Calculation Method for Reinforcement Stress in Ultra-High Performance Concrete Beams Considering Bond-Slip Effect
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摘要:
为建立适用于配筋超高性能混凝土（UHPC）梁的钢筋应力计算方法，对6片UHPC-T形截面梁开展四点弯曲试验，研究钢筋应力的变化规律. 从钢筋-UHPC受力平衡与变形协调机理出发，应用微元体建立平衡、变形以及黏结-滑移微分方程，导出能综合反映钢筋与UHPC界面黏结-滑移影响及钢纤维抗拉贡献的钢筋应力计算公式，并通过简化应变不均匀系数与裂缝截面钢筋应力计算，提出便于工程应用的钢筋应力简化公式. 研究表明：单位荷载下钢筋应力的增幅随配筋率的提高而减小，而与钢纤维体积率的变化无关；与普通混凝土梁相比，UHPC梁的钢筋应力在开裂截面处偏小，但其分布在相邻裂缝间的不均匀程度更高；钢筋应力建议公式计算值与本文、既有文献的试验值均吻合良好；钢筋应力简化公式计算值与试验值之比的均值为1.03，变异系数为0.06，表明该简化式可用于UHPC梁的钢筋应力计算.
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关键词:
- 超高性能混凝土（UHPC） /
- 钢筋应力 /
- 黏结-滑移 /
- 应变不均匀系数 /
- 微元体
Abstract:Four-point bending tests were conducted on six ultra-high performance concrete T-shaped (UHPC-T) section beams to establish a reinforcement stress calculation method for reinforced UHPC beams and study the variation law of reinforcement stress. Based on the mechanism of force balance and deformation coordination between reinforcement and UHPC, a reinforcement stress calculation formula was derived using the differential equations of equilibrium, deformation, and bond-slip established by micro elements, which could comprehensively reflect the influence of bond-slip between reinforcement and UHPC interfaces and the contribution of steel fibers to tensile strength. By simplifying the calculation of the strain non-uniformity coefficient and the reinforcement stress in cracked sections, a simplified formula for reinforcement stress suitable for engineering applications was proposed. The results show that the increase in reinforcement stress under unit load decreases with the increase in reinforcement ratio, but it is not related to the change in steel fiber volume fraction. Compared with ordinary concrete beams, the reinforcement stress in UHPC beams is relatively small in the cracked section, but the uneven distribution of reinforcement stress between adjacent cracks is intensified. The calculation value of the suggested formula for reinforcement stress is in good agreement with the experimental values in this article and existing literature. The average ratio of the calculated value of the simplified formula for reinforcement stress to the experimental value is 1.03, and the coefficient of variation is 0.06, indicating that this simplified formula can be used for calculating reinforcement stress in UHPC beams.
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图 7 平均裂缝间距计算值与实测值的对比
Figure 7. Comparison between calculated and measured values of average crack spacing
图 9 计算值与文献实测值的对比
Figure 9. Comparison between calculated values and measured values in literature
图 10 简化计算值与文献实测值的对比
Figure 10. Comparison between calculated values of simplified formula and measured values in literature
表 1 试件的编号与参数
Table 1. Number and parameters of specimens
变量 梁号 Vf/% 纵筋配置 ρs/% c/mm 标准梁 T1 2 2 
1.60 15 钢纤维
体积率T2 1 2 1.60 T3 3 配筋率 T4 2 2 0.89 T5 2 2.51 T6 4 3.20 
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表 2 基本力学指标
Table 2. Basic mechanical indicators
Vf/% fcu/MPa fc/MPa ft/MPa Ec/GPa 1 121.22 83.72 6.35 41 2 133.71 89.14 7.84 42 3 141.53 97.82 9.32 44
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表 3 钢筋应力的实测结果
Table 3. Measured results of reinforcement stress
梁号 Fcr/kN Ft/kN σcr/MPa σt/MPa Vm/（MPa•kN−1） T1 55.24 321.42 37.77 593.75 2.09 T2 37.27 311.31 32.23 602.22 2.08 T3 69.72 334.27 44.53 579.63 2.02 T4 43.43 218.51 41.82 581.70 3.08 T5 60.67 454.88 48.34 579.06 1.35 T6 61.14 529.20 39.25 578.51 1.15
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表 4 系数n与S1的取值
Table 4. Values of coefficients n and S1
梁号 n S1 T1 0.64 1.10 T2 0.66 0.90 T3 0.60 0.99 T4 0.62 1.17 T5 0.64 0.95 T6 0.71 0.87
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