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Test Verification of the Effect of Stress Gradient on the Webs of Cee and Zee Sections

-research update-Ben Schafer

Asst. ProfessorThe Johns Hopkins University

July 2001

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acknowledgments

� Sponsors and Suppliers� AISI and MBMA� CECO Buildings, VP Buildings, Clark Steel

� People� Cheng Yu - graduate RA� Sam Phillips - undergraduate RA� Liakos Ariston - undergraduate RA� Jack Spangler - technician� Chuck Pearson - Prosser Steel

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objective

� New tests are needed to definitively determine the proper expression for the web effective width

� Requirements� Simple repeatable tests on industry Cees and Zees� Account for issues in practice related to local buckling of

these members, such as attachment to sheeting� Focus on local buckling limit states

leave distortional and lateral buckling issues for later� Aside, the tests should also�

� assess local web/flange interaction� provide a basis for future distortional buckling work

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members

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testing setup

spreader beam to apply the load at 1/3 points

tubes at ends and at support pointsbolting the two specimens together,top of tube flush with top of purlin toavoid crippling at loading point.

4x4x1/4 angles bolted to endplates and specimens to avoidcrippling at ends.

1 1/4 x 1 1/4 x 0.057 anglesconnecting tension flanges of 2specimens to insure they act asa unit 12� on center

standard decking fastened through flanges ofpurlins to retard lateral and distortional buckling. fastener patterns and spacing investigated.

each span is 5� 4� on center. Length is selectedconsidering: shear demands, actuator capacity,actuator stroke, and future testing (dist.

buckling when panel is removed)

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overall view

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collapse

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response

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elastic buckling modes

local distortional

½λ ~ 5 in. ½λ ~ 20 in.

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elastic buckling

0.50

0.90

1.30

1.70

70.0 90.0 110.0 130.0

web slenderness (h/t)

M/M

y

Local ElasticDistortional Elastic

h=8.5 in.b=2.5 in.d=0.8 to 1.0 in.t=0.059 in. to 0.120 in.fy=60 ksi

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continuous spring analysis (finite strip)

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fe (elastic) model to develop detail

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(single screw pattern, t=0.073 in.)

panels removed forvisual purposes only

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influence of details

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(paired screw pattern, t=0.073 in.)

panels removed forvisual purposes only

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influence of detailsSpecimen Mtest/My Mtest/Maisi 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

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0

0.2

0.4

0.6

0.8

1

1.2

0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60

web slenderness = λλλλweb = (fy/fcrweb)0.5

test

-to-p

redi

cted

ratio

S136: 8.5 in. deep ZeesS136: 8 in. deep CeesAISI: 8.5 in. deep ZeesAISI: 8 in. deep Cees

testing to determine panel-to-purlin fastener

configuration

specimens damaged prior to testing

test-to-predicted ratios

controlling specimens test-to-predicted ratiosAISI Zees: 0.97

Cees: 0.96S136 Zees: 1.02

Cees: 1.01

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web effective width(experimental effective width back-calculated from moment capacity)

0%

20%

40%

60%

80%

100%

120%

140%

0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60

web slenderness = λλλλweb = (fy/fcrweb)0.5

web

effe

ctiv

enes

s =

ρ ρ ρ ρ =

(b1+

b 2)/b

com

p (%

)

AISI (1996)S136 (1991)8" C8.5" Z

accuracy of web prediction, assuming AISI (1996) flange equations are 100% accurate

testing to determine panelto-purlin fastener

configuration

specimens damaged prior to testing

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local buckling with web/flange interaction

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

1 2 3 4 5 6 7 8 9 10

ratio of web height to flange width (h/b)

plat

e bu

cklin

g co

effic

ient

for t

he fl

ange

kf

ξ = 3ξ = 2ξ = 1.4ξ = 1

local bucklingfinite strip analysis

ξ = 3

ξ = 2, pure bending

ξ = 1.4

ξ = 1

ZC next study (projected

completion - August)

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direct strength

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Distortional Curve

Local Curve

Zees

Cees

λmax = M My cr

MMtest

y controlling specimens test-to-predicted ratiosDirect Zees: 1.00Strength Cees: 1.00

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comments� Test detail

� panel-to-purlin details are important, and the selected detail maximizes the bending resistance provided by the panel

� this test provides flexural capacity in local buckling� Strength prediction (AISI and S136)

� both are reasonable compared with data collected to date� both approx. local buckling capacity, not distortional� progress report summarizes problems with web, flange, and lip expressions� the �correct� web effective width is linked to the �correct� flange and lip effective

width - the next data set on Cees with varying h/b will aid this study significantly� incorporating web/flange interaction is correct (see direct strength results) and

will benefit the appropriate sections and be a detriment to others

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future work

� testing� Cees with varying height� closer look at strain distribution� 11.5 in. deep Zees

� analysis (local buckling only!)� AISI, S136, direct strength evaluations� web/flange interaction

� future, second phase of work?� take of panels and determine distortional strength

