Bridge Lecture note simple to understand.pdf

Fundamentals of Bridge Design
Instructor: Shewangizaw T. Page 1
1. Introduction
1.1 Definition: A bridge is a structure that crosses over a river, bay or other
obstructions, permitting the smooth and safe passage of vehicles, trains and
pedestrians. A bridge structure is divided into upper part (the super structure),
which consists of the slab, the floor system, and the main truss or girders, and a
lower part (the substructure), which are columns, piers, towers, footings, piles
and abutments. The super structure provides horizontal spans, elevating above
the ground surface.
Bridge Terminologies
Approach: It is a part of a bridge length wise to the communication route at the ends of
the bridge. It can be either a part of the bridge or a separated small bridge.
Superstructure: comprises all the components of a bridge above the supports carrying
a communication route.
- Wearing surface, deck, primary members distribute loads longitudinally and are
designed to resist flexure(stringers, girders, trusses,…), secondary members
bracings between primary members and designed to resist cross sectional
deformations of the superstructure frame and help distribute part of the vertical
load between stringers(diaphragms, cross beams, lateral bracings,…)
Substructure: consists of all components of bridge required to support the
superstructure.
o Piers: are structural elements, which sustain superstructure dead and live loads,
carry their own weight and transmit all loads to the foundation soil. They are
constructed of masonry or reinforced concrete.
o Bearings: Support the superstructure (girders, slabs, ---) and transmit the loads
to the substructure (abutments and piers). They connect the upper and lower
structures and are designed to resist these reaction forces.
o Abutments: are particular types of walls (retaining walls) that support the end of a
bridge superstructure. They resist loads from the bridge superstructure & earth
pressure.

o Wing Walls: is a wall constructed at both sides subjected side ways to lateral
earth pressures. Assist in confining the earth/backfill behind the abutment.
o Pedestals: short columns on an abutment or pier that directly support a
superstructure primary member.
o Bearings: mechanical devices used to transmit loads from superstructure to
substructure.
- Transmit vertical loads and horizontal loads to abutment and piers.
- Facilitate movement caused by thermal changes
- Provide rotational movement of the primary member/girder and may be
classified as Fixed and Expansion.
Free (clear) span: the face to face distance between supported components measured
perpendicular to the supports.
Span Length: is the distance between the centers of bearings.
Total width of a bridge: is defined as the distance between the inside of the ower railings
including walkways.
Waterway: area through which the water flows under the superstructure of the bridge.
Natural waterway: unobstructed area of the river.
Linear waterway: the width of the water surface measured from edge to edge along the
design high flood level.
Waterway afflux: the vertical increase of water due to vertical supports.
Freeboard: The vertical distance between the crown and the level of the bottom of the
girder taking in to account the backwater effects.
The waterway below the superstructure must be designed to pass the design flood and
the floating debris carried on it. This should apply even after several years of
sedimentation under or downstream of the bridge. Therefore, the free board above the
design water level should not be less than the table given below.
Discharge Q (m3/s) Vertical Clearance (m)
0 – 3.0 0.3
3.0 – 30.0 0.6
30.0 – 300.0 0.9
> 300.0 1.2

These clearance measurements should be increased on rivers with a history of
unusually large floating debris or for navigational requirements.
The width of bridge for different number of lanes is given below
Application Width (m)
Two-lane in “urban” area 10.30
Two-lane in “urban” area 7.30
Single lane 4.20
Pedestrian 3.0
Vertical clearance: - the height above roadways. (5.3m)
1.2 A Bridge Is the Key Element in a Transportation System
A bridge is a key element in a transportation system for three reasons:
It likely controls the capacity of the system
It is the highest cost per mile of the system
If the bridge fails, the system fails.
If the width of a bridge is insufficient to carry the number of lanes required to handle the
traffic volume, the bridge will be a constriction to the flow of traffic. If the strength of a
bridge is deficient and unable to carry heavy trucks, load limits will be posted and truck
traffic will be rerouted. The bridge controls both the volume and weight of the traffic
carried by the system. When a bridge is removed from service and not replaced, the
transportation system may be restricted in its function. Traffic may be detoured over
routes not designed to handle the increase in volume. Users of the system experience
increased travel times and fuel expenses. Normalcy does not return until the bridge is
repaired or replaced.
Because a bridge is a key element in a transportation system, balance must be achieved
between handling future traffic volume and loads and the cost of a heavier and wider
bridge structure. Strength is always a foremost consideration but so should measures to
prevent deterioration. The designer of new bridges has control over these parameters
and must make wise decisions so that capacity and cost are in balance, and safety is not
compromised.

