基于三角级数解的钢-混凝土组合梁弹性弯曲变形计算方法

A novel theoretical method of elastic bending deformation of steel-concrete composite beams based on trigonometric series solution

目前针对考虑界面滑移效应的钢-混凝土组合梁的弯曲变形计算公式缺乏广泛适应性,不便于组合梁结构设计。为此,采用三角级数构造组合梁弹性弯曲变形和界面滑移的位移函数,根据最小势能原理和变分法,推导了简支组合梁在不同荷载类型下的弹性弯曲变形和界面滑移的计算公式,进而得到考虑滑移效应的组合梁抗弯刚度和界面滑移值的统一显式解。通过与大量已有文献中的试验值和既有计算方法比较,验证了其有效性和准确性。结果表明:根据三角级数解推导出的钢-混凝土组合梁弯曲刚度计算公式简洁直观,物理意义明确,结果可靠,所提出的方法适用于精确计算正常使用状态下组合梁弯曲变形。

The current bending deformation calculation formula for steel-concrete composite beams considering interface slip effects lacks wide adaptability and is inconvenient for the structural design.To address this issue,a triangular series was used to characterize the displacement function of elastic bending deformation and interface slip of composite beams,and a theoretical calculation model of elastic bending deformation and interface slip was derived for simply supported composite beams under different loading conditions based on the principle of minimum potential energy and variational method.Consequently,a unified explicit solution for the bending stiffness and interface slip value of composite beams was obtained.The effectiveness and accuracy of the proposed method were verified against with a large number of experimental results and existing calculation methods.The results showed that the bending stiffness calculation formula for steel-concrete composite beams derived from the triangular series solution was concise,intuitive,and physically meaningful,and the results were reliable.Therefore,the proposed novel method can accurately calculate the bending deformation of composite beams in serviceability limit state.