Deflection Calculation of New Type Composite Box Girder with Corrugated Steel Webs Based on Reddy Theory
-
摘要: 为准确计算新型波形钢腹板（CSW）组合箱梁的挠度，基于Reddy高阶剪切变形理论，考虑钢-混接触面滑移变形和全截面高阶剪切变形效应，以形函数作为单元内高度变化的插值函数，利用最小势能原理推出新型CSW组合箱梁等参有限元行列式；以一根8.0 m新型波形钢腹板简支组合箱型试验梁为例，基于本文理论编制了相应的计算程序，计算了集中、均布荷载作用下该梁的竖向挠度，并通过模型试验和有限元模拟验证了本文解析计算方法的可靠性；最后分析了剪力键剪切刚度、波形腹板型号、子梁高度比、跨高比等参数对新型CSW组合箱梁挠度的影响程度. 研究结果表明：考虑新型CSW组合箱梁全截面剪切变形效应后的挠度值较初等梁理论值增大约10%，较Timoshenko理论值增大约1.87%. 全截面剪切变形效应对挠度贡献随跨高比逐渐增大而减小. 跨高比和剪力键剪切刚度越小或子梁高度比越大，剪切变形效应对结构竖向挠度的影响越发显著，而波形钢腹板型号对箱梁挠度影响较小.Abstract: In order to accurately calculate the deflection of a new type of composite box girder with corrugated steel webs (CSWs), Reddy high-order theory is used to analyze the slip deformation of the steel-concrete interface and the high-order shear deformation effect of the whole section; the isoparametric finite element determinant of the new-pattern composite box girder with CSWs is derived by the principle of minimum potential energy, using the shape function as the interpolation function of height variation in the element. Taking an 8.0 m long new-pattern simply supported composite box girder with CSWs as an example, the corresponding calculation program is compiled by the proposed methodology and applied to calculate vertical deflections of the beam under concentrated and uniform load. Results of the finite element simulation are then compared with those of model tests to verify the reliability of the analytical calculation method. Finally, influences of the shear stiffness of shear key, type of corrugated web, height ratio of sub-beams, and height-span ratio on the deflection of the new type of composite box girder with CSWs are analyzed. The results show that after taking into consideration the full-section shear deformation effect of the new type of composite box girder with CSWs, its deflection is increased by about 10% compared with the theoretical value of the elementary beam, and increased by about 1.87% compared with Timoshenko ’s theoretical value. As the span-to-height ratio increases gradually, the contribution of the full-section shear deformation effect to the deflection gradually decreases. With a smaller span-to-height ratio, a smaller shear stiffness of shear key, or a larger height ratio of sub-beams, shear deformation displays more significant effect on the vertical deflection of the structure, while the CSW type has little effect on the box deflection.
-
Key words:
- Reddy theory /
- corrugated steel web /
- composite box girder /
- shearing deformation /
- deflection
-
图 1 新型CSW组合箱梁轴向位移场假定
Figure 1. Axial displacement hypothesis of a new type of composite box girder with CSWs
图 7 关键参数对组合箱梁挠度的影响
Figure 7. Effect of key parameters on deflection of composite box girder
表 1 材料特性
Table 1. Material propoties
材料 Ei/GPa 质量密度 ρ/（kg•m−3） 混凝土 34.3 2556 Q235钢材 208.0 7860 
下载: 导出CSV
表 2 箱梁跨中挠度（工况1）
Table 2. Midspan deflection of box girder (case 1)
mm 荷载/（kN•m−1） 初等梁理论 本文理论 FEM 值 Timoshenko 理论 实测 3 1.902 2.081 2.064 2.060 1.969 6 3.804 4.159 4.128 4.121 4.032 9 5.705 6.240 6.192 6.181 6.160
下载: 导出CSV
表 3 箱梁跨中挠度（工况2）
Table 3. Midspan deflection of box girder (case 2)
mm 荷载/kN 初等梁理论 本文理论 FEM 值 Timoshenko 理论 实测 40 5.297 5.667 5.633 5.561 5.658 80 10.594 11.334 11.266 11.123 11.084 100 13.243 14.167 14.083 13.903 14.026
下载: 导出CSV
-
