Structural analysis and design of cold formed steel sigma purlins

Cold formed steel (CFS) sigma sections are commonly used as purlins in the construction of modern industrial and residential buildings due to their excellent strength-to-weight ratio. This thesis reports investigations on the structural behaviour of CFS sigma purlins in three different parts of modern roof systems. In the first investigation, the pre-buckling, buckling, post-buckling and post-failure behaviour of continuous CFS sigma purlins near internal supports was studied by experimental and numerical methods. In the second investigation, the moment-rotation response as well as the moment resistance of the sleeve connection of sigma purlins was studied by laboratory tests. Engineering models were developed to predict the behaviour of this connection and a good correlation was observed with the experimental data. In the third investigation, the flexural stiffness and moment resistance of CFS sigma purlins fastened to roof sheeting with large screw spacing was studied experimentally. The purlin-sheeting assemblies were subjected to both downward and uplift loadings, from which different behavioural aspects such as flexural stiffness, failure modes and ultimate load were examined. Test results are utilized to develop design proposals for sigma purlins that codes or standards have not yet covered.

[1]  Cristopher D. Moen,et al.  COMPUTATIONAL MODELING OF COLD-FORMED STEEL , 2010 .

[2]  J. M. Davies,et al.  First-order generalised beam theory , 1994 .

[3]  W. M. Quach,et al.  Finite element predictions of residual stresses in press-braked thin-walled steel sections , 2006 .

[4]  K. F. Chung,et al.  Structural behavior of lapped cold-formed steel Z sections with generic bolted configurations , 2006 .

[5]  N. L. Ings,et al.  Lateral buckling of restrained roof purlins , 1984 .

[6]  Y. K. Cheung,et al.  Analysis of shallow shells by spline finite strip method , 1983 .

[7]  Cristopher D. Moen,et al.  Prediction of residual stresses and strains in cold-formed steel members , 2008 .

[8]  Xiao-ting Chu,et al.  Lateral-torsion buckling analysis of partial-laterally restrained thin-walled channel-section beams , 2004 .

[9]  Long-yuan Li,et al.  An analytical model for analysing distortional buckling of cold-formed steel sections , 2008 .

[10]  Lei Zhang,et al.  Moment resistance and flexural rigidity of lapped connections in multi-span cold-formed Z purlin systems , 2008 .

[11]  T. P. Desmond,et al.  Edge Stiffeners for Thin-Walled Members , 1981 .

[12]  Kim J.R. Rasmussen,et al.  Tests of Unstiffened Plate Elements Under Combined Compression and Bending , 2004 .

[13]  Viorel Ungureanu,et al.  Effect of imperfections on numerical simulation of instability behaviour of cold-formed steel members , 2002 .

[14]  Benjamin W. Schafer,et al.  Simplified models for cross-section stress demands on C-section purlins in uplift , 2010 .

[15]  Faris Albermani,et al.  Modelling of cold-formed purlin-sheeting systems— Part 1: Full model , 1997 .

[16]  K. F. Chung,et al.  Analytical prediction on deformation characteristics of lapped connections between cold-formed steel Z sections , 2006 .

[17]  Ahmad A. Ghosn,et al.  Governing Stresses in Z-Purlin Lap Joints , 1995 .

[18]  Kwok-Fai Chung,et al.  Finite element investigation on the structural behaviour of cold-formed steel bolted connections , 2001 .

[19]  James B.P. Lim,et al.  Finite element idealization of a cold-formed steel portal frame , 2004 .

[20]  D. B. Moore Moment-rotation Characteristics of Purlin Connections , 1990 .

[21]  Benjamin W. Schafer,et al.  Inelastic Bending Capacity of Cold-Formed Steel Members , 2012 .

[22]  M. M. Alinia,et al.  A study into optimization of stiffeners in plates subjected to shear loading , 2005 .

[23]  B. P. Sinha,et al.  ADVANCED CONNECTION TECHNIQUES FOR COLD-FoRMED STEEL STRUCTURES , 1997 .

