SPECIFICATIONS
The attached document provides recommended modifications to Article 1.3 in Section I "Introduction" of the
AASHTO LRFD Bridge Design Specifications. The modifications provide a method to include system factors that
account for system ductility and redundancy during the design and safety evaluation of highway bridges.
1.3 DESIGN PHILOSOPHY
1.3.1 General
Bridges shall be designed for specified limit states to achieve the objectives of constructability, safety and
serviceability, with due regard to issues of inspectability, economy and aesthetics, as specified in Article 2.5.
Regardless of the type of analysis used, Equation 1.3.2.1 -1 shall be satisfied for all specified force effects
and combinations thereof.
1.3.2 Limit States
1.3.2.1 General
Each component and connection shall satisfy Eq. 1.3.2.1-1 for each limit state, unless otherwise
specified. For service and extreme event limit states, resistance factors shall be taken as 1.0, except for bolts, for
which the provisions of Article 6.5.5 shall apply, and for concrete columns in Seismic Zones 2, 3, and 4, for which
the provisions of Articles 5.10.11.3 and 5.10.11.4.1b shall apply. All limit states shall be considered of equal
importance.
  Q   R
i
i
s
n
 Rr
(1.3.2.1-1)
where:
s=system factor: relating to ductility, redundancy and operational classification as specified in Article 1.3.6
for the design of structural components for strength and extreme event limit states. For all other limit states,
the system factors shall be taken as 1.0
=resistance factor: a statistically based multiplier applied to nominal resistance, as specified in Sections, 5,
6, 7, 8, 10, 11 and 12
i=load factor: a statistically based multiplier applied to force effects
Rn = nominal resistance
Rr = factored resistance: sRn
Qi = force effect
1.3.2.2 Service Limit State
The service limit state shall be taken as restrictions on stress, deformation and crack width under regular
service conditions.
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1.3.2.3 Fatigue and Fracture Limit State
The fatigue limit state shall be taken as a set of restrictions on stress range due to a single fatigue truck
occurring at the number of expected stress range cycles.
The fracture limit state shall be taken as a set of material toughness requirements of the AASHTO Material
Specifications.
1.3.2.4 Strength Limit State
Strength limit state shall be taken to ensure that strength and stability, both local and global, are provided to
resist the specified statistically significant load combinations that a bridge is expected to experience in its design life.
1.3.2.5 Extreme Event Limit States
The extreme event limit state shall be taken to ensure the structural survival of a bridge during a major
earthquake or flood, or when collided by a vessel, vehicle or ice flow possibly under scoured conditions.
1.3.3 Ductility
The structural system of a bridge shall be proportioned and detailed to ensure the development of significant
and visible inelastic deformations at the strength and extreme event limit states before failure.
Energy-dissipating devices may be substituted for conventional ductile earthquake resisting systems and the
associated methodology addressed in these Specifications or in the AASHTO Guide Specifications for Seismic
Design of Bridges.
1.3.4 Redundancy
The structural system of a bridge shall be configured and its members designed to ensure that it meets three
system strength conditions: a) limited functionality and b) resistance to collapse if the strength of its most critical
member is exceeded, and c) ability to carry some level of live load in a damaged state. Therefore, multiple-loadpath, ductile and continuous structures should be used unless there are compelling reasons not to use them.
A system factor s shall be applied during the design of bridge members to account for a bridge’s system
level of redundancy as specified in Article 1.3.6.
1.3.5 Operational Importance
This Article shall apply to the strength and extreme event limit states only.
The Owner may declare a bridge or any structural component and connection thereof to be of increased
operational priority.
The Owner may also declare a structural component or connection to be damage-critical.
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1.3.6 System Factor
The system factor, s, is a multiplier applied to the nominal resistances of the structural components of a
bridge system or subsystem to reflect the level of ductility, redundancy and operational classification.
For bridge superstructures under the effect of vertical loads, s, shall be taken as specified in Article 1.3.6.1.
For bridge substructures under the effect of horizontal lateral or longitudinal loads, s, shall be taken as
specified in Article 1.3.6.2.
1.3.6.1 System Factors for Bridge Superstructures under Vertical Loads

For the superstructures of bridges classified as being of increased operational priority and for trusses
and arch bridges, and for bridges not covered in Tables 1.3.6.1.-1 through 1.3.6.1.-4.:
s shall be calculated using an incremental non-linear analysis following the provisions of
Article 1.3.6.1.1.

