Direct Strength Design for Cold-Formed Steel Members with Perforations Progress Report 2 C. Moen and B.W. Schafer AISI-COS Meeting August 2006 Outline • Objective and challenges • Project overview • FE elastic stability studies – slotted hole spacing limits – flange holes in SSMA studs • FE strength studies – – – – nonlinear solution methods (ABAQUS) task group isolated plates with holes studies on effective width SSMA structural stud with hole (initial study) • Conclusions Perforation patterns in CFS next? Objective Development of a general design method for cold-formed steel members with perforations. Direct Strength Method Extensions Pn = f (Py, Pcre, Pcrd, Pcrl)? Does f stay the same? Gross or net, or some combination? Explicitly model hole(s)? Accuracy? Efficiency? Identification? Just these modes? DSM for columns no holes 267 columns , b = 2.5, f = 0.84 Progress Report 1 Highlight DSM prediction* for stub columns with holes 1.4 1 D buckling controls L buckling controls DSM Pnl 1.2 0.8 DSM Pnd 0.6 0.8 P test /P y,g 1 0.4 0.6 0.4 0.2 mean test-to-predicted = 1.04 0 standard deviation = 0.16 0.2 0 0 0 0.2 0.5 0.4 1 1.5 0.6 0.8 2 2.5 1 3 (Py,g/Pcrl)0.5,(Py,g/Pcrd)0.5 *P by FE reflects test boundary conditions, minimum D mode selected, P =P Progress Report 1 Highlight Global buckling in long columns with holes 1.4 1 Global buckling controls, P ne=Pnl All Long Column Specimens DSM Pne 1.2 0.8 1 0.6 0.8 Local buckling controls DSM Pnl 0.8 1 ne,g 0.6 0.8 /P test 0.4 0.6 P test P 1 1.2 /P y,g 1.4 0.4 0.6 0.4 0.2 0.2 0.4 0 0.2 0 0 0 0.2 0.5 0.4 1 1.5 0.6 0.8 2 2.5 Slenderness, (P ne/Pcrl)0.5 mean test-to-predicted = 1.14 standard deviation = 0.09 0 0.2 0 0 0 0.2 0.5 0.4 1 1.5 0.6 0.8 2 Slenderness, (P y,g/Pcre)0.5 2.5 1 3 1 3 Project Update • Year 1 of 3 complete • Project years 1: Elastic buckling studies, identifying modes, benefiting from existing data 2: Ultimate strength studies, modal composition, connecting elastic stability to strength 3: Experimental validation & software Outline • Objective and challenges • Project overview • FE elastic stability studies – slotted hole spacing limits – flange holes in SSMA studs • FE strength studies – – – – nonlinear solution methods (ABAQUS) task group isolated plates with holes studies on effective width SSMA structural stud with hole (initial study) • Conclusions Slotted Hole Spacing in Plates • Motivation – Evaluate influence of hole spacing on elastic buckling of plates – Study buckling modes with multiple holes, observe critical buckling stress as hole spacing changes – Provide code-based recommendations on slotted hole spacing Influence of a single hole (benchmark: stiffened plate in compression) 1.2 1 (a) f /f cr,hole cr,no hole 1 (a) 0.8 0.8 (b) hhole/h=0.66 0.6 hhole/h=0.44 0.6 hhole/h=0.19 0.4 (a) L 0.4 0.2 (a) (b) 0 Rhole (b) hhole 0 hhole/h=0.26 Lhole 0.2 0 (b) 0 h 0.2 5 0.4 10 0.6 15 L/Lhole 0.8 1 20 25 Influence of multiple holes S/2 S Lhole h hhole Fixed length plate, vary spacing and quantity of holes (note clear space between holes = S – Lhole) models compared at equal numbers of DOF Influence of multiple holes 1.2 1 1.2 1 1 /f f /f holes cr,holes cr,no cr,holes cr,no holes hhole/h=0.44 0.8 1 f hhole/h=0.66 hhole/h=0.19 0.8 hhole/h=0.26 0.8 0.6 0.9 0.8 