Extending Direct Strength Design to Cold-Formed Steel Columns with Holes Cris Moen, Virginia Tech Ben Schafer, Johns

Extending Direct Strength Design to Cold-Formed Steel Columns with Holes Cris Moen, Virginia Tech Ben Schafer, Johns Hopkins University Structural Stability Research Council Annual Conference Thursday, May 13, 2010 Orlando, FL

Outline • Direct Strength methodology • Elastic buckling (including holes!) • DSM design expressions ( considering holes!) • Nonlinear finite element modeling • Distortional buckling study • Local-global buckling interaction study • DSM (Holes) validation • Conclusions and future work

Direct Strength methodology • The basic idea… use elastic buckling properties and the column squash load to predict capacity Elastic buckling loads • Pcrl, Pcrd, Pcre Column squash load • Py

for columns with holes Direct Strength methodology including holes • The basic idea… use elastic buckling properties and the column squash load to predict capacity including holes Elastic buckling loads • Pcrl, Pcrd, Pcre Column squash load • Py Limit capacity to net section • Pynet

Elastic Buckling (with holes) Moen, C. D., and Schafer, B. W. (2009). "Elastic buckling of thin plates with holes in compression or bending." Thin-Walled Structures, 47(12), 1597-1607. Moen, C. D., and Schafer, B. W. (2009). "Elastic buckling of cold-formed steel columns and beams with holes." Engineering Structures, 31(12), 2812-2824. Global buckling– “weighted average” approach Calculation example at www.moen.cee.vt.edu Local buckling – finite strip and classical plate approximations Distortional buckling– finite strip and classical plate approximations

DSM Design Expressions • How do holes affect CFS column capacity in the inelastic buckling regime? We used nonlinear finite element modeling to explore.

Nonlinear FE Modeling Protocol • We took great care (and about 2.5 years) to develop reliable simulation capabilities considering: • -Solution algorithms (e.g., arc length..) • -Initial geometric imperfections-Metal plasticity-Boundary conditions-Hole geometry • -Manufacturing residual stresses\plastic strains The protocol was validated with experimental results: Moen, C. D., and Schafer, B. W. (2008). "Experiments on cold-formed steel columns with holes." Thin-Walled Structures, 46, 1164-1182.

Nonlinear FE Modeling Protocol Mesh density, Riks Method, artificial damping, isotropic hardening…. Schafer, B. W., Li, Z., and Moen, C. D. (2010). "Computational Modeling of Cold-Formed Steel." Thin-Walled Structures, (In Press) Moen, C. D. (2008). "Direct Strength Design for Cold-Formed Steel Members with Perforations," Ph.D. Thesis, Johns Hopkins University, Baltimore. Incorporating the cold work of forming effect into simulations (and design): Moen, C. D., Igusa, T., and Schafer, B. W. (2008). "Prediction of Residual Stresses and Strains in Cold-Formed Steel Members." Thin-Walled Structures, 46(11), 1274-1289. Gao, T., and Moen, C. D. (2010). "The cold work of forming effect in structural steel members." International Colloquium, Stability and Ductility of Steel Structures, Rio de Janeiro, Brazil.

Distortional Buckling • Studied a group of lipped C-section columns predisposed to a distortional buckling failure. • 20 SSMA cross-sections • Two hole diameters: 60% and 80% of cross-sectional area

Distortional Buckling ld1 ld2

Distortional Buckling Net section strength cap transition through inelastic buckling regime

Local-global buckling interaction • Global buckling only: • Local-global buckling interaction: 18 C-section columns Higher sheet thickness to limit local bucklingHole diameter: 80% and 90% of gross area lc ranges between 0.3 and 3.6 Hole spacing vary from 8 in. to 22 in. 11 C-section columns Hole diameter: 65% and 80% of gross area ll ranges between 0.3 and 3.0 Hole spacing vary from 12 in. to 17 in.

Global buckling This study: Pynet/Py=0.80 Strength trend toward Pynet cap Pcre (including holes) is performing well as strength predictor

Local-global buckling interaction Lots of possibilities: (1) lc low,ll low, (2) lc high,ll high, (3) lc low,ll high (1) (2) Pcre (including holes) is performing well as strength predictor (3)

Local-global buckling interaction Global buckling Local buckling Pynet cap when both local and global slenderness are low

DSM Holes Validation • Constructed column test database: • -78 existing column experiments from the past 30 years • -385 column simulations (performed with modeling protocol) • Compare tests to DSM predictions: Simulations Experiments LRFD resistance factor f calculated with AISI Chapter F approach (1st order second moment reliability approximation)

Conclusions and future work • Elastic buckling infrastructure and DSM design expressions are ready for implementation • DSM for beams with holes coming soon • DSM for members with stiffened holes – work is underway Journal article is on its way… Moen, C. D., and Schafer, B. W. (Submitted). "Direct Strength Method for the Design of Cold-Formed Steel Columns with Holes." ASCE Journal of Structural Engineering.

Thanks for your attention! DSM Holes design example: SSMA 550S162-33 structural stud with slotted holesis available at: www.moen.cee.vt.edu

Preliminary validation Moen, C. D., Schafer, B.W. (2006). "Direct strength design for cold-formed steel members with perforations, Progress Report #1." American Iron and Steel Institute, Washington, D.C. Employed thin shell finite element eigen-buckling analysis to calculate Pcrl, Pcrd, and Pcre including holes and experimental boundary conditions. We convinced ourselves that using elastic buckling properties including holes was a viable approach.

Extending Direct Strength Design to Cold-Formed Steel Columns with Holes Cris Moen, Virginia Tech Ben Schafer, Johns