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Transverse Stiffener Requirementsin Straight and Horizontally CurvedSteel I-Girders
Yoon Duk Kim, Se-Kwon Jung andDonald W. White
Georgia Institute of TechnologySchool of Civil and Environmental EngineeringAtlanta, GA
2005 AASHTO Bridge Committee Agenda Item 38
June 27, 2005
Problem Statement
Identify the demands on transversestiffeners in curved and straightI-girders designed within theAASHTO (2004) limits: Transversely-stiffened I-girders with
do/D < 3 D/tw < 150
Longitudinally-stiffened I-girders with do/D < 1.5 D/tw < 300
FEA Parametric Studies,Test Configuration
Parametric Studies (Transversely-Stiffened I-Girders)
D = 96 in (8 ft) do/D = 0.5, 1, 2 & 3 Straight & Curved with R = max(10do, 100 ft) D/tw = 150 (other D/tw values considered for flat webs)
Fyw = Fys = 70 ksi (other Fy values considered for flat webs)
Fyf = 100 ksi (other Fy values considered for flat webs)
bf/2tf = 6.47 (compact limit),except bf/2tf = 5 for do/D = 3
bf determined such that Mu ~ 0.75Mn based on theone-third rule
bt/tp = 10 in primary studies (other bt/tp considered insupplementary studies)
Various one- and two-sided stiffener sizes
Parametric Studies (Longitudinally-Stiffened I-Girders)
D = 96 in (8 ft) do/D = 0.5, 1 & 1.5 Straight & Curved with R = max(10do, 100 ft) D/tw = 300 (other D/tw values considered for flat webs)
Fyw = Fys = 70 ksi (other Fy values considered for flat webs)
Fyf = 100 ksi (other Fy values considered for flat webs)
bf/tf = 6.47 (compact limit) bf determined such that Mu ~ 0.75Mn based on the
one-third rule bt/tp = 10 in primary studies (other bt/tp considered in
supplementary studies)
Various one- and two-sided stiffener sizes Longitudinal stiffener not included in models
TFA Strength vs It/Itcrdo/D = 1, D/tw = 150
Itcr = It req’d to develop Vn = VcrIt = ntpbt3/3It = nbt
4/3/(bt/tp)It = As2(bt/tp)/3n
TFA Strength vs It/Itcrdo/D = 1, D/tw = 150
AASHTO (2004)area requirement,two-sided stiffeners
AASHTO (2004)area requirement,one-sided stiffeners
Recommended
Shell Model - Perspective View ofDeformed Geometry at Max LoadIt = Itcr, do/D = 1, D/tw = 150, 1-sided stiffener
Straight I-girder (note: 18.5Itcr is req’d to satisfy the AASHTO (2004) area reqmt)
Undeformed geometry
Deformed geometry
(Scale Factor = 5.0)
Shell Model – Mid-thickness Von MisesStress Distribution at Max LoadIt = Itcr, do/D = 1, D/tw = 150, 1-sided stiffener
Straight I-girder (note: 18.5Itcr is req’d to satisfy the AASHTO (2004) area reqmt)
(Scale Factor = 5.0)
Perspective View of DeformedGeometry at Max LoadIt = 6Itcr, do/D = 1, D/tw = 150, 1-sided stiffener
Curved I-girder
(Scale Factor = 5.0)
Undeformed geometry
Deformed geometry
Mid-thickness Von Mises StressDistribution at Max LoadIt = 6Itcr, do/D = 1, D/tw = 150, 1-sided stiffener
Curved I-girder
(Scale Factor = 5.0)
TFA Strength vs It/Itcrdo/D = 1, D/tw = 300
Rahal and Harding (1990a)
“… the important panel influence on the stiffeneris lateral loading induced by panel buckling. Forpanels bounded by actual flange members there isevidence of a significant tension field loading onthe stiffener, but the effect of this, even for themore slender plates considered, is less than thebeneficial effect resulting from the lateral stiffenerbending restraint provided by the flange. Thisindicates that bending rigidity rather than axialstiffness is the most important parameter for thedesign of the stiffener, which supports theemphasis placed on stiffener rigidity in the studyby Horne and Grayson.”
