Mapping Web-Tapered Member to a Prismatic Member for Buckling Analysis of Sway Frames-Closed Form Equation

Web-tapered members are widely used among steel designers in industrial buildings for economic purposes. Nevertheless, buckling analysis of web-tapered members isn't as easy as prismatic ones. It takes up much time and effort since calculating the effective buckling length requires usage of charts other than the widely popular alignment chart for prismatic members. In addition, previous charts for tapered members have no mathematical expression, which do not lend themselves to computerized programming. In an effort to put an end to the above stumbling block, closed form equations are proposed in this study to cover most of the practical cases encountered by design engineers. Sway uninhibited frame buckles in a sway mode when it loses its lateral stiffness. Therefore, the lateral stiffness of sway uninhibited frame is the main controlling parameter in buckling analysis. To map a tapered member to a prismatic one, the two members have to contribute the same to lateral stiffness. Equating the contribution to lateral stiffness from the tapered member and its equivalent prismatic one results in an equivalent prismatic moment of inertia. The mapping between the two is through a simple closed form equation. This procedure has endless uses as it can be applied to a linearly web-tapered member with equal or unequal flanges, or tapered-constant-web member (i.e. part of the web member is tapered while the rest is prismatic) to cover all practical cases for sway frame structures encountered by steel designers. 

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