钢-UHPC组合板栓钉抗剪承载力、滑移与刚度计算

李聪; 陈宝春; 胡文旭; 苏家战

doi:10.6052/j.issn.1000-4750.2021.11.0881

钢-UHPC组合板栓钉抗剪承载力、滑移与刚度计算

doi: 10.6052/j.issn.1000-4750.2021.11.0881

李聪^1,,
陈宝春^{2, 3, ,},
胡文旭^2,,
苏家战^2,

1.
广西大学土木建筑工程学院，广西，南宁 530004
2.
福州大学土木工程学院，福建，福州 350108
3.
桥梁技术创新与风险防治国家级国际联合研究中心，福建，福州 350108

基金项目: 国家重点研发计划项目(2018YFC0705400)；广西大学高层次人才资助项目(A3030051017，A3030051026)；广西青年自然基金项目(2021GXNSFBA220006)

详细信息

作者简介:
李　聪(1990−)，男，河南汝南人，助理研究员，博士，主要从事钢-UHPC组合结构研究(E-mail: congli@gxu.edu.cn)

胡文旭(1997−)，男，浙江温州人，硕士生，主要从事UHPC研究(E-mail: 1056768983@qq.com)

苏家战(1983−)，男，福建泉州人，副研究员，博士，主要从事UHPC桥梁结构研究(E-mail: jiazhansu@fzu.edu.cn)

通讯作者:
陈宝春(1958−)，男，福建罗源人，教授，博士，博导，主要从事桥梁与结构工程研究(E-mail: baochunchen@fzu.edu.cn)

中图分类号: TU398+.9
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出版历程
- 收稿日期: 2021-11-11
- 修回日期: 2022-03-10
- 录用日期: 2022-03-25
- 网络出版日期: 2022-03-25
- 刊出日期: 2023-06-25

CALCULATION OF SHEAR BEARING CAPACITY, SLIP AND STIFFNESS OF HEADED STUDS IN STEEL-UHPC COMPOSITE SLAB

LI Cong^1
,,
CHEN Bao-chun^{2, 3
, ,},
HU Wen-xu^2
,,
SU Jia-zhan^2
,

1.
College of Civil Engineering and Architecture, Guangxi University, Nanning, Guangxi 530004, China
2.
College of civil engineering, Fuzhou University, Fuzhou, Fujian 350108, China
3.
National Center for Joint International Research of Bridges Technology Innovation and Risk Mitigation, Fuzhou, Fujian 350108, China

摘要

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。
- Ultra-high performance concrete /
- 栓钉 /
- 抗剪承载力 /
- 滑移模型 /
- 抗剪刚度 /
- 焊缝系数 /
- 破坏模式
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.
- Ultra-high performance concrete /
- headed stud /
- shear bearing capacity /
- slip model /
- shear stiffness /
- weld coefficient /
- failure mode

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图 1 试件构造细节　/mm

Figure 1. Details of specimen

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图 2 试验装置

Figure 2. Test set-up

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图 3 荷载-滑移曲线

Figure 3. Load-slip curves

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图 4 界面破坏照片

Figure 4. Photos of interface failure

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图 5 UHPC中栓钉焊缝贡献系数拟合结果

Figure 5. Fitting results of contribution coefficient of stud weld in UHPC

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图 6 荷载-滑移曲线预测结果

Figure 6. Load-slip curve prediction results

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图 7 栓钉受力状态与不同荷载取值、滑移量的关系

Figure 7. The relationship between the force state of the stud and different load and slip values

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图 8 栓钉抗剪刚度计算结果

Figure 8. Calculation results of stud shear stiffness

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图 9 栓钉荷载-滑移预测曲线与抗剪刚度关系

Figure 9. Relationship between load-slip prediction curve and shear stiffness of headed stud

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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

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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
试件编号	极限荷载N_u	单钉承载力P_s	单钉承载力平均值P_s,ave	极限滑移S_u	极限滑移平均值S_u,ave	最大滑移S_max	最大滑移平均值S_max,ave	破坏模式
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

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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]。

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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)
		式(1)~式(3)	式(4)	式(5)	$\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

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表 5 采用文献数据的计算结果讨论

Table 5. Discussion on calculation results using literature data

计算结果	式(1)	式(2)~式(4)	式(5)	式(6)
计算结果	式(1)	式(2)~式(4)	式(5)	$\varphi $=2.5^[12]	$\varphi $=2.0^[9]	$\varphi $=1.5^[8]
平均值	0.67	0.84	0.66	1.10	1.05	1.01
标准差	0.13	0.13	0.12	0.24	0.22	0.20

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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。

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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V_S，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V_S0.66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。
理论与规范计算		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。

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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
组号	编号	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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参考文献(44)

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