Restrained Torsion Analysis of Box Girders with Corrugated Steel Webs Based on Reissner’s Principle
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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.
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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 
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