Acknowledgments. Specification complication. Cold-Formed Steel Design by the Direct Strength Method

Transcription

1 Acknowledgments Cold-Formed Steel Design by the Direct Strength Method Mid-Atlantic Steel Framing Conference May 2005 Ben Schafer, Ph.D. Johns Hopkins University American Iron and Steel Institute Dr. Cheng Yu (UNT) Jack Spangler Sam Phillips, Liakos Ariston, Tom Lydigsen, Andrew Meyers, Brent Bass Introduction and motivation Buckling and the finite strip method Experiments and design of beams Direct Strength Method for Beams and Columns Advocacy and extensions (as time allows) Specification complication Anyone who has ever attempted to design a light-gage member following the Specification provisions probably realized how tedious and complex the process was. When such [cold-formed] framing is needed one of two things tend to happen to the engineers: they either uncritically rely on the suppliers literature, or simply avoid any cold-formed design at all Alexander Newman 1997, in Metal Building Systems

2 Kesti (2000) - Finland Rinchen (1998) - Australia Landolfo and Mazzolani (1990) - Italy Specification complication explained Sections are not doubly-symmetric Element elastic buckling calculation (k s) Effective width effective width = f(stress,geometry) stress = f(effective properties: e.g., A eff, I eff ) iteration results Web crippling calculations Inclusion of system effects Specification complication explained Plate vs. cross-section buckling Sections are not doubly-symmetric Mechanics elastic buckling Element elastic buckling calculation (k s) Effective width effective width = f(stress,geometry) Direct strength curves stress = f(effective properties: e.g., A eff, I eff ) iteration results Web crippling calculations Inclusion of system effects f cr 2 π E = k ( ν ) 2 t b f cr P = A f cr g cr plate buckling coefficient for the flange k f Why cross-section buckling? (element interaction) ξ = 3 ξ = 2, pure bending ξ = 1.4 ξ = 1 ξ = 3 ξ = 2 ξ = 1.4 ξ = 1 ξ = local buckling finite strip analysis f f 1 2 f ratio of web height to flange width (hb) f 2 f 1 How to find cross-section buckling? Tables and charts essentially limited to two elements not widely available Finite element solutions requires more advanced modeling (plate elements) generality of method is great, but complicates too not widely available Other methods? finite element variant called the finite strip method

3 Modeling a CFS member Finite Strip Analysis b θ1 a v1 u1 θ2 v2 u2 z y x ½ sine wave finite element finite strip w1 w2 cubic beam function CUFSM (Cornell University Finite Strip Method) Free, open source, software that allows you to explore the elastic buckling of any cold-formed steel cross-section using the finite strip method Mechanics employed are IDENTICAL to the mechanics used to derive the plate buckling coefficient k values in current use M y =192 kip-in.

4 Local buckling Distortional Lateral-torsional DEMO (

5 finite strip resource Introduction and motivation Buckling and the finite strip method Experiments and design of beams Direct Strength Method for Beams and Columns Advocacy and extensions (as time allows) Conclusions from part 1?

6 Current design Direct Strength Design k? b e? M cr?mcr M n? L cr Cross-section buckling of a typical beam Part 2: DSM and an experimental investigation of beams M cr L cr local buckling distortional buckling lateral-torsional buckling Direct strength prediction M n = f (M y, M cre, M crd, M crl )? Input Yield moment, M y Euler buckling load, M cre Distortional buckling load, M crd Local buckling load, M crl Output Strength, M n strength P cr (M cr ) P n (M n ) Elastic buckling Yield Global Local Distortional slenderness

7 Motivation for recent experimental research Problems: 1. Current Specifications AISI (1996), S136 (1994), NAS (2001) do not have sufficient procedures for the design of distortional buckling. 2. The Direct Strength Method (proposed by Schafer and Peköz 1998) provides specific strength predictions for distortional buckling. 3. Previous tests did not distinguish between local and distortional buckling. Existing data is not representative of sections currently used in practice. 25 tests... Tests of CFS Beams Local Buckling (Phase 1) Therefore, two series of bending tests were performed to study the local and distortional buckling of CFS beams separately and analysis was also performed to develop complete design methods. Tests of CFS Beams - range of specimens Tests of CFS Beams - panel fastener configuration for Phase 1 tests Z-section C-section Tested industry standard CFS Z and C-sections local buckling Panel fastener configuration continuous spring analysis (FSM) fe (elastic) model to develop detail

8 distortional predicted as lowest eigenmode (single screw pattern, t=0.073 in.) local predicted as lowest eigenmode (paired screw pattern, t=0.073 in.) panels removed for visual purposes only panels removed for visual purposes only influence of details Specimen M y M aisi note 8.5Z073-5E6W single panel-to-purlin screws - 12" o.c. 8.5Z073- single panel-to-purlin screws E2W on both sides of raised corrugation 8.5Z073- paired panel-to-purlin screws E3W on both sides of raised corrugation Tests of CFS Beams - distortional buckling tests on CFS beams (Phase 2) Total 24 beams, 1.5 years to complete Distortional buckling shape 8.5Z073-5E6W 8.5Z073-4E3W Test 8.5Z092 Tests of CFS Beams - comparison of two series of tests Tests of CFS Beams - test summary P P crd P y local distortional Total 25 local buckling tests and 24 distortional buckling tests have been completed. Comparison with design methods P Test 8C043 P crd distortional P y P crl local Local buckling test Distortional buckling test 99% of NAS 83% of NAS Local buckling test Distortional buckling test 106% of NAS 90% of NAS Local buckling tests Distortional buckling tests µ σ µ σ M AISI M S M NAS M AN 0.07 M EN App1 M DSM

