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