[24]  Benjamin W. Schafer,et al.  Local, Distortional, and Euler Buckling of Thin-Walled Columns , 2002 .

[25]  Teoman Peköz,et al.  Limit Design in Cold-Formed Steel , 1983 .

[26]  Noel W. Murray,et al.  Introduction to the theory of thin-walled structures , 1984 .

[27]  Gregory J. Hancock,et al.  Compression Tests of High Strength Steel Channel Columns with Interaction between Local and Distortional Buckling , 2004 .

[28]  G. H. Bryan,et al.  On the Stability of a Plane Plate under Thrusts in its own Plane, with Applications to the “Buckling” of the Sides of a Ship , 1890 .

[29]  R. S. Khurmi.pdf,et al.  Strength of Materials , 1908, Nature.

[30]  Teoman T Peköz,et al.  The finite element method for thin-walled members—basic principles , 2003 .

[31]  Christopher T. Willis,et al.  Behavior of Cold-Formed Steel Purlins Under Gravity Loading , 1990 .

[32]  Gregory J. Hancock,et al.  Distortional Buckling Formulas for Channel Columns , 1987 .

[33]  Kim J.R. Rasmussen,et al.  Design Provisions for Sections Containing Unstiffened Elements with Stress Gradient , 2004 .

[34]  R. Gutiérrez,et al.  Analysis of cold-formed purlins with slotted sleeve connections , 2011 .

[35]  Gregory J. Hancock,et al.  Experimental Investigation of High Strength Cold-Formed C-Sections in Combined Bending and Shear , 2010 .

[36]  Long-yuan Li,et al.  Buckling behavior of cold-formed zed-purlins partially restrained by steel sheeting , 2002 .

[37]  Gregory J. Hancock,et al.  Cold-Formed Steel Structures to the AISI Specification , 2001 .

[38]  Kwok-Fai Chung,et al.  Structural performance of modern roofs with thick over-purlin insulation—Experimental investigation , 1996 .

[39]  Herbert Becker,et al.  Handbook of Structural Stability Part I: Buckling of Flat Plates , 1957 .

[40]  R. M. Lawson,et al.  Structural performance of shear resisting connections between cold-formed steel sections using web cleats of cold-formed steel strip , 2000 .

[41]  James B.P. Lim,et al.  Stiffness prediction for bolted moment-connections between cold-formed steel members , 2004 .

[42]  R. M. Schuster,et al.  Multiple Stiffened Deck Profiles , 1994 .

[43]  Teoman Peköz,et al.  Unstiffened Compression Elements , 1977 .

[44]  E. R. Bryan The design of bolted joints in cold-formed steel sections , 1993 .

[45]  Long-yuan Li Calculation of moment capacity of cold-formed steel members , 2011 .

[46]  Francesc Roure,et al.  Open cross-section beams under pure bending II. Finite element simulation , 2009 .

[47]  Webs for cold formed steel flexural members structural behavior of beam webs subjected primarily to shear stress , 1978 .

[48]  Gülay Altay,et al.  Finite element modeling of bolted steel connections designed by double channel , 2004 .

[49]  Lev Zetlin Unsymmetrical Bending of Beams with and without Lateral Bracing , 1955 .

[50]  Benjamin W. Schafer,et al.  Simulation of cold-formed steel beams in local and distortional buckling with applications to the direct strength method , 2007 .

[51]  K. B. Katnam,et al.  Design of Cold-Formed Steel Purlins Attached to Roof Sheeting Based on Eurocode 3: Effect of Gravity Load , 2008 .

[52]  Jeong Kim,et al.  Finite element analysis and modeling of structure with bolted joints , 2007 .

[53]  Long Chen FINITE ELEMENT METHOD , 2013 .

[54]  Pentti Mäkeläinen,et al.  Advanced method for lightweight steel joining , 1999 .

[55]  Carlos Graciano,et al.  Failure mechanism of slender girder webs with a longitudinal stiffener under patch loading , 2003 .

