Tăng cường độ ổn định trong dầm thép

Tăng cường độ ổn định trong dầm thép

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

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)

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)

 Various one- and two-sided stiffener sizes

 Longitudinal stiffener not included in models

TFA Strength vs I t /I tcr

AASHTO (2004) area requirement, two-sided stiffeners

AASHTO (2004) area requirement, one-sided stiffeners

Recommended

Shell Model - Perspective View of

Deformed Geometry at Max Load

Shell Model – Mid-thickness Von Mises Stress Distribution at Max Load

It = 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 Deformed

Geometry at Max Load

It = 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 Stress

Distribution at Max Load

It = 6Itcr, do/D = 1, D/tw = 150, 1-sided stiffener

Curved I-girder(Scale Factor = 5.0)

TFA Strength vs I t /I tcr

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)

(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

D/tw

[Is/I's

bs/bscr(C=1), bs/bscr(C=1),

bs/bscr(C=1), bs/bscr(C=1),

b f = for I-sections, full width of the widest

compression flange within the field sectionunder consideration; for tub girder sections, fullwidth of the widest top flange within the fieldsection under consideration; for closed box

sections, the limit of b f /4 does not apply (in.)

t p = 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 < v V cr in both panels, the moment of inertia ofthe transverse stiffener shall satisfy the smaller of thefollowing limits:

J

bt

5 1 3

1 4

40

yw

t t

E

F D

b = the smaller of d o and D (in.)

d o = the smaller of the adjacent web panel widths

(in.)

I t = moment of inertia of the transverse stiffener

taken 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

D / d

consideration due to factored loads (kip)

v = resistance factor for shear specified in Article

6.5.4.2

t = the larger of F yw /F crs and 1.0

F crs = local buckling stress for the stiffener (ksi)

2

0.31

ys t

p

E F b

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

J t d

D d

5 2

two 3

b

t 2 I

stiffeners sided

one 3

b

t I

3 t p t

3 t p t

Required J to Develop the Buckling

Strength (Flat Webs, no TFA)

Bleich (1952) Timoshenko and Gere (1961)

) 0 I ( V ) I

( V

) 0 I ( V ) I ( V u

t cr t

cr

t cr t

cr cr

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)

stiffener sizes vs the AASHTO (2004) area

reqmt, except in the “dip” where the area

reqmt does not govern

equal girder strengths regardless of whether the stiffeners are 1- or 2-sided

of practical cases + one size is often selected for all the stiffeners in practice

size for all transverse stiffeners, since it is also

Thank You for your Attention

I’d be happy to address any

questions

Additional Slides

Required stiffener sizes, d o /D = 3, sided stiffeners (F yw = 70 ksi, b t /t p = 10)

one-yw

w 1 12 Ek F t

D /  /

Recommended

Required stiffener sizes, d o /D = 2, sided stiffeners (F yw = 70 ksi, b t /t p = 10)

/

Recommended

Required stiffener sizes, d o /D = 1.5,

/

Recommended

Required stiffener sizes, d o /D = 0.5,

Relative frequency polygon vs the

normal distribution, V test /V n

122 ExperimentalShear Strength tests(White & Barker 2004)