1.3 Bridge Classification
Bridge Type
Depending on the objective of classification bridges can be classified according to:
i) Materials
- Steel, concrete, Timber, metal alloy bridges….
ii) Objective/usage
- Highway, Railway, Combined, pedestrian bridges…
iii) Structural System (Super Structure)
- Plate girder, Box girder, T-Girder, Composite girder, Truss, Arch, Frame,
Cable-stayed, Suspension bridges.
iv) Span
- Short, medium, long
v) Support Condition
- Simply supported, continuous, cantilever
Vi) The obstacle for the traffic lane
- Valley bridge or viaduct, River bridges, Flood bridges
vii)The arrangement of the bridge in ground plan
- Straight bridges, skew bridges, curved bridges
None of these classifications are mutually exclusive they all seem to contain parts of one
another within each other. The best that can be done is to describe the characteristics of
the different bridge type, to realize that they overlap one another, and that no one bridge
type has an exclusive advantage in particular application. Experience, modeling, peer
review, public review, architectural review, and landscape review all may play important
roles in selection of a bridge type.
The classification of bridge types in this chapter will be according to the structural
system of the super structure.
SLAB BRIDGE
The simplest type of bridge to construct and design and is perhaps the most common
bridge. It requires less labour and form work and economical for length up to 15m.
Normally the slab is made with a uniform depth over the whole bridge and the required
depth is usually 5.5 – 6% of the span length. Slab bridges carry loads primarily in shear
and flexural bending.

Continuous Reinforced Concrete Bridge
Advantages
I. Lesser number of bearings than simply supported bridge since one line of
bearings are used over the piers
II. Reduced width of piers, thus less flow obstruction and less amount of material
III. Require less number of expansion joints due to which both the initial cost and
maintenance cost become less. The rigidity quality over the bridge is thus
improved.
IV. Lesser depth of girder, hence economical supports
V. Better architectural appearance
VI. Lesser vibration and deflection
Disadvantages
I. Analysis is laborious and time consuming
II. Not suitable on yielding foundations
GIRDER BRIDGES
Girders are not as efficient as trusses in resisting loads over long spans. However, for
short and medium spans the difference in material weight is small and girder bridges are
competitive. In addition, the girder bridges have greater stiffness and are less subject to
vibrations. This characteristic was important to the railroads and resulted in the early
application of plate girders in their bridges. Girder bridges are structurally simple and
common. They consist of a floor slab, girders and the bearings, which support and
transmit gravity loads to the substructure. Girders resist bending moments and shear
forces are used for spans 12m to 90m. Girders are classified into T-Girder (cast-insitu),
concrete Box-Girder (RC or Prestressed), and steel plate Girder.
T – Girder
It is usually used for a single span bridge spanning between 12-20m. The design depth
of a normal girder bridge may vary between 7-10% of the span length depending on the
number of beams.

Box Girder
Are used for span length of between 30-90m, especially if a slender structure is desired
or for curved bridges with small horizontal curves where a great resistance to torsion is
required with no loss of strength is bending and shear.
Steel girder bridges are most favorable over deep or muddy waters since scaffolding
from the ground is not necessary.

