mbma what's new in the aisi spec 2009

CivilEngineeringat JOHNS HOPKINS UNIVERSITY

CivilEngineeringat JOHNS HOPKINS UNIVERSITY

What’s new in the 2007 AISI SpecificationMBMA Workshop, July 2009

Ben Schafer, Ph.D., P.E.Swirnow Family Faculty ScholarAssociate Professor and ChairDepartment of Civil EngineeringJohns Hopkins University

Overview• Introduction• 2004 Supplement• 2007 Specification• Distortional Buckling• 2008 Design Manual (as time allows)• Biggies in the pipeline (as time allows)• Conclusions

AISI Specifications• 1946 1st Edition• 1962 (26 pages small format)• 1986 Unified effective width method• 1991 Combined LRFD/ASD• 2001 North American Specification• 2004 Supplement: Direct Strength added• 2007 2nd order analysis added, distortional

buckling added, anchorage + more.

Major Changes since 2001• 2004 Supplement

– A1.1 Rational engineering analysis clause added– B3.2 Unstiffened elements with stress gradients– C3.4 Web crippling coefficients,

changed for multi-web deck sections– C3.6 Bearing stiffener provisions– C4.7 Compression of Z’s with

one flange fastened to standing seam roof– Appendix 1, the

Direct Strength Method for beams and columns

A1.1 Rational engineering analysis

2007 version..

A1.1 Rational engineering analysis• How many have used this clause?

• Why/Why not?

• Potential situations for use?

B3.2 Unstiffened elements with stress gradient

• pity the simple lip stiffener, calcs got harder

B3.2 Unstiffened elements with stress gradient

• Lip on a Zee may get a tinybump up in effective width

• Other opportunities toutilize these improvedcapacities?– in framing this matters for track in bending

C3.4 Web crippling coefficients 2001

2007

C3.4 Web crippling coefficients 2001

2007

Do you ever let web cripplingcontrol? Do you ever test?Analysis?

C3.6* Bearing Stiffeners

* in 2007 this was moved to C3.7** rational analysis extension to Z’s seems reasonable

web crippling capacity of the member to be stiffened

axial capacity of the stiffener

**

C3.6* Bearing Stiffeners

* in 2007 this was moved to C3.7** rational analysis extension to Z’s seems reasonable

web crippling capacity of the member to be stiffened

axial capacity of the stiffener

**

Do you ever use bearing stiffeners, why/why not?

C4.7 Compression of Z + standing seamD6.1.4 in 2007

D6.1.4 Compression of Z-section members having one flange fastened to a standing seam roof

This is weak axis only.

C4.7 Compression of Z + standing seamD6.1.4 in 2007

D6.1.4 Compression of Z-section members having one flange fastened to a standing seam roof

This is weak axis only. In my personal opinion thisis an odd approach and should be used with care.Stay inside the dimensional limits. Your reaction?

Appendix 1: Direct Strength Method• This was the topic of the MBMA Workshop

we enjoyed together a few years ago.• In 2004 the method was formally adopted

into the Specification as Appendix 1

Pcr PnPcrl,Pcrd,Pcre Pnl,Pnd,Pne

FSM –direct strength curves capacity

anyone trying out DSM at all? Framing industry has several folks now doing it...

Major Changes since 2001• 2007 Specification

– Reorganization “systems” to Chapter D– B4 Effective width and edge stiffeners– B5 Effective width and intermediate stiffeners– C3.1.4 Distortional buckling in bending– C3.6 Combined Bending and Torsion– C4.2 Distortional buckling in compression– D3.3 Bracing of Axially loaded compression members– D6.2.1 Standing Seam Roof Panels (revisions)– D6.3 Roof System Bracing and Anchorage– App1 Direct Strength – new prequalified limits– App2 2nd order analysis provisions– COFS Standards all updated in 2007 too!

2007 Reorganization• Chapter D: “systems” provisions

– D1 Built-up Sections– D2 Mixed Systems– D3 Lateral and Stability Bracing– D4 Cold-Formed Steel Light-Frame Construction– D5 Floor, Roof, or Wall Steel Diaphragm Construction– D6 Metal Roof and Wall Systems

• Mostly cobbled together from all around the Spec. does provide some clarity between members and systems



• These are the “metal building provisions”. New anchorage work here, base test, etc. here.

• Some opportunity here to think bigger now...



• Do you ignore these standards?• Why?• Opportunities here? (more later)

B4 Effective Width and Edge Stiffeners• Prior to 2007 all types of edge stiffeners

covered, now only simple lip edge stiffeners are covered

• For sections with compound/complex lip stiffeners Appendix 1 Direct Strength Method is the preferred solution

B4 Effective Width and Edge Stiffeners• Justification came

from nonlinear FE studies, sample of results:

• test-to-predicted ratio

AISI DSMsimple lip 0.96 1.02inside angled 0.89 0.99outside angled 0.90 1.08inside hooked 0.88 1.00outside hooked 0.87 1.04..see Schafer et al. 2006 for further information

• poor performance of 2001 Spec. method lead to restriction of main Spec. method to only simple lips.

