Bridges Functionality and Aesthetics

Describing A
Bridge!
Choosing
A Bridge
Factors in
Bridge
Design
Aesthetic
Bridge
Feasibility
2

6
 Bridges are often referred to by their
superstructure types.
 The superstructure system of members carry the
roadway over a crossing and transfer load to a
substructure.
 Superstructures are categorized by;
 Support type (simply supported ,continuous,
cantilever)
 Design type (slab, slab on stringer, arch, rigid
frame, etc.)
 Material type (Concrete, Steel, etc.)

 Bridge Bearings: These are supports on a bridge pier, which carry the
weight of the bridge and control the movements at the bridge
supports, including the temperature expansion and contraction.
They may be metal rockers, rollers or slides or merely rubber or
laminated rubber (Rubber with steel plates glued into it).
 Bridge Dampers & Isolators: Bridge dampers are devices that absorb
energy generated by earthquake waves and lateral load
 Bridge Pier: for carrying loads as a support for a bridge.
 Bridge Cap: The highest part of a bridge pier on which the bridge
bearings or rollers are seated.
 Bridge Deck: The load bearing floor of a bridge which carries and
spreads the loads to the main beams. It can be reinforced concrete,
pre-stressed concrete, welded steel, etc.
 Abutment: A support of an arch or bridge etc which may carry a
horizontal force as well as weight.
 Expansion Joints : These are provided to accommodate the
translations due to possible shrinkage and expansions due to
temperature changes.
7

 Durability is a major design consideration. Routine inspection
and maintenance are must!
 Bridges are subjected to large moving, repetitive loads (i.e.
Vehicles) , thus Fatigue is of primary concern (accumulated
damage/cracking due to repeat loading)
 Bridge failures thought to pose a smaller threat to human life,
but is this true?
 Earthquake engineering of bridges is lagging behind
Gravity Loads
Permanent Loads - Bridge own weight!
Transient Loads - Vehicle loads, Pedestrian loads, Braking loads
Lateral Loads
Water Loads
Earthquake Loads
Ice Loads
Deformation-induced Loads
Temperature
Creep and Shrinkage
Collision Loads - Vehicular & Vessel Collision!
8

 The bridge controls both the volume and
weight of the traffic carried by the
transportation system.
 As bridge is the key element in a
transportation system,
 Balance must be achieved between
handling future traffic volume and loads
and the cost of heavier and wider bridge
structure.
9

Material &
Fabrication
•Steel
•Concrete
•Hybrid
•Other (Stone ,
Brick , wood)
Usage
•Highway
•Rail Road
•Pedestrian
•Others
(Pipeline,
utility, Airport,
etc)
Span
•Extra Long,
Over 150 m
•Long, 50 – 150
m
•Medium, 15 –
50 m
•Short, less
than 15 m
Traffic Level &
Structure
•Main structure
below the
deck line
•Above the
deck line
•On the same
level with
deck line
Structural
Form
•Slab Bridge
•Arch
•Truss
•Girder (Beam)
•Rigid Frame
Bridge
•Cantilever
Bridges
•Suspension
•Cable-Stayed
•Movable
Bridges
10

 Reinforced Concrete (RC) Beam
 Steel Hot rolled or prefabricated Plate Girder
 Steel Truss Girder
 Pre-stressed Concrete (PC) Girders
› I, U and T Beams
› Segments Box Beam
 Currently most of beam bridges are precast RC
or PC
 Most Pre-stressed and Precast sections are I
shaped.
12

 Any of these
spans may be
constructed
using beams,
girders or
trusses.
 A cantilever
bridge may
also include a
suspended
span.
15

 Culvert Bridge
 Slab Bridges
 T-Beam Bridge
 Pre-cast Concrete Box Beam Bridge
 Pre-cast Concrete I-Beam Bridge
 Rolled Steel Beam Bridge
16

 Pre-cast Concrete Box Beam & Pre-cast
Concrete I-Beam
 Composite Rolled Steel Beam Bridge
 Composite Steel Plate Girder Bridge
 Cast-in-place RCC Box Girder Bridge
 Cast-in-place Post-Tensioned Concrete
Box Girder
 Composite Steel Box Girder
17

 Composite Steel Plate Girder Bridge
 Cast-in-place Post-Tensioned concrete
Box Girder
 Post-Tensioned Concrete Segmental
Construction
 Concrete Arch and Steel Arch
18

 Cable Stayed Bridge
 Suspension Bridge
Note; Cable-stayed bridges may appear to
be similar to suspension bridges, but in fact
they are quite different in principle and in their
construction.
o In suspension bridges, large main cables
(normally 2) hang between the towers (normally
2), and are anchored at each end to the
ground.
o In the cable-stayed bridge, the towers are the
primary load-bearing structures which transmit
the bridge loads to the ground.
19

Bridge Type Min Span Max Span
Slab 0 12
Concrete Girder 10 220
Steel Girder 10 270
Cable-Stayed Concrete 90 250
Cable-Stayed Steel 90 350
Steel Truss 90 550
Concrete Arch 90 300
Steel Truss Arch 250 500
Steel Rib Arch 120 370
Steel Suspension 300 2000
20

 Span length is influenced by the cost of the
superstructure (Cost / Meter) and substructure
(Cost / Pier);
› If the substructure cost is about 25% of total cost,
then shorter spans are more cost effective.
› If the substructure cost is about 50% of total cost,
then longer spans are more economical.
 For medium to major span bridges with deep
foundation, the cost of supporting system of the
superstructure of one span nearly equals the cost
of one pier with its foundation.
 Note – if the water is shallow, substructure is
inexpensive compared to the superstructure.
21

 The following may be taken as rough guide for the selection
of span lengths for bridges to give economical design;
› For masonry arch bridges: S = 2H
› For R.C.C. slab bridges: S = 1.5H
 Beam spacing determine the number of girders
 Large Girder Spacing
› Fewer girders (faster to erect)
› Deeper and heavier size girders (can it be transported?)
› Reduced redundancy
› Thicker slab
 Smaller Girder Spacing
› More girders
› Smaller size girders
› More redundancy (but more beams to inspect)
› Thinner slab
22

 In a Deck
configuration,
traffic travels on
top of the main
structure;
 in a Pony
configuration,
traffic travels
between parallel
superstructures
are not cross-
braced at the top;
 in a Through
configuration,
traffic travels
through the
superstructure
(usually a truss is
cross-braced
above and below
the traffic).
24

