Unified LFRD Steel Design Specification

Unified Straight and Curved Steel Girder Design Specifications

Introduction Unified Steel Specifications Straight Curved One Spec!

Unified Steel Girder Design Specification

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Unified Steel Girder Design ü Fundamentals ü Design Checks ü Examples

Fundamentals ü Primary-Strength Flexural & Shear Effects ü Lateral Flange Effects ü Differential Deflection Effects ü Torsion Effects ü Lateral Force Effects ü Second-Order Effects ü Cross Frame Forces


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6.10.8 Flexural Resistance - Composite I FLB and LTB Flexure & Sections B a s i c F oinr m o f Negative All FLB & LTB Eqs Noncomposite I Sections -  (cont’d)    F n or M

Fm a x or M M max max

Fy r L − Lp  b Fnc = Cb 1 − 1 −     RhFy c   Lr − L p

Anchor point 1

n

Fnc =RbRhFyc

  Fyr Fnc = 1 − 1 −  R Fyc h  

  λ f − λpf    λrf − λpf 

  Rb RhFy c ≤ RbR hFy c  

   R bR hFyc  

Anchor point 2 F r or M Mr r

compact

Fnc = Fcr ≤ RbRhFyc

noncompact

 Lb  r  t

(inelastic buckling) nonslender

C bR b π 2 E

slender

   

2

(elastic buckling) L p oλ r pλ p f

L r λo rr λ rf

L b or b

fc /

2 tf c

Post Web Buckling Strength f bu ≤ φ f F yf ⇒ f bu ≤ φ f R b R h F yf Rb R h Buckled Web Sheds Stress to the Compression Flange Reducing Flange Yielding Moment

Dc

Tension Flange

Rb =

Moment First Yield with Buckled Web ≤ 1.0 M y = Fy S



 2 Dc  awc − λ rw  ≤ 1.0   1200 + 300 awc  tw 

Rb = 1 − 


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Fundamentals ü Primary Flexural & Shear Effects ü Lateral Flange Effects ü Differential Deflection Effects ü Torsion Effects ü Lateral Force Effects ü Second-Order Effects ü Cross Frame Forces



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Differential Load/Deflection Effects

• Outside girder carries more load • Vertical Deflection is not equal between adjacent girders => Torsional Effects on Girders, Lateral Flange Bending, and Affects fitup during construction

L1

OUTSIDE GIRDER

L2

PIER AB UT

UT AB

PLAN VIEW

INSIDE GIRDER



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Torsion Effects

ü Deformations

ü Stresses

Torsion Deformations ü Twisting

ü Warping

=> Affect fit-up during construction


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6.7.2 Dead Load Camber l

Contract documents should state: • Intended erected position: • Webs vertical or plumb, or • Webs out-of-plumb

6.7.2 Dead Load Camber, cont’d l

Contract documents should state: • Condition for intended position: • No-load, • Steel dead load, or • Full dead load


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Torsion Stresses • St. Venant • Warping l ta era L

g din n e eB g n Fla

Normal Stresses

XX Shear Stresses



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Lateral Force Effects

f bu ± ? f l ≤ F r

f bu Bending stress due to vertical loads

fl

flange lateral bending stress due to wind, skew, or curvature

“One-Third” Rule 1.2

Fyf – fl / 3 (Hall and Yoo 1998)

1

0.856Fyf – fl / 3

fbu / Fyf

0.8

Flange Plastic Strength 0.6 0.4

0.7Fyf – fl / 3

0.2

AISC/AASHTO BeamColumn Interaction Curves

0 0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

f l / F yf


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=> Lateral Force Effects & “One-Third” Rule

1 f l ≤ φ f Fnc 3 1 + f l ≤ φ f F yt 3

f bu + f bu

f bu Bending stress due to vertical loads

fl

flange lateral bending stress due to wind, skew, or curvature

f bu +

1 f l ≤ Fr 3

Mu +

1 f l S x ≤ M r Strength Limit State – Compact Straight 3

f bu + f l ≤ Fr

f bu +

Continuously Braced Flanges

Discretely Braced Flanges

Implementation of “One-Third” Rule

1 f l ≤ Fr 2

f bu ≤ F r


Strength Limit State, Constructibility-Compression

1 ⇒1 3 1 1 Service Limit State ⇒ 3 2 Constructibility Yielding

ALL L.S., Continuously Braced Flanges, f l = 0

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f bu +

1 f l ≤ Fr 3

Mu +


f bu + f l ≤ Fr

f bu +




1 f l ≤ Fr 2

f bu ≤ F r




f bu +

1 f l ≤ Fr 3

Mu +


f bu + f l ≤ Fr

f bu +




1 f l ≤ Fr 2

f bu ≤ F r





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f bu +

1 f l ≤ Fr 3

Mu +


f bu + f l ≤ Fr

f bu +




1 f l ≤ Fr 2

f bu ≤ F r




f bu +

1 f l ≤ Fr 3

Mu +


f bu + f l ≤ Fr

f bu +




1 f l ≤ Fr 2

f bu ≤ F r





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Fundamentals ü Primary Flexural & Shear Effects ü Lateral Flange Effects ü Differential Deflection Effects ü Torsion Effects ü Lateral Force Effects ü Second-Order Effects ü Cross Frame Forces (Primary Members)