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influence of detailsSpecimen Mtest/My Mtest/Maisi note

8.5Z059-1E2W 0.75 0.91 paired panel-to-purlin screws

on both sides of raised corrugation and in pan8.5Z059-4E3W 0.76 0.91 paired panel-to-purlin screws

on both sides of raised corrugation

8.5Z059-1E2W 8.5Z059-4E3W

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detailed testing planout-to-out-dimensi inner nondimensional ratios studied

h b d r θ t E fy h/t h/b b/t d/t d/b(in.) (in.) (in.) (in.) (deg) (in.) (ksi) (ksi)8.5 2.5 0.71 0.313 50 0.059 29500 60 144.1 3.4 42.4 12.0 0.288.5 2.5 0.78 0.313 50 0.065 29500 60 130.8 3.4 38.5 12.0 0.318.5 2.5 0.92 0.313 50 0.073 29500 60 116.4 3.4 34.2 12.6 0.378.5 2.5 0.94 0.313 50 0.082 29500 60 103.7 3.4 30.5 11.4 0.388.5 2.5 0.96 0.313 50 0.092 29500 60 92.4 3.4 27.2 10.4 0.388.5 2.5 0.98 0.313 50 0.105 29500 60 81.0 3.4 23.8 9.4 0.398.5 2.5 1.01 0.313 50 0.120 29500 60 70.8 3.4 20.8 8.4 0.4111.5 3.5 0.92 0.313 50 0.073 29500 60 157.5 3.3 47.9 12.6 0.2611.5 3.5 0.94 0.313 50 0.082 29500 60 140.2 3.3 42.7 11.4 0.2711.5 3.5 0.96 0.313 50 0.092 29500 60 125.0 3.3 38.0 10.4 0.2711.5 3.5 0.98 0.313 50 0.105 29500 60 109.5 3.3 33.3 9.4 0.2811.5 3.5 1.01 0.313 50 0.120 29500 60 95.8 3.3 29.2 8.4 0.29

8 2 0.63 0.076 90 0.033 29500 60 242.4 4.0 60.6 18.9 0.318 2 0.63 0.045 90 0.043 29500 60 186.0 4.0 46.5 14.5 0.318 2 0.63 0.085 90 0.054 29500 60 148.1 4.0 37.0 11.6 0.318 2 0.63 0.107 90 0.068 29500 60 117.6 4.0 29.4 9.2 0.318 2 0.63 0.153 90 0.097 29500 60 82.5 4.0 20.6 6.4 0.31

12 2 0.63 0.085 90 0.054 29500 60 222.2 6.0 37.0 11.6 0.3110 2 0.63 0.085 90 0.054 29500 60 185.2 5.0 37.0 11.6 0.318 2 0.63 0.085 90 0.054 29500 60 148.1 4.0 37.0 11.6 0.316 2 0.63 0.085 90 0.054 29500 60 111.1 3.0 37.0 11.6 0.314 2 0.63 0.085 90 0.054 29500 60 74.1 2.0 37.0 11.6 0.31

3.62 2 0.63 0.085 90 0.054 29500 60 67.0 1.8 37.0 11.6 0.31

AISI and S136differentZ

C

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h/t b/t d/t h/b d/b min max min max min max min max min maxMBMA Z�s 53 170 17 47 5 17 3.1 3.7 0.28 0.45SSMA members 25 318 11 132 1 33 1.0 10.9 0.12 0.33Rack members 23 136 16 45 6 15 1.0 3.2 0.27 0.38Elhouar and Murray (1985) 68 165 24 52 3 24 2.6 3.8 0.09 0.49Schafer and Peköz (1999) 43 270 15 75 3 34 1.5 13.7 0.14 0.70

industry and academic testing

h/b=1.0 3.3 10.0

available membersexperimental data

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testing matrix

� Dimensions: h, b, d, t.� Isolation of h/t variation sought� MBMA �Z�s (purlins): h,b,d, fixed, t varied� SSMA �C�s (studs, joists): b,d fixed, h and t varied

h/t h/b b/t d/t d/bTests to be performed num min max min max min max min max min maxbracing configuration 3Z: h,b,~d fixed, t varied 7 71 144 3.4 same 21 42 8 13 0.28 0.41Z: h,b,~d fixed, t varied 5 96 158 3.3 same 29 48 8 13 0.26 0.29C: h,b,d fixed, t varied 5 82 242 4.0 same 21 61 6 19 0.31 sameC: b,d,t fixed, h varied 5 67 222 1.8 6.0 37 same 12 same 0.31 samemiscellaneous 4

TOTAL 29 67 242 1.8 6.0 21 61 6 19 0.26 0.41

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background / motivation

� Effective width of a web of a cold-formed steel beam?� Unification of design? North American Specification� American (AISI) vs. Canadian (S136) method� AISI expressions inconsistent and discontinuous� AISI predicted strength > S136 predicted strength� Industry skeptical of academic test data showing

problems with AISI predicted strength� Definitive testing needed