i PART 2 THE AASHTO LRFD SPECIFICATIONS 1.0 INTRODUCTION 1.1 Limit State 1.2. Load Combinations 1.3. Design Vehicle Live Load 1.4. Fatigue Load 1.5. Impact (Dynamic Load Allowance = IM) 1.6. Wind 1.7. Distribution Factor 2.0 STEEL STRUCTURES 2.1 Steel Material 2.2 Fatigue and Fracture Limit State 2.3 Resistance Factor 2.4 Tension Members 2.5 Compression Members 2.6 I-Section Flexural Members 2.7 Cross-Section Proportion Limits 2.8 Constructibility 2.9 Service Limit State (Permanent Deformations) 210 Fatigue and Fracture Limit State 2.11 Strength Limit State 2.12 Flexural Resistance-Composite Sections in Positive Flexure 2.13 Composite Sections in Negative Flexure and Noncomposite Sections 2.14 Shear Resistance 2.15 Shear Connectors 2.16 Transverse Stiffeners 2.17 Bearing Stiffeners 2.18 Longitudinal Stiffeners
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i
PART 2
THE AASHTO LRFD SPECIFICATIONS
1.0 INTRODUCTION
1.1 Limit State
1.2. Load Combinations
1.3. Design Vehicle Live Load
1.4. Fatigue Load
1.5. Impact (Dynamic Load Allowance = IM)
1.6. Wind
1.7. Distribution Factor
2.0 STEEL STRUCTURES
2.1 Steel Material
2.2 Fatigue and Fracture Limit State
2.3 Resistance Factor
2.4 Tension Members
2.5 Compression Members
2.6 I-Section Flexural Members
2.7 Cross-Section Proportion Limits
2.8 Constructibility
2.9 Service Limit State (Permanent Deformations)
210 Fatigue and Fracture Limit State
2.11 Strength Limit State
2.12 Flexural Resistance-Composite Sections in Positive Flexure
2.13 Composite Sections in Negative Flexure and Noncomposite Sections
2.14 Shear Resistance
2.15 Shear Connectors
2.16 Transverse Stiffeners
2.17 Bearing Stiffeners
2.18 Longitudinal Stiffeners
2-1
PART 2
THE AASHTO LRFD SPECIFICATIONS
1.0 INTRODUCTION
The AASHTO LRFD Specifications are written based on probabilistic limit state theory
with several load combinations listed. These load combinations correspond to four limit states,
Service, Fatigue, Fracture, Strength and Extreme-Event.
Service limit states are restrictions on stress, deformation and crack width under regular
service conditions. They are intended to allow the bridge to perform acceptably for its service
life.
Fatigue and fracture limit states are restrictions on stress range under regular service
conditions reflecting the number of expected stress range excursions. They are intended to limit
crack growth under repetitive loads to prevent fracture during the design life of the bridge.
Strength limit states are intended to ensure that strength and stability, both local and
global, are provided to resist the statistically significant load combinations that a bridge will
experience in its design life. Extensive distress and structural damage may occur under strength
limit states, but overall structural integrity is expected to be maintained.
Extreme event limit states are intended to ensure the structural survival of a bridge during
a major earthquake, or when collided by a vessel, vehicle or ice flow, or where the foundation is
subject to the scour which would accompany a flood of extreme recurrence, usually considered
to be 500 years. They are considered to be unique occurrences whose return period is
significantly greater than the design life of the bridge.