Second-Order Effects (Art. 6.10.1.6) l

If

Lb > 1. 2L p

Cb Rb fbu Fyc

Second-order compression-flange lateral bending stresses may be approximated by amplifying first-order value:

    0.85   f ≥ f l1 fl = f bu  l1  1 − F   cr 


Fcr =

Cb Rbπ 2 E L   b   rt 

2

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Fundamentals ü Primary Flexural & Shear Effects ü Lateral Flange Effects ü Differential Deflection Effects ü Torsion Effects ü Lateral Force Effects ü Second-Order Effects ü Cross Frame Forces (Primary Members)

Unified Curved Steel Girder Design ü Fundamentals ü Design Checks ü Examples


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Design Checks

ü Constructibility ü Service Limit State ü Fatigue Limit State ü Strength Limit State

6.10.3.2 Constructibility - Flexure lDiscretely

braced compression flanges 1 f bu + f l ≤ φ f Fnc ( FLB or LTB , max = R h F yc ) 3 f bu + fl ≤ φ f Rh Fyc fbu ≤ φ f Fcrw

l

⇒ Fcrw =

Discretely braced tension flanges

0.9 Ek D    tw 

2

k=

9

( Dc D )2

( Rb = 1 .0 )

fbu + f l ≤ φ f Rh Fyt l

Continuously braced flanges fbu ≤ φ f Rh Fyf


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Design Checks


6.10.4.2 Service Limit State Permanent Deformations l

Composite:

f f ≤ 0 .95 Rh Fyf

(

f c ≤ Fcrw M − only

)

f f f + l ≤ 0.95 Rh F yf 2

l

Noncomposite:

ff +

f c ≤ Fcrw


ff +

fl ≤ 0.80 Rh Fyf 2 fl ≤ 0.80 Rh Fyf 2

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Design Checks


6.10.5 Fatigue & Fracture Limit State Fatigue stress ranges due to major-axis plus lateral bending shall be investigated


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Design Checks


6.10.7 Flexural Resistance Composite Sections in Positive Flexure

+

l

6.10.7.2 Noncompact Sections • Compact sections are not permitted for horizontally curved girders. • Compression flanges

f b u ≤ φ f R b R h F yc • Tension flanges

fbu +

1 f l ≤ φ f R h F yt 3

• Ductility Requirements - Concrete Crushing Prior to Plastification of Steel Section


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-

6.10.8 Flexural Resistance Composite Sections in Negative Flexure and Noncomposite Sections • Discretely braced compression flanges f bu +

•

1 f l ≤ φ f Fnc ( FLB or LTB , max = Rb Rh F yc ) 3

Discretely braced tension flanges f bu +

1 f l ≤ φ f Rh Fyt 3

• Continuously braced flanges f bu ≤ φ f Rh Fyf

Additional Provisions for “STRAIGHT” Girder Design


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Additional Provisions for “STRAIGHT” Girder Design ü Compact Sections in Positive Flexure - Appendix A ü Moment Redistribution - Appendix B

Appendix A -- Flexural Resistance Composite Sections in Negative Flexure & Noncomposite Sections w/ Compact or Noncompact Webs l

Discretely braced compression flanges Mu +

l

1 f l S xc ≤ φ f M nc 3

Discretely braced tension flanges Mu +


1 f l S xt ≤ φ f R pt M 3

yt

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Additional Provisions for Straight Girder Design ü Compact Sections in Positive Flexure - Appendix A ü Moment Redistribution - Appendix B

Appendix B - Moment Redistribution from InteriorPier Sections in Continuous-Span Bridges l

Replaces traditional 10 percent redistribution rule

l

Service II load combination and Strength Limit State

l

Refined and simplified methods

d fine e R


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Unified Steel Girder Design ü Fundamentals ü Design Checks ü Examples

FHWA - NSBA


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NCHRP 12-52

TNDOT


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TNDOT

SUMMARY Unified Steel Specifications Straight Curved One Spec! Enough Said!


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