H

B d+a

B d+a

H

B

d+a

B

d+a

H

B

d

B d

a

a

H

B

d

B

d a

a

H

B d

B d

2a2

a

2a2

a

H

B

d

B

d 2a

2a

2a

2a

(a) (b) (c)

(d) (e) (f)

C3.1.4 Distortional Buckling in BendingThis will be discussed in significant detail in the 2nd part of this presentation. Recall:

local buckling distortional buckling lateral-torsional buckling

Lcr

Mcr

B4 Effective width and edge stiffeners• Why we are on the subject...

Angling the stiffener is bad news for distortional buckling. As you add more lip (to counteract DB say) the angle becomes even more critical. Old optimals about lip angle are likely to be upset by the new DB provisions.

Reactions?from Schafer (1997)

C3.6 Bending + Torsion

exception clause applies to flexural members withone flange through-fastened to deck or sheathingor fastened to standing seam (R factors and base test)

Mn=RSeFy


exception clause applies to flexural members withone flange through-fastened to deck or sheathingor fastened to standing seam (R factors and base test)

Mn=RSeFy

Z??


Location in the unfolded section (mm)

Long

. Stre

ss (M

Pa)

8

6

4

2

0

-2

-4

-6

-8

100 200 300 400

σ + σM Bσ M

0

Mn=RSeFy R=σm/(σm+σb)<1

15% overstress allowed here, but nearby? intent is to check at fold lines?

example R values...


-8

-6

-4

-2

0

2

4

6

8

0 100 200 300 400 500


Long

. Str

ess

(MPa

) Rotational spring +lateral supportRotational Spring

No restriction

Restrained in bothflanges, M.y / I

-8

-6

-4

-2

0

2

4

6

8

0 100 200 300 400 500


Long

. Str

ess

(MPa

) Rotational spring +lateral supportRotational Spring

No restriction

Restrained in bothflanges, M.y / I

from Vieira et al. 2009


AISI D6.1.1 AISI C3.6 Direct Strength Methodσ=1.0σM σ=αMσM+αBσB*

section span RD MnR RT* MnT MnDSM1 MnDSM2 MnDSM2/SeFy

(m) (kN.m) (kN.m) (kN.m) (kN.m)150x60x20x1.5 4.8 0.7 4.26 0.70 4.26 4.45 2.92 0.48

6.5 0.76 4.63 3.35 0.55200x75x20x2 5.8 0.65 8.69 0.71 9.49 9.02 6.14 0.46

8.2 0.77 10.29 7.33 0.55250x85x25x2 7.5 0.4 7.86 0.71 13.95 11.70 8.14 0.41

9.6 0.74 14.54 8.74 0.44250x85x25x3 7.5 0.4 12.17 0.74 22.52 17.64 14.83 0.49

9.6 0.79 24.04 15.38 0.51* 15% increase for max stress at web/flange juncture not applied.

A comparison from Vieira et al. 2009 with “base test” R factors





6.5 0.76 4.63 3.35 0.55200x75x20x2 5.8 0.65 8.69 0.71 9.49 9.02 6.14 0.46

8.2 0.77 10.29 7.33 0.55250x85x25x2 7.5 0.4 7.86 0.71 13.95 11.70 8.14 0.41

9.6 0.74 14.54 8.74 0.44250x85x25x3 7.5 0.4 12.17 0.74 22.52 17.64 14.83 0.49



-40

-30

-20

-10

0

10

20

30

40

50

0 50 100 150 200 250 300 350


Long

. Stre

ss (M

Pa)

-2.000

-1.500-1.000

-0.5000.000

0.5001.000

1.5002.000

2.500

0 50 100 150 200 250 300 350


Long

. Str

ess

(MPa

)

(a) span = 2.7 m (b) span = 17.1 m

impact of torsional stresses decrease for longer spanlengths leading to increased “R”s. In the limit (L=infinity)the R factor will come back to 1 (of course LTB will go tozero, but you get the point..)





