introduction to bridge engineering design

LECTURE No.2
LECTURE No.2
INTRODUCTION TO
INTRODUCTION TO
BRIDGE ENGINEERING
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 Specification

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

INTRODUCTION
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

IMPORTANCE OF LOAD
IMPORTANCE OF LOAD
PREDICTION
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
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
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 NON-STRUCTURAL 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 A3.4.1-1 and A3.4.1-2 apply here.
(From AASHTO LRFD 1994 Bridge Design Specifications).
A.

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
A3.4.1-1 and A3.4.1-2 (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.

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 A3.4.1-1 and A3.4.1-2 apply here.
(From AASHTO LRFD Bridge Design Specifications).
EV has a maximum and minimum load factor of 1.35 and
0.9 respectively.
A.

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.

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.

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 LANE

DESIGN LANES
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

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 HS20-44(denoting Highway Semitrailer 20 tons with year of
publication 1944).

DESIGN TANDEM
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
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.

•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.

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.

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 mode
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.

Nowak (1993) compared survey vehicles with others in the same lane to the AASHTO
load model and the results are shown in the figure.

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
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
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
ADTTSL = p(ADTT)
Where p is the fraction of traffic assumed to be in one lane as defined in
table4.3.

PEDESTRIAN LOADS
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
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
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
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
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
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 = Ddyn
Dstat
Here Dstat is the maximum static deflection and Ddyn is the
additional defection due to the dynamic effects.

DYNAMIC EFFECTS
DYNAMIC EFFECTS
According to AASHTO specifications, DLA is illustrated in table 4.7[A3.6.2].

DYNAMIC EFFECTS
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
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,
ar = 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 ar in the Newton’s second law of motion,
Fr = m V² …..4.2
r
Where Fr is the force on the truck.
Since mass m = W
g

CENTRIFUGAL FORCES
CENTRIFUGAL FORCES
So, we can substitute ‘ m ‘ in eq.4.2 to obtain an expression similar to that given by
AASHTO,
Fr = V² W
rg
Fr = 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
•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
PERMIT VEHICLES AND MISCELLANEOUS
CONSIDERATIONS
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
LATERAL LOADS
Following forces are considered under lateral loads:
• Fluid forces
• Seismic Loads
• Ice Forces

FLUID 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
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 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
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
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
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
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
TEMPERATURE
Two types of temperature changes must be included in the analysis of the
superstructure.
i. Uniform temperature change
ii. Gradient or non-uniform 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 Non-uniform temperature change:
In this type the temperature change is gradient or non-uniform heating or cooling
of the superstructure across its depth. Subjected to sunshine, bridge deck heats
more than the girder below. This non-uniform 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
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 0C.
Table 4.21 gives the temperature ranges. The temperature range is used to
establish the change in temperature used in the analysis.
TEMPERATURE
TEMPERATURE

CREEP & SHRINKAGE
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
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
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
Collision loads include:
1.Vessel Collision load
2.Rail Collision Load
3.Vehicle Collision Load

COLLISION LOADS
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

LECTURE No.2
LECTURE No.2
SECTION 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
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
DESIGN PHILOSOPHY
A general statement for assuring safety in engineering
design is that
Resistance (of material & x-section) 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.

PROCEDURES
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 Anet = effect of the load = T
allowable stress ft
• For compression members, the required area is given by :
required Agross = effect of the load = C
allowable stress fc
• For beams in bending, a required section modulus ‘S’ is determined as :
required S = effect of the load = M
allowable stress fb

SHORTCOMINGS OF ALLOWABLE
SHORTCOMINGS OF ALLOWABLE
STRESS DESIGN
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 Qi
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 = ηd ηr ηi 0.95
≥
Where ηd is the ductility factor, ηr is the redundancy factor and ηi is the
operational importance factor.