TRUSS BRIDGES
In truss bridges, the floor slab, which carries the live load, is supported by the floor
system of stringers and cross beams. The load is transmitted to the main trusses at
nodal connections, are on each side of the bridge, through the floor system and finally to
the bearings. Lateral braces, which also are truss frame, are attached to the upper and
lower chords to resist horizontal forces such as wind and earthquake loads as well as
forsional moments. Truss bridges can take the form of a deck bridge as well as a
through bridge. A truss composed of upper and lower chords, joined by diagonal and
vertical members. Trusses are an assembly of bars, net plates and this are
comparatively easier to erect on site and are often the choice for long bridges.
Types of Truss Bridges
Warren Truss
It is the most common and is a frame composed of isosceles triangles, where the
members are either in compression or tension.
Pratt Truss
In this type of truss the members are vertical and diagonal where the diagonals are
inclined toward the center and resist only tension. It is suitable for steel bridges since it is
tension that is most effectively resisted but the vertical members are in compression.
Howe Truss
It is similar to Pratt truss except that the diagonals are inclined toward the ends, leading
to axial compression forces and the vertical members resist tension.

K – Truss
As the name indicates, the members form a ‘K’, is most economical in large bridges
because the short member lengths reduce the risk of buckling.
FRAME BRIDGES
The members are rigidly connected in “rahmen” structures or rigid frames. Unlike the
truss and the arch bridge, all the members are subjected to both axial force and bending
moments. The members in rigid frame bridges are much larger than these in a typical
building. The supports of frame bridges are either hinged or fixed, making it an externally
indeterminate structure and it is therefore not suitable when the foundation is likely to
sink. The reactions at the supports are horizontal and vertical forces at hinges, with the
addition of a bending moment at a fixed base.
Additional advantages of rigid frame bridges over continuous ones are
I. More rigidity of the structure
II. Less moments in deck being partly transferred to the supporting members
III. No bearings are required
IV. Better aesthetic appearance than the continuous span structure
As in continuous span bridges, these structures also require unyielding foundation
materials. The analysis is however more laborious than the former. The frames may be
fixed or hinged at the base.
There are different types of frame bridges such as portal frame, ∏-Rahmen, V-Leg
Rahmen, Vierendeel frame.
Portal Frame
A portal frame is the simplest design and is widely used for the piers of elevated highway
bridges because the space underneath can be effectively used for other roads of parking
lets.
∏ – Rahmen
The ∏- rahmen design is usually used for bridges in mountainous regions where the
foundation is firm, passing over deep valleys with a relatively long span or for bridges
crossing over expressways.

V – Leg Rahmen
A v – leg Rahmen is similar to a ∏– Rahmen bridge but can span longer distances with
no axial force in the center span of the girder.
Vierendeel Bridge
The vierendeel bridge is a rigid frame whose upper and lower chords are connected
rigidly to the vertical members. All the members are subjected to axial and shear forces
as well as bending moments. This is internally a highly indeterminate system.
ARCH BRIDGES
An arch acts like a circular beam restrained not only vertically but also horizontally at
both ends, and thus results, in vertical and horizontal reactions at the supports. The
horizontal reaction causes axial compression in addition to bending moments in the arch
rib. The bending moments caused by the horizontal forces balances those due to gravity
loads in the super structure and they are economical in material compared with an
equivalent straight, simply supported girder or truss. Arch bridges may have high
fabrication and erection cost. The most suitable site for arch bridges is a valley, with the
arch foundations located on dry rock slopes. Aesthetically, the arch can be the most
successful of all bridge types and it appears as understandable and expressive.
Types of Arch Bridges
An arch bridge includes the road deck and the supporting arch. Arch bridges are
generally classified into the deck, through-deck and semi-through-deck types. Since the
deck is both types of bridges is sustained by either vertical columns or hangers to the
arch, structurally the same axial force action, either compression or tension, is in effect
in the members. The difference is that the vertical members of deck bridges take
compressive forces and the hangers of through-deck bridges take tension.
Two-hinge arch
It is the basic structural type for an arch and has one degree of indeterminacy externally
because there are four end reactions. The structure is not affected due to rotation of the
abutments but is affected due to the displacement of the same-may be designed with
small displacement of the supports.

