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Introduction to Elastic Buckling CUFSM and the Direct Strength Method

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Title: Introduction to Elastic Buckling CUFSM and the Direct Strength Method


1
Introduction 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

2
Acknowledgments
  • American Iron and Steel Institute
  • Structural Stud Manufacturers Association
  • Metal Building Manufacturers Association
  • National Science Foundation
  • Cornell University
  • Johns Hopkins University

3
Acknowledgments
  • 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

5
The Stud
and that is just for local buckling...
6
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

7
Rinchen (1998) - Australia
Kesti (2000) - Finland
Landolfo and Mazzolani (1990) - Italy
8
Specification 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

9
Specification 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

10
Plate vs. cross-section buckling
fcr
11
Why cross-section buckling? (element interaction)
f1
beam
k
f2
column
web height/flange width
12
How 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

13
Modeling a CFS member
14
Finite Strip Analysis
15
CUFSM(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

16
My192 kip-in.
17
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18
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19
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20
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21
Local buckling
22
Distortional
23
Lateral-torsional
24
typical modes in a thin-walled beam
FSM ?
Mcr
Lcr
25
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26
http//www.arch.mcgill.ca/prof/mellin/arch671/wint
er2004/student/Morris/pics/A2-black-box-pic-2.jpg
27
http//www.arch.mcgill.ca/prof/mellin/arch671/wint
er2004/student/Morris/pics/A2-black-box-pic-2.jpg
28
  • Conclusions from part 1?

29
Current design
k? be?
30
Direct 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

33
Cross-section buckling of a typical beam
Mcr
Lcr
34
Direct 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

35
Pcr (Mcr) ? Pn (Mn)
36
Motivation 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.

37
Tests of CFS Beams Local Buckling (Phase 1)
25 tests...
38
Tests of CFS Beams- range of specimens
Z-section
C-section
Tested industry standard CFS Z and C-sections
39
Tests of CFS Beams- panel fastener configuration
for Phase 1 tests
local buckling
Panel fastener configuration
40
continuous spring analysis (FSM)
41
fe (elastic) model to develop detail
42
distortional predicted as lowest
eigenmode(single screw pattern, t0.073 in.)
panels removed for visual purposes only
43
local predicted as lowest eigenmode (paired
screw pattern, t0.073 in.)
panels removed for visual purposes only
44
influence of details
8.5Z073-5E6W
8.5Z073-4E3W
45
Tests of CFS Beams- distortional buckling tests
on CFS beams (Phase 2)
Total 24 beams, 1.5 years to complete
Distortional buckling shape
46
Tests 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
?
47
Tests 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

49
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50
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51
Mne
X
MneMy in our case
52
Mnl
53
Mnd
54
Tests of CFS Beams - test summary
  • Total 25 local buckling tests and 24
    distortional buckling tests have been
    completed.

Comparison with design methods
App1
55
Pcr (Mcr) ? Pn (Mn)
56
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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

59
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

60
Direct Strength design
Pn?
61
Elastic buckling
62
Elastic buckling
63
Direct Strength Curve(university of sydney
testing)
64
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)
65
267 columns , b 2.5, f 0.84
66
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67
Pnmin(Pne,Pnl,Pnd)
68
Beams
  • 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

69
569 beams, b2.5, f0.9
70
Reliability
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

72
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.
73
  • Introduction and motivation
  • Buckling and the finite strip method
  • Experiments and design of beams
  • Direct Strength Method for Beams and Columns
  • Advocacy

74
Concluding 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....
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