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
ηd = 1.05 for non-ductile components and connections
ηd = 0.95 for ductile components and connections
DUCTILITY FACTOR
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
ηR = 1.05 for non-redundant members
ηR = 0.95 for redundant members
REDUNDANCY FACTOR
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.
ηi = 1.05 for non-ductile components and connections
ηi = 0.95 for ductile components and connections
For all other limit states: ηi = 1.0
OPERATIONAL IMPORTANCE FACTOR
OPERATIONAL IMPORTANCE FACTOR

ADVANTAGES OF LRFD
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
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
LOAD COMBINATIONS & LOAD
FACTORS
FACTORS

Back
LOADS In AASHTO LOAD COMBINATIONS) (AASHTO TABLE 3.4.1-1)
PERMANENT LOADS

Back
LOADS In AASHTO LOAD COMBINATIONS) (AASHTO TABLE 3.4.1-1)
TRANSIENT LOADS

Back
LOAD COMBINATION TABLE (AASHTO TABLE 3.4.1-1)
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 γp 1.75 1.00 - - 1.00 0.50/1.20 γTG
γSE - - - -
STRENGTH - II γp 1.35 1.00 - - 1.00 0.50/1.20 γTG
γSE - - - -
STRENGTH - III γp - 1.00 1.40 - 1.00 0.50/1.20 γTG
γSE - - - -
STRENGTH – IV
EH, EV, ES, DW,
DC ONLY
γp
1.5
- 1.00 - - 1.00 0.50/1.20 - - - - - -
STRENGTH – V γp 1.35 1.00 0.40 0.40 1.00 0.50/1.20 γTG
γSE - - - -
EXTREME EVENT
– I
γp
γEQ 1.00 - - 1.00 - - - 1.00 - - -
EXTREME EVENT
– II
γp 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 γTG
γSE - - - -
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 γTG
γSE - - - -
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
 At-Rest
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 3.4.1-2)

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
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 γi are equal to 1.0.
• There are three service limit conditions given in the table to
cover different design situations.
SERVICE LIMIT STATE
SERVICE LIMIT STATE

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:
combination relating only to steel structures and is intended to
control yielding and slip of slip critical connections.
Service III:
combination relating only to tension in pre-stressed
concrete structures with the objective of crack control.
SERVICE LIMIT STATE
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 non-zero load factor in the
table 3.1
FATIGUE AND FRACTURE LIMIT STATE
FATIGUE AND FRACTURE LIMIT STATE

• 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

Strength-I:
This strength limit is the basic load combination
relating to the normal vehicular use of the bridge without wind.
Strength-II:
This strength limit is the basic load
combination relating to the use of the bridge by permit
vehicles without wind.
Strength-III:
combination relating to the bridge exposed to wind velocity
exceeding 90 km/h.

Strength-IV:
This strength limit is the basic load combination
relating to very high dead load/live load force effect ratios.
Strength-V:
combination relating to the normal vehicular use of the
bridge with wind of 90 km/h velocity. It differs from the
Strength-III limit state by the presence of the live load on
the bridge, wind on the live load and reduced wind on the
structure.

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

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.

• 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

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
A sample is a set of values which may be
discrete or continuous.
discrete or continuous.
Sample size is the total number of
Sample size is the total number of
elements in a sample and is referred by
elements in a sample and is referred by
‘n’.
‘n’.

Mean Value
The sum of all elements of the data set
The sum of all elements of the data set
divided by the number of elements.
divided by the number of elements.
x =
x = Σ
Σ x
xi
i / n
/ n
___
___

Mode
It is the data element which occurs most frequently. For example, in a sample having
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’.
elements 1,3,4,3,5,7, the mode is ‘3’.
Empty Mode set
Empty Mode set
If there is no repeated value in a sample, there is no mode for this sample or the mode
If there is no repeated value in a sample, there is no mode for this sample or the mode
is
is
said to have an empty set.
said to have an empty set.
Bi-modal Data
Bi-modal Data
If two elements (values) are repeated for equal number of times within a sample
If two elements (values) are repeated for equal number of times within a sample
then the sample data is said to be bimodal.
then the sample data is said to be bimodal.
Multi-modal Data
Multi-modal Data
If more than two elements (values) are repeated for equal number of times within a
If more than two elements (values) are repeated for equal number of times within a
sample
sample
then the sample data is said to be multi-modal.
then the sample data is said to be multi-modal.

