框架中钢-混凝土组合梁等效弯曲刚度分析

框架体系中钢-混凝土组合梁在竖向荷载作用下的弯矩分布与其端部受到的转动约束条件密切相关，而在不同方向的弯矩作用下钢-混凝土组合梁截面的抗弯刚度又差异显著，要准确计算竖向荷载作用下组合梁的等效弯曲刚度必须充分考虑与其相连的梁柱变形对其端部产生的转动约束刚度。为此，采用分段刚度建立了框架中组合梁在竖向荷载作用下的等效刚度理论模型，以考虑不同梁端转动约束刚度和楼板开裂前后截面特性差异对组合梁等效刚度的影响。基于该理论模型进行大量参数分析，识别了影响组合梁等效弯曲刚度的两个关键参数：转动约束刚度与组合梁开裂后截面线刚度比和梁开裂前后截面刚度比，得到了随梁端转动约束刚度变化的组合梁在竖向荷载作用下等效弯曲刚度的计算式，在框架设计时可方便地用于组合梁的变形和内力计算。对比讨论了建议算式和现有公式的计算精度，并通过结构体系的非线性全过程分析对建议算式的合理性做了进一步的验证。理论分析和设计方法表明,组合梁在竖向均布荷载作用下的负弯矩区长度和等效弯曲刚度随梁端转动约束刚度变化显著，必须在设计中准确考虑。

Analysis of equivalent bending stiffness of steel-concrete composite beams in frame

In the frame system, the bending moment distribution of steel-concrete composite beam under vertical loads is closely related to the rotational constraint condition at the beam ends. In addition, the flexural rigidity of the cross section at different direction is significantly different. The rotational constraints at beam ends should be considered to accurately calculate the equivalent flexural rigidity of the composite beam under vertical loads, which are related to the deformation of the beams and columns connected to it. A theoretical model for the equivalent flexural rigidity of the composite beam under vertical loads in the frame was established by segmenting the flexural rigidity of the composite beam. This considered the influence of rotational stiffness of beam end constraints and sectional characteristics before and after the cracking of concrete slab on the equivalent flexural rigidity of the composite beam. Based on this theoretical model, a parametric analysis was carried out to identify two key factors affecting the equivalent flexural rigidity of the composite beam: the ratio between rotational constraint stiffness and section line stiffness and the ratio between section stiffness of the beam before and after the cracking of the concrete slab. A design formula for the equivalent rigidity of the composite beam under vertical loads was also obtained, which accounts for the effect of rotational stiffness of beam end constraints. The proposed design formula can be easily used in the frame design practice. The computational accuracy between the proposed design formula and some existing formulas was compared, and the rationality of the proposed design formula was also validated by a series of numerical results of whole-process nonlinear analysis of a structural system. The theoretical analysis and design methods show that the length of the negative moment region and the equivalent flexural rigidity of the composite beam under the vertical uniformly-distributed loads changed significantly with the changing of end rotational constraints, which should be accurately considered in the design.