 Arch Bridge
› Masonry Arch
› Concrete Arch
› Inclined Leg Frame Arch
› Rigid Frame Arch
 Truss-Arch Bridge
› Steel Truss-Arch
› Steel Deck Truss
25

 Suspension Bridges
 Cable Stayed Bridges
 Through-Truss Bridge
26

 Slab (solid and voided)
 T-Beam (cast-in-place)
 I-beam (pre-cast or pre-stressed
 Girder (Beam) Bridge - Wide-flange
beam (composite & non- composite
 Concrete Box (cast-in-place, segmental
& pre-stressed
 Steel Plate Girder (straight & haunched)
 Steel box (Orthotropic deck)
27

 Simply supported solid slab bridges are generally found
to be economic for spans up to 9 meters. These are
constructed with reinforced concrete slab of uniform
thickness.
 Slab bridges are selected where bed scour is negligible
and foundation cost is much less as in shallow raft
foundations
 Solid slab box-cell bridges are used in road underpass
or subways. These may also be used in channels where
the scour is negligible or in canals where the velocity is
non-sourcing and non-silting.
 The box-cells are either square or nearly square so that
the thicknesses of the deck slab, base slab and the
verticals are the same.
30

 In slab bridges the deck itself is the structural frame or the entire deck is
a thin beam acting entirely as one primary member. Slab Bridges are
used where depth of structure is a critical factor.
 Solid Slabs and voided slabs are used for spans up to 60 feet in length,
because of the replacement of the deck is expensive, designers
attempt to stay away from slab bridges.
 Solid slabs range in thickness from 8 to 17 inches, voided slabs range in
thickness from 18 inches to 2 ft 4 inches
 Slabs can be used with pre-stressed I girders, commonly, (slab on
stringer bridge). The deck distributes the loads transversely to the
girders. The girders carry the loads longitudinally (down the length of the
bridge) to the supports, (abutments and intermediate bents).
 One of the advantages of the slab on stringer bridge is that the deck
can be replaced without having to tear down the entire bridge.
31

 In reinforced concrete slab and girder bridges, the
deck slab transfers the superimposed load to the
supporting girders through transverse bending and also
acts as flange of the T-beam to resist longitudinal
bending moments.
 Concrete being good in compression, the deck slab
takes nearly the entire compressive force due to
longitudinal bending of the girders.
 In bridges with deck slab simply resting on
prefabricated girders, either steel or concrete, no such
advantage can be taken unless the cast-in-situ deck
slab is made monolithic with the girders by using pins /
ties.
32

 The weight of the
load is carried
outward along the
curve of the arch to
the abutments at
each end of the
arch. Semi-circle
Arch (has vertical
reaction forces only)
 A tied arch resists
spreading (drift) at its
bearings by using the
deck as a tie piece.
 Because Arch is
predominantly a
Compression
member, buckling
must be worked so
as to avoid
reductions in
allowable stresses.
34

 The type of
connections
(hinges) used
at the supports
and the
midpoint of the
arch may be
used to classify
arch bridges.
 A through arch
is shown, but
this applies to
all type of arch
bridges.
35

 The hinge-less arch allows no rotation at the foundations. As a result a
great force is generated at the foundation (horizontal, vertical, and
bending forces) and can only be built where the ground is very stable.
 The two hinged arch uses hinged bearings which allow rotation. The only
forces generated at the bearings are horizontal and vertical forces. Most
commonly used variation for steel arches and is very economical design.
 The three-hinged arch adds an additional hinge at the top or crown of the
arch. The three-hinged arch suffers very little if there is movement in either
foundation (due to earthquakes, sinking, etc.). However, the three-hinged
arch experiences much more deflection , it is rarely used anymore.
 The tied arch is a variation on the arch which allows construction even if
the ground is not solid enough to deal with the horizontal forces. Rather
than relying on the foundation to restrain the horizontal forces, the girder
itself ties both ends of the arch together.
36

 A true Arch bridge relies
on vertical members to
transmit the load which
is carried by the arch.
 A solid-ribbed arch is
commonly constructed
using curved girder
sections.
 A brace-ribbed arch has
a curved through truss
rising above the deck.
 A spandrel-braced arch
or open spandrel deck
arch carries the deck on
top of the arch.
 The tied arch (bowstring)
is used for suspension
bridges; the arch may
be trussed or solid. The
trusses which comprise
the arch varies in
configuration, but
commonly use Pratt or
Warren webbing.
37

 Masonry
bridges,
constructed in
stone and
concrete, may
have open or
closed
spandrels.
 A closed
spandrel is
usually filled
with rubble and
faced with
dressed stone
or concrete.
 Occasionally,
reinforced
concrete is
used in building
pony arch
types.
38

 An arch bridge is composed of abutments on each end and a
curved structure which provides a high resistance to bending forces.
 The Arch bridge is economical compared to equivalent straight
simply supported Girder or Truss bridge as arch action reduces
bending moments.
 Conventional curved arch rib has high Fabrication and Erection
costs
 Erection easiest for Cantilever Arch and most difficult for Tied Arch
 Classic arch form tends to favor Concrete as a construction material
 Near the crown of the arch and the region where Spandrel Columns
are short, undesirable bending moment can occur. By using Pin
ended columns it can be avoided
 Curved shaped is always very pleasing and arch is the most
successful and beautiful structure
 Spans can be longer than beam or truss in an ach bridge.
39

 Composed of
connected
elements (typically
straight)
 Oldest types of
modern bridges.
 Efficient use of
materials
 If designed and
built well, no
horizontal resultant
forces!
 The primary
member forces are
axial loads
41

 The basic identifying
features are the diagonal
web members angle
toward the center and
bottom of bridge forming
V-shape.
 The center section
commonly has crossing
diagonal members.
Additional counter braces
may be used of a smaller
size, to form an X shape on
panels toward the center.
 A "camelback" Pratt truss
creates a lighter structure
with less dead load at the
ends and more strength
concentrated in the center.
 Baltimore is a Pratt truss with
additional members
branching off of the
diagonals for strength.
 Parker is a modified the
Pratt that uses fewer
materials to get the similar
load capacity. The
downside is complexity.
43

 The Whipple truss was
developed as stronger
version of the Pratt truss and
gained popularity with the
railroads while few were
built for highways
 It was also known as the
"Double-intersection Pratt"
because the diagonal
tension members cross two
vertical members before
reaching the bottom chord,
those on the Pratt cross one.
 The Whipple truss was most
commonly used in the
trapezoidal form, straight top
and bottom chords
although bowstring Whipple
trusses were also built.
 Further developments of the
subdivided variations of the
Pratt, led to the decline of
the Whipple truss.
44

