The messy world of distortional buckling

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The messy world of distortional buckling and how
DSM helps
Ben Schafer, Ph.D., P.E.
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Overview

• Introduction
• Research
• Distortional buckling
• Restrained distortional buckling
• AISI Design provisions
• CFSEI Design Aid
• Example 1 Table lookup
• Example 2 Table lookup
• Example 3 The whole enchilada

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consider your friend, the floor
http//i240.photobucket.com/albums/ff31/medscntst/
Dscf0148.jpg
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floor joist buckling modes
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Cross-section Instability- distortional buckling
of CFS beams
Mcr
Lcr
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Overview

• Introduction
• Research
• Distortional buckling
• Restrained distortional buckling
• AISI Design provisions
• CFSEI Design Aid
• Example 1 Table lookup
• Example 2 Table lookup
• Example 3 The whole enchilada

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Research background

• Early 80s Cornell research developed a mixed
  local-distortional buckling effective width
  provision (B4 of the AISI Spec.)
• Late 80s early 90s U Sydney research, showed
  problems, and generated a new design method
  (Adopted in Australia, proposed to U.S. in 95)
• Complication 80s Cornell research, and others
  conducted in 90s did not distinguish between
  local and distortional buckling beam failures
• Resolution AISI funded a series of experiments
  and analysis conducted at JHU
• Today AISI-S100-07 adopted distortional buckling
  provisions in C3.1.4 for beams (columns too)

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Tests on CFS beams
Phase 1 tests(Local Buckling)
Phase 2 tests(Distortional Buckling)
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Comparisons
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
?
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Overview

• Introduction
• Research
• Distortional buckling
• Restrained distortional buckling
• AISI Design provisions
• CFSEI Design Aid
• Example 1 Table lookup
• Example 2 Table lookup
• Example 3 The whole enchilada

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Moment Gradient
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Modeling
FE model
Buckled shape
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Mcr boost for distortional buckling
Proposed equation for the MG effect
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Ultimate strength boost?
Moment gradient r 0.5
Moment gradient r 0
Geometric imperfection and material nonlinearity
were considered. 55 industry standard C and
Z-sections were analyzed.
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Verificaton of model parameters
Local buckling test 11.5Z092-1E2W
Distortional buckling test D11.5Z092-3E4W
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Moment Gradient Effect on Distortional Buckling
- for ultimate strength of DB
Moment gradient r 0.5
Moment gradient r 0
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Comparison with predictions
case with no moment gradient(shows model works)
moment gradient present, but ignored in
design(too conservative!)
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Comparison with predictons (cont.)
DSM for DB of CFS beams
MG is included in the elastic buckling moment,
strength prediction is still conservative...
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Restraint from sheeting/sheathing
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Restraint from sheeting/sheathing
f
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Models to account for sheathing
FE result including panel details
8.5Z092 section in bending
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Numerical vs. hand methods
f
1. Finite strip method (CUFSM)
2. Analytical method
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Overview

• Introduction
• Research
• Distortional buckling
• Restrained distortional buckling (in framing)
• AISI Design provisions
• CFSEI Design Aid
• Example 1 Table lookup
• Example 2 Table lookup
• Example 3 The whole enchilada

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Restraint of DB in framing systems
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Restraint of DB in framing systems
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Restraint of DB in framing systems
Eq. C3.1.4-10 of AISI-S100-07
(c) model in AISI distortional buckling provisions
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DB and cantilever test for kf
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details of cantilever test to quantify kf
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test matrix
The goal in the testing is not to test every
condition and fill out a test matrix... We
attempt to do the testing required to inform
simple mechanical models of the behavior and make
corrections, modifications, enhancements as
needed.
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typical response
(178 N-mm/mm)
OSB
M
Plywood
q2
(57.3 deg.)
800S200-54 joist with 6 fasteners spaced 12 in.
(25mm) on-center attached to OSB, plywood, and
gypsum sheathing (24 in. (610mm) long, 54 in.
(1372 mm) wide)
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rotational stiffness (kf) decomposition
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typical component response
(178 N-mm/mm)
OSB
Plywood
(28.6 deg.)
(28.6 deg.)
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sample of plywood sheathed results
(67 N-mm/mm)
(57.3 deg.)
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rotational stiffness (kf) decomposition

• kf (1/kfw 1/kfc)-1

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test-to-predicted ratio for kf
connection rotational stiffness is determined
from the average tested values for a given joist
thickness
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kfw

• kfw SEIw/Li
• EIw sheathing bending rigidity, for plywood
  and OSB use EIw values of APA (2004), for gypsum
  board use minimum EIw values of GA (2001) note
  gypsum may be used for serviceability only, not
  for ultimate strength
• Li one half the joist spacing

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kfc
(1112 N-mm/mm)
(2.54 mm)
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Overview

• Introduction
• Research
• Distortional buckling
• Restrained distortional buckling
• AISI Design provisions
• CFSEI Design Aid
• Example 1 Table lookup
• Example 2 Table lookup
• Example 3 The whole enchilada

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AISI-S100-07
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AISI-S100-07

• Find the distortional buckling stress by
• (a) simplified provisions
• (b) C and Z provisions
• (c) rational elastic buckling analysis

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C3.1.4(a) simplified provisions
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C3.1.4(b) C and Z provisions
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C3.1.4(b) C and Z provisions
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C3.1.4(c)
free, open source, software www.ce.jhu.edu/bschafe
r select a link to CUFSM tutorials, etc. available
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Overview

• Introduction
• Research
• Distortional buckling
• Restrained distortional buckling
• AISI Design provisions
• CFSEI Design Aid
• Example 1 Table lookup
• Example 2 Table lookup
• Example 3 The whole enchilada

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Table 3 excerpt
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80S200-54, beam, Table 3
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80S200-54, beam, Table 3
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(note, 46.5ksi w/o kf)
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(compare with 62.4 kip-in. when no
rotational restraint was included)
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• Section properties
• Local buckling
• Lateral-torsional buckling
• continuous bracing, including brace forces
• Distortional buckling
• C3.1.4(a), simplified quickie equationswithout
  rot. restraint
• C3.1.4(b), detailed full and bloody methodwith
  and without rot. restraint
• C3.1.4(c), rational elastic buckling
  analysiswith rot. restraints

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• Section properties
• Local buckling
• Lateral-torsional buckling
• continuous bracing, including brace forces
• Distortional buckling
• C3.1.4(a), simplified quickie equationswithout
  rot. restraint
• C3.1.4(b), detailed full and bloody
  methodwithout rot. restraint and with rot.
  restraint kf
• C3.1.4(c), rational elastic buckling
  analysiswith rot. restraints

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