Direct Strength Prediction of Cold-Formed Steel Beam-Columns

Y. Shifferaw, B.W. SchaferResearch 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 fromrelatively complex calculations, that we may summarize as..

Py and My might behave, but what about all these“cr”’s, local, distortional and global buckling??

Traditional CFS interaction approach(locally slender example)

Mn McrlMy

Pn

Pcrl

Py

Let’s 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 0.25Py,0.75My

0.25Py0.75My

Applied as referenceloads 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!

+0.25MZZy -0.25MZZy

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, Mx, Mz) 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)

Mn McrlMy

Pn

Pcrl

Py

Revisited

CFS interaction(locally slender example)

Mn McrlMy

Pn

Pcrl

Py

unsymmetric bending axis..

CFS interaction(locally slender example)

Mn McrlMy

Pn

Pcrl

Py

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), • NUCON1 (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-columnsTruss

Selecting industry relevant beam-columnsCFS Framing

Model buildings from• Devco (CFS-NEES)• Adtek• Nucon

CFS-NEES building

Selecting industry relevant beam-columnsMetal building

Focus on Secondary (CFS) members

Like eave strut.. and of course purlins and girts

Enjoying learning integrated building design

0.68

0.68

0.94

0.25 0.25

0.14 0.14

0.36 0.36

d=1.079”t=0.068”

Combined axial and bending stress index

M only P+MIdentifying 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

Mn McrlMy

Pn

Pcrl

Py

Demands set thePr/Mr ratio of interest,which is the slope of thisline!

bn

bcrl

by

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

y

Automating CUFSM (P+Mx)

Automating CUFSM (P+Mz)

Current Progress

Selecting industry relevant beam-columnsCFS Framing

Model buildings from• Devco (CFS-NEES)• Adtek• Nucon

CFS-NEES building

Focusing on most efficient sections

Most efficient

Pn/A

Mn/A

All CFSframingmembers

Selection based on predicted limit states

Loca

l onl

y!

Dist

ortio

nal o

nly!

Axia

l loc

alBe

ndin

g di

st.

Axia

l dist

Bend

ing

loca

l

Axia

l loc

alBe

ndin

g yi

eld

Axia

l dist

Bend

ing

yiel

d

Focus is here in the limited year one work,

expansion to more complicated cases in years

2 and 3 if fundedColor indicates an efficient section

Modeling• Nonlinear shell FE

models of imperfect CFS member

• End displacements over desired P, Mx, My

• Boundary conditions and lengths to isolate local and distortional buckling

• Preliminary models completed with success

P-Mmajor, distortional, C section

P-Mminor, distortional, C section

Local DSM vs minor axis strength bounds for C

-1.5 -1 -0.5 0 0.5 1 1.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Mz/Mz,y

P/P

yDSM vs Strength Bounds-362Cloc,minor

FE-LocDSM anchor pts

Yield

Loccr

DSM proposedInteraction

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.