Elastic-plastic Buckling Analysis Of Pure Frames And Braced Frames

As an essential system, steel frames are widely used in engineering practices. According to the lateral resistance elements, framed structures can be divided into two categories, pure and braced frames. Pure frames resist horizontal and vertical loads through member bending deformation. However, braced frames are dual-systems which can ensure stability by bracings and frames.The present member-based frame stability design methods include two primary steps. Firstly performs a first-order or second elastic analysis to determine the most adverse structural internal forces; then checks member load capacities using strength or buckling interaction equations. The interaction between structural system and members or initial imperfections is considered by effective length factor or notional loads. Over the past decades, researchers have developed and validated various advanced analyses, which could predict ultimate strength, behaviors accurately and avoid tedious procedures of member calculations. The two traditional methods are simple and efficient, but cannot account for redistribution of member plasticity; meanwhile, advanced analyses cannot be daily design tools due to high computing costs and violating superposition principle.In order to balance efficiency and precision, story-based frame models are extensively studied and series of formulae are presented.Based on the story buckling and axial force negative stiffness, a story stability coefficient is defined and is related to story slenderness using the traditional column strength curves. By considering non-sway buckling and bucking mode interactions, numerical analysis of axially loaded frames shows the modified story stability coefficient approach agrees well with FEM results.The principle and notional load factor are introduced; the differences from effective length factor approach are summarized. A detailed comparison of notional load, modified effective length factor, and proposed story-based approaches with FEM are made. It is found that the notional load approachis unstable and fails to consider inter-column interaction.Second-order elastic-plastic analytical equations are deduced for single portal frames under lateral and gravity loading. The three typical failure modes including beam, sway and combined mechanisms are investigated. Comparisons between available methods and FEM are provide, results indicate that first-order rigid plastic and analytical equations tend to be unsafe, M-R empirical equation either overestimate or underestimate limit load of frames, and suggested loading interaction equation is usually conservative.Failure modes of story models and its responding interaction equations are presented; the story-based methods are established by adopting lower boundary of those equations. Typical frames incorporating effects of nonlinearities, residual stresses, initial geometric imperfections and different load distributions are studied with FEM.The change of buckling mode with increasing of bracing stiffness was analyzed and relationship between the ultimate load capacity and the bracing rigidity was achieved. The threshold stiffness of the bracing just enough to make frames buckle in a non-sway mode was obtained. Horizontal loads produce stresses in the bracings, and thus make the bracings yield prematurely and result in decrease of bracing stiffness. This will change the buckling mode of the braced frame. Nonlinear analysis of braced frames loaded both vertically and horizontally was also made. A simple and easy-to-use criterion was established for judging the buckling mode of braced frames including the effect of thehorizontal loads.The story-based equations of pure and braced frames are all good accuracy, economic, clear meaning, and simple.