矩形空心墩等效塑性铰模型
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摘要
为准确计算矩形空心墩变形能力,基于弯曲、剪切和纵筋滑移三分量变形模型分析影响有效刚度和等效塑性铰长度的主要因素。通过考虑剪切变形的贡献引入空心率的影响,确定计算有效刚度和等效塑性铰长度的公式形式。通过对48根发生弯曲破坏的矩形空心墩拟静力试验结果进行回归分析,分别标定出有效刚度和等效塑性铰长度计算公式中的参数。利用基于建议公式的等效塑性铰模型计算矩形空心墩荷载-位移骨架曲线,并与另外3根试件的试验结果进行比较。基于48根矩形空心墩拟静力试验结果,对各国规范关于有效刚度和等效塑性铰长度的计算公式进行评估。研究结果表明:矩形空心墩有效刚度随轴压比、纵筋率和剪跨比的增大而增大,随■和空心率的增大而减小;等效塑性铰长度随墩高、截面高度、纵筋率、空心率及■的增大而增大;利用基于建议公式的等效塑性铰模型得到的矩形空心墩荷载-位移骨架曲线与试验结果吻合较好;各国规范关于有效刚度和等效塑性铰长度的计算公式对矩形空心墩试验结果的估计均偏于不安全,建议公式具有更高的精度和更小的离散性。
To calculate the deformation capacity of rectangular hollow piers accurately, a deformation model considering bend, shear, and reinforcement slip was used to analyze the effective stiffness and equivalent plastic hinge length of rectangular hollow piers. The ratio of the rectangular hollow piers was determined based on shear deformation, and formulas were proposed for effective stiffness and the equivalent plastic hinge length. After pseudo-static test results showed that 48 rectangular hollow specimens failed in the flexural mode, regression analysis was conducted to calibrate the coefficients of the above-proposed formulas. A load-deformation skeleton of rectangular hollow piers was obtained based on an equivalent plastic hinge model composed of the proposed formulas, and compared with the experimental results of the other three specimens. The formulas for effective stiffness and equivalent plastic length of various countries were evaluated based on the pseudo-static test results of 48 rectangular hollow specimens. The results show that the effective stiffness of rectangular hollow piers increases with the axial load ratio, the longitudinal reinforcement ratio, and the aspect ratio, and decreases with an increase in the hollow ratio and ■. The equivalent plastic hinge length of rectangular hollow piers grows longer with the specimen length, the section height, the longitudinal reinforcement ratio, the hollow ratio and ■. The formulas proposed by various countries for effective stiffness and equivalent plastic length are not conservative for experimental results of rectangular hollow piers, but have higher accuracy and less discreteness. Based on the proposed formulas, the equivalent plastic hinge model can provide a load-deformation skeleton curve close to the experimental results.
To calculate the deformation capacity of rectangular hollow piers accurately, a deformation model considering bend, shear, and reinforcement slip was used to analyze the effective stiffness and equivalent plastic hinge length of rectangular hollow piers. The ratio of the rectangular hollow piers was determined based on shear deformation, and formulas were proposed for effective stiffness and the equivalent plastic hinge length. After pseudo-static test results showed that 48 rectangular hollow specimens failed in the flexural mode, regression analysis was conducted to calibrate the coefficients of the above-proposed formulas. A load-deformation skeleton of rectangular hollow piers was obtained based on an equivalent plastic hinge model composed of the proposed formulas, and compared with the experimental results of the other three specimens. The formulas for effective stiffness and equivalent plastic length of various countries were evaluated based on the pseudo-static test results of 48 rectangular hollow specimens. The results show that the effective stiffness of rectangular hollow piers increases with the axial load ratio, the longitudinal reinforcement ratio, and the aspect ratio, and decreases with an increase in the hollow ratio and ■. The equivalent plastic hinge length of rectangular hollow piers grows longer with the specimen length, the section height, the longitudinal reinforcement ratio, the hollow ratio and ■. The formulas proposed by various countries for effective stiffness and equivalent plastic length are not conservative for experimental results of rectangular hollow piers, but have higher accuracy and less discreteness. Based on the proposed formulas, the equivalent plastic hinge model can provide a load-deformation skeleton curve close to the experimental results.