-2
1.1 Limit State
Definition: A condition beyond which the bridge or component ceases to satisfy the
0º ≤ θ ≤ 60º, 3′-5″ ≤ S ≤ 16′-0″, 20′ ≤ L ≤ 240′, Nb ≥ 4
2-17
TABLE 1-6 AASHTO TABLE FOR THE SHEAR DISTRIBUTION FACTOR OF THE
INTERIOR BEAMS (AASHTO LRFD Table 4.6.2.2.3a-1 – Distribution of Live Load Per Lane for Shear in Interior Beams)
Type of Superstructure
Applicable Cross-Section from
Table 4.6.2.2.1-1
One Design lane Loaded
Two or More Design Lanes Loaded
Range of Applicability
Wood Deck on Wood or Steel Beams
a, l See Table 4.6.2.2.2a-1
Concrete Deck on Wood Beams
l Lever Rule Lever Rule N/A
0.2535.0 S
+ 0.2
3122.0 ⎟
⎠⎞
⎜⎝⎛−+
SS
3.5 ≤ S ≤ 16.0 20 ≤ L ≤ 240 4.5 ≤ ts ≤ 12.0 10,000 ≤ Kg ≤ 7,000,000 Nb ≥ 4
Concrete Deck, filled Grid, Partially Filled Grid, or Unfilled Grid Deck Composite with Reinforced Concrete Slab on Steel or Concrete Beams; Concrete T-Beams, T- and Double T-Sections
a, e, k and also i, j
if sufficiently connected to act as
a unit Lever Rule Lever Rule Nb = 3
Cast-in-Place Concrete Multicell Box
d 1.06.0
0.125.9⎟⎠⎞
⎜⎝⎛
⎟⎠⎞
⎜⎝⎛
LdS
1.06.0
0.123.7⎟⎠⎞
⎜⎝⎛
⎟⎠⎞
⎜⎝⎛
LdS
6.0 ≤ S ≤ 13.0 20 ≤ L ≤ 240 35 ≤ ts ≤ 110 Nc ≥ 3
b, c 1.06.0
0.1210⎟⎠⎞
⎜⎝⎛
⎟⎠⎞
⎜⎝⎛
LdS 1.08.0
0.124.7⎟⎠⎞
⎜⎝⎛
⎟⎠⎞
⎜⎝⎛
LdS
6.0 ≤ S ≤ 18.0 20 ≤ L ≤ 140 18 ≤ d ≤ 65 Nb ≥ 3
Concrete Deck on Concrete Spread Box Beams
Lever Rule Lever Rule S > 18.0 Concrete Box Beams Used in Multi-Beam Decks
f, g 05.015.0
130⎟⎠⎞
⎜⎝⎛
⎟⎠⎞
⎜⎝⎛
JI
Lb
⎟⎠⎞
⎜⎝⎛
⎟⎠⎞
⎜⎝⎛
⎟⎠⎞
⎜⎝⎛
⎟⎠⎞
⎜⎝⎛
480.12156
05.01.04.0 bJI
Lbb
0.148
>b
35 ≤ b ≤ 60 20 ≤ L ≤ 120 5 ≤ Nb ≤ 20 25,000 ≤ J ≤ 610,000 40,000 ≤ I ≤ 610,000
h Concrete Beams Other Than Box Beams Used in Multi-Beam Decks
i, j if connected only enough to prevent relative vertical
displacement at the interface
Lever Rule Lever Rule N/A
Open Steel Grid Deck on Steel Beams
a Lever Rule Lever Rule N/A
Concrete Deck on Multiple Steel Box Beams
b, c As specified in Table 4.6.2.2.2b-1
2-18
TABLE 1-7 AASHTO TABLE FOR THE SHEAR DISTRIBUTION FACTOR OF THE
EXTERIOR BEAMS (AASHTO LRFD Table 4.6.2.2.3b-1 – Distribution of Live Load Per Lane for Shear in Exterior Beams)
Type of Superstructure Applicable Cross-Section from
Table 4.6.2.2.1-1
One Design Lane Loaded
Two or more Design Lanes Loaded
Range of Applicability
Wood Deck on Wood or Steel Beams
a, l Lever Rule Lever Rule N/A
Concrete Deck on Wood Beams
l Lever Rule Lever Rule N/A
g = e ginterior
10
6.0 ede +=
-1.0 ≤ de ≤5.5 Concrete Deck, Filled Grid, Partially Filled Grid, or Unfilled Grid Deck Composite with Reinforced Concrete Slab on Steel or Concrete Beams; Concrete T-Beams, T- and Double T-Beams
a, e, k and also i, j
if sufficiently connected to act
as a unit
Lever Rule
Lever Rule Nb = 3
Lever Rule g = e ginterior
5.12
64.0 ede +=
Case-in-Place Concrete Multicell Box
d
Or the provisions for a whole-width design specified in Article 4.6.2.2.1
-2.0 ≤ de ≤ 5.0
g = e ginterior
10
8.0 ede +=
0 ≤ de ≤ 4.5 Concrete Deck on Concrete Spread Box Beams
b, c Lever Rule
Lever Rule S > 18.0 Concrete Box Beams Used in Multi-Beam Decks
f, g g = e ginterior 0.1
2025.1 ≥+= ede
g = e ginterior
