https://www.sefindia.org/forum/files/direct_strenght_method_105.pdf

Review: the direct strength method of cold-formed steel member design

The objective of this paper is to provide the theoretical background and illustrative examples for elastic buckling analysis of cold-formed steel members with general boundary conditions as implemented in the forthcoming update to CUFSM. CUFSM is an open source finite strip elastic stability analysis program freely distributed by the senior author. Although the finite strip method presents a general methodology, the conventional implementation (e.g. CUFSM v 3.13 or earlier) employs only simply-supported boundary conditions. In this paper, utilizing specially selected longitudinal shape functions, the conventional finite strip method is extended to general boundary conditions, including the conventional case: simply-simply supported, as well as: clamped-clamped, clamped-simply supported, clamped-free, and clamped-guided. The solution remains semi-analytical as the elastic and geometric stiffness matrices are derived in a general form with only specific integrals depending on the boundary conditions. An example of the stability solution is provided. The selection of longitudinal terms to be included in the analysis is discussed in terms of balancing accuracy with computational efficiency. Also herein, the constrained finite strip method is extended to general boundary conditions. Both modal decomposition and identification can be carried out based on the new bases developed for the constrained finite strip method, and illustrative examples are provided. This extension of CUFSM is intended to aid the implementation of the direct strength method to the case of general boundary conditions.

/pdf/buckling-analysis-of-cold-formed-steel-members-with-general-mpqu0wj21j.pdf

Buckling Analysis of Cold-formed Steel Members with General Boundary Conditions Using CUFSM Conventional and Constrained Finite Strip Methods

The objective of this paper is to provide an overview of computational modeling, both elastic buckling and nonlinear collapse analysis, for cold-formed steel members. Recent research and experiences with computational modeling of cold-formed steel members conducted within the first author's research group at Johns Hopkins University are the focus of the presented work. This admittedly biased view of computational modeling focuses primarily on the use of the semi-analytical finite strip method and collapse modeling using shell finite elements. Issues addressed include how to fully compare finite strip and finite element solutions, and the importance of imperfections, residual stresses, material modeling, boundary conditions, element choice, element discretization, and solution controls in collapse modeling of cold-formed steel. Examples are provided to demonstrate the expected range of sensitivity in cold-formed steel collapse modeling. The paper concludes with a discussion of areas worthy of future study that are within the domain of cold-formed steel modeling.

Computational modeling of cold-formed steel

Current stainless steel design standards are based on elastic, perfectly plastic material behaviour providing consistency with carbon steel design expressions, but often leading to overly conservative results, particularly in the case of stocky elements. More economic design rules in accordance with the actual material response of stainless steel, which shows a rounded stress–strain curve with significant strain hardening, are required. Hence, the continuous strength method (CSM) was developed. The CSM replaces the concept of cross-section classification with a cross-section deformation capacity and replaces the assumed elastic, perfectly plastic material model with one that allows for strain hardening. This paper summarises the evolution of the method and describes its recent simplified form, which is now suitable for code inclusion. Comparison of the predicted capacities with over 140 collected test results shows that the CSM offers improved accuracy and reduced scatter relative to the current design methods. The reliability of the approach has been demonstrated by statistical analyses and the CSM is currently under consideration for inclusion in European and North American design standards for stainless steel structures.

/pdf/the-continuous-strength-method-for-structural-stainless-2let3r3ttu.pdf

The continuous strength method for structural stainless steel design.

This paper presents the fundamentals and illustrates the application and potential of the recent 2.0 release of the software G BTul – a computer program developed by the authors and made available as freeware on the website of the Department of Civil Engineering of the University of Lisbon. The program is based on Generalised Beam Theory (GBT), a bar theory accounting for cross-section in-plane and out-of-plane (warping) deformation, and performs linear buckling and undamped free vibration analyses of prismatic thin-walled members. Its domain of application is much wider than that of the previous release (1.0β), making it possible to analyse single or multi-span members (i) with various support conditions, namely those due to discrete bracing systems, (ii) exhibiting arbitrary (open, closed or “mixed”) flat-walled cross-sections and (iii) acted by fairly general loadings, including concentrated and/or distributed transverse forces applied away from the member shear centre axis. After providing a brief overview on the GBT fundamentals, the program capabilities and innovative aspects are addressed, and its application is illustrated by means of a few relevant numerical examples. Moreover, the program Graphical User Interface is described and the procedures and/or options associated with its main commands are mentioned.

GBTul 2.0 − A second-generation code for the GBT-based buckling and vibration analysis of thin-walled members

Application of the finite strip method in cold-formed steel member design

The stability of thin-walled members is decidedly complex. The recently developed constrained Finite Strip Method (cFSM) provides a means to simplify thin-walled member stability solutions through its ability to identify and decompose mechanically meaningful stability behavior, notably the formal separation of local, distortional, and global deformation modes. The objective of this paper is to provide a review of the most recent developments in cFSM. This review includes: fundamental advances in the development of cFSM; applications of cFSM in design and optimization; identifying buckling modes and collapse mechanisms in shell finite element models; and, additional stability research initiated by the cFSM methodology. A brief summary of the cFSM method, in its entirety, is provided to explain the method and highlight areas where research remains active in the fundamental development. The application of cFSM to cold-formed steel member design and optimization is highlighted as the method has the potential to automate generalized strength prediction of thin-walled cold-formed steel members. Extensions of cFSM to shell finite element models is also highlighted, as this provides one path to bring the useful identification features of cFSM to general purpose finite element models. A number of alternative methods, including initial works on a constrained finite element method, initiated by cFSM methods, are also detailed as they provide insights on potential future work in this area. Research continues on fundamentals such as methods for generalizing cFSM to arbitrary cross-sections, improved design and optimization methods, and new ideas in the context of shell finite element method applications.

Review: Constrained finite strip method developments and applications in cold-formed steel design

The objective of this paper is to present constrained optimization results for a cold-formed steel (CFS) cross-section shape with maximum axial capacity. In the authors׳ previous work unconstrained shape optimization was performed via stochastic search and gradient-based algorithms. Unconstrained shape optimizations produced a significant capacity increase, more than 140%, above standard CFS cross-sections, but many of the solutions are highly unconventional and have potential limitations both with respect to end use (e.g. attaching boards for walls and floors) and cost of manufacturing. Column capacity is determined using the Direct Strength Method (DSM) which requires inputs for the local, distortional and global critical buckling loads. These critical loads are obtained using the finite strip method, as implemented in the open source software CUFSM, which allows essentially any potential cross-section to be evaluated. To advance the applicability of the optimized results, end-use constraints and manufacturing constraints on the number of rollers employed in forming were both successfully incorporated in the shape optimization presented in this paper, resulting in optimized cross-sections that are more practical and economical with only marginally decreased capacity (usually less than 10%) from the earlier unconstrained optimized solutions. The constraints are implemented within a simulated annealing (SA) algorithm for the optimization. Optimized sections from multiple runs show uniformity, partially indicating the robustness of the final optimized shapes. The implemented constrained shape optimization provides a thorough search with high computational efficiency. The optimized cross-sections from this research provide promising potential shapes for the development of new commercial product families, and the member-level optimization methodology can also be integrated into building optimization in the future.

Zhanjie Li

Papers

Buckling Analysis of Cold-formed Steel Members with General Boundary Conditions Using CUFSM Conventional and Constrained Finite Strip Methods

Computational modeling of cold-formed steel

Application of the finite strip method in cold-formed steel member design

Review: Constrained finite strip method developments and applications in cold-formed steel design

Shape optimization of cold-formed steel columns with fabrication and geometric end-use constraints