Experimental and theoretical calculation on the flexural capacity of steel fiber reinforced concrete beams with hybrid reinforcing bars
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摘要: 为研究玻璃纤维增强聚合物复合材料(GFRP)筋与普通钢筋混合配筋钢纤维增强混凝土(SF/混凝土)梁的受弯性能及其受弯承载力计算方法,在考虑受拉区混凝土抗拉强度的基础上,给出混合配筋SF/混凝土梁的界限配筋率及受弯承载力计算公式;在此基础上设计制作了三种配筋方式的SF/混凝土梁,重点探讨了混合配筋率及筋材面积比(Af/As)对试验梁失效模式和受弯承载力的影响;同时,借助已有相关试验结果,对比分析了混凝土强度对混合配筋SF/混凝土梁受弯性能的影响。试验和对比分析结果表明:混合配筋SF/混凝土梁正截面应变仍符合平截面假定;相同配筋形式下,混合配筋SF/混凝土梁的受弯承载力和跨中挠度随筋材面积比Af/As的增加而增大;单层配筋梁的受弯承载力比双层配筋梁大;合理提高混凝土强度可在充分发挥GFRP筋抗拉作用的同时进一步提高混合配筋SF/混凝土梁的受弯承载力;采用本文给出的界限配筋率公式能有效预测混合配筋SF/混凝土梁的失效模式;梁受弯承载力建议公式的预测值与试验值吻合较好,具有良好的适用性。Abstract: In order to investigate the flexural behaviors and the calculation method of the flexural capacity of steel fiber reinforced concrete(SF/concrete) beams with hybrid glass fiber reinforced polymer composites(GFRP) and steel bars, the proposed formula of the boundary reinforcement ration and the flexural capacity of hybrid reinforced SF/concrete beams were derived on the basis of considering the tensile strength of concrete in the tension zone. Based on this, three kinds of SF/concrete beams with different reinforcement methods were designed and fabricated, and the influence of the hybrid reinforcement ration and the area ratio of GFRP bars to steel bars(Af/As) on the failure modes and the flexural capacity of test beams were mainly discussed. At the same time, the variation characteristics of the flexural behaviors of the hybrid reinforced concrete beams under different concrete strengths were compared and analyzed by relying on relevant test data. The results of the test and the comparative analysis show that the cross section of the hybrid reinforced SF/concrete beams still conform to the flat section assumption. The flexural capacity and the mid-span deflection of the hybrid reinforced SF/concrete beams under the same reinforcement form increase with the increase of the area ratio of GFRP bars to steel bars Af/As. The flexural capacity of the concrete beams with single-layer reinforcement is larger than that of the double-layer reinforcement. Reasonably increasing the concrete strength can further improve the flexural capacity of the hybrid reinforced concrete beams while fully satisfying the tensile effect of GFRP bars. The reliability of the failure modes of the hybrid reinforced concrete beams predicted by the theory of boundary reinforcement ration is higher. The predicted values of the proposed calculation formula of the flexural capacity are in good agreement with the experimentally measured values, and it has good applicability.
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Key words:
- GFRP bar /
- hybrid reinforcement /
- steel fiber /
- concrete beam /
- flexural capacity /
- proposed calculation formula
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表 1 GFRP筋和钢筋的力学性能
Table 1. Mechanical properties of GFRP and steel bars
Type Elastic modulus/GPa Yield strength/MPa Tensile strength/MPa GFRP12 bar 40.06 – 868.22 GFRP16 bar 45.69 – 958.20 S12 bar 200.00 506.51 610.16 表 2 混凝土配合比
Table 2. Mix ratio of concrete
Water cement ratio Material density/(kg·m−3) Cement Water Sand Stone Steel fiber 0.36 447 160 658 1 146 39 表 3 钢纤维(SF)特征参数
Table 3. Characteristic parameters of steel fiber(SF)
Fiber type Length/
mmEquivalent diameter/mm Tensile strength/MPa Cold pull end hook 30 0.5 ≥1 000 表 4 混合配筋SF/混凝土梁设计参数
Table 4. Main parameters of SF/concrete beams with hybrid reinforcing bars
Form Specimen fcu/MPa Steel bar GFRP bar As/mm Af/mm Af/As Single-layer