 A Warren truss can be
identified by the
presence of
equilateral or
isoceles triangles
formed by Alternating
diagonal members
forming a repeating V
shape.
 A true Warren does
not have vertical
members.
 Double-Intersection
Warren, looks like two
Warren trusses offset
and superimposed on
each other, forming a
repeating X shape.
 Warren truss may also
be found in covered
bridge designs.
45

 Howe truss appears similar to a
Pratt truss, but the Howe diagonal
web members are inclined toward
the center of the span to form A-
shapes. The vertical members are
in tension while the diagonal
members are in compression,
exactly opposite of a Pratt.
 The lenticular truss (Pauli truss)
named because of the lens shape,
forming an oval or eye-like shape.
Its opposing arches combine the
benefits of a suspension bridge and
an arch bridge. Some of its strength
is expressed in its flexibility.
 The Wichert truss was developed as
forces on spans in lenticular truss
were difficult to calculate. In
Wichert by introducing hinged over
intermediate piers, each span
could be calculated
independently.
 The Bollman & Frank truss were
common in Railroads bridges.
46

 The Warren truss is perhaps the most common truss for both
simple and continuous trusses.
 For smaller spans, no vertical members are used lending
the structure a simple look.
 For longer spans vertical members are added providing
extra strength. Warren trusses are typically used in spans of
between 50-100m.
 The Pratt truss is identified by its diagonal members which,
except for the very end ones, all slant down and in toward
the center of the span. Except for those diagonal members
near the center, all the diagonal members are subject to
tension forces only while the shorter vertical members
handle the compressive forces. This allows for thinner
diagonal members resulting in a more economic design.
 The Howe truss is the opposite of the Pratt truss. The
diagonal members face in the opposite direction and
handle compressive forces. This makes it very uneconomic
design for steel bridges and its use is rarely seen.
47

 The open web system permits the use of a greater overall depth than for an
equivalent solid web girder, hence reduced deflections and rigid structure
which lead to Economy in material and a reduced dead weight.
 The truss due to its high maintenance and fabrication costs have been used
recently less as stand alone bridge and more as stiffening structure especially
for the suspension bridges due to its acceptable aerodynamic behavior since
the wind gusts can pass through the truss which is not the case with girder or
arch bridges.
 In large span structures poor aesthetic appearance of the truss bridge is
compensated with the large scale of the structure. For moderate spans its best
to provide a simple and regular structure.
 The small size of individual parts of a truss makes it the ideal bridge for places
where large parts or sections cannot be shipped or where large cranes and
heavy equipment cannot be used during erection.
 Because the truss is a hollow skeletal structure, the roadway may pass over or
even through the structure, however, allowing for clearance below the bridge
is often not possible compared to other bridge types.
48

 The beam carry load in
Shear and Flexural
bending, If designed and
built well, no horizontal
resultant forces
 Decks and girder usually
act together to support
the entire load in
highway bridges
 When the load pushes
down on the beam the
top edge is compressed,
while the bottom of the
beam is stretched or is
put under tension.
 The beam bridge must
be strong enough so that
it doesn't bend under its
own weight and the
added weight of the
traffic crossing it.
50

 Simple deck
beam bridges
are usually
metal or
reinforced
concrete.
 The end section
of the two deck
configuration
shows the
cross-bracing
commonly used
between
beams.
 The pony end
section shows
knee braces
which prevent
deflection
where the
girders and
deck meet.
51

 A beam bridge is basically a rigid horizontal
structure that rest on two supports. It is the most
constructed and most basic bridge type, but
may be heavier than other bridge designs.
 Usually used for Short and Medium spans rarely
exceeding 250 feet. This is why a truss bridge is a
variation of the simple beam bridge.
 The two most common girders are I-beam girders
and box-girders (used both in steel and
concrete). Other girder shapes are available.
52

 Pre-stressed I-Girder bridges are used for spans up to 90
feet. Their use in this range is economic to build.
 Pre-stressed Concrete bulb Tees are efficient and
economical for a span range of 60 ft. to 180 ft.
 Pre-stressed double Tee bridges can be used for spans
up to 50 feet. Their use in this range is economic to
build.
 Pre-stressed box girder bridges may be used for spans
up to 80 feet in length.
 Since the introduction of the pre-stressed I-Girder and
the Pre-stressed Double Tee Girder, the Pre-stressed box
Girder is used only for widening of existing Box girder
bridges or for the construction of Pedestrian Overpasses.
53

 Plate Girder bridges are built similar to the pre-stressed slab
on girder bridges
 Plate Girder have some advantages over the pre-stressed
girders such as
› The span length is not as limited as the pre-stressed girders (130 ft
hauling)
› Curved plate girder bridges can be built with tighter radius.
› Can give better clearance for longer spans (lesser depth).
 Draw backs are;
› Maintenance
› Can be more expensive than pre-stressed girders
54

 Welded plate girder members can be used for spans up
to 250 feet in length when the girder depth is constant.
Span can extend to 450 feet when using variable depth.
 Hot rolled wide flange beam bridges are used for spans
up to 70 feet in length.
 Since the introduction of the more economic pre-
stressed I-Girder, the hot rolled wide flange girder has
been used primarily for widening of existing structures.
 Welded box shaped plate girders are not in common
use due to labor cost of welding and the more
economical use of the I shaped welded plate girder.
 The use of the box shaped member is limited to
situations where vertical clearance for traffic
underneath the structure is not available for the I
shaped member.
55

 Haunches at the
supported ends
are added to
increase girder's
load capacity
while minimizing its
web depth.
 The rigid frame has
superstructure and
substructure which
are integrated as a
single piece with
components
riveted.
 Orthotropic beams
are modular
shapes which resist
stress in multiple
directions. They
vary in cross-
section and may
be open or closed
shapes.
57

 Similar to continues span bridges, this type of
superstructure need unyielding foundation materials
such as good rock otherwise differential settlement may
cause harmful effects on the safety of the structure.
 This is why in ordinary soil; this type of bridge is not
suitable.
 Slab and girder type portal frame superstructure may
be found useful for spans between 20.0 to 40.0 meters.
 However, the span of solid slab portal frame
superstructure should not generally exceed 25.0 meters.
 Portal frame structures are ideally suitable for over
bridges and underpasses.
58