引文
[1] 孙治国,王东升,杜修力,等.钢筋混凝土桥墩塑性铰区约束箍筋用量研究[J].中国公路学报,2010,23(3):48-57. SUN Zhi-guo, WANG Dong-sheng, DU Xiu-li, et al.Research on Amount of Confining Reinforcement in Potential Plastic Hinge Regions of RC Bridge Columns [J]. China Journal of Highway and Transport, 2010, 23 (3): 48-57.
[2] 朱晞,江辉.桥梁墩柱基于性能的抗震设计方法[J].土木工程学报,2009,42(4):85-92. ZHU Xi, JIANG Hui. Performance-based Seismic Design Method for RC Bridge Piers [J]. China Civil Engineering Journal, 2009, 42 (4): 85-92.
[3] Caltrans-2010, Seismic Design Criteria [S].
[4] Eurocode 8-2005, Design Provisions for Earthquake Resistance of Structures—Part 2: Bridges [S].
[5] JTG/T B02-01—2008,公路桥梁抗震设计细则[S]. JTG/T B02-01—2008, Guidelines for Seismic Design of Highway Bridges [S].
[6] JRA—2002, Design Specifications for Highway Bridges, Part V: Seismic Design [S].
[7] 艾庆华,王东升,李宏男,等.基于塑性铰模型的钢筋混凝土桥墩地震损伤评价[J].工程力学,2009,26(4):158-166. AI Qing-hua, WANG Dong-sheng, LI Hong-nan, et al. Seismic Damage Evaluation of RC Bridge Columns Based on Plastic Hinge Model [J]. Engineering Mechanics, 2009, 26 (4): 158-166.
[8] KOWALSKY M J, PRIESTLEY M J, MACRAE G A. Displacement-based Design of RC Bridge Columns in Seismic Regions [J]. Earthquake Engineering & Structural Dynamics, 1995, 24 (12): 1623-1643.
[9] MEHANNY S S F, KURAMOTO H, DEIERLEIN G G. Stiffness Modeling of Reinforced Concrete Beam-columns for Frame Analysis [J]. ACI Structural Journal, 2001, 98 (2): 215-225.
[10] PANAGIOTAKOS T B, FARDIS M N. Deformations of Reinforced Concrete Members at Yielding and Ultimate [J]. ACI Structural Journal, 2001, 98 (2): 135-148.
[11] BERRYM P, LEHMAN D E, LOWES L N. Lumped-plasticity Models for Performance Simulation of Bridge Columns [J]. ACI Structural Journal, 2008, 105 (3): 270-279.
[12] HASELTON C B, LIEL A B, LANGE S T, et al. Beam-column Element Model Calibrated for Predicting Flexural Response Leading to Global Collapse of RC Frame Buildings[R]. Berkeley: Pacific Earthquake Engineering Research Center, 2008.
[13] ELWOOD K J, EBERHARD M O. Effective Stiffness of Reinforced Concrete Columns [J]. ACI Structural Journal, 2009, 106 (4): 476-484.
[14] 郑罡,李贵乾.钢筋混凝土桥墩有效刚度[J].土木工程学报,2013,46(6):44-52. ZHENG Gang, LI Gui-qian. Effective Stiffness of Reinforced Concrete Bridge Piers [J]. China Civil Engineering Journal, 2013, 46 (6): 44-52.
[15] PRIESTLEY M J N, PARK R. Strength and Ductility of Concrete Bridge Columns Under Seismic Loading [J]. ACI Structural Journal, 1987, 84 (1): 61-76.
[16] 孙治国,王东升,李宏男,等.钢筋混凝土空心桥墩应用及抗震性能研究综述[J].交通运输工程学报,2013,13(3):22-32. SUN Zhi-guo, WANG Dong-sheng, LI Hong-nan, et al. Application of RC Hollow Bridge Pier and Review of Seismic Behavior Research [J]. Journal of Traffic and Transportation Engineering, 2013, 13 (3): 22-32.
[17] 孙治国,郭迅,王东升,等.钢筋混凝土空心墩延性变形能力分析[J].铁道学报,2012,34(1):91-96. SUN Zhi-guo, GUO Xun, WANG Dong-sheng, et al. Analysis on Ductile Deformability of Hollow Reinforced Concrete Bridge Piers [J]. Journal of the China Railway Society, 2012, 34 (1): 91-96.
