This paper examined the dynamic instability of a shallow arch according to the response characteristics when nearing critical loads. The frequency changing feathers of the time-domain increasing the loads are analyzed using Fast Fourier Transformation (FFT), while the response signal around the critical loads are analyzed using Hilbert-Huang Transformation (HHT). This study reveals that the models with an arch shape of h = 3 or higher exhibit buckling, which is very sensitive to the asymmetric initial conditions. Also, the critical buckling load increases as the shape increases, with its feather varying depending on the asymmetric initial conditions. Decomposition results show the decrease in predominant frequency before the threshold as the load increases, and the predominant period doubles at the critical level. In the vicinity of the critical level, sections rapidly manifest the displacement increase, with the changes in Instantaneous Frequency (IF) and Instant Energy (IE) becoming apparent.

A stadium roof that uses the pin-jointed spatial truss system has to be designed by taking into account the unstable phenomenon due to the geometrical non-linearity of the long span. This phenomenon is mainly studied in the single-free-node model (SFN) or double-free-node model (DFN). Unlike the simple SFN model, the more complex DFN model has a higher order of characteristic equations, making analysis of the system’s stability complicated. However, various symmetric conditions can allow limited analysis of these problems. Thus, this research looks at the stability of the DFN model which is assumed to be symmetric in shape, and its load and equilibrium state. Its governing system is expressed by nonlinear differential equations to show the double Duffing effect. To investigate the dynamic behavior and characteristics, we normalize the system of the model in terms of space and time. The equilibrium points of the system unloaded or symmetrically loaded are calculated exactly. Furthermore, the stability of these points via the roots of the characteristic equation of a Jacobian matrix are classified.

본 연구에서는 비탄성 영역 내 비지지 길이가 존재하고 양단 및 일단 계단식 단면을 가지는 일축대칭 변단면 I형보의 해석적·이론적 연구를 토대로 하여 비탄성 횡-비틀림 좌굴 강도 해석을 실시하였다. 하중조건으로는 비지지 길이 내 모멘트가 0인 지점이 개수에 따라 모델을 구분지어 적용시켰으며, 플랜지 길이방향 비, 너비 방향 비, 두께의 비로 변단면 I형보를 나타내었다. 비선형 횡-비틀림 좌굴 해석을 위해 단순직선분포를 잔류응력으로 가정하였으며, 국내 I형강 표준 치수 허용치에 근거하여 부재 길이의 0.1%를 초기 최대 횡변위로 적용하여 초기변형으로 고려하였다. 유한요소해석에 사용된 프로그램은 ABAQUS(2009)이며, 회귀분석프로그램인 MINITAB(2006)을 이용해 간편한 설계식을 제안하고 있다. 본 연구 결과에서 개발·제안된 식은 향후 비탄성 횡-비틀림 좌굴 강도에 대한 연구에 많은 도움이 될 것이다.