0.1/48 ≤b
0.140
0.2121
5.0
≥⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛ −++=
bde
e
de ≤2.0 35<b<60
h Concrete Beams Other Than Box Beams Used in Multi-Beam Decks
i, j if connected only enough to prevent relative vertical displacement at
the interface
Lever Rule Lever Rule N/A
Open Steel Grid Deck on Steel Beams
a Lever Rule Lever Rule N/A
Concrete Deck on Multiple Steel Box Beams
b, c As specified in Table 4.6.2.2.2b-1
-19
TABLE 1-8 AASHTO TABLE FOR THE DISTRIBUTION CORRECTION FACTOR
FOR SUPPORT SHEAR OF THE OBTUSE CORNER (AASHTO LRFD Table 4.6.2.2.3c-1 – Correction Factors for Load Distribution Factors for Support Shear of
the Obtuse Corner)
Type of Superstructure Applicable Cross-Section
from Table 4.6.2.2.1-1
Correction Factor Range of Applicability
a, e, k Concrete Deck, Filled Grid, Partially Filled Grid, or Unfilled Grid Deck Composite with Reinforced Concrete Slab on Steel or Concrete Beams; Concrete T-Beams, T- and Double T Section
i, j if sufficiently connected to act as a unit
θtan0.1220.00.13.0
3
⎟⎟⎠
⎞⎜⎜⎝
⎛+
g
s
KLt
0º ≤ θ ≤ 60º 3.5 ≤ S ≤ 16.0 20 ≤ L ≤ 240 Nb ≥ 4
Cast-in-Place Concrete Multicell Box
d θtan
700.1225.00.1 ⎥⎦
⎤⎢⎣⎡ ++
dL
0º ≤ θ ≤ 60º 6.0 ≤ S ≤ 13.0 20 ≤ L ≤ 240 35 ≤ d ≤ 110 Nc ≥ 3
Concrete Deck on Spread Concrete Box Beams
b, c
θtan6
0.120.1S
Ld
+
0º ≤ θ ≤ 60º 6.0 ≤ S ≤ 11.5 20 ≤ L ≤ 140 18 ≤ d ≤ 65 Nb ≥ 3
Concrete Box Beams Used in Multi-Beam Decks
f, g θtan
900.120.1dL
+ 0º ≤ θ ≤ 60º 20 ≤ L ≤ 120 17 ≤ d ≤ 60 35 ≤ b ≤ 60 5 ≤ Nb ≤ 20
2-1
2.0 STEEL STRUCTURES
2.1 Steel Material (LRFD Art. 6.4)
AASHTO Equiv. ASTM M270 Grade 36 A709 Grade 36 Structural 50 50 Steel 50W 50W 70W 70W 100/100W 100/100W Pins, Rollers M169 A108 Grade 36 Rockers M102 A668 Class C 33 Class D 37.5 Class F 50
Class G 50 Bolts A307 M164 A325 M253 A490 Nuts M291 A563 Washers M239 F436 Studs M169 A108 Cap A109 Cast Steel M192 A486 M103 A27 M163 A743 Ductile Iron A536 Ferritic Malleable A47 Grade 35018 Iron Castings Cast Iron M105 Class 30 A48 Casting Stainless A176 Steel A240 A276 A666 Wires A510 (Cables) A641(Zinc-Coated) A99 (Epoxy-Coated) A603(Zinc-Coated Wire Rope) A586(Zinc-Coated Parallel and Helical )
-2
.2 Fatigue and Fracture Limit State (LRFD Art. 6.6)
The fatigue provisions of the Steel Structures Section of the AASHTO LRFD
Specification for Highway Bridge Design combine aspects of both the AASHTO Standard
Specification for Highway Bridges (AASHTO 1996) and the Guide Specification for Fatigue
Design of Steel Bridges (AASHTO 1989). These provisions are based upon two principles of
fatigue of welded steel details:
If all of the stress ranges that a welded steel detail experiences in its lifetime are less than the
constant-amplitude fatigue threshold (i.e., the maximum stress range is less than the
threshold), the detail will not experience fatigue crack growth; otherwise
the fatigue life of the detail can be estimated considering an effective (weighted average of
sorts) stress range, which represents all of the varying magnitudes of stress range
experienced by the detail during its lifetime.