6.5 0.76 4.63 3.35 0.55200x75x20x2 5.8 0.65 8.69 0.71 9.49 9.02 6.14 0.46

8.2 0.77 10.29 7.33 0.55250x85x25x2 7.5 0.4 7.86 0.71 13.95 11.70 8.14 0.41

9.6 0.74 14.54 8.74 0.44250x85x25x3 7.5 0.4 12.17 0.74 22.52 17.64 14.83 0.49



-40

-30

-20

-10

0

10

20

30

40

50

0 50 100 150 200 250 300 350


Long

. Stre

ss (M

Pa)

-2.000

-1.500-1.000

-0.5000.000

0.5001.000

1.5002.000

2.500

0 50 100 150 200 250 300 350


Long

. Str

ess

(MPa

)

(a) span = 2.7 m (b) span = 17.1 m


0

1

2

3

4

5

6

10 100 1000 10000 100000

Half-wavelength (mm)

Mcr

/My

Analyzed Spans

What can FSM tell us?

Here we have added lateralrestraint, but used σ=My/I forthe applied stress. We seerestrained LTB...





6.5 0.76 4.63 3.35 0.55200x75x20x2 5.8 0.65 8.69 0.71 9.49 9.02 6.14 0.46

8.2 0.77 10.29 7.33 0.55250x85x25x2 7.5 0.4 7.86 0.71 13.95 11.70 8.14 0.41

9.6 0.74 14.54 8.74 0.44250x85x25x3 7.5 0.4 12.17 0.74 22.52 17.64 14.83 0.49



-40

-30

-20

-10

0

10

20

30

40

50

0 50 100 150 200 250 300 350


Long

. Stre

ss (M

Pa)

-2.000

-1.500-1.000

-0.5000.000

0.5001.000

1.5002.000

2.500

0 50 100 150 200 250 300 350


Long

. Str

ess

(MPa

)

(a) span = 2.7 m (b) span = 17.1 m


What can FSM tell us?

7524, 1.58158.5, 0.86

0

1

2

3

4

5

6

7

8

9

10 100 1000 10000 100000

half-wavelength (mm)

λcr/ λ

y

If we apply the actual stressdistribution we see the above





6.5 0.76 4.63 3.35 0.55200x75x20x2 5.8 0.65 8.69 0.71 9.49 9.02 6.14 0.46

8.2 0.77 10.29 7.33 0.55250x85x25x2 7.5 0.4 7.86 0.71 13.95 11.70 8.14 0.41

9.6 0.74 14.54 8.74 0.44250x85x25x3 7.5 0.4 12.17 0.74 22.52 17.64 14.83 0.49



finally we get DSM generated ‘R’ factors.globally, they look a lot like the base test....

C4.2 Distortional Buckling in Compression• Again, more discussion on this issue in the

2nd part of the presentation. For now, recall

100 101 102 1030

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

half-wavelength (in.)

Pcr

/ P

y

Z-section with lips (AISI 2002 Ex. I-10)

Py=45.23kips

Local Pcr/Py=0.16 Distortional Pcr/Py=0.29

Flexural

D3.3 Bracing of Axially loaded...• AISC style bracing provisions are coming

note use of Pn instead of Pr (demand)

How have AISC bracing provisions impacted your practice?

What would it mean if AISI had similar provisions? good/bad/indifferent?

Bracing has a long way to go...Torsional brace – (1) restricts torsion due to loads not applied through s.c. (2) restrict torsion due to enforcing bending about a non-principal axes Stability brace – restricts buckling at the brace location, (1) flexural: restricts translation –column-, (2) flexural-torsional, or lateral-torsional restricts appropriate translation and rotation –beam and column-

Discrete BracingCross-section singly point doubly

Bending (Beam)Torsion Brace

Stiffness ? ? ?Strength D3.2.1 (Cee) D3.2.1 (Zed) same as Cee

Stability BraceStiffness ? ? AISC?Strength ? ? Can D3.1.1 more? AISC?

Torsion + Stability BraceCombining stiffness don't need to? don't need to? don't need to?Combining strength simply add? simply add? simply add?

Compression (Column)Stability Brace

Stiffness D3.3 lateral, FT needed! D3.3 lateral, FT needed! D3.3 lateralStrength D3.3 lateral, FT needed! D3.3 lateral, FT needed! D3.3 lateral

Bending + Compression (Beam-column)Torsional Brace see beam see beam see beamStability Brace (beam) see beam see beam see beamStability Brace (column) see column see column see columnTorsion+Stability (beam+column) Brace

Combining stiffness max stiffness? max stiffness? max stiffness?Combining strength all additive? all additive? all additive?

the above was compiled by Ben Schafer and Tom Trestain in April 2009

D6.2.1 standing seam roof panels (revisions)

basic idea is to holdon to tests that have

already been run, that isthe intent.. implementation?

no free lunch

discussion?

D6.3 Roof system bracing and anchorage • I defer to the master

App1 Direct Strength• New in 2004• Minor updates in the 2007 version

• Significant updates coming in next version

App2 2nd order analysis

e.g., C5 ASD:

becomes

( ) 011

222 ./M

M/M

M/KP

P

bny

ndOrdery

bnx

ndOrderx

cn

ndOrder ≤Ω

+Ω

+Ω=

How to generate these 2nd order demands?

