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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/M
z,y
P/P
yDSM vs Strength Bounds-362C
loc,minor
FE-Loc
DSM anchor pts
Yield
Loccr
DSM proposed
Interaction
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.