Direct Strength Design of Cold-formed C-sections in Combined Bending and Shear

The paper describes a research program including tests on both plain C- and SupaCee ® purlin sections in combined bending and shear, and bending only. The high strength SupaCee ® profile steel sections contain additional return lips and web stiffeners which enhance the bending and shear capacity of the sections. They are used widely in Austra lia as purlins in roof and wall systems. The tests were performed at the University of Sydney with and without straps on the flange and thus allowed distortional buckling in the latter case. Design methods for these sections are normally specified in the Australian/New Zealand Standard for Cold-Formed Steel Structur es or the North American Specification for Cold-Formed Steel Structural Memb ers. Both the Effective Width Method (EWM) and the Direct Strength Method (D SM) can be used for the design of C- sections although rules for the DSM in combined bending and shear are not provided in either standard/specificati on. New DSM design rules for C-sections in shear both with and without tension field action are presented and discussed in a separate paper at this conference. This paper proposes DSM design rules for C-sections in combined bending and shear both with and without the effect of distortional buckling included. Both series of test results are compared with the proposed design rules

Direct Strength Method of Design for Shear of Cold-formed Channels Based on a Shear Signature Curve

Thin-walled sections in compression and/or bending may undergo one of the three modes of local, distortional or overall (Euler) buckling, or combinations of these. The Semi-Analytical Finite Strip Method (SAFSM) developed by YK Cheung has been widely used in computer software (THIN-WALL, CUFSM) to develop the signature curve of the buckling stress versus buckling half wavelength for a thin-walled section under compression or bending to allow identification of these modes. The minimum points on the signature curve are now used in the Direct Strength Method (DSM) of design of cold-formed sections in the American Specification and Australian/New Zealand Standard for cold-formed steel structures. Plank and Wittrick (1974) included shear in the SAFSM theory for calculating the stiffness and stability matrices by using complex mathematics. The complex mathematics is needed to allow for the phase shifts in the buckling modes (eigenvectors) for sections under shear. This paper briefly summarises the theory then applies it to the buckling of channel sections in pure shear. Signature curves for shear are developed for channel sections and compared with classical solutions, and those produced by the Spline Finite Strip Method (SFSM) previously published by the authors. A proposed Direct Strength Method (DSM) of design for shear is explained in the paper

Developments in the Finite Strip Buckling Analysis of Plates and Channel Sections under Localised Loading

Thin-walled sections under localised loading may lead to web crippling of the sections. This paper develops the Semi-Analytical Finite Strip Method (SAFSM) for thin-walled sections subject to localised loading to investigate web crippling phenomena. The method is benchmarked against analytical solutions, Finite Element Method (FEM) solutions, as well as Spline Finite Strip Method (SFSM) solutions

Direct Strength Design of Cold-formed C-sections for Shear

The Direct Strength Method (DSM) rece ntly included in the North American Specification and Australian/New Zealand Standard AS/NZS 4600:2005 gives design rules for compression and bending. No rules are presente d at this stage for shear. Two series of tests on C-section can be used to develop and calibrate rules for design in shear. These are the University of Missouri Rolla tests of the 1970’s and recent tests on high strength C-sections at the University of Sydney. Both series of tests use a similar test rig altho ugh different levels of tension field action have been observed. Two features research ed are the effect of full section shear buckling (as opposed to web only shear buckling), and tension field action. Full section buckling is a feature of the DSM bu t requires software that can evaluate full sections for shear. The paper proposes DSM design rules for C-sections in shear both with and without tension field action. Both series of test results are compared with the pro posed design rules

Buckling Studies of Thin-walled Channel Sections under Combined Bending and Shear

Thin-walled section members can be subjected to axial force, bending and shear. In the cases of cantilever beams and continuous lapped purlins, where combined bending and shear occur at the purlin section just outside the end of the lap, thin-walled sections may buckle at a lower stress than if only one action was present without the other. The computational modelling of the thin-walled steel sections is implemented by means of a spline finite strip analysis to determine the elastic buckling stresses of channel sections subject to bending and shear alone and interaction relations under combined bending and shear. Both unlipped and lipped channels are studied where the main variables are the flange width, different boundary conditions and shear flow distribution. Comparisons between cases, and with classical solutions are included in this report

A Direct Strength Method (DSM) of Design for Channel Sections in Shear with Square and Circular Web Holes