Median
Median is the middle element in a data set when
Median is the middle element in a data set when
the set is arranged in order of magnitude.
the set is arranged in order of magnitude.
For example, for a data set
For example, for a data set 3, 4, 2, 7, 9, 13, 1
3, 4, 2, 7, 9, 13, 1
the median is 4.
the median is 4.
1, 2, 3,
1, 2, 3, 4
4, 7, 9, 13
, 7, 9, 13

Mid Range
Midrange is the arithmetic mean of the highest and
Midrange is the arithmetic mean of the highest and
lowest data element.
lowest data element.
the Midrange is calculated as:
the Midrange is calculated as:
Midrange
Midrange = (x
= (xmax
max+ x
+ xmin
min) / 2
) / 2
So,
So, Midrange
Midrange = (1+ 13) / 2 =
= (1+ 13) / 2 = 7
7

Please Remember:
Mean, Median and Midrange always exist
Mean, Median and Midrange always exist
and are unique.
and are unique.
Mode may or may not be unique and
Mode may or may not be unique and
even
even
may not exist at all.
may not exist at all.

Dispersion of Data
Dispersion of Data
Dispersion of data is the measure of each element as to how
Dispersion of data is the measure of each element as to how
far it is from some measure of central tendency (average).
far it is from some measure of central tendency (average).
There are several ways to measure the dispersion of the data.
There are several ways to measure the dispersion of the data.
Some are:
Some are:
1.
1. Range
Range
2. Standard Deviation
2. Standard Deviation
3. Variance
3. Variance

Range
Range is the difference between the highest and the
Range is the difference between the highest and the
lowest element.
lowest element.
Range is a measure of dispersion of the data set.
Range is a measure of dispersion of the data set.
For example, for a data set 3, 4, 2, 7, 9, 13, 1 the
For example, for a data set 3, 4, 2, 7, 9, 13, 1 the
range is calculated as:
range is calculated as:
Range
Range = (x
= (xmax
max- x
- xmin
min)
)
So,
So, Range
Range = (13 - 1) =
= (13 - 1) = 12
12

Standard Deviation
This is the most common and useful measure
This is the most common and useful measure
to determine the dispersion of data because
to determine the dispersion of data because
it is the average distance of each score
it is the average distance of each score
(element or value) from the mean.
(element or value) from the mean.
Standard deviation of a data set is often used by
Standard deviation of a data set is often used by
scientists as a measure of the precision to which an
scientists as a measure of the precision to which an
experiment has been done.
experiment has been done.
Also, it can indicate the reproducibility of the result.
Also, it can indicate the reproducibility of the result.
That is the probability of the outcomes to occur.
That is the probability of the outcomes to occur.

Standard Deviation
Standard deviation is measured as:
Standard deviation is measured as:
Σ
Σ ( x – x
( x – xi
i )
)2
2

 =
=
n - 1

 = Standard Deviation
= Standard Deviation
X = Mean
X = Mean
X
Xi
i = Any specific element
= Any specific element
n = Size of sample (total number of elements)

Variance is the square of the standard deviation.
Variance is the square of the standard deviation.
It is the third method of measuring dispersion of
It is the third method of measuring dispersion of
data.
data.
Conventionally, Statisticians use Variance while scientists
Conventionally, Statisticians use Variance while scientists
use Standard Deviation to determine dispersion.
use Standard Deviation to determine dispersion.
Variance

