Generalized Plastic Hinge Method For Ultimate Strength Analysis And Design Of Steel Frames

Steel frame structures have the characteristics of lightweight,excellent ductility and short construction period,which have been widely used in industries and buildings.Many scholars currently are devoted to exploring the advanced analysis and design method of steel frames based on the second-order inelastic analysis to overcome the problems in the current two-stage design method.The refined plastic hinge method(RPHM)is the most widely used second-order inelastic analysis method in the advanced analysis and design of steel frames.Since the RPHM contains the axial force in its structural stiffness matrix,it has to solve nonlinear equilibrium equations through large numbers of iterative trials,resulting in complexity theory and lower computational efficiency.On the contrary,the traditional first-order plastic hinge method(FPHM)utilizes the proportionality property to evaluate the ultimate strength of frames with high efficiency.However,the FPHM has many limitations,such as the plastic hinge formation being judged only by the single internal force(bending moment)of the section and taking no account of the axial force increment of plastic hinges,residual stress and geometric nonlinearity.In view of this,this paper focuses on using the proportionality property between linear elastic internal forces and external loads to rapidly evaluate the ultimate strength and failure mode of frames.Then,a second-order inelastic analysis method is established and used to guide the analysis and design of steel frame plane structures.The new structural analysis method uses linear elastic analysis as its calculation format.It can accurately carry out the second-order inelastic analysis with high efficiency and high accuracy.The main research contents are as follows:(1)The FPHM only utilizes the single internal force(bending moment)of the section to judge the development of the plastic hinge,which overestimates the ultimate strength of some steel frame structures.In this paper,the GPHM featuring proportionality property is proposed for steel framed structures with significant multiple internal forces combined action to overcome the drawbacks of the FPHM.Firstly,the new standardized dimensionless internal forces,considering the effect of the existing cumulative internal forces,in the generalized yield criterion(GYC)are presented by introducing the strength reduction factor to modify the sectional strength.Secondly,the homogeneous generalized yield function is established through regression analysis based on the GYC to define the element bearing ratio(EBR).The EBR is proportional to the external load and can fully represent the plastic yield degree of the section under the combined action of the bending moment and the axial force.Finally,according to the proportionality property between the EBR and the loading,the plastic hinge’s location and the corresponding external load increment can be rapidly determined to analyze the ultimate strength of frames.In the GPHM,the EBR is adopted to consider the combined influence of the bending moment and the axial force on plastic hinge development to replace the standardized dimensionless bending moment in the FPHM.The analysis shows that the proposed GPHM has high calculation accuracy and efficiency to estimate the ultimate strength of steel frames and overcomes the limitation of the FPHM.(2)During the continuous loading process,the axial forces on existing plastic hinges would inevitably increase,while the incremental bending moments keep zero,which would lead to mistakes in estimating the ultimate strength of frames.In this paper,the balance vector is developed by means of the GYC and the slopedeflection relation to make the plastic hinge element return to the equilibrium state to consider the influence of the incremental axial force on the ultimate strength of the structure.Then,the modified GPHM calculation format is established.On the other hand,the residual stress would make some parts of components yield in advance,weakening the bending stiffness of the structure.Hence,the residual stress would reduce the ultimate strength of steel frame structures.The influence of the residual stress is considered by the stability coefficient developed to modify the initial axial strength of the section.Next,the modified GPHM is used to rapidly evaluate the ultimate strength of steel frame structures under the influence of residual stress,which further improves the calculation accuracy and application scope of the GPHM.(3)In order to further consider the geometric nonlinearity,a second-order GPHM(s GPHM)featuring proportionality property is developed.The s GPHM can effectively consider the influence of material and geometric nonlinearity on the ultimate strength of steel frame structures.First,the new GYC characterized by the linear elastic internal forces is established by introducing the approximate second-order bending moment into the original GYC.Then,a homogeneous generalized yield function that considers the influence of geometric nonlinearity is established through regression analysis to define the EBR.Finally,according to the proportionality property between the EBR and the loading,the plastic hinge’s location and the corresponding external load increment can be directly determined.The analysis shows that the s GPHM estimates the ultimate strength and failure mode of frames based on the hinge-by-hinge analysis featuring proportionality property with high efficiency and high accuracy.(4)Based on the s GPHM,the advanced analysis design method(AADM)of steel frame plane structures is established,using the structural linear elastic analysis as its calculation format.In the AADM,the ultimate strength of frames is used to guide the analysis and design and the redistribution of internal forces during the loading process can be accurately considered.The AADM fully meets the needs of engineering designers for simple and fast design methods and the habit of using structural linear elastic analysis.The AADM considers the influence of the geometric imperfections of frames by the explicit imperfection modeling method or the equivalent notional load method.All informations required for the design can be obtained by one structural analysis.The tedious design checking calculation for each component is no longer needed,significantly simplifying the design work.The analysis shows that the proposed AADM can account for inelastic internal forces redistribution,and thus may allow some reduction of steel weigth,which is more economical and reasonable.