Introduction To Bridge Engineering

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LECTURE No.
2
INTRODUCTION TO
BRIDGE ENGINEERING
LECTURE No.2 (TOPICS)
1. Loads:
1. Gravity Loads
2. Lateral Loads
3. Forces due to deformation
4. Collision Loads
2. Development of Design Procedures
3. ASD and LRFD Design Philosophies
Continued…
References:
Bakht and Aftab A. Mufti
AASHTO (LRFD 1994)
PCPHB
AASHTO Standard Specifications
LECTURE No.2 (TOPICS)
4. Limit States:
4. Service Limit State
5. Strength Limit State
6. Fatigue and Fracture Limit State
7. Extreme Event Limit State
5. Principles of Probabilistic Design
6. Geometric Design Considerations
7. Relevant Portions of AASHTO And PCPHB
LOADS
INTRODUCTION
Some Basic Definitions:
Load: It is the effect of acceleration, including that
due to gravity, imposed deformation or
volumetric change.
Nominal Load: An arbitrary selected design load level.
Load Factor: A coefficient expressing the probability of
variations in the nominal load for the
expected service life of the bridge.
Permanent Loads: Loads or forces which are, or assumed to be,
constant upon completion of construction.
Force Effects: A deformation or a stress resultant, i.e.,
thrust, shear, torque/or moment, caused by
applied loads, imposed deformation or
volumetric changes.
IMPORTANCE OF LOAD PREDICTION
A structural engineer has to make a structure safe against
failures.
The reasons for a structure being susceptible to failures are:
a) The loads that a structure will be called upon to sustain,
cannot be predicted with certainty.
b) The strength of the various components cannot be
assessed with full assertion.
c) The condition of a structure may deteriorate with time
causing it to loose strength.
TYPES OF LOADS
Loads considered in Bridge analysis are:
1. Gravity Loads
2. Lateral Loads
3. Forces due to deformation
4. Collision Loads
GRAVITY LOADS
Gravity loads are the loads caused by the weight
of an object on the bridge and applied in a
downward direction toward the center of the
earth. Such loads may be:
A. Permanent Gravity Loads
B. Transient Gravity Loads
A. Permanent Gravity Loads
Permanent gravity loads are the loads that remain on the bridge
for an extended period of time or for the whole service life.
Such loads include:
1. Dead load of structural components and non
structural attachments  (DC)
2. Dead load of wearing surfaces and utilities  (DW)
3. Dead load of earth fill  (EV)
4. Earth pressure load  (EH)
5. Earth surface load  (ES)
6. Downdrag  (DD)
DEAD LOAD OF STRUCTURAL COMPONENTS
AND NONSTRUCTURAL ATTACHMENTS (DC)
In bridges, structural components refer to the elements
that are part of load resistance system.
Nonstructural attachments refer to such items as curbs,
parapets, barriers, rails, signs , illuminators, etc. Weight of
such items can be estimated by using unit weight of
materials and its geometry.
Load factors per table A3.4.11 and A3.4.12 apply here.
(From AASHTO LRFD 1994 Bridge Design Specifications).
A. Permanent Gravity Loads
DEAD LOAD OF WEARING SURFACES AND UTILITIES (DW)
This load is estimated by taking the unit weight times
the thickness of the surface.
This value is combined with the DC loads per table
A3.4.11 and A3.4.12 (From AASHTO LRFD Bridge
Design Specifications).
The maximum and minimum load factors for the DC
loads are 1.25 and 0.90 respectively and for DW loads
are 1.5 and 0.65 respectively .
A. Permanent Gravity Loads
DEAD LOAD OF EARTH FILL (EV)
This load must be considered for buried structures such as
culverts.
It is determined by multiplying the unit weight times the
depth of the materials.
Load factors per table A3.4.11 and A3.4.12 apply here.
(From AASHTO LRFD Bridge Design Specifications).
EV has a maximum and minimum load factor of 1.35 and 0.9
respectively.
A. Permanent Gravity Loads
EARTH SURFACE LOAD (ES)
The earth surcharge load (ES) is calculated like the EV loads
with the only difference being in the load factors.
This difference is attributed to the variability.
Part or all of this load could be removed in the future or the
surcharge material (loads) could be changed.
ES has a maximum and minimum load factor of 1.5 and 0.75
respectively.
A. Permanent Gravity Loads
DRAGDOWN (DD)
It is the force exerted on a pile or drilled shaft due to the
soil movement around the element. Such a force is permanent
and typically increases with time.
Details regarding DD are outlined in AASHTO (LRFD 1994)
Section 10, Foundations.
A. Permanent Gravity Loads
As the name implies these loads change with time and may be applied from
several directions or locations.
Such loads are highly variable.
Transient loads typically include gravity load due to the vehicular, rail or
pedestrian traffic as well as lateral loads such those due to wind, water, ice, etc.
Engineer should be able to depict…
____ which of these loads is appropriate for the bridge under consideration
____ magnitude of the loads
____ how these loads are applied for the most critical load effect.
B. Transient Gravity Loads
For transient load each code has described the following criterion:
Design lanes
Vehicular Design loads
Fatigue Loads
Pedestrian Loads
Deck and Railing Loads
Multiple Presence
Dynamic Effects
Centrifugal Forces
B. Transient Gravity Loads
Number of lanes a bridge may accommodate must be established.
Two such terms are used in the lane design of a bridge:
a) Traffic lane
b) Design Lane.
Traffic Lane:
The traffic lane is the number of lanes of traffic that the traffic
engineer plans to route across the bridge. A lane width is associated with a
traffic lane and is typically 3.6 m.
Design Lane:
Design lane is the lane designation used by the bridge engineer for
the live load placement.
The design lane width may or may not be the same as the traffic lane.
DESIGN LANE
DESIGN LANES
According to AASHTO specifications,
•AASHTO uses a 3m design lane and the vehicle is to be
positioned within that lane for extreme effect.
•The number of design lanes is defined by taking the integral
part of the ratio of the clear roadway width divided by
3.6m.[A3.6.1.1.1]
•The clear width is the distance between the curbs and/or
barriers.
VEHICULAR DESIGN LOADS
•A study by the transportation Research Board (TRB) was used as the basis for the
AASHTO loads TRB (1990).
•Loads that are above the legal weight and are /or length limits but are regularly
allowed to operate were cataloged. Those vehicles that were above legal limits but
were allowed to operate routinely due to grandfathering provisions are referred to
as „Exclusion Vehicles‟.
•These exclusion trucks best represents the extremes involved in the present truck
traffic.
•For analysis, simpler model was developed which represents the same extreme
load effects as the exclusion vehicles.
This model consists of three different loads:
1.Design truck
2.Design tandem
3.Design Lane
VEHICULAR DESIGN LOADS
Design Truck:
According to AASHTO design specifications(1996), the design truck is a model
that resembles the semitrailor truck. as shown in the figure.[A3.6.1.2].
Variable Spacing
The variable spacing provide a more
satisfactory loading for continuous
spans and the heavy axle loads may
be so placed on adjoining spans as to produce maximum –ve moments.
This design truck has the same configuration since 1944 and is commonly
referred to as HS2044(denoting Highway Semitrailer 20 tons with year of
publication 1944).
DESIGN TANDEM
The second configuration is the design tandem and is illustrated in the figure.It
consists of two axles weighing 110kN each spaced at 1.2m.
TANDEM: A tandem can be defined as two closely spaced and mechanically
