有腹筋混凝土梁的剪切刚度分析模型

钢筋混凝土梁的挠度计算通常不计入剪切变形的贡献,然而对于斜向开裂的有腹筋混凝土梁,斜裂缝会显著降低梁体的有效剪切刚度,导致剪切变形值显著增大,因此在验算评估时应予以考虑.为评价钢筋混凝土梁斜向开裂后的有效剪切刚度,首先,基于变角桁架模型推导了钢筋混凝土梁在箍筋屈服状态下的有效剪切刚度;与弹性剪切刚度比较发现,剪切刚度退化系数的主要影响因素为材料弹模比、配箍率和斜压杆倾角.其次,基于试验剪切变形曲线表现出的刚度退化规律,提出了可用于不同开裂程度下剪切刚度计算的恒定切线刚度退化模式,并采用开裂后的剪力增量作为反映开裂程度的定量指标.最后,根据最小能量原理得到了剪切刚度退化中两个关键参数:斜压杆倾角和剪切刚度退化系数的解析公式.通过2根薄腹混凝土梁剪切变形试验以及收集的15个受剪梁段的剪切变形数据对模型有效性进行了验证,验证结果表明:有腹筋混凝土梁剪切刚度分析模型能较为准确地预测箍筋屈服状态的剪切刚度,并能反映不同开裂程度下的剪切刚度退化规律.

ANALYTICAL MODEL FOR SHEAR STIFFNESS OF REINFORCED CONCRETE BEAM WITH STIRRUPS 1)

The calculation of deflection of reinforced concrete (RC) beams generally ignores the contribution of shear deformation. However, diagonal crack will significantly reduce the effective shear stiffness of RC beams, and result in remarkable increase of shear deformation, which should not be neglected in the assessment stage. To evaluate the effective shear stiffness of diagonally cracked RC beams with stirrups, an analytical model of shear stiffness was proposed in the paper. Firstly, the shear stiffness of RC beam at stirrup yielding status was derived based on variable angle truss model. Compared to the elastic shear stiffness, the shear stiffness degradation factor was mainly influenced by the material modulus ratio, stirrup ratio and the inclination angle of strut. Secondly, based on the observed shear stiffness degradation law of shear deformation curve, a constant tangent stiffness degradation mode, which considers the influence of cracking level, was proposed. The shear increment after shear cracking was used as a quantitative indicator for the cracking level. Finally, the analytical formulas of the inclination angle and shear stiffness degradation factor were obtained based on the
principle of minimum strain energy. To verify, two thin-webbed concrete beams were tested and corresponding shear deformation were carefully measured. In addition, shear deformation data of fifteen shear segments of RC beams in literature were collected. The comparison results showed that the proposed shear stiffness degradation model gives good prediction of the shear stiffness at stirrup yielding status and reflects the degradation law of shear stiffness at different cracking level.