05.17: Modeling the stiffness reduction conditions of steel beam‐columns

Abstract

ABSTRACTThe stiffness reduction that results from yielding of the cross‐section due to major and minor axis bending under axial compression and tension conditions is studied in detail for compact wide‐flange sections with an ECCS residual stress distribution pattern. For a given moment (m = M/Mp), axial load (p = P/Py), and residual stress ratio (cr = σr\σy), the distribution of stresses throughout the cross‐section and associated reduced stiffness (τ = EIep/EI) are evaluated using a fiber element model with 2,046 elements. Using increments of m and p of 0.01, detailed three‐dimensional m‐p‐τ surface plots for a given wide‐flange section are used to discuss the various stress states of the cross‐section and associated reduced flexural stiffness. Equations are provided for the m and p conditions around the perimeter of the 3‐D surfaces and for the various conditions at which yielding initiates in the flanges and web. For minor axis bending, figures are provided on the progression through the various stress states as m is increased from the initial yield point up to the fully plastic state for the axial compression conditions of p = 0.2 and 0.75. The m‐p‐τ surface plots are used to develop material models for direct implementation in MASTAN2. To study the effects of simplifying the 3‐D surface plots using a linear variation of stiffness between the initial yield surface and fully plastic conditions, the El‐Zanaty portal frame is modeled using MASTAN2 with p = 0.4 and 0.6 to compare the maximum lateral load and deflection results with published results. Discussion and recommendations are provided regarding the development and use of the m‐p‐τ surface plots for research and design purposes.