多个集中荷载作用下工字形截面简支钢梁弯扭屈曲临界弯矩研究

RESEARCH ON CRITICAL MOMENT OF SIMPLY SUPPORTED I-BEAMS SUBJECTED TO MULTIPLE CONCENTRATED LOADS

  • 摘要: 为拓展工字形截面简支钢梁弯扭屈曲临界弯矩计算的荷载工况,降低复合荷载作用下临界弯矩的计算难度,该文推导了基于轴压构件整体稳定临界荷载的临界弯矩计算式和矩阵形式的复合弯矩系数计算式。继而针对简支钢梁弯扭屈曲的临界弯矩计算,推导了单个任意位置集中荷载作用下的“3C”系数的表达式,两个任意位置集中荷载作用下的相关系数和复合弯矩系数的表达式,以及n个等间距集中荷载作用下的复合弯矩系数;采用理论分析和有限元软件LTBeamN验证了该文的推导结果。研究表明:简支钢梁上作用任意位置单个集中荷载、任意位置两个集中荷载以及n个等间距集中荷载的临界弯矩计算式均具有较高精度;对于简支钢梁上作用荷载数量较多的荷载工况,基于矩阵形式的复合弯矩系数计算式进行推导或计算,可大大减小复合弯矩系数的计算难度。

     

    Abstract: In order to expand the load cases for calculating the critical moment of simply supported steel I-beams failed by flexural-torsional buckling (FTB), and to reduce the difficulty of calculating the critical moment for combined loads, a formula of critical moment expressed in terms of the critical loads of axial compression members was derived firstly in this paper, as well as a formula of combined moment coefficient in matrix form. Then, with regard to FTB of simply supported steel I-beams, expressions of “3C” coefficient for single concentrated load located at an arbitrary position, and interaction coefficient and combined moment coefficient for two concentrated loads located at two different positions, were derived respectively. The combined moment coefficient for n concentrated loads distributed in equal distance was also derived. Theoretical analysis and finite element software LTBeamN were used to verify the derived results. The results show that, the formulas for calculating the critical moment of single concentrated load located at an arbitrary position, two concentrated loads at two different positions, and n concentrated loads distributed in equal distance, is of high accuracy. For the case of more concentrated loads acting on simply supported steel I-beams, the difficulty of calculating combined moment coefficient is greatly reduced by employing the formula of combined moment coefficient in matrix form.

     

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