CALCULATION OF SHEAR BEARING CAPACITY, SLIP AND STIFFNESS OF HEADED STUDS IN STEEL-UHPC COMPOSITE SLAB
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摘要: 钢-Ultra-high performance concrete (UHPC)组合桥面板在大跨桥梁中具有较多应用,栓钉连接件对其组合作用的发挥起关键作用。为探究钢-UHPC组合板中栓钉抗剪性能,开展了6个栓钉抗剪推出试验,收集了6种抗剪承载力计算方法、5种抗剪滑移预测模型和10种抗剪刚度计算方法,根据试验结果分别进行计算分析。试验结果表明:所有试件中的栓钉均表现为焊缝与根部交界处剪断,UHPC板除在栓钉根部位置出现局部破损外,基本保持完好;栓钉的抗剪滑移曲线经历弹性、弹塑性和下降3个阶段;所有试件最大滑移量均小于3.5 mm,可取0.1 mm作为弹性极限滑移量。计算结果表明:现有部分规范计算UHPC中栓钉抗剪承载力时不考虑焊缝影响,计算结果偏低,根据该文2组试验数据和收集29组有效数据,提出考虑焊缝影响的计算式,建议UHPC中栓钉焊缝贡献系数取1.1;不同抗剪滑移模型预测结果差异大,建议采用反比例函数形式的模型预测,较为精确;栓钉的抗剪刚度取值由于未考虑栓钉实际处于受力状态,计算结果差异大,建议取滑移量0.1 mm对应的刚度作为弹性抗剪刚度;建立了栓钉抗剪滑移模型与抗剪刚度的关系式,在缺少试验数据时可为近似计算提供参考。Abstract: Steel-Ultra-high performance concrete (UHPC) composite slab has many applications in long-span bridges, in which the headed stud connectors play a key role. To explore the shear resistance of headed studs in steel-UHPC composite slab, six push-out specimens of headed stud were carried out, and different calculation methods were evaluated based on the test results, including six methods to calculate the shear bearing capacity, five models to predict the shear slip, and ten methods to calculate the shear stiffness. The test results show that the headed studs in all specimens appeared to break at the junction of the weld root, and the UHPC slabs remain intact except for partial damage at the root of the studs. The shear-slip curves of headed stud were divided into three stages, i.e., the elastic stage, the elastic-plastic stage and the descending stage. The maximum slip of all specimens is less than 3.5 mm, and the limit of elastic slip can be taken as 0.1 mm. The results show that the calculated shear resistance of headed stud in UHPC was lower than the test results according to some specifications without considering the contribution of stud welds. It is recommend that the stud welds contribution coefficient can be taken as 1.1 on the basis of the results of 2 sets of tests in this research and 29 sets of other effective data. The prediction results of different shear-slip models were different from the test results. It is suggested that the inverse proportional function model should be used to achieve accurate prediction. The actual force state of stud was not considered in the calculation of shear stiffness, resulting in significant difference in the calculation results. It is recommended that the shear stiffness corresponding to the slip of 0.1 mm can be taken as the elastic shear stiffness. The relationship between the shear-slip model and the shear stiffness of headed stud was established to provide a reference for calculation without test data.
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表 1 钢材材性指标
Table 1. Mechanical properties of steel
钢材类型 屈服强度/MPa 极限强度/MPa 弹性模量/GPa 栓钉 350.0 440.0 207.0 钢板 345.5 470.3 206.2 钢筋 500.4 590.2 210.8 表 2 试验主要结果