Users of AISC 2nd order provisions / Direct Analysis Method??

App 2 2nd order analysis (cont.)• 2.2.1 General

– Must include P-δ and P-Δ– For ASD do analysis at 1.6xASD loads, ASD demand=result/1.6

• 2.2.2 Types of Analysis– Analyze the model with initial imperfections, or– use notional loads

• 2.2.3 Reduced Stiffnesses– EA*=0.8τEA and EI*=0.8τEI

for members that contribute to the lateral stability of the structure– Can ignore τ which kicks in at axial loads > 50% squash load, by

bumping up the notional load an additional (1/1000)xGravity –

• 2.2.4 Notional Loads– Ni=(1/240)xGravity Load– 1/240 is based on 1/240 Δ imperfection. can adjust (>1/500

App 2 2nd order analysis (cont.)• 2.2.1 General

– Must include P-δ and P-Δ– For ASD do analysis at 1.6xASD loads, ASD demand=result/1.6

• 2.2.2 Types of Analysis– Analyze the model with initial imperfections, or– use notional loads

• 2.2.3 Reduced Stiffnesses– EA*=0.8τEA and EI*=0.8τEI

for members that contribute to the lateral stability of the structure– Can ignore τ which kicks in at axial loads > 50% squash load, by

bumping up the notional load an additional (1/1000)xGravity –

• 2.2.4 Notional Loads– Ni=(1/240)xGravity Load– 1/240 is based on 1/240 Δ imperfection. can adjust (>1/500

do not assume..

advantage LRFD

do this

follows AISC, not research, J? Cw?τ is from hot-rolled....

bump up the imperfection instead (rationaleng. analysis extension)

All of this came from research on racks!

Development of 2nd order analysis..

Effective length

Notional load

Notional load EI*=0.9EIrecall Spec uses 0.8τEI very conservative

Notional load EI*=0.9EIrecall Spec uses 0.8τEI very conservative

As “Kx” = 1 this frame is going froma sway frame to a no-sway frame, what are the implications of this high level of conservatism for no-sway frames.. in AISC? troublesome

COFS Standards• North American Standards for Cold-Formed Steel

Framing include: – General Provisions (AISI S200-07), – Product Data (AISI S201-07), – Floor and Roof System Design (AISI S210-07), – Wall Stud Design (AISI S211-07), – Header Design (AISI S212-07), – Lateral Design (AISI S213-07), and – Truss Design (AISI S214-07).

• These standards attempt, when possible, to treat the system as opposed to the individual members.

users?

Floor and Roof System Design (AISI S210-07) • Covers the design of floors and roofs by either

the discretely braced design or continuously braced design philosophy.

• For continuously braced design prescriptive sheathing requirements are provided (insuring a level of rigidity for the brace) along with the forces required to counteract rolling of the joists.

• S210 also provides a simple means to design clip angle bearing stiffeners, based on recent research (Fox 2006).

The Wall Stud Design standard (AISI S211-07)• Covers the design of wall studs by either the all steel

design or sheathing braced design philosophy.• Prescriptive load limits are provided for gypsum

sheathed designs based on experimental testing (Miller and Pekoz 1994).

• Sheathing braced design does not imply diaphragm-based design methods, which were essentially abandoned for sheathed walls, based on the observation that local fastener deformations, not sheathing in shear, dominates the response.

• Also covered in this Standard are stud-to-track connection strength including web crippling (Fox and Schuster 2000) and deflection track strength.

Header Design (AISI S212-07)• The general built-up section provisions in AISI

Spec. (2007) are rudimentary, but significant research has been conducted on built-up headers used in light frame construction (Elhajjand LaBoube 2000; Stephens and LaBoube2000; Stephens and LaBoube 2003)

• This research has lead to provisions for box headers, double L headers, and single L headers covering web crippling, bending and web crippling, and simplified moment calculations.

Lateral Design (AISI S213-07)• Has had a significant impact on practice as this standard

provides a means to determine the lateral strength of cold-formed steel systems used in wind and seismic demands.

• The standard provides compiled test results for cold-formed steel shear walls and diaphragms with a variety of sheathing, fastener spacing, stud spacing, etc.

• Specific seismic detailing provisions are provided, for example for strap-braced shear walls (Al-Kharat and Rogers 2007).

• In addition to strength, expressions are provided for deflection calculations (Serrette and Chau 2006).

Truss Design (AISI S214-07)• Provides specific guidance on beam-column

design for chord and web members of cold formed steel trusses.