interconnected axles of equal weight.
DESIGN LANE LOAD
The third load is the design lane load that consists of a uniformaly distributed load of
9.3 N/mm and is assumed to occupy a region 3m transversly. This load is same as
uniform pressure of 64 lbs/ft² applied in a 10ft (3m) design lane.
The load of design truck and design tandem must each be superimposed with the load
effects of the design lane load. This combination of load and axle loads is a major
deviation from the requirements of the earlier AASHTO standard specifications where
the loads were considered separately.
COMPARISON OF HS20 & PRESENT TRAFFIC
Kulicki and Mertz(1991) compared the load effects (shear and
moments) for one and two span continuous beams for the
previous AASHTO loads and those presently prescribed.
In their study, the HS20 truck and lane loads were compared to
the maximum load effect of 22 trucks representative of today's
traffic. The ratio of the maximum moments and shear to the HS20
moments is illustrated in figure.
COMPARISON OF HS20 & PRESENT TRAFFIC
•In the figure there is significant variation in the ratios and most ratios are
greater than 1, indicating that the exclusion vehicle maximums are greater than
the model load, a nonconservative situation.
COMPARISON OF HS20 & PRESENT TRAFFIC
A perfect model would contain ordinates of unity for all span lengths. This model is
practically not possible, but the combination of design truck with the design lane and
the design tandem with the design lane gives improved results , as illustrated in the
figure below.
•The variation is much less as the ratios are more closely grouped over the span range,
for both moment and shear, and for both simple and continuous spans.
•The implication is that the present model adequately represents today's traffic and a
single load factor may be used for all trucks.
COMPARISON OF HS20 & PRESENT TRAFFIC
As it is quite likely that an exclusion vehicle could be closely followed by another heavily
load truck, it was felt that a third live load combination was required to model this event.
This combination is specified in AASHTO[A3.6.1.3.1] as illustrated in the figure.
“ for negative moment over the interior supports 90 percent of the load effect of two
design trucks spaced at minimum of15m between lead axle of one truck and rear axle of
the other truck and 4.3m between two 145kN axles, combined with 90 % of the effect of
the design lane load.
COMPARISON OF HS20 & PRESENT TRAFFIC
Nowak (1993) compared survey vehicles with others in the same lane to the AASHTO load
model and the results are shown in the figure.
COMPARISON OF HS20 & PRESENT TRAFFIC
In summary three design loads should be considered , the design truck, design tandem
and design lane. These loads are superimposed three ways to yield the live load effects
, which are combined with the other load effects as shown in tables.
The above mentioned three cases are illustrated in the table where the number in the
table indicate the appropriate multiplier to be used prior to superposition.
FATIGUE LOADS
• A bridge is vulnerable to repeated stressing or fatigue.
• When the load is cyclic the stress level is below the nominal
yield strength.
This load depends upon:
1. Range of live load stress
2. Number of stress cycles under service load conditions.
FATIGUE LOADS
1. Under service load conditions, majority of trucks do not exceed the legal
weight limit. So it would be unnecessary to use the full live load model.
Instead it is accommodated by using a single design truck with the variable
axle spacing of 9m and a load factor of 0.75 as prescribed in
table.[A3.4.1.1].
2. The number of stress load cycles is based on traffic surveys. In lieu of
survey data, guidelines are provided in AASHTO [A3.6.1.4.2]. The average
daily truck traffic (ADTT) in a single lane may be estimated as
ADTT
SL = p
(ADTT)
Where p is the fraction of traffic assumed to be in one lane as defined in
table4.3.
PEDESTRIAN LOADS
• The AASHTO pedestrian load is 3.6 x 10
3
MPa, which is applied to sidewalk that are
integral with a roadway bridge.
• If load is applied on bridge restricted to pedestrian or bicycle traffic , then a 4.1 x 10
3
MPa is used.
• The railing for pedestrian or bicycle must be designed for a load of 0.73 N/mm both
transversely and vertically on each longitudinal element in the railing system.[A13.8 and
A18.9].
• In addition as shown in the figure , the railing must be designed to sustain a single
concentrated load of 890 N applied to the top rail in any direction and at any location.
DECK & RAILING LOAD
• The deck must be designed for the load effect due to design truck or design tandem ,
whichever creates the most extreme effect.
• The deck overhang, located outside the facia girder and commonly referred to as the
cantilever is designed for the load effect of a uniform line load of 14.6 N/mm located
3m from the face of the curb or railing as shown in the figure.
• The gravity load for the deign of deck system are outlined in AASHTO[A3.6.1.3.3].
• The vehicular gravity loads for decks may be found in AASHTO [A3.6.1.3].
MULTIPLE PRESENCE
Trucks will be present in adjacent lanes on roadways with multiple design lanes but it is
unlikely that three adjacent lanes will be loaded simultaneously with the three heavy
loads.
Therefore, some adjustment in the design load is necessary. To account for this effect
AASHTO [A3.6.1.1.2] provides an adjustment factor for the multiple presence. A table
for these factors is provided.
DYNAMIC EFFECTS
Dynamics : The variation of any function with respect to
time.
Dynamic Effects : The effects i.e., deformation or stress
resultant due to the dynamic loads.
• Due to the roughness of the road, the oscillation of the
suspension system of a vehicle creates axle forces. These forces
are produced by alternate compression and tension of the
suspension system.
• This phenomenon which is also known as IMPACT is more
precisely referred to as dynamic loading.
• These axle forces exceed the static weight during the time the
acceleration is upward and is less than the static weight when the
acceleration is downward.
DYNAMIC EFFECTS
• As the dynamic effects are not consistent & is well portrayed by
Bakht & Pinjarker (1991 ) & Paultre (1992 ). It is most common to
compare the static & dynamic deflection.
• A comparison of static and dynamic deflections is illustrated in
the fig.4.12.
DYNAMIC EFFECTS
From this figure dynamic effect is the amplification factor applied
to the static response.
This effect is also called dynamic load factor, dynamic load
allowance or impact factor and is given by,
IM = D
dyn
D
stat
Here D
stat
is the maximum static deflection and D
dyn
is the
additional defection due to the dynamic effects.
DYNAMIC EFFECTS
According to AASHTO specifications, DLA is illustrated in table 4.7[A3.6.2].
DYNAMIC EFFECTS
Paultre(1992) outlines various factors used to increase the static loads to account for
dynamic load effect. The following illustration shows various bridge design
specifications from around the world.
CENTRIFUGAL FORCES
As a truck moves along a curvilinear path, the change in the direction of the velocity
causes a centrifugal acceleration in the radial direction. This acceleration is given by,
a
r
= V² ….4.1
r
Where „ V ‟ is the truck speed and „ r ‟ is the radius of curvature of the truck movement.
Since F= ma , so substituting a
r
in the Newton‟s second law of motion,
F
r
= m V² …..4.2
r
Where F
r
is the force on the truck.
Since mass m = W
g
CENTRIFUGAL FORCES
So, we can substitute „ m „ in eq.4.2 to obtain an expression similar to that given by
AASHTO,
F
r
= V² W
rg
F
