考虑残余应力影响下刚架极限承载力分析的广义塑性铰法

Generalized Plastic Hinge Method for Ultimate Strength Analysis of Steel Frames Considering Residual Stress

一阶塑性铰法利用外荷载与线弹性弯矩之间的比例特性快速确定塑性铰的位置和结构的极限承载力,理论简洁,计算效率高,但不能考虑截面轴力和弯矩对塑性铰形成的组合作用。精细塑性铰法克服了一阶塑性铰法的局限性,但其只能通过不断增量调整外荷载、迭代试算来确定塑性铰的位置和结构的极限承载力,丧失了一阶塑性铰法的比例特性,理论复杂,计算效率低。广义塑性铰法结合了一阶塑性铰法与精细塑性铰法的优点,但未考虑残余应力的影响,对于立柱承受较大竖向集中荷载作用的刚架结构会高估其极限承载力。有鉴于此,文中通过在广义屈服准则的截面初始轴向强度中引入稳定系数来考虑残余应力的影响,进而有效利用广义塑性铰法快速评估考虑残余应力影响下刚架结构的极限承载力。首先,利用强度折减因子建立了各加载步的修正截面强度,结合回归分析建立了广义屈服函数的齐次化表达式,据此定义了与外荷载保持相同比例关系的单元承载比。然后,在截面初始轴向强度中引入稳定系数来考虑残余应力的影响,并依据单元承载比与外荷载的比例关系快速确定塑性铰的位置和相应的外荷载增量,据此建立了考虑残余应力影响的改进广义塑性铰法。最后,通过与不同方法就国内外文献中几个校准算例的对比分析,发现文中改进方法的计算效率约为当前主流结构分析方法的3~12倍。

The first-order plastic hinge method(FPHM)is simple in theory and efficient in calculation because it can rapidly estimate the position of plastic hinges and the ultimate strength of steel frames according to the proportionality property between the external load and the linear elastic bending moment.However,it ignores the combined action of axial force and bending moment on the development of plastic hinge.The refined plastic hinge method(RPHM)overcomes the limitation of the FPHM,but it determines the position of plastic hinges and the ultimate strength of the structure only by incremental adjustment of external load and iterative trial calculation,which results in the loss of proportionality property and makes the formulation complex and the computation efficiency low.The generalized plastic hinge method(GPHM)possesses the advantages of both the FPHM and the RPHM but ignores the effect of the residual stress,which leads to the overestimating of the ultimate strength of frames with columns objected to large vertical concentrated loads.To solve these problems,this paper introduces the stability coefficient to modify the initial axial strength of the section under the generalized yield criterion,and then an improved GPHM is established to rapidly evaluate the ultimate strength of steel frames with the consideration of the influence of residual stress.In the investigation,firstly,each loading step’s modified section strength is established using the strength reduction factor.Next,the homogeneous generalized yield function is established through regression analysis and the element bearing ratio,which maintains the same proportional relationship with the external load,is defined.Then,the stability coefficient is introduced to modify the initial axial strength of the section to consider the influence of residual stress.Finally,according to the proportional relationship between the element bearing ratio and the external load,the position of the plastic hinge and the corresponding load increment in each loading step are determined.By comparing and analyzing several calibration examples in literatures with different methods,it is found that the computational efficiency of the proposed method is approximately 3~12 times that of the current general structural analysis method.