 In a standard girder bridge type, the girder and the piers are separate
structures. However, a rigid frame bridge is one in which the piers and
girder are one solid structure.
 Though there are many possible shapes, the styles used almost
exclusively these days are the pi-shaped frame, the batter post
frame, and the V shaped frame.
 The batter post rigid frame bridge is particularly well suited for river
and valley crossings because piers , tilted at an angle, can straddle
the crossing more effectively without requiring the construction of
foundations in the middle of the river or piers in deep parts of a valley.
 V shaped frames make effective use of foundations. Each V-shaped
pier provides two supports to the girder, reducing the number of
foundations and creating a less cluttered profile.
 Pi shaped rigid frame structures are used frequently as piers and
supports for inner city highways. The frame supports the raised
highway and at the same time allows traffic to run directly under the
bridge.
59

 Cantilever bridges are
constructed using
trusses, beams, or
girders.
 They may include a
suspended span
which hangs between
the ends of cantilever
arms.
 The classic cantilever
design is the through
truss which extends
above the deck.
Some have trusses
which extend both
above and below.
 Some bridges which
appear to be arch
type are, in fact,
cantilever truss.
identified by the
diagonal braces used
in the open spandrel.
61

 Major element is a
flexible cable,
shaped and
supported in such a
way that it transfers
the loads to the
towers and
anchorage
(abutments)
 A suspension
bridge must
withstand forces of
tension on its
cables and large
amounts of
compression on its
towers. Cables can
be up to three feet
in diameter!
 Highly susceptible
to winds and
swaying, thus the
bridge must be
stabilized!
63

 The longest
bridges in the
world are
suspension
bridges or their
cousins, the
cable-stayed
bridge.
 The deck is hung
from suspenders
of wire rope, eye
bars or other
materials.
 Materials for the
other parts also
vary: piers may
be steel or
concrete; the
deck may be
made of girders
or trussed. A tied
arch resists
spreading (drift)
at its bearings by
using the deck as
a tie piece.
64

 The cables are commonly constructed from High Strength wires, either
spun at site or formed from component, spirally formed wire ropes. In
either case allowable stresses are of the order of 600 MPA.
 The main cables are stiffened either by a pair of stiffening trusses (a
deck truss) or by a system of girders at deck level. This stiffening system
serves to
 Control aerodynamic movements and
 Reduce the tendency of the roadway / deck to sway and ripple.
 The economy of the cable must be balanced against the cost of the
associated anchorage and towers. The anchorage cost may be high
where foundation material is poor.
 The complete structure can be erected without intermediate staging
from the ground
 The main structure is elegant and neatly expresses its function.
 It is the only alternative for spans over 600m, and it is generally regarded
as competitive for spans down to 300m. However, shorter spans have
also been built.
 The height of the main towers can be a disadvantage in some areas; for
example, within the approach road for an AIRPORT.
65

 All the forces are
transferred from the
deck to the Pylon in
cable-stayed
bridges.
 Many cables
arrangements two
shown; Fan & Harp.
 Cables and (box)
girders are the
primary force
resisting elements
 Cables resist forces
through tension.
 Girders resist forces
through bending
67

 A typical cable stayed bridge is a continuous girder with one or
more towers erected above piers in the middle of the span.
 From these towers, cables stretch down diagonally (usually to both
sides) and support the girder.
 Steel cables are extremely strong but very flexible. Cables are very
economical as they allow a slender and lighter structure which is
still able to span great distances.
 For longer span cable-stayed bridges, careful studies must be
made to guarantee the stability of the cables and the bridge in the
wind.
 The lighter weight of the bridge, though a disadvantage in a heavy
wind, is an advantage during an earthquake.
 The modern yet simple appearance of the cable-stayed bridge
makes it an attractive and distinct landmark.
 Towers can be single, double, portal, with various shapes like A, H ,
and Diamond.
 Cable arrangements also vary. Some typical varieties are mono,
harp, fan, and star arrangements.
 In some cases, only the cables on one side of the tower are
attached to the girder, the other side being anchored to a
foundation or other counterweight.
68

 Less costly than suspension, can be quickly constructed. There is a great
freedom of choice in selecting the structural arrangement
 The use of high strength cables in tension leads to economy in material,
weight, and cost.
 As compared with the stiffened suspension bridge, the cables are straight
rather than curved. As a result, the stiffness is greater.
 The cables are anchored to the deck and cause compressive forces in the
deck. For economical design, the deck must participate in carrying these
forces.
 Individual cables are normally constructed of individual wire ropes, supplied
complete with end fittings, pre-stretched and not spun.
 Less efficient under Dead Load but more efficient in support Live Load. It is
economical over 100-350m.
 Aerodynamic stability has not been found to be a problem in structures
erected to date
 When the cables are arranged in the single plane, at the longitudinal center
line of the deck, the appearance of the structure is simplified and avoids
cable intersections when the bridge is viewed obliquely.
 The mono-tower is the slimmest form of tower possible and it has the most
favorable aesthetics.
 Diamond Tower is the most complex and slowest in construction.
69

Bridge Structure Component Approximate
Cost Of total
Cost
Foundations 30%
Concrete Towers & Piers including anchorage 10-15%
Deck Steelwork / Concrete 30 - 40%
Stay Cables 5 - 10%
70

Mono
Tower
H
Shape
Diamond
Shape
A Frame
TOWER COST LOW HIGH HIGH HIGH
FOUNDATION COST LOW HIGH MEDUIM HIGH
Duration of Tower
Construction
Shortest Short Longest -
Critical
Longest –
Non Critical
Deck TYPE ANY BOX
GIRDER
ONLY
ANY ANY
71

Functional Cross Section Deck Type Maintenance Aesthetics
Two Corridor
(Mono Tower)
Box Girder
(Single / Twin)
MED - LOW GOOD
Vented Ladder Beam
(Box Beams, Plate
Girder)
Composite Plate
Girder
HIGH POOR
Single Corridor
( H, Diamond, A Frame)
Box Girder (Single) MED - LOW GOOD
Ladder Beam
Composite Plate
Girder
HIGH POOR
72

 Central span turned 90 degrees on pivot pier
placed in middle of waterway
 Double swing possible
74

 Central span extends between two towers
 Balanced by counterweights
75

 One or two sections not supported by piers
 Balanced on one end by counterweights
 Section jackknifes up to allow passage of
ships
 Most common type of highway drawbridge
76

