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浙江大学学报(工学版)
浙江大学学报(工学版)  2023, Vol. 57 Issue (3): 598-605    DOI: 10.3785/j.issn.1008-973X.2023.03.018
土木工程     
具有杆间扭转约束的轴心压杆稳定性研究
陈廷国(),郭召迪
大连理工大学 建设工程学部 土木工程学院，辽宁 大连 116024
Stability of axial compression bars with inter-bar torsional constraints
Ting-guo CHEN(),Zhao-di GUO
School of Civil Engineering, Faculty of Infrastructure Engineering, Dalian University of Technology, Dalian 116024, China
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摘要：

针对具有杆间扭转约束的轴心压杆稳定性问题，进行理论推导. 简化工程模型为理论模型，求解两端固定压杆的稳定承载力，提出稳定承载力与杆间扭转弹簧刚度的关系公式. 以理论模型为基础，用横梁代替扭转弹簧，使用杆间横梁支撑压杆进行失稳试验，调整横梁截面以改变横梁抗扭刚度. 进行6组不同抗扭刚度下的杆件稳定承载力试验，试验结果验证了理论解的正确性. 建立有限元模型，依据试验结果对模型可靠性进行验证，基于经过验证的有限元模型进行12种工况下的算例分析，并与理论曲线比较. 试验和有限元结果验证了理论解的正确性，提出了可供工程设计使用的计算公式.
关键词： 压杆;  扭转约束;  稳定性;  有限元分析    
Abstract:

Theoretical derivation was conducted for the stability of axial compression bars with inter-bar torsional constraints. A theoretical model was established by simplifying engineering examples, the stability bearing capacity of compression bars with fixed ends was solved, and the relationship formula between buckling load and torsional spring stiffness of inter-bar was put forward. According to the theoretical model, the torsional spring was replaced by a beam, and then the buckling test was carried out using the beam as the support of the compression bar. The torsional stiffness of the beam was altered through changing its cross section. Six groups of compression bars having different torsional stiffness were tested to verify the correctness of the theoretical solution. A finite element model was also established, and its reliability was verified by the test results. Based on the verified finite element model, the analysis of twelve cases was carried out, and compared with the theoretical curve. The correctness of the theoretical solution was demonstrated by experiments and finite element analysis, and a promising calculation formula was put forward for engineering design.
Key words: compression bar    torsional constraint    stability    finite element analysis
收稿日期: 2022-03-17 出版日期: 2023-03-31
CLC:  TU 391  
作者简介: 陈廷国（1957—），男，教授，博士，从事大型及新型工程结构力学分析及实验研究. orcid.org/0000-0002-4768-5065.E-mail： chentg@dlut.edu.cn
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引用本文:

陈廷国,郭召迪. 具有杆间扭转约束的轴心压杆稳定性研究[J]. 浙江大学学报(工学版), 2023, 57(3): 598-605.

Ting-guo CHEN,Zhao-di GUO. Stability of axial compression bars with inter-bar torsional constraints. Journal of ZheJiang University (Engineering Science), 2023, 57(3): 598-605.

链接本文:

https://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2023.03.018    或    https://www.zjujournals.com/eng/CN/Y2023/V57/I3/598

图 1  简化的钢塔架局部受力模型
图 2  压杆理论模型
图 3  扭转弹簧约束下侧的隔离体
图 4  包含扭转弹簧的隔离体
图 5  压杆稳定承载力与扭转弹簧刚度关系曲线
图 6  试验压杆
图 7  杆间横梁支撑
图 8  具有杆间横梁支撑的两端固定压杆
图 9  具有杆间横梁支撑的两端固定压杆试验模型对应的理论模型
图 10  压杆拉伸试验
试验编号 E/GPa $ \nu $ G/GPa
1 202 0.306 77
2 204 0.298 79
3 206 0.301 79
平均值 204 0.302 78
表 1  压杆拉伸试验结果
图 11  MX-1模型失稳形态
图 12  MX-1模型横梁扭转
图 13  MX-1荷载位移曲线
模型编号 横梁截面尺寸/mm GJ/（N·m） Pe/kN
n=1 n=2 n=3 平均值
MX-1 Φ10×1 274 18.47 18.52 18.59 18.53
MX-2 Φ22×1 3 446 23.56 23.25 22.82 23.21
MX-3 Φ22×2 6 000 24.99 25.76 25.78 25.51
MX-4 Φ26×2 10 336 26.97 27.63 28.27 27.62
MX-5 Φ26×4 16 336 29.07 29.35 29.35 29.26
MX-6 Φ26×8 20 744 30.51 29.99 31.10 30.53
表 2  不同试验模型压杆试件的稳定承载力
模型编号 $ \gamma $ $ \eta $ Pe/kN Pt/kN e/%
MX-1 0.07 2.90 18.53 20.61 +11.2
MX-2 0.88 3.22 23.21 25.42 +9.5
MX-3 1.53 3.37 25.51 27.84 +9.1
MX-4 2.64 3.54 27.62 30.72 +11.2
MX-5 4.17 3.67 29.26 33.01 +12.8
MX-6 5.29 3.73 30.53 34.10 +11.7
表 3  不同试验模型的压杆承载力试验值与理论值对比
图 14  6组试验模型的失稳荷载
图 15  具有杆间横梁支撑的压杆
试验编号 Pe/kN Pt/kN Pf /kN ef /% et /%
MX-1 18.53 20.61 20.82 +12.4 +11.2
MX-2 23.21 25.42 25.95 +11.8 +9.5
MX-3 25.51 27.84 28.62 +12.2 +9.1
MX-4 27.62 30.72 31.50 +14.0 +11.2
MX-5 29.26 33.01 33.74 +15.3 +12.8
MX-6 30.53 34.10 34.75 +13.8 +11.7
表 4  不同试验模型压杆承载力的试验值、理论值与有限元值对比
c/（N·m） $\gamma $ Pt/kN Pf/kN e/%
0.000 1 0 20.29 20.25 ?0.2
1 984 0.5 23.66 23.59 ?0.3
3 968 1 26.19 26.12 ?0.3
7 936 2 29.66 29.56 ?0.3
11 904 3 31.82 31.71 ?0.3
15 872 4 33.26 33.14 ?0.4
23 808 6 35.02 34.89 ?0.4
35 712 9 36.41 36.27 ?0.4
51 584 13 37.35 37.20 ?0.4
79 360 20 38.12 37.97 ?0.4
3 968 000 1 000 39.66 39.48 ?0.5
3 968 000 000 1 000 000 39.68 39.51 ?0.4
表 5  压杆承载力在不同弹簧刚度下的理论解和有限元解对比
图 16  压杆承载力理论曲线与有限元曲线对比
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