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考虑外荷载作用为竖向集中荷载,采用狄拉克函数处理由外荷载引起的势能,建立箱梁的总势能泛函,对总势能泛函求一阶变分可以得到箱梁挠度和附加挠度的域内控制微分方程及边界条件。求解附加挠度的二阶常系数非齐次线性微分方程可以得到集中荷载作用在梁任意位置时附加挠度的一般表达式。针对边界条件为左端固定右端自由的悬臂箱型梁,结合经典梁挠度,可以得到箱梁挠度和应力的表达式。在此基础上,推导了剪力滞系数的表达式。算例分析表明:基于附加挠度定义的应力计算方法与传统解析方法和试验方法吻合良好,但是附加挠度物理意义明确,边界条件容易处理,实际中容易量测;相对于传统基于应力定义的剪力滞系数在接近零弯矩截面时剪力滞系数就有趋于无穷大的趋势,基于挠度定义的剪力滞系数能够反映沿着远离固定端截面,剪力滞效应逐渐降低的趋势。
Taking the external load as vertical concentrated load, the Dirac function is used to deal with the potential energy caused by the external load, and the general potential energy functional of the box girder is established. For the first potential variation of the general potential energy function, the deflection and additional deflection of the box girder can be obtained Domain control differential equations and boundary conditions. The general expression of the additional deflection when the concentrated load acts on any position of the beam can be obtained by solving the second order constant coefficient inhomogeneous linear differential equation with additional deflection. Aiming at the cantilever box girder with the right end fixed at the left end and the deflection of the classic girder, the expression of the deflection and the stress of the box girder can be obtained. On this basis, the expression of shear lag coefficient is deduced. The case study shows that the method of stress calculation based on the definition of additional deflection is in good agreement with the traditional analytical method and experimental method, but the physical meaning of additional deflection is clear, the boundary conditions are easy to handle and the measurement is easy in practice. Compared with the traditional shear stress defined by stress The shear lag coefficient tends to infinity near zero bending moment section, and the shear lag coefficient based on deflection can reflect the trend of shear lag effect decreasing along the section away from the fixed end.