Linear-elastic analysis method of ultimate bearing capacity of dumbbell-shaped CFST arch rib
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摘要: 为了提高哑铃型钢管混凝土拱肋极限承载力的计算效率, 提出了极限承载力分析的高效自适应弹性模量缩减法; 根据连续条件和截面塑性承载性能, 建立了钢管混凝土哑铃型构件压弯承载力相关方程, 通过回归分析得到了相应的齐次广义屈服函数; 采用单一组合材料梁单元建立了拱肋的线弹性有限元迭代模型, 通过自适应缩减高承载单元弹性模量模拟结构在加载过程中的刚度损伤, 确定拱肋的极限承载力, 并与模型试验、非线性有限元法和等效梁柱法计算结果进行了对比。计算结果表明: 建立的齐次广义屈服函数计算结果稳定、可靠, 克服了传统广义屈服函数计算结果受荷载初始值影响的缺陷; 采用自适应弹性模量缩减法只需较少的离散单元数与迭代步数即可获得稳定的极限承载力, 且与模型试验结果误差小于3%, 计算耗时小于16s, 相对非线性有限元法具有良好的计算精度和效率; 哑铃形截面拱肋相比圆形截面拱肋具有更好的承载性能, 矢跨比、含钢率和荷载作用方式是影响钢管混凝土拱肋极限承载力的重要因素; 随着矢跨比增大, 极限承载力增速减缓; 随着含钢率增大, 极限承载力几乎呈线性增长; 随着集中力与均布力比值增大, 其对极限承载力的影响逐渐减弱; 轴力与弯矩是拱肋的主要内力, 随着矢跨比增大, 弯矩对极限承载力的影响更加显著。Abstract: In order to improve the computational efficiency of ultimate bearing capacity of dumbbell-shaped CFST (concrete filled steel tube) arch rib, a high-efficiency self-adaptive elastic modulus reduction method (EMRM) was proposed to analyze the ultimate bearing capacity. Based on the continuity conditions and the plastic bearing property of section, the correlation equations of compressing-bending capacity of dumbbell-shaped component for CFST were established, and the corresponding homogeneous generalized yield function (HGYF) wasdetermined by means of regression analysis. A linear-elastic finite element iterative model of arch rib was developed by using simplex beam element with combined material parameters, and the elastic modulus of highly loaded element was reduced through self-adaption to simulate the structural stiffness damage in the loading process, so as to confirm the ultimate bearing capacity of arch rib. The proposed method was compared with model test, non-linear finite element method and equivalent beam-column method. Calculation result shows that the calculation result of HGYF is stable and reliable, and the impact of initial loads on the calculation result of traditional generalized yield function is overcomed. The proposed method has higher accuracy and efficiency than the nonlinear finite element method, the stable ultimate bearing capacity is obtained by only small amount of discretized meshes and iteration steps, the relative error is less than 3% compared with test result data, and the computation time is less than 16 s. Compared with the circular section arch rib, the dumbbell-shaped CFST arch rib has better bearing property, and the main influence factors are rise-span ratio, steel ratio and loading condition. The increasing speed of ultimate bearing capacity reduces with the increase of rise-span ratio. With the increase of steel ratio, the ultimate bearing capacity increases almost linearly. The larger the ratio of concentrated load to uniform load is, the less its influence on the bearing capacity is. The axial force and bending moment are the governing internal forces of arch rib, while the bending moment becomes more significant with the increase of rise-span ratio.
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图 8 不同加载方式下EMRM收敛曲线
Figure 8. Convergence curves of EMRM under different loading modes
图 9 不同加载方式下EMRM迭代过程
Figure 9. Iteration processes of EMRM under different loading modes
图 10 极限承载力与矢跨比关系
Figure 10. Relationship between ultimate bearing capacity and rise-span ratio
图 11 极限承载力与含钢率关系曲线
Figure 11. Relationship between ultimate bearing capacity and steel ratio
图 13 极限承载力与荷载工况关系
Figure 13. Relationship between ultimate bearing capacity and loading modes
图 14 极限承载力与截面形式和内力的关系
Figure 14. Relationships between ultimate bearing capacity and cross section, internal force
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