Deflection of reinforced concrete beams strengthened with FRP grid-engineered cementitious composite matrix composite
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摘要: 为研究纤维增强复合材料(FRP)网格-工程用水泥基复合材料(ECC)复合加固方式对钢筋混凝土梁的挠度影响,对10根钢筋混凝土梁进行抗弯性能试验,分析了各试验变量对FRP网格-ECC复合材料加固钢筋混凝土梁挠度的影响,并推导加固梁挠度计算模型。试验结果表明:FRP网格-ECC复合加固方式能显著提升试验梁极限承载力和抗弯刚度,其中加固梁极限承载力提升27.9%~67.4%、跨中挠度降低30.7%~43.7%,且发生延性特征明显的适筋破坏;FRP网格对加固梁抗弯性能影响较大,网格厚度与加固效果成正比;ECC加固层的厚度、配合比和界面处理方式对加固梁抗弯性能影响较小,其中磨砂处理对加固层界面粘结性能提高较好;基于规范推导了加固梁挠度计算模型,其计算值与试验值吻合较好,该模型为FRP网格-ECC复合材料加固梁挠度计算提供一定的参考。
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关键词:
- FRP网格 /
- 工程用水泥基复合材料(ECC) /
- 加固梁 /
- 挠度分析 /
- 挠度计算
Abstract: To study the effect of fiber reinforced plastic (FRP) grid-engineered cementitious composite (ECC) matrix strengthened method on the deflection of reinforced concrete (RC) beams, flexural performance test was carried out on 10 RC beams. Each test variable which does effect on the deflection of RC beams strengthened with FRP grid-ECC matrix composite was analyzed, and a model for calculating the deflection of reinforced beams was derived. The test results show that the FRP grid-ECC matrix strengthened method can significantly improve the ultimate bearing capacity and flexural stiffness of the test beams, in which the ultimate load carrying capacity of the reinforced beam increases from 27.9% to 67.4%, the mid-span deflection decreases from 30.7% to 43.7%, and the reinforced beams occur suitable reinforcement damage with obvious ductile characteristics. The FRP grid has a strong influence on flexural performance of reinforced beams, and its grid thickness is proportional to the strengthening effection. The thickness, matching ratio and interface treatment method of ECC reinforcement layer have little effect on the flexural performance of the reinforced beam, and the sanding treatment improves the interface bonding performance of the reinforcement layer better than other interface treatment methods. The deflection calculation model of reinforced beams is derived based on the specification, and its calculating values agree well with the testing values, so the model is a reference for the deflection calculation of RC beams strengthened with FRP grid-ECC matrix composite. -
图 7 FRP网格-ECC复合材料加固钢筋混凝土梁开裂前后的换算截面
Figure 7. Converted cross sections of RC beams strengthened with FRP grid-ECC matrix composite before and after cracking
$ {h_0} $ and $ {h_{\text{f}}} $—Vertical distances from the top of the beam to the center of the tensile reinforcement and the center of the FRP grid, respectively; $ {x_{\text{c}}} $ and $ {x_{{\text{cr}}}} $—Height of the compression zone of the reinforced beam before and after concrete cracking, respectively; $ {A_{\text{s}}} $, $ {A_{\text{f}}} $ and $ {A_{\text{e}}} $—Cross-sectional areas of the reinforcement in the tension zone, FRP grid and ECC layer , respectively; b—Section width of reinforced beam; $ {\varepsilon _{\text{c}}} $, $ {\varepsilon _{\text{s}}} $ and $ {\varepsilon _{\text{f}}} $—Stresses at the top of the beam, the center of the tensile reinforcement and the center of the FRP grid, respectively; ns, ns-1, nf, ne—