Similar conclusions have been reachedby
Rahal and Harding (1990b & 1991) Horne and Grayson (1983) Stanway, Chapman and Dowling
(1993 & 1996) Xie (2000) Lee, Yoo and Dong (2002 & 2003)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
50 100 150 200 250 300
D/tw
[Is/I
'scr
(C=1
)]^0
.25
bs/bscr(C=1) (AASHTO 2004)bs/bscr(C=1) (Horne & Grayson 1983)bs/bscr(C=1) (Stanway et al. 1996)bs/bscr(C=1) FEA, this studybs/bscr(C=1),bs/bscr(C=1),
bt/b
' tcr(
C=
1)
D/tw
bt/b'tcr(C=1) (AASHTO 2004)bt/b'tcr(C=1) (Horne & Grayson 1983)bt/b'tcr(C=1) (Stanway et al. 1996)bt/b'tcr(C=1) FEA, this study
bt = b'tcr(C=1), yww F/Ek12.1t/D
Required Stiffener Sizes, do/D = 1, one-sided stiffeners
D/tw = 1.12 (Ek/Fyw)0.5 tw = D (Fyw/E/k)0.5 / 1.12 I’tcr = btw3J
b’tcr(C=1) = [3(bt/tp) I’tcr/n]0.25
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
50 100 150 200 250 300
D/tw
[Is/I
'scr
(C=1
)]^0
.25
bs/bscr(C=1) (AASHTO 2004)bs/bscr(C=1) (Horne & Grayson 1983)bs/bscr(C=1) (Stanway et al. 1996)bs/bscr(C=1) FEA, this studybs/bscr(C=1),bs/bscr(C=1),
bt/b
' tcr(
C=
1)
D/tw
bt/b'tcr(C=1) (AASHTO 2004)bt/b'tcr(C=1) (Horne & Grayson 1983)bt/b'tcr(C=1) (Stanway et al. 1996)bt/b'tcr(C=1) FEA, this study
bt = b'tcr(C=1), yww F/Ek12.1t/D
Required Stiffener Sizes, do/D = 1, one-sided stiffeners
Recommended
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
50 100 150 200 250 300
D/tw
[Is/
I 'scr
(C=
1)]^0
.25
[IsAASHTO/Is 'cr(C=1)]^0.25[Is/I 'scr(C=1)]^0.25 (Horne & Grayson 1983)
[Isd/I'scr(C=1)]^0.25 (Stanway et al. 1996)[Isd/I'scr(C=1)]^0.25 for FEA girders[IsFEA/I'scr(C=1)]^0.25
Series6
b t/b' tc
r(C
=1)
D/tw
bt/b'tcr(C=1) (AASHTO 2004)bt/b'tcr(C=1) (Horne & Grayson 1983)bt/b'tcr(C=1) (Stanway et al. 1996)bt/b'tcr(C=1) FEA, this study
bt = b'tcr(C=1), yww F/Ek12.1t/D
Required stiffener sizes, do/D = 1, two-sided stiffeners
Recommended
6.10.11.1.2 Projecting Width
The width, bt, of each projecting stiffener elementshall satisfy:
3002
D.bt (6.10.11.1.2-1)
and
16 / 4p t ft b b (6.10.11.1.2-2)
where:
bf = for I-sections, full width of the widestcompression flange within the field sectionunder consideration; for tub girder sections, fullwidth of the widest top flange within the fieldsection under consideration; for closed boxsections, the limit of bf/4 does not apply (in.)
tp = thickness of the projecting stiffener element(in.)
6.10.11.1.3 Moment of Inertia
For transverse stiffeners adjacent to web panels inwhich Vu < vVcr in both panels, the moment of inertia ofthe transverse stiffener shall satisfy the smaller of thefollowing limits:
JbtI wt3 (6.10.11.1.3-1)
51314
40
.yw
.t
t E
FDI
(6.10.11.1.3-2)
where:
b = the smaller of do and D (in.)
do = the smaller of the adjacent web panel widths(in.)
It = moment of inertia of the transverse stiffenertaken about the edge in contact with the webfor single stiffeners and about the mid-thickness of the web for stiffener pairs (in.4)
J = stiffener bending rigidity constant
5002
522 ..
D/d
.
o
(6.10.11.1.3-3)
Vcr = shear-buckling resistance defined by Eq.6.10.9.2-1 (kip)
Vu = shear in the web at the section underconsideration due to factored loads (kip)
v = resistance factor for shear specified in Article6.5.4.2
t = the larger of Fyw/Fcrs and 1.0
Fcrs = local buckling stress for the stiffener (ksi)
2
0.31ys
t
p
EF
bt
(6.10.11.1.3-4)
Fys = specified minimum yield strength of thestiffener (ksi)
For transverse stiffeners adjacent to web panels inwhich Vu > vVcr in one or both panels, the moment ofinertia of the transverse stiffeners shall satisfy Eq. 2.
