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连续薄壁箱梁约束扭转分析的方法
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Force method for restrained torsion analysis of continuous thin-walled box girder
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    摘要:

    力法是超静定结构弯曲分析的经典方法,根据连续箱梁弯曲和约束扭转问题的相似性,将力法应用于约束扭转分析,解决图乘法无法计算柔度的关键问题. 利用薄壁箱梁约束扭转微分方程的初参数解,推导赘余力和荷载(集中扭矩、均布扭矩、集中双力矩和均布双力矩)作用于基本结构时其状态向量(扭角、翘曲位移、双力矩和扭矩)的理论解析;利用理论解析直接计算基本结构的柔度,利用叠加法进行状态向量后处理. 状态向量的理论解和后处理方法为连续薄壁箱梁约束扭转力法分析奠定了基础. 算例结果表明,连续薄壁箱梁约束扭转的力法分析结果与超越有限元结果一致,表明力法是连续薄壁箱梁约束扭转分析中的精确方法. 本文提出以基本结构状态向量解析解、状态向量后处理的叠加法为基础的完整力法分析方法,为力法推广应用解决了关键问题.

    Abstract:

    The force method is a classical approach for bending analysis of statically indeterminate structures. Based on the similarity between the bending and restrained torsion problems of a continuous box girder, the force method is applied to the analysis of restrained torsion, addressing the critical limitation of the graph multiplication method, which fails to calculate flexibility in such cases. Initial parameter solutions to the differential equations governing the restrained torsion of thin-walled box girder are used to derive theoretical expressions for state vectors (twist angle, warping displacement, bimoment and torque) in the released structure subjected to unit redundant and loads (concentrated torque, uniformly distributed torque, concentrated bimoment and uniformly distributed bimoment). The theoretical solutions are then applied to calculate the flexibility of the released structure. The superposition method is implemented to conduct the post-processing of state vectors. Theoretical formulae and post-processing method of state vectors lay a concrete groundwork for the force method applied to the restrained torsion analysis of continuous thin-walled box girder. The example results by the force method are consistent with the exact finite elements in a continuous thin-walled box girder, which demonstrates the precision of the force method applied to the restrained torsion analysis of a continuous thin-walled box girder. The integral force method presented in this paper is based on the analytical solutions of state vectors in the released structure and the superposition method for the post-processing of state vectors. Critical questions are solved to expand the applications of the force method.

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夏桂云 ?,杨翱蔚 ,温睿.连续薄壁箱梁约束扭转分析的方法[J].湖南大学学报:自然科学版,2026,53(3):55~62

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  • 在线发布日期: 2026-04-07
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