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: Pr + M r y = f
A
I
Pr
Mr
+
£1
Afy (I / c) fy
Pr M r
+
£1
Py M y
Origins of a different approach (cont.)
• First yield (for section symmetric about axis of bending)
follows this linear interaction: Pr + M r £1
Py M y
but, basically nothing else!
• In CFS design it is presumed that first yield
may be replaced by nominal capacity:
Pr M r
CFS recall that these capacities are determined from
+
£ 1 For
relatively complex calculations, that we may summarize as..
Pn M n
Pr
Mr
+
£1
Pn = f (Py , Pcr , Pcrd , Pcre ) M n = g(M y , M cr , M crd , M cre )
Py and My might behave, but what about all these
“cr”’s, local, distortional and global buckling??
Traditional CFS interaction approach
(locally slender example)
Py
Pn
Pcrl
Mn My
Mcrl
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
0.25Py Applied as reference
0.75My loads 1/3 P/M ratio…
Comparing stability solutions
P ref
Py
0.25Py
0.25P y
0
M XXref
0
0.75My
0.75M y
My
M ZZref
0
0
0
0
l
0.19
0.81
0.60
1.02
ld
0.84
0.43
0.69
0.30
l e (100 in.)
0.27
0.50
0.51
0.58
if linear
actual
Stability does not follow the linear interaction, can be better, worse or same…
P,Mxx,Mzz all at the same time!
+0.25MZZy
P ref
Py
0.25P y
0.25P y
0.25P y
0
M XXref
0
0.75M y
0.75M y
0.75M y
My
M ZZref
0
0
+0.25My(ZZ)
-0.25My(ZZ)
0
l
0.19
0.60
0.60
0.60
1.02
-0.25MZZy
ld
0.84
0.69
0.61
0.79
0.30
l e (100 in.)
0.27
0.51
0.47
0.56
0.58
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)
Revisited
Py
Pn
Pcrl
Mn My
Mcrl
CFS interaction
(locally slender example)
unsymmetric bending axis..
Py
Pn
Pcrl
Mn My
Mcrl
CFS interaction
(locally slender example)
unsymmetric bending axis..
Py
Pn
Pcrl
Mn My
Mcrl
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
Year 1
Su Fa
1. Industry survey on beam-columns in applications
a. Survey industry (metal buildings, racks, metal studs, truss, etc.)
b. Write a brief “summary of the practice” document
2. Development of enabling tools for preliminary studies
a. Develop extensions to elastic stability analysis via finite strip analysis (CUFSM)
b. Develop a preliminary, explicit, DSM beam-column formulation
c. Automate AISI-S100-07 traditional beam-column strength prediction
3. Preliminary studies for identifying targeted CFS beam-columns
a. Identify ~ 5 industry standard and 5 common/archteypical CFS beam-columns
b.,c. Use task 2 tools to find regions of predicted beneficial strength gain
4. Development and shakedown of testing program
a. Develop nonlinear FEA collapse models of members to be studied
b.,c. Detail and acquire testing fixtures, perform shakedown testing
5. Phase 1 Experimental Examination of targeted CFS Beam-Columns
a. Develop testing matrix (approximately 30 total tests)
b.-d. Perform tests to collapse, post-process, write test report
e. Examine comparison to predictions
6. Nonlinear FEA and Parametric studies for Strength and Sensitivities
a. Examine members in each of the limit states, local, distortional, global,
b.-e. Examine members with large neutral axis shift, modal interactions, other issues
f.
Provide strength predictions for a wider class of members
7. Phase 2 Experimental Testing to Expand Validation Base
a. Develop phase 2 testing matrix (expand database, explore specific issues)
b.,c. Perform testing, condensation of data, and test report
8. Development of design provisions and outreach
a.-d. Finalize DSM expressions and provide reliability
f.
Write provisions in specification language with commentary,
g.,h. Design examples and industry specific benefit to strength guidance
Sp
Year 2
Su Fa
Sp
Year 3
Su Fa
Sp
Current Progress
Year 1
Su Fa
Sp
%comp
1. Industry survey on beam-columns in applications
a. Survey industry (metal buildings, racks, metal studs, truss, etc.)
