考虑剪切和界面滑移的钢-混凝土组合箱梁变分解法

贺桂超^{1, 2}，周凌宇¹

(1. 中南大学 土木工程学院，湖南 长沙，410075；
2. 中航规划建设长沙设计研究院有限公司，湖南 长沙，410014)

摘 要：根据组合箱梁剪切变形和界面滑移模式，以能量变分原理为基础，考虑剪切变形和滑移双重效应，建立组合箱梁的控制微分方程和边界条件，利用最小势能原理推导出组合箱梁挠度和滑移联合微分方程的解析解。推导不同荷载作用下的滑移效应附加弯矩，利用附加弯矩表达公式和结构力学挠度计算公式计算滑移对挠度的影响，并与试验结果进行对比。研究结果表明，该方法解析解与试验结果吻合良好，更符合实际情况，证明了该方法的有效性，同时为组合箱梁承载力的有限元分析奠定了基础。

关键词：钢-混凝土组合箱梁；变分法；剪切变形；滑移效应

Energy variational method of shear deformation and slip effect of steel-concrete composite box beam

HE Gui-chao^{1, 2}, ZHOU Ling-yu¹

(1. School of Civil Engineering, Central South University, Changsha 410075, China;
2. China Aviation Planning and Construction Changsha Design and Research Co. Ltd., Changsha 410014, China)

Abstract:The differential governing equations of composite beams were presented based on minimum potential energy and variational method. Both shear deformation and interfacial slip were taken into account. The energy variation principle was applied to establish the governing differential equations and corresponding natural boundary conditions of the st, eel-concrete composite box beam. The closed-form solutions of the equations were obtained using the minimum potential energy principle. The expressions of additional bending moment due to interfacial ship for concentrated and distributed loads were presented. Using the expressions of additional bending moment and structure mechanics deflection formula, the effect of slip on deflection was analyzed, and the calculated results were compared with the test results. The results show that the analytical solutions of this paper are exact, simple and effective, and lay the foundation for the composite box beam finite element analysis of bearing capacity.

Key words:steel-concrete composite box beam; energy variational principle; shear deformation; slip effect