The Study Of The Ductility Of Beam-Columns

The ductility of structure system is of importance of significance to earthquake resistance of the buildings,it is normally expressed by ductility factor. The concept of ductility is composed of three levels of material. section and member. Specifically,the ductility of material is mainly described in the σ—ε curve of material,the ductility of section mainly in the M—Φ curve of section,and the ductility of member mainly in the P—Δ (or M—θ) curve of member. In addition,the concept of ductility is also related to the levels of joint and frame,the ductility of these two levels is not only associated with the ductility of member,but also has difference with it.Furthermore,the influencing factor of the ductility of member involves the influencing factor of the ductility of material and section.Therefore,the study of the ductility of member is of significance.This article mainly studies the ductility of cantilever beam-columns(cantilever columns) which are loaded by axial force and concentrative horizontal force at the top. The study is divided into three parts.Firstly,this article computes and analyses cantilever columns of three self-selected sections(I100×100×10×10,,I100×100×15×15, I100×100×20×20) and three practical sections(HW250×250×9×14, HW300×300×10×15, HW400×400×13×21) by Ansys modeling and preferences,in order to get the F-u curve of the columns of different section at every axial ratio and slenderness ratio. Then according to the definition of ductility factor, the ductility factor of cantilever columns is calculated for each case,so we can get a clear view of the ductility of columns. In accordance with the obtained ductility factor,this article suggests the formula for ductility classification. The ductility of columns is classified asfollows:high ductility when the ductility factor η ≥ 5;low ductility when η<3;middleductility when 3 ≤ η < 5 . Secondly, this article proceeds with second-order elasticanalysis and second-order plastic analysis in theory for columns in six kinds of section,in order to gain the equations of second-order elastic analysis and second-order plastic analysis.The curves of these equations are the upper limit for second-order elastic-plastic analysis.By the equations obtained theoretically,together with the F-u curves by Ansys FEA,we can verify whether the Ansys FEA is correct or not,and these equations can help to determine the ductility factor of cantilever columns when the results of FEA is not ideal.Thirdly,this article programs based on the principle of simplified numerical methods of integration.The results by this program ,which has a great increase of efficiency, are reasonable.