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Unified Steel Girder Design Specification 2-1
Unified Straight and Curved Steel Girder Design Specifications
IntroductionUnified Steel Specifications
StraightCurved
One Spec!
Unified Steel Girder Design Specification 2-2
Unified Steel Girder Design
ü Fundamentals
ü Design Checks
ü Examples
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
Fundamentals
Unified Steel Girder Design Specification 2-3
6.10.8 Flexural Resistance - Composite I Sections in Negative Flexure & Noncomposite I Sections - (cont’d)B a s i c F o r m o f A l l F L B & L T B E q s
M m a x
M r
λ p λ r
c o m p a c t n o n c o m p a c t
n o n s l e n d e r s l e n d e r
( i n e l a s t i c b u c k l i n g )
( e l a s t i c b u c k l i n g )
M m a x
M r
λ p λ r
c o m p a c t n o n c o m p a c t
n o n s l e n d e r s l e n d e r
( i n e l a s t i c b u c k l i n g )
( e l a s t i c b u c k l i n g )
A n c h o r p o i n t 1
A n c h o r p o i n t 2
L b o r b fc / 2 tfcL p o r λ p f L r o r λ rf
F n o r M n
F m a x o r M m a x
F r o r M r
ychbcrnc FRRFF ≤=
ychbnc FRRF =ychb
pfrf
pff
ych
yrnc FRR
FR
F11F
λ−λλ−λ
−−=
2
t
b
2bb
rL
ERC
π
FLB and LTB
y chby chbpr
pb
y ch
y rbnc FRRFRR
LL
LL
FR
F11CF ≤
−
−
−−=
Post Web Buckling Strength
Buckled Web Sheds Stress to the Compression Flange Reducing Flange Yielding Moment
Tension Flange 0.1
SFMWeb Buckled withYield First Moment
Ryy
b ≤=
=
Dc
21 1.01200 300
wc crwb
wc w
a DRa t
= − − λ ≤+
yffhb
bu FRR
fφ≤ yfhbfbu FRRf φ≤⇒
Unified Steel Girder Design Specification 2-4
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
Fundamentals
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
Unified Steel Girder Design Specification 2-5
• Outside girder carries more load
• Vertical Deflection is not equal between adjacent girders
=> Torsional Effects on Girders, Lateral Flange Bending, and Affects fit-up during construction
Differential Load/Deflection Effects
L1 L2 OUTSIDEGIRDER
ABUT
PIER
ABUT
INSIDEGIRDER
PLAN VIEW
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
Unified Steel Girder Design Specification 2-6
Torsion Effects
ü Deformations
ü Stresses
ü Twisting
ü Warping
=> Affect fit-up during construction
Torsion Deformations
Unified Steel Girder Design Specification 2-7
6.7.2 Dead Load Camber
l Contract documents should state:
• Intended erected position:
• Webs vertical or plumb, or
• Webs out-of-plumb
l Contract documents should state:
• Condition for intended position:
• No-load,• Steel dead load, or• Full dead load
6.7.2 Dead Load Camber, cont’d
Unified Steel Girder Design Specification 2-8
• St. Venant
• Warping
Torsion Stresses
Normal Stresses Shear Stresses
X XLat
eral Fla
nge Bend
ing
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
Unified Steel Girder Design Specification 2-9
Lateral Force Effects
Bending stress due to vertical loads
flange lateral bending stress due to wind, skew, or
curvature
rbu Fff ≤± l?
lf
buf
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 1.6
fl / Fyf
f bu
/ Fyf Flange Plastic Strength
Fyf – fl / 3 (Hall and Yoo 1998)
AISC/AASHTO Beam-Column Interaction Curves
0.7Fyf – fl / 3
0.856Fyf – fl / 3
“One-Third” Rule
Unified Steel Girder Design Specification 2-10
=> Lateral Force Effects & “One-Third” Rule
Bending stress due to vertical loads
flange lateral bending stress due to wind, skew, or
curvature
ytfbu
ncfbu
Fff
Fff
φ
φ
≤+
≤+
l
l
3131
lf
buf
Implementation of “One-Third” Rule
rbu Fff ≤+ l31
rxu MSfM ≤+ l31
rbu Fff ≤+ l
rbu Fff ≤+ l21
rbu Ff ≤ ALL L.S., Continuously Braced Flanges,
Service Limit State
Strength Limit State, Constructibility-Compression
Strength Limit State – Compact Straight
0=lf
21
31
⇒
Constructibility Yielding 131
⇒
Disc
rete
ly Br
aced
Fla
nges
Cont
inuo
usly
Brac
ed F
lang
es
Unified Steel Girder Design Specification 2-11
Implementation of “One-Third” Rule
rbu Fff ≤+ l31
rxu MSfM ≤+ l31
rbu Fff ≤+ l
rbu Fff ≤+ l21
rbu Ff ≤ ALL L.S., Continuously Braced Flanges,
Service Limit State
Strength Limit State, Constructibility-Compression
Strength Limit State – Compact Straight
0=lf
21
31
⇒
Constructibility Yielding 131
⇒
Disc
rete
ly Br
aced
Fla
nges
Cont
inuo
usly
Brac
ed F
lang
es
Implementation of “One-Third” Rule
rbu Fff ≤+ l31
rxu MSfM ≤+ l31
rbu Fff ≤+ l
rbu Fff ≤+ l21
rbu Ff ≤ ALL L.S., Continuously Braced Flanges,
Service Limit State
Strength Limit State, Constructibility-Compression