Three – hinge arch
If one hinge is added at the crown of the arch, the arch becomes a three-hinge arch
results in rendered determinate. Even with rotation and small displacement of the
foundation or unequal settlement of the foundation, the thrust and moments are not
significantly affected in three-hinged arch bridges.
Fixed Arch
If the two ends are clamped turning it into a fixed arch, it becomes indeterminate to the
third degree. Need absolute unyielding foundation because forces and moments in fixed
arches change both due to rotation and displacement of the supports.
Trussed Arch
Due to difficulty in structural analysis diagonal members are not used in arch bridges but
in trussed arch diagonal truss bars are used instead of vertical members. Diagonal web
members increase the stiffness of a bridge more so than vertical members.
CABLE –STAYED BRIDGES
A cable stayed bridge hangs the girders form diagonal cables that are tensioned from
the tower. The cables of cable-stayed bridges are anchored in the girders. The girders
are most often supported by movable or fixed hinges. Due to the diagonally tensioned
cables, axial forces and bending moments are imposed on the girder and the tower. For
long span bridges, stability under strong wind currents should be carefully considered in
the design.
Longitudinal cable arrangement
I. Radiating (converging)-Fan: because the cables are at maximum angle of
inclination to the girders, the cables take maximum component of DL & LL loads.
Therefore, the axial loads in the girders are minimal. (fig. a)
II. Harp:
- it causes bending moment in the tower

- the harp pattern is not the best from the static of economic point of views
- it is superior aesthetically (fig. b)
III. Fan/Modified fan: combination of radiating and harp types and combining the
advantages of both. Large number of cable-stayed bridges have been built using
this. (fig. c)
The cable stayed bridge is usually analyzed using linear elastic frame analysis. The
cable is modeled as a bar element with hinged ends. Most of the load is transmitted to
the substructure through the cables and the tower. But some goes to the girder directly.
The smaller the bending stiffness of the girder, the less the load is taken by the girder. In
the preliminary design, the bridge is modeled as a plane frame. For the details, however,
more precise analyses such as three-dimensional stress analyses may be used. It is
recommended to be economical over the range 100-350m, but the maximum span used
is 890m of the Tatarn Bridge in Japan.

The following three general principles are to be considered in determining cable tension:
1. Avoid having any bending moments (generated by dead loads) in the tower.
This is accomplished by balancing the horizontal components of the cable
tension in the left and right ends of the tower.
2. Keep the bending moments in the girder small. It depends on the location and
the distance between joints in the cable small distance (multi-cable) will result
in small bending moments on the girders.
3. Close the girder by connecting the center block lastly without using any
compelling forces. The cable tension is selected such that zero sectional
force exists at the center of the girder.
SUSPENSION BRIDGES
Suspension bridges use two main cables suspended between two towers and anchored
to blocks at the ends. Stiffening girders are either truss or box type and hung from the
main cables using hangers. The suspension bridge is most suitable for long spans. The
longest is the Akashi Kaikyo Bridge, which has the main span of 1908.8m in Japan.
The flow of forces in a suspension bridge: The load on the girder is transmitted to the
towers through the hangers and the main cables, and then to the anchor blocks. It can
be seen that anchor blocks are essential to take the horizontal reaction force from the

