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The design of cold-formed steel flexural members using the Direct Strength Method (DSM), use signature curves of cross-sections with the assumption of equal end moments and uniform stresses in the longitudinal direction. However, for beams subjected to general transverse loads, the assumption of longitudinal uniform stress is conservative. In calculating elastic critical loads of thin-walled flexural members, to incorporate a non-uniform variation of longitudinal stresses, this paper presents a spline finite strip computational procedure, which can also be used for beams with intermediate restraints. To the authors’ knowledge, such a procedure using spline finite strip is presented for the first time in the literature. The present formulation is comprehensive in its generality compared with similar works published. The membrane and shear stresses due to transverse loads on the beam are determined in the local direction of the plate at section knots of the spline strip. These stresses are incorporated in the geometric stiffness matrix, and buckling analysis is performed for calculating the elastic buckling load. Restraint matrices are incorporated in buckling analysis for the decomposition of buckling modes and for calculating mode participation. The proposed formulation is compared with generalized beam theory (GBT) for lipped channel cross-section with variation in span, general loading, and intermediate restraints. This method is demonstrated to be good for calculating elastic buckling stresses for the practical design of thin-walled flexural members. © 2020 Elsevier Ltd

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Thin-Walled Structures

Spline finite strip analysis of thin-walled flexural members subjected to general loading with intermediate restraints

This paper presents the application of constrained spline finite strip method (cSFSM) for cold-formed steel members with complex edge stiffeners. In this method, the principles of GBT are used to develop restraint matrices corresponding to local, distortional and global buckling. These matrices are applied in generalized eigen value equation by using transformation technique. The critical buckling stresses were calculated separately for pure local, distortional and global buckling. Based on the formulation, cross sectional geometries having complex lips are analysed to study the variations in buckling stresses developed. The increase in complexity of lip stiffeners increases the local buckling capacity of the cross section. However, for distortional buckling, the cross sections with inward lip stiffener offer higher buckling capacity than those with outward lips. The influence of lip stiffeners on global buckling was observed to be marginal from the present study. Copyright © 2018 by The Hong Kong Institute of Steel Construction.

Proceedings of the 9th International Conference on Advances in Steel Structures, ICASS 2018

Elastic buckling of cold-formed steel complex cross sections using constrained spline finite strip method (CSFSM)

A new design method, Direct Strength Method (DSM), has been introduced by researchers in recent years for calculating the ultimate design strength of cold-formed steel sections. DSM is basically a stress-based approach, wherein the strength of the section is reduced to take care of buckling effects. The ultimate strengths corresponding to three buckling modes, local, distortional, and global modes are distinguished in DSM, in which the elastic buckling stresses are determined using analytical expressions or by using numerical methods like finite element, finite strip, or spline finite strip method. A finite strip computational procedure for evaluating the critical elastic buckling stresses has been proposed in the present study. Also, decomposition of buckling modes into pure modes can be performed using the formulation. This formulation has been validated for a range of cross-sectional dimensions under uniaxial compression and flexure and can be used as a design utility for IS 801 based on DSM. © 2019, Springer Nature Singapore Pte Ltd.

Lecture Notes in Civil Engineering

Twlight-iitm—a computational utility for elastic buckling stress predictions of cold-formed steel elements

Direct strength method (DSM) for the design of cold-formed steel members recommends finite strip method (FSM) for calculating the elastic buckling stresses corresponding to local, distortional and global buckling, which are considered to be the basic input parameters for design. This paper presents application of constrained spline finite strip method (cSFSM) developed by authors for calculating pure elastic buckling stresses in DSM and hence predicting the ultimate member capacity in uniform flexure and axial compression. The elastic buckling stresses are determined for a specified set of experiments available in literature using cSFSM by considering different end conditions and failure modes and the elastic stress values are applied in DSM for calculating ultimate member capacity. For beams with simply supported-warping free ends and columns with simply supported-warping fixed ends, the DSM evaluated results using cSFSM produces results comparable with experiments. The results obtained by the comparison of DSM with experiments were not satisfactory for fixed columns and beams with simply supported-warping fixed ends. © 2019, Korean Society of Steel Construction.

International Journal of Steel Structures

Direct Strength Design of Cold-Formed Steel Members Using Constrained Spline Finite Strip Method

Department Of Civil Engineering

Spline functions are well established mathematical tools for interpolation problems encountered in engineering. This has been well recognized in the structural analysis by the so called spline finite strip method for the analysis of prismatic thin plated structures. This paper presents briefly the properties of cubic B3-splines and exemplifies its applicability to some selected problems encountered in structural analysis. Some inconsistencies in the boundary amendment schemes published in the literature, which could destroy the symmetricity of stiffness matrices has been identified here. By suitably modifying the coefficients, symmetric boundary amendment schemes that retain symmetricity even up to second derivative are proposed in this study. The approximating properties of spline functions are exemplified by few simple examples and the amended splines are incorporated in spline finite strip program for analysis of plates under various edge conditions.

Journal of Structural Engineering (India)

Amendment schemes for cubic end splines used in structural analysis

In this paper, an analysis procedure has been presented for cold-formed steel sections, for decomposing the buckling modes obtained using spline finite strip method (SFSM) into their primary and independent buckling modes such as local, distortional and global buckling. This procedure utilizes principles of generalized beam theory (GBT) to evaluate the restraint matrices corresponding to different modes. The restraint matrices are integrated in to spline stiffness matrices using transformation technique to extract pure modes corresponding to local, distortional and global modes. The proposed analysis technique termed as constrained spline finite strip method (cSFSM) has been validated for cold-formed steel open cross-sections subjected to axial compression and bending under various boundary conditions. The results are in agreement with buckling stresses evaluated using constrained finite strip method (cFSM) and GBT. © 2017 Elsevier Ltd

A constrained spline finite strip method for the mode decomposition of cold-formed steel sections using GBT principles

In this paper, a mode identification technique in the context of spline finite strip method (SFSM) is presented to compute the contribution of primary (global, distortional and local) and secondary (shear/transverse extension) buckling modes. The base vectors corresponding to individual buckling modes are developed based on the principles of generalized beam theory. The buckling mode shape in SFSM is approximated as a linear combination of these orthonormal base vectors to evaluate the participation of individual buckling mode. The proposed mode identification technique is able to successfully quantify the participation of different buckling modes and the mode participation is comparable with mode identification using finite strip method (FSM) and generalized beam theory (GBT). Illustrative examples are presented to calculate the participation of individual modes in cold-formed steel sections under different loading and boundary conditions. Also the specific application of mode identification in SFSM is demonstrated. © 2017 Elsevier Ltd

Identification of buckling modes in generalized spline finite strip analysis of cold-formed steel members

The expressions for elastic distortional buckling stress predictions available in literature are used with reasonable accuracy, but are either iterative or involve increased calculation effort for design. It is an accepted fact among researchers that these expressions are not evaluated enough for the distortional stress prediction of sections with complex lip stiffeners. In this paper, a candidate model for distortional buckling stress predictions is presented which is semi analytical in nature and is simple to incorporate in the direct strength method (DSM) of cold-formed steel design. The proposed expression incorporates the effect of complex lip stiffeners on the elastic distortional buckling capacities of cold formed steel flexural members. In the proposed model, the (i) translational stiffness at lip-flange junction and (ii) rotational stiffness at the flange-web junction, are derived from regression analysis of wide range of cross sectional dimensions. The proposed method is calibrated with semi-analytical finite strip method presented in the literature and this formulation has been demonstrated to be good in comparison with recently published numerical based distortional buckling predictions. © 2016 Elsevier Ltd. All rights reserved.