r
= CW
Where C = 4 v²
3 Rg
Here v is the highway design speed(m/s), R is the radius of the curvature of
traffic lane(m), and F is applied at the assumed centre of mass at a distance 1800 mm
above the deck surface.[A3.6.3]
Because the combination of design truck with the design lane load gives a load
approximately four thirds of the effect of the design truck considered independently, a
four third factor is used to model the effect of a train of trucks.
Multiple presence factor may be applied to this force as it is unlikely that all the lanes
will be fully loaded simultaneously.
BRAKING FORCES
•Braking forces are significant in bridge loads consideration. This force is transmitted to
the deck and taken into the substructure by the bearings or supports.
•This force is assumed to act horizontally at 1800 mm above the roadway surface in
either longitudinal direction.
•Here , the multiple presence factor may be applied as it is unlikely that all the trucks in
all the lanes will be at the maximum design level.
•The braking force shall be taken as 25% of the axle weights of the design truck or the
design tandem placed in all lanes.
PERMIT VEHICLES AND MISCELLANEOUS
CONSIDERATIONS
•Transportation agencies may include vehicle loads to model characteristics of their
particular jurisdiction.
For example the Department of Transportation in California (Caltrans) uses a different
load model for their structures as shown in the fig.4.19.
•In all such cases, the characteristics of truck loads should be based on survey data. If
such data is not available or achievable, then professional judgment should be used.
LATERAL LOADS
Following forces are considered under lateral loads:
• Fluid forces
• Seismic Loads
• Ice Forces
FLUID FORCES
• Fluid forces include
1. Water forces and
2. Wind forces.
• The force on a structural component due to a fluid
flow (water or air) around a component is established
by Bernoulli‟s equation in combination with empirically
established drag coefficients.
WIND FORCES
• The velocity of the wind varies with the elevation above the
ground and the upstream terrain roughness and that is why
pressure on a structure is also a function of these parameters.
• If the terrain is smooth then the velocity increases more rapidly
with elevation.
• The wind force should be considered from all directions and
extreme values are used for design.
• Directional adjustments are outlined in AASHTO[A3.8.1.4].
• The wind must also be considered on the vehicle.This load is
1.46 N/mm applied at 1.8 m above the roadway
surface.[A3.8.1.3].
WATER FORCES
• Water flowing against and around the substructure
creates a lateral force directly on the structure as well
as debris that might accumulate under the bridge.
• If the substructure is oriented at an angle to the
stream flow, then adjustments must be made. These
adjustments are outlined in the AASHTO [A3.7.3.2].
• Scour of the stream bed around the foundation should
also be considered as it can result in the structural
failure. AASHTO [A2.6.4.4.1] outlines an extreme limit
state for design.
SEISMIC LOADS
• Depending on the location of the bridge site, the
anticipated earthquake/seismic effects can govern the
design of the lateral load resistance system.
• In many cases the seismic loads are not critical and
other lateral loads such as wind govern the design.
PROVISIONS FOR SEISMIC LOADS
• The provision of the AASHTO specifications for seismic design
are based on the following principles[C3.10.1]:
1. Small to moderate earthquakes should be resisted within the
elastic range of the structural components without significant
damage.
2. Realistic seismic ground motion intensities and forces are used
in the design procedures.
3. Exposure to shaking from large earthquakes should not cause
collapse of all or part of the bridge. Where possible damage
should be readily detectable and accessible for inspection and
repair.
ICE FORCES
• Forces produced by ice must be considered when a
structural component of a bridge, such as a pier, is
located in water and the climate is cold enough to
cause the water to freeze.
• Due to the freeze up and break up of ice in different
seasons ice forces are produced.
• These are generally static which can be horizontal
when caused by thermal expansion and contraction or
vertical if the body of water is subject to changes in
water level.
• Relevant provisions are given in AASHTO section 3.9.
FORCES DUE TO DEFORMATION
In bridge we have to consider the following forces due to
deformation:
1. Temperature
2. Creep and Shrinkage
3. Settlement
TEMPERATURE
Two types of temperature changes must be included in the analysis of the
superstructure.
i. Uniform temperature change
ii. Gradient or nonuniform temperature change
Uniform temperature change:
In this type of temperature change, the entire superstructure changes temperature by a
constant amount. This type of change lengthens or shortens the bridge or if the
supports are constrained it will induce reactions at the bearings and forces in the
structure. This type of deformation is illustrated in the figure.
Gradient or Nonuniform temperature change:
In this type the temperature change is gradient or nonuniform heating or cooling of the
superstructure across its depth. Subjected to sunshine, bridge deck heats more than the
girder below. This nonuniform heating causes the temperature to increase more in the
top portion of the system than in the bottom and the girder attempts to bow upward as
shown in the figure.
TEMPERATURE
The temperature change is considered as a function of climate. AASHTO defines two
climatic conditions, moderate and cold.
Moderate climate is when the number of freezing days per year is less than 14.
A freezing day is when the average temperature is less than 0C.
Table 4.21 gives the temperature ranges. The temperature range is used to establish the
change in temperature used in the analysis.
TEMPERATURE
CREEP & SHRINKAGE
The effects of creep and shrinkage can have an effect on the
structural strength, fatigue and serviceability.
Creep is considered in concrete where its effects can lead
unanticipated serviceability problems that might lead to secondary
strength.
Creep and shrinkage are highly dependent on material and the
system involved.
SETTLEMENT
•Settlements occur usually due to elastic and inelastic deformation
of the foundation.
•Elastic deformation include movements that affect the response
of the bridge to other loads but do not lock in permanent actions.
•This type of settlement is not a load but rather a support
characteristic that should be included in the structural design.
•Inelastic deformations are movements that tend to be permanent
and create locked in permanent actions.
SETTLEMENT
•Such movements may include settlement due to consolidation,
instabilities, or foundation failures. Some such movements are the
results are the loads applied to the bridge and these load effects
may be included in the bridge design.
•Other movements are attributed to the behavior of the
foundation independent of the loads applied to the bridge.
•These movements are treated as loads and are called imposed
support deformations.
•Imposed support deformations are estimated based on the
geotechnical characteristics of the site and the system involved.
Detailed suggestions are given in AASHTO, section 10.
COLLISION LOADS
Collision loads include:
1.Vessel Collision load
2.Rail Collision Load
3.Vehicle Collision Load
COLLISION LOADS
Vessel Collision load:
On bridge over navigable waterways the possibility of vessel
collision with the pier must be considered. Typically, this is of