cables. The gravity of the anchor blocks resists the upward component of the cable
tension force and the shear force between the anchor blocks and the foundation resists
the horizontal component. Unlike the cable-stayed bridge, no axial force is induced in the
girders of a suspension bridge.
The sag in the main cable affects the structural behavior of the suspension bridge: the
smaller the sag, the larger the stiffness of the bridge and thereby large horizontal forces
are applied to anchor blocks. In general the ratio of the sag to the main span is selected
to the about 1:10. It is economical over the span of 600m.
Cable Design
For the cable, the high strength steel wire, i.e. usually 5mm in diameter with a strength of
1760 N/mm2 and zinc-galvanized is used. There are several types of cables: stand rope,
spiral rope, locked coil rope, and parallel wine stand.
Stiffening Girder
Truss or box type girders are used to stiffen suspension bridges. The girder must be
carefully designed to have sufficient stiffness for wind stability. For very long spans
trusses are most effective in improving the stiffness and stability. The box girder is often
adopted due to its ease of fabrication.
Tower
The tower is designed to be subjected to large axial compression and bending moment.
It is designed to have smaller bending stiffness in the longitudinal direction since the
horizontal forces coming from both sides of the tower keep it balanced.

1.4 SELECTION OF BRIDGE TYPE
One of the key submittals in the design process is the engineer’s report to the bridge
owner of the type, size and location of the proposed bridge. Selection of a bridge type
involves consideration of a number of factors. In general, these factors are related to
economy, safety, and aesthetics. It is difficult to prepare a list of factors without implying
and order of priority, but a list is necessary even if the priority changes form bridge to
bridge.
Geometric conditions of the site: - The type of bridge selected will often depend on the
horizontal and vertical alignment of the highway route and on the clearances above and
below the roadway. Generally skewed crossings should be avoided, because skewed
bridges are more difficult to calculate, are longer and need more reinforcement, which
means they are more costly. Skewed bridges should be avoided due to the eccentric
earth pressure on each of the front walls that may cause the whole structure to rotate.
For example, if the roadway is on a curve, continuous box-girders and slabs are a good
choice because they have a pleasing appearance can readily be built on a curve, and
have a relatively high torsion resistance.
Geotechnical or soil condition of the site: - The foundation soils at a site are very
important in the total cost of the structure. If the soil for the adjacent road embankment
are very poor and require piling or a pile deck, this should be compared to the cost of a
longer bridge. For example, π-frame bridge required strong foundation material that can
resist both horizontal and vertical thrust.
Functional Requirements: - In addition to geometric alignment that allows a bridge to
connect two points on a highway route, the bridge must also function to carry present
and future volumes of traffic. Decision must be made on the number of lanes of traffic,
inclusion of sidewalks and /or bike paths, whether the width of the bridge deck should
include medians, drainage of the surface waters, snow removal and future wearing
surface.

Architectural and sculptural aspects: - Close to cities and large towns the architectural
and sculptural aspects of the bridge should be considered. If a pleasing bridge is desired
a competition between architects shall be arranged before or parallel with the actual pre-
design of the bridge. It should be the goal of every bridge designer to obtain a positive
aesthetic response to the bridge type selected.
Economics and Ease of Maintenance: - It is not possible to separate first cost and
maintenance cost over the life of the bridge when comparing the economics of different
bridge types. A general rule is that the bridge with the minimum number of spans, fewest
deck joints, and widest spacing of girders will be the most economical. By reducing the
number of spans in a bridge layout by one span the construction cost of one pier is
eliminated. Deck joints are a high maintenance cost item, so minimizing their number will
reduce the life cycle cost of the bridge.
Construction and Erection Consideration: - The selection of the type of bridge to be built
is often governed by construction and erection considerations. The length of time
required to construct a bridge is important and will vary with bridge type. In general, the
larger the prefabricated or Precast member the shorter the construction time. However,
the larger the members, the more difficult they are to transport and lift into place. Cast in
place concrete bridges are generally economical for grade separations unless the false
work supporting the non-hardened concrete becomes a traffic problem.

