﻿ 钢筋混凝土框架结构动力超自由度单元

# 钢筋混凝土框架结构动力超自由度单元Dynamic Super-Degree-of-Freedom Element of Reinforced Concrete Frame Structures

Abstract: The super-degree-of-freedom element, which is an element of beam-column joint of reinforced concrete frame structures, is developed to be suitable for dynamic analysis of reinforced concrete frame structures. The element is called dynamic-super-degree-of-freedom element. According to UEL interface provided by ABAQUS platform, the element is applied to ABAQUS dynamic analysis. By means of comparison with the results of a shaking table test of 3-story-3-bay reinforced concrete frame building under minor-moderate, moderate-severe and severe ground motions, reliabilities of the user subroutine and the element were validated. The results show that the subroutine can well reflect strength and stiffness degradation of reinforced concrete frame structures produced by earthquake loading. The subroutine and the element are widely applicable to refined dynamic simulation of concrete frame structures.

1. 引言

2. 超自由度单元简述

$U={\left\{\begin{array}{cccc}{D}_{1}& {D}_{2}& {D}_{3}& {D}_{4}\end{array}\right\}}^{T}$ (1)

${D}_{1}={\left\{\begin{array}{ccccc}{\Delta }_{1}& {\Delta }_{2}& {\Delta }_{3}& {u}_{1}& {v}_{1}\end{array}\right\}}^{T}$ (2)

Figure 1. (a) Node and degree of freedom in the element; (b) degree of freedom in the internal node

*USER ELEMENT, NODES=4, TYPE=U4, PROPERTIES=36, ……

1, 2, 6, 14, 15

3. 单元动力分析的质量矩阵

$M=\left[\begin{array}{cccc}{M}_{1}& & & 0\\ & {M}_{2}& & \\ & & {M}_{3}& \\ 0& & & {M}_{4}\end{array}\right]$ (3)

${M}_{i}=\left[\begin{array}{ccccc}m& & & & 0\\ & m& & & \\ & & I& & \\ & & & \alpha & \\ 0& & & & \alpha \end{array}\right]$ (4)

4. ABAQUS用户程序设计

ABAQUS用户程序UEL，就是为每一个计算步提供单元所需的AMATRX与RHS。其中，AMATRX在静力分析时主要是当前运算步的单元刚度矩阵，而在动力分析时，则根据系统的LFLAGS数组的指令，可以是刚度矩阵、质量和阻尼矩阵。而RHS则是单元的节点抗力向量，动力分析时要考虑惯性力以及上一计算步的节点抗力等。

$AMATRX=\left(1+\alpha \right)K+\frac{M}{\beta {\left(\Delta t\right)}^{2}}$ (5)

$RHS={F}_{J}\left(t+\Delta t\right)-\left(1+\alpha \right)F\left(t+\Delta t\right)+\alpha F\left(t\right)$ (6)

5. 验证

5.1. 试验简介

5.2. ABAQUS分析模型

5.3. 数值分析结果

Figure 2. Third floor displacement time history for 0.05 G

Figure 3. First floor shear force time history for 0.05 G

Figure 4. Third floor displacement time history for 0.2 G

Figure 5. First floor shear force time history for 0.2 G

Figure 6. Third floor displacement time history for 0.3 G

Figure 7. First floor shear force time history for 0.3 G

9. 结论

[1] Mitra, N. and Lowes, L.N. (2007) Evaluation, Calibration, and Verification of a Reinforced Concrete Beam-Column Joint Model. Journal of Structural Engineering, 133, 105-120.
https://doi.org/10.1061/(ASCE)0733-9445(2007)133:1(105)

[2] Lowes, L.N. and Altoontash, A. (2003) Modeling Reinforced Concrete Beam-Column Joints Subjected to Cyclic Loading. Journal of Structural Engineering, 129, 1686-1697.
https://doi.org/10.1061/(ASCE)0733-9445(2003)129:12(1686)

[3] Youssef, M. and Ghobarah, A. (2001) Modelling of RC Beam-Column Joints and Structural Walls. Journal of Earthquake Engineering, 5, 93-111.
https://doi.org/10.1080/13632460109350387

[4] Lafave, J.M. and Kim, J.R. (2011) Joint Shear Behavior Prediction for RC Beam-Column Connections. International Journal of Concrete Structures and Materials, 5, 57-64.
https://doi.org/10.4334/IJCSM.2011.5.1.057

[5] Saito, T. and Kikuchi, M. (2012) A New Analytical Model for Reinforced Concrete Beam-Column Joints Subjected to Cyclic Loading. Proceedings of15th World Conference on Earthquake Engineering, Lisbon, 3108-3118.

[6] 方自虎, 周尧. 基于平面4节点单元的钢筋混凝土梁柱节点单元[J]. 厦门大学学报(自然科学版), 2017, 56(2): 287-293.

[7] 方自虎, 洪博恺. 基于8节点平面单元的RC梁柱节点单元[J]. 力学季刊, 2016, 37(4): 149-156.

[8] 方自虎, 李向鹏, 简旭阳, 等. 钢筋混凝土梁柱节点超自由度单元[J]. 哈尔滨工业大学学报, 2017, 49(6): 53-57.

[9] Bracci, J.M., Reinhorn, A.M. and Mander, J.B. (1992) Seismic Resistance of Reinforced Concrete Frame Structures Designed Only for Gravity Loads: Part I—Design and Properties of One-Third Scale Model Structure. Report NCEER- 92-0027, State University of New York at Buffalo, Buffalo.

[10] Bracci, J.M., Reinhorn, A.M. and Mander, J.B. (1992) Seismic Resistance of Reinforced Concrete Frame Structures Designed Only for Gravity Loads: Part III—Experimental Performance and Analytical Study of a Structural Model. Report NCEER-92-0029, State University of New York at Buffalo, Buffalo.

[11] 方自虎, 李向鹏. 钢筋混凝土结构的钢筋滞回模型[J]. 武汉大学学报(工学版). (即将发表)

[12] 方自虎, 李向鹏. 全尺寸钢筋混凝土桥墩柱ABAQUS动力分析[J]. 土木工程, 2017, 6(6): 564-575.

Top