 Functional Cross Section – What the bridge is
required to carry and how that will be arranged on
the deck in terms of location of traffic lanes etc.
 Deck Type – The construction material and structural
arrangement of the deck.
 Tower Form – The appearance of the towers which
will be the major aesthetic feature of the bridge.
 Approach Bridge Type – The construction material
and structural arrangement of the approach bridge.
 Foundation Type – The construction form of the
foundations.
 Bridge Efficiency= Load Supported / Bridge Weight
78

BridgeSurvey
flood plain cross
sections
inspection
reports
existing bridge
(scour, etc)
water elevations
existing roadway
profile
GeotechnicalReport
soil / geological
formations
slopes and
grading
foundation
problems
soil properties
ChoiceofSuperstructure
location, city or
rural
span length
vertical
clearance
maintainability
environmental
concerns
transportation to
site issues
cost
ChoiceofSubstructure
location and
geometry
subsoil
conditions
height of column
79

1. A plan of the site showing all obstacles to be bridged such as rivers, streets,
roads or railroads, the contour lines of valleys and the desired alignment of
the new traffic route.
2. Longitudinal section of the ground along the axis of the planned bridge with
the conditions for clearances or required flood widths, desired vertical
alignment of the new route, etc.
3. Required width of the bridge, width of lanes, median, walkways, safety rails.
4. Soil conditions for foundations, results of borings with a report on the
geological situation and soil mechanics data.
5. Local accessibility conditions for the transport of equipment, materials and
structural elements. Which materials are available and economical . Is
water or electric power available. Can a high technology be used , etc?
6. Weather and environmental conditions, floods, high and low tide levels,
periods of drought, range of temperatures, and length of frost periods.
7. Topography of the environment - The scale of the environment has an
influence on the design. Like open land, flat or mountainous land, country
scenic - town with small old houses or city with high rise buildings.
8. Aesthetic quality. Bridges in Cities affect the urban environment and are
frequently seen at close range, thus more delicate shaping is needed.
9. Safety. Is protection of pedestrians against spray and noise needed? Is
noise protection necessary for houses close to the bridge?
10. Effects on adjacent structures like dwelling, water table, vibration effects,
etc.
80

 The phase of conceptual and aesthetic design needs
comparatively small amount of time, but its decisive for the
expressive quality of the work.
 Before design begin, the architect should start from sketching
the probable road direction, beam shape , approximate depth ,
the piers and abutments.
 The sketch is then analyzed critically for the span proportions,
the clearance under the beam, the curvature of the vertical
alignment, etc.
 Also analysis is made for the number of piers and adaptive-ness
of the piers and abutments to the surroundings / soil conditions.
 Preliminary design data allows the preliminary designer to
determine the appropriate structure that will meet the needs of
the project while producing a cost efficient design. This process
is very much complete once a Layout is assembled.
 More accurate data at the outset of the preliminary design
results in better overall quality and cost efficiency of the design.
Different types of bridges allow different solutions.
81

Preliminary Design Process
Bridge Survey
Geotechnical Report
Hydraulic Analysis
Most economical type of structure
and span arrangement
Foundation Borings
Foundation Type
Preliminary Cost Estimate
Final Design Process
Top Bottom Design Approach
Design methods per AASHTO
Computer Aided Analysis
Detail plans (Micro-Station)
Plans are checked
Quantities computed
Special Provisions written
Plans are advertised for bidding
The objective is to Foster collaboration in process design from
clients and master planners to architects and structural engineers.
82

 For any bridge, selection of the type of requires careful
examinations of all the factors governing economy, safety,
durability, time of erection, availability of materials and
equipment and maintenance cost.
 As a rule, economy demands that the number of spans
should be as small as possible for bridges where difficult
conditions are anticipated in the construction of the
foundations.
 Provision of lesser number of piers in the rivers, improves
the flow of water, but longer span mean greater cost per
unit length of the superstructure.
 It is, therefore, important to compare the cost of both the
superstructure and the substructure including the
foundation so that the one which is economical and at the
same time satisfy other requirements is adopted.
85

 Where foundation can be supported on good rock or
where foundation soil is such that differential settlement
of supports can be eliminated, continuous span
superstructure is an idea solution.
 In such cases, due to continuity, both the span and
support design moments are reduced compared to a
simply supported superstructure.
 Span ranges between;
› 10.0 to 20.0 meters continues solid slab bridges
› 20.0 to 40.0 meters for slab & girder bridges .
› up to 100 meters for hollow-box continues structure
86

 Beam (girder) bridges are the most basic type of a bridge
typically inexpensive to build and can be simply supported, over hung
(cantilever), multi span (continuous).
 The truss creates a more rigid structure compared to a beam bridge
and can more effectively distributes the load across the span.
 Girder (RC T-beam), arch and truss bridges are constructed for
medium to moderately large spans where solid slab bridges
are found uneconomical.
 Choice of girder and truss bridges may be justified compared
to cable-stayed bridges and suspension bridges where
› Deep foundations are required from scour and soil strata
considerations
› and navigation clearance or free-board is comparatively less
› Also in narrow valley’s where good rock is available on both the
banks.
 Arch bridges are unsuitable at locations where abutment
foundations are susceptible to large movements both
downwards and sideways.
87

 Cable-stayed bridges and suspension bridges are
constructed for large and extra large spans especially where
large clearance or free-board is required above H.F.L. or
H.T.L. for the passage of large vessels.
 Also these bridges are favored where the channels are deep,
where construction of superstructure by staging or false-work
is not possible.
 Remember - forces are transferred from the deck to the Pylon
in cable-stayed bridges and to the abutments in suspension
bridges.
 In cable-stayed & suspension bridges; roadway deck can be;
› (Pre-stressed) concrete box deck
› Steel Box Deck
› Steel Truss Deck
88

The selection of the type of bridge depends
on;
 Traffic Studies
 Site Geometry
 Geotechnical – Subsurface Studies
 Hydro-Technical Studies
 Environmental Considerations
 Functional Requirements
 Aesthetics
 Frequency & Ease of Maintenance
 Construction and Erection Consideration
 Legal Considerations
 Economic Feasibility – Iterative Process
THEN - Bridge Selection and Design BEGINS
90

