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FRP筋UHPC梁受弯承载力计算方法

薛文远 胡翔 薛伟辰

薛文远, 胡翔, 薛伟辰. FRP筋UHPC梁受弯承载力计算方法[J]. 复合材料学报, 2022, 39(11): 5109-5121. doi: 10.13801/j.cnki.fhclxb.20220809.001
引用本文: 薛文远, 胡翔, 薛伟辰. FRP筋UHPC梁受弯承载力计算方法[J]. 复合材料学报, 2022, 39(11): 5109-5121. doi: 10.13801/j.cnki.fhclxb.20220809.001
XUE Wenyuan, HU Xiang, XUE Weichen. Calculation method of flexural capacity of ultra-high performance concrete beams reinforced with FRP rebars[J]. Acta Materiae Compositae Sinica, 2022, 39(11): 5109-5121. doi: 10.13801/j.cnki.fhclxb.20220809.001
Citation: XUE Wenyuan, HU Xiang, XUE Weichen. Calculation method of flexural capacity of ultra-high performance concrete beams reinforced with FRP rebars[J]. Acta Materiae Compositae Sinica, 2022, 39(11): 5109-5121. doi: 10.13801/j.cnki.fhclxb.20220809.001

FRP筋UHPC梁受弯承载力计算方法

doi: 10.13801/j.cnki.fhclxb.20220809.001
基金项目: 国家自然科学基金(51878478;52130806);宁波市科技创新2025重大专项(2020Z034)
详细信息
    通讯作者:

    薛伟辰,博士,教授,博士生导师,研究方向为土木工程复合材料应用 Email: xuewc@tongji.edu.cn

  • 中图分类号: TU377.9

Calculation method of flexural capacity of ultra-high performance concrete beams reinforced with FRP rebars

Funds: National Natural Science Foundation of China (51878478;52130806); The Science and Technology Innovation 2025Major Project of Ningbo (2020Z034)
  • 摘要: 目前国内外尚未提出纤维增强树脂复合材料(FRP)筋超高性能混凝土(UHPC)梁受弯承载力的显式计算公式。基于ABAQUS中的塑性损伤模型,建立了FRP筋UHPC梁的受弯性能非线性有限元分析模型,通过已有试验结果验证了该模型的有效性。开展了40根UHPC梁的参数分析,重点研究了截面尺寸、UHPC强度、FRP筋抗拉强度和配筋率等因素对梁受弯性能的影响规律。基于目前国际上最常用的法国NF P 18-710规范,对UHPC受拉本构模型进行了简化,推导了UHPC受压区和受拉区等效矩形应力图块系数,提出了FRP筋UHPC梁平衡配筋率的计算方法,建立了受压破坏和受拉破坏模式下梁截面受弯承载力的理论计算公式。该公式计算值与试验结果、有限元分析结果和条带法计算结果均吻合良好。

     

  • 图  1  有限元模型中采用的超高性能混凝土(UHPC)受拉应力-应变本构模型

    CDP—Concrete damage plasticity; K—Reduction factor

    Figure  1.  Stress-strain constitutive model of ultra-high performance concrete (UHPC) in the finite element model under tension

    图  2  有限元分析和试验结果得到的纤维增强树脂复合材料(FRP)筋UHPC梁受弯性能对比[17]

    FEM—Finite element analysis; BC12—Reinforced with φ12 carbon fiber reinforced composite (CFRP) rebar; BG20—Reinforced with φ20 glass fiber reinforced composite (GFRP) rebar; φ—Diameter

    Figure  2.  Comparison of flexural performance of fiber reinforced composite (FRP)-UHPC beams obtained from tests and finite element analysis[17]

    图  3  UHPC抗压强度对FRP筋UHPC梁受弯性能的影响规律

    Figure  3.  Influence of compressive strength of UHPC on flexural performance of FRP-UHPC beams

    图  4  FRP筋极限拉应变对FRP筋UHPC梁受弯性能的影响规律

    Figure  4.  Influence of ultimate tensile strain of FRP rebar on flexural performance of FRP-UHPC beams

    图  5  梁截面高度对FRP筋UHPC梁受弯性能的影响规律

    Figure  5.  Influence of beam height on flexural performance of FRP-UHPC beams

    图  6  FRP筋配筋率对FRP筋UHPC梁受弯性能的影响规律

    Figure  6.  Influence of reinforcement ratio of FRP rebar on flexural performance of FRP-UHPC beams

    图  7  FRP筋UHPC梁与钢筋UHPC梁和钢绞线UHPC梁的受弯性能对比

    Figure  7.  Comparison of flexural performance of FRP-UHPC beams with UHPC beams reinforced with steel rebars and steel strands

    图  8  基于法国NF P 18-710的UHPC本构模型[8]

    Figure  8.  Constitutive model of UHPC based on NF P 18-710[8]