表 1 纤维增强复合材料(FRP)网格-纤维增强复合材料(ECC)复合材料加固钢筋混凝土(RC)梁设计表
Table 1. Design table of reinforced concrete (RC) beams strengthened with fiber reinforced plastic (FRP) grid-engineered cementitious composite (ECC) matrix composite
Test piece number ECC layer FRP thickness/mm Interface treatment method U-shaped hoop B0 — — — — JB-1 ECC1-40 2 Sanding Exist JB-2 ECC1-40 3 Sanding Exist JB-3 ECC1-40 5 Sanding Exist JB-4 ECC1-40 3 Grooving Exist JB-5 ECC1-40 3 Chiseling Exist JB-6 ECC1-50 3 Sanding Exist JB-7 ECC2-40 3 Sanding Exist JB-8 ECC1-40 3 Sanding — JB-9 ECC1-40 — Sanding Exist Notes: B0—Contrast beam; JB-x—Strengthened beams; in ECC1-40, “1”—ECC cement-based materials prepared by No.1 matching ratio, “40”—Thickness of ECC layer (mm). 表 2 混凝土力学性能指标
Table 2. Mechanical properties of concrete
Material Elastic modulus/GPa Tensile strength/MPa Compressive strength/MPa C30 35 2.58 30.4 表 3 钢筋材料力学性能指标
Table 3. Mechanical properties of rebars
Specification Elastic modulus/GPa Yield strength/MPa Tensile strength/MPa Elongation/% C8 200 457 625 10.7 C10 200 528 671 12.3 表 4 ECC配合比设计
Table 4. Design of ECC matching ratio
Specimen Cement Water Fly ash Silica fume Quartz sand Water reducing admixture ECC-1 1 0.9 1.5 0.05 1 0.014 ECC-2 1 0.5 20.4 0.05 0.36 0.007 表 5 FRP网格力学性能指标
Table 5. Mechanical properties of FRP grid
Thickness/mm Cross-section/mm2 Elastic modulus/GPa Tensile strength/MPa Elongation/% 2 3.62 171.3 1550 2.72 3 5.43 210.7 1913 2.46 5 9.06 224.6 2018 2.07 表 6 ECC力学性能指标
Table 6. Mechanical properties of ECC
Specimen Compressivestrength/MPa Cracking-strength/MPa ECC-1 28.6 3.6 ECC-2 31.2 4.8 表 7 FRP网格-ECC复合材料加固RC梁试验结果汇总
Table 7. Summary of the test results of RC beams strengthened with FRP grid-ECC matrix composite
Test piece number Cracking state Yield state Limit state Destruction
mode$ {P_{{\text{cr}}}} $/
kN$ {f_{{\text{cr}}}} $/
mm$ {P_{{\text{cr}}}} $
increment/%$ {P_{\text{y}}} $/
kN$ {f_{\text{y}}} $/
mm$ {P_{\text{y}}} $
increment/%$ {P_{\text{u}}} $/
kN$ {f_{\text{u}}} $/
mm$ {P_{\text{u}}} $
increment/%B0 28 0.46 0 70 5.3 0 86 26.06 0 C JB-1 40 0.48 42.8 91 5.14 30 110 18.05 27.9 F+C+P JB-2 40 0.51 42.8 103 4.90 47.1 128 15.30 48.8 F+C+P JB-3 44 0.50 57.1 112 5.06 60 144 16.57 67.4 C JB-4 38 0.55 35.7 97 5.31 38.5 120 17.90 39.5 F+C+P JB-5 40 0.49 42.8 100 5.26 42.8 124 16.53 44.2 F+C+P JB-6 42 0.46 50 102 5.29 45.7 124 17.68 44.2 F+C+P JB-7 44 0.44 57.1 104 4.45 48.6 126 16.85 46.5 F+C+P JB-8 42 0.39 50 102 4.90 45.8 126 14.66 46.5 F+C+P JB-9 40 0.50 42.8 79 4.70 12.9 90 22.94 4.7 E+C Notes: $ {P_{{\text{cr}}}} $—Cracking load of