reinforcementSteel-SF/concrete 51.46 4S12 – 452 – 0 GFRP12-SF/concrete 50.93 – 4G12 – 452 – GFRP12-steel-SF/concrete 50.82 2S12 2G12 226 226 1 GFRP16-steel-SF/concrete 51.64 2S12 2G16 226 402 1.78 Double-layer reinforcement Steel-SF/concrete(D) 51.31 4S12 – 452 – 0 GFRP12-steel-SF/concrete(D) 51.88 2S12 2G12 226 226 1 GFRP16-steel-SF/concrete(D) 52.17 2S12 2G16 226 402 1.78 Notes: D—Double-layer reinforcement; fcu—Measured value of 28 days compressive strength of concrete standard cube; The symbol of “4S12” means 4 steel bars with a diameter of 12 mm; The symbol of “4G12” means 4 GFRP bars with a diameter of 12 mm; As—Cross-sectional area of steel bars; Af—Cross-sectional area of GFRP bars; Af/As—Area ratio of GFRP bars to steel bars. 表 5 混合配筋SF/混凝土梁试验结果及对比分析
Table 5. Test results of SF/concrete beams with hybrid reinforcing bars and comparative analysis
Data
sourceSpecimen Strength
gradeρbh,F/% ρbh,E/% ρh,F/% ρh,E/% $M_{\rm{u} }^{\rm{m}}$/
(kN·m)$M_{\rm{u} }^{\rm{p}}$/
(kN·m)$M_{\rm{cr} }^{\rm{m}}$/
(kN·m)Failure
modesBeams corresponding
to Ref. [15]This paper Steel-SF/concrete CF50 – – 0.98 0.98 68.52 62.25 14.00 SY-CC1 S-1 GFRP12-SF/concrete CF50 – – 1.18 0.20 78.08 71.91 11.30 CC – GFRP12-steel-SF/concrete CF50 1.13 3.81 1.08 0.59 75.42 67.04 12.88 SY-CC-FF GS-1 GFRP16-steel-SF/concrete CF50 1.23 3.88 1.64 0.69 81.23 85.28 12.63 SY-CC2 GS-2 Steel-SF/concrete(D) CF50 – – 1.07 1.07 65.53 63.34 13.00 SY-CC1 S-3 GFRP12-steel-SF/concrete(D) CF50 1.13 3.87 1.17 0.64 69.64 64.60 13.79 SY-CC-FF GS-5 GFRP16-steel-SF/concrete(D) CF50 1.22 3.89 1.79 0.75 76.52 75.91 10.01 SY-CC2 GS-6 Zhang[15] S-1 C30 – – 0.98 0.98 59.12 53.80 11.89 SY-CC1 – GS-1 C30 0.81 2.57 1.08 0.59 57.50 50.19 9.64 SY-CC2 – GS-2 C30 0.83 2.57 1.64 0.69 63.30 60.64 9.80 SY-CC2 – S-3 C30 – – 1.07 1.07 60.77 55.97 12.01 SY-CC1 – GS-5 C30 0.81 2.57 1.17 0.64 53.79 51.14 9.70 SY-CC2 – GS-6 C30 0.83 2.57 1.79 0.75 50.56 54.20 9.87 SY-CC2 – Notes: ρbh,F and ρbh,E are the limit (balance) reinforcement ratios corresponding to the two equilibrium states; ρh,F and ρh,E are two kinds of hybrid reinforcement ratios; $M_{\rm{u} }^{\rm{m}}$ is the measured flexural capacity; $\ M_{\rm{u} }^{\rm{p}}$ is the predicted flexural capacity; $M_{\rm{cr} }^{\rm{m}}$ is the measured crack moment; SY-CC1 is the SF/Concrete crushing in the compression zone after the steel bar yielded; CC is the SF/Concrete crushing in the compression zone; SY-CC-FF is the GFRP bar fractured after the steel bar yielded and SF/Concrete crushing in compression zone; SY-CC2 is the SF/Concrete crushing in the compression zone after the steel bar yielded, and the GFRP bar is not fractured; S-1 is the single-layer reinforced concrete beam (the diameter of steel bars is 12 mm); GS-1 is the single-layer concrete beam reinforced with hybrid GFRP bars and steel bars (the diameter of steel bars and GFRP bars are 12 mm); GS-2 is the single-layer concrete beam reinforced with hybrid GFRP bars and steel bars (the diameter of steel bars is 12 mm and the diameter of GFRP bars is 16 mm); S-3 is the double-layer reinforced concrete beam (the diameter of steel bars is 12 mm); GS-5 is the double-layer concrete beam reinforced with hybrid GFRP bars and steel bars (the diameter of steel bars and GFRP bars are 12 mm); GS-6 is the double-layer concrete beam reinforced with hybrid GFRP bars and steel bars (the diameter of steel bars is 12 mm and the diameter of GFRP bars is 16 mm). -
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