The Direct Strength Method (DSM) design rules for cold-formed steel members in shear have been incorporated recently into the North American Specification (AISI S100-12) and are being implemented in the Australian standard (AS/NZS 4600:2005). The method, which was calibrated for unperforated members only, requires two inputs including the buckling load Vcr and the shear yielding load Vy. For members with square web cut-outs, Vcr can be computed by either the Spline Finite Strip Method (SFSM) or the tabulated values based on the shear buckling coefficients kv as studied by CH Pham or the Finite Element Method (FEM). However, Vy has not been accurately formulated including holes. This paper represents a practical model to obtain Vy for members with central openings subjected to predominantly shear. The model ranges from very small holes where traditional shear yielding predominates to large holes where Vierendeel action dominates. The model is verified with the DSM design formulae using the predominantly shear tests recently conducted at the University of Sydney and Queensland University of Technology with both square and circular web openings and for shear spans with aspect ratios of 1.0

New Proposals for the Direct Strength Method of Design of Cold-Formed Steel Beams with Holes in Shear

In the latest North American Specification for the design of cold-formed steel structural members AISI S100-16, an empirical approach is specified to design beams with web holes in shear. Recently, a Direct Strength Method (DSM) of design for shear for perforated beams with the aspect ratio (shear span / web depth) of 1.0 has been proposed. This paper presents a comprehensive review of the proposal and an experimental validation using a test series on beams with the aspect ratio of 2.0 and with various square and circular web opening sizes conducted at the University of Sydney, and other experimental data collected from the literature. As a result, it is proven that the earlier proposal reliably predicts the shear strength of perforated structures with centrally located square and circular web holes and with an aspect ratio up to 2.0

EFFECT OF REDUCED CARBON SUPPLY ON ENHANCED BIOLOGICAL PHOSPHORUS REMOVAL AND DENITRIFICATION

Joint Research on Environmental Science and Technology for the Eart

Experimental and Numerical Investigations of High Strength Cold-formed Lapped Z Purlins under Combined Bending and Shear

Plain C or Z- sections are two of the most common cold-formed steel purlins in use for roof systems throughout the world. Especially for Z- sections, their lapping ability provides continuity and double thickness material at the support regions results in greater performance and more economical designs. At the region just outside the end of the lap, the purlin may fail under a combination of high bending and shear. Design methods for these sections are normally specified in the Australian/New Zealand Standard for Cold-Formed Steel Structures (AS/NZS 4600:2005) or the North American Specification for Cold- Formed Steel Structural Members (2007). Both Effective Width Method (EWM) and the newly developed Direct Strength Method (DSM) can be used for the design. The DSM presented [Chapter 7 of AS/NZS 4600:2005, Appendix 1 of (AISI 2007)] is developed for columns and beams and is limited to pure compression and pure bending. The situation of combined bending and shear as occurs in a continuous purlin system is not considered. This paper presents a testing program performed at the University of Sydney to determine the ultimate strength of high strength cold-formed lapped Z purlins with two different lap lengths. Tests were also conducted both with and without straps screwed on the top flanges. These straps provide torsion/distortion restraints which may enhance the capacity of the purlins. Numerical simulations using the Finite Element Method (FEM) were also performed. The simulations are compared with and calibrated against tests. The accurate results from FEM allowed extension of the test data by varying the lap lengths. The results of both the experimental tests and FEM were used and plotted on the design interaction curves. The proposals for an extension to the DSM in combined bending and shear are given in the paper

Experimental Study of Longitudinally Stiffened Web Channels Subjected Predominantly to Shear

The Direct Strength Method (DSM) of design of cold-formed sections has recently been extended in the North American Specification for Cold-Formed Steel Structural Members-NAS S100:2012 to include shear. The two new features of the DSM rules for shear researched are the effect of full-section shear buckling as opposed to web-only shear buckling and Tension Field Action (TFA). The prequalified sections in the rules include sections with flat webs and webs with small intermediate longitudinal stiffeners. In order to extend the range to larger intermediate stiffeners as occurs in practice, a series of fourteen shear tests have been performed at the University of Sydney for C-sections with rectangular stiffeners of varying sizes. Six different types of stiffeners were tested with an additional preferred plain section. Each type of sections was tested twice to ensure accuracy. As the web stiffener sizes increase, the shear buckling and strength of the sections are expected to improve accordingly. However, the tests show that the shear ultimate strengths only increase slightly in association with the respective increase of stiffener sizes. The test results are compared with the DSM design rules for shear and found to be lower than those predicted by the DSM curve for shear with TFA. The test failures were observed mainly due to the combined bending and shear modes. The effect of the bending is therefore significant and starts to govern when the shear capacity is significantly strengthened by adding the large longitudinal web stiffener. The test results are subsequently plotted against the DSM interaction curves between bending and shear where the interaction is found to be significant. Modifications and recommendations for prequalified sections with longitudinally stiffened web channels in shear are proposed in the paper