Effects of Longitudinal Reinforcement Ratio on Flexural Capacity of One-Way Slab of UHPC Waffle Bridge Deck
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摘要:
为研究超高性能混凝土（UHPC）华夫桥面单向板中纵筋率对其抗弯承载力的影响，利用等效宽度的原理对其进行简化，设计制作了6根不同纵筋率的足尺T梁模型. 首先，通过加载试验分别对UHPC的基本力学性能和T型截面UHPC梁的抗弯性能和破坏模式进行研究；其次，根据材料性能试验结果，提出UHPC抗拉与抗压的本构模型，并通过截面分析推导T型截面UHPC梁的极限抗弯承载力计算公式；最后，基于既有研究结果，对所提出的T形截面UHPC梁极限抗弯承载力计算公式进行适用性验证. 研究结果表明：由于UHPC具有优异的抗拉强度和拉伸韧性，尽管减小纵筋率会降低T形截面UHPC梁的极限抗弯承载力和延性，但不会改变构件的破坏形式，即T形截面UHPC梁在纵筋率较少甚至不配筋的情况下依然具备延性破坏的特征；根据截面分析推导结果，受拉侧UHPC极限抗拉强度变化系数与纵筋率成正比关系，纵筋率的增大可以更加显著地发挥UHPC的抗拉作用；所提出的公式具有良好的适用性.
Abstract:To study the effect of longitudinal reinforcement ratio on the flexural capacity of a one-way slab of an ultra-high performance concrete (UHPC) wafer bridge deck, six full-scale T-beam models with varying longitudinal reinforcement ratios were produced by using the principle of equivalent width to simplify the analysis. Firstly, the basic mechanical properties of UHPC were studied, followed by the flexural behavior and failure mode of T-shaped UHPC beams through loading experiments. Secondly, a constitutive model for the tensile and compressive strength of UHPC was proposed based on the results of material performance tests. Through section analysis, a formula for calculating the ultimate flexural capacity of T-shaped UHPC beams was derived. Finally, the applicability of the proposed formula was validated based on previous research results. The research findings indicate that although reducing the longitudinal reinforcement ratio will weaken the ultimate flexural capacity and ductility of T-shaped UHPC beams, the failure mode of the components will not change, and T-shaped UHPC beams will still exhibit ductile failure characteristics, even with low or no reinforcement, due to the excellent tensile strength and toughness of UHPC. Moreover, the results of section analysis derivation indicate that the coefficient of variation of the ultimate tensile strength of UHPC under tension is proportional to the longitudinal reinforcement ratio. Therefore, increasing the longitudinal reinforcement ratio can significantly enhance the tensile strength of UHPC. The proposed formula was found to be applicable.
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表 3 UHPC的单轴拉伸性能
Table 3. Uniaxial tensile behavior of UHPC
参数 初裂强度/
MPa初裂
应变极限强度/
MPa极限强度
对应应变取值 4.14 0.0001 8.42 0.0071 
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表 4 钢筋的抗拉力学性能
Table 4. Tensile properties of steel bars
直径/mm 屈服强度/MPa 极限强度/MPa 表面 6 529.7 537.0 螺纹 10 519.9 623.6 12 479.2 662.2 16 429.9 618.6 20 415.5 604.1 22 470.5 651.0
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表 5 试件设计参数
Table 5. Design parameters of specimens
试件编号 底部纵筋 纵筋率$\mathop \rho \nolimits_1 $/% 顶部纵筋 UT-00 无 0 5$\phi $10@100 UT-06 1D6 0.15 UT-12 1D12 0.61 UT-16 1D16 1.08 UT-20 1D20 1.69 UT-22 1D22 2.04
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表 6 T梁试验结果
Table 6. Results of T-shaped beam tests
kN 试件编号 开裂荷载 屈服荷载 峰值荷载 UT-00 17.0 22.6 UT-06 14.0 14.7 26.4 UT-12 19.0 29.1 50.5 UT-16 23.0 38.1 66.7 UT-20 27.0 44.3 91.8 UT-22 43.0 63.4 112.7
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表 7 T梁受弯承载力计算值与试验值对比
Table 7. Comparison between calculated and experimental flexural capacity of T-shaped UHPC beams
试件
编号xe/mm k Mu_exp/
（kN•m）Mu_cal/
（kN•m）Mu_cal/
Mu_expUT-00 6.91 −0.11 10.17 9.78 0.96 UT-06 7.28 −0.12 11.88 12.92 1.09 UT-12 8.48 0.26 22.73 21.84 0.96 UT-16 9.75 0.54 30.02 29.97 1.00 UT-20 11.60 0.91 41.31 41.18 1.00 UT-22 13.05 1.12 50.72 51.12 1.01
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表 8 既有文献的公式验证
Table 8. Validation of proposed equations in previous studies
来源 试件 xe
/mmk Mu_exp/
（kN•m）Mu_cal/
（kN•m）Mu_cal/ Mu_exp 文献[23] B-S65-16 13.49 0.37 56.16 53.19 0.95 B-S65-20 16.44 0.64 87.21 79.98 0.92 文献[24] T-1 30.38 0.95 172.94 160.61 0.93 T-2 44.23 1.64 236.43 238.17 1.01 T-3 48.76 2.04 286.47 256.84 0.90 T-4 59.73 2.54 297.32 340.77 1.15 T-5 48.18 1.64 281.61 275.65 0.98 文献[25] T1 20.49 0.62 105.12 108.22 1.03 T2 38.76 2.07 179.42 192.62 1.07
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