[56]  K. F. Chung,et al.  Experimental investigation into the structural behaviour of lapped connections between cold-formed steel Z sections , 2004 .

[57]  K. Weynand,et al.  Connections in cold-formed steel , 1993 .

[58]  R. Clough The Finite Element Method in Plane Stress Analysis , 1960 .

[59]  Gregory J. Hancock,et al.  Design of Cold-Formed Channels Subjected to Web Crippling , 2001 .

[60]  Roger A. LaBoube,et al.  Webs for cold formed steel flexural members structural behavior of beam webs subjected to a combination of bending and shear , 1978 .

[61]  Gregory J. Hancock,et al.  Failure Modes of Bolted-Sheet-Steel Connections Loaded in Shear , 2000 .

[62]  Nicholas S. Trahair,et al.  Lateral Buckling Strengths of Cold-Formed Channel Section Beams , 1998 .

[63]  Viorel Ungureanu,et al.  Behaviour of multi-span cold-formed Z-purlins with bolted lapped connections , 2010 .

[64]  G. Winter Strength of Thin Steel Compression Flanges , 1947 .

[65]  R. P. Johnson,et al.  General rules and rules for buildings , 2004 .

[66]  Francesc Roure,et al.  Open cross-section beams under pure bending. I. Experimental investigations , 2008 .

[67]  Gregory J. Hancock,et al.  A theoretical analysis of the plastic-moment capacity of an inclined yield line under axial force , 1993 .

[68]  Antonio Rodríguez-Ferran,et al.  Experimental testing of joints for seismic design of lightweight structures. Part 3: gussets, corner joints, x-braced frames , 2007 .

[69]  Teoman Peköz,et al.  Partial Moment Redistribution in Cold‐Formed Steel , 1985 .

[70]  Maria Kotełko,et al.  Load-capacity estimation and collapse analysis of thin-walled beams and columns—recent advances , 2004 .

[71]  Mahen Mahendran,et al.  Lateral buckling strength of simply supported LiteSteel beams subject to moment gradient effects , 2009 .

[72]  Man-fai Wong,et al.  Bolted moment connections in cold-formed steel beam-column sub-frames , 2002 .

[73]  M. Stein Analytical results for post-buckling behaviour of plates in compression and in shear , 1984 .

[74]  Qiang Liu,et al.  Pseudo-plastic moment resistance of continuous beams with cold-formed sigma sections at internal supports: An experimental study , 2011 .

[75]  Joachim Lindner,et al.  Load-carrying capacity of cold-formed beams subjected to overall lateral-torsional buckling and local plate buckling , 1994 .

[76]  Gregory J. Hancock,et al.  Calibration of the AISI R-factor design approach for purlins using Australian test data , 1994 .

[77]  Sung C. Lee,et al.  Mechanics of Web Panel Postbuckling Behavior in Shear , 2006 .

[78]  D. A. Heinz Application of generalized beam theory to the design of thin-walled purlins , 1994 .

[79]  Cheng Yu,et al.  Effect of longitudinal stress gradient on the ultimate strength of thin plates , 2006 .

[80]  Long-yuan Li,et al.  Buckling behaviour of cold-formed channel sections under uniformly distributed loads , 2005 .

[81]  E. E. Sechler,et al.  The Strength of Thin Plates in Compression , 1932, Journal of Fluids Engineering.

[82]  Gregory J. Hancock,et al.  Direct Strength Design of Cold-Formed Purlins , 2009 .

[83]  Gregory J. Hancock,et al.  Numerical Simulation of High-Strength Steel Box-Shaped Columns Failing in Local and Overall Buckling Modes , 2006 .

[84]  Antonio Rodríguez-Ferran,et al.  Experimental testing of joints for seismic design of lightweight structures. Part 1. Screwed joints in straps , 2006 .

[85]  Markku Laine,et al.  Testing and design of gravity-loaded steel purlins restrained by sheeting , 1999 .

