Distortion Effect of Single Box Double-Cell Box Girders with Rectangular Cross Section
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摘要:
为准确研究单箱双室箱梁在偏心竖向荷载作用下的畸变效应，引入双室箱梁反对称和正对称畸变的概念，补充矩形截面单箱双室箱梁畸变研究的假定. 采用不同定义的畸变角分别描述箱梁的反、正对称畸变，用板元分析法和能量变分法分析单箱双室箱梁的畸变；采用2个参数分别描述顶板、底板和腹板上的畸变正应力分布，以适应双室箱梁正对称畸变；考虑正对称畸变对双室箱梁畸变效应的影响，比较对应单室和双室箱梁的畸变效应，研究中腹板厚度改变时双室箱梁畸变角沿梁长的变化. 研究结果表明：考虑了正对称畸变影响的单箱双室箱梁畸变正应力的解析解和有限元数值解更吻合，误差不超过8.71%；正对称畸变正应力较小，最大只占反对称畸变正应力的28.08%；箱梁中腹板能有效减弱偏心竖向荷载作用引起的箱梁畸变，可使角点处的畸变正应力降低到对应单室箱梁的49.09%；采用2个参数描述箱梁正对称畸变时各板件上畸变正应力的分布比传统方法的更合理；改变中腹板厚度可使单箱双室箱梁畸变发生明显的变化，厚度增大时畸变逐渐减小.
Abstract:To accurately investigate the distortional effect of single box double-cell box girders (SBDBG) under vertical eccentric load, the concepts of antisymmetrical and positive-symmetrical distortion were introduced, and the distortional assumption of rectangular cross section of SBDBG was supplemented. The antisymmetrical and positive-symmetrical distortion of SBDBG were described by different definitions of distortional angles. The distortion of SBDBG was researched by plate element analysis and energy variation methods. Two parameters were used to describe the distribution of stress on top, bottom, and web plates respectively to adapt to the positive-symmetrical distortion. The influence of positive-symmetrical distortion on SBDBG was considered, compared difference of distortion effect between single-cell and double-cell box girder, discussed variation of distortional angle along the length of SBDBG with the change of mid-web thickness. The results show that the analytical solution of SBDBG distortion is more consistent with the finite element solution when considering the influence of positive-symmetrical distortion, the error is less than 8.71%. The normal stress of positive-symmetrical distortion is small, and the maximum is only 28.08% of the antisymmetrical distortion. The mid-web can effectively reduce distortion effect caused by eccentric vertical load, and make the distortion normal stress decrease to 49.09% of the single-cell box girder. The distribution of the distortional normal stress on each plate is more reasonable when using two parameters to describe the positive-symmetrical distortion. The change of the mid-web thickness can make the SBDBG distortion alter obviously, and distortion will gradually decrease when the thickness increases.
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图 7 结构AKFD的变形和横向弯矩
Figure 7. Deformation and transverse bending moment of structure AKFD
图 11 中腹板厚度对箱梁畸变角的影响
Figure 11. Influence of mid-web thickness on distortional angle of box girder
表 1 箱梁反对称畸变计算值
Table 1. Antisymmetrical distortional values
方法 Iωd1/m6 IR1/m2 ωdD/m2 ωdA/m2 β1 γd1/（ × 10−10 rad） Bd/（N·m2） σdA/kPa σdD/kPa 单箱单室箱梁畸变 12.1728 0.0040 2.5426 1.2075 0.4749 3.3961 2.6279 0.5213 1.0978 单箱双室箱梁反对称畸变 12.1728 0.0096 2.5426 1.2075 0.4749 1.7660 2.1110 0.2094 0.4409 
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表 2 箱梁正对称畸变计算值
Table 2. Positive-symmetrical distortional values
方法 角点应力比 γd/（ × 10−10 rad） σdA/kPa σdD/kPa 单箱双室箱梁正对称畸变 β1 = 0.5000， β2 = 0.6241 0.0160 0.05897 0.11795 单箱单室箱梁畸变 0.3229 3.7516 0.28055 0.86898
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表 3 箱梁角点畸变正应力
Table 3. Corner distortion normal stress of box girder
畸变正应力 单箱双室箱梁畸变解析解/kPa 有限元解 ②/kPa 误差（（①−②）/② × 100） /% 反对称畸变 正对称畸变 最终结果 ① σdA 0.20940 0.05897 0.26837 0.26380 1.73 σdD 0.44090 0.11795 0.55885 0.61220 −8.71
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