0.6 0.6 0.85 0.4 0.6 0.8 0.4 0.4 0.75 0.2 2 0.4 0.2 0.2 0 0.2 0 0 0 0 0 hhole/h=0.66 hhole/h=0.26 5 4 3 S/Lhole Lhole S 0.2 0 0 /h=0.44 h hole Decrease in fcr when hole /h=0.19 hhole small spacing becomes 0.4 h 0.6 hhole 0.8 Simply supported plate (all four sides), S=4Lhole shown 5 0.2 5 0.6 15 100.4 S/Lhole 15 10 S/Lhole 1 0.8 20 125 20 25 Comparison of findings on spacing • Elastic buckling study: Old D4 rules on holes... S/Lhole > 5 implies • S > 24 in. • Sclear-end > 10 in. • S > 5Lhole and • Lhole < 4.5 in. • Sclear > 4Lhole implies • S > 5.3Lhole • Send > 2.5Lhole and • Sclear-end > 2.2Lhole • Sclear-end > 2Lhole old rules look reasonable, but we need to non-dimensionalize Critical buckling stress equation Lhole S S/2 5 hhole 1Data points from eigenbuckling analysis 4.5 4 plate buckling coeff., k h 0.8 3.5 0.6 3 Fitted curve 2.5 2 h h k 6 hole 4 hole 4 4 h h 0.4 2 1.5 for S/Lhole > 5 0.2 1 0.5 0 0 0 0 0.2 0.2 0.4 0.4 0.6 0.6 hhole/h 0.8 0.8 1 1 Outline • Objective and challenges • Project overview • FE elastic stability studies – slotted hole spacing limits – flange holes in SSMA studs • FE strength studies – – – – nonlinear solution methods (ABAQUS) task group isolated plates with holes studies on effective width SSMA structural stud with hole (initial study) • Conclusions Flange holes in SSMA studs (Western States Clay Products Association Design Guide for Anchored Brick Veneer over Steel Studs) Flange holes and elastic buckling B b R L H bhole b t D r ¼”,½”,¾”, 1”, 1¼” dia. holes in a 1⅝” flange (362S162-33) Local buckling (LH mode) caused by large diameter holes Influence of flange holes on elastic buckling modes 1 1 D GFT L LH 0.9 0.8 D, no hole 0.8 0.7 0.6 cr P /P y 0.6 0.5 GFT, no hole 0.4 0.4 0.3 0.2 0.2 0.1 0 0 0 L, no hole 0 0.2 0.2 0.4 0.4 0.6 0.6 LH 0.8 0.8 bhole/b Keep bhole/b < 0.5 in this study to avoid problems 1 1 Outline • Objective and challenges • Project overview • FE elastic stability studies – slotted hole spacing limits – flange holes in SSMA studs • FE strength studies – – – – nonlinear solution methods (ABAQUS) task group isolated plates with holes studies on effective width SSMA structural stud with hole (initial study) • Conclusions Evaluate nonlinear solution methods • Motivation – Gain experience with nonlinear FEM analysis using ABAQUS – Use modified Riks method (arc length or work method) and artificial damping method to predict the strength of a plate with a hole – Explore solution controls and identify areas of future research (task group only..) Loading and boundary conditions P h Simply supported plates (a) Modifed Riks method employed with a uniform compressive load applied to the ends of the plate P h (b) Artificial damping method – employed with uniform longitudinal displacement applied at the member ends (task group only..) Modified Riks Solution 1 RIKS1 RIKS2 0.8 0.6 cannot move past peak load 0.4 P/Py,g 0.2 1 compression 0 tension 2 -0.2 Initial imperfection shape (scale exaggerated) P b -0.4 -0.6 3 -0.8 -1 -2 -1.5 -1 -0.5 0 /t 0.5 1 1.5 P b 2 (task group only..) Artificial Damping Solution 1 0.38 STAB1 STAB2 y,g 0.9 P/P 0.8 0.34 Highly nonlinear post-peak equilibrium path found with STAB1 and STAB2 0.7 0.3 0.25 P/P y,g 0.6 0.3 /t 0.5 0.35 0.4 0.3 0.2 P h Displacement