[18] 夏樟华,宗周红.钢筋混凝土箱型墩延性抗震性能研究[J].振动与冲击,2013,32(23):151-158. XIA Zhang-hua, ZONG Zhou-hong. Ductility a Seismic Performance of Reinforced Concrete Box Piers [J]. Journal of Vibration and Shock, 2013, 32 (23): 151-158.
[19] MANDERJ B, PRIESTLEY M J N, PARK R. Behaviour of Ductile Hollow Reinforced Concrete Columns [J]. Bulletin of the New Zealand National Society for Earthquake Engineering, 1983, 16 (4): 273-290.
[20] TAKAHASHIY, IEMURA H. Inelastic Seismic Performance of RC Tall Piers with Hollow Section[C]// New Zealand Society for Earthquake Engineering. Proceedings of the 12th World Conference on Earthquake Engineering. Auckland: New Zealand Society for Earthquake Engineering, 2000: 1953-1961.
[21] KENMOTSUY, KAWASHIMA K. Seismic Performance of Hollow Reinforced Concrete Columns with Densely Confined Zones [J]. Japan Society of Civil Engineers, 2001, 682: 57-70.
[22] YEH Y K, MO Y L, YANG C Y. Seismic Performance of Rectangular Hollow Bridge Columns [J]. Journal of Structural Engineering, 2002, 128 (1): 60-68.
[23] YEH Y K, MO Y L, YANG C Y. Full-scale Tests on Rectangular Hollow Bridge Piers [J]. Materials and Structures, 2002, 35 (2): 117-125.
[24] MO Y L, NIEN I C. Seismic Performance of Hollow High-strength Concrete Bridge Columns [J]. Journal of Bridge Engineering, 2002, 7 (6): 338-349.
[25] 崔海琴,贺拴海,宋一凡.空心矩形薄壁墩延性抗震性能试验[J].公路交通科技,2010,27(6):58-63. CUI Hai-qin, HE Shuan-hai, SONG Yi-fan. Experimental Study on Antiseismic Ductility of Hollow Rectangular Thin-walled Pier [J]. Journal of Highway and Transportation Research and Development, 2010, 27 (6): 58-63.
[26] 韩强,周雨龙,杜修力.钢筋混凝土矩形空心桥墩抗震性能[J].工程力学,2015,32(3):28-40. HAN Qiang, ZHOU Yu-long, DU Xiu-li. Seismic Performance of Reinforced Concrete Rectangular Hollow Bridge Columns [J]. Engineering Mechanics, 2015, 32 (3): 28-40.
[27] 方志,王飞,殷新锋,等.钢筋混凝土箱型柱抗震性能的试验研究[J].工业建筑,2012,42(3):12-19. FANG Zhi, WANG Fei, YIN Xin-feng, et al. Experimental Study on Seismic Performance of RC Box Piers [J]. Industrial Construction, 2012, 42 (3): 12-19.
[28] 罗征,李建中.低周往复荷载下空心矩形墩抗震性能试验研究[J].振动与冲击,2013,32(8):183-188. LUO Zheng, LI Jian-zhong. Tests for a Seismic Performance of Rectangular Hollow Thin-walled Bridge Columns Under Low-cycle Reversed Loading [J]. Journal of Vibration and Shock, 2013, 32 (8): 183-188.
[29] 宋晓东.桥梁高墩延性抗震性能的理论与试验研究[D].上海:同济大学,2004. SONG Xiao-dong. Theoretical and Experimental Research on Ductile Seismic Performance of High Bridge Columns [D]. Shanghai: Tongji University, 2004.
[30] 王军文,张伟光,艾庆华.PC 与 RC 空心墩抗震性能试验对比[J].中国公路学报,2015,28(4):76-85. WANG Jun-wen, ZHANG Wei-guang, AI Qing-hua. Comparative Experiment on Seismic Performance of PC and RC Hollow Piers [J]. China Journal of Highway and Transport, 2015, 28 (4): 76-85.
[31] SEZEN H, SETZLER E J. Reinforcement Slip in Reinforced Concrete Columns [J]. ACI Structural Journal, 2008, 105 (3): 280-289.