For the superstructures of straight bridges of types (a), (b), (c), (d), and (k) as defined in Table
4.6.2.2.1-1 having damage-critical components:
s = min (su, sd)

For the superstructures of straight bridges of types (a), (b), (c), (d) and (k) that are not damage
critical:
s = su
where:
su = system factor for superstructure functionality and resistance to collapse conditions.
sd =system factor for superstructure strength in damage state condition.

s is applied to all members affected by the vertical load. A minimum value of s=0.80 is
recommended but in no instance should s be taken greater than 1.20.
Recommended values for su, for typical straight superstructures are specified in Table 1.3.6.1-1 for
I-girder superstructures of type (a) and (k) and Table 1.3.6.1-2 for spread box girder bridges
superstructures of type (b) and (c) and Table 1.3.6.1-3 for multi-cell boxes of type (d).
Recommended values for su, for typical straight superstructures are specified in Table 1.3.6.1-4 for
I-girder superstructures of type (a) and (k) and Table 1.3.6.1-5 for spread box girder bridges
superstructures of type (b) and (c) and Table 1.3.6.1-6 for multi-cell boxes of type (d).
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Table 1.3.6.1-1 System factors for straight I-girder superstructures of types (a) and (k)
for system functionality and resistance to collapse conditions under vertical loading
Bridge cross section type
System
Continuous steel I-girder bridges
with non-compact
negative bending sections

1
su  0.80  0.16 D

1
LF  1.16LF  0.75
and
factor
All other simple span and continuous
I-beam bridges
su  1 
R
1  1.5  D / R 
2
1  LF12
Table 1.3.6.1-2 System factors for straight spread box girder superstructures of types (b) and (c)
for system functionality and resistance to collapse conditions under vertical loading
Bridge cross section type
System
Simple span box girder bridges  24-ft
wide
su  0.83  0.14 D
Simple span box girder bridges  24-ft
wide
su  1 
Continuous box girder bridges  24-ft wide
su  1 
Continuous steel box-girder bridges with
non-compact negative bending sections and
su  1 
LF1  1.75LF1
Continuous box girder bridges with
compact negative bending sections
factor
R
1  1.5  D / R 
2
1  LF12
1  1.5  D / R 
2
1  LF12
1  1.5  D / R 
su  1  4 
2
1  LF12
1  1.5  D / R 
2
1  LF12
Where:
D/R = dead load to resistance ratio for the member being evaluated.
LF1 = load factor related to the capacity of the system to resist the failure of its most critical member.
LF1  LF1 
R+  D+
L1+
LF1  LF1 =

R D
L1
when

when
LF1
 1.0
LF1
(1.3.6.1-1)