control 0.1 0 Initial imperfection shape (scale exaggerated) P h 0 0.25 0.5 0.75 1 1.25 1.5 1.75 /t (task group only..) Ultimate strength of a plate with a hole • Motivation – Use knowledge gained from solution control study to predict strength and failure modes – What happens at failure when we add a hole? – Study the influence of initial imperfections on strength and load-displacement response (task group only..) Considering initial imperfections fundamental buckling mode of plate initial geometric imperfections fundamental buckling mode mapped to plate with slotted hole (task group only..) Imperfections and strength Plate WITHOUT a hole 1 1 no imperfections d1/t=0.14 0.9 0.8 0.8 d1/t=0.34 Pn=0.58Py,g (DSM Prediction) d1/t=0.66 0.7 0.6 P/P y,g 0.6 d1/t=1.35 d1/t=3.85 0.5 0.4 0.4 0.3 0.2 0.2 0 0.1 0 0 0 0.2 0.25 0.5 0.4 0.75 0.6 1 0.8 1.25 1.5 1 1.75 /t (task group only..) Imperfections and strength Plate WITH a hole 1 1 Pn=0.56Py,g 0.8 0.8 d1/t=0.66 0.6 0.6 y,g d1/t=0.34 Pn=0.38Py,g (DSM Prediction, Pne=Py,net) 0.7 P/P no imperfections d1/t=0.14 (DSM Prediction, Pne=Py,g) 0.9 d1/t=1.35 d1/t=3.85 0.5 0.4 0.4 0.3 0.2 0.2 0 0.1 0 0 0 0.2 0.25 0.5 0.4 0.75 0.6 1 0.8 1.25 1.5 1 1.75 /t (task group only..) Plate strength summary 1 1 plate without hole plate with hole 0.9 without hole 0.8 0.8 Pn=0.58Py,g (DSM Prediction) u P /P y,g 0.7 with hole Pn=0.56Py,g (DSM Prediction, Pne=Py,g) 0.6 0.6 0.5 0.4 * *P(∆<d1)=0.50 0.4 * 0.3 0.2 with hole 0.2 0.1 0 0 0 Pn=0.38Py,g (DSM Prediction, Pne=Py,net) d1 0 0.5 0.2 1 0.4 1.5 2 d1/t 0.6 2.5 0.8 3 1 3.5 4 (task group only..) Outline • Objective and challenges • Project overview • FE elastic stability studies – slotted hole spacing limits – flange holes in SSMA studs • FE strength studies – – – – nonlinear solution methods (ABAQUS) task group isolated plates with holes studies on effective width SSMA structural stud with hole (initial study) • Conclusions Simply supported plate models fundamental buckling mode of plate initial geometric imperfections fundamental buckling mode mapped to plate with slotted hole Effective width – basic concepts distribute area (A) to edges of plate A/2 he/2 h t s11dy thef y calculate area under stress curve (A) h 0 membrane stress (S11) he/2 A/2 yield stress Effective width Plate WITHOUT hole +S11 +S11 Plan view of element Elevation (a) membrane stress in 1 direction (S11) h he/2 (b) variation in effective width along plate effective width average standard deviation max min he/h 0.51 0.02 0.55 0.48 Effective Width Plate WITH hole +S11 +S11 Plan view of element effective width average standard deviation max min Elevation (a) membrane stress in 1 direction (S11) h he/2 (b) variation in effective width along plate he/h 0.38 0.03 0.41 0.34 Through thickness stresses in a plate +S11 +S11 Plan view of element Top Membrane stress Midplane Bottom Elevation view of element Membrane stress Through thickness stress variation A A A Longitudinal (S11) stress variation across width of plate 1 top of plate midplane of plate bottom of plate 0.9 0.8 0.7 x/h 0.6 0.5 Top of plate is fully effective Stress distribution used to calculate code-based effective width 0.4 0.3 Tension and compression stresses counteract each other when calculating effective width at