Research Of Computational Model Of Plate Bearings Considering The Effect Of Ultra-low Cycle Fatigue Damage

Catastrophic earthquake(the earthquake exceeding the design intensity)is an important emergency that threatens the safety of cities.In history,different seismic fortification levels can only protect the safety of life and property within the fortification level.The safety of the city will face great challenges when the catastrophic earthquake exceeds the fortification level.The space grid structure is an important part of the future "resilient city" with the function of earthquake shelter.If the bearing of the grid structure is damaged in the catastrophic earthquake,it will lose the function of earthquake shelter and seriously affect the emergency rescue after the disaster.Therefore,the research on the resilience of bearing joints during a catastrophic earthquake will become an important topic in the future construction of "resilient cities".At present,bearing joints are generally assumed as ideal rigid or hinged joints in current codes,and their stiffness attenuation is not considered in seismic design.During a catastrophic earthquake,when the upper grid structure is deformed greatly,the bearing joints often undergo seismic fatigue failure due to the large strain ultra-low-cycle reciprocating loading.At this time,the dynamic stiffness of the bearing joints will have a great influence on the dynamic response of the superstructure,and its change will directly affect the whole destructive state of the structure.To analyze the collapse failure process of grid structures more accurately,it is necessary to systematically study the influence of dynamic attenuation of bearing constraint stiffness on grid structures,further study the stiffness degradation model of such bearings considering the influence of ultra-low-cycle fatigue damage,and establish a grid calculation model considering the stiffness attenuation of bearings.In this paper,experimental study and numerical simulation were combined to study the constraint stiffness calculation model including the influence of ultra-low-cycle fatigue damage with the plate bearing joints as the main research object.The main research contents and conclusions are as follows:(1)In this study,ultra-low-cycle fatigue tests were undertaken on six groups of eighteen plate bearings under constant vertical loading and horizontal large displacement reciprocating loading,the effects of vertical load and anchor bolt diameter on the failure mode,hysteretic performance,skeleton curve,stiffness degradation,rib plate,bearing dip angle and anchor bolt tilt were studied.Additionally,the fracture evolution law and failure mechanism of the anchor bolt are revealed by combining with the fracture morphology analysis.The damage assessment model of the plate bearing joints is proposed based on energy dissipation.It was found that the failure of the plate bearing joints goes through four stages: slip stage,elastic stage,strengthening stage,and failure stage,and the failure modes are mainly anchor bolt failure and buckling in the middle and lower part of the plate.The anchor bolt cracks are all initiated in the stress concentration area on the root surface,and their sections have the typical characteristics of ultra-low-cycle fatigue fracture.(2)The finite element model of plate bearing joints was established by the finite element software ABAQUS/Explicit,and the influence of ductile damage,geometric nonlinearity,and initial defect of steel were taken into account.The failure modes,hysteresis curves and skeleton curves of the model were compared and analyzed to verify the feasibility of the model and discuss the failure mechanism of the main damaged parts(anchor bolt and rib plate).It was found that the numerical simulation results are in good agreement with the experimental data,which verifies the feasibility of the numerical calculation method.The initiation of ultra-lowcycle fatigue crack of anchor bolt is mainly caused by the mixed damage.The local buckling of the free edge of the rib plate is elastoplastic buckling,which can delay the failure of the anchor bolt and the failure process of the plate bearing to some extent.(3)Based on the finite element model,parameterized analysis of ultra-low-cycle fatigue performance of plate bearing joints under different bolt diameters,rib plate thickness,bearing heights and vertical loads was carried out,and the ultra-low-cycle fatigue bearing capacity and damage degradation of the joints were analyzed in detail.Established the approximate formula for calculating the bearing capacity of plate bearing joints and fitted it to the formula for calculating the elastic-plastic buckling critical load of the rib plate in this model.The results of parameter analysis show that the horizontal yield capacity and peak bearing capacity of plate bearing joints are determined by the anchor bolt.The diameter of the anchor bolt and the thickness of rib plate have an important influence on the failure mode of bearing joints.When the diameter of the anchor bolt is small and the thickness of the rib plate is large,the failure of the anchor bolt occurs prematurely due to the limited bending and shear stiffness of the anchor bolt.On the contrary,the plate is prone to elastoplastic buckling,resulting in post-buckling strength,so that the failure mode of plate bearing joints is characterized by plate buckling and anchor bolt fracture.(4)Based on the above test and finite element analysis results,a four-fold skeleton curve model considering slip and stiffness damage was established.A horizontal stiffness degradation model with energy dissipation as the damage index was proposed to describe the mechanical property degradation law of plate bearings under constant vertical loading and horizontal large displacement reciprocating loading.A restorative force model of plate bearing joints considering the effects of slip and ultra-low-cycle fatigue damage was established.It was found that the restoring force model can well reflect the nonlinear mechanical behavior of ultra-lowcycle fatigue of the bearing joints.(5)Based on the restoring force model of plate bearing joints,a simplified calculation model of plate bearing joints considering slip and horizontal stiffness attenuation was established.Additionally,the simplified calculation model is applied to SAP2000 software,and the nonlinear time-history dynamic analysis of the gymnasium of Lushan County Middle School in Ya’an earthquake was analyzed.The results show that the simplified calculation model of plate bearing joints has good applicability.Considering the horizontal stiffness attenuation of the supports,the failure modes of the grid model of the middle school gymnasium in Lushan County under the actual earthquake are consistent with the earthquake damage.It can provide a reference for accurate analysis of the collapse process of grid structure under catastrophic earthquakes.