• In addition due to the presence of concentrated loads (Ibrahim et al. 1998) in locations with compression and bending a unique interaction equation check for compression, bending, and web crippling is provided.

• Specific guidance is also provided for gusset plate design (Lutz and Laboube 2005) and

• methods for testing trusses.

Distortional Buckling 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

• DSM Design Manual Aids...

consider your friend, the floor

http://i240.photobucket.com/albums/ff31/medscntst/Dscf0148.jpg

or purlins, if you must

http://www.axiominspection.com/images/g_purlins.jpg

joist/purlin buckling modes

(a) applied stress (b) local (c) distortional (d) lateral-torsional

Figure 1: Stability modes of an 800S200-54 joist under major-axis bending stress*

Cross-section Instability- distortional buckling of CFS beams


Lcr

Mcr

Research background• Early 80’s Cornell research developed a mixed local-

distortional buckling effective width provision (B4 of the AISI Spec.)

• Late 80’s early 90’s U Sydney research, showed problems, and generated a new design method (Adopted in Australia, proposed to U.S. in ’95)

• Complication: 80’s Cornell research, and others conducted in 90’s 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)

Phase 1 tests(Local Buckling)

Phase 2 tests(Distortional Buckling)

Tests on CFS beams

Tested industry standard CFS Z and C-sections

Z-section C-section

Range of test specimens

Details

Panel fastener configurationlocal buckling

Phase 1 – local buckling tests

continuous spring analysis

adding a springboosts Mcra great deal

(Elastic) FE model to develop detail

single fastener – still get distortional buckling

panels removed forvisual purposes only

single vs. double fastener

paired fastener – now local buckling is first

panels removed forvisual purposes only

Specimen Mtest/My Mtest/Maisi96 note

8.5Z073-5E6W 0.78 0.86 single panel-to-purlin screws - 12" o.c.

8.5Z073-1E2W 0.80 0.88 single panel-to-purlin screws

on both sides of raised corrugation8.5Z073-4E3W 0.86 0.96 paired panel-to-purlin screws

on both sides of raised corrugation

8.5Z073-5E6W 8.5Z073-4E3W

Test results with different fastener details

Distortional buckling

Phase 2 – distortional buckling tests

Test 8.5Z092

Local buckling test Distortional buckling test

Test 8C043

Local buckling test Distortional buckling test

99% of NAS’01 83% of NAS’01

106% of NAS’01 90% of NAS’01

Pcrd

Py

localdistortional

Pcrd

Py

localdistortional

Δ

P

Py

PcrL

localdistortional

Pcrd

Py

PcrL

localdistortional

Pcrd

Δ

P

Comparisons

9 pairs of tests having nominally identical geometry and material yield stresses

Comparisons (cont.)

• Total 25 local buckling tests and 24 distortional buckling testshave been completed.

Comparison with design methods

σ

μ

σ

μ

0.070.090.070.090.080.08

1.010.961.010.870.920.86Distortional buckling

tests

0.060.060.080.070.060.08

1.041.011.011.021.071.01Local buckling

tests

Mtest/MDSM

Mtest/MEN’94

Mtest/MAN’95

Mtest/MNAS’01

Mtest/MS136’94

Mtest/MAISI’96

App1

Code comparison

Overview• Introduction• Research




p

Moment diagram


MG effect ignored MG effect unaddressed MG effect considered

Moment Gradient

FE model Buckled shape

1

2

3

Fix 1, 2 for all nodes at end


Fix 1, 2, 3 for one node at the corner

M1

M2

1

2

3 1

2

3



Fix 1, 2, 3 for one node at the corner

M1

M2

Modeling

0 1 2 3 4 5 6 7 8 9 10 111

1.05

1.1

1.15

1.2

1.25

1.3

1.35

1.4

1.45

1.5

L/Lcrd

Md/Mcrd

r = 0

Md/Mcrd=1.0<=1+0.4(Lcrd/L)0.7<=1.3

( ) ( ) 31140101 7021

70 .MM/LL../MM ..crdcrdd ≤−+≤= |||| 21 MM ≤

Proposed equation for the MG effect:

Mcr boost for distortional buckling

4PL

P

L

Moment diagram

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.

Ultimate strength boost?

Local buckling test 11.5Z092-1E2W Distortional buckling test D11.5Z092-3E4W

Verificaton of model parameters

Moment gradient r = 0.5

Moment gradient r = 0

P

P

Moment Gradient Effect on Distortional Buckling - for ultimate strength of DB

0.4 0.6 0.8 1 1.2 1.4 1.60.5

0.6

0.7

0.8

0.9

1

1.1

1.2

(My/Mcrd)0.5

DSM-distMFEd

MFEd/My

mean FE-to-predicted = 1.04

0.4 0.6 0.8 1 1.2 1.4 1.60.5

0.6

0.7

0.8

0.9

1

1.1

1.2

(My/Mcr)0.5

DSM-distMDSd r = 0.5MDSd r = 0

MFEd/My


case with no moment gradient(shows model works)

moment gradient present, but ignored in design(too conservative!)

