Title: Introduction to Elastic Buckling CUFSM and the Direct Strength Method
1Introduction to Elastic Buckling (CUFSM) and the
Direct Strength Method
- ClarkWestern
- May 2009
- Ben Schafer, Ph.D., P.E.
- Associate Professor and Swirnow Family Faculty
Scholar - Johns Hopkins University
2Acknowledgments
- American Iron and Steel Institute
- Structural Stud Manufacturers Association
- Metal Building Manufacturers Association
- National Science Foundation
- Cornell University
- Johns Hopkins University
3Acknowledgments
- Hopkins Technicians
- Jack Spangler, Jim Kelly, Nickolay Logvinovsky
- Hopkins Grad Students
- Dr. Cheng Yu (UNT), Dr. Cris Moen (VTech), Yared
Shifferaw, Zhanjie Li, Vahid Zeinoddini, Mina
Seif, Luiz Viera - Hopkins Undergraduates
- Sam Phillips, Liakos Ariston, Tom Lydigsen,
Andrew Meyers, Brent Bass,
4- Introduction and motivation
- Buckling and the finite strip method
- Experiments and design of beams
- Direct Strength Method for Beams and Columns
- Advocacy
5The Stud
and that is just for local buckling...
6Specification 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
7Rinchen (1998) - Australia
Kesti (2000) - Finland
Landolfo and Mazzolani (1990) - Italy
8Specification complication explained
- Sections are not doubly-symmetric
- Element elastic buckling calculation (ks)
- Effective width
- effective width f(stress,geometry)
- stress f(effective properties e.g., Aeff,
Ieff) - iteration results
- Web crippling calculations
- Inclusion of system effects
9Specification complication explained
- Sections are not doubly-symmetric
- Element elastic buckling calculation (ks)
- Effective width
- effective width f(stress,geometry)
- stress f(effective properties e.g., Aeff,
Ieff) - iteration results
- Web crippling calculations
- Inclusion of system effects
10Plate vs. cross-section buckling
fcr
11Why cross-section buckling? (element interaction)
f1
beam
k
f2
column
web height/flange width
12How to find cross-section buckling?
- Tables and charts
- essentially limited to two elements
- not widely available
- Finite element solutions
- requires more advanced modeling (plate elements)
- generality of method is great, but complicates
too - not widely available
- Other methods?
- finite element variant called the finite strip
method - free (CUFSM), also available CFS, THINWALL
13Modeling a CFS member
14Finite Strip Analysis
15CUFSM(Cornell University Finite Strip Method)
- Free, open source, software that allows you to
explore the elastic buckling of any cold-formed
steel cross-section using the finite strip method - Mechanics employed are IDENTICAL to the mechanics
used to derive the plate buckling coefficient k
values in current use
16My192 kip-in.
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21Local buckling
22Distortional
23Lateral-torsional
24typical modes in a thin-walled beam
FSM ?
Mcr
Lcr
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26http//www.arch.mcgill.ca/prof/mellin/arch671/wint
er2004/student/Morris/pics/A2-black-box-pic-2.jpg
27http//www.arch.mcgill.ca/prof/mellin/arch671/wint
er2004/student/Morris/pics/A2-black-box-pic-2.jpg
28 29Current design
k? be?
30Direct Strength Design
Mcr? Mn?
31- Introduction and motivation
- Buckling and the finite strip method
- Experiments and design of beams
- Direct Strength Method for Beams and Columns
- Advocacy and extensions (as time allows)
32- Part 2
- DSM and an
- experimental investigation of beams
33Cross-section buckling of a typical beam
Mcr
Lcr
34Direct strength prediction
- Mn f (My, Mcre, Mcrd, Mcrl)?
- Input
- Yield moment, My
- Euler buckling load, Mcre
- Distortional buckling load, Mcrd
- Local buckling load, Mcrl
- Output
- Strength, Mn
35Pcr (Mcr) ? Pn (Mn)
36Motivation for recent experimental research
- Problems
- Current Specifications AISI (1996), S136 (1994),
NAS (2001) do not - have sufficient procedures for the design of
distortional buckling. - The Direct Strength Method (proposed by Schafer
and Peköz 1998) - provides specific strength predictions for
distortional buckling. - Previous tests did not distinguish between local
and distortional buckling. - Existing data is not representative of sections
currently used in practice. - Therefore, two series of bending tests were
performed to study the local - and distortional buckling of CFS beams separately
and analysis was also - performed to develop complete design methods.
37Tests of CFS Beams Local Buckling (Phase 1)
25 tests...
38Tests of CFS Beams- range of specimens
Z-section
C-section
Tested industry standard CFS Z and C-sections
39Tests of CFS Beams- panel fastener configuration
for Phase 1 tests
local buckling
Panel fastener configuration
40continuous spring analysis (FSM)
41fe (elastic) model to develop detail
42distortional predicted as lowest
eigenmode(single screw pattern, t0.073 in.)
panels removed for visual purposes only
43local predicted as lowest eigenmode (paired
screw pattern, t0.073 in.)
panels removed for visual purposes only
44influence of details
8.5Z073-5E6W
8.5Z073-4E3W
45Tests of CFS Beams- distortional buckling tests
on CFS beams (Phase 2)
Total 24 beams, 1.5 years to complete
Distortional buckling shape
46Tests of CFS Beams- comparison of two series of
tests
Test 8.5Z092
P
Local buckling test
Distortional buckling test
99 of NAS01
83 of NAS01
?
Test 8C043
P
Local buckling test
Distortional buckling test
106 of NAS01
90 of NAS01
?
47Tests of CFS Beams - test summary
- Total 25 local buckling tests and 24
distortional buckling tests have been
completed.
Comparison with design methods
App1
48- Application of the Direct Strength Method
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51Mne
X
MneMy in our case
52Mnl
53Mnd
54Tests of CFS Beams - test summary
- Total 25 local buckling tests and 24
distortional buckling tests have been
completed.
Comparison with design methods
App1
55Pcr (Mcr) ? Pn (Mn)
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57- Introduction and motivation
- Buckling and the finite strip method
- Experiments and design of beams
- Direct Strength Method for Beams and Columns
- Advocacy
58- Part 3
- DSM
- columns, more beams!, reliability
59Direct 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
60Direct Strength design
Pn?
61Elastic buckling
62Elastic buckling
63Direct Strength Curve(university of sydney
testing)
64Columns
- 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)
65267 columns , b 2.5, f 0.84
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67Pnmin(Pne,Pnl,Pnd)
68Beams
- Lipped and plain channels
- Lipped zeds
- Hats with and without intermediatestiffener(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
69569 beams, b2.5, f0.9
70Reliability
U.S. LRFD format fRngtSgiQi
bt 2.5
71- Introduction and motivation
- Buckling and the finite strip method
- Experiments and design of beams
- Direct Strength Method for Beams and Columns
- Advocacy
72Direct 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.
73- Introduction and motivation
- Buckling and the finite strip method
- Experiments and design of beams
- Direct Strength Method for Beams and Columns
- Advocacy
74Concluding thoughts
- Direct Strength Method
- Price Careful calculation of member buckling
- Reward No effective width, no iteration,
Simple strength equations for all limit
states,Optimization potential....