Direct Strength Design for Cold-Formed Steel Members with Perforations Progress Report 1 C. Moen and B.W. Schafer AISI-COS Meeting February 21, 2006

Outline Objective and challenges Project overview FE stability studies –fundamentals, plates and members with holes Modal identification and c FSM Existing experimental column data –elastic buckling studies: hole effect, boundary conditions –strength prediction by preliminary DSM stub columns, long columns Conclusions

Objective Development of a general design method for cold-formed steel members with perforations.

Direct strength for members with holes 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?

Project Update Originally proposed as a three year project. Year 1 funding was provided, we are currently ½ way through year 1. Project years 1: Benefiting from existing data 2: Identifying modes and extending data 3: Experimental validation & software

Outline Objective and challenges Project overview FE stability studies –fundamentals, plates and members with holes Modal identification and c FSM Existing experimental column data –elastic buckling studies: hole effect, boundary conditions –strength prediction by preliminary DSM stub columns, long columns Conclusions

Local plate stability with a hole 4w

SSMAS w/ hole Member Study L = 1220mm = 48 in.

Local (L) buckling P cr no hole = 0.28P y, with hole = 0.28P y

Distortional (D) buckling P crd no hole = 0.64P y, with hole = 0.65P y

Global flexural torsional (GFT) buckling P crd no hole = 0.61P y, with hole = 0.61P y

Distortional (DH) buckling around the hole P crd no hole = 0.64P y, with hole = 0.307P y

Hole size* and member buckling modes *this graph depicts effect of a circular hole, not the ‘SSMA’ oval hole

Modal identification Mixing of modes (a) complicates the engineer/analyst work (b) may point to post-buckling complications We need an unambiguous way to identify the buckling modes A significant future goal of this research is the extension of newly developed modal identification tools to members with holes

c FSM and modal decomposition

c FSM and modal identification

Outline Objective and challenges Project overview FE stability studies –fundamentals, plates and members with holes Modal identification and c FSM Existing experimental column data –elastic buckling studies: hole effect, boundary conditions –strength prediction by preliminary DSM stub columns, long columns Conclusions

Study of experimentally tested members Collection of experimental column data Estimation of elastic buckling P cr, P crd, P cre using FE to capture influence of hole and reflect test boundary conditions Examination of initial DSM strength predictions for tested sections

Elastic local buckling in stub columns increasing hole size P cr,no hole = pin free- to-warp boundary conditions

Boundary condition effect: local buckling

Distortional buckling (effect of holes) (stub column data) identification of D modes can be challenging, minimum D mode = “DH” mode

Stub column testing restrains distortional buckling

Global buckling in long columns (effect of holes) Effect of holes on global buckling modes greater than anticipated, still under study...

Preliminary DSM for stub columns Local strength Distortional strength P ne set to P y ? P y,net P y,gross ? P y,net P y,gross lowest local mode in an FE model with hole and test boundary conditions lowest distortional mode (includes DH) in an FE model w/ hole and test bc’s ? P y,net P y,gross ? P y,net P y,gross

DSM prediction for stub columns mean test-to-predicted = 1.18 standard deviation = 0.16 *P cr by FE reflects test boundary conditions, minimum D mode selected, P y =P y,net NET quite a few specimens have strength greater than P y,net

DSM prediction* for stub columns 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 GROSS

Preliminary DSM for long columns Global buckling Local buckling Distortional buckling

Global buckling in long columns

Local-global in long columns

Preliminary DSM for long columns member length/web depth (L/H)

Conclusions We are off and running on columns with holes Local buckling (a) doesn’t really follow unstiffened element approximation (at least for elastic buckling) (b) should be modeled consistent with application, i.e., stub column boundary conditions, no square plates Distortional buckling is even more of a mess than usual as it appears to get mixed with local buckling, particularly around hole locations. What does P crd  P cr imply? We need better modal identification tools! Global buckling needs further study, P cre sensitivity to isolated holes here is a bit surprising DSM (preliminary) based on gross section yield instead of net section yield has the best accuracy, what does this imply? The boundary conditions of the test and the hole should be explicitly modeled for finding P cr. Existing data does not cover distortional buckling well. We need additional experimental work and nonlinear FE modeling!