1

1
LF
 1.0
LF
R = load carrying capacity.
D = dead load moment effect.
L1= moment effect of applied live load due to two side-by-side LRFD design trucks applied at the middle of
the span or due to two trucks in one lane applied in each of two contiguous spans.
L1  D.F .  LL
D.F. = load distribution factor
LL = effect of the LRFD design truck with no impact factor and no lane load.
The negative superscript refers to negative bending and the positive superscript refers to positive bending.
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Table 1.3.6.1-3 System factors for single cell and multi-cell box girder superstructures of type (d)
for system functionality and resistance to collapse conditions under vertical loading
Bridge cross section type
System
factor
Single cell box girder bridges
su  0.80
Multi-cell box girder bridges
su  1.00
Table 1.3.6.1-4 System factors for straight I-girder superstructures
of types (a) and (k) in damaged state condition under vertical loads.
Bridge cross section type
Simple span I-girder
Bridges
Continuous steel I-girder
bridges with non compact
sections in negative
bending
Continuous prestressed
concrete and steel Igirder bridges with
compact sections in
negative bending
Redundancy ratio
Rd
System factor
Rd  1  0.056 S  transverse  weight
Rd  1.00  0.08 S  transverse
Rd  1.35  0.08 S   transverse
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sd 
Rd
0.47  (0.47  Rd )
D
R
Table 1.3.6.1-5 System factors for straight spread box girder superstructures
of types (b) and (c) in damaged state condition under vertical loads
Bridge cross section type
Fractured simple span steel
box girder bridges less than
24-ft wide
Narrow simple span steel
box girder bridges less than
24-ft
with no torsional rigidity
All other simple span box
girder bridges
Redundancy ratio
LF
Rd  d
LF1
System factor
Non-redundant
sd=0.80
Rd  0.46 transverse
Rd  0.72 transverse
sd 
Continuous steel box-girder
bridges with non-compact
negative bending sections
and LF1  1.75LF1
Rd  0.72 transverse
All other continuous box
girder bridges

4.50 
Rd   0.59 
  transverse
LF1 

Rd
0.47  (0.47  Rd )
D
R
Where
Rd = redundancy ratio for damaged bridge systems
S  beam spacing in feet.
 weight  1.23  0.23beam (kip / ft )
beam = total dead weight on the damaged beam in kip per unit length.
M transverse
 transverse  0.50
 0.50  1.10
13.5 kip. ft / ft
Mtransverse= combined moment capacity of the slab and transverse members including diaphragms
expressed in kip-ft per unit slab width.
Table 1.3.6.1-6 System factors for single cell and multi-cell box girder superstructures of type (d)
in damaged state condition under vertical loads
Bridge cross section type
System
factor
Single cell box girder bridges
sd  0.80
Multi-cell box girder bridges
sd  1.20
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1.3.6.1.1 Incremental Non-linear Redundancy Analysis for Bridges under Vertical Loads
For trusses and arch bridges, bridges classified to be of operational importance, and for bridges not covered
in Tables 1. 3.6.1–1 through 1.3.6.1-4, the system factor of Equation 1.3.2.1-1 for the structural components of a
system subjected to vertical loads shall be calculated from the results of an incremental analysis using Equation
1.3.6.1.-2:
R f Rd 
 R
s  min  u ,
,

 1.30 1.10 0.50 
(1.3.6.1-2)
A minimum value of s=0.80 is recommended but in no instance should s be taken as greater than 1.20.
Where:
Ru = system reserve ratio for resistance to collapse condition Ru 
Rf = system reserve ratio for the functionality condition, R f 
Rd = system reserve ratio for damaged state condition, Rd 
LFu
LF1
LFf
LF1
LFd
LF1
LFu, LFf, LFd and LF1 are obtained from the incremental non-linear analysis
where:
LFu = vertical load factor that causes the collapse of the superstructure
LFf = vertical load factor that causes the maximum vertical deflection of the superstructure to reach a
value equal to span length/100.
LFd = vertical load factor that causes the failure of a damaged superstructure
LF1 = vertical load factor that causes the first member of the intact superstructure to reach its limit
capacity
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1.3.6.2 System Factors for Structural Components of Bridge Substructures under Horizontal Loads
Design of abutments, piers and walls shall be investigated for structural safety at the strength and extreme
event limit states for each structural component and joint using Equation 1.3.2.1-1 for bridge systems subjected to
horizontal loads.
Bridge systems evaluated using the displacement-based approach
The displacement based approach of the AASHTO Guide Specifications for LRFD Seismic Bridge Design
may be used in lieu of the force-based approach of Eq. 1.3.2.1-1. The displacement-based approach compares the
seismic displacement demand to the seismic displacement capacity such that:
demand  s capacity
(1.3.6.2-1)
where:
s= 0.75, a system factor relating to ductility and redundancy of structural components evaluated for
seismic extreme event limit states.
capacity = nominal seismic displacement capacity of the bridge substructure element.
demand = nominal seismic displacement demand.