1.5 Design Philosophy
General
A general statement for assuring safety in engineering design is that the resistance of
the components supplied exceed the demands put on them by applied loads, that is,
Resistance ≥ effect of the loads
When applying this simple principle, both sides of the inequality are evaluated for the
same conditions.
When a particular loading condition reaches its limit, failure is the assumed result, that
is, the loading condition becomes a failure mode. Such a condition is referred to as a
limit state that can be defined as: A limit state is a condition beyond which a bridge
system or bridge component ceases to fulfill the function for which it is designed.
Examples of limit states for girder-type bridges include deflection, cracking, fatigue,
flexure, shear, torsion, buckling, settlement, bearing, and sliding. Well-defined limit
states are established so that a designer knows what is considered to be unacceptable.
Development of Design Procedures
Allowable
Stress Design
Safety in the design was obtained by specifying that the effect of the loads should
produce stresses that were a fraction of the yield stress fy : for example, one half. This
value would be equivalent to providing a safety factor F of 2; that is,
Because the specifications set limits on the stresses, this became known as allowable
stress design (ASD).
These techniques were used as early as the 1860s to design many successful statically
determinate truss bridges. Similar bridges are built today, but they are no longer
statically determinate because they are not pin connected. As a result, the stresses in
the members are no longer uniform because of the bending moments that occur due to
the more rigid connections.
Implied in the ASD method is the assumption that the stress in the member is zero
before any loads are applied, that is, no residual stresses are introduced when the
members are formed. Not only are these residual stresses highly non uniform, they are

also difficult to predict. Consequently, adjustments have to be made to the allowable
bending stresses, especially in compression elements, to account for the effect of
residual stresses.
Another difficulty in applying ASD to steel beams is that bending is usually accompanied
by shear, and these two stresses interact. Another definition of yield stress that
incorporates the effect of shear stress would be more logical. ASD methods were
developed for the design of statically determinate metallic structures. They do not
necessarily apply in a straightforward and logical way to other materials and other levels
of redundancy. In regard to uncertainties in design, one other point concerning the ASD
method needs to be emphasized. Allowable stress design does not recognize that
different loads have different levels of uncertainty. Dead, live, and wind loads are all
treated equally in ASD.
Shortcomings
Of Allowable
Stress Design
As just shown, ASD is not well suited for design of modern structures. Its major
shortcomings can be summarized as follows:
1. The resistance concepts are based on elastic behavior of materials.
2. It does not embody a reasonable measure of strength, which is a more fundamental
measure of resistance than is allowable stress.
3. The safely factor is applied only to resistance. Loads are considered to be
deterministic (without variation).
4. Selection of a safety factor is subjective, and it does not provide a measure of
reliability in terms of probability of failure.
What is needed to overcome these deficiencies is a method that is (a) based on the
strength of material, (b) considers variability not only in resistance but also in the effect
of loads, and (c) provides a measure of safety related to probability of failure.

Load and
Resistance
Factor Design
To account for the variability on both sides of the inequality in Eq. 3.1, the resistance
side is multiplied by a statistically based resistance factor φ, whose value is usually less
than one, and the load side is multiplied by a statistically based load factor γ , whose
value is usually greater than one. Because the load effect at a particular limit state
involves a combination of different load types (Qi) that have different degrees of
predictability, the load effect is represented by a summation of γiQi values. If the nominal
resistance is given by Rn, the safety criterion is
φRn ≥ effect of ∑ γiQi
Because the above eqn involves both load factors and resistance factors, the design
method is called load and resistance factor design (LRFD). The resistance factor φ for a
particular limit state must account for the uncertainties in
Material properties.
Equations that predict strength.
Workmanship
Quality control
Consequence of a failure
The load factor γi chosen for a particular load type must consider the uncertainties in
Magnitudes of loads
Arrangement (positions) of loads
Possible combinations of loads
In selecting resistance factors and load factors for bridges, probability theory has been
applied to data on strength of materials, and statistics on weights of materials and
vehicular loads.
Some of the pros and cons of the LRFD method can be summarized as follows:
Advantages of LRFD Method
1. Accounts for variability in both resistance and load.
2. Achieves fairly uniform levels of safety for different limit states and bridge types
without involving probability or statistical analysis.
3. Provides a rational and consistent method of design.