Strength Limit State – Compact Straight
0=lf
21
31
⇒
Constructibility Yielding 131
⇒
Disc
rete
ly Br
aced
Fla
nges
Cont
inuo
usly
Brac
ed F
lang
es
Unified Steel Girder Design Specification 2-12
Implementation of “One-Third” Rule
rbu Fff ≤+ l31
rxu MSfM ≤+ l31
rbu Fff ≤+ l
rbu Fff ≤+ l21
rbu Ff ≤ ALL L.S., Continuously Braced Flanges,
Service Limit State
Strength Limit State, Constructibility-Compression
Strength Limit State – Compact Straight
0=lf
21
31
⇒
Constructibility Yielding 131
⇒
Disc
rete
ly Br
aced
Fla
nges
Cont
inuo
usly
Brac
ed F
lang
es
Implementation of “One-Third” Rule
rbu Fff ≤+ l31
rxu MSfM ≤+ l31
rbu Fff ≤+ l
rbu Fff ≤+ l21
rbu Ff ≤ ALL L.S., Continuously Braced Flanges,
Service Limit State
Strength Limit State, Constructibility-Compression
Strength Limit State – Compact Straight
0=lf
21
31
⇒
Constructibility Yielding 131
⇒
Disc
rete
ly Br
aced
Fla
nges
Cont
inuo
usly
Brac
ed F
lang
es
Unified Steel Girder Design Specification 2-13
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
Second-order compression-flange lateral bending stresses may be approximated by amplifying first-order value:
ycbu
bbpb Ff
RCLL 2.1>
111
85.0lll ff
Ff
f
cr
bu≥
−=
2
2
=
t
b
bbcr
rL
ERCF
π
Unified Steel Girder Design Specification 2-14
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)
Fundamentals
Unified Curved Steel Girder Design
ü Fundamentals
ü Design Checks
ü Examples
Unified Steel Girder Design Specification 2-15
ü Constructibility
ü Service Limit State
ü Fatigue Limit State
ü Strength Limit State
Design Checks
6.10.3.2 Constructibility - FlexurelDiscretely braced compression flanges
)max,(31
ychncfbu FRLTBorFLBFff =≤+ φl
yfhfbu FRf φ≤
ythfbu FRff φ≤+ l
ychfbu FRff φ≤+ l
crwfbu Ff φ≤2
9.0
=⇒
w
crw
tD
EkF ( )2
9
DDk
c
=
l Discretely braced tension flanges
l Continuously braced flanges
)0.1( =bR
Unified Steel Girder Design Specification 2-16
ü Constructibility
ü Service Limit State
ü Fatigue Limit State
ü Strength Limit State
Design Checks
6.10.4.2 Service Limit State Permanent Deformations
l Composite:
l Noncomposite:
yfhf FRff 95.02
≤+ l
crwc Ff ≤
yfhf FRf 95.0≤
yfhf FRff 80.02
≤+ l
yfhf FRff 80.02
≤+ l
( )onlyMFf crwc−≤
Unified Steel Girder Design Specification 2-17
ü Constructibility
ü Service Limit State
ü Fatigue Limit State
ü Strength Limit State
Design Checks
6.10.5 Fatigue & Fracture Limit State
Fatigue stress ranges due to major-axis plus lateral bending shall be investigated
Unified Steel Girder Design Specification 2-18
Design Checks
ü Constructibility
ü Service Limit State
ü Fatigue Limit State
ü Strength Limit State
6.10.7 Flexural ResistanceComposite Sections in Positive Flexurel 6.10.7.2 Noncompact Sections
• Compact sections are not permitted for horizontally curved girders.
• Compression flanges
• Tension flanges
• Ductility Requirements - Concrete Crushing Prior to Plastification of Steel Section
13b u f h ytf f R F+ ≤ φl
b u f b h ycf R R F≤ φ
+
Unified Steel Girder Design Specification 2-19
6.10.8 Flexural ResistanceComposite Sections in Negative Flexure
and Noncomposite Sections• Discretely braced compression flanges
• Discretely braced tension flanges
• Continuously braced flanges
)max,(31
ychbncfbu FRRLTBorFLBFff =≤+ φl
yfhfbu FRf φ≤
ythfbu FRff φ≤+ l31
-
Additional Provisions for
“STRAIGHT” Girder Design
Unified Steel Girder Design Specification 2-20
ü Compact Sections in Positive Flexure - Appendix A
ü Moment Redistribution - Appendix B
Additional Provisions for
“STRAIGHT” Girder Design
l Discretely braced compression flanges
l Discretely braced tension flanges
ncfxcu MSfM φ≤+ l31
Appendix A -- Flexural Resistance -Composite Sections in Negative Flexure &
Noncomposite Sections w/ Compact or Noncompact Webs
ytptfxtu MRSfM φ≤+ l31
Unified Steel Girder Design Specification 2-21
ü Compact Sections in Positive Flexure - Appendix A
ü Moment Redistribution - Appendix B
Additional Provisions for
Straight Girder Design
Appendix B - Moment Redistribution from Interior-Pier 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
Refined
Unified Steel Girder Design Specification 2-22
Unified Steel Girder Design
ü Fundamentals
ü Design Checks
ü Examples
FHWA - NSBA
Unified Steel Girder Design Specification 2-23
NCHRP 12-52
TNDOT
Unified Steel Girder Design Specification 2-24
TNDOT
SUMMARYUnified Steel Specifications
StraightCurved
One Spec!Enough Said!