concern for structures that are classified as long span bridges.
Vessel collision loads are classified in AASHTO [A3.14].
Rail Collision Load:
If a bridge is located near a railway, the possibility of collision of
the bridge as a result of a railway derailment exists. As this
possibility is remote, the bridge must be designed for collision
forces using extreme limit states.
Vehicle Collision Load:
The collision force of a vehicle with the barrier, railing and parapet
should be considered in bridge design.
LECTURE No.2
SECTION 2
1. Development of Design Procedures
2. ASD and LRFD Design Philosophies
3. Limit States:
4. Service Limit State
5. Strength Limit State
6. Fatigue and Fracture Limit State
7. Extreme Event Limit State
4. Principles of Probabilistic Design
5. Geometric Design Considerations
6. Relevant Portions of AASHTO And PCPHB
DEVELOPMENT OF DESIGN
PROCEDURES
DESIGN PHILOSOPHY:
•It is not economical to design a bridge so that none of its
components could ever fail.
• It is necessary to establish an acceptable level of risk or
probability of failure.
• To determine an acceptable margin of safety, opinions should
be sought from experienced and qualified group of engineers.
• Design procedures have been developed by engineers to
provide an satisfactory margin of safety.
DESIGN PHILOSOPHY
A general statement for assuring safety in engineering design is
that
Resistance (of material & xsection) ≥ Effect of applied load
• When applying this principle ,it is essential that both sides of
inequality are evaluated for the same condition. For example if
the effect of the applied load is to produce compressive stress
on soil, then it should be compared with bearing capacity of
soil.
DEVELOPMENT OF DESIGN
PROCEDURES
Two distinct procedures employed by engineers are:
1. Allowable stress Design (ASD)
2. Load & Resistance Factor Design (LRFD)
ALLOWABLE STRESS DESIGN
• Safety in the design was obtained by specifying that the effect of the load
should produce stresses that were a fraction of the yield stress fy, say one
half. This value will be equivalent to providing a safety factor of two,i.e.,
F.O.S = Resistance,R = fy = 2
Effect of load, Q 0.5fy
• Since the specification set limits on the stresses , so this became known as
allowable stress design.
• For steel bridge design, the required net area of a tension member is selected by :
required A
net
= effect of the load = T
allowable stress f
t
• For compression members, the required area is given by :
required A
gross
= effect of the load = C
allowable stress f
c
• For beams in bending, a required section modulus „S‟ is determined as :
required S = effect of the load = M
allowable stress f
b
ALLOWABLE STRESS DESIGN
SHORTCOMINGS OF ALLOWABLE
STRESS DESIGN
ASD is not suited for design of modern structures due to the following
shortcomings:
1. The resistance concept is based on the elastic behavior of homogeneous
materials.
2. It does not give reasonable measure of strength which is more fundamental
measure of resistance than as allowable stress.
3. The safety factor is applied only to the resistance and loads are considered
to be deterministic (i.e., without variation).
4. Selection of a safety factor is subjective and it doesnot provide a measure of
reliability interms of probability of failure.
LOAD & RESISTANCE FACTOR DESIGN
To overcome the deficiencies of ASD, the LRFD method was developed
which is based on
a) The strength of material
b) Consider variability not only in resistance but also in the effect of loads.
c) Provide a measure of safety related to probability of failure.
Thus the safety criteria is:
ΦRn ≥ η Σ γ
Q
i
Where Φ is the resistance factor, Rn is the nominal resistance, γ is the
statistically based load factor and Qi is the effect of load and η is the load
modification factor.
This equation involves both load factors and resistance factors.
In the general equation for LRFD method of design
ΦRn ≥ η Σ γi Qi
η is the load modification factor that takes into its account the ductility, redundancy
and operational importance of the bridge.It is given by the expression
η = η
d
η
r
η
i
≥ 0.95
Where η
d
is the ductility factor, η
r
is the redundancy factor and η
i
is the operational
importance factor.
LOAD & RESISTANCE FACTOR DESIGN
Ductility Factor:
• Ductility is important to the safety of the bridge.
• If ductility is present overloaded portion of the structure can redistribute the
load to other portions that have reserve strength.
• This redistribution is dependent on the ability of the overloaded component
and its connections to develop inelastic deformations without failure.
• Brittle behavior is to be avoided, because it implies a sudden loss of load
carrying capacity when the elastic limit is exceeded.
• The value to be used for the strength limit state, ductility factors are
η
d
= 1.05 for nonductile components and connections
η
d
= 0.95 for ductile components and connections
DUCTILITY FACTOR
Redundancy Factor:
• A statically indeterminate structure is redundant, that is, it has more
restraints than necessary to satisfy conditions of equilibrium.
• For example, a three span continuous bridge girder would be classified as
statically indeterminate to second degree. Any combination of two supports
or two moments or one support and one moment could be lost without
immediate collapse, because the loads could find alternative paths to the
ground.
• Redundancy in a bridge system will increase its margin of safety and this is
reflected in the strength limit state redundancy factors given as
η
R
= 1.05 for nonredundant members
η
R
= 0.95 for redundant members
REDUNDANCY FACTOR
Operational Importance Factor:
• Bridges can be considered of operational importance if they are on the
shortest path between residential areas and a hospital or a school or provide
access for police, fire, and rescue vehicles to homes, businesses, industrial
plants, etc.
• It is difficult to find a situation where a bridge would not be operationally
important.
• One example of a non important bridge could be on a secondary road
leading to a remote recreation area, that is not open year around.
• In the event of an earthquake, it is important that all lifelines, such as
bridges remain open. Therefore, following requirements apply to the
extreme event limit state as well as to the strength limit state.
η
i
= 1.05 for nonductile components and connections
η
i
= 0.95 for ductile components and connections
For all other limit states: η
i
= 1.0
OPERATIONAL IMPORTANCE FACTOR
ADVANTAGES OF LRFD
1. LRFD accounts for both variability in resistance and
load
2. It achieves fairly uniform factor of safety for different
limit states.
3. It provides a rationale and consistent method of
design.
1. It requires a change in design philosophy (from
previous AASHTO methods).
2. It requires an understanding of the basic concepts of
probability and statistics.
3. It requires availability of sufficient statistical data and
probabilistic design algorithms to make adjustments in
the resistance factors to meet individual situation.
DISADVANTAGES OF LRFD
Load Factor: “A factor accounting for the variability
of loads, the lack of accuracy in
analysis and the probability of
simultaneous occurrence of different
loads.
The load factors for various load combinations and
permanent loads are given in the table 3.1 and 3.2
respectively.
LOAD COMBINATIONS & LOAD
FACTORS
Back
LOAD COMBINATION TABLE (AASHTO TABLE 3.4.11)
Load
Combination
Limit State
DC
DD
DW
EH
EV
ES
LCE
BR
PL
LS
WA WS WL FR
TU
CR
SH
TG SE
Use one of these at a time
EQ IC CT CV
STRENGTH – I γ
p
1.75 1.00   1.00 0.50/1.20 γ
TG
γ
SE
   
