Transverse Stiffener Requirements in Straight and Horizontally Curved Steel I-Girders Yoon Duk Kim, Se-Kwon Jung and Donald W. White Georgia Institute of Technology School of Civil and Environmental Engineering Atlanta, GA 2005 AASHTO Bridge Committee Agenda Item 38 June 27, 2005
Problem Statement
Identify the demands on transverse stiffeners in curved and straight I-girders designed within the AASHTO (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 (TransverselyStiffened 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 d o/D = 3 bf determined such that Mu ~ 0.75Mn based on the one-third rule bt/tp = 10 in primary studies (other bt/tp considered in
Various one- and two-sided stiffener sizes
supplementary studies)
Parametric Studies (LongitudinallyStiffened 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/t w 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/Itcr do/D = 1, D/tw = 150
3 ) It = A s2nb (b It = /3/(b Itt4/t = ntpb p)/3n t/t t p/3
Itcr = It req’d to develop Vn = Vcr
TFA Strength vs It/Itcr do/D = 1, D/tw = 150 AASHTO (2004) area requirement, one-sided stiffeners AASHTO (2004) area requirement, two-sided stiffeners
Recommended
Shell Model - Perspective View of Deformed Geometry at Max Load It = Itcr, do/D = 1, D/tw = 150, 1-sided stiffener Undeformed geometry
Deformed geometry (Scale Factor = 5.0) Straight I-girder
(note: 18.5It cr is req’d to satisfy the AASHTO (2004) area reqmt)
Shell Model – Mid-thickness Von Mises Stress Distribution at Max Load It = Itcr, do/D = 1, D/tw = 150, 1-sided stiffener
(Scale Factor = 5.0) Straight I-girder
(note: 18.5It cr is req’d to satisfy the AASHTO (2004) area reqmt)
Perspective View of Deformed Geometry at Max Load It = 6Itcr, do/D = 1, D/tw = 150, 1-sided stiffener
Undeformed geometry
Deformed geometry
(Scale Factor = 5.0) Curved I-girder
Mid-thickness Von Mises Stress Distribution at Max Load It = 6Itcr, do/D = 1, D/tw = 150, 1-sided stiffener
(Scale Factor = 5.0) Curved I-girder
TFA Strength vs It/Itcr do/D = 1, D/tw = 300
Rahal and Harding (1990a) “… the important panel influence on the stiffener is lateral loading induced by panel buckling. For panels bounded by actual flange members there is evidence of a significant tension field loading on the stiffener, but the effect of this, even for the more slender plates considered, is less than the beneficial effect resulting from the lateral stiffener bending restraint provided by the flange. This indicates that bending rigidity rather than axial stiffness is the most important parameter for the design of the stiffener, which supports the emphasis placed on stiffener rigidity in the study by Horne and Grayson.”
Similar conclusions have been reached by Rahal and Harding (1990b & 1991) Horne and Grayson (1983) Stanway, Chapman and Dowling (1993 & 1996) Xie (2000) Lee, Yoo and Dong (2002 & 2003)
Required Stiffener Sizes, do/D = 1, onesided stiffeners 0.5 1.6 D/tw = 1.12 (Ek/F yw)
tw = D (Fyw/E/k)0.5 / 1.12
I’tcr = btw3J
b’tcr(C=1) = [3(bt/tp) I’tcr/n]0.25
1.4
[I s/Ib'scr /b' (C=1)] t tc r(C =1)