These two principles result in two branches in the flow of fatigue design, infinite life design and
finite life design.
Fatigue details for bridges with higher truck traffic volumes are designed for infinite life.
This practice is carried over from both the Standard Specifications and the Guide Specifications.
Bridges with lower truck traffic volumes are designed for the fatigue life required by the
estimated site-specific traffic volumes projected for their lifetimes.
( ) ( )nFf Δ≤Δγ (LRFD Eq. 6.6.1.2.2-1)
(1) Infinite Fatigue Life (When the design stress range is less than one-half of the constant-
amplitude fatigue threshold, the detail will theoretically provide infinite life.)
Detail Category 75-year (ADTT)SL equivalent to Infinite Life
A 535
B 865
B′ 1035
C 1290
C′ 745
D 1875
E 3545
E′ 6525
-3
(2) Finite Fatigue Life
( )THFNAFFn Δ≥⎟
⎠⎞
⎜⎝⎛=Δ=
213
1
; ( )( )( )( ) lanesingleADTT75365 −= nN
Category A ( Δ F)TH (ksi) n
A 2.5 x 1010 24 Ρ > 40′ Ρ < 40′ B 1.2 x 1010 16 Simple-span 1.0 2.0 B′ 6.1 x 109 12 C 4.4 x 109 10 Continuous C′ 4.4 x 109 12 (1) Near Interior 1.5 2.0 D 2.2 x 109 7 Support E 1.1 x 109 4.5 (2) Elsewhere 1.0 2.0 E′ 3.9 x 108 2.6
(a) Interior - min. of {beamsadjacentofspacingaverage
wandtoft
L
topflangewebslab
eff
)21
21(.max12
41
+
(b) Exterior - min. of { )41
21(.max6
81
topflangewebslab
eff
wandoverhangtheofwidthtoft
L
+
2008: Interior - one-half the distance to the adjacent girder on each side of the component;
Exterior – one-half the distance to the adjacent girder plus the full overhang width.
(2) Yield Moment Resistance My = MD1 + MD2 + MAD
Solve for the MAD from
ST
AD
LT
DL
NC
Dy S
MSM
SMF ++= 1 (LRFD D6.2.2-1)
SNC = Non-composite section modulus
SST = Short-term composite section modulus
SLT = Long-term composite section modulus
MD1, MD2 & MAD = Moments due to the factored loads
(3) Depth of Web in Compression
– Elastic (Dc)
• Positive flexure (distance from web top to elastic neutral axis)
ftC
Cc td
fff
D −⎥⎥⎦
⎤
⎢⎢⎣
⎡
+= (LRFD D 6.3.1-1)
• Negative flexure (distance from web bottom to elastic neutral axis)
Dc may be computed for the section consisting of the steel girders plus the
longitudinal reinforcement.
-11
– Plastic (Dcp), Positive flexure (distance from web top to plastic neutral axis)
• The plastic natural axis is in the web.