STRENGTH  II γ
p
1.35 1.00   1.00 0.50/1.20 γ
TG
γ
SE
   
STRENGTH  III γ
p
 1.00 1.40  1.00 0.50/1.20 γ
TG
γ
SE
   
STRENGTH – IV
EH, EV, ES, DW,
DC ONLY
γ
p
1.5
 1.00   1.00 0.50/1.20      
STRENGTH – V γ
p
1.35 1.00 0.40 0.40 1.00 0.50/1.20 γ
TG
γ
SE
   
EXTREME EVENT
– I
γ
p
γ
EQ
1.00   1.00    1.00   
EXTREME EVENT
– II
γ
p
0.50 1.00   1.00     1.00 1.00 1.00
SERVICE  I 1.00 1.00 1.00 0.30 0.30 1.00 1.00/1.20 γ
TG
γ
SE
   
SERVICE – II 1.00 1.30 1.00   1.00 1.00/1.20      
SERVICE  III 1.00 0.80 1.00   1.00 1.00/1.20 γ
TG
γ
SE
   
FATIGUE – LL, IM,
AND CE ONLY
 0.75           
Back
Type of Load
Use One of These at a Time
Maximum Minimum
DC: Component and Attachments 1.25 0.90
DD: Downdrag 1.80 0.45
DW: Wearing Surfaces and Utilities 1.50 0.65
EH: Horizontal Earth Pressure
Active
AtRest
1.50
1.35
0.90
0.90
EV: Vertical Earth Pressure
Overall Stability
Retaining Structure
Rigid Buried Structure
Rigid Frames
Flexible Buried Structures other than
Metal Box Culverts
Flexible Metal Box Culverts
1.35
1.35
1.30
1.35
1.95
1.50
N/A
1.00
0.90
0.90
0.90
0.90
ES: Earth Surcharge 1.50 0.75
LOAD FACTORS FOR PERMANENT LOADS,
(AASHTO table 3.4.12)
Limit State:
“A limit state is a condition beyond which a structural system or
structural component ceases to fulfill the function for which it is
designed”.
Bridges shall be designed for specified limit states to achieve the objectives of
constructability, safety and serviceability.
Generally the limit states that are considered in bridge design are:
1. Service limit state
2. Fatigue and fracture limit state
3. Strength limit state
4. Extreme Event limit state
LIMIT STATES
This limit state refers to restrictions on stresses, deflections and
crack widths of bridge components that occur under regular
service conditions.[A1.3.2.2]
• For the limit state the resistance factors Φ = 1.0 and nearly all
the load factors γ
i
are equal to 1.0.
• There are three service limit conditions given in the table to
cover different design situations.
SERVICE LIMIT STATE
Back
LOAD COMBINATION TABLE (AASHTO TABLE 3.4.11)
Load
Combination
Limit State
DC
DD
DW
EH
EV
ES
LCE
BR
PL
LS
WA WS WL FR
TU
CR
SH
TG SE
Use one of these at a time
EQ IC CT CV
STRENGTH – I γ
p
1.75 1.00   1.00 0.50/1.20 γ
TG
γ
SE
   
STRENGTH  II γ
p
1.35 1.00   1.00 0.50/1.20 γ
TG
γ
SE
   
STRENGTH  III γ
p
 1.00 1.40  1.00 0.50/1.20 γ
TG
γ
SE
   
STRENGTH – IV
EH, EV, ES, DW,
DC ONLY
γ
p
1.5
 1.00   1.00 0.50/1.20      
STRENGTH – V γ
p
1.35 1.00 0.40 0.40 1.00 0.50/1.20 γ
TG
γ
SE
   
EXTREME EVENT
– I
γ
p
γ
EQ
1.00   1.00    1.00   
EXTREME EVENT
– II
γ
p
0.50 1.00   1.00     1.00 1.00 1.00
SERVICE  I 1.00 1.00 1.00 0.30 0.30 1.00 1.00/1.20 γ
TG
γ
SE
   