    εu,el, fctk,el—Cracking strain and cracking strength; εu,pic, fctfk—Peak tensile strain and post-cracking strength; εu,1%, fctfk,1%—Characteristic tensile strain and characteristic tensile strength; εu,lim—Ultimate tensile strain; εc0d, fcd —Design compressive strain and design compressive strength; εcud—Ultimate compressive strain; Ec—Elastic modulus; γcf—Partial factor; K—Orientation factor

    图  9  条带法计算流程

    Figure  9.  Computation procedure of the strip method

    i—Number of iterations; Δε—Increment of strain; εf—Tensile strain of FRP rebar; εfu—Ultimate tensile strain of FRP rebar; εcu—Ultimate compressive strain of UHPC; F—Sum of the force of each element; Mi—Sum of the moment from each element towards the neutral axis during the ith loop

    图  10  FRP筋UHPC梁受弯时截面应力应变的分布与简化

    Figure  10.  Distribution and simplification of strain and stress of FRP-UHPC beam cross-section under flexure

    ft—Tensile strength of UHPC; εfu, ffu—Ultimate strain and tensile strength of FRP rebar; εc,top, σc,top—Strain and stress of UHPC at the top of the section; εt,bot—Strain of UHPC at the bottom of the section; εf, σf—Strain and stress of FRP rebar; x—Height of the compression zone; α1, β1—Equivalent rectangular stress block parameters for UHPC compression zone under compressive failure; α1', β1'—Equivalent rectangular stress block parameters for UHPC compression zone under tensile failure; α2, β2—Equivalent rectangular stress block parameters for UHPC tension zone

    图  11  FRP筋UHPC梁受弯承载力理论公式计算流程

    k—Number of iterations; ρb—Balanced reinforcement ratio; ρf—Reinforcement ratio; x—Depth of compression zone; x(k)—Value of x in kth iteration; η—Parameter; η(k)—Value of η in kth iteration.

    Figure  11.  Computation procedure of the theoretical equations for the flexural capacity of FRP-UHPC beams

    表  1  混凝土塑性损伤(CDP)模型参数取值

    Table  1.   Values of parameters for the concrete damage plasticity (CDP) model

    ParameterPoisson’s ratioDilation angle/(°)EccentricityKcfb0/fc0Viscosity parameter
    Value0.2350.12/31.050.005
    Notes: Kc—Ratio of the second stress invariant on the tensile meridian to the second stress invariant on the compressive meridian; fb0/fc0—Ratio of initial equibiaxial compressive yield strength to the initial uniaxial compressive yield strength.
    下载: 导出CSV

    表  2  FRP筋UHPC梁受弯承载力的有限元模拟值、条带法计算值和理论公式计算值与试验结果的对比[17]

    Table  2.   Comparison of flexural capacity of FRP-UHPC beams obtained from finite element analysis, strip method and theoretical equations with test results[17]

    ResourceSpecimenExperiment resultsFEM analysisStrip methodTheoretical equations
    Mexp/
    (kN·m)
    Failure
    mode
    MFEM/
    (kN·m)
    MFEM/
    Mexp
    Mu,1/
    (kN·m)
    Mu,1/
    Mexp
    Mu,2/
    (kN·m)
    Mu,2/
    Mexp
    [17]BC12131.3T126.50.96137.11.04134.61.02
    [17]BG20167.1C169.51.01171.01.02176.21.05
    Notes: Mexp, MFEM, Mu,1, Mu,2—Flexural capacities obtained from experiment, finite element analysis, strip method and theoretical equations, respectively; T—Tensile failure (FRP rebar rupture); C—Compression failure (UHPC crushing).
    下载: 导出CSV

    表  3  FRP筋UHPC梁受弯性能的有限元分析结果、条带法计算结果和理论公式计算结果

    Table  3.   Flexural performance of FRP-UHPC beams, obtained from finite element analysis, strip method and theoretical equations