For the substructures of bridges classified as being of increased operational priority, capacity shall be
calculated using the incremental non-linear analysis approach provided in AASHTO (2011) Guide
Specifications for LRFD Seismic Bridge Design.

For the substructures of bridges classified to be damage-critical, the bridge system must also satisfy
the provisions of the nonlinear analysis procedure specified in Article 1.3.6.1.1 for vertical loading.

For the substructures of all other bridge systems evaluated using the displacement based approach
capacity shall be calculated using the appropriate provisions in AASHTO (2011) Guide Specifications
for LRFD Seismic Bridge Design for seismic loading.

Bridge systems evaluated using the force-based approach

For the substructures of bridges classified as being of increased operational priority and for bridges
not covered in Table 1.3.6.2-1, s shall be calculated using the incremental non-linear analysis
approach following the provisions of Article 1.3.6.2.1.

For the substructures of bridges classified to be damage-critical, s shall be calculated using the
incremental non-linear analysis approach following the provisions of Article 1.3.6.2.1 for horizontal
loads. For systems with damage-critical columns, an incremental non-linear analysis of the
complete system under vertical loading should also be performed following the provisions of Article
1.3.6.1.1.
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
For the substructures of straight bridges with single-column and multi-column bents of equal heights
under lateral load being evaluated using the force-based approach

s    Fmc  C

 u  tunc 

tconf  tunc 
(1.3.6.2-2)
s is applied to all the bridge members affected by the applied load. A minimum value of s=0.80
and a maximum value of s=1.20 are recommended.
where
 = Risk factor specified in Table 1.3.6.2 -1.
Fmc = multi-column factor specified in Table 1.3.6.2 -1.
C = curvature factor specified in Table 1.3.6.2 -1.
 u = ultimate curvature at failure of the weakest column or connecting member in the
system calculated using Eq. 1.3.6.2-3.
tunc = constant curvature for typical unconfined columns specified in Table 1.3.6.2 -1.
tconf = constant curvature for typical confined columns specified in Table 1.3.6.2 -1.
  = curvature reduction factor for substructure systems with deficient detailing calculated
using Eq. 1.3.6.2-4
The ultimate curvature at failure  u is calculated from the ultimate plastic analysis of the
column’s cross section:
u 
u
c
(1.3.6.2-3)
where
u = maximum strain at failure equal to the concrete crushing strain or steel rupture strain
c = distance from the fiber that fails first to the Neutral axis.
For the cases where the shear capacity or the detailing of the columns or the capacity of the cap
beams and pile caps are not sufficient to develop a mechanism in the columns but the bridge columns
reach their plastic moment capacity under the effect of the applied loads, a correction factor   is
applied in Eq. 1.3.6.2-2 to reduce the ultimate column curvature
 
M available  M p column
M u column  M p column
   1.0
if M u column  M available  M p column
otherwise
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(1.3.6.2-4)
Where
M available =moment capacity of the connecting elements such as cap beams and pile caps or the reduced
moment that can be supported by the column based on the available shear reinforcement, development
length, splice or connection detailing.
M p column = plastic moment capacity of column,
M u column = ultimate overstrength moment capacity of column.

For bridges with nontypical configurations which are not covered in Tables 1.3.6.2-1, the
incremental non-linear analysis approach of Article 1.3.6.2.1 shall be used.

