Stochastic Stability Bearing Capacity Analysis Of Plane Semi-Rigid Steel Frames Based On QR Method

The steel frame has a thinner cross section and a relatively large height and width,which is prone to instability and damage.Therefore,how to prevent the instability of the steel frame has become an urgent problem.Based on the overall stability bearing capacity of the steel frame,the deterministic stability bearing capacity of the plane steel frame is analyzed by QR method,and the influence of the uncertainty factors on the stability bearing capacity of the steel frame is analyzed by using modified perturbation method.The calculation program has been programmed by C language.The research mainly includes:(1)The characteristic equations of the elastic stability analysis of the plane semi-rigid steel frame are established based on the QR method.The critical load of the steel frame is obtained by solving the eigenvalues.(2)The nonlinear plastic hinge model is used to simulate the nonlinearity of the cross-section material of the member.The generalized yield function is introduced to consider the influence of the combined internal force.The elastoplastic stability bearing capacity of the semi-rigid steel frame is analyzed based on the QR method.(3)The distributed plastic model is used to describe the plasticity development.The fiber layer is divided along the height of the section.The secant stiffness of the section is calculated according to the stress-strain of each fiber layer to describe the extension of the plastic along the height of the section.The distributed stiffness model describes the expansion of plastic along the length of the element.Based on the QR method,the elastoplastic stability bearing capacity of steel frames with rectangular box,I-shaped and round tubes section is analyzed.(4)Combining the QR method of steel frame deterministic analysis with modified perturbation method of uncertainty analysis,the stochastic stable bearing capacity analysis of the plane semi-rigid steel frame is established,and the plane semi-rigid steel frame was established based on the modified perturbation method.The computational format of the stochastic stable bearing capacity analysis.The results show that:(1)The generalized yield function is introduced to consider the combined effect of internal forces,and the concentrated plastic model is adopted to describe the plastic expansion along the section,whose precision is close to the plastic zone model,and the whole process reaction of the entire loading history can be obtained to predict the failure mode of the steel frame.(2)The layer fiber model is used to simulate the development of plasticity along the height of the section,and the three-stage distributed stiffness model is used to simulate the expansion of plasticity along the direction of the rod length,which can accurately predict the plastic development and stable bearing capacity of the structure,and describe the continuous decline process of the stiffness along with the plastic expansion and the extension length of the plastic region.(3)The modified perturbation method adopted in this paper needs only a few sampling times to obtain a higher computational accuracy,and avoids the problem that the traditional perturbation method needs to calculate the partial derivatives of the structural matrix with respect to random variables.It has good adaptability to the random problem with low coefficient of variation,dealing with random problems of complex structures has obvious advantages.