^0 .25
1.2 1.0 0.8 0.6
btbs/bscr(C=1) /b'tcr(C=1) (AASHTO 2004) (AASHTO 2004) btbs/bscr(C=1) /b'tcr(C=1) (Horne (Horne & Grayson & Grayson 1983) 1983) (Stanway et al. 1996) btbs/bscr(C=1) /b'tcr(C=1) (Stanway et al. 1996) study btbs/bscr(C=1) /b'tcr(C=1) FEA,FEA, thisthis study
0.4
bs/bscr(C=1), bs/bscr(C=1),D / t w
0.2
bt = b'tcr(C=1),
1. 12 Ek / Fyw
0.0 50
100
150
200
D/t ww
250
300
Required Stiffener Sizes, do/D = 1, onesided stiffeners 1.6
Recommended 1.4
[I s/Ib'scr /b' (C=1)] t tc r(C =1)
^0 .25
1.2 1.0 0.8 0.6
btbs/bscr(C=1) /b'tcr(C=1) (AASHTO 2004) (AASHTO 2004) btbs/bscr(C=1) /b'tcr(C=1) (Horne (Horne & Grayson & Grayson 1983) 1983) (Stanway et al. 1996) btbs/bscr(C=1) /b'tcr(C=1) (Stanway et al. 1996) study btbs/bscr(C=1) /b'tcr(C=1) FEA,FEA, thisthis study
0.4
bs/bscr(C=1), bs/bscr(C=1),D / t w
0.2
bt = b'tcr(C=1),
1. 12 Ek / Fyw
0.0 50
100
150
200
D/t ww
250
300
Required stiffener sizes, do/D = 1, twosided stiffeners [IsA SHT O /Is'cr(C =1 )]^02004) .2 5 b t /b'Atcr(C=1) (AASHTO [Is/I'scr(C =1)]^0 .25 (Ho rne & G rayso n 19 83 ) b /b' (Horne & Grayson 1983) t
1.6
tcr(C=1)
[Isd /I'scr(C =1(Stanway )]^0.2 5 (S tanway et al. 1 99 6) b t /b' et al. 1996) tcr(C=1) [Isd /I'scr(C =1FEA, )]^0.2this 5 forstudy F EA gird ers b t /b' tcr(C=1) [IsF E A /I'scr(C =1)]^0.25
1.4
b = b'
S et ries6tcr(C=1)
,
D / t w 1.12 Ek / Fyw
[I s/Ib'scr /b' (C=1)] t tcr(C=1)
^0.25
1.2 1.0 0.8
Recommended
0.6 0.4 0.2 0.0 50
100
1 50
2 00
D/t D/tww
250
30 0
6.10.11.1.2 Projecting Width The width, bt, of each projecting stiffener element shall satisfy:
D bt 2.0 30
(6.10.11.1.2-1)
and 16t p bt b f / 4
(6.10.11.1.2-2)
where: bf
=
for I-sections, full width of the widest compression flange within the field section under consideration; for tub girder sections, full width of the widest top flange within the field section under consideration; for closed box sections, 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 in which V u < vV cr in both panels, the moment of inertia of the transverse stiffener shall satisfy the smaller of the following limits:
I t bt w J 3
D Fyw It 40 E where: 4 1 .3 t
b
=
(6.10.11.1.3-1) 1 .5
(6.10.11.1.3-2)
the smaller of d o and D (in.)
do =
the smaller of the adjacent web panel widths (in.)
It
moment of inertia of the transverse stiffener taken about the edge in contact with the web for single stiffeners and about the midthickness of the web for stiffener pairs (in.4)
=
J
=
stiffener bending rigidity constant
2 .5
d o / D 2
2.0 0 .5
(6.10.11.1.3-3)
Vcr =
shear-buckling resistance 6.10.9.2-1 (kip)
Vu =
shear in the web at the section under consideration due to factored loads (kip)
v =
resistance factor for shear specified in Article 6.5.4.2
t =
the larger of Fyw /Fcrs and 1.0
Fcrs =
local buckling stress for the stiffener (ksi)
Fys =
0.31 E bt t p
2
Fys
defined by Eq.
(6.10.11.1.3-4)
specified minimum yield strength of the stiffener (ksi)
For transverse stiffeners adjacent to web panels in which Vu > vVcr in one or both panels, the moment of inertia of the transverse stiffeners shall satisfy Eq. 2.