Comparison with predictions

0.4 0.6 0.8 1 1.2 1.4 1.60.5

0.6

0.7

0.8

0.9

1

1.1

1.2

(My/M*crd-MG)0.5

DSM-distMDSd r = 0.5MDSd r = 0

MFEd/My


6730.≤dλ

6730.>lλ

yy

crd

y

crdnd M

MM

MM

M5050

2201..

. ⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

ynd MM =

DSM for DB of CFS beams:

MG is included in the elastic buckling moment, strength prediction is still conservative...

Comparison with predictions (cont.)

Restraint from sheeting/sheathing

Restraint from sheeting/sheathing

φ

100 101 102 1030

100

200

300

400

500

600

half wavelength (in.)

k = 0k = 0.79k = 1.0

Mcr

(kips-in.) Mcrd-FE

distortional buckling

8.5Z092 section in bending

FE result including

panel details

Models to account for sheathing

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 150

60

70

80

90

100

110

120

130

140

150

160

k (kips-in./rad/in.)

6C054

local buckling moment by CUFSMdistortional buckling moment by CUFSMdistortional buckling moment by Eq. 8.2

Mcr(kips-in.)

wgfgd

wgfg

wefeppd k~k~

kf

k~k~kkk

fφφ

φ

φφ

φφφ− +

+=+

++=

k

1. Finite strip method (CUFSM)

2. Analytical method

Numerical vs. hand methodsφ

Available sheeting test data• For members with profiled steel panels

providing kφ: – Testing on 8 in. and 9.5 in.

(203 and 241 mm) deep Z-sections with a thickness between 0.069 in. (1.75 mm) and 0.118 in. (3.00 mm), through-fastened 12 in. (205 mm) o.c., to a 36 in. (914 mm) wide, 1 in. (25.4 mm) and 1.5 in. (38.1 mm) high steel panels, with up to 6 in. (152 mm) of blanket insulation between the panel and the Z-section,

– results in a kφ between 0.15 to 0.44 kip-in./rad./in. (0.667 to 1.96 kN-mm/rad./mm) (MRI 1981).

kφ

Available sheeting test data• Additional testing on C- and Z-sections with

pairs of through-fasteners provides considerably higher rotational stiffness: – for 6 and 8 in. deep C-sections with a thickness

between 0.054 and 0.097 in., fastened with pairs of fasteners on each side of a 1.25 in. high steel panel flute at 12 in. o.c., kφ is 0.4 kip-in./rad./in.; and

– for 8.5 in. deep Z-sections with a thickness between 0.070 in. and 0.120 in., fastened with pairs of fasteners on each side of 1.25 in. high steel panel flute at 12 in. o.c., kφ is 0.8 kip-in./rad./in. (Yu and Schafer 2003, Yu 2005).

kφ

Available sheeting test data• Typical 0.15-0.44 kip-in/rad/in• Upperbound 0.40-0.80 kip-in/rad/in• Source Commentary to C3.1.4

• Discussion that follows provides a way to fine tune this much further, but keep these typical and upperbound numbers in mind.

kφ


– Distortional buckling– Restrained distortional buckling (in framing)



Restraint of DB in framing systems


exterior joist

interior joist

(a) typical floor system (SFA 2000) (b) distortional buckling of a sheathed floor joist


kφkφ

(c) model in AISI distortional buckling provisions

wgfg

wefed

k~k~kkk

Fφφ

φφφ

+

++β=

Eq. C3.1.4-10 of AISI-S100-07

exterior joist

interior joist

(a) typical floor system (SFA 2000) (b) distortional buckling of a sheathed floor joist

DB and cantilever test for kφ

L

L

L

L

details of cantilever test to quantify kφ

L

tw

ho

tΔH

ΔV

L

tw

ho

tΔH

ΔV

test matrix

conducted testsSheathing --> Plywood OSB Gypsum

Joist Spacing (L) --> 12" 24" 24" 12" 24"Fastener # --> 6 10 6 6 10 6 10 6 10

Fastener Spacing --> 6" 12" 6" 12" 12" 12" 12" 12" 12" 12" 12"362S162-33 1 1362S162-68 1 1800S200-54 2 4 1 3 1 1 1 1 1 1800S250-54 1 1800S200-97 1 4 1 21200S200-54 2 11200S200-97 2 1

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.

“typical” response

0 0.2 0.4 0.6 0.8 1 1.20

5

10

15

20

25

30

35

40

15/32 in. Plywood

7/16 in. OSB

1/2 in. Gypsum

overall response (slope = kφ2)

800S200-54 L=24in. #6@12in.

