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该文基于Reddy高阶梁理论,提出了小变形双层组合梁的隐式运动学假定;应用拉格朗日乘子法,将该隐式关系引入到组合梁的最小势能原理,得到了考虑各子梁和粘结滑移层非线性材料特性的高阶组合梁非线性位移法有限单元,且该单元可以容易地转化为非线性Timoshenko和Euler-Bernoulli组合梁有限单元。随后,该研究分别应用提出的Reddy、Timoshenko和Euler-Bernoulli组合梁有限单元对双跨连续钢-混凝土组合梁进行了准静力分析,考察剪切效应对组合梁构件的挠度、粘结层滑移和截面应力的影响,且参数分析了组合梁的跨高比对剪切效应的影响。参数分析表明:短粗组合梁结构往往表现出显著的剪切效应,Newmark假定不再适用。
Based on Reddy’s theory of high-order beams, the implicit kinematic assumption of a small deformation double-layer composite beam is proposed. By applying the Lagrange multiplier method, the implicit relation is introduced into the principle of minimum potential energy of a composite beam. The finite element method of the nonlinear displacement method for high-order composite beams with nonlinear material properties of each beam and slip layer can be easily transformed into the finite elements of nonlinear Timoshenko and Euler-Bernoulli composite beams. Subsequently, the proposed finite element method of Reddy, Timoshenko and Euler-Bernoulli composite beams was applied to the quasi-static analysis of two-span continuous steel-concrete composite beams. The effect of shear on the deflection, And cross-section stress. The influence of the span-height ratio of the composite beam on the shearing effect is also analyzed. Parametric analysis shows that the stubby composite beam structure often exhibits significant shear effect, and Newmark’s assumption is no longer applicable.