Experiment And Calculation Methods Studying For Second-order Effect Of The Cantilever Column Of SDOF And Portal-rigid Frame

Under vertical loading, two categories of second-order effects exist in deformedstructures, i.e. P-Δ effect and P-δ effect. In the view of the achievement of thesecond-order effect in our country and abroad, deep research has been performed on therule of the static second-order effect, especially some systematic,reliable and simplifiedcalculation methods have been proposed,which can be used to carry out by handcomputation. However, the research achievement on the dynamic second-order effect isvery few and mainly is the theoretical research, meanwhile, the experimental studying isscarce. Further more, the simplified methods should be verified whether it is suitable forboth shearing-type and bending-type structures and whether it has sufficient precisionwhen calculating the dynamic second-order effect.Contrapose the second-order effect ofthe portal-rigid frame and the cantilever column structure of SDOF, experiment andcalculation method have been accomplished in this paper, the main topics in this thesisare as follows:①Based on five groups of test specimen, five different experiments wereaccomplished, i.e. static pushover test which did not consider the second-order effect,static pushover test which considered the second-order effect, shaking table test underhorizontal earthquake, shaking table test under vertical earthquake, shaking table testunder horizontal and vertical earthquake;②Processed and analysed the data of the static pushover test and the shakingtable test, also did the numerical simulation for these tests by the Opensees program;③Theoretical derivation and brief introduction about the FEM which based onthe stiffness method when considering the second-order effect were accomplished.Contrapose shearing-type and bending-type structure, numerical calculation werecompleted by SAP2000and compared the results with theoretical value and calculatedvalue which used the flexibility method.The conclusions are listed as follows via the work above:①Through the comparative analysis between the results of the static test and thenumerical simulation by Opensees, the force-displacement curves of the static test areclose to the calculation results;②Through the analysis of the results of the shaking table test, the dynamiccharacteristics of the experimental models is reliable after the white-noise scanning and the data which collected in the test is basically reliable and available;③Through the comparative analysis between the results of the shaking-table testand the numerical simulation by Opensees,it is found that:1) In accordance the theoretical method which analyses the second-order effect ofthe cantilever column structure of SDOF and the portal-rigid frame by linear first-ordermethod using the reduced stiffness, the simplified calculation method is feasible andaccuracy when calculate the dynamic second-order effect;2) Because the response of structure is very complex, and the influence factors arenumerous which contain the stability factor, the dynamic characteristics of structures,and the spectrum characteristics of the horizontal and vertical seismic wave, and so on,the vertical seismic action will not necessarily increase the response;3) Once the structure turns into the elastoplastic phase, the dynamic response isinfluenced by the geometrical and material nonlinearities and the impact can never beignored.④There are two optional parameters which used to consider the geometricalnonlinearity in SAP2000, the P-Δ effect (the virtual column method) and the P-Δ and large deformation effect (the accurate stiffness method). When using the virtualcolumn method which makes the nonlinear problem linearized, it assumed that thestiffness only affected by the axial force. While using the accurate stiffness methodwhich contains the influence by the lateral displacement, the calculation should bebased on the iteration;⑤Through theoretical derivation and example analysis, the equivalent horizontalforce method (the virtual column method) can consider the P-Δ effect of shearingand bending type structures approximatively. However, it should choose the accuratestiffness method when considering the P-δ effect or the accurate dynamicsecond-order effect.