SERVICE – II 1.00 1.30 1.00   1.00 1.00/1.20      
SERVICE  III 1.00 0.80 1.00   1.00 1.00/1.20 γ
TG
γ
SE
   
FATIGUE – LL, IM,
AND CE ONLY
 0.75           
Service I:
This service limit state refers to the load combination
relating to the normal operational use of the bridge with 90 km/h
wind.
Service II:
This service limit state refers to the load
combination relating only to steel structures and is intended to
control yielding and slip of slip critical connections.
Service III:
This service limit state refers to the load
combination relating only to tension in prestressed concrete
structures with the objective of crack control.
SERVICE LIMIT STATE
• This limit state refers to restrictions on stress range caused by a design
truck.
• The restrictions depend upon the stress range excursions expected to occur
during the design life of the bridge.[A1.3.2.3].
• This limit state is used to limit crack growth under repetitive loads and to
prevent fracture due to cumulative stress effects in steel elements,
components, and connections.
• For the fatigue and fracture limit state, Φ = 1.0
• Since, the only load that causes a large number of repetitive cycles is the vehicular
live load, it is the only load effect that has a nonzero load factor in the table 3.1
FATIGUE AND FRACTURE LIMIT STATE
Back
LOAD COMBINATION TABLE (AASHTO TABLE 3.4.11)
Load
Combination
Limit State
DC
DD
DW
EH
EV
ES
LCE
BR
PL
LS
WA WS WL FR
TU
CR
SH
TG SE
Use one of these at a time
EQ IC CT CV
STRENGTH – I γ
p
1.75 1.00   1.00 0.50/1.20 γ
TG
γ
SE
   
STRENGTH  II γ
p
1.35 1.00   1.00 0.50/1.20 γ
TG
γ
SE
   
STRENGTH  III γ
p
 1.00 1.40  1.00 0.50/1.20 γ
TG
γ
SE
   
STRENGTH – IV
EH, EV, ES, DW,
DC ONLY
γ
p
1.5
 1.00   1.00 0.50/1.20      
STRENGTH – V γ
p
1.35 1.00 0.40 0.40 1.00 0.50/1.20 γ
TG
γ
SE
   
EXTREME EVENT
– I
γ
p
γ
EQ
1.00   1.00    1.00   
EXTREME EVENT
– II
γ
p
0.50 1.00   1.00     1.00 1.00 1.00
SERVICE  I 1.00 1.00 1.00 0.30 0.30 1.00 1.00/1.20 γ
TG
γ
SE
   
SERVICE – II 1.00 1.30 1.00   1.00 1.00/1.20      
SERVICE  III 1.00 0.80 1.00   1.00 1.00/1.20 γ
TG
γ
SE
   
FATIGUE – LL, IM,
AND CE ONLY
 0.75           
• This limit state refers to providing sufficient strength or resistance to satisfy the
inequality
ΦRn ≥ η Σ γi Qi
• This limit state include the evaluation of resistance to bending, shear, torsion, and
axial load.
• The statically determined resistance factor Φ will be less than 1.0 and will have
values for different materials and strength limit states.
STRENGTH LIMIT STATE
StrengthI:
This strength limit is the basic load combination
relating to the normal vehicular use of the bridge without wind.
StrengthII:
This strength limit is the basic load combination
relating to the use of the bridge by permit vehicles without
wind.
StrengthIII:
This strength limit is the basic load combination
relating to the bridge exposed to wind velocity exceeding 90
km/h.
STRENGTH LIMIT STATE
Back
LOAD COMBINATION TABLE (AASHTO TABLE 3.4.11)
Load
Combination
Limit State
DC
DD
DW
EH
EV
ES
LCE
BR
PL
LS
WA WS WL FR
TU
CR
SH
TG SE
Use one of these at a time
EQ IC CT CV
STRENGTH – I γ
p
1.75 1.00   1.00 0.50/1.20 γ
TG
γ
SE
   
STRENGTH  II γ
p
1.35 1.00   1.00 0.50/1.20 γ
TG
γ
SE
   
STRENGTH  III γ
p
 1.00 1.40  1.00 0.50/1.20 γ
TG
γ
SE
   
STRENGTH – IV
EH, EV, ES, DW,
DC ONLY
γ
p
1.5
 1.00   1.00 0.50/1.20      
STRENGTH – V γ
p
1.35 1.00 0.40 0.40 1.00 0.50/1.20 γ
TG
γ
SE
   
EXTREME EVENT
– I
γ
p
γ
EQ
1.00   1.00    1.00   
EXTREME EVENT
– II
γ
p
0.50 1.00   1.00     1.00 1.00 1.00
SERVICE  I 1.00 1.00 1.00 0.30 0.30 1.00 1.00/1.20 γ
TG
γ
SE
   
SERVICE – II 1.00 1.30 1.00   1.00 1.00/1.20      
SERVICE  III 1.00 0.80 1.00   1.00 1.00/1.20 γ
TG
γ
SE
   
FATIGUE – LL, IM,
AND CE ONLY
 0.75           
StrengthIV:
This strength limit is the basic load combination
relating to very high dead load/live load force effect ratios.
StrengthV:
This strength limit is the basic load combination
relating to the normal vehicular use of the bridge with wind of
90 km/h velocity. It differs from the StrengthIII limit state by
the presence of the live load on the bridge, wind on the live
load and reduced wind on the structure.
STRENGTH LIMIT STATE
This load effect refers to the structural survival of a bridge
during a major earthquakes or floods or when collided by a
vessel, vehicle, or ice flow[A1.3.2.5].
These loads are specified to be applied separately, as the
probability of these events occurring simultaneously is very low.
EXTREME EVENT LIMIT STATE
Back
LOAD COMBINATION TABLE (AASHTO TABLE 3.4.11)
Load
Combination
Limit State
DC
DD
DW
EH
EV
ES
LCE
BR
PL
LS
WA WS WL FR
TU
CR
SH
TG SE
Use one of these at a time
EQ IC CT CV
STRENGTH – I γ
p
1.75 1.00   1.00 0.50/1.20 γ
TG
γ
SE
   
STRENGTH  II γ
p
1.35 1.00   1.00 0.50/1.20 γ
TG
γ
SE
   
STRENGTH  III γ
p
 1.00 1.40  1.00 0.50/1.20 γ
TG
γ
SE
   
STRENGTH – IV
EH, EV, ES, DW,
DC ONLY
γ
p
1.5
 1.00   1.00 0.50/1.20      
STRENGTH – V γ
p
1.35 1.00 0.40 0.40 1.00 0.50/1.20 γ
TG
γ
SE
   
EXTREME EVENT
– I
γ
p
γ
EQ
1.00   1.00    1.00   
EXTREME EVENT
– II
γ
p
0.50 1.00   1.00     1.00 1.00 1.00
SERVICE  I 1.00 1.00 1.00 0.30 0.30 1.00 1.00/1.20 γ
TG
γ
SE
   