    Specimens for parametric studyFEM analysisStrip methodTheoretical equations
    SpecimenParameter studiedValuesMFEM/
    (kN·m)
    Δmax/mmFailure
    mode
    Mu,1/
    (kN·m)
    Failure
    mode
    Mu,2/
    (kN·m)
    Failure
    mode
    BC12 126.5 72.2 T 137.1 T 136.2 T
    BC12-C120 fcu 120 MPa 123.5 73.3 T 132.3 T 134.6 T
    BC12-C180 180 MPa 129.0 69.3 T 141.4 T 137.9 T
    BC12-C200 200 MPa 128.2 66.3 T 143.5 T 138.8 T
    BC12-EP1 εfu 1% 106.9 54.6 T 116.5 T 114.8 T
    BC12-EP1.5 1.5% 144.6 89.1 T 158.4 T 158.2 T
    BC12-EP2 2% 154.3 107.3 C 163.4 C 168.2 C
    BC12-EP2.5 2.5% 154.3 107.3 C 163.4 C 168.2 C
    BC12-H150 h 150 mm 56.4 144.5 C 60.7 C 62.8 C
    BC12-H200 200 mm 93.4 98.2 T 100.9 T 101.6 T
    BC12-H300 300 mm 157.2 56.4 T 176.0 T 172.4 T
    BC12-R0.5 ρf 0.5% 103.4 66.5 T 113.2 T 112.0 T
    BC12-R1 1% 186.5 88.7 T 197.5 C 205.4 T
    BC12-R2 2% 236.4 59.5 C 256.5 C 266.1 C
    BC12-R3 3% 277.0 51.4 C 293.7 C 305.7 C
    BC12-R4 4% 306.5 46.9 C 320.9 C 334.6 C
    BC12-R5 5% 328.8 44.2 C 342.1 C 357.1 C
    BG20 169.5 108.2 C 171.0 C 176.2 C
    BG20-C120 fcu 120 MPa 142.6 99.2 C 145.3 C 147.4 C
    BG20-C180 180 MPa 188.4 107.9 C 199.3 C 208.9 C
    BG20-C200 200 MPa 185.8 116.4 T 217.0 C 213.2 T
    BG20-EP1 εfu 1% 123.5 59.8 T 132.1 T 130.7 T
    BG20-EP1.5 1.5% 164.8 101.0 T 171.0 C 176.2 C
    BG20-EP2 2.0% 169.5 108.2 C 171.0 C 176.2 C
    BG20-EP2.5 2.5% 169.5 108.2 C 171.0 C 176.2 C
    BG20-H150 h 150 mm 57.1 129.8 C 61.7 C 63.8 C
    BG20-H200 200 mm 106.9 123.9 C 111.1 C 115.1 C
    BG20-H300 300 mm 213.6 88.6 C 240.2 C 245.9 C
    BG20-R0.5 ρf 0.5% 62.5 73.8 T 70.0 T 67.3 T
    BG20-R1 1% 116.9 101.6 T 126.3 T 124.4 T
    BG20-R2 2% 173.2 106.8 C 179.4 C 185.0 C
    BG20-R3 3% 194.6 81.0 C 210.6 C 217.8 C
    BG20-R4 4% 208.9 63.7 C 234.6 C 242.9 C
    BG20-R5 5% 244.6 60.0 C 253.6 C 263.3 C
    Notes: Specimen BC12 and BG20 are in the control group. For BC12, fcu=148 MPa, εfu=1.25%, h=250 mm, ρf=0.63%. For BG20, fcu=148 MPa, εfu=1.78%, h=250 mm, ρf=1.78%. The other specimens are in the experimental group. They are designed by changing one parameter compared to the corresponding specimen in the control group. i.e., BC12-C120 is designed based on BC12 by setting fcu=120 MPa, BG20-R2 is designed based on BG20 by setting ρf=2%. fcu—Cubic compressive strength of UHPC; εfu—Ultimate tensile strain of FRP rebar; h—Height of the beam section; ρf—Reinforcement ratio of FRP rebar, obtained from the reinforcement area divided by bh0, where b is the width of the beam section and h0 is the depth of FRP rebar; Δmax—Displacement of mid-span at the peak moment.
    下载: 导出CSV

    表  4  筋材基本参数

    Table  4.   Material parameters of rebars

    Rebar typeElastic modulus
    /GPa
    Yielding
    strength
    /MPa
    Ultimate strength
    /MPa
    CFRP rebar1441100
    GFRP rebar 621800
    HRB500 500 500 500
    1860 MPa steel strand wire158115811860
    Note: HRB500—Deformed steel bar.
    下载: 导出CSV

    表  5  钢筋UHPC梁和钢绞线UHPC梁受弯承载力的有限元模拟值

    Table  5.   Flexural capacity of UHPC beams reinforced with steel rebars and steel strands obtained from finite element analysis

    SpecimenReinforcementρ*/%ρ/%MFEM
    /(kN·m)
    Δmax
    /mm
    Failure mode
    G-R0.5HRB
    500
    0.51.1082.219.9F
    G-R11.02.20133.322.4F
    G-R22.04.40233.629.5F
    C-R0.51860 MPa steel strand wire0.50.57112.947.7F
    C-R11.01.14200.360.4F
    C-R22.02.28285.552.3C
    C-R33.03.42299.339.9C
    C-R44.04.55349.841.2C
    Notes: ρ*—Reinforcement ratio of FRP-UHPC comparative specimens; ρ—Actual reinforcement ratio designed according to the rule of equivalent tensile force; F—Flexural failure (failure after rebar yielding); C—Compression failure (UHPC crushing before rebar yielding).
    下载: 导出CSV
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出版历程
  • 收稿日期:  2022-04-26
  • 修回日期:  2022-07-05
  • 录用日期:  2022-07-20
  • 网络出版日期:  2022-08-09
  • 刊出日期:  2022-11-01

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