Table 2. Main test results
试件编号 荷载/kN 滑移/mm 破坏模式 极限荷载Nu 单钉承载力Ps 单钉承载力平均值Ps,ave 极限滑移Su 极限滑移平均值Su,ave 最大滑移Smax 最大滑移平均值Smax,ave SI-1 269.1 67.3 61.8 1.50 1.51 2.80 3.09 双侧 SI-2 232.7 58.2 1.46 3.36 单侧 SI-3 240.0 60.0 1.58 3.11 双侧 SII-1 468.2 58.5 58.8 2.25 2.05 3.02 2.78 双侧 SII-2 452.0 56.5 1.65 2.50 双侧 SII-3 490.5 61.3 2.25 2.81 双侧 表 3 栓钉抗剪承载力部分规范的计算方法
Table 3. Calculation formula for stud shear strength in some codes
公式编号 资料来源 计算式 计算说明 式(1) EC4[23] ${V_{\rm{S,c} } } = {\text{min} }\left\{ \begin{gathered} 0.29{A_{\rm{s} } }\sqrt { {f_{ {\text{ck} } } }{E_{\text{c} } } } \\ {\text{ } }\phi {A_{\rm{s} } }{f_{\rm{u} } }/{\gamma _{\rm{v} } } \\ \end{gathered} \right.$ 原式中抗力折减系数$ \phi $取0.8和荷载分项系数$ {\gamma _{\rm{v}}} $取1.25。 式(2) AASHTO[24] ${V_{\rm{S,c} } } = {\text{min} }\left\{ \begin{gathered} 0.43{A_{\rm{s} } }\sqrt { {f_{\rm{ck} } }{E_{\rm{c} } } } \\ {\text{ } }\phi {A_{\rm{s} } }{f_{\rm{u} } } \\ \end{gathered} \right.$ 原式在设计时,抗力折减系数$ \phi $取0.85。 式(3) AISC 360-10[25] ${V_{\rm{S,c} } } = {\text{min} }\left\{ \begin{gathered} 0.5{A_{\text{s} } }\sqrt { {f_{\rm{ck} } }{E_{\rm{c} } } } \\ {\text{ } }{\eta _{\rm{g} } }{\eta _{\rm{p} } }{A_{\rm{s} } }{f_{\rm{u} } } \\ \end{gathered} \right.$ 原式中群钉效应折减系数${\eta _{\rm G}}$取1.0,栓钉位置折减系数${\eta _{\rm P}}$取0.75。 式(4) GB 50017−2017[19] ${V_{\rm{S,c} } } = {\text{min} }\left\{ \begin{gathered} 0.43{A_{\text{s} } }\sqrt { {E_{\text{c} } }{f_{\text{c} } } } \\ {\text{ } }0.7{A_{\text{s} } }\gamma f \\ \end{gathered} \right.$ 式中,$ {\gamma _{}} $在栓钉材料性能等级为4.6时,取1.67,$f$取215 MPa。 式(5) GB 50917−2013[26] ${V_{\rm{S,c} } } = {\text{min} }\left\{ \begin{gathered} 0.43{\eta _{\rm{g} } }{A_{\rm{s} } }\sqrt { {f_{ {\rm{cd} } } }{E_{\rm{c} } } } \\ {\text{ } }1.19{A_{\rm{s} } }{f_{\rm{u} } }{\left(\dfrac{ { {E_{\text{c} } } } }{ { {E_{\text{s} } } } }\right)^{0.2} }{\left(\dfrac{ { {f_{ {\text{cu} } } } } }{ { {f_{\text{s} } } } }\right)^{0.1} } \\ \end{gathered} \right.$ 式中,依据结构破坏形式分别给出相应的抗剪承载力计算公式。 式(6) DOINGHAUS等[27] ${V_{\rm{S,c}}} = (\phi {A_{\rm{s}}}{f_{\rm{u}}}{\text{ + }}\varphi {f_{{\rm{cu150}}}}{d_{\rm{wc}}}{l_{\rm{wc}}})/{\gamma _{\rm{v}}}$ 原式中抗力折减系数$ \phi $取0.8和荷载分项系数 $ {\gamma _{\rm{v}}} $取1.25;$ \varphi $可取2.5[12]、2.0[9]和1.5[8]。 表 4 抗剪承载力计算值与实测值
Table 4. Calculated and measured values of shear capacity
试件编号 $ {V_{{\rm{S,e}}}} $ 部分规范($ {V_{{\rm{S,c}}}}/{V_{{\rm{S,e}}}} $) 考虑焊缝影响($ {V_{{\rm{S,c}}}}/{V_{{\rm{S,e}}}} $) 式(1)~式(3) 式(4) 式(5) 式(6) $\varphi $=2.5[12] $\varphi $=2.0[9] $\varphi $=1.5[8] SI-1 67.3 0.73 0.87 0.70 1.04 0.98 0.92 SI-2 58.2 0.85 1.00 0.81 1.20 1.13 1.06 SI-3 60.0 0.82 0.97 0.79 1.17 1.10 1.03 SII-1 58.5 0.84 1.00 0.81 1.20 1.13 1.06 SII-2 56.5 0.87 1.03 0.84 1.24 1.17 1.10 SII-3 61.3 0.80 0.95 0.77 1.14 1.08 1.01 平均值 60.3 0.82 0.97 0.79 1.17 1.10 1.03 标准差 3.47 0.04 0.05 0.04 0.06 0.06 0.06 表 5 采用文献数据的计算结果讨论