9 Application of the Direct Strength Method Beam Design The nominal flexural strength, M n, is the minimum of M ne, M nl and M nd as given below. For beams meeting the geometric and material criteria of Section , Ω b and φ b are as follows: USA and Mexico Canada Ω b (ASD) φ b (LRFD) φ b (LSD) For all other beams, Ω and φ of Section A1.1(b) apply. M ne Lateral-Torsional Buckling The nominal flexural strength, M ne, for lateral-torsional buckling is for M cre < 0.56M y M ne = M cre (Eq ) for 2.78M y > M cre > 0.56M y 10 10M y M ne = M y Mcre (Eq ) for M cre > 2.78M y M ne = M y (Eq ) where M y = S f F y, where S f is the gross section modulus referenced to (Eq ) the extreme fiber in first yield M cre = Critical elastic lateral-torsional buckling moment determined in accordance with Section X M ne =M y in our case M nl Local Buckling The nominal flexural strength, M nl, for local buckling is for λ l M nl = M ne (Eq ) for λ l > M M nl = cr M cr l l M ne M ne M (Eq ) ne where λ l = M ne M cr l (Eq ) M crl = Critical elastic local buckling moment determined in accordance with Section M ne is defined in Section M nd Distortional Buckling The nominal flexural strength, M nd, for distortional buckling is for λ d M nd = M y (Eq ) for λ d > M M nd = crd M crd M y (Eq ) M y M y where λ d = M y M crd (Eq ) M crd = Critical elastic distortional buckling moment determined in accordance with Section M y is given in Eq

10 Tests of CFS Beams - test summary Total 25 local buckling tests and 24 distortional buckling tests have been completed. Comparison with design methods App P cr (M cr ) P n (M n ) Elastic buckling Yield Global Local Distortional M AISI96 M S136 M NAS M AN M EN M DSM strength 0.6 Local buckling tests Distortional buckling tests µ σ µ σ slenderness M y DSM-Local DSM-Distortional Local buckling tests Distortional buckling tests Introduction and motivation Buckling and the finite strip method Experiments and design of beams Direct Strength Method for Beams and Columns Advocacy and extensions (as time allows) (M y M cr ) 0.5 Direct strength prediction P n = f (P y, P cre, P crd, P crl )? Part 3: DSM columns, more beams!, reliability Input Squash load, P y Euler buckling load, P cre Distortional buckling load, P crd Local buckling load, P crl Output Strength, P n

11 Direct Strength design Elastic buckling P n? Elastic buckling Direct Strength Curve (university of sydney testing) strength (F u F y ) or (P u P y ) channel rack rack+lip hat channel+web st. (d) (a) (b) (c) (e) distortional slenderness (F y F cr ).5 or (P y P cr ).5 Columns 267 columns, β = 2.5, φ = 0.84 Lipped channels Lipped zeds Lipped channels with intermediate web stiffener Hat sections Rack post sections Kwon and Hancock (1992), Lau and Hancock (1987), Loughlan (1979), Miller and Peköz (1994), Mulligan (1983), Polyzois et al. (1993), Thomasson (1978)

12 P n =min(p ne,p nl,p nd ) Beams Lipped and plain channels Lipped zeds Hats with and without intermediate stiffener(s) in the flange Trapezoidal decks with and without intermediate stiffener(s) in the web and the flange 569 beams, β=2.5, φ=0.9 Cees and Zeds: Cohen 1987, Ellifritt et al. 1997, LaBoube and Yu 1978, Moreyara 1993, Phung and Yu 1978, Rogers 1995, Schardt and Schrade 1982, Schuster 1992, Shan 1994, Willis and Wallace 1990 Hats and Decks: Acharya 1997, Bernard 1993, Desmond 1977, Höglund 1980, König 1978, Papazian et al Reliability U.S. LRFD format: φr n >Σγ i Q i β t = 2.5 φ φ Beams Columns AISI Specification Specified 0.90 or Data Direct Strength Local Distortional Combined not all members in the data set can be designed by AISI Spec. these members are omitted from the AISI summary statistics Introduction and motivation Buckling and the finite strip method Experiments and design of beams Direct Strength Method for Beams and Columns Advocacy and extensions (as time allows)

13 Direct strength advocacy No effective width, no elements, no iteration Gross properties Element interaction Distortional buckling Wider applicability and scope Encourage cross-section optimization 2004 Supplement at AISI click on publications Your computer performs analysis that employs fundamental mechanics instead of just mimicking old hand calculations. DSM integrates known behavior into a straightforward design procedure. provided examples AISI is sponsoring the creation of a design guide (under development) Plenty of future research needed Potential for DSM in beam-columns optimization your product, made better beam-columns and eccentric loads, (NSF) isolated and patterned perforations, (AISI) significant neutral axis shift in the post-buckling regime, geometric limitations and definition of applicability, fine-tuning and further calibration of strength expressions, interaction of distortional buckling with other modes, shear and shear interaction issues, calibration of new cross-sections. work motivated by Rusch and Lindner (2001)

14 Eccentric axial load Minor axis interaction diagram Major axis interaction diagram Introduction and motivation Buckling and the finite strip method Experiments and design of beams Direct Strength Method for Beams and Columns Advocacy and extensions (as time allows) Concluding thoughts Direct Strength Method Price: Careful calculation of member buckling Reward: No effective width, no iteration, Simple strength equations for all limit states, Optimization potential... The method is on the street, please think about using it! More tools to ease the use are coming. Resources Research Finite strip Direct Strength Appendix 1: Direct Strength Method click on publications get the 2004 Supplement to the North American Specification for CFS...