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) –isolated plates with holes –studies on effective width –SSMA structural stud with hole (initial study) Conclusions task group

Perforation patterns in CFS next?

Objective Development of a general design method for cold-formed steel members with perforations. Direct Strength Method Extensions P n = f (P y, P cre, P crd, P cr )? 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,  = 2.5,  = 0.84

Progress Report 1 Highlight DSM prediction* for stub columns with holes mean test-to-predicted = 1.04 standard deviation = 0.16 *P cr by FE reflects test boundary conditions, minimum D mode selected, P y =P y,g

Progress Report 1 Highlight Global buckling in long columns with holes mean test-to-predicted = 1.14 standard deviation = 0.09

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) –isolated plates with holes –studies on effective width –SSMA structural stud with hole (initial study) Conclusions task group

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)

Influence of multiple holes models compared at equal numbers of DOF Fixed length plate, vary spacing and quantity of holes (note clear space between holes = S – L hole )

Influence of multiple holes

Comparison of findings on spacing Elastic buckling study: S/L hole > 5 implies S > 5L hole and S clear > 4L hole S end > 2.5L hole and S clear-end > 2L hole Old D4 rules on holes... S > 24 in. S clear-end > 10 in. L hole < 4.5 in. implies S > 5.3L hole S clear-end > 2.2L hole old rules look reasonable, but we need to non-dimensionalize

Critical buckling stress equation for S/L hole > 5

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) –isolated plates with holes –studies on effective width –SSMA structural stud with hole (initial study) Conclusions task group

Flange holes in SSMA studs (Western States Clay Products Association Design Guide for Anchored Brick Veneer over Steel Studs)

Flange holes and elastic buckling 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 Keep b hole /b < 0.5 in this study to avoid problems

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) –isolated plates with holes –studies on effective width –SSMA structural stud with hole (initial study) Conclusions task group

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 Simply supported plates (task group only..)

Modified Riks Solution (task group only..)

Artificial Damping Solution (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 mapped to plate with slotted hole fundamental buckling mode of plate initial geometric imperfections (task group only..)

Imperfections and strength Plate WITHOUT a hole (task group only..)

Imperfections and strength Plate WITH a hole (task group only..)

Plate strength summary (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) –isolated plates with holes –studies on effective width –SSMA structural stud with hole (initial study) Conclusions task group

Simply supported plate models SS     fundamental buckling mode mapped to plate with slotted hole fundamental buckling mode of plate initial geometric imperfections

Effective width – basic concepts

Effective width Plate WITHOUT hole

Effective Width Plate WITH hole

Through thickness stresses in a plate

Through thickness stress variation A A A

Through thickness effective width Top of Plate Middle of Plate Bottom of Plate

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) –isolated plates with holes –studies on effective width –SSMA structural stud with hole (initial study) Conclusions task group

SSMA Structural Stud – Ultimate Strength (362S162-33) Also modeled – fixed-fixed end conditions No warping allowed at member ends!

Elastic Buckling Modes Pinned-pinned shown ( fixed-fixed similar)

Influence of hole and end conditions on strength baseline response: initial imperfections not considered here

SSMA stud failure mechanisms 33 ksi yield stress Fixed ends P u =0.77P y,g Fixed ends with hole P u =0.61P y,g Pinned ends P u =0.64P y,g Pinned ends with hole P u =0.53P y,g Yielding occurs only at the hole Yielding occurs in the web, flange, and lip stiffener

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/L hole >5, S end /L hole >2.5 to avoid interaction –Flange holes: b hole /b < 0.5 to avoid reduced P cr 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 post- buckling capacity and some concern with using DSM local buckling curve for members with holes.

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 What’s Next?