Restrained Torsion Analysis of Box Girders with Corrugated Steel Webs Based on Reissner’s Principle
-
摘要:
为更加合理地分析波形钢腹板箱梁约束扭转效应，考虑波形钢腹板的褶皱效应推演了翘曲正应力和剪应力计算式，应用Reissner原理建立了波形钢腹板箱梁约束扭转控制微分方程，给出了不同于乌曼斯基第二理论的翘曲系数公式. 通过简支梁数值算例验证了所推导公式的正确性，并分析了腹板厚度和悬臂板宽度变化对箱梁横截面应力的影响. 研究结果表明：相对于乌曼斯基第二理论，基于Reissner原理计算的应力与有限元解吻合更好；按乌曼斯基第二理论与按Reissner原理计算的翘曲系数的比值可达到4.70；波形钢腹板主要承担剪应力，几乎不承担翘曲正应力，而顶底板既承担翘曲正应力也承担剪应力，应对顶底板予以重视，防止斜裂缝的产生；腹板厚度增大能减小翘曲正应力；随着悬臂板宽度的增大，当悬臂板宽度比大于0.10时，翘曲正应力减小，而当悬臂板宽度比大于0.30时，总剪应力几乎无变化.
Abstract:To analyze the restrained torsion effect of the box girder with corrugated steel webs (CSWs) more reasonably, the calculation formulas of warping normal stress and shear stress were deduced considering the accordion effect of CSWs. Moreover, the governing differential equation for analyzing the restrained torsion was established using Reissner’s principle, and the warping coefficient formula differing from Umanskii’s second theory was presented. The calculation formulas were then verified through a numerical simulation of a simply supported box girder, and the influence of web thickness and cantilever slab width on cross-section stresses of the box girder was analyzed. The results show that the stresses calculated based on Reissner’s principle are in better agreement with the finite element solution than those based on Umanskii’s second theory. The ratio of warping coefficient calculated by Umanskii’s second theory to that calculated by Reissner’s principle can reach 4.70. CSWs mainly bear shear stress and almost no warping normal stress, while top and bottom slabs bear both warping normal stress and shear stress. Therefore, more attention should be paid to top and bottom slabs to prevent oblique cracks. In addition, growing web thickness can reduce warping normal stress. With the increase of the cantilever slab width, warping normal stress decreases when the cantilever slab width ratio is above 0.10, while the total shear stress hardly changes when the cantilever slab width ratio is above 0.30.
-
图 5 跨中左截面应力分布（单位：kPa）
Figure 5. Stress distribution at left section from mid-span （unit： kPa）
图 6 翘曲系数比值随腹板厚度和悬臂板宽度比的变化曲线
Figure 6. Variation of warping coefficient ratio with web thickness and cantilever slab width ratio
图 7 翘曲正应力随腹板厚度和悬臂板宽度比的变化曲线
Figure 7. Variation of warping normal stress with web thickness and cantilever slab width ratio
图 8 总剪应力随腹板厚度和悬臂板宽度比的变化曲线
Figure 8. Variation of total shear stress with web thickness and cantilever slab width ratio
表 1 距跨中1.6 m左截面应力比较
Table 1. Comparison of stresses at left section 1.6 m from mid-span
名称 计算点 有限元
解/kPa本文方
法/kPa乌-Ⅱ
理论/kPa相对误差/% 本文
方法乌-Ⅱ
理论${\sigma}$ Ⅰ 54.06 57.35 63.61 6.09 17.67 Ⅱ −27.83 −25.42 −28.18 −8.66 1.28 Ⅴ −75.83 −81.24 −90.10 7.13 18.82 $ {\tau _{\text{z}}} $ Ⅲ 82.37 84.59 77.37 2.70 −6.07 Ⅳ 1670.20 1480.32 1354.03 −11.37 −18.93 Ⅵ 154.55 154.50 176.98 −0.03 15.51 
下载: 导出CSV
-
[1] 李立峰,周聪,王连华,等. 基于纽玛克法的变截面波形钢腹板组合箱梁畸变效应分析[J]. 中国公路学报,2018,31(6): 217-226.LI Lifeng, ZHOU Cong, WANG Lianhua, et al. Analysis on distortion effect of non-prismatic composite box girders with corrugated steel webs based on Newmark method[J]. China Journal of Highway and Transport, 2018, 31(6): 217-226. [2] ZHU Y B, WAN S, SHEN K J, et al. Theoretical study on the nonlinear performance of single-box multi-cell composite box-girder with corrugated steel webs under pure torsion[J]. Journal of Constructional Steel Research, 2021, 178: 106487.1-106487.20. [3] JIANG R J, AUF T K, XIAO Y F. Prestressed concrete girder bridges with corrugated steel webs: review[J]. Journal of Structural Engineering, 2015, 141(2): 04014108.1-04014108.9. [4] 杨丙文,黎雅乐,万水,等. 波形钢腹板箱梁的扭转应力分析[J]. 