[32] 孙治国,王东升,郭迅,等.地震作用下 RC 薄壁空心墩抗剪强度比较研究[J].土木工程学报,2013,46(12):81-89. SUN Zhi-guo, WANG Dong-sheng, GUO Xun, et al. Comparative Study on Shear Strength of RC Thin-walled Hollow Bridge Piers Under Seismic Effect [J]. China Civil Engineering Journal, 2013, 46 (12): 81-89.
[33] 李贵乾,唐光武,郑罡.圆形钢筋混凝土桥墩等效塑性铰长度[J].土木工程学报,2016,49(2):87-97. LI Gui-qian, TANG Guang-wu, ZHENG Gang. Equivalent Plastic Hinge Length of Circular Reinforced Concrete Bridge Columns [J]. China Civil Engineering Journal, 2016, 49 (2): 87-97.
[34] ACI 318-08, Building Code Requirements for Structural Concrete and Commentary [S].
[35] MAZZONIS, MCKENNA F, SCOTT M H, et al. OpenSees Command Language Manual[M]. Berkeley: Pacific Earthquake Engineering Research (PEER) Center, 2006.
[36] 王建民,朱晞.圆截面RC桥墩曲率极限状态和延性的概率分析[J].土木工程学报,2006,39(12):88-94. WANG Jian-min, ZHU Xi. Probability Analysis of the Curvature Limit State and Ductility of Circular RC Bridge Piers [J]. China Civil Engineering Journal, 2006, 39 (12): 88-94.
[37] 过镇海.钢筋混凝土原理[M].北京:清华大学出版社,2013. GUO Zhen-hai. Reinforced Concrete Principals [M]. Beijing: Tsinghua University Press, 2013.
[38] PINTOA V, MOLINA J, TSIONIS G. Cyclic Tests on Large-scale Models of Existing Bridge Piers with Rectangular Hollow Cross-section [J]. Earthquake Engineering & Structural Dynamics, 2003, 32 (13): 1995-2012.
[39] ZHANG Y, HARRIES K A, YUAN W. Experimental and Numerical Investigation of the Seismic Performance of Hollow Rectangular Bridge Piers Constructed with and Without Steel Fiber Reinforced Concrete [J]. Engineering Structures, 2013, 48: 255-265.
[2] 朱晞,江辉.桥梁墩柱基于性能的抗震设计方法[J].土木工程学报,2009,42(4):85-92. ZHU Xi, JIANG Hui. Performance-based Seismic Design Method for RC Bridge Piers [J]. China Civil Engineering Journal, 2009, 42 (4): 85-92.
[3] Caltrans-2010, Seismic Design Criteria [S].
[4] Eurocode 8-2005, Design Provisions for Earthquake Resistance of Structures—Part 2: Bridges [S].
[5] JTG/T B02-01—2008,公路桥梁抗震设计细则[S]. JTG/T B02-01—2008, Guidelines for Seismic Design of Highway Bridges [S].
[6] JRA—2002, Design Specifications for Highway Bridges, Part V: Seismic Design [S].
[7] 艾庆华,王东升,李宏男,等.基于塑性铰模型的钢筋混凝土桥墩地震损伤评价[J].工程力学,2009,26(4):158-166. AI Qing-hua, WANG Dong-sheng, LI Hong-nan, et al. Seismic Damage Evaluation of RC Bridge Columns Based on Plastic Hinge Model [J]. Engineering Mechanics, 2009, 26 (4): 158-166.
[8] KOWALSKY M J, PRIESTLEY M J, MACRAE G A. Displacement-based Design of RC Bridge Columns in Seismic Regions [J]. Earthquake Engineering & Structural Dynamics, 1995, 24 (12): 1623-1643.
[9] MEHANNY S S F, KURAMOTO H, DEIERLEIN G G. Stiffness Modeling of Reinforced Concrete Beam-columns for Frame Analysis [J]. ACI Structural Journal, 2001, 98 (2): 215-225.
[10] PANAGIOTAKOS T B, FARDIS M N. Deformations of Reinforced Concrete Members at Yielding and Ultimate [J]. ACI Structural Journal, 2001, 98 (2): 135-148.
