Design formulas for channels subject to combined compression, shear and major axis bending
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ORIGINAL PAPER
Design formulas for channels subject to combined compression, shear and major axis bending Osama Bedair1 Received: 22 March 2020 / Accepted: 20 August 2020 © Springer Nature Switzerland AG 2020
Abstract In this work, analytical formulas are presented for channel design subject to multiple load combinations. Common design procedures found in the North American and Eurocode ignore the rotational and lateral restraints. Furthermore, limited design rules are available to predict buckling of channels subject to combination of compression, shear and major axis bending. The proposed formulas account for rotational and lateral restraints and result in significant weight reduction. Comparisons are made with other numerical procedures to confirm accuracy and suitability of the proposed expressions to use in practice. Influence of channel parameters on buckling behaviour of cold form steel (CFS) channels is also highlighted. It is shown that shear buckling stress (τcr) decreases by increasing (h/b) ratio. The difference in (Δτcr) reaches 14% for (h/D) = 25. Furthermore, much of the decrease in (τcr) values occurs for (h/b) between 2 and 4. It is also shown that a decrease in (τcr) up to 18.2% is attained by fully restraining the web edges against lateral movement. Keywords Cold formed steel (CFS) · Channels · Buckling · Steel design · Stability Abbreviations a Channel length h Web width b Flange width D Lip width E Channel elastic modulus K Buckling coefficient σcr Buckling stress x\, y\ Oblique coordinate system τcr Buckling shear stress t Channel thickness; v Poisson ratio ξ, η Non-dimensional web coordinates θ1, θ2 Displacement coefficients Π Strain energy. γ Stress gradient coefficient
* Osama Bedair [email protected] 1
OB Engineering Ltd., 415‑249 Craig Henry Drive, Ottawa, ON, Canada
Introduction Cold-formed steel (CFS) channels are extensively used in commercial and industrial buildings. Common examples are; bearing wall studs, flooring systems, roof purlins and wall girts. Channel members are also used for assembly of temporary structures such as shelters, sheds/garages and are used in pipe-racks to support cable trays and pipelines. The demand for light-weight cold formed steel structures continues to rise to achieve economical designs. Since the thickness of cold formed steel members is smaller than hotrolled steel, stability is mainly the governing design criteria. However, buckling stress and post-buckling stiffness of (CFS) channels can be enhanced by adding an edge stiffeners (or lips) that can easily be roll-formed on the free edge of the flange. Much of the literature on stability analysis focused on developing numerical and experimental procedures for channels subject to either uniform compression or bending load conditions. Little attention was given to the combined shear, compression and bending loadings. Although this load combination is frequently encountered in practice, little design rules are available in published literature. Gosowski et al. (2015) analyzed chan
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