⎥⎥⎦
⎤
⎢⎢⎣
⎡+
−′−−= 1
85.02 wyw
ryrsccyctytcp AF
AFAfAFAFDD (LRFD D 6.3.2-1)
• All others, DCP = 0
– Plastic (Dcp), Negative flexure (distance from web bottom to plastic neutral axis)
• The plastic natural axis is in the web
( )cycryrwywtytyww
cp AFAFAFAFFA
DD −++=2
(LRFD D 6.3.2-2)
• All others, DCP = D
Figure 2-4 Computation of Dc at sections in Positive Flexure
-12
TABLE 2-1 AASHTO TABLE OF THE PLASTIC MOMENT FOR THE POSITIVE
BENDING SECTIONS
(AASHTO LRFD Table D6.1-1 – Calculation of y and Mp for Positive ending Sections)
CASE PNA CONDITION y AND Mp I In Web Pt + Pw ≥ Pc + Ps + Prb + Prt
⎥⎦
⎤⎢⎣
⎡+
−−−−⎟⎠⎞
⎜⎝⎛= 1
2 w
rbrtsct
PPPPPPDy
( )[ ] [ ]ttccrbrbrtrtssw
p dPdPdPdPdPyDyD
PM +++++−+=22
2
II In Top Flange
Pt + Pw + Pc ≥ Ps + Prb + Prt ⎥⎦
⎤⎢⎣
⎡+
−−−+⎟⎠⎞
⎜⎝⎛= 1
2 c
rbrtstwc
PPPPPPty
( )[ ] [ ]ttwwrbrbrtrtsscc
cp dPdPdPdPdPyty
tPM +++++−+=
22
2
III Slab, Below Prb
Pt + Pw + Pc ≥ ⎟⎟⎠
⎞⎜⎜⎝
⎛
s
rb
tC Ps + Prb + Prt ( ) ⎥
⎦
⎤⎢⎣
⎡ −−++=
s
rbrttwcs P
PPPPPty
[ ]ttwwccrbrbrtrts
sp dPdPdPdPdP
tPyM +++++
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛=
2
2
IV Slab, at Prb Pt + Pw + Pc + Prb ≥ ⎟⎟⎠
⎞⎜⎜⎝
⎛
s
rb
tC Ps + Prt rbCy =
[ ]ttwwccrtrts
sp dPdPdPdP
tPyM ++++
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛=
2
2
V Slab, Above Prb, Below Prt
Pt + Pw + Pc + Prb+ Prt ≥ ⎟⎟⎠
⎞⎜⎜⎝
⎛
s
rt
tC Ps ( ) ⎥
⎦
⎤⎢⎣
⎡ −+++=
s
rttwcrbs P
PPPPPty
[ ]ttwwccrbrbrtrts
sp dPdPdPdPdP
tPyM +++++
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛=
2
2
VI Slab, at Prt Pt + Pw + Pc + Prb ≥ ⎟⎟⎠
⎞⎜⎜⎝
⎛
s
rb
tC Ps + Prt ( ) ⎥
⎦
⎤⎢⎣
⎡ −+++=
s
rttwcrbs P
PPPPPty
[ ]ttwwccrbrbrtrts
sp dPdPdPdPdP
tPyM +++++
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛=
2
2
VII Slab, above Prt
Pt + Pw + Pc + Prb < ⎟⎟⎠
⎞⎜⎜⎝
⎛
s
rt
tC Ps + Prt ( ) ⎥
⎦
⎤⎢⎣
⎡ −+++=
s
rttwcrbs P
PPPPPty
[ ]ttwwccrbrbrtrts
sp dPdPdPdPdP
tPyM +++++
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛=
2
2
-13
TABLE 2-2 AASHTO TABLE OF THE PLASTIC MOMENT FOR THE NEGATIVE
BENDING SECTIONS
(AASHTO LRFD Table D6.1-2 – Calculation of y and Mp for Negative Bending Sections)
CASE PNA CONDITION y and Mp I In Web Pc + Pw ≥ Pt + Prb + Prt
⎥⎦
⎤⎢⎣
⎡+
−−−⎟⎠⎞
⎜⎝⎛= 1
2 w
rbrttc
PPPPPDy
( )[ ] [ ]ccttrbrbrtrtw
p dPdPdPdPyDyD
PM ++++−+=22
2
II In Top Flange
Pc + Pw + Pt ≥ Prb + Prt ⎥⎦
⎤⎢⎣
⎡+
−−+⎟⎠
⎞⎜⎝
⎛= 12 t
rbrtcwt
PPPPPt
y
( )[ ] [ ]ccwwrbrbrtrttt
tp dPdPdPdPyty
tPM ++++−+=
22
2
-14
2.6.2 Noncomposite Sections
Sections where the concrete deck is not connected to the steel section by shear connectors designed in this section shall be considered noncomposite sections.