[11] BERRYM P, LEHMAN D E, LOWES L N. Lumped-plasticity Models for Performance Simulation of Bridge Columns [J]. ACI Structural Journal, 2008, 105 (3): 270-279.
[12] HASELTON C B, LIEL A B, LANGE S T, et al. Beam-column Element Model Calibrated for Predicting Flexural Response Leading to Global Collapse of RC Frame Buildings[R]. Berkeley: Pacific Earthquake Engineering Research Center, 2008.
[13] ELWOOD K J, EBERHARD M O. Effective Stiffness of Reinforced Concrete Columns [J]. ACI Structural Journal, 2009, 106 (4): 476-484.
[14] 郑罡,李贵乾.钢筋混凝土桥墩有效刚度[J].土木工程学报,2013,46(6):44-52. ZHENG Gang, LI Gui-qian. Effective Stiffness of Reinforced Concrete Bridge Piers [J]. China Civil Engineering Journal, 2013, 46 (6): 44-52.
[15] PRIESTLEY M J N, PARK R. Strength and Ductility of Concrete Bridge Columns Under Seismic Loading [J]. ACI Structural Journal, 1987, 84 (1): 61-76.
[16] 孙治国,王东升,李宏男,等.钢筋混凝土空心桥墩应用及抗震性能研究综述[J].交通运输工程学报,2013,13(3):22-32. SUN Zhi-guo, WANG Dong-sheng, LI Hong-nan, et al. Application of RC Hollow Bridge Pier and Review of Seismic Behavior Research [J]. Journal of Traffic and Transportation Engineering, 2013, 13 (3): 22-32.
[17] 孙治国,郭迅,王东升,等.钢筋混凝土空心墩延性变形能力分析[J].铁道学报,2012,34(1):91-96. SUN Zhi-guo, GUO Xun, WANG Dong-sheng, et al. Analysis on Ductile Deformability of Hollow Reinforced Concrete Bridge Piers [J]. Journal of the China Railway Society, 2012, 34 (1): 91-96.
[18] 夏樟华,宗周红.钢筋混凝土箱型墩延性抗震性能研究[J].振动与冲击,2013,32(23):151-158. XIA Zhang-hua, ZONG Zhou-hong. Ductility a Seismic Performance of Reinforced Concrete Box Piers [J]. Journal of Vibration and Shock, 2013, 32 (23): 151-158.
[19] MANDERJ B, PRIESTLEY M J N, PARK R. Behaviour of Ductile Hollow Reinforced Concrete Columns [J]. Bulletin of the New Zealand National Society for Earthquake Engineering, 1983, 16 (4): 273-290.
[20] TAKAHASHIY, IEMURA H. Inelastic Seismic Performance of RC Tall Piers with Hollow Section[C]// New Zealand Society for Earthquake Engineering. Proceedings of the 12th World Conference on Earthquake Engineering. Auckland: New Zealand Society for Earthquake Engineering, 2000: 1953-1961.
[21] KENMOTSUY, KAWASHIMA K. Seismic Performance of Hollow Reinforced Concrete Columns with Densely Confined Zones [J]. Japan Society of Civil Engineers, 2001, 682: 57-70.
[22] YEH Y K, MO Y L, YANG C Y. Seismic Performance of Rectangular Hollow Bridge Columns [J]. Journal of Structural Engineering, 2002, 128 (1): 60-68.
[23] YEH Y K, MO Y L, YANG C Y. Full-scale Tests on Rectangular Hollow Bridge Piers [J]. Materials and Structures, 2002, 35 (2): 117-125.
[24] MO Y L, NIEN I C. Seismic Performance of Hollow High-strength Concrete Bridge Columns [J]. Journal of Bridge Engineering, 2002, 7 (6): 338-349.
[25] 崔海琴,贺拴海,宋一凡.空心矩形薄壁墩延性抗震性能试验[J].公路交通科技,2010,27(6):58-63. CUI Hai-qin, HE Shuan-hai, SONG Yi-fan. Experimental Study on Antiseismic Ductility of Hollow Rectangular Thin-walled Pier [J]. Journal of Highway and Transportation Research and Development, 2010, 27 (6): 58-63.
