工字梁腹板在局部承压和剪力作用下的弹性屈曲及极限承载力
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摘要
工字形截面梁在弯矩、剪力以及局部荷载单独或者联合作用下,腹板的部分板面会偏离原来的位置而发生波形凸曲。目前,吊车轮压荷载作用下工字梁腹板的局部屈曲鲜有研究,这主要是由于无法得到轮压荷载作用下承压应力在腹板内的分布规律。对于轮压荷载作用下工字梁腹板的承压应力计算,我国钢结构设计规范GB50017-2003比GBJ17-88更加偏离了国际上通行的计算方法,而这一方法实际上并未进行过研究。另外,目前研究工字梁腹板在局部荷载及剪力作用下的稳定时,都没有合理考虑翼缘的约束作用。本文采用有限元方法对包括吊车轮压荷载在内的局部荷载和剪力作用下工字梁腹板的弹性屈曲及极限承载力进行分析,以期合理考虑翼缘对腹板的约束作用。
本文首先对有轨道的工字梁在轮压荷载作用下腹板的局部承压应力进行了参数分析。影响承压应力分布的主要因素为腹板的厚度以及轨道的抗弯刚度,翼缘自身的抗弯刚度也有一定的影响;吊车梁的跨度和高度以及梁的支座条件都对其影响很小。采用经典的弹性地基梁理论解释了腹板局部压应力与腹板厚度以及轨道惯性矩间的关系,并在此基础上得到了等效承压长度的计算公式。还得到承压应力沿腹板高度及沿梁纵向的变化规律,提出了近似的计算公式。
采用有限元方法对局部荷载以及轮压荷载作用下不同边界条件的矩形板进行了分析,包括四边简支板、两边简支,两边固支板以及三边简支,一边固支的矩形板。得到了各种情况下矩形板屈曲系数的近似公式。
对局部荷载和轮压荷载作用下工字梁模型进行了特征值屈曲分析。通过引入与翼缘扭转刚度和腹板弯曲刚度的比值有关的参数,将翼缘对腹板的约束程度进行量化。通过大量计算得到了能考虑翼缘转动约束的腹板屈曲系数的近似计算公式。
分析了局部荷载作用在上翼缘时工字梁腹板的弹性屈曲系数,考虑了腹板宽高比、高厚比、荷载作用宽度等影响因素。在有限元分析结果的基础上,提出了建议公式。将计算得到的弹性屈曲系数代入已有的极限承载力公式,从而合理考虑了翼缘的约束作用。
Local buckling may occur in web plates in I-girders subjected to bending, shear and patch loading. The local buckling of web plates in I-girders under wheel loading has been rarely investigated, due to the unknown distribution of bearing stresses in the web plates. The recommended method for calculating bearing stresses on the edge of web plates in GB50017-2003 is deviated further from the accepted method in the world than that of GBJ17-88. In fact, no study has been carried out on this recommended method. On the other hand, although much has been done to study the stability of web plates under patch loading and shear, the rotational restraint from the flange to the web plate has not been reasonably accounted for. In order to evaluate this rotational restraint properly, the finite element method was utilized to analyze the elastic buckling and ultimate strength of web plates in I-girders under patch loading, wheel loading as well as shear forces.An extensive parametric study was conducted on the bearing stresses of web plates in crane runway I-girders under wheel loading. It was found that the most important factors influencing the stress dispersion are the web thickness and the inertia moment of the rail, while the inertia moment of the top flange has a minor influence. The depth and length of the girder and its boundary conditions have a negligible effect. Based on the theory of beams on elastic foundation and the numerical results, design equations are proposed to predict the bearing stresses on the edge of the web plates. The distribution of bearing stresses along the depth and the span of the girder was also obtained.The behavior of rectangular plates under patch loading and wheel loading, with all four edges being simply supported and two opposite edges being simply supported and fixed as well as three edges being simply supported and the rest edge being fixed, were analyzed with the finite element method. The regression formulae were obtained to determine elastic buckling coefficients of the forementioned rectangular plates.
An eigenvalue buckling analysis was carried out on I-girders under patch loading and wheel loading with ANSYS. A parameter correlating the torsional stiffness of the flange and the flexural stiffness of the web was introduced to quantify the rotational restriction from the flange to the web plate. A formula with good accuracy was suggested to determine elastic buckling coefficients, which accounting for the rotational restraint reasonably.The investigation on elastic buckling coefficients of web plates in I-girders loaded by patch load on top flanges was carried out and the effects from parameters such as aspect ratio and slenderness of web plate, length of patch load were taken into account.The behavior of rectangular plates under shear, with all four edges being simply supported and two opposite edges being simply supported and fixed as well as three edges being simply supported and the rest edge being fixed, were also analyzed with ANSYS. An improved formula was suggested to evaluate the elastic buckling coefficients of the simple-fixed rectangular plates, and another formula for plates with three edges being simply supported and the rest edge being fixed was also brought forth.Based on numerical results of 690 I-girders, a formula accounting for the rotational restraint provided to the web plate by the flange was obtained to calculate the shear buckling coefficients of web plates. Subsequently, a method to predict the ultimate shear strength was suggested. It is worth noting that the effect from the rotational restraint on the elastic buckling strength and the contribution from the flange itself were both considered in the suggested method. The correlation between the experiments and the suggested method is good, especially for web plates with great aspect ratio or slenderness, for which the ultimate shear strength has not been predicted satisfactorily through currently available method.