θ (rad)

Mom

ent (

lbf-i

n./in

.)

θ2

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)

M

θ2

OSB

Plywood

(57.3 deg.)

(178 N-mm/mm)

rotational stiffness (kφ) decomposition

kφw

~ ~

kφw

kφc

kφw

~ ~

kφw

kφc

0 0.1 0.2 0.3 0.4 0.50

5

10

15

20

25

30

35

40

15/32 in. Plywood

7/16 in. OSB

1/2 in. Gypsum

sheathing response (slope = kφw )

800S200-54 L=24in. #6@12in.

θ (rad)

Mom

ent (

lbf-i

n./in

.)

0 0.1 0.2 0.3 0.4 0.50

5

10

15

20

25

30

35

40

15/32 in. Plywood

7/16 in. OSB

1/2 in. Gypsum

connection response (slope = kφc2)

800S200-54 L=24in. #6@12in.

θ (rad)

Mom

ent (

lbf-i

n./in

.)

θw θc2

OSB

Plywood

(28.6 deg.)(28.6 deg.)

(178 N-mm/mm)

“typical” component response

0 0.2 0.4 0.6 0.8 1 1.20

5

10

15

ID:1 800S200-54 L=24in. #6@12

ID:1 ID:1

ID:4 800S200-54 L=24in. #6@12

ID:4 ID:4

ID:5 800S200-54 L=24in. #6@12

ID:5 ID:5

θ (rad)

Mom

ent (

lbf-i

n./in

.)

θ2

θw

θc2

(67 N-mm/mm)

(57.3 deg.)

sample of plywood sheathed results

rotational stiffness (kφ) decomposition

kφ = (1/kφw + 1/kφc)-1

kφw

~ ~

kφw

kφc

kφw

~ ~

kφw

kφc

test-to-predicted ratio for kφ

0.211.300.261.470.231.03proposed eq.industry EIw

0.160.920.140.970.220.98proposed eq.test ave. EIw

0.160.920.140.970.220.98thickness only*test ave. EIw

0.021.000.061.000.210.97tested valuestest ave. EIw

st. dev.ave.st.

dev.ave.st. dev.ave.kφc2kφw

gypsum boardOSBPlywood

* connection rotational stiffness is determined from the average tested values for a given joist thickness

kφw

kφw = ΣEIw/LiEIw = 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

0

50

100

150

200

250

0 0.02 0.04 0.06 0.08 0.1 0.12

thickness (in.)

k φc2

(lbf

-in./i

n./ra

d)

mean (tests)

Plywood

OSB

Gypsum Board

whiskers denote one standarddeviation above and below the mean

kφc2=0.00035Et2+75

kφc

(2.54 mm)

(1112 N-mm/mm)

AISI-S100-07

AISI-S100-07

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

C3.1.4(a) simplified provisions

C3.1.4(b) C and Z provisions

C3.1.4(c)

free, open source, softwarewww.ce.jhu.edu/bschaferselect a link to CUFSMtutorials, etc. available

AISI-S210 adopted kφ methodsB6 Continuously Braced Design for Distortional Buckling Resistance

Calculation of the nominal distortional buckling strength [resistance] in flexure inaccordance with Section C3.1.4 of AISI S100 [CSA S136] or Appendix 1 of AISI S100 [CSA S136]shall be permitted to utilize the beneficial restraint provided by structural sheathing attached tothe compression flange of floor joists, ceiling joists, and/or roof rafters through determination ofthe rotational stiffness provided to the bending member, kφ of Eq. B6-1. It is also permitted, andconservative, to assume no rotational restraint exists, i.e., kφ = 0.

Calculation of the nominal distortional buckling strength [resistance] in compression inaccordance with Section C4.2 of AISI S100 [CSA S136] or Appendix 1 of AISI S100 [CSA S136]shall be permitted to utilize the beneficial restraint provided by structural sheathing attached toboth flanges of floor joists, ceiling joists, and/or roof rafters through determination of therotational stiffness provided to the bending member, kφ of Eq. B6-1. It is also permitted, andconservative, to assume no rotational restraint exists, i.e., kφ = 0.