[26] 韩强,周雨龙,杜修力.钢筋混凝土矩形空心桥墩抗震性能[J].工程力学,2015,32(3):28-40. HAN Qiang, ZHOU Yu-long, DU Xiu-li. Seismic Performance of Reinforced Concrete Rectangular Hollow Bridge Columns [J]. Engineering Mechanics, 2015, 32 (3): 28-40.
[27] 方志,王飞,殷新锋,等.钢筋混凝土箱型柱抗震性能的试验研究[J].工业建筑,2012,42(3):12-19. FANG Zhi, WANG Fei, YIN Xin-feng, et al. Experimental Study on Seismic Performance of RC Box Piers [J]. Industrial Construction, 2012, 42 (3): 12-19.
[28] 罗征,李建中.低周往复荷载下空心矩形墩抗震性能试验研究[J].振动与冲击,2013,32(8):183-188. LUO Zheng, LI Jian-zhong. Tests for a Seismic Performance of Rectangular Hollow Thin-walled Bridge Columns Under Low-cycle Reversed Loading [J]. Journal of Vibration and Shock, 2013, 32 (8): 183-188.
[29] 宋晓东.桥梁高墩延性抗震性能的理论与试验研究[D].上海:同济大学,2004. SONG Xiao-dong. Theoretical and Experimental Research on Ductile Seismic Performance of High Bridge Columns [D]. Shanghai: Tongji University, 2004.
[30] 王军文,张伟光,艾庆华.PC 与 RC 空心墩抗震性能试验对比[J].中国公路学报,2015,28(4):76-85. WANG Jun-wen, ZHANG Wei-guang, AI Qing-hua. Comparative Experiment on Seismic Performance of PC and RC Hollow Piers [J]. China Journal of Highway and Transport, 2015, 28 (4): 76-85.
[31] SEZEN H, SETZLER E J. Reinforcement Slip in Reinforced Concrete Columns [J]. ACI Structural Journal, 2008, 105 (3): 280-289.
[32] 孙治国,王东升,郭迅,等.地震作用下 RC 薄壁空心墩抗剪强度比较研究[J].土木工程学报,2013,46(12):81-89. SUN Zhi-guo, WANG Dong-sheng, GUO Xun, et al. Comparative Study on Shear Strength of RC Thin-walled Hollow Bridge Piers Under Seismic Effect [J]. China Civil Engineering Journal, 2013, 46 (12): 81-89.
[33] 李贵乾,唐光武,郑罡.圆形钢筋混凝土桥墩等效塑性铰长度[J].土木工程学报,2016,49(2):87-97. LI Gui-qian, TANG Guang-wu, ZHENG Gang. Equivalent Plastic Hinge Length of Circular Reinforced Concrete Bridge Columns [J]. China Civil Engineering Journal, 2016, 49 (2): 87-97.
[34] ACI 318-08, Building Code Requirements for Structural Concrete and Commentary [S].
[35] MAZZONIS, MCKENNA F, SCOTT M H, et al. OpenSees Command Language Manual[M]. Berkeley: Pacific Earthquake Engineering Research (PEER) Center, 2006.
[36] 王建民,朱晞.圆截面RC桥墩曲率极限状态和延性的概率分析[J].土木工程学报,2006,39(12):88-94. WANG Jian-min, ZHU Xi. Probability Analysis of the Curvature Limit State and Ductility of Circular RC Bridge Piers [J]. China Civil Engineering Journal, 2006, 39 (12): 88-94.
[37] 过镇海.钢筋混凝土原理[M].北京:清华大学出版社,2013. GUO Zhen-hai. Reinforced Concrete Principals [M]. Beijing: Tsinghua University Press, 2013.
[38] PINTOA V, MOLINA J, TSIONIS G. Cyclic Tests on Large-scale Models of Existing Bridge Piers with Rectangular Hollow Cross-section [J]. Earthquake Engineering & Structural Dynamics, 2003, 32 (13): 1995-2012.
[39] ZHANG Y, HARRIES K A, YUAN W. Experimental and Numerical Investigation of the Seismic Performance of Hollow Rectangular Bridge Piers Constructed with and Without Steel Fiber Reinforced Concrete [J]. Engineering Structures, 2013, 48: 255-265.