For bridges with one-column bents and those subjected to longitudinal loading with bearing
connections between superstructures and substructures:
s  
(1.3.6.2-5)
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Table 1.3.6. 2 -1 Recommended values for redundancy parameters for bridges with one-column and multi-column bents under
horizontal load
Variable
 , risk factor

Applicability
Recommended value
Seismic hazards
All other lateral loads
 =0.75
 =0.85
Non-redundant systems
s  
s, system factor for:
 One column bents
 Longitudinal loading of systems with
bearing connections between
superstructures and substructures
 Systems where failure is controlled
by shear.
 Systems with insufficient detailing to
allow plastic moment capacity of the
columns to be reached.
 Systems connected to components
with plastic moment capacities
weaker than those of the columns.
 Systems evaluated using the
displacement based approach
s, system factor for:
 Multi-column bents under lateral load
 Longitudinal loading of systems with
integral connections between
superstructures and substructures.
 Systems with sufficient detailing to
allow plastic moment capacity of the
columns to be reached.
 Systems connected to components
with plastic moment capacities
stronger than those of the columns.

Redundant systems
s    Fmc  C

 u  tunc 

tconf  tunc 
Two-column systems
Fmc =1.10
Three-column systems
Fmc =1.16
Systems with four or more
columns
Fmc =1.18
C , curvature factor
Constant for all systems
C =0.24
tunc , typical unconfined column ultimate
Constant for all systems
tunc =3.64 x 10-4 (1/in)
Constant for all systems
tconf =1.55 x 10-3 (1/in)
Fmc ,multi-column factor:


For bridges loaded laterally, count the
number of columns in each bent
For bridges loaded longitudinally
with integral connections between
superstructure and substructure, count
the number of bents between
expansion joints
curvature
tconf , typical confined column ultimate
curvature
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1.3.6.2.1 Incremental Non-linear Redundancy Analysis for Bridges under Horizontal Loads
For bridges classified to be of operational importance and for bridges not covered in Table 1. 3.6.2- 1 that are
being evaluated using the force-based approach, the system factor of Equation 1. 3.2.1-1 for the structural
components of a system subjected to horizontal load shall be calculated from the results of a nonlinear pushover
analysis using Equation 1.3.6.2-6:
R f Rd 
 R
s  min  u ,
,
  1.20
 1.20 1.20 0.50 
(1.3.6.2-6)
where:
Ru = system reserve ratio for resistance to collapse condition, Ru 
Rf = system reserve ratio for the functionality condition, R f 
Rd = system reserve ratio for damaged state condition, Rd 
Pu
Pp1
Pf
Pp1
Pd
Pp1
Pu, Pf, Pd and P1 are obtained from the incremental pushover analysis
Pu = lateral load that causes the failure of the superstructure
Pf = lateral load that causes a maximum lateral deflection equal to clear column height /50.
Pd = the lateral load that causes the failure of a damaged superstructure
Pp1 = lateral load that causes the first member of the intact substructure to reach its limit capacity
REFERENCES

Ghosn, M. and Yang, J., (2013) NCHRP 12-86, BRIDGE SYSTEM SAFETY AND REDUNDANCY,
Transportation Research Board, Washington DC

Ghosn, M., and Moses, F., (1998). Redundancy in Highway Bridge Superstructures. National Cooperative
Highway Research Program, NCHRP Report 406, Transportation Research Board, Washington DC:
National Academy Press.

Liu, D., Ghosn, M., Moses, F., and Neuenhoffer, A., (2001). Redundancy in Highway Bridge
Substructures. National Cooperative Highway Research Program, NCHRP Report 458, Transportation
Research Board, Washington, DC: National Academy Press.

Buckle, I, Friedland, I, Mander, J., Martin, G,, Nutt, R., Power, M. (2006), Seismic Retrofitting Manual
for Highway Structures, Part 1 Bridges, FHWA-HRT-06-032, Turner-Fairbanks Highway Research
Center, McLean, VA

AASHTO (2011) Guide Specifications for LRFD Seismic Bridge Design, 2nd Edition, Washington, DC.
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