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

Extending Direct Strength Design to Cold-Formed Steel Beamswith Holes Cris Moen, Virginia Tech Ben Schafer, Johns Hopkins University 20th International Specialty Conference on Cold-Formed Steel Structures Wednesday, November 3, 2010 St. Louis, MO

Outline • Direct Strength methodology • Elastic buckling (including holes!) • DSM design expressions ( considering holes!) • Global buckling • Local buckling • Distortional buckling • Validation • DSM (Holes) example • Conclusions and future work

Direct Strength methodology • The basic idea… use elastic buckling properties and the beam yield moment topredict capacity Elastic buckling moments • Mcrl, Mcrd, Mcre Beam yield moment • My Distortional buckling failure Picture - Yu, C., and Schafer, B.W. "Distortional buckling tests on cold-formed steel beams", ASCE Journal of Structural Engineering, 132(4), 2006, 515-528.

for beamswith holes Direct Strength methodology including holes • The basic idea… use elastic buckling properties and the beam yield moment topredict capacity including holes Elastic buckling moments • Mcrl, Mcrd, Mcre Unstiffened holes decrease distortional buckling capacity Beam yield moment • My Limit capacity to net section • Mynet

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. Local buckling – finite strip and classical plate approximations Global buckling– “weighted average” approach Holes decrease bending and torsional stiffness Distortional buckling– finite strip Assume local buckling dominates at a hole or between holes Reduce web thickness to simulate reduced web bending stiffness

Global buckling Use simplified methods or thin shell FE to calculate…

Local-global buckling interaction Limit capacity to the net section Use simplified methods or thin shell FE to calculate…

Distortional Buckling Limit capacity to the net section transition through inelastic buckling regime Use simplified methods or thin shell FE to calculate…

Distortional Buckling Holes decrease flexural capacity by 8%. Mynet/My=0.90 No holes

DSM Holes Validation • Beam test database: • SSMA sections, 204 simulations (laterally braced) • Compare tests to DSM Holes predictions: LRFD resistance factor f calculated with AISI Chapter F approach

DSM Holes Validation • Existing test data (unstiffened holes): Shan, M.Y., and LaBoube, R.A. "Behavior of Web Elements With Openings Subjected to Bending, Shear, and the Combination of Bending and Shear", Civil Engineering Study 94-2, Cold-formed Steel Series, University of Missouri-Rolla, Rolla, 1994. Small holes, only local buckling considered… • Recent experiments (unstiffened holes): Soroori Rad, B.H.T. (2010). "Experiments on Cold-Formed Steel Beams with Holes," M.S. Thesis, Virginia Tech, Blacksburg. Schudlich, A., von der Heyden, A., Moen, C.D. (2011) “Distortional buckling of cold-formed steel joists with unstiffened holes,” Sixth International Conference on Thin-Walled Structures, Timisoara, Romania. L, D, and G considered… Focused on distortional buckling… We are slowly building an experimental database. Tests on CFS beams with stiffened holes are coming soon…

Design Example Laterally braced… SSMA 550S162-33 joist with typical slotted holes All example files (CUFSM, Mathcad) are available at www.moen.cee.vt.edu

Local Buckling • Mcrl=min(Mcrlnh, Mcrlh) Local buckling between holes

Local Buckling • Mcrl=min(Mcrlnh, Mcrlh) Local buckling at a hole

Local Buckling Local buckling at a hole controls. • Mcrl=min(17.5 kip-in., 10.5 kip-in.) Local buckling dominates at the holes…

Distortional Buckling Unstiffened holes decrease Mcrd

Design Summary • My=29.1 kip-in. • Mynet=29.0 kip-in. • Mne=29.0 kip-in. (29.1 kip-in.) • Mnl=17.5 kip-in. (20.1 kip-in.) • Mnd=19.4 kip-in. (21.9 kip-in.) Holes have minimal effect on yield moment. Holes No holes Local buckling at a hole controls flexural capacity… The DSM prediction is contrary to AISI-S100-07 Section B2.4 which allows holes with dh/h<0.38 to be ignored when calculating flexural capacity.

Conclusions and future work • Elastic buckling infrastructure and DSM design expressions are ready for implementation • DSM for beams with holes coming soon • DSM for columns with holes – AISI ballot • DSM for members with stiffened holes – coming soon Publications on theirway… Moen, C. D., and Schafer, B. W. (In Press). "Direct Strength Method for the Design of Cold-Formed Steel Columns with Holes." ASCE Journal of Structural Engineering. Moen, C. D., and Schafer, B. W. (In Preparation). "Direct Strength Method for the Design of Cold-Formed Steel Beams with Holes." ASCE Journal of Structural Engineering. Grey, C., Moen, C. D., and Yu, C. (2011). ”Elastic buckling simplified methods for cold-formed steel columns and beams with stiffened holes.” SSRC Annual Conference, Pittsburg, PA.

Thanks for your attention! DSM Holes design example: SSMA 550S162-33 joist with slotted holesis available at: www.moen.cee.vt.edu Mechanics Strength prediction of CFS members with holes

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