Catenary action of restrained steel beam against progressive collapse of steel frameworks

The changing law of internal forces during the whole deformation development process was analyzed. The process was divided into five stages based on the internal force state of the beam and the assumptions of internal force relationship of five stages were proposed. Then, the formulas for determining the midspan deflection of the steel beam under distributed load, which was restrained both in rotational and axial directions, were obtained using restraint coefficient method and rigid-plastic mechanism, thereby the deformation development process was expressed accurately in a quantified way. Priority was given to the analysis of the process from bending to tension-bending, then the final state totally depends on tension to resist the external loads, that is the problem of catenary action of the restrained beam under distributed load. Additionally, finite element analysis was carried out with soitware ABAQUS6.7 on a restrained steel beam under distributed load with different axial and rotational restraint coefficients. The accuracy of the formulas presented was verified by the results of the behavior of the restrained beams. Finally, error analysis was conducted and some formulas were corrected according to the reasons of errors. The calculated results of corrected formulas match the FEM analysis results better, thus the accuracy of these formulas is improve .

Study of the mechanics of progressive collapse of FPB isolated beam-pier substructures

The horizontal stiffness of the isolated layer is reduced substantially by a friction pendulum bearing(FPB)toprotectthe structure from potential damages caused by earthquakes.However,horizontal stiffness is essential to progressive collapse resistance of structures.This paper presents a simplified model to assess the progressive collapse response of beam-pier substructure isolated by FPB.Progressive collapse resistance by flexural action of the beam and additional resistance owing to the horizontal restraining force was achieved.The influences of the equivalent radius and friction coefficient of the FPB,the applied axial force on the FPB,and span-depth ratio of the beam on the additional resistance were investigated.Simulations were conducted to verify the proposed model.The results show that progressive collapse resistance provided by horizontal restraining can be reduced as large as 46%and 88%during compressive arching action(CAA)and catenary action(CA),respectively.The equivalent radius of the FPB shows limited effect on the progressive collapse response of FPB isolated structures,but friction coefficient and applied axial force,as well as depth ratio of the beam,show significant influences on the additional progressive collapse resistance capacity.Finite element method(FEM)results are in good agreement with the result obtained by the proposed method.