PLASTIC DEFORMATION DEMAND OF MULTI-STORY BRACED STEEL FRAMES

Abstract

 1. Introduction

 It is important for structural design to comprehend plastic deformation demand of members against large earthquakes. We have proposed a predicton method of plastic deformation demand for members in single-story steel frames with braces. To extend the scope of application of the current proposal, this paper discusses with plastic deformation demand for multi-story steel frames with braces. In the case of multi-story braced frames designed as archieving overall collapse mechanism, damages during vibration concentrate on the story where horizontal strength of braces is small. From this viewpoint, this paper develops the method to predict the demanded plastic deformation of braces and beams in each story.

 2. Substitution to equivalent SDOF system

 In order to substitute multi-story braced frame to equivalent SDOF, following assumptions are adopted; total weight and natural period of SDOF are identical to those of multi-story frame, and story moment-interstory drift angle relationship of the equivalent SDOF is obtained approximately from the overturning moment-effective structure rotation angle relationship of the multi-story frame.

 3. Prediction in equivalent SDOF system

 According to Ref.1), the maximum drift angle, the plastic dissipated energy of the braces and the main frame are predicted based on the balance equation of earthquake input energy and energy dissipated by the equivalent SDOF system.

 4. Prediction of demanded plastic deformation of braces and beam in each story

 Maximum drift angle in each story of multi-story frame is calculated based on the results of static analysis. Using the results, the dissipated energy of brace in each story is obtained by dividing the dissipated energy of the braces of the equivalent SDOF. The maximum plastic rotation angle of the beam is calculated by subtracting the elastic rotation angle of the column and the beam from the maximum interstory drift angle, considering that the damage concentrates on the beam plasticized in early stage. The cumulative plastic rotation angle of the beam in each story is calculated so that the energy dissipated by the main frame element of the equivalent SDOF is equal to the energy dissipated by the beam in the multi-story frame.

 5. Comparison between prediction results and time history analysis results

 Time history response analyses are conducted to confirm validity of the proposed prediction method. The main frame is modeled as a fishbone-shaped model, and the braces are modeled by the method in Ref. 11). The analysis parameters are horizontal strength sharing ratio of brace, height direction distribution of horizontal strength sharing ratio of braces, normalized slenderness ratio of brace, number of story, and input level.

 6. Conclusion

 As a result, it is clarified that the prediction with r_cycle = 0.25 captures most of the analysis results for the maximum drift angle and the maximum plastic rotation angle of the beam, and it envelops the analysis results of about 80% of the cumulative plastic rotation angle of the beam. Further, the upper envelope of the prediction with r_cycle = 0.1 to 0.4 envelops the analysis results of about 60% of the dissipated energy of braces.