 Traffic studies are needed to determine
Economic Feasibility of the Bridge
 Traffic Studies provide;
› Traffic forecast on Bridge immediately after opening
› Traffic forecast at various times during life of the Bridge
› Traffic Mix i.e. number of motorcars, buses, heavy trucks
and other vehicles
› Effect of the new link on existing road network
› Predominant Origin and Destination traffic that will use the
Bridge
› Strategic importance of the new/improved Bridge
 Such Studies are done with help of Traffic
Software such as TransCAD, EMME2 etc.
91

 Bridge type depends on bridge length and the horizontal
and vertical alignment of the highway route and on the
clearances above and below the roadway. Illustrations;
 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, on the other hand , Precast
I-Girder cannot be curved while Segmental pre-stressed can
have slight curve.
 Relatively high bridges with larger spans over navigable
waterways require a different bridge type than one with
medium spans crossing a flood plain
 The site geometry dictates how traffic can be handled during
construction, which is an important safety issue and must be
considered early in the planning stage!
92

 Geotechnical studies provide;
› The types of Rocks, Dips, Faults and Fissures
› Subsoil Ground Water Level, Quality, Artesian Conditions, if any.
› Location and extent of soft layers including their physical properties.
› Identification of hard bearing strata
› The potential for seismic activity
 Examples that can influence the choice of substructure
components which in turn influence the choice of superstructure
› The foundation soils at site determines whether abutments and piers
can be founded on spread footings, driven piles, or drilled shafts. For
Example, An inclined leg frame bridge requires strong foundation
material that can resist both horizontal and vertical thrust.
› If the subsurface investigation indicates that creep settlement is going
to be a problem, the bridge type selected must be one that can
accommodate differential settlement.
› Drainage conditions on the surface and below ground must be
understood because they influence the magnitude of earth pressures,
movement of embankments, and stability of cuts or fills.
93

 Channel characteristics;
 Bed materials,
 Depth of water during dry seasons or flood
season,
 Water velocity
 Tidal variation,
 Scour depth – sediments removal depth
 Design discharge etc.
 Frequency and duration of flood.
 Navigation requirements
94

 Impact on Following Features of Environment need
to considered:
› River Ecology which includes:
 Marine Life
 Wildlife along river banks
 Riverbed
 Flora and fauna along river banks
› Impact upon dwellings along the river if any
› Impact upon urban environment if the bridge in
an urban area
› Possible impact upon archeological sites in
vicinity
95

 Bridge must function to carry present and future volumes of
traffic.
 Decisions should be made on the number of lanes of traffic,
inclusion of sidewalks and/or bike paths, whether width of the
bridge deck should include medians, drainage of the surface
waters, snow removal, etc.
 In the case of stream and flood plain crossings, the bridge
must continue to function during periods of high water and
not impose a constriction or obstruction to the flow.
 Requirement for preserving shipping channels leads to long
span bridge
 If future widening and replacement of bridge decks is a
concern, multiple girder bridge types are preferred over
concrete segmental box girders.
 Satisfaction of functional requirements leads to a selection of
a bridge type over other types.
96

 Well-designed bridges should handle traffic efficiently and safely
while fitting nicely into their surroundings with smooth transition
among its members without unnecessary decorations.
 An ugly bridge, however safe, serviceable, and inexpensive, is
not a good bridge.
 Bridges typically do not have architects; Structural Engineers are
responsible for aesthetics!
 The Structural system is always exposed (both good and bad).
 The Bridge should have an appearance of adequate strength!!!
 Bridges are owned by the public , thus focus is primarily on
lowest initial cost, with aesthetics playing a minor role. Thus
minimum cost and aesthetics can be competing objectives.
 Trade-offs are often made on functionality, aesthetics ,cost and
other factors.
97

In order of importance;
 Vertical and horizontal geometry relative to
surrounding topography and other structures
 Superstructure type; arch, girder, etc…
 Pier placement
 Abutment placement
 Superstructure shape, parapet and railing
 Pier shape
 Color, surface, texture, ornamentations
 Signing, lighting, landscaping.
98

 The initial cost and maintenance cost over the life of the
bridge govern when comparing the economics of different
bridge types.
 A general rule , the bridge with the minimum number of
spans, fewest deck joints, and widest spacing of girders will
be the most economical.
 Example (1) - By reducing the number of spans in a bridge
layout by one span, the construction cost of one pier is
eliminated.
 Example (2) - Deck joints are a high maintenance cost item,
so minimizing their number will reduce the life cycle cost of
the bridge.
 Generally, concrete structures require less maintenance
compared to steel structures. The cost and hazard of
maintenance & painting of steel structures should be
considered!
99

 The time required to construct a bridge is important and varies with
the bridge type. Bridge construction-ability is another issue!
 Generally, the larger prefabricated or pre-cast members, the shorter
the construction time, thus in urban areas pre-fabricated precast
members can be the only choice.
 The larger the superstructure members, the more difficult they are to
transport and lift into place , however, as substructure construction
disrupt traffic more than the superstructure erection, longer spans
are preferred!
 In urban areas The availability of skilled labor and specified
materials also influence the choice of a particular bridge type.
 Questions to be asked;
› Is shipping channel required to shipping prefabricated pieces to site?
› Is the temporary false work required? Can it be done at site?
A GOOD WAY TO DETERMINE WHICH BRIDGE TYPE IS MORE
ECONOMICAL IS TO BID FOR ALTERNATIVE DESIGNS!!!!
100

 A segmental bridge consists of “small” Pieces stressed
together by external tendons.
 Segmental construction technique is gaining popularity;
 Where local terrain and/or traffic prohibit the erection of
conventional false work.
 Segmental construction facilitates construction of longer span
bridges, reduces intermediate piers and thus obstruction to water
flow or traffic.
 Segmental pieces may be easier to ship in narrow urban streets
 Segmental Bridge Construction can be accomplished by
either
› Cantilever Construction – Constructed from one pier equally on
both sides so that the weight is counter balanced. Usually
requires large section at the support to resist negative moments.
› Span-by-span construction – finish one span at a time
101

Regulations are beyond the control of an
engineer, but they are real and must be
considered especially in Design- Build projects.
Examples of certain regulations are as follows:
 Permits Over Navigable Waterways
 National Environmental polices.
 Historic preservation polices.
 Clean Air polices.
 Noise Control polices.
 Fish and Wildlife polices.
 Endangered Species polices.
105

 Aesthetic qualities of design are intangible, perceived qualities
arising from the relationship of design elements.
 The properties of aesthetic qualities are proportion, rhythm, order,
harmony, balance, contrast, scale and unity.
 The primary aesthetic goal is to achieve a slander superstructure
while maintaining continuity and proportion.
 An attractive bridge in appearance should not necessarily cost more
than a less presentable bridge, thus, aesthetic considerations should
be integrated early in the planning stage of a bridge design.
 A proper method of construction should have a balance between
aesthetic consideration and ease of construction, disturbance to
traffic flow or to the environment.
 Maintenance should be properly considered and planned so it does
not impact the appearance of the bridge.
 Corners, joints, edges and other minor items contribute a great deal
to the overall appearance and, if done badly, can create an eyesore.

