A DYNAMIC STIFFNESS MATRIX METHOD FOR STEEL-CONCRETE COMPOSITE BEAMS BASED ON THE TIMOSHENKO BEAM THEORY
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摘要: 基于Timoshenko梁理论提出了适用于分析钢-混组合梁自振特性的动力刚度矩阵法，该计算模型中考虑了钢-混结合面剪切滑移、剪切变形和转动惯量的综合影响。动力刚度矩阵推导过程中未引入近似位移场或力场，因此，计算结果是准确的。与其他Timoshenko梁模型最大的不同是假设混凝土子梁和钢梁分别具有独立的剪切角，这个假设更加符合组合梁的实际运动，因此，计算结果更加准确。与已发表文章中的试验梁频率计算结果作对比分析；并讨论了不同剪力键刚度、跨高比时，剪切变形和转动惯量对钢-混组合梁自振频率的影响。结果表明：相对于已有的Euler-Bernoulli组合梁、子梁转角相同假设的Timoshenko组合梁模型，文中计算方法具有更高的计算精度，尤其是对于高阶频率；频率越高、剪力键刚度越大或跨高比越小，Euler-Bernoulli组合梁模型计算结果误差越大；对于1阶、2阶和3阶频率，高跨比分别大于10、18和25后，Euler-Bernoulli组合梁模型计算结果误差小于5%。
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关键词:
- 桥梁工程 /
- 动力刚度矩阵法 /
- Timoshenko梁理论 /
- 子梁独立剪切角 /
- 跨高比
Abstract: A dynamic stiffness matrix method for the free vibration of steel-concrete composite beams is proposed based on the Timoshenko beam theory. In this method, the effects of interfacial shear slip, shear deformation and rotational inertia are considered. The results are exact because no approximate displacement and/or force fields are introduced in the element derivation. Compared with other Timoshenko composite beam models, the main advantage of the proposed method is that it assumes that each sub-beam has an independent rotary angle. This assumption is more consistent with the reality, leading to more accurate results. The eigenfrequencies obtained by the proposed method are compared with those by other methods in the literature using experimental models. The influence of shear deformation and rotational inertia on the frequency of composite beams with different shear connector stiffnesses and span-to-depth ratios is discussed in detail. The results show that the proposed method is more accurate than EBT and TBT with assumed identical rotary angles for the two sub-beams, especially for higher modes. Higher frequency, greater shear connector stiffness and smaller span-to-depth ratio result in larger relative errors for the Euler-Bernoulli beam theory. For the first, second and third frequencies, the errors of the Euler Bernoulli composite beam model are less than 5% when the span-to-depth ratio is greater than 10, 18 and 25, respectively. -
图 6 前3阶自振频率随剪力键刚度的变化情况
Figure 6. Effect of shear connector stiffness on first three eigenfrequencies
图 7 前3阶自振频率随跨高比的变化情况
Figure 7. Effect of depth-to-span on first three eigenfrequencies
表 1 梁材料参数
Table 1. Material parameters of composite beam
参数 实验梁 混凝土子梁 钢梁 Ei/MPa 3.0×104 2.06×105 Gi/MPa 1.4375×104 7.9231×104 ρi/(kg/m3) 2600 7850 ki 0.83 0.38 Ai/m2 0.51 0.0406 Ii/m4 3.825×10−3 2.495×10−3 
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表 2 实验梁2自振频率分析结果对比表
Table 2. Comparison of eigenfrequencies obtained by different methods for experimental beam 2
阶数 测试结果 ANSYS 理论计算结果 文献[23] 文献[24] 本文理论 1 19.38 21.08 22.86 (4.9) 22.04 (1.2) 21.79 2 63.13 63.09 73.99 (12.9) 72.92 (11.3) 65.52 3 − 116.71 156.37 (24.0) 143.63 (13.9) 126.07 4 − 172.08 263.46 (35.6) 231.45 (19.2) 194.23 5 − 224.48 402.66 (48.2) 333.06 (22.6) 271.65 注：文献[23]为Euler-Bernoulli组合梁模型；文献[24]为Timoshenko组合梁模型，但假设混凝土子梁和钢梁具有相同的剪切角。括号中数值为相对于本文理论计算结果的误差/(%)。
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