本文首先对有轨道的工字梁在轮压荷载作用下腹板的局部承压应力进行了参数分析。影响承压应力分布的主要因素为腹板的厚度以及轨道的抗弯刚度,翼缘自身的抗弯刚度也有一定的影响;吊车梁的跨度和高度以及梁的支座条件都对其影响很小。采用经典的弹性地基梁理论解释了腹板局部压应力与腹板厚度以及轨道惯性矩间的关系,并在此基础上得到了等效承压长度的计算公式。还得到承压应力沿腹板高度及沿梁纵向的变化规律,提出了近似的计算公式。
采用有限元方法对局部荷载以及轮压荷载作用下不同边界条件的矩形板进行了分析,包括四边简支板、两边简支,两边固支板以及三边简支,一边固支的矩形板。得到了各种情况下矩形板屈曲系数的近似公式。
对局部荷载和轮压荷载作用下工字梁模型进行了特征值屈曲分析。通过引入与翼缘扭转刚度和腹板弯曲刚度的比值有关的参数,将翼缘对腹板的约束程度进行量化。通过大量计算得到了能考虑翼缘转动约束的腹板屈曲系数的近似计算公式。
分析了局部荷载作用在上翼缘时工字梁腹板的弹性屈曲系数,考虑了腹板宽高比、高厚比、荷载作用宽度等影响因素。在有限元分析结果的基础上,提出了建议公式。将计算得到的弹性屈曲系数代入已有的极限承载力公式,从而合理考虑了翼缘的约束作用。
Local buckling may occur in web plates in I-girders subjected to bending, shear and patch loading. The local buckling of web plates in I-girders under wheel loading has been rarely investigated, due to the unknown distribution of bearing stresses in the web plates. The recommended method for calculating bearing stresses on the edge of web plates in GB50017-2003 is deviated further from the accepted method in the world than that of GBJ17-88. In fact, no study has been carried out on this recommended method. On the other hand, although much has been done to study the stability of web plates under patch loading and shear, the rotational restraint from the flange to the web plate has not been reasonably accounted for. In order to evaluate this rotational restraint properly, the finite element method was utilized to analyze the elastic buckling and ultimate strength of web plates in I-girders under patch loading, wheel loading as well as shear forces.An extensive parametric study was conducted on the bearing stresses of web plates in crane runway I-girders under wheel loading. It was found that the most important factors influencing the stress dispersion are the web thickness and the inertia moment of the rail, while the inertia moment of the top flange has a minor influence. The depth and length of the girder and its boundary conditions have a negligible effect. Based on the theory of beams on elastic foundation and the numerical results, design equations are proposed to predict the bearing stresses on the edge of the web plates. The distribution of bearing stresses along the depth and the span of the girder was also obtained.The behavior of rectangular plates under patch loading and wheel loading, with all four edges being simply supported and two opposite edges being simply supported and fixed as well as three edges being simply supported and the rest edge being fixed, were analyzed with the finite element method. The regression formulae were obtained to determine elastic buckling coefficients of the forementioned rectangular plates.
An eigenvalue buckling analysis was carried out on I-girders under patch loading and wheel loading with ANSYS. A parameter correlating the torsional stiffness of the flange and the flexural stiffness of the web was introduced to quantify the rotational restriction from the flange to the web plate. A formula with good accuracy was suggested to determine elastic buckling coefficients, which accounting for the rotational restraint reasonably.The investigation on elastic buckling coefficients of web plates in I-girders loaded by patch load on top flanges was carried out and the effects from parameters such as aspect ratio and slenderness of web plate, length of patch load were taken into account.The behavior of rectangular plates under shear, with all four edges being simply supported and two opposite edges being simply supported and fixed as well as three edges being simply supported and the rest edge being fixed, were also analyzed with ANSYS. An improved formula was suggested to evaluate the elastic buckling coefficients of the simple-fixed rectangular plates, and another formula for plates with three edges being simply supported and the rest edge being fixed was also brought forth.Based on numerical results of 690 I-girders, a formula accounting for the rotational restraint provided to the web plate by the flange was obtained to calculate the shear buckling coefficients of web plates. Subsequently, a method to predict the ultimate shear strength was suggested. It is worth noting that the effect from the rotational restraint on the elastic buckling strength and the contribution from the flange itself were both considered in the suggested method. The correlation between the experiments and the suggested method is good, especially for web plates with great aspect ratio or slenderness, for which the ultimate shear strength has not been predicted satisfactorily through currently available method.
引文
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