Coming Soon:
A Simpler, Faster, Cold-Formed Steel Design
(The Direct Strength Method)
ASCE-SEI Structures Congress
May 2003
Ben Schafer, Ph.D.
Specification complication
• “Anyone who has ever attempted to design a
light-gage member following the Specification
provisions probably realized how tedious and
complex the process was.”
• “When such [cold-formed] framing is needed one
of two things tend to happen to the engineers:
they either uncritically rely on the suppliers’
literature, or simply avoid any cold-formed
design at all…”
Alexander Newman 1997, in Metal Building Systems
Rinchen (1998) - Australia
Kesti (2000) - Finland
Landolfo and Mazzolani (1990) - Italy
Specification complication explained
• Sections are not doubly-symmetric
• Element elastic buckling calculation (k’s)
• Effective width
– effective width = f(stress,geometry)
– stress = f(effective properties: e.g., Aeff, Ieff)
– iteration results
• Web crippling calculations
• Inclusion of system effects
Specification complication explained
• Sections are not doubly-symmetric
Mechanics
/
elastic
buckling
• Element elastic buckling calculation (k’s)
• Effective width
– effective width = f(stress,geometry)
Direct strength curves
– stress = f(effective properties: e.g., Aeff, Ieff)
– iteration results
• Web crippling calculations
• Inclusion of system effects
www.ce.jhu.edu/bschafer/cufsm
finite strip resource
My=192 kip-in.
Local buckling
Distortional
Lateral-torsional
Direct strength prediction
Pn = f (Py, Pcre, Pcrd, Pcrl)?
• Input
–
–
–
–
Squash load, Py
Euler buckling load, Pcre
Distortional buckling load, Pcrd
Local buckling load, Pcrl
• Output
– Strength, Pn
Elastic buckling
Elastic buckling
Direct Strength Curve
(university of sydney testing)
1
channel
rack
rack+lip
hat
channel+ web st.
strength (Fu/F y) or (Pu /Py )
0.8
0.6
(a)
(b)
(c)
(d)
(e)
0.4
0.2
0
0
0.5
1
1.5
2
2.5
3
3.5
.5
4
.5
distortional slenderness (Fy /Fcr) or (Py /Pcr)
4.5
5
Effective width and direct strength
Columns
•
•
•
•
•
Lipped channels
Lipped zeds
Lipped channels with intermediate web stiffener
Hat sections
Rack post sections
Kwon and Hancock (1992), Lau and Hancock (1987), Loughlan (1979),
Miller and Peköz (1994), Mulligan (1983), Polyzois et al. (1993), Thomasson (1978)
267 columns , β = 2.5, φ = 0.84
Pn=min(Pne,Pnl,Pnd)
Beams
• Lipped and plain channels
• Lipped zeds
• Hats with and without intermediate
stiffener(s) in the flange
• Trapezoidal decks with and without intermediate
stiffener(s) in the web and the flange
Cees and Zeds: Cohen 1987, Ellifritt et al. 1997, LaBoube and Yu 1978, Moreyara
1993, Phung and Yu 1978, Rogers 1995, Schardt and Schrade 1982,
Schuster 1992, Shan 1994, Willis and Wallace 1990
Hats and Decks: Acharya 1997, Bernard 1993, Desmond 1977, Höglund 1980,
König 1978, Papazian et al. 1994
569 beams, β=2.5, φ=0.9
Direct strength advocacy
•
•
•
•
•
•
No effective width, no elements, no iteration
Gross properties
Element interaction
Distortional buckling
Wider applicability and scope
Encourage cross-section optimization
Your computer performs analysis that employs
fundamental mechanics instead of just mimicking old
hand calculations. DSM integrates known behavior
into a straightforward design procedure.
provided examples
Plenty of future research needed
•
•
•
•
•
•
•
•
•
•
beam-columns and eccentric loads,
isolated and patterned perforations,
laterally un-braced flexural members,
significant neutral axis shift in the post-buckling regime,
geometric limitations and definition of applicability,
fine-tuning and further calibration of strength expressions,
interaction of distortional buckling with other modes,
shear and shear interaction issues,
calibration of new cross-sections, and
elastic distortional buckling of all cross-sections.
Concluding thoughts
• DSM represents an opportunity for a new direction
in cold-formed steel design.
• By taking advantage of simple, yet fundamental,
mechanics solutions (member elastic buckling via
finite strip) we have the means to vastly simplify
and at the same time improve design.
• DSM can be used now for unusual sections via the
rational analayis clause in AISI, and will be
adopted as an alternative design procedure in the
next Specification.
Resources
• Research
www.ce.jhu.edu/bschafer
• Finite strip
www.ce.jhu.edu/bschafer/cufsm
• Direct Strength
www.ce.jhu.edu/bschafer/direct_strength
LGSI Z12-25-14g
How does Direct Strength work?
• ELASTIC BUCKLING
– You must determine all relevant elastic buckling
values for your section, e.g., for a column the local,
distortional, and flexural-torsional buckling loads.
• DIRECT STRENGTH CURVES
– Given the elastic buckling loads and the yield load
empirical expressions (e.g., SSRC column curves)
are used to predict the capacity.
How does Direct Strength work?
• ELASTIC BUCKLING
– You must determine all relevant elastic buckling
values forFinite
your section,
for a column the local,
Strip e.g.,
(CUFSM)
distortional, and flexural-torsional buckling loads.
• DIRECT STRENGTH CURVES
– Given the elastic buckling loads and the yield load
empirical expressions (e.g., SSRC column curves)
are used to predict the capacity.