王力,刘世忠,丁万鹏,等. 干寒地区新型波形钢腹板组合箱梁温度效应分析[J]. 工程科学与技术,2021,53(1): 60-66.WANG Li, LIU Shizhong, DING Wanpeng, et al. Analysis on temperature effect of new-pattern corrugated steel web composite box girder in dry cold region[J]. Advanced Engineering Sciences, 2021, 53(1): 60-66. ELGAALY M, HAMILTON R W, SESHADRI A. Shear strength of beams with corrugated webs[J]. Journal of Structural Engineering, 1996, 122(4): 390-398. doi: 10.1061/(ASCE)0733-9445(1996)122:4(390) LBRAHIM S A,EI-DAKHAKHNI W W,ELGAALY M. Fatigue of corrugated-web plate girders: analytical study[J]. Journal of Structural Engineering,2006,132(9): 1381-1392. DRIVER R G, ABBAS H H, SAUSE R. Shear behavior of corrugated web bridge girders[J]. Journal of Structural Engineering, 2006, 132(2): 195-203. doi: 10.1061/(ASCE)0733-9445(2006)132:2(195) 李丽园,周茂定,冀伟,等. 基于剪切附加挠度的波形钢腹板组合箱梁挠度计算[J]. 东南大学学报(自然科学版),2019,49(2): 296-302.LI Liyuan, ZHOU Maoding, JI Wei, et al. Deflection calculation of composite box girder with corrugated steel webs based on shear additional deflection[J]. Journal of Southeast University (Natural Science Edition), 2019, 49(2): 296-302. 姚浩,程进. 基于变分原理的波形钢腹板箱梁挠度计算解析法[J]. 工程力学,2016,33(8): 177-184. doi: 10.6052/j.issn.1000-4750.2015.06.0527YAO Hao, CHENG Jin. Analytical method for calculating defection of corrugated box girders based onvariational principle[J]. Engineering Mechanics, 2016, 33(8): 177-184. doi: 10.6052/j.issn.1000-4750.2015.06.0527 陈卓异,黄侨,李传习,等. 波形钢腹板组合槽型梁静载试验与有效预应力分析[J]. 土木工程学报,2018,51(8): 60-70.CHEN Zhuoyi, HUANG Qiao, LI Chuanxi, et al. Static test and effective pre-stress analysis of composite trough girder with corrugated steel webs[J]. China Civil Engineering Journal, 2018, 51(8): 60-70. 冀伟,蔺鹏臻,刘世忠. 波形钢腹板PC组合箱梁桥的挠度计算与分析[J]. 西南交通大学学报,2018,53(1): 46-55. doi: 10.3969/j.issn.0258-2724.2018.01.006JI Wei, LIN Pengzhen, LIU Shizhong. Deflection calculation and analysis of PC box girder bridges with corrugated steel webs[J]. Journal of Southwest Jiaotong University, 2018, 53(1): 46-55. doi: 10.3969/j.issn.0258-2724.2018.01.006 马磊,万水,蒋正文. 单箱双室波形钢腹板箱梁扭转与畸变性能研究[J]. 中国公路学报,2016,29(10): 77-85. doi: 10.3969/j.issn.1001-7372.2016.10.009MA Lei, WAN Shui, JIANG Zhengwen. Research on torsion and distortion performance of single box double-cell girder with corrugated steel webs[J]. China Journal of Highway and Transport, 2016, 29(10): 77-85. doi: 10.3969/j.issn.1001-7372.2016.10.009 IKARASHI K, KOZAKA K, NAKAMURA Y. Plastic deformation capacity of corrugated web girder under shear bending[J]. Journal of Structural and Construction Engineering (Transactions of AIJ), 2012, 77(673): 443-451. doi: 10.3130/aijs.77.443 SAUSE R, BRAXTAN T N. Shear strength of trapezoidal corrugated steel webs[J]. Journal of Constructional Steel Research, 2011, 67(2): 223-236. doi: 10.1016/j.jcsr.2010.08.004 JOHNSON R P, CAFOLLA J. Corrugated webs in plate girders for bridges[J]. Structures and Buildings, 1997, 122(2): 157-164. doi: 10.1680/istbu.1997.29305 HE Jun, LIU Yuqing, CHEN Airong. Elastic bending theory of composite bridge with corrugated steel web considering shear deformation[J]. Key Engineering Materials, 2009, 25(4): 575-580. 聂建国,李法雄,樊健生. 波形钢腹板梁变形计算的有效刚度法[J]. 工程力学,2012,29(8): 71-79. doi: 10.6052/j.issn.1000-4750.2010.08.0618NIE Jianguo, LI Faxiong, FAN Jiansheng. Effective stiffness method for calculating deflection of corrugated web girder[J]. Engineering Mechanics, 2012, 29(8): 71-79. doi: 10.6052/j.issn.1000-4750.2010.08.0618 冀伟,刘世忠,蔺鹏臻. 均布荷载作用下波形钢腹板简支箱梁的挠度[J]. 公路交通科技,2012,29(12): 69-73,89. doi: 10.3969/j.issn.1002-0268.2012.12.011JI Wei, LIU Shizhong, LIN Pengzhen. Deflection of simple-supported box girder with corrugated steel webs under uniform load[J]. Journal of Highway and Transportation Research and Development, 2012, 29(12): 69-73,89. doi: 10.3969/j.issn.1002-0268.2012.12.011 REDDY J N. A simple higher-order theory for laminated composite plates[J]. Journal of Applied Mechanics, 1984, 51(4): 745-752. doi: 10.1115/1.3167719 吴鸿庆. 结构有限元分析[M]. 北京: 中国铁道出版社, 2012: 288-302. 史守峡,杨嘉陵. 罚函数法分析一类不可压缩橡胶的大变形[J]. 应用基础与工程科学学报,1999(2): 185-191.SHI Shouxia, YANG Jialing. Plane strain incompressible rubber for large deformation by penalty fem[J]. Journal of Basic Science and Engineering, 1999(2): 185-191. -
下载:
点击查看大图
图(7) / 表(3)
计量
- 文章访问数: 539
- HTML全文浏览量: 263
- PDF下载量: 21
- 被引次数: 0