华南理工大学学报(自然科学版),2012,40(2): 19-22,34.YANG Bingwen, LI Yale, WAN Shui, et al. Stress analysis of box girder with corrugate steel webs under torsion[J]. Journal of South China University of Technology (Natural Science Edition), 2012, 40(2): 19-22,34. [5] 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.MA 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. [6] 邓文琴,毛泽亮,刘朵,等. 单箱三室波形钢腹板悬臂梁扭转与畸变分析及试验研究[J]. 建筑结构学报,2020,41(2): 173-181.DENG Wenqin, MAO Zeliang, LIU Duo, et al. Analysis and experimental study on torsion and distortion of single box three-cell cantilever girder with corrugated steel webs[J]. Journal of Building Structures, 2020, 41(2): 173-181. [7] NIE J G, ZHU Y J, TAO M X, et al. Optimized prestressed continuous composite girder bridges with corrugated steel webs[J]. Journal of Bridge Engineering, 2017, 22(2): 04016121.1-04016121.17. [8] HE J, LIU Y Q, WANG S H, et al. Experimental study on structural performance of prefabricated composite box girder with corrugated webs and steel tube slab[J]. Journal of Bridge Engineering, 2019, 24(6): 04019047.1-04019047.17. [9] 张元海,孙成成. 波形钢腹板箱梁考虑腹板局部纵向刚度影响的扭转效应分析[J]. 东南大学学报(自然科学版),2021,51(2): 195-201.ZHANG Yuanhai, SUN Chengcheng. Analysis on the torsion effect of box girders with corrugated steel webs considering local longitudinal stiffness of webs[J]. Journal of Southeast University (Natural Science Edition), 2021, 51(2): 195-201. [10] 强士中,李乔. 关于闭口薄壁杆件约束扭转的周边不变形理论[J]. 桥梁建设,1985(1): 63-75. [11] 张元海,刘泽翔,王晨光. 带悬臂板薄壁箱梁极惯性矩的合理计算方法[J]. 铁道学报,2019,41(8): 94-99.ZHANG Yuanhai, LIU Zexiang, WANG Chenguang. Rational method for computing polar inertia moment of thin-walled box girders with cantilever slab[J]. Journal of the China Railway Society, 2019, 41(8): 94-99. [12] KATO H, NISHIMURA N. Practical analysis methods for continuous girder and cable stayed bridges composed of beams with corrugated steel webs[J]. Structural Engineering/Earthquake Engineering, 2004, 21(2): 207-222. doi: 10.2208/jsceseee.21.207s [13] 李运生,陈留剑,刘蓓,等. 波形钢腹板曲线结合梁弯扭效应的解析解推导及参数分析[J]. 铁道学报,2019,41(1): 101-108.LI Yunsheng, CHEN Liujian, LIU Bei, et al. Analytical solution derivation and parametrical analysis of bending-torsional effects of curved composite beam with corrugated steel webs[J]. Journal of the China Railway Society, 2019, 41(1): 101-108. [14] 徐勋,叶华文,强士中. 带悬臂板薄壁箱梁的扭转和畸变分析[J]. 铁道学报,2015,37(10): 83-91.XU Xun, YE Huawen, QIANG Shizhong. Torsion and distortion analysis of thin-walled box girder with cantilever flanges[J]. Journal of the China Railway Society, 2015, 37(10): 83-91. [15] 鲍永方,黄文彬. 矩形箱梁约束扭转理论的分析与比较[J]. 工程力学,1997,14(3): 132-137.BAO Yongfang, HUANG Wenbin. Analysis and comparison of restrained torsion theories for rectangular box-shaped beam[J]. Engineering Mechanics, 1997, 14(3): 132-137. [16] JOHNSON R P, CAFOLLA J. Corrugated webs in plate girders for bridges[J]. Proceedings of the Institution of Civil Engineers, Structures and Buildings, 1997, 122(2): 157-164. doi: 10.1680/istbu.1997.29305 [17] 李宏江. 波形钢腹板预应力混凝土组合箱梁扭转与畸变研究进展[J]. 建筑结构学报,2017,38(7): 59-67.LI Hongjiang. Review on torsion and distortion in prestressed concrete box girders with corrugated steel webs[J]. Journal of Building Structures, 2017, 38(7): 59-67. [18] 杜国华, 毛昌时, 司徒妙龄. 桥梁结构分析[M]. 上海: 同济大学出版社, 1994: 62-79. [19] 郭金琼, 房贞政, 郑振. 箱形梁设计理论[M]. 2版. 北京: 人民交通出版社, 2008: 59-71. [20] ZHOU C, LI L F, WANG L H. Improved softened membrane model for prestressed composite box girders with corrugated steel webs under pure torsion[J]. Journal of Constructional Steel Research, 2019, 153: 372-384. doi: 10.1016/j.jcsr.2018.10.023 -
下载:
点击查看大图
计量
- 文章访问数: 284
- HTML全文浏览量: 104
- PDF下载量: 19
- 被引次数: 0