Suggested Modification to AASHTO (2004) Rigidity Requirement (to develop the buckling strength of a flat web panel, no TFA)
It do t 3w J b = min(d o, D)
t pb 3t It 3 t pb 3t It 2 3
2 .5 J 2 0.5 2 do D
one sided stiffeners two sided stiffeners
Required J to Develop the Buckling Strength (Flat Webs, no TFA) 1.6 Stanway et al. (1993), μcr = 0.95 1.4
Stanway et al. (1993), μcr = 0.90 Stanway et al. (1993), μcr = 0.80
1.2
AASHTO (2004) Bleich (1952)
J
1.0
Timoshenko and Gere (1961)
V (I ) Vcr (It 0 ) ucr cr t Vcr (It ) Vcr (It 0 )
0.8 0.6 0.4
0.2 0.0 0.5
1
1.5
2
do/D
2.5
3
Behavior of Equations, Plate Stiffeners Varied Parameters n Fyw Fys D/bf bt/tp do/D (ksi) (ksi) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
50 50 50 50 50 50 50 50 50 50 50 50 50 50 50
50 50 50 50 50 50 50 50 50 50 50 50 50 50 50
2 3 4 5 6 2 3 4 5 6 2 3 4 5 6
10 10 10 10 10 5 5 5 5 5 16 16 16 16 16
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
D/tw
150 150 150 150 150 150 150 150 150 150 150 150 150 150 150
Recommended AASHTO Eqs bt/D bt/D bt/D Eq (2-2) Eq (2-1) Eq (2-1) D = 4 ft D = 20 ft 0.125 0.075 0.042 0.083 0.075 0.042 0.063 0.075 0.042 0.050 0.075 0.042 0.042 0.075 0.042 0.125 0.075 0.042 0.083 0.075 0.042 0.063 0.075 0.042 0.050 0.075 0.042 0.042 0.075 0.042 0.125 0.075 0.042 0.083 0.075 0.042 0.063 0.075 0.042 0.050 0.075 0.042 0.042 0.075 0.042
AASHTO (2004) bt/D bt/D bt/D bt/D Eq (3-2) Eq (3-1) Eq (3-1) Eq (4-1) 0.086 0.086 0.086 0.086 0.086 0.072 0.072 0.072 0.072 0.072 0.108 0.108 0.108 0.108 0.108
… more than 1,200 parametric cases considered (see spreadsheet)
0.046 0.046 0.046 0.046 0.046 0.039 0.039 0.039 0.039 0.039 0.052 0.052 0.052 0.052 0.052
0.046 0.046 0.046 0.046 0.046 0.039 0.039 0.039 0.039 0.039 0.052 0.052 0.052 0.052 0.052
0.079 0.079 0.079 0.079 0.079 0.056 0.056 0.056 0.056 0.056 0.120 0.120 0.120 0.120 0.120
Summary
For 1-sided plate stiffeners, the recommended It eqs give comparable or slightly smaller stiffener sizes vs the AASHTO (2004) area reqmt, except in the “dip” where the area reqmt does not govern The recommended It eqs result in approx equal girder strengths regardless of whether the stiffeners are 1- or 2-sided
Summary
The recommended eqs are independent of the applied shear Vu
Simpler, avoid dependency of shear resistance on Vu The V u/ vV n term in the AASHTO (2004) area reqmt causes the actual Vn to be smaller than the computed Vn Fortunately, Eqs. (2-1) and (2-2) govern the stiffener size in a number of practical cases + one size is often selected for all the stiffeners in practice
Eq. (3-2) facilitates the calculation of a single size for all transverse stiffeners, since it is also independent 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 any questions
Additional Slides
Required stiffener sizes, do/D = 3, onesided stiffeners (Fyw = 70 ksi, bt/tp = 10)
D / t w 1.12 Ek / Fyw
Recommended
Required stiffener sizes, do/D = 2, onesided stiffeners (Fyw = 70 ksi, bt/tp = 10) b s/b'scr(C=1) (AASHTO 2004) b s/b'scr(C=1) (Horne & Grayson 1983) b s/b'scr(C=1) (Stanway et al. 1996) b s/b'scr(C=1) FEA, this study b's/b'scr(C=1) b s = b' scr(C=1), D / t w 1.12 Ek / Fyw
1.6
1.4
bs/b' scr(C=1)
1.2 1.0 0.8
Recommended
0.6 0.4 0.2 0.0 50
100
150
200
D/t w
250
300
Required stiffener sizes, do/D = 1.5, onesided stiffeners (Fyw = 70 ksi, bt/tp = 10) 1.6 1.4
Recommended
bs /b' scr(C=1)
1.2 1.0
0.8
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 b's/b'scr(C=1) bs = b'scr(C=1), D / t w 1.12 Ek / Fyw
0.6 0.4 0.2 0.0 50
100
150
D/tw
200
250
300
Required stiffener sizes, do/D = 0.5, onesided stiffeners (Fyw = 70 ksi, bt/tp = 10) 1.6 1.4
Recommended
[I s /I 'scr (C=1)]
^0 .25
1.2 1.0 0.8 0.6
[IsAASHTO/I'scr(C=1)]^0.25 [Is/I'scr(C=1)]^0.25 (Horne & Grayson 1983)
0.4
[Isd/I'scr(C=1)]^0.25 (Stanway et al. 1996) [Isd/I'scr(C=1)]^0.25 for FEA girders
0.2
[IsFEA/I'scr(C=1)]^0.25 , D / t w 1.12 Ek / Fyw 0.0 50
100
150
200
D/tw
250
300
Relative frequency polygon vs the normal distribution, Vtest/Vn 122 Experimental Shear Strength tests (White & Barker 2004)
0.25
Relative Frequency 0.2
Frequency
Normal Distribution 0.15
0.1
0.05
0 0.6
0.7
0.8
0.9
1
Vtest /Vn
1.1
1.2
1.3
1.4