Disadvantages of LRFD Method
1. Requires a change in design philosophy (from previous AASHTO methods).
2. Requires an understanding of the basic concepts of probability and statistics.
3. Requires availability of sufficient statistical data and probabilistic design algorithms to
make adjustments in resistance factors.
Design Limit States
The basic design expression in the AASHTO (2004b) LRFD Bridge Specifications that
must be satisfied for all limit states, both global and local, is given as:
∑ ηiγiQi ≤ φRn
where Qi is the force effect, Rn is the nominal resistance, γi is the statistically based load
factor applied to the force effects, φ is the statistically based resistance factor applied to
nominal resistance, and ηi is a load modification factor.
For all nonstrength limit states, φ = 1.0.
The load modifier is a factor that takes into account the ductility, redundancy, and
operational importance of the bridge. It is given for loads for which a maximum value of
γi is appropriate by:
ηi = ηDηRηI ≥ 0.95
and for loads for which a minimum value of γi is appropriate by:
ηi = 1/ηDηRηI ≤ 1.0
where ηD is the ductility factor, ηR is the redundancy factor, and ηI is the operational
importance factor. The first two factors refer to the strength of the bridge and the third
refers to the consequence of a bridge being out of service. For all nonstrength limit
states ηD = ηR = 1.0
DUCTILITY FACTOR ηD
Ductility is important to the safety of a bridge. If ductility is present, overloaded portions
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. Components and
connections in reinforced concrete can be made ductile by limiting the flexural
reinforcement and by providing confinement with hoops or stirrups.

The values to be used for the strength limit state ductility factor are:
ηD ≥ 1.05 for non ductile components and connections
ηD = 1.00 for conventional designs and details complying with the specifications
ηD ≥ 0.95 for components and connections for which additional ductility-enhancing
measures have been specified beyond those required by the specifications
For all other limit states:
ηD = 1.00
REDUNDANCY FACTOR ηR
Redundancy significantly affects the safety margin of a bridge structure. A statically
indeterminate structure is redundant, that is, has more restraints than are necessary to
satisfy equilibrium. For example, a three-span continuous bridge girder in the old days
would be classified as statically indeterminate to the second degree. Any combination of
two supports, or two moments, or one support and one moment could be lost without
immediate collapse because the applied loads could find alternative paths. The concept
of multiple-load paths is the same as redundancy. Single-load paths or nonredundant
bridge systems are not encouraged. Redundancy in a bridge system increases its
margin of safety, and this is reflected in the strength limit state by redundancy factors
given as:
ηR ≥ 1.05 for nonredundant members
ηR = 1.00 for conventional levels of redundancy
ηR ≥ 0.95 for exceptional levels of redundancy
ηR = 1.00
OPERATIONAL IMPORTANCE FACTOR ηI
Bridges can be considered of operational importance if they are on the shortest path
between residential areas and a hospital or school or provide access for police, fire, and
rescue vehicles to homes, businesses, and industrial plants. Bridges can also be
considered essential if they prevent a long detour and save time and gasoline in getting
to work and back home again. One example of a less important bridge could be on a
secondary road leading to a remote recreation area that is not open year round, bridges
remain open.

Therefore, the following requirements apply to the extreme event limit state as well as to
the strength limit state:
ηI ≥ 1.05 for a bridge of operational importance
ηI = 1.00 for typical bridges
ηI ≥ 0.95 for relatively less important bridges
ηI = 1.00
Bridge Design Specifications
Set of rules and regulations to be followed in designing the nation’s highway bridges
1914 AASHO was formed
1921 AASHO’s Bridges and Allied Structures Committee Organized
1932 First edition of AASHO standard specifications for Highway Bridges and Incidental
structures was published
1963 AASHO became AASHTO

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