 A bridge should be built to complement and exist in harmony with
its surroundings.
 Architectural should establish aesthetic and visual compatibility
with the highway corridor.
 Aesthetics of the bridge should identify with aspects of architectural
history, environmental, topographical, structural, geological,
geometrical, social, cultural and archeological.
 The bridge primary & secondary members should be shaped to
support its loads in the most appealing manner so that the emphasis
on the structural efficiency shall not be at the expense of its visual
appearance.
 The approach road alignment to a major bridge can be slightly
curved to create awareness to the bridge users upon approaching
the structure and enable them to appreciate the aesthetic qualities
of the structure.

 The natural landscaping in the area should be
maintained. The same species of trees or
shrubs should be planted around the bridge.
 The vegetation at both ends of the bridge
should be in visual balance.
 A proper landscaping can reduce the visual
mass of large and plain abutment or wall.
 The type of plant that can grow to obscure the
essential elements of the structural form or
function should be avoided.

 The horizontal alignment of a long and sloping bridge
should be done with a smooth and elegant curve.
 Horizontal alignment should not have irregular curves
as it interrupts the flow of the structure, disturbing its
order and harmony.
 Vertical profile of a bridge should coincide with the
approach road gradient.
 Road vertical profile should preferably have a crest at
the center of the bridge to create an impression of
efficiency and safety.
 A vertical curve on a bridge allows users to feel the
sensation of entering and leaving the bridge.

 Generally a long span bridge with the smallest possible girder depth is
preferable to a short multiple span bridge, However, if a multiple span
bridge is avoidable, it should be designed for balance, visual continuity and
harmony.
 Also a continuous girder design enables shallower depths and avoids
numerous expansion joints.
 In box girder structures, the apparent depth of the superstructure can be
reduced by:-
› Using narrow main beam, large cantilever and shallow parapet height
› Slanting the girder fascia to vary the relative brightness of the surface.
 In cable-stayed Bridges, to produce aesthetically appealing bridges, the
cables pattern should have clarity and unity:-
› For best clarity, use single plane cables.
› For two or more planes, adopt the harp configuration so that all cables on one side
of the tower are parallel from the oblique view where cable crossings are avoided.
 In cable-stayed Bridges, the deck fascia should run undisturbed through the
outside of the cable anchors. The cable anchors should not be attached to the
outside of the beam and interrupt the visual line flows of the deck fascia.
 Anchorages in bridges should express their function of transferring loads
and not to appear dominant or made invisible.

 Piers should be of sufficient size to perform their function. Too slander a pier
gives an impression of instability whereas a short or large pier is unsightly.
 Multiple piers stacking should be in visual continuity when viewed from the
oblique angle.
 The pier shape should be integrated with the form and shape of
superstructure.
 Piers should not be the visual focal point of a bridge composition. However,
they could be considered as a focal point for aesthetics.
 Piers that appear larger than necessary are undesirable because attention is
directed away from the superstructure.
 A pylon tower should be seen rising from the ground or water to the top as a
single element, unless the bridge is an opening type, which can be visually
broken at the pivot point.
 Aesthetic treatment to the top of the pylon should be given careful
consideration as it is a prominent feature.

 The top of a retaining wall should be developed into a
graceful profile.
 Abrupt termination to the retaining wall should be
avoided.
 Weep holes and drainage system should be designed to
filter, collect and drain water away from the exposed
face of the retaining as they may cause staining.
 Where a retaining wall and sloped grade are combined
to provide a grade separation, the wall should be placed
at the top of the slope. This could provide more open
space at the roadway level.

 A design features is considered architectural when it influences appearance
without structural necessity.
 The best use of architectural features incorporate structural requirements
in the solution, thereby combining both structural and architectural
considerations to enhance the overall solution.
 Architectural features, adornments should not be superfluous and
unnecessary as they can appear odd and out of place.
 Architectural should be sensibly applied to disguise unsightly component
such as cable anchorage and discontinuity.
 Art features should be considered from the start as an integral part of the
design and not as an afterthought.
 Structures and sculptures can be incorporated at the bridge ends to signify
its entry and exit points.
 Sculptures and decorations enhancing a bridge should not cause
maintenance problems.

 A deck cantilever can maximize the shadows
cast on the fascia girder, thus reducing the
apparent depth of the girder and the
harshness of a bright fascia.
 The relative brightness of bridge surface could
be varied by changing its inclination to catch
more or less light.
 Appropriate detailing to pier shapes and
textures to create shadows can enhance their
slenderness.

Bridge accessories can impair the visual appearance of a bridge.
Attention should be given to the placement, size and detail of the
fixtures to enhance the overall appearance.
 Signage
› Signage should be placed off the bridge whenever possible.
› Signage be attached to bridges should not extend beyond the bridge
structure and they should be consistent height.
› Internally lit signage should be used where elimination of the external
light sources is beneficial.
 Lightings
› Lights can be mounted under the structure or on top.
› When locating lights, the designer should recognize the inherent
symmetries, logical or consistent relationship to the structure or other
major characteristics of the overall structure.
› Floodlights can be utilized to accentuate the forms of the structure, e.g.
the tower pylons of a suspension bridge.
› The basic form of a bridge can be portrayed by outlining features with
illumination or light to create a profile, eg. Stringing lights along the
cables of a suspension bridge.

 Bridge features could be emphasized or diminished by colors. Light colors
tend to emphasize while dark colors diminish the features.
 Full hued colors are not harmonious with the naturally occurring
environment; therefore the use of these colors should be limited to built-up
settings.
 Bright and intense colors should be used with discretion.
 The color of fixtures such as signage ’ s, railings and posts should
complement each other and blend with the structure.
 The color of the drainage pipes and conduits should be the same as the
structure element on which they are mounted.
 The color on the fascia girder should be of a darker shade than on the
parapet. The darker color will tend to make the fascia girder less dominant
than its brighter counterpart.
 Concrete dye can be used to improve the appearance of structures. The color
could also hide tarnished surfaces as well as seal and protect the concrete.

