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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研究

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研究[J]. 复合材料学报, 2022, 40(0): 1-13
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研究[J]. 复合材料学报, 2022, 40(0): 1-13
Bo WANG, Yuanyuan WANG, Zhengpeng WANG, Junlei ZHANG, Tiansong WANG. Study on calculation method of RC beam’s shear bearing capacity of CFRP grid-polymer cement mortar[J]. Acta Materiae Compositae Sinica.
Citation: Bo WANG, Yuanyuan WANG, Zhengpeng WANG, Junlei ZHANG, Tiansong WANG. Study on calculation method of RC beam’s shear bearing capacity of CFRP grid-polymer cement mortar[J]. Acta Materiae Compositae Sinica.

CFRP网格-聚合物水泥砂浆加固RC梁抗剪承载力计算方法研究

基金项目: 陕西省青年科技新星项目(2021 KJXX-17)
详细信息
    通讯作者:

    王博,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

  • 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)梁的受剪机理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(单位:mm)

    Figure  1.  Drawing of specimen size and reinforcement (Unit: mm)

    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(单位: mm)

    Figure  3.  Position of displacement gauge and strain gauge (Unit: mm)

    图  4  CFRP网格-PCM加固RC梁有限元模型

    Figure  4.  CFRP grid-PCM reinforced 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

    Figure  9.  Load-CFRP grids strain curves

    图  10  纵横向CFRP网格筋应变的关系曲线

    Figure  10.  Strain curves of CFRP grid in horizontal and vertical directions

    图  11  纵、横向CFRP网格与箍筋之间的相互作用

    Figure  11.  Interactions between the vertical and horizontal CFRP grids and the stirrups

    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

    Specimen numberExisting steel barsFRP gridShear spanλPCM thickness /mmExisting vertical reinforcement ratio/%Anti-shear reinforcement ratio/%
    Tensile reinforcementHandling reinforcementStirrup
    BSD32-SD345D10-SD345D10-SD345@200-2.63-5.80.36
    BGD32-SD345--CR8-100×100205.60.22
    BGSD32-SD345D10-SD345D6-SD345@200CR8-100×100205.80.35
    Notes:B-Reinforced concrete beam; S-The 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·m³)
    WaterCementFine aggregateCoarse aggregateAdmixture
    2012055.64.515828479211261.3
    下载: 导出CSV

    表  3  混凝土和PCM材料性能

    Table  3.   Properties of concrete and 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CFRP网格的力学性能

    Table  4.   Mechanical properties of steel and CFRP grids

    MaterialTypeCross-sectional area/mm²Yield strength
    /MPa
    Modulus of elasticity/GPaTensile strength
    /MPa
    Concrete ironD32794.2389200587
    D1071.3413200561
    D631.7417200570
    CFRP gridCR826.4-1001400
    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
    ψ
    Offsetε$ {\sigma _{{\text{b0}}}}/{\sigma _{{\text{c0}}}} $KcCoefficient of viscosity μ
    Value380.11.160.66670.0005
    Notes:$ {\sigma _{{\text{b0}}}}/{\sigma _{{\text{c0}}}} $is the ratio of biaxial and uniaxial compression limit strength;
    Kc is the 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 numberPeak load P/kN
    $ {P_{\text{t}}}/{P_{\text{c}}} $
    Cross-mid deflection D/mm
    $ {D_{\text{t}}}/{D_{\text{c}}} $
    Shear cracking load $ {P_{\text{s}}} $/kN
    $ {P_{{\text{st}}}}/{P_{{\text{sc}}}} $
    Test value
    $ {P_{\text{t}}} $/kN
    Simulation value
    $ {P_{\text{c}}} $/kN
    Test value
    $ {D_{\text{t}}} $/mm
    Simulation value
    $ {D_{\text{c}}} $/mm
    Test value
    $ {P_{{\text{st}}}} $/kN
    Simulation value
    $ {P_{{\text{sc}}}} $/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

    Specimen numberStirrupStirrup 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; S-Stirrup spacing; H-Horizontal grid spacing; V-Vertical grid spacing; D-Diameter; SD-Reinforcement strength grade; CR8-CFRP grid of 8 mm in diameter.
    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
    The first groupNRS-506-D32-SD3452-D10-SD345D6-SD345@200---
    RGS-50CR8@50200.44
    The second groupNRS-100---
    RGS-100CR8@100200.22
    The 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); S-Stirrup spacing; D-Diameter; SD-Reinforcement strength grade; CR8-CFRP grid of 8 mm in diameter.
    下载: 导出CSV

    表  9  纵横向CFRP网格应变信息汇总

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

    Specimen numberShear span λConcrete strength/ MPaCFRP gridPCM 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}}} $
    TypeRatio$ {\rho _{\text{g}}} $/ %
    RGS12.62.9234.1CR8@500.44202853.17367.52
    2993.50511.91
    2919.94548.94
    RGS22.62.9234.1CR8@1000.222581.23551.82
    2837.571003.05
    2599.29920.19
    RGS32.62.9234.1CR8@1500.152029.87825.87
    3905.371088.63
    3461.74988.99
    RGS41.82.9234.1CR8@1000.223735.11913.96
    3564.481299.26
    3570.801245.58
    RGS52.22.9234.1CR8@1000.223625.541150.78
    3141.041094.90
    3260.701078.79
    RGS62.62.2026.6CR8@1000.222337.90571.62
    2200.77770.38
    2289.55794.90
    RGS72.62.6438.0CR8@1000.222494.30704.24
    3012.341069.08
    2389.03834.12
    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 RC beams strengthened with different FRP grids

    Data sourcesSpecimen number$ {P_{{\text{exp}}}} $/kN$ {P_{{\text{cal}}}} $[5]
    /kN
    $ {P_{{\text{cal}}}} $
    /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}}}} $[5]analysis
    Mean valueVariable coefficientMean valueVariable coefficient
    TextBG6173304661.871.321.220.161.850.32
    BGS7574145621.831.35
    Literature
    [5]
    RCF48817686251.151.41
    RCF69498877041.071.35
    RCF89439397691.001.23
    RCF4’9508107211.171.32
    RCF648608237041.041.22
    Literature
    [10]
    S150-CGM6774494581.511.48
    S250-CGM5712484282.301.33
    Literature
    [11]
    NO.25883204081.841.44
    NO.46313324981.901.27
    Literature
    [12]
    L33731863852.000.97
    L45112533852.011.33
    Literature
    [21]
    SB13762453041.531.24
    SB24492304461.951.01
    SB34711906012.480.78
    Literature
    [22]
    SB2-34492294411.961.02
    Literature
    [23]
    D1951222551.600.76
    Literature
    [24]
    PGB3521052903.351.21
    Literature
    [25]
    C35 S3-M2-G26742614722.581.43
    C40 S0-M2-G2 bc4841813952.671.22
    Notes:$ {P_{{\text{cal}}}} $means the shear bearing capacity of the FRP grid reinforced RC beam which is calculated based on the proposed method; $ {P_{{\text{exp}}}} $means the shear bearing capacity of the FRP grid reinforced RC beam which is calculated based on the corresponding test.
    下载: 导出CSV
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  • 收稿日期:  2022-01-20
  • 录用日期:  2022-04-12
  • 修回日期:  2022-04-11
  • 网络出版日期:  2022-04-29

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