SERVICE – II 1.00 1.30 1.00   1.00 1.00/1.20      
SERVICE  III 1.00 0.80 1.00   1.00 1.00/1.20 γ
TG
γ
SE
   
FATIGUE – LL, IM,
AND CE ONLY
 0.75           
Extreme Event I:
This extreme event limit state is the load
combination relating to earthquake. This limit state also include
water load and friction.
Extreme Event I:
This extreme event limit state is the load
combination to ice load, collision by vessels, vehicles and to
certain hydraulic events with reduced live loads.
EXTREME EVENT LIMIT STATE
Back
LOAD COMBINATION TABLE (AASHTO TABLE 3.4.11)
Load
Combination
Limit State
DC
DD
DW
EH
EV
ES
LCE
BR
PL
LS
WA WS WL FR
TU
CR
SH
TG SE
Use one of these at a time
EQ IC CT CV
STRENGTH – I γ
p
1.75 1.00   1.00 0.50/1.20 γ
TG
γ
SE
   
STRENGTH  II γ
p
1.35 1.00   1.00 0.50/1.20 γ
TG
γ
SE
   
STRENGTH  III γ
p
 1.00 1.40  1.00 0.50/1.20 γ
TG
γ
SE
   
STRENGTH – IV
EH, EV, ES, DW,
DC ONLY
γ
p
1.5
 1.00   1.00 0.50/1.20      
STRENGTH – V γ
p
1.35 1.00 0.40 0.40 1.00 0.50/1.20 γ
TG
γ
SE
   
EXTREME EVENT
– I
γ
p
γ
EQ
1.00   1.00    1.00   
EXTREME EVENT
– II
γ
p
0.50 1.00   1.00     1.00 1.00 1.00
SERVICE  I 1.00 1.00 1.00 0.30 0.30 1.00 1.00/1.20 γ
TG
γ
SE
   
SERVICE – II 1.00 1.30 1.00   1.00 1.00/1.20      
SERVICE  III 1.00 0.80 1.00   1.00 1.00/1.20 γ
TG
γ
SE
   
FATIGUE – LL, IM,
AND CE ONLY
 0.75           
• This is a review to understand the basic concepts of
statistics and probability.
• Probabilistic analysis are not necessary to apply the
LRFD method in practice except for rare situations that
are not included by the code.
• The following section define and discuss the statistical
and probabilistic terms .
PRINCIPLES OF PROBABALISTIC DESIGN
PRINCIPLES OF PROBABALISTIC DESIGN
This section includes :
1. Sample, Mean, Mode, Median, Midrange
2. Standard deviation
3. Probability density function
4. Bias factor
5. Coefficient of variation
6. Probability of failure
Sample and Sample Size
A sample is a set of values which may be
discrete or continuous.
Sample size is the total number of elements
in a sample and is referred by „n‟.
Mean Value
The sum of all elements of the data set
divided by the number of elements.
x = Σ x
i
/ n
___
Mode
It is the data element which occurs most frequently. For example, in a sample having
elements 1,3,4,3,5,7, the mode is „3‟.
Empty Mode set
If there is no repeated value in a sample, there is no mode for this sample or the mode is
said to have an empty set.
Bimodal Data
If two elements (values) are repeated for equal number of times within a sample
then the sample data is said to be bimodal.
Multimodal Data
If more than two elements (values) are repeated for equal number of times within a sample
then the sample data is said to be multimodal.
Median
Median is the middle element in a data set when
the set is arranged in order of magnitude.
For example, for a data set 3, 4, 2, 7, 9, 13, 1
the median is 4.
1, 2, 3, 4, 7, 9, 13
Mid Range
Midrange is the arithmetic mean of the highest and lowest
data element.
For example, for a data set 3, 4, 2, 7, 9, 13, 1
the Midrange is calculated as:
Midrange = (x
max
+ x
min
) / 2
So, Midrange = (1+ 13) / 2 = 7
Please Remember:
Mean, Median and Midrange always exist
and are unique.
Mode may or may not be unique and even
may not exist at all.
Dispersion of Data
Dispersion of data is the measure of each element as to how
far it is from some measure of central tendency (average).
There are several ways to measure the dispersion of the data.
Some are:
1. Range
2. Standard Deviation
3. Variance
Range
Range is the difference between the highest and the lowest
element.
Range is a measure of dispersion of the data set.
For example, for a data set 3, 4, 2, 7, 9, 13, 1 the
range is calculated as:
Range = (x
max
 x
min
)
So, Range = (13  1) = 12
Standard Deviation
This is the most common and useful measure
to determine the dispersion of data because
it is the average distance of each score
(element or value) from the mean.
Standard deviation of a data set is often used by
scientists as a measure of the precision to which an
experiment has been done.
Also, it can indicate the reproducibility of the result.
That is the probability of the outcomes to occur.
Standard Deviation
Standard deviation is measured as:
Σ ( x – x
i
)
2
=
n  1
= Standard Deviation
X = Mean
Xi = Any specific element
n = Size of sample (total number of elements)
Variance is the square of the standard deviation.
It is the third method of measuring dispersion of
data.
Conventionally, Statisticians use Variance while scientists
use Standard Deviation to determine dispersion.
Variance
Variance is measured as:
Σ ( x – x
i
)
2
v =
n  1
v = variance
X = Mean
Xi = Any specific element
n = Size of sample (total number of elements)
Variance
Bell Shape Distribution Function
As the name implies, it is a bell
shaped figure obtained by
approximating a histogram drawn
for a sample set.
The is done by joining the tops
of the ordinate values of a
histogram with the help of a curve.
It is the graphical representation of frequency distribution.
HISTOGRAM
Bell Shape Distribution Function
Consider a histogram of 28 day compressive
strength distribution of 176 concrete cylinders,
all intended to provide a design strength of
20.7 MPa. In this case the number of times a
particular compressive strength (1.38 MPa)
intervals was observed.
The symmetrical histogram in the previous
figure represents the frequency distributions
graphically.
The same histogram can be used to represent
the probability distribution of the data if the
area under the curve is set to „1‟.
Probability Distribution Functions
Probability density function is the probability
distribution function obtained from the
histogram constructed in the case of
continuous data (values).
Probability Density Functions
Bias factor is the ratio of the mean value
to the nominal value.
i.e, λ = x / x
n
Bias Factor
To provide a measure of dispersion, it is
convenient to define a value that is expressed as
a fraction or percentage of the mean value.
The most common measure of dispersion is
coefficient of variation
i.e, V = / x
Coefficient of Variation
Failure is defined as the realization of one of a
number of predefined limit states.
The probability of failure can be determined if
the mean and standard deviations of the
resistance and load distribution functions are
known.
Probability of Failure
Consider the probability density functions for
the random variables of load Q and Resistance
density functions for a hypothetical example
limit state.
As long as the resistance R is greater than the
effects of the load Q, there is a margin of
safety for the limit state under consideration.
Probability of Failure
Probability of Survival,
p
s
= P (R > Q)
Probability of Failure,
p
f
= 1 P (R < Q)
Probability of Failure
Probability of Failure
GEOMETRIC DESIGN CONSIDERATIONS
• When two highways intersect at a grade separation or
interchange, the geometric design of the intersection
will often determine the span lengths and selection of
bridge type.
• The bridge engineer must be aware of the design
elements that the highway engineer considers to be
important.
• The document that gives the geometric standards is „A
Policy Of The Geometric Design Of Highways And
Streets, AASHTO(1994a)‟.
• Roadway width and vertical clearance are discussed in
the following sections.
• When traffic is crossing over a bridge there
should not be a sense of restriction.
• To avoid a sense of restriction, requires that
the roadway on the bridge be the same as that
of the approaching highway.
ROADWAY WIDTH
• A typical overpass structure of a four lane divided
freeway crossing a secondary road is shown in the
figure below.
ROADWAY WIDTH
• The recommended minimum width of shoulders and
traffic lanes for the roadway on the bridge are given in
the table below.
ROADWAY WIDTH
• For bridge over highways, the vertical
clearances are given by „A Policy on Geometric
Design of Highways and Streets(AASHTO
1994a)[A2.3.3.2]
• For freeways and arterial systems a minimum
vertical clearance is 4.9 m plus an allowance for
several resurfacing of about150 mm.
• In general , a desired minimum vertical
clearance of all structures above the traveled
way and shoulders is 5m.
VERTICAL CLEARANCES
Thank you all for attending the lecture
Back
LOAD COMBINATION TABLE (AASHTO TABLE 3.4.11)
Load
Combination
Limit State
DC
DD
DW
EH
EV
ES
LCE
BR
PL
LS
WA WS WL FR
TU
CR
SH
TG SE
Use one of these at a time
EQ IC CT CV
STRENGTH – I γ
p
1.75 1.00   1.00 0.50/1.20 γ
TG
γ
SE
   