[86]  Nicholas S. Trahair,et al.  Lateral buckling strengths of cold-formed Z-section beams , 1999 .

[87]  Kwok-Fai Chung,et al.  Experimental investigation on bolted moment connections among cold formed steel members , 1999 .

[88]  Viorel Ungureanu,et al.  Recent research advances on ECBL approach.: Part I: Plastic–elastic interactive buckling of cold-formed steel sections , 2004 .

[89]  Gregory J. Hancock,et al.  Cold-formed steel structures , 2003 .

[90]  Leopold Sokol,et al.  Stability of cold formed purlins braced by steel sheeting , 1996 .

[91]  J. M. Davies,et al.  Second-order generalised beam theory , 1994 .

[92]  Long-Yuan Li,et al.  Lateral–torsional buckling of cold-formed zed-purlins partial-laterally restrained by metal sheeting , 2004 .

[93]  Kwok-Fai Chung,et al.  Finite element modeling of bolted connections between cold-formed steel strips and hot rolled steel plates under static shear loading , 2000 .

[94]  Gregory J. Hancock,et al.  Comparison of tests of bridged and unbridged purlins with a non-linear analysis model , 1997 .

[95]  Dinar Camotim,et al.  Distortional buckling formulae for cold-formed steel C and Z-section members: Part I—derivation , 2004 .

[96]  Teoman Peköz,et al.  The finite element method for thin-walled members-applications , 2003 .

[97]  Gregory J. Hancock Design for distortional buckling of flexural members , 1997 .

[98]  Cheng Yu,et al.  Local Buckling Tests on Cold-Formed Steel Beams , 2003 .

[99]  Dinar Camotim,et al.  Local/distortional mode interaction in cold-formed steel lipped channel beams , 2010 .

[100]  Colin A. Rogers,et al.  Comparison of the Distortional Buckling Method for Flexural Members with Tests , 1996 .

[101]  P. S. Bulson,et al.  The stability of flat plates , 1969 .

[102]  Parviz Soroushian,et al.  Behavior of C- and Z-purlins under Wind Uplift , 1981 .

[103]  K. F. Chung,et al.  Analysis and design of lapped connections between cold-formed steel Z sections , 2005 .

[104]  Venkatakrishnan Kalyanaraman,et al.  Experimental study on the lateral buckling behaviour of cold-formed beams , 1990 .

[105]  Teoman T Peköz,et al.  Direct Strength Prediction of Cold-formed Steel Members Using Numerical Elastic Buckling Solutions , 1998 .

[106]  Benjamin W. Schafer,et al.  Complex Edge Stiffeners for Thin-Walled Members , 2006 .

[107]  J M Davies,et al.  Design of thin-walled purlins for distortional buckling , 1997 .

[108]  James Rhodes Design of cold formed steel members , 1991 .

[109]  Benjamin W. Schafer,et al.  Distortional Buckling Tests on Cold-Formed Steel Beams , 2006 .

[110]  Benjamin W. Schafer,et al.  Computational modeling of cold-formed steel: characterizing geometric imperfections and residual stresses , 1998 .

[111]  Benjamin W. Schafer,et al.  REVIEW: THE DIRECT STRENGTH METHOD OF COLD-FORMED STEEL MEMBER DESIGN , 2008 .

[112]  R. Kettle,et al.  Local and distortional buckling of cold-formed zed-section beams under uniformly distributed transverse loads , 2006 .

[113]  Gregory J. Hancock,et al.  Shear buckling of thin-walled channel sections , 2009 .

[114]  Gregory J. Hancock,et al.  Tests of Channels Subjected to Combined Bending and Web Crippling , 2002 .

[115]  Gregory J. Hancock,et al.  Numerical simulation of high strength cold-formed purlins in combined bending and shear , 2010 .

[116]  M. M. Alinia,et al.  A parametric study on the longitudinal stiffeners of web panels , 2008 .

