• CN:11-2187/TH
  • ISSN:0577-6686

机械工程学报 ›› 2015, Vol. 51 ›› Issue (15): 46-52.doi: 10.3901/JME.2015.15.046

• 核电装备先进制造技术专栏 • 上一篇    下一篇

基于等效梁长法的组合深梁临界预紧力计算模型

董晓传1,2, 金淼1, 姚阳1, 张杰1   

  1. 1.燕山大学先进锻压成形技术与科学教育部重点实验室
    2.天津职业技术师范大学天津市高速切削与精密加工重点实验室
  • 出版日期:2015-08-05 发布日期:2015-08-05
  • 基金资助:
    国家自然科学基金(50975248)和国家科技重大专项(2010ZX04017-013) 资助项目

Calculation Model of Critical Preload of Prestressed Composite Deep Beam Based on the Method of Equivalent-beam-length

DONG Xiaochuan1,2, JIN Miao1, YAO Yang1, ZHANG Jie1   

  1. 1.Key Laboratory of Advanced Forging & Stamping Technology and Science of Ministry of Education, Yanshan University
    2.Tianjin Key Laboratory of High Speed Cutting and Precision Machining, Tianjin University of Technology and Education
  • Online:2015-08-05 Published:2015-08-05

摘要: 为确定合理的临界预紧力,保证预紧组合结构横梁的整体性,提出采用等效梁长法修正传统Airy应力函数计算结果,从而得到更准确的临界预紧力。基于平面应变理论,建立临界预紧力的理论计算模型,通过叠加原理,分别得到弯曲模型和压缩模型中间截面x方向应力的傅里叶三角级数形式解,分析误差原因;采用等效梁长法进一步修正,结合临界开缝判据,得到临界预紧力理论计算公式。试验结果表明:等效梁长法修正的临界预紧力理论计算结果与试验结果最小误差为10.1%,最大误差为13.5%,与试验结果吻合较好,能够为大型成形设备的预紧组合结构横梁的设计提供理论依据。

关键词: 傅里叶级数, 临界预紧力, 深梁, 整体性, 组合结构

Abstract: To determine a reasonable critical preload and ensure the integration of prestressed composite deep beam, the method of equivalent-beam-length is proposed to revise the traditional theoretical results of airy stress function. Then a more accurate critical preload is obtained. Firstly, the theoretical calculation model of critical preload is established based on the plane strain theory. Secondly, based on the principle of superposition, the stress in the direction of x in the middle section of bending model and prestressed model are deduced and were presented in the way of Fourier series. The reasons for error are analyzed. Then, it is further revised with the method of equivalent-beam-length. Finally the theoretical formula of critical preload is derived combined with the critical criterion. Experimental results show that the minimum error between theoretical results of critical preload revised with the method of equivalent-beam-length and experimental results is 10.1%, while the maximum error is 13.5%. The theoretical results are in good agreement with the experimental results. It is able to provide theoretical basis for the design of prestressed composite beams in large mechanical equipments.

Key words: composite structure, critical preload, deep beam, Fourier series, integration

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