STRENGTH  II γ
p
1.35 1.00   1.00 0.50/1.20 γ
TG
γ
SE
   
STRENGTH  III γ
p
 1.00 1.40  1.00 0.50/1.20 γ
TG
γ
SE
   
STRENGTH – IV
EH, EV, ES, DW,
DC ONLY
γ
p
1.5
 1.00   1.00 0.50/1.20      
STRENGTH – V γ
p
1.35 1.00 0.40 0.40 1.00 0.50/1.20 γ
TG
γ
SE
   
EXTREME EVENT
– I
γ
p
γ
EQ
1.00   1.00    1.00   
EXTREME EVENT
– II
γ
p
0.50 1.00   1.00     1.00 1.00 1.00
SERVICE  I 1.00 1.00 1.00 0.30 0.30 1.00 1.00/1.20 γ
TG
γ
SE
   
SERVICE – II 1.00 1.30 1.00   1.00 1.00/1.20      
SERVICE  III 1.00 0.80 1.00   1.00 1.00/1.20 γ
TG
γ
SE
   
FATIGUE – LL, IM,
AND CE ONLY
 0.75           
Back
Type of Load
Use One of These at a Time
Maximum Minimum
DC: Component and Attachments 1.25 0.90
DD: Downdrag 1.80 0.45
DW: Wearing Surfaces and Utilities 1.50 0.65
EH: Horizontal Earth Pressure
Active
AtRest
1.50
1.35
0.90
0.90
EV: Vertical Earth Pressure
Overall Stability
Retaining Structure
Rigid Buried Structure
Rigid Frames
Flexible Buried Structures other than
Metal Box Culverts
Flexible Metal Box Culverts
1.35
1.35
1.30
1.35
1.95
1.50
N/A
1.00
0.90
0.90
0.90
0.90
ES: Earth Surcharge 1.50 0.75
LOAD FACTORS FOR PERMANENT LOADS,
(AASHTO table 3.4.12)
Back
LOAD COMBINATION TABLE (AASHTO TABLE 3.4.11)
Load
Combination
Limit State
DC
DD
DW
EH
EV
ES
LCE
BR
PL
LS
WA WS WL FR
TU
CR
SH
TG SE
Use one of these at a time
EQ IC CT CV
STRENGTH – I γ
p
1.75 1.00   1.00 0.50/1.20 γ
TG
γ
SE
   
STRENGTH  II γ
p
1.35 1.00   1.00 0.50/1.20 γ
TG
γ
SE
   
STRENGTH  III γ
p
 1.00 1.40  1.00 0.50/1.20 γ
TG
γ
SE
   
STRENGTH – IV
EH, EV, ES, DW,
DC ONLY
γ
p
1.5
 1.00   1.00 0.50/1.20      
STRENGTH – V γ
p
1.35 1.00 0.40 0.40 1.00 0.50/1.20 γ
TG
γ
SE
   
EXTREME EVENT
– I
γ
p
γ
EQ
1.00   1.00    1.00   
EXTREME EVENT
– II
γ
p
0.50 1.00   1.00     1.00 1.00 1.00
SERVICE  I 1.00 1.00 1.00 0.30 0.30 1.00 1.00/1.20 γ
TG
γ
SE
   
SERVICE – II 1.00 1.30 1.00   1.00 1.00/1.20      
SERVICE  III 1.00 0.80 1.00   1.00 1.00/1.20 γ
TG
γ
SE
   
FATIGUE – LL, IM,
AND CE ONLY
 0.75           
Back
Type of Load
Use One of These at a Time
Maximum Minimum
DC: Component and Attachments 1.25 0.90
DD: Downdrag 1.80 0.45
DW: Wearing Surfaces and Utilities 1.50 0.65
EH: Horizontal Earth Pressure
Active
AtRest
1.50
1.35
0.90
0.90
EV: Vertical Earth Pressure
Overall Stability
Retaining Structure
Rigid Buried Structure
Rigid Frames
Flexible Buried Structures other than
Metal Box Culverts
Flexible Metal Box Culverts
1.35
1.35
1.30
1.35
1.95
1.50
N/A
1.00
0.90
0.90
0.90
0.90
ES: Earth Surcharge 1.50 0.75
LOAD FACTORS FOR PERMANENT LOADS,
(AASHTO table 3.4.12)