[117]  Tomáš Vraný Effect of loading on the rotational restraint of cold-formed purlins , 2006 .

[118]  David Nash,et al.  An investigation of web crushing behaviour in thin-walled beams , 1998 .

[119]  Teoman Peköz,et al.  Inelastic Strength of Cold-Formed Steel Beams , 1975 .

[120]  Y. K. Cheung,et al.  FINITE STRIP METHOD IN STRUCTURAL ANALYSIS , 1976 .

[121]  R. Van Impe,et al.  A theoretical numerical study of the rotational restraint in cold-formed steel single skin purlin-sheeting systems , 2007 .

[122]  Jian Yang,et al.  Pseudo-plastic moment resistance of continuous beams with cold-formed sigma sections at internal supports: A numerical study , 2011 .

[123]  R. N. White,et al.  Stability of Plates under Partial Edge Loading , 1962 .

[124]  Paul Grundy,et al.  Effect of pre- and postbuckling behaviour on load capacity of continuous beams , 1990 .

[125]  N S Trahair,et al.  Lateral Buckling Tests on Cold-Formed Channel Beams , 1999 .

[126]  Viorel Ungureanu,et al.  Plastic mechanisms database for thin-walled cold-formed steel members in compression and bending , 2010 .

[127]  C. H. Yoo,et al.  Shear buckling coefficients of plate girder web panels , 1996 .

[128]  Wei-wen Yu,et al.  Webs for cold formed steel flexural members structural behavior of beam webs subjected to web crippling and a combination of web crippling and bending , 1978 .

[129]  Michael R. Bambach Local buckling and post-local buckling redistribution of stress in slender plates and sections , 2006 .

[130]  N. W. Murray,et al.  Some basic plastic mechanisms in the local buckling of thin-walled steel structures , 1981 .

[131]  Ye,et al.  Stress and Buckling Analysis of Cold-formed Zed-purlins Partially Restrained by Steel Sheeting , 2003 .

[132]  Dinar Camotim,et al.  ON THE DISTORTIONAL POST-BUCKLING BEHAVIOUR OF COLD-FORMED LIPPED CHANNEL STEEL BEAMS , 2002 .

[133]  K. C. Rockey,et al.  Buckling of plate girder webs under partial edge loadings , 1970 .

[134]  Wei-Xin Ren,et al.  Analysis and design of cold-formed steel channels subjected to combined bending and web crippling , 2006 .

[135]  R. Van Impe,et al.  Modelling of cold-formed steel sandwich purlin-sheeting systems to estimate the rotational restraint , 2007 .

[136]  Faris Albermani,et al.  Modelling of cold-formed purlin-sheeting systems—Part 2. Simplified model , 1997 .

[137]  Eduardo de Miranda Batista Effective section method: A general direct method for the design of steel cold-formed members under local―global buckling interaction , 2010 .

[138]  Dinar Camotim,et al.  Distortional buckling formulae for cold-formed steel C- and Z-section members: Part II—Validation and application , 2004 .

[139]  Dinar Camotim,et al.  FEM-based analysis of the local-plate/distortional mode interaction in cold-formed steel lipped channel columns , 2007 .

[140]  Nicholas S. Trahair,et al.  Lateral Buckling Tests on Cold-Formed Z-Beams , 1999 .

[141]  Ton Tomà,et al.  Design of cold-formed purlins and rails restrained by sheeting , 1994 .

[142]  Kwok-Fai Chung,et al.  Analysis of bolted moment connections in cold-formed steel beam–column sub-frames , 2005 .

[143]  Benjamin W. Schafer,et al.  Yield-line analysis of cold-formed steel members , 2005 .

[144]  Dan Dubina,et al.  Stiffness of joints in bolted connected cold-formed steel trusses , 2006 .

[145]  Bill Bill Wong,et al.  Plastic Analysis And Design Of Steel Structures , 2008 .

[146]  Nicholas S. Trahair Lateral buckling strengths of unsheeted cold-formed beams , 1994 .