Direct Strength Prediction of Cold-Formed Steel Beam-Columns Y. Shifferaw, B.W. Schafer Research Progress Report to MBMA February 2012

Origins of a different approach Steel beam-column design (hot-rolled and cold-formed) traditionally follows an interaction equation approach. The origins of which can be traced back to the much beloved engineering solution to stress in a beam:

Origins of a different approach (cont.) First yield ( for section symmetric about axis of bending ) follows this linear interaction: but, basically nothing else! In CFS design it is presumed that first yield may be replaced by nominal capacity: For CFS recall that these capacities are determined from relatively complex calculations, that we may summarize as.. P y and M y might behave, but what about all these cr s, local, distortional and global buckling??

Traditional CFS interaction approach (locally slender example) MnMn M crl MyMy PnPn P crl PyPy

Lets fire up my favorite tool and explore what stability does under the more complex demands of a beam column

CUFSM

Approx. 8 ZS 225 x 065 (55ksi)

Axial only

Stability under axial only

Restrained bending only

Stability under bending only

Reference stress 0.25P y,0.75M y 0.25P y 0.75M y Applied as reference loads 1/3 P/M ratio…

Comparing stability solutions Stability does not follow the linear interaction, can be better, worse or same…

P,Mxx,Mzz all at the same time! +0.25M ZZy -0.25M ZZy

Origins of a different approach (cont.) Conclusion from this little FSM study is that elastic buckling is dependent on cross-section and on applied demands (P, M x, M z ) in a nonlinear fashion. Cross-section stability analysis which picks up this dependency is available. Standard interaction approach is limited and can not take advantage of situations when stability is favorable, instead always assumes a worst case linear reduction…

Traditional CFS interaction approach (locally slender example) MnMn M crl MyMy PnPn P crl PyPy Revisited

CFS interaction (locally slender example) MnMn M crl MyMy PnPn P crl PyPy unsymmetric bending axis..

CFS interaction (locally slender example) MnMn M crl MyMy PnPn P crl PyPy unsymmetric bending axis.. How to generalize formulation to take advantage of this, is the research!

Research Proposal goes back to 2008, solicited from AISI 2011 MBMA partnered with AISI to help fund the first year of the work Research is now underway Long term potential is greater than CFS, but with DSM in AISI-S100 it is the logical starting place

Current Progress

Year 2-3 work (if funded)

Current Progress

Industry assistance ADTEK (Jeffrey Klaiman), NUCON 1 (Rick Haws, Anwar Merchant & Bao Pham), MESCO (Harley Davidson), BUTLER (Al Harrold and Frederico Bueno) ALPINE (Tamil Samiappan and Bill Babich). and MBMA (Lee Shoemaker) AISI (Jay Larson) 1. R.I.P.

Selecting industry relevant beam-columns Truss

Selecting industry relevant beam-columns CFS Framing Model buildings from Devco (CFS-NEES) Adtek Nucon CFS-NEES building

Selecting industry relevant beam-columns Metal building

Focus on Secondary (CFS) members Like eave strut..and of course purlins and girts

Enjoying learning integrated building design

d=1.079 t=0.068 M onlyP+M Identifying key beam-columns…

W( 1.0D+0.750L) P=( f(0.750WPA2)) LC30=1.0D+0.750L+0.750WPA2 Continuous Eave strut design example

Current Progress

Preliminary formulation MnMn M crl MyMy PnPn P crl PyPy Demands set the P r /M r ratio of interest, which is the slope of this line! n crl y

Preliminary formulation (2) For local buckling of a stub section, P or M simply replaced by ! y

Automating CUFSM (P+Mx)

Automating CUFSM (P+Mz)

Current Progress

Selecting industry relevant beam-columns CFS Framing Model buildings from Devco (CFS-NEES) Adtek Nucon CFS-NEES building

Focusing on most efficient sections Most efficient P n /A M n /A All CFS framing members

Selection based on predicted limit states Local only! Distortional only! Axial local Bending dist. Axial dist Bending local Axial local Bending yield Axial dist Bending yield Focus is here in the limited year one work, expansion to more complicated cases in years 2 and 3 if funded Color indicates an efficient section

Modeling Nonlinear shell FE models of imperfect CFS member End displacements over desired P, M x, M y Boundary conditions and lengths to isolate local and distortional buckling Preliminary models completed with success

P-M major, distortional, C section

P-M minor, distortional, C section

Local DSM vs minor axis strength bounds for C Potential!

Current Progress

Related Recent Testing (Setup)

Related Recent Testing (Demands)

Related Recent Testing (Results)

Testing Plan is for paired specimens to remove global modes and focus on local and distortional modes End fixtures to be pinned about axis of bending to provide controlled boundary conditions Will spread out horizontal load to create constant moment region (as opposed to single point load) Will create end and load fixtures that can be oriented at an angle so that biaxial bending + compression explored on the members Bracing/sheathing will be used to remove distortional buckling for local buckling tests Focused on lipped channels at this stage as providing sufficient initial exploration of the P+M space, a topic for discussion though.. Drawings complete, end fixtures under fabrication in the coming weeks – larger testing rig already in place

Wrapup Modestly behind, but good progress being made. Test results by the summer; hopeful that funding for years 2 and 3 can be secured.