力学与实践 ›› 2019, Vol. 41 ›› Issue (4): 453-457.DOI: 10.6052/1000-0879-18-453

• 教育研究 • 上一篇    下一篇

任意复杂截面梁的扭转中心 1)

路晓明*,2), 曹海*,3), 龚耀清†, 4)   

  1. **郑州科技学院土建学院,郑州 450000;
    黄河科技学院新型桥梁工程技术研究中心,郑州 450063
  • 发布日期:2019-08-26
  • 作者简介:2) 路晓明,讲师,从事结构工程研究;
    3) 曹海,助教,从事结构工程研究;
    4) 龚耀清,教授,从事结构力学研究。E-mail: gongyq@163.com
  • 基金资助:
    1) 国家自然科学基金(51178164)和河南省重点学科(660715/004)资助项目。

TORSIONAL CENTER OF BEAMS OF ARBITRARY COMPLEX CROSS-SECTION 1)

LU Xiaoming*,2), CAO Hai*,3), GONG Yaoqing†,4)   

  1. *Zhengzhou Institute of Science & Technology, Zhengzhou 450000, China;
    Modern Bridge Institute of Structures Technology, Huanghe S & T University, Zhengzhou 450063, China
  • Published:2019-08-26

摘要: 为了计算任意复杂非圆截面梁横截面扭转中心的位置,用节线法将其约束受扭后所有横截面面外变形的形状用一族包含节线未知函数的曲面表示,建立梁约束受扭时的控制方程后,再用常微分方程求解器分别求出单纯扭矩与横向载荷单独作用时节线未知函数的数值解,最后用刚度等效原理导出复杂截面梁横截面扭转中心的位置。算例计算结果表明:该方法是合理的、有效的,是计算任意复杂非圆截面梁横截面扭转中心位置的可靠方法。

关键词: 任意复杂截面梁, 扭转中心, 节线法, 约束扭转, 异形柱

Abstract: In order to determine the position of the torsional center of a beam of arbitrary complex non-circular section, the shape of all the out-of-plane deformation of the beam of non-circular section caused by non-uniform torsion is expressed by the nodal-line method as a family of surfaces containing unknown functions of the nodal lines. After establishing the governing equations of the beam caused by its non-uniform torsion, the numerical solutions of these unknown functions are obtained by using an ODE (ordinary differential equation) solver for a torque and a transverse load separately. Finally, the position of the torsional center of the beam of a complex cross section is derived by using the principle of stiffness equivalence. The computational results of examples show that the method is reliable for computing the torsional center position of a beam of arbitrary complex non-circular section.

Key words: arbitrarily complex cross-sectional beams, torsional center, nodal-line method, non-uniform torsion, special-shaped columns

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