b. Write a brief “summary of the practice” document
100%
90%
2. Development of enabling tools for preliminary studies
a. Develop extensions to elastic stability analysis via finite strip analysis (CUFSM)
b. Develop a preliminary, explicit, DSM beam-column formulation
c. Automate AISI-S100-07 traditional beam-column strength prediction
55%
75%
0%
3. Preliminary studies for identifying targeted CFS beam-columns
a. Identify ~ 5 industry standard and 5 common/archteypical CFS beam-columns
b.,c. Use task 2 tools to find regions of predicted beneficial strength gain
50%
0%
4. Development and shakedown of testing program
a. Develop nonlinear FEA collapse models of members to be studied
b.,c. Detail and acquire testing fixtures, perform shakedown testing
25%
30%
5. Phase 1 Experimental Examination of targeted CFS Beam-Columns
a. Develop testing matrix (approximately 30 total tests)
b.-d. Perform tests to collapse, post-process, write test report
e. Examine comparison to predictions
15%
0%
0%
Year 2-3 work (if funded)
6. Nonlinear FEA and Parametric studies for Strength and Sensitivities
a. Examine members in each of the limit states, local, distortional, global,
b.-e. Examine members with large neutral axis shift, modal interactions, other issues
f.
Provide strength predictions for a wider class of members
7. Phase 2 Experimental Testing to Expand Validation Base
a. Develop phase 2 testing matrix (expand database, explore specific issues)
b.,c. Perform testing, condensation of data, and test report
8. Development of design provisions and outreach
a.-d. Finalize DSM expressions and provide reliability
f.
Write provisions in specification language with commentary,
g.,h. Design examples and industry specific benefit to strength guidance
Current Progress
Year 1
Su Fa
Sp
%comp
1. Industry survey on beam-columns in applications
a. Survey industry (metal buildings, racks, metal studs, truss, etc.)
b. Write a brief “summary of the practice” document
100%
90%
2. Development of enabling tools for preliminary studies
a. Develop extensions to elastic stability analysis via finite strip analysis (CUFSM)
b. Develop a preliminary, explicit, DSM beam-column formulation
c. Automate AISI-S100-07 traditional beam-column strength prediction
55%
75%
0%
3. Preliminary studies for identifying targeted CFS beam-columns
a. Identify ~ 5 industry standard and 5 common/archteypical CFS beam-columns
b.,c. Use task 2 tools to find regions of predicted beneficial strength gain
50%
0%
4. Development and shakedown of testing program
a. Develop nonlinear FEA collapse models of members to be studied
b.,c. Detail and acquire testing fixtures, perform shakedown testing
25%
30%
5. Phase 1 Experimental Examination of targeted CFS Beam-Columns
a. Develop testing matrix (approximately 30 total tests)
b.-d. Perform tests to collapse, post-process, write test report
e. Examine comparison to predictions
15%
0%
0%
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-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
Identifying key beam-columns…
0.25
M only
P+M
0.68
0.25
0.68
0.36
0.14
0.94
0.36
0.14
Combined axial and bending stress index
d=1.079”
t=0.068”
Continuous Eave strut design example
LC30=1.0D+0.750L+0.750WPA2
P=( f(0.750WPA2))
Current Progress
Year 1
Su Fa
Sp
%comp
1. Industry survey on beam-columns in applications
a. Survey industry (metal buildings, racks, metal studs, truss, etc.)
b. Write a brief “summary of the practice” document
100%
90%
2. Development of enabling tools for preliminary studies
a. Develop extensions to elastic stability analysis via finite strip analysis (CUFSM)
b. Develop a preliminary, explicit, DSM beam-column formulation
c. Automate AISI-S100-07 traditional beam-column strength prediction
55%
75%
0%
3. Preliminary studies for identifying targeted CFS beam-columns
a. Identify ~ 5 industry standard and 5 common/archteypical CFS beam-columns
b.,c. Use task 2 tools to find regions of predicted beneficial strength gain
50%
0%
4. Development and shakedown of testing program
a. Develop nonlinear FEA collapse models of members to be studied
b.,c. Detail and acquire testing fixtures, perform shakedown testing
25%
30%
5. Phase 1 Experimental Examination of targeted CFS Beam-Columns
a. Develop testing matrix (approximately 30 total tests)
b.-d. Perform tests to collapse, post-process, write test report
e. Examine comparison to predictions
15%
0%
0%
Preliminary formulation
Demands set the
Pr/Mr ratio of interest,
which is the slope of this
line!