Variance is measured as:
Variance is measured as:
Σ
Σ ( x – x
( x – xi
i )
)2
2
v =
v =
n - 1
v = variance
v = variance
X = Mean
X = Mean
X
Xi
i = Any specific element
= Any specific element
Variance

Bell Shape Distribution Function
As the name implies, it is a bell
As the name implies, it is a bell
shaped figure obtained by
shaped figure obtained by
approximating a histogram drawn
approximating a histogram drawn
for a sample set.
for a sample set.
The is done by joining the tops
The is done by joining the tops
of the ordinate values of a
of the ordinate values of a
histogram with the help of a curve.
histogram with the help of a curve.
It is the graphical representation of frequency distribution.
It is the graphical representation of frequency distribution.
HISTOGRAM

Bell Shape Distribution
Function
Consider a histogram of 28 day compressive
Consider a histogram of 28 day compressive
strength distribution of 176 concrete
strength distribution of 176 concrete
cylinders, all intended to provide a design
cylinders, all intended to provide a design
strength of 20.7 MPa. In this case the
strength of 20.7 MPa. In this case the
number of times a particular compressive
number of times a particular compressive
strength (1.38 MPa) intervals was observed.
strength (1.38 MPa) intervals was observed.

introduction to bridge engineering design

The symmetrical histogram in the previous
The symmetrical histogram in the previous
figure represents the frequency distributions
figure represents the frequency distributions
graphically.
graphically.
The same histogram can be used to
The same histogram can be used to
represent the probability distribution of the
represent the probability distribution of the
data if the area under the curve is set to ‘
data if the area under the curve is set to ‘1
1’.
’.
Probability Distribution Functions

Probability density function is the probability
Probability density function is the probability
distribution function obtained from the
distribution function obtained from the
histogram constructed in the case of
histogram constructed in the case of
continuous data (values).
continuous data (values).
Probability Density Functions

Bias factor is the ratio of the mean value
Bias factor is the ratio of the mean value
to the nominal value.
to the nominal value.
i.e,
i.e, λ
λ = x / x
= x / xn
n
Bias Factor

Coefficient of Variation
To provide a measure of dispersion, it is convenient
To provide a measure of dispersion, it is convenient
to define a value that is expressed as a fraction or
to define a value that is expressed as a fraction or
percentage of the mean value.
percentage of the mean value.
The most common measure of dispersion is
The most common measure of dispersion is
coefficient of variation
coefficient of variation
i.e,
i.e,
x
CV



Failure is defined as the realization of one of
Failure is defined as the realization of one of
a number of pre-defined limit states.
a number of pre-defined limit states.
The probability of failure can be determined
The probability of failure can be determined
if the mean and standard deviations of the
if the mean and standard deviations of the
resistance and load distribution functions
resistance and load distribution functions
are known.
are known.
Probability of Failure

Consider the probability density functions for
Consider the probability density functions for
the random variables of load Q and
the random variables of load Q and
Resistance density functions for a
Resistance density functions for a
hypothetical example limit state.
hypothetical example limit state.
As long as the resistance R is greater than
As long as the resistance R is greater than
the effects of the load Q, there is a margin of
the effects of the load Q, there is a margin of
safety for the limit state under
safety for the limit state under
consideration.
consideration.

Probability of Survival,
Probability of Survival,
p
ps
s = P (R > Q)
= P (R > Q)
Probability of Failure,
Probability of Failure,
p
pf
f = 1- P (R < Q)
= 1- P (R < Q)

GEOMETRIC DESIGN CONSIDERATIONS
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
ROADWAY WIDTH

• A typical overpass structure of a four lane divided
freeway crossing a secondary road is shown in the
figure below.
ROADWAY WIDTH
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
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
VERTICAL CLEARANCES
VERTICAL CLEARANCES

Thank you all for attending the
lecture

introduction to bridge engineering design

More Related Content

Similar to introduction to bridge engineering design (20)

Recently uploaded (20)

introduction to bridge engineering design