the ECC layer; $ {P_{\text{y}}} $—Yielding load of the test beam, that is the load corresponding to the inflection point of the load deflection curve; $ {P_{\text{u}}} $—Limit load of the test beam, that is the load corresponding to the peak point of the load deflection curve; $ {f_{{\text{cr}}}} $, $ {f_{\text{y}}} $ and $ {f_{\text{u}}} $—Deflection of the corresponding state of the reinforced beam respectively; C—Concrete in the pressurized area is crushed; F—FRP grid is pulled off; E—Fracture of ECC layer; P—Partial peeling of ECC. 表 8 FRP网格-ECC复合材料加固钢筋混凝土梁挠度试验值与计算值汇总
Table 8. Deflection summary of tested values and calculated values of RC beams strengthened with FRP grid-ECC matrix composite
Test piece number Crack state Yield state Limit state ${f_{\text{t}}}$ ${f_{\text{c}}}$ ${f_{\text{t}}}/{f_{\text{c}}}$ ${f_{\text{t}}}$ ${f_{\text{c}}}$ ${f_{\text{t}}}/{f_{\text{c}}}$ ${f_{\text{t}}}$ ${f_{\text{c}}}$ ${f_{\text{t}}}/{f_{\text{c}}}$ B0 0.46 0.42 0.915 5.3 3.694 0.697 26.06 28.59 1.097 JB-1 0.48 0.45 0.939 5.14 4.34 0.844 18.05 13.10 0.726 JB-2 0.51 0.45 0.882 4.90 4.65 0.949 15.30 13.20 0.863 JB-3 0.50 0.45 0.917 5.06 4.98 0.986 16.57 18.11 1.093 JB-4 0.55 0.45 0.818 5.31 4.65 0.876 17.90 13.20 0.737 JB-5 0.49 0.45 0.915 5.26 4.65 0.886 16.53 13.20 0.799 JB-6 0.46 0.45 0.985 5.29 4.75 0.899 17.68 13.27 0.751 JB-7 0.44 0.45 1.032 4.45 4.93 1.108 16.85 13.29 0.789 JB-8 0.39 0.45 1.154 4.90 4.65 0.949 14.66 13.20 0.900 JB-9 0.50 0.45 0.896 4.70 3.91 0.832 22.94 25.51 1.112 Average value 0.945 — — 0.903 — — 0.887 Standard dviation 0.088 — — 0.103 — — 0.149 Coefficient of variation 0.093 — — 0.114 — — 0.168 Notes: ${f_{\text{t}}} $—Tested value of deflection; ${f_{\text{c}}} $—Calculated value of deflection. Test piece number Cracking state Yield state ${f_{\text{t}}}$ $f_{\text{c}}^{\text{D}}$ $f_{\text{c}}^{\text{D}}/{f_{\text{t}}}$ $f_{\text{c}}^{\text{Z}}$ $f_{\text{c}}^{\text{Z}}/{f_{\text{t}}}$ ${f_{\text{t}}}$ $f_{\text{c}}^{\text{D}}$ $f_{\text{c}}^{\text{D}}/{f_{\text{t}}}$ $f_{\text{c}}^{\text{Z}}$ $f_{\text{c}}^{\text{Z}}/{f_{\text{t}}}$ BB0 0.25 0.28 1.12 0.32 1.28 4.42 3.34 28.59 4.09 0.93 BB1 0.39 0.32 0.82 0.34 0.87 3.16 3.64 13.10 4.19 1.33 BB2 0.57 0.32 0.56 0.34 0.60 4.76 3.64 13.20 4.19 0.88 BB3 0.6 0.35 0.58 0.34 0.57 4.38 3.59 18.11 4.19 0.96 BB4 0.56 0.32 0.57 0.34 0.54 5.13 3.54 13.20 4.20 0.82 BB5 0.49 0.32 0.65 0.34 0.69 4.56 3.54 13.20 4.19 0.92 BB6 0.45 0.32 0.71 0.34 0.76 4.17 3.49 13.27 4.18 1.00 BB7 0.58 0.34 0.59 0.34 0.59 5.63 3.50 13.29 4.18 0.74 Average value 0.701 0.737 0.802 0.946 Standard deviation 0.191 0.246 0.157 0.174 Coefficient of variation 0.273 0.335 0.196 0.183 Notes: ${f_{\text{t}}}$—Tested value of deflection; $f_{\text{c}}^{\text{D}}$, $f_{\text{c}}^{\text{Z}}$—Calculated values of this paper and reference [24]. -
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