the bottom of the plate 0.2 0.1 Compression 0 -1.5 -1 -0.5 Tension 0 fplate/fy 0.5 SECTION A-A 1 1.5 Through thickness effective width Effective width calculated with longitudinal stresses (S11) at top, midplane, and bottom of the plate Top of Plate Middle of Plate Bottom of Plate ht s11dxdy thef y 00 Outline • Objective and challenges • Project overview • FE elastic stability studies – slotted hole spacing limits – flange holes in SSMA studs • FE strength studies – – – – nonlinear solution methods (ABAQUS) task group isolated plates with holes studies on effective width SSMA structural stud with hole (initial study) • Conclusions SSMA Structural Stud – Ultimate Strength (362S162-33) Centroid restrained in Rigid translational connection to centroid in 1, 2, and 3 (u, v, and w) translation: 2 and 3 (v=w=0) No warping allowed at member ends! rotation: 4, 6 (Θ1=Θ3=0) Rigid translational connection to centroid in 1, 2, and 3 (u, v, and w) Displacement control 2 6 3 5 Pinned End Conditions 4 Centroid restrained in translation: 1, 2, and 3 (u=v=w=0) rotation: 4, 6 (Θ1=Θ3=0) 1 Also modeled – fixed-fixed end conditions Elastic Buckling Modes L Pcrl=0.42Py,g L Pcrl=0.42Py,g L+DH Distortional modes unique to a column with a hole Pcrd1=0.52Py,g DH2 Pcrd2=0.54Py,g D D+L Pcrd=1.15Py,g Pcrd3=1.16Py,g Pinned-pinned shown ( fixed-fixed similar) Influence of hole and end conditions on strength 1 1 0.9 0.8 Fixed ends Pu=0.77Py,g 0.8 0.7 y,g 0.6 P/P Fixed ends with hole Pu=0.61Py,g 0.6 0.5 0.4 Pinned ends Pu=0.64Py,g 0.4 0.3 0.2 0.2 0 0.1 0 0 0 Displacement control 0.2 0.25 0.5 0.4 0.75 Pinned ends with hole Pu=0.53Py,g 0.8 1 0.6 1 1.25 1.5 1.75 /t baseline response: initial imperfections not considered here SSMA stud failure mechanisms Yielding occurs in the web, flange, and lip stiffener Fixed ends Pu=0.77Py,g 33 ksi yield stress Yielding occurs only at the hole Fixed ends with hole Pu=0.61Py,g Pinned ends Pu=0.64Py,g Pinned ends with hole Pu=0.53Py,g Conclusions • Progress report 1 shows – holes create new mixed buckling modes, for web holes this means triggering distortional buckling earlier – DSM style methods are working in an average sense, when reduced elastic buckling for holes is accounted for • New elastic buckling studies show that – Hole spacing: S/Lhole>5 , Send/Lhole>2.5 to avoid interaction – Flange holes: bhole/b < 0.5 to avoid reduced Pcr in SSMA stud • Ultimate Strength of Plates/Members with holes – – – – – Nonlinear FEA is v. sensitive to solution algorithm Net section “revealed” for stocky sections, small imperfections Imperfection sensitivity not markedly increased due to hole Hole impacts “effective width” and through thickness rigidity Yielding patterns with hole are more “like” distortional buckling mechanisms than local mechanisms suggesting reduced postbuckling capacity and some concern with using DSM local buckling curve for members with holes. What’s Next? •Elastic buckling and nonlinear FEM of COLUMNS with holes •Elastic buckling and nonlinear FEM of BEAMS with holes •Modal decomposition of failure modes with GBT •Laboratory testing of intermediate length SSMA studs with holes •Moving closer to a formal connection between elastic buckling and ultimate strength for cold-formed steel members with holes