AISI-S210 adopted kφ methodsThe rotational stiffness kφ shall be determined as follows:

kφ = (1/kφw + 1/kφc) -1 (Eq. B6-1)where kφw = Sheathing rotational restraint = EIw/L1 + EIw/L2 for interior members (joists or rafters) with structural sheathing

fastened on both sides (Eq. B6-2) = EIw/L1 for exterior members (joists or rafters) with structural sheathing

fastened on one side (Eq. B6-3)where EIw = Sheathing bending rigidity = Values as given in Table B6-1(a) for plywood and OSB Values as given in Table B6-1(b) for gypsum board shall be permitted only for

serviceability calculations in accordance with AISI S100 Appendix 1 Section 1.1.3. L1, L2 = One half joist spacing to the first and second sides respectively, as illustrated

in Figure B6-1 kφc = Connection rotational restraint = Values as given in Table B6-2 for fasteners spaced 12 in. o.c. or closer (Eq. B6-4)


kφ = (1/kφw + 1/kφc) -1 (Eq. B6-1)

Table B6-1 (a)1,2 Plywood and OSB Sheathing Bending Rigidity, EIw (lbf-in2/ft)

Strength Parallel to Strength Axis Stress Perpendicular to Strength Axis Plywood Plywood Span

Rating 3-ply 4-ply 5-ply OSB

3-ply 4-ply 5-ply OSB

24/0 66,000 66,000 66,000 60,000 3,600 7,900 11,000 11,000 24/16 86,000 86,000 86,000 86,000 5,200 11,500 16,000 16,000 32/16 125,000 125,000 125,000 125,000 8,100 18,000 25,000 25,000 40/20 250,000 250,000 250,000 250,000 18,000 39,500 56,000 56,000 48/24 440,000 440,000 440,000 440,000 29,500 65,000 91,500 91,500 16oc 165,000 165,000 165,000 165,000 11,000 24,000 34,000 34,000 20oc 230,000 230,000 230,000 230,000 13,000 28,500 40,500 40,500 24oc 330,000 330,000 330,000 330,000 26,000 57,000 80,500 80,500 32oc 715,000 715,000 715,000 715,000 75,000 615,000 235,000 235,000 48oc 1,265,000 1,265,000 1,265,000 1,265,000 160,000 350,000 495,000 495,000

Note: 1. To convert to lbf-in2/in., divide table values by 12. To convert to N-mm2/m, multiply the table values by 9415. To convert to N-mm2/mm, multiply the table values by 9.415. 2. Above Plywood and OSB bending rigidity is obtained in accordance APA, Panel Design Specification (2004).


kφ = (1/kφw + 1/kφc) -1 (Eq. B6-1)

Table B6-21 Connection Rotational Restraint

t t kφc kφc

(mils) (in.) (lbf-in./in./rad) (N-mm/mm/rad)

18 0.018 78 348 27 0.027 83 367 30 0.03 84 375 33 0.033 86 384 43 0.043 94 419 54 0.054 105 468 68 0.068 123 546 97 0.097 172 766

Note: 1. Fasteners spaced 12 in. (25.4 mm) o.c. or less.

• www.cfsei.org• focused on resources for engineers• key market is framing, but much of the

information could be of value to you• CFSEI is part of the AISI family and has

become a secondary pathway for dissemination and outreach

• encourage you to join and become involved

*full disclosure: I am a Past-President of CFSEI

TechNotes:

Table 3 excerpt

80S200-54, beam, Table 3

(note, 46.5ksi w/o kφ)

(compare with 62.4 kip-in. when no rotationalrestraint was included)

• 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

• 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 kφ

– C3.1.4(c), rational elastic buckling analysiswith rot. restraints

Highlights - 2008 Design Manual• I – Dimensions and Properties

– DB flange properties– Z: effective section properties illustrating new

lip under stress gradient provisions– Delicious little note buried in Section 3.6

about avoiding large r/t, or if needed use DSM

Highlights – 2008 Design Manual• II-Beam Design

– Extensively covered (toc)– Beam strength table (note, no DB)– Beam charts, note diamond– Z section DB tables– Complete four span purlin example– Full DB example, like technote– Combined bending and torsion example– DSM for a sigma section

Highlights – 2008 Design Manual• III-Columns

– nearly as complete as beams– beam-colums treated here– Full DB table for Z’s– Full DB examples– Frame design (for a rack) using 2nd order...

In the Pipeline (next Ed.)• Tension members

– finally merged between U.S. and Canada• Diaphragm Standard

– patterned after SDI, but coming under the AISI Standards umbrella

• Direct Strength Method– how to handle holes– how to handle inelastic reserve (Mn>My)– unique beam-column method

Conclusions/Discussion• Hopefully brought you back up to speed a

little bit on the cold-formed steel universe• Distortional buckling provisions are a big

change, you can mitigate them, but they have an influence on design – no doubt

• Some nice resources..– 2007 Spec. and Commentary, – 2007 COFS standards too!– CFSEI documents– 2008 Design Manual

mbma what's new in the aisi spec 2009

Documents

formed steel light

b4 effective width

web crippling capacity

exception clause applies

standing seamd6

intermediate stiffeners c3

direct strength method

standing seam roof