为解决钢结构柱脚抗剪键埋深的设计难题,基于Timoshenko梁理论,利用奇异函数表示抗剪键所受力的分布,通过积分变换、逆变换和对偶函数求解微分方程,分别采用混凝土应力-应变关系的理想弹塑性模型和非线性弹塑性模型推导了抗剪键的变形曲线方程,得到了抗剪键埋深的计算公式并建立了可供实际应用的表格.计算结果表明,依据理想弹塑性理论计算得到的抗剪键埋深稍大,偏于安全;抗剪键设计埋深主要与抗剪键承受的剪力、泊松比、抗弯刚度、剪切刚度4个因素有关.抗剪键所受分布力的合力会对柱脚产生附加弯矩,从而影响钢柱脚底板尺寸及锚栓面积等其他参数的设计.
Two deformation curve equations of shear connector were deduced considering the perfect elastoplastic and nonlinear concrete stress-strain relationships respectively in order to determinate the embedded length of shear connector in steel column base. In the deducing process, the Timoshenko-beam differential equations were solved by dual function integral transformation and inverse transformation while the distributed forces impacting on the shear connector were expressed by singular function. Furthermore, the formulae of the embedded length of shear connector were given and the design tables were listed for rapid determination by numerical method. The analytical results show that the embedded length of shear connector calculated with the perfect elasto-plastic model is longer than that obtained with the nonlinear elastoplastic model and is safe in practice. The determination of the embedded length of shear connector mainly depends on four factors including: the magnitude of shear force, Poisson's ratio, connector section's flexural rigidity and shearing rigidity. Meanwhile, the additional flexural moment caused by the distributed forces acting on the shear connector will influence other parameters' design in column base, such as the dimensions of base plate and the anchor bolt section.