Table 5. Discussion on calculation results using literature data
表 6 抗剪荷载与滑移关系模型
Table 6. Relationship between shear load and slip
公式编号 资料来源 预测模型公式 计算说明 式(7) OLLGAARD等[32] $ \dfrac{P}{{{P_{\rm{u}}}}}{\text{ = }}{(1 - {{\rm{e}}^{ - 0.71S}})^{0.4}} $ 研究对象主要为LAWC和NC 式(8) AN等[33] $ \dfrac{P}{{{P_{\rm{u}}}}}{\text{ = }}\dfrac{{4.44(S - 0.031)}}{{1 + 4.24(S - 0.031)}} $ 研究对象为HSC 式(9) SU等[34] $ \dfrac{P}{{{P_{\text{u}}}}}{\text{ = }}{(1 - {{\rm{e}}^{ - 0.61S}})^{0.34}} $ 研究对象为HSC;对荷载-滑移曲线进行拟合。 式(10) WANG等[6] $ \dfrac{P}{{{P_{\rm{u}}}}}{\text{ = }}{(1 - {{\rm{e}}^{ - 1.1S}})^{0.96}} $ 研究对象为NC和UHPC;对荷载-滑移曲线进行拟合。 式(11) WANG等[7] $ \dfrac{P}{{{P_{\rm{u}}}}}{\text{ = }}\dfrac{{S/d}}{{0.006 + 1.02 \cdot S/d}} $ 研究对象为NC和UHPC;考虑栓钉直径影响。 表 7 抗剪刚度计算方法
Table 7. Calculation method of shear stiffness
计算方法 公式编号 资料来源 抗剪刚度计算式 计算说明 滑移曲线 按$ {V_{\rm{S}}} $倍数 式(15) EC4[23] $K{\text{ = 0} }{\text{.7} }{V_{\text{S} } }/S$ 取栓钉抗剪承载力$ {V_{\rm{S}}} $的0.7倍除以对应的滑移量S。 式(16) JOHNSON等[35] $K{\text{ = 0} }{\text{.5} }{V_{\text{S} } }/S$ 取栓钉抗剪承载力$ {V_{\rm{S}}} $的0.5倍除以对应的滑移量S。 式(17) JSSC[36] $K{\text{ = 1/3} }{V_{\text{S} } }/S$ 取栓钉抗剪承载力$ {V_{\rm{S}}} $的1/3倍除以对应的滑移量S。 按滑移量${ {{S} }_i}$ 式(18) 蔺钊飞等[17] $K{\text{ = } }{V_{ { {\rm{S} }_{0.2} } } }/{ {{S} }_{0.2} }$ 取滑移量S在0.2 mm时,对应荷载进行求解,即0.2 mm割线刚度法。 式(19) GB 50017−2017[19] $K{\text{ = } }{V_{\text{S} } }/{ {{S} }_{1.0} }$ 取栓钉抗剪承载力VS,S取1.0 mm。 式(20) 聂建国[37] $K{\text{ = } }{0.66V_{\text{S} } }/{ {{S} }_{1.0} }$ 取栓钉承载力的VS0.66倍时,S取1.0 mm。 式(21) WANG[38] $K{\text{ = } }{V_{ { {\rm{S} }_{0.8} } } }/{ {{S} }_{0.8} }$ 取滑移量S在0.8 mm时,对应荷载进行求解,即0.8 mm割线刚度法。 式(22) 周安等[39] $K{\text{ = } }{V_{ { {\rm{S} }_{0.5} } } }/{ {{S} }_{0.5} }$ 取滑移量S在0.5 mm时,对应荷载进行求解,即0.5 mm割线刚度法。 理论与规范计算 式(23) 蔺钊飞等[18] $K = 0.32{d_{\rm{s}}}E_{\rm{s}}^{1/4}E_{\rm{c}}^{3/4} $ 基于推力桩小变形理论推导,并结合试验和收集数据拟合得到0.32。 式(24) JTG/TD 64-01−2015[40] $K = 13.0{d_{\rm{s}}}\sqrt { {E_{\rm{c}}}{f_{\rm{ck}} }} $ 基于试验结果拟合得到,在未开展试验时可用于估算。 表 8 抗剪刚度计算结果
Table 8. Calculation results of shear stiffness
组号 编号 按荷载倍数计算 按滑移量计算 理论与规范计算 式(15) 式(16) 式(17) 式(18) 式(19) 式(20) 式(21) 式(22) 本文 式(23) 式(24) SI组 1 314.0 739.5 962.9 262.5 67.5 44.6 76.4 108.4 450.0 − − 2 302.0 694.8 1004.1 222.5 51.3 33.8 78.9 100.0 375.0 − − 3 287.9 544.2 559.9 268.2 52.5 34.7 75.7 100.0 375.0 − − 平均值 301.3 659.5 842.3 251.1 57.1 37.7 77.0 102.8 400.0 − 变异性 3.5 12.7 23.8 8.1 12.9 13.0 1.8 3.9 8.8 − SII组 1 343.8 731.7 1000.0 250.0 55.0 36.3 64.8 111.4 400.0 − − 2 393.8 687.5 750.0 225.0 53.8 35.5 67.3 100.0 416.7 − − 3 425.0 882.4 1000.0 250.0 58.1 38.4 69.3 111.3 437.5 − − 平均值 387.5 767.2 916.7 241.7 55.6 36.7 67.1 107.6 418.1 − 变异性 8.6 10.9 12.9 4.9 3.3 3.3 2.7 5.0 3.7 − 平均值 344.4 713.4 879.5 246.4 56.4 37.2 72.1 105.2 409.0 595.4 481.0 变异性 14.4 13.9 19.2 7.0 9.6 9.7 7.2 5.0 7.0 − − -
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