An Analytical Criterion for Buckling Strength of Built-up Compression Members

In current design practice, North American and European specifications differ significantly regarding the rules governing the design of stitched built-up struts. The British and German specifications treat such members essentially like battened columns and apply more stringent provisions to limit their shear flexibility. Consequently, built-up struts designed according to these specifications must be closely stitched. Furthermore, the strength of built-up members are reduced due to shear flexibility. The American and Canadian specifications (except for recent AISC-LRFD), on the other hand, do not treat stitched built-up struts in a way similar to battened columns. They only require that minimum individual slenderness ratio between stitches not exceed the governing slenderness ratio of the built-up strut as a whole. Thus, in strength calculation, the detrimental effect of shear flexibility is not taken into account. Recently, AISC-LRFD Specification introduced an empirical equation to modify the overall slenderness ratio of built-up struts, including stitched members, in order to take into account the detrimental effect of shear flexibility on their strength. The criterion is based on experimental study by Zandonini on stitched double channel struts and verification by Astaneh and Goel on double angle bracing members. In 1952, Bleich proposed a similar but analytical criterion to modify the overall slenderness ratio of battened columns. The equation has the limitation of being strictly applicable to battened columns because of simplifications made in the derivation process. Another limitation of Bleichs equation is that it was derived strictly for hinged-end members. This paper presents a generalized version of the analytical equation proposed by Bleich. Thus, it does not have the limitations of Bleichs equation. Therefore, the proposed analytical equation is applicable to all built-up struts with general end conditions. The equation is verified both analytically and experimentally. For analytical verification, a parametric study is performed in which, for different over-all and individual slenderness ratios, the buckling load is calculated according to the proposed analytical equation, Bleichs approximate analytical equation, and the LRFD empirical equation. The results are compared and discussed. For experimental verification, test results from another study by the authors are compared with the calculated buckling load according to the proposed analytical equation and the LRFD empirical equation. All comparisons verify the validity of the proposed analytical equation.