The influence of inter-module connections on the effective length of columns in multi-story modular steel frames

In stability analysis of steel frames, the effective length method requires the calculation of the K-factors, which can be difficult and subject to error in many moment frame configurations and requires significant engineering judgment for some frame types. This is of crucial importance for the design of modular prefabricated buildings, made of volumetric frames, and connected through corner inter-module connections, where the K-factors account for the contribution of complex boundary conditions to the axial load carrying capacity of a column. The direct use of effective lengths, provided by the conventional buildings' standards for the stability analysis and design of modular buildings may lead to either unsafe or conservative results, depending on the performance of inter-modular connections as an important roleplaying boundary condition. This paper studies the effective length factors (K-factors) of columns in both sway and non-sway frames, in corner-supported steel modular buildings. For each case, first, the governing equations for the elastic buckling load of a typical column in an assemblage of a corner-supported modular frame are derived and solved numerically to obtain the effective length factors for two different systems: vertically connected and horizontally connected modular frames. Alignment charts are provided for different relative bending stiffness ratios of joints. Then, parametric studies are conducted to investigate the influence of relative stiffness ratios of inter-modular connections and their type on the effective length factors. Finally, modified formulas based on American Institute of Steel Construction (AISC) standard codes are proposed to obtain the effective length factor of columns in both sway and non-sway modular frames.