 The designer should recognize and plan for the
pattern created by the construction joints, tie
holes and weep holes.
 The appearance of a solid wall parapet could be
enhanced by creating patterns and texture to its
surface.
 Distance and driving speed alter the viewer’s
perception of surface patterns and textures.
Hence, large pattern elements should be used for
higher speed traffic. Finer and more complicated
elements should be adopted for slow-moving
zones.

 Free-fall drainage system outlets should be concealed and their
placement should not cause staining to the bridge.
 Drainage pipes should be placed on the least visible side of piers in a
configuration that is consistent with the pier shape.
 Pipe and conduit systems should be kept simple with minimal
fittings.
 Conduits and pipes also should be concealed. Installation should
only take place in locations such special grooves or in-between
beams.
 Placement of the systems on the outside of the fascia girder or along
the barrier system should be avoided.
 Drip grooves should be provided on the underside of the bridge to
avoid staining and should be deep, wide and continuous for effective
flow.

Time
CostsStreamBenefitsStream
Construction
Stage
100 years Project Life
ProjectStart
Date
ProjectLife
EndDate
Salvage
Value
121
Periodic
Maintenance
30–40Years
Major
Rehabilitation

 Economic Analysis is Required at Feasibility Stage to justify expenditure
of public or private funds. A Bridge is the most expensive part of a road
transportation network.
 Analysis should compares competing alternatives like other bridge type,
other modes of transport. Time spans may vary!
 Estimate the Monetized & Non-Monetized Benefits that will accrue from
the Project including time savings to road users, benefits to business
activities (and to the economy in general) and salvage value benefits
like Right-of-Way and substructure use, if applicable
 Estimate the costs associated with the Project during Construction and its
service life. These include all significant costs like construction costs +
users costs for using the bridge + routine maintenance costs + major
Rehab Costs + salvage costs for removal
 Bring down the costs and benefits to a common reference point in time
i.e. just prior to start of project (present worth) by discounting costs (spent
money) & benefits (collected or earned money) using appropriate
“DISCOUNT RATE”.
122

Monetized Benefits
 Time savings to road users
 Growth in Target Area economic activity
 Saving of Vehicular wear and tear
 Reduction of accidents if applicable
Other Non-Monetized Benefits
 Strategic Benefits – General Growth in
Country economic activity
123

 Annual Maintenance cost associated with the upkeep of the structure varies
on the basis of size of the structure. Best Guess Annual Values
› Concrete, 0.03 % of Initial Cost
› Structural Steel, 0.05 % of Initial Cost
 Inspection Cost varies on the basis of size of the structure and
construction material. Best Guess Biannual Values
› Concrete, 0.15 % of Initial Cost
 Painting Costs apply to structural steel structures mostly. Best Guess
Values every 20 years
 Rehabilitation Costs frequency is a function of time , growing traffic
volume (shortens rehab cycles)and the structural system. Best Guess
Values
› Concrete, every 40 years, 20 % of Initial Cost
› Structural Steel , every 30 years, 25 % of Initial Cost
 Salvage Value and Removal Costs occurs once at end of life of
structure. Best Guess Values (GREATLY VARIES)
› Removal cost 10 % of Initial Cost
› Concrete Deck Salvage Value, 0 % of Initial Cost
› Salvage Value of Piers & Abutments, 25 % of Initial Cost
› Structural Steel Salvage Value, 5% - 15 % of Initial Cost
124

 Types of Economic Analyses;
 Benefit Cost Ratio (B/C)
(Present Value of Benefits / Present Value of Costs), > 1 , GOOD
 Net Present Value (NPV)
(Present Value of Benefits – Present Value of Costs), + . GOOD
 Internal Rate of Return (IRR)
(solve for IRR by setting Present Value of Benefits & Costs = 0.0 or
BCR = 1.0), IRR > WACC, GOOD
 Notes;
 In Benefit Cost Ratio and in NPV , the discount rate is
assumed while in IRR, the discount rate is soled for.
 WACC is defined as the Weighted Average Cost of Capital ;
i.e. the Overall Cost of Borrowing & Cost of Equity.
 IRR is a better measure of economic viability as it is an
indicator of how much inflation increase and interest rate hike
a project can tolerate and still be viable.
125

Maintenance and
Inspection
Cost
Initial Cost
Costs
Present Worth
Years
Rehabilitation Cost
Salvage
Value
Salvage
Costs
 Construction Cost Spread generally assumed over 3 Years
 Bridge life cycle today is based on a probabilistic model of 100 years
126
User, Business & General Economic Benefits

 An estimate of discount rate can be made as
(US Treasury Bond Rate + Country Risk+ Inflation Rate)
 Notes:
 Inflation Rate can be removed or kept in the discount rate
, but it should be stated.
 Discount Rate varies among countries and ranges from 6-
12% (inflation subtracted)
 Example Asian Development Bank uses a Discount rate
near 12% for projects evaluation
 Discount Rate is less than the Real (commercial) interest
rate offered by Banks / Financial Institutions as
Governments do not take a purely commercial view of
infrastructure project.
127

Traffic Assumptions
Average Annual Daily Traffic - Cars --- Cars / Day
Average Annual Daily Traffic - Trucks --- Trucks / Day
Average Annual Daily Traffic - Buses --- Buses / Day
Traffic Growth 0.5 to 1.5% Typical
Average Occupancy of Single Car 3 Passengers
Average Occupancy of Single Truck 2 Passengers
Average Occupancy of Single Bus 50 Passengers
Benefit Time Saving (Time Value of a single User) generally assumed at 10$ / Hr
but largely varies among countries – PER CAPITA INCOME BASED!
128

Cost of the bridge (C) = n*(aS+bS2)+(n-1)*P+2A+2B
Symbol Cost Item
a Cost per meter of deck slab, wearing course, railing
aS Cost of span deck slab, wearing course, railing bridge
b Cost per meter square of main girder, cross girder etc.
bS2 Cost per span of main girder, cross girder etc.
P Cost of one pier with its foundation
A Cost of abutment, wing wall etc.
B Cost of each approach
C The Total Cost of the bridge
Where;
L, length of the bridge = nS
S, Length of the clear span
n, Number of spans
129

131
Loay Ghazaleh, MBA, BSc. Civil Eng.
Advisor, Undersecretary Office
Ministry of Works, Bahrain
loay.ghz@gmail.com, +973-36711547

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