rho _{\text{g}}} $/%PCM thickness/ mmVertical grid strain
    $ {\varepsilon _{{\text{ver}}}} $/$ {10^{ - 6}} $
    Horizontal grid strain
    $ {\varepsilon _{{\text{hor}}}} $/$ {10^{ - 6}} $
    Tensile
    strength $ {f_{\text{t}}} $
    Compression strength
    $ {f_{\text{c}}} $
    RGS1 2.6 2.92 34.1 CR8@50 0.44 20 2853.17 367.52
    2993.50 511.91
    2919.94 548.94
    RGS2 2.6 2.92 34.1 CR8@100 0.22 2581.23 551.82
    2837.57 1003.05
    2599.29 920.19
    RGS3 2.6 2.92 34.1 CR8@150 0.15 2029.87 825.87
    3905.37 1088.63
    3461.74 988.99
    RGS4 1.8 2.92 34.1 CR8@100 0.22 3735.11 913.96
    3564.48 1299.26
    3570.80 1245.58
    RGS5 2.2 2.92 34.1 CR8@100 0.22 3625.54 1150.78
    3141.04 1094.90
    3260.70 1078.79
    RGS6 2.6 2.20 26.6 CR8@100 0.22 2337.90 571.62
    2200.77 770.38
    2289.55 794.90
    RGS7 2.6 2.64 38.0 CR8@100 0.22 2494.30 704.24
    3012.34 1069.08
    2389.03 834.12
    下载: 导出CSV

    表  10  不同FRP网格抗剪加固RC梁抗剪承载力计算值与试验值比较

    Table  10.   Comparison of calculated and experimental values of shear capacity of RCbeams strengthened with different FRP grids

    Data
    sources
    Specimen
    $ {P_{{\text{exp}}}} /{\rm{kN}}$$ {P_{{\text{cal}}}} $[5]/kN$ {P_{{\text{cal}}}}/{\rm{kN}} $$ {P_{{\text{exp}}}}/{P_{{\text{cal}}}} $[5]$ {P_{{\text{exp}}}}/{P_{{\text{cal}}}} $$ {P_{{\text{exp}}}}/{P_{{\text{cal}}}} $ analysis$ {P_{{\text{exp}}}}/{P_{{\text{cal}}}} $[5] analysis
    Mean
    value
    Variable
    coefficient
    Mean
    value
    Variable
    coefficient
    TextBG6173304661.871.321.220.161.850.32
    BGS7574145621.831.35

    [5]
    RCF48817686251.151.41
    RCF69498877041.071.35
    RCF89439397691.001.23
    RCF4’9508107211.171.32
    RCF648608237041.041.22

    [6]
    PGB3521052903.351.21

    [11]
    S150-CGM6774494581.511.48
    S250-CGM5712484282.301.33

    [12]
    L33731863852.000.97
    L45112533852.011.33

    [21]
    NO.25883204081.841.44
    NO.46313324981.901.27

    [22]
    SB13762453041.531.24
    SB24492304461.951.01
    SB34711906012.480.78

    [23]
    SB2-34492294411.961.02

    [24]
    D1951222551.600.76

    [25]
    C35 S3-M2-G26742614722.581.43
    C40 S0-M2-G2 bc4841813952.671.22
    Notes: $ {P_{{\text{cal}}}} $—Shear bearing capacity of the FRP grid reinforced RC beam which is calculated based on the proposed method; $ {P_{{\text{exp}}}} $—Shear bearing capacity of the FRP grid reinforced RC beam which is calculated based on the corresponding test; RCF4, RCF6 and RCF8—Reinforced by CR4 CFRP, CR6 CFRP and CR8 CFRP grid whose vertical reinforcement interval was 50 mm compared with 150 mm of other specimens (CR4, CR6 and CR8 are the type of the CFRP grid in ABAQUS); RCF4'—Reinforced by CR4 CFRP grid whose vertical reinforcement interval was 50 mm compared with 50 mm of other specimens; RCF64—Reinforced by CR6&4 CFRP grid whose horizontal grid was CR4 and vertical grid was CR6; PGB—Beam was strengthened with high strength PCM and high strength carbon fiber-reinforced plastics (CFRP) gride bars; S150-CGM and S250-CGM—Beam with CFRP grid embedded in mortar (CGM), and the beam with 6 mm stirrups @150 mm c/c and @250 mm c/c; L3—Fiber grid and polymer mortar reinforced concrete beams (FRP GRID&NC-RC); L4—Fiber grid and engineered cementitous composite (ECC) reinforced concrete beams (FRP GRID&ECC-RC); NO.2 and NO.4—Beam with 2 row and 4 row of CFRP grid; SB1, SB2, SB3—FRP grid used in the ultra high toughness cementitious composite (UHTCC) layer (Measured thickness: 1 mm, 3 mm and 5 mm respectively); SB2-3—A 3 mm BFRP grid reinforced ECC composite SB2 reinforced concrete beam; D—RC beam strengthened with FRP grid; C35 S3-M2-G2—Beam C35 S3 with stirrup was strengthed by the use of mortar 2 and grid M; C40 S0-M2-G2 bc—Beam C40 S0 without stirrup but was strengthed by the use of mortar 2 and grid M; c/c—Center/Center; BFRP—Boron fiber reinforced plastic.
    下载: 导出CSV
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出版历程
  • 收稿日期:  2022-01-20
  • 修回日期:  2022-04-11
  • 录用日期:  2022-04-12
  • 网络出版日期:  2022-04-20
  • 刊出日期:  2023-02-15

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