【作者】 李勇；

【导师】 舒兴平；

【作者基本信息】 湖南大学 ， 结构工程， 2013， 硕士

【摘要】 蜂窝梁是在常规实腹梁的基础上，在腹板上开有规则孔洞而成的钢梁。蜂窝梁具有节约层高、经济、美观等优点，具有很高的实用价值，在工程中的应用也日趋广泛。整体稳定是蜂窝梁面临的一个重要问题，整体失稳时蜂窝梁将发生弯扭屈曲。对于长细比l i y较大的梁，容易发生弹性失稳；而对于中等长细比l i y的梁，容易发生弹塑性失稳。本文利用能量法建立了蜂窝梁弹性弯扭屈曲总势能方程，利用势能驻值原理和瑞利-里兹法求解出弹性弯扭屈曲临界弯矩表达式。通过对腹板的惯性矩分段积分再加权平均的方法计算了蜂窝梁的侧向抗弯刚度，并在此基础上求解了蜂窝梁的自由扭转刚度和翘曲刚度。此方法推导的理论公式经有限元验证是正确并偏保守的。利用有限元软件ANSYS分析了蜂窝梁弹塑性阶段的整体稳定性能。考虑初始缺陷、几何非线性和材料非线性，计算了三种典型荷载形式、5种孔高比d hw和6种距高比s hw的蜂窝梁弹塑性弯扭屈曲临界弯矩值。定义换算实腹梁整体稳定临界弯矩与蜂窝梁整体稳定临界弯矩的比值为修正系数k。将蜂窝梁整体稳定的弹性理论推导公式结果及弹塑性有限元计算结果分别与相应的换算实腹梁结果相比较，得出修正系数k在三种典型荷载和不同孔况下的值，发现其值在1.01~1.09范围内变化。分析多种因素对蜂窝梁整体稳定修正系数k的影响，得出孔高比的影响要大于距高比的影响，腹板开孔对弹塑性阶段失稳梁的影响要大于对弹性阶段失稳梁的影响。综合上述多种计算和分析结果，偏于安全的取六边形孔蜂窝梁整体稳定修正系数k=1.1。在此基础上提出了六边形孔简支蜂窝梁的整体稳定计算公式，为工程设计人员提供参考。更多还原

【Abstract】 Castellated beams are a kind of steel beam with regular holes on the web on thebasis of conventional solid web beams. Castellated beams have a high practical valuebecause of its advantages of economy for floor height, beautiful look and low price;therefore, castellated beams are being more widely used.Castellated beams should ensure its overall stability, because it can easily occurflexural-torsional buckling in the presence of overall instability. Elastic instabilityeasily happens whenl i yis large while the elastic-plastic instability easily happenswhenl i yis medium.The equation of total potential energy of elastic flexural-torsional buckling is builtin the basis of energy method and the critical moment expression of elasticflexural-torsional buckling is solved by using principle of stationary total potentialenergy and Raylleigh-Ritz method in this thesis. The lateral flexural rigidity ofcastellated beams is calculated through the weighted average of the webs’segmentation of moment of inertia, on this basis, free torsional stiffness and warpingstiffness is solved. Verified by the finite element method, the theoretical formulasdeducted by this method are right and relatively orthodox.Analyzed castellated beams’ elastic-plastic overall stability by using the finiteelements method software ANSYS. In consideration of initial defect, geometricnonlinearity and material nonlinearity, three kinds of typical load, five kinds ofd hwand six kinds ofs hw are calculated.The ratio of the overall stability critical moment between solid web beams andcastellated beams is the correction factor k.After comparing results of the elastictheoretical derivation of the formula, elastic-plastic finite element method and thecorresponding equivalent solid web beams, we find that the correction factor k isdifferent in three typical load and different hole condition, varying from1.01to1.09.After analyzing the factors which influence the k, we find out that the influence ofd hw is greater thans hw,and the influence of elastic-plastic instability is greaterthan elastic instability. Taken the above calculation and analysis results, k=1.1isgot to simplify things. On the basis of the above understanding, the hexagon holesimply supported castellated beams’ overall stability devise formulas is put forward, providing a reference for engineering design personnel.更多还原