Py
Pn
Pcrl
by
bn
bcrl
Mn My
Mcrl
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
Year 1
Su Fa
Sp
%comp
1. Industry survey on beam-columns in applications
a. Survey industry (metal buildings, racks, metal studs, truss, etc.)
b. Write a brief “summary of the practice” document
100%
90%
2. Development of enabling tools for preliminary studies
a. Develop extensions to elastic stability analysis via finite strip analysis (CUFSM)
b. Develop a preliminary, explicit, DSM beam-column formulation
c. Automate AISI-S100-07 traditional beam-column strength prediction
55%
75%
0%
3. Preliminary studies for identifying targeted CFS beam-columns
a. Identify ~ 5 industry standard and 5 common/archteypical CFS beam-columns
b.,c. Use task 2 tools to find regions of predicted beneficial strength gain
50%
0%
4. Development and shakedown of testing program
a. Develop nonlinear FEA collapse models of members to be studied
b.,c. Detail and acquire testing fixtures, perform shakedown testing
25%
30%
5. Phase 1 Experimental Examination of targeted CFS Beam-Columns
a. Develop testing matrix (approximately 30 total tests)
b.-d. Perform tests to collapse, post-process, write test report
e. Examine comparison to predictions
15%
0%
0%
Selecting industry relevant beam-columns
CFS Framing
Model buildings from
• Devco (CFS-NEES)
• Adtek
• Nucon
CFS-NEES building
Focusing on most efficient sections
Pn/A
All CFS
framing
members
Most efficient
Mn/A
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
Axial dist
Bending yield
Axial local
Bending yield
Axial dist
Bending local
Axial local
Bending dist.
Distortional only!
Local only!
Selection based on predicted limit states
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
Potential!
Local DSM vs minor axis strength bounds for C
DSM vs Strength Bounds-362Cloc,minor
1
FE-Loc
DSM anchor pts
0.9
Y ield
Loc cr
0.8
DSM proposed
Interaction
0.7
P/P
y
0.6
0.5
0.4
0.3
0.2
0.1
0
-1.5
-1
-0.5
0
Mz /Mz,y
0.5
1
1.5
Current Progress
Year 1
Su Fa
Sp
%comp
1. Industry survey on beam-columns in applications
a. Survey industry (metal buildings, racks, metal studs, truss, etc.)
b. Write a brief “summary of the practice” document
100%
90%
2. Development of enabling tools for preliminary studies
a. Develop extensions to elastic stability analysis via finite strip analysis (CUFSM)
b. Develop a preliminary, explicit, DSM beam-column formulation
c. Automate AISI-S100-07 traditional beam-column strength prediction
55%
75%
0%
3. Preliminary studies for identifying targeted CFS beam-columns
a. Identify ~ 5 industry standard and 5 common/archteypical CFS beam-columns
b.,c. Use task 2 tools to find regions of predicted beneficial strength gain
50%
0%
4. Development and shakedown of testing program
a. Develop nonlinear FEA collapse models of members to be studied
b.,c. Detail and acquire testing fixtures, perform shakedown testing
25%
30%
5. Phase 1 Experimental Examination of targeted CFS Beam-Columns
a. Develop testing matrix (approximately 30 total tests)
b.-d. Perform tests to collapse, post-process, write test report
e. Examine comparison to predictions
15%
0%
0%
Related Recent Testing (Setup)
Related Recent Testing (Demands)
P, Δ
H
2
He
2
He
H, δ
HL
4
L
He
2
H
2
Loading Idealization
Axial Load
Moment
(drawn on tension side)
Shear Force
Torsion
Related Recent Testing (Results)
30
OO
GO
OG
GG
OB or BO
BB
P axial load (kip)
25
20
15
10
5
0
0
0.5
1
1.5
H horizontal load (kip)
2
2.5
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
Year 1
Su Fa
Sp
%comp
1. Industry survey on beam-columns in applications
a. Survey industry (metal buildings, racks, metal studs, truss, etc.)
b. Write a brief “summary of the practice” document
100%
90%
2. Development of enabling tools for preliminary studies
a. Develop extensions to elastic stability analysis via finite strip analysis (CUFSM)
b. Develop a preliminary, explicit, DSM beam-column formulation
c. Automate AISI-S100-07 traditional beam-column strength prediction
55%
75%
0%
3. Preliminary studies for identifying targeted CFS beam-columns
a. Identify ~ 5 industry standard and 5 common/archteypical CFS beam-columns
b.,c. Use task 2 tools to find regions of predicted beneficial strength gain
50%
0%
4. Development and shakedown of testing program
a. Develop nonlinear FEA collapse models of members to be studied
b.,c. Detail and acquire testing fixtures, perform shakedown testing
25%
30%
5. Phase 1 Experimental Examination of targeted CFS Beam-Columns
a. Develop testing matrix (approximately 30 total tests)
b.-d. Perform tests to collapse, post-process, write test report
e. Examine comparison to predictions
15%
0%
0%
Modestly behind, but good progress being made. Test results by the summer;
hopeful that funding for years 2 and 3 can be secured.