Suggested Modification to AASHTO(2004) Rigidity Requirement
JtdI 3wot 5.02
Dd
5.2J 2
o
stiffenerssidedtwo3
bt2I
stiffenerssidedone3
btI
3tp
t
3tp
t
(to develop the buckling strength of a flat web panel, no TFA)
b = min(do, D)
Required J to Develop the BucklingStrength (Flat Webs, no TFA)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0.5 1 1.5 2 2.5 3
do/D
J
Stanway et al. (1993), μcr = 0.95
Stanway et al. (1993), μcr = 0.90
Stanway et al. (1993), μcr = 0.80
AASHTO (2004)
Bleich (1952)
Timoshenko and Gere (1961)
)0I(V)I(V)0I(V)I(V
utcrtcr
tcrtcrcr
Behavior of Equations, Plate Stiffeners
… more than 1,200 parametric cases considered
(see spreadsheet)
Varied Parameters Recommended AASHTO Eqs AASHTO (2004)n Fyw Fys D/bf bt/tp do/D D/tw bt/D bt/D bt/D bt/D bt/D bt/D bt/D
(ksi) (ksi) Eq (2-2) Eq (2-1) Eq (2-1) Eq (3-2) Eq (3-1) Eq (3-1) Eq (4-1)D = 4 ft D = 20 ft
1 50 50 2 10 1 150 0.125 0.075 0.042 0.086 0.046 0.046 0.0791 50 50 3 10 1 150 0.083 0.075 0.042 0.086 0.046 0.046 0.0791 50 50 4 10 1 150 0.063 0.075 0.042 0.086 0.046 0.046 0.0791 50 50 5 10 1 150 0.050 0.075 0.042 0.086 0.046 0.046 0.0791 50 50 6 10 1 150 0.042 0.075 0.042 0.086 0.046 0.046 0.0791 50 50 2 5 1 150 0.125 0.075 0.042 0.072 0.039 0.039 0.0561 50 50 3 5 1 150 0.083 0.075 0.042 0.072 0.039 0.039 0.0561 50 50 4 5 1 150 0.063 0.075 0.042 0.072 0.039 0.039 0.0561 50 50 5 5 1 150 0.050 0.075 0.042 0.072 0.039 0.039 0.0561 50 50 6 5 1 150 0.042 0.075 0.042 0.072 0.039 0.039 0.0561 50 50 2 16 1 150 0.125 0.075 0.042 0.108 0.052 0.052 0.1201 50 50 3 16 1 150 0.083 0.075 0.042 0.108 0.052 0.052 0.1201 50 50 4 16 1 150 0.063 0.075 0.042 0.108 0.052 0.052 0.1201 50 50 5 16 1 150 0.050 0.075 0.042 0.108 0.052 0.052 0.1201 50 50 6 16 1 150 0.042 0.075 0.042 0.108 0.052 0.052 0.120
Summary
For 1-sided plate stiffeners, the recommendedIt eqs give comparable or slightly smallerstiffener sizes vs the AASHTO (2004) areareqmt, except in the “dip” where the areareqmt does not govern
The recommended It eqs result in approxequal girder strengths regardless of whetherthe stiffeners are 1- or 2-sided
Summary
The recommended eqs are independent of theapplied shear Vu Simpler, avoid dependency of shear resistance on Vu
The Vu/vVn term in the AASHTO (2004) area reqmt causes the actual Vnto be smaller than the computed Vn
Fortunately, Eqs. (2-1) and (2-2) govern the stiffener size in a numberof practical cases + one size is often selected for all the stiffeners inpractice
Eq. (3-2) facilitates the calculation of a singlesize for all transverse stiffeners, since it is alsoindependent of D/tw and do/D
Eq. (3-1) gives a constant It reqmt for do/D > 1
Thank You for your Attention
I’d be happy to address anyquestions
Additional Slides
Required stiffener sizes, do/D = 3, one-sided stiffeners (Fyw = 70 ksi, bt/tp = 10)
yww FEk121tD /./
Recommended
Required stiffener sizes, do/D = 2, one-sided stiffeners (Fyw = 70 ksi, bt/tp = 10)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
50 100 150 200 250 300D/tw
b s/b'
scr(
C=
1)
b's/b'scr(C=1)
bs/b'scr(C=1) (AASHTO 2004)bs/b'scr(C=1) (Horne & Grayson 1983)bs/b'scr(C=1) (Stanway et al. 1996)bs/b'scr(C=1) FEA, this study
bs = b'scr(C=1), yww F/Ek12.1t/D
Recommended
Required stiffener sizes, do/D = 1.5, one-sided stiffeners (Fyw = 70 ksi, bt/tp = 10)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
50 100 150 200 250 300D/tw
b s/b
' scr(
C=
1)
b's/b'scr(C=1)
bs/b'scr(C=1) (AASHTO 2004)bs/b'scr(C=1) (Horne & Grayson 1983)bs/b'scr(C=1) (Stanway et al. 1996)bs/b'scr(C=1) FEA, this study
bs = b'scr(C=1), yww F/Ek12.1t/D
Recommended
Required stiffener sizes, do/D = 0.5, one-sided stiffeners (Fyw = 70 ksi, bt/tp = 10)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
50 100 150 200 250 300
D/tw
[Is/
I 'scr
(C=1
)]^0
.25
[IsAASHTO/I'scr(C=1)]^0.25
[Is/I'scr(C=1)]^0.25 (Horne & Grayson 1983)
[Isd/I'scr(C=1)]^0.25 (Stanway et al. 1996)
[Isd/I'scr(C=1)]^0.25 for FEA girders
[IsFEA/I'scr(C=1)]^0.25yww FEk121tD /./,
Recommended
Relative frequency polygon vs thenormal distribution, Vtest/Vn
0
0.05
0.1
0.15
0.2
0.25
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
Vtest/Vn
Freq
uenc
y
Relative Frequency
Normal Distribution
122 ExperimentalShear Strength tests(White & Barker 2004)
Recommended