Coming Soon:A Simpler, Faster, Cold-Formed Steel Design

(The Direct Strength Method)

ASCE-SEI Structures CongressMay 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• 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

Mechanics / elastic buckling

Direct strength curves

www.ce.jhu.edu/bschafer/cufsm

finite strip resource

My=192 kip-in.

Local buckling

Distortional

Lateral-torsional

Direct strength predictionPn = 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)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.2

0.4

0.6

0.8

1

channelrackrack+liphatchannel+web st.

distortional slenderness (Fy/Fcr).5 or (Py/Pcr)

.5

stre

ngth

(Fu/

Fy)

or (

Pu/

Py)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.2

0.4

0.6

0.8

1

channelrackrack+liphatchannel+web st.

distortional slenderness (Fy/Fcr).5 or (Py/Pcr)

.5

stre

ngth

(Fu/

Fy)

or (

Pu/

Py)

(a) (b) (c)(d)

(e)

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, Moreyara1993, 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 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.

Finite Strip (CUFSM)