-1
unfactored
dead load
= 186 kNm
the
Proceedings
of Bridge
Engineering
2 Conference
2009
April 2009, University of Bath, Bath, UK
A CRITICAL ANALYSIS OF THE RAMA VIII BRIDGE, BANGKOK
J.S. Lee1
1
Undergraduate Student – Civil Engineering, University of Bath
Abstract: This paper presents a critical assessment of the Rama VIII Bridge, crossing the Chao Phraya River in
Bangkok. Included are sections relating to bridge aesthetics, structural design, and construction. Various design
load models are also formulated using the British Standard (BS) relating to bridge design (BS 5400). These are
used to analyse the structural performance of the bridge in regards to BS specified limit state design.
Keywords: Rama VIII, Asymmetric, Cable-Stayed, Inverted-Y Pylon, BS 5400
1 General Information
Bangkok is said to have an official population of 8
million, however due to unregistered migrant influxes’
it is estimated at 15 million. This places a huge demand
on public infrastructure and congestion is rife.
The Chao Phraya River runs through central
Bangkok separating east from west. 4 bridges existed
over the river but this was not enough causing some of
the cities worst congested areas. The Bangkok
Metropolitan Association (BMA) commissioned a 5th
bridge at what was believed to be the worst traffic
bottleneck as a measure of relief. This would become
the Rama VIII Bridge, named after the brother of the
current King of Thailand.
Feasibility studies started in 1995 but economic
reasons shelved the project until 1998. Construction
started in 1999 and the bridge opened in 2002.
Design criteria set by the BMA required the bridge
to be cable-stayed but with only 1 tower so not to
overshadow historically important structures on the
eastern bank (The Bank of Thailand and a Palace).
Rama VIII is a 475m long, asymmetric cable-stayed
bridge, supported by a 160m tall, inverted-Y pylon. The
bridge has a 300m main span and three land spans; two
50m back spans and one 75m anchor span (as seen in
Fig. 1). Rama VIII provides a low level river crossing
with a 10.4m vertical clearance. Two planes of stays
support either side of the main span, whilst one centrally
arranged plane is used to anchor the pylon. The bridge is
designed for both vehicular and pedestrian traffic, with
the main span having two traffic lanes and a 5.3m
sidewalk in each direction [1].1
2 Aesthetics
During the 20th century Engineer Fritz Leonhardt
proposed 10 rules, each relating to an area of bridge
aesthetics that he believed needed fulfilling to create
visually appealing bridges. Obviously design is
subjective and obeying these rules doesn’t ensure
beautiful bridges, but does give a good platform on
which to base an objective analysis.
1
James S. Lee – jsl21@bath.ac.uk
50m
P45
P42
Anchor Span
=75m
50m 20m
27@10m =270m
Tower
Height =161m
P41
Back Spans
=100m
P39
Main Span =300m
Figure 1: Elevation Showing General Arrangement [1]
Figure 2: Rama VIII at Night [1]
It is generally accepted that the most important
aspect of bridge aesthetics is fulfillment of function. If
this is done simply and efficiently a designer can show
how a bridge works and impart a sense of stability on
the user, creating a positive first impression.
For cable stayed bridges apparent structural
simplicity is easily portrayed, through easy to see load
paths (i.e. deck supported by the pylon through the
stays).
There is often a danger of bridges with poor
aesthetics being built as they tend to be primarily
designed in elevation. The view when travelling across a
bridge is that which is most commonly seen so it is
essential that thought is put into this view. On Rama
VIII the stays regularly span from either side of the
main deck converging upwards towards the leg of the Y
pylon. Doing this has helped impart a sense of stability
by creating a closed triangular shape which is inherently
stronger than if the stays were separated and the section
open.
Asymmetric cable-stayed bridges have to avoid
looking like they may overturn due to a heavy looking
main span. On Rama VIII carefully chosen proportions
have avoided this. The size and amount of stays
anchoring the pylon looks sufficient to be able to
provide restraint. Also the main span deck has been kept
particularly slender. The use of a thin light fascia edge
beam helps this effect.
The proportions of the slender deck do not look out
of place as the amount of stays creates deck spans that
don’t appear to have an excessive length.
The sleek and slender deck has also allowed the
pylon to be kept slender. Even though the pylon looks
slender a good structural hierarchy has been
implemented causing it to appear much stiffer and
heavier than that it is supporting. As previously
mentioned a thin fascia edge beam with a darker fascia
below helps the deck to look lightweight. The stays
have been painted gold differentiating them from the
deck and pylon plus have been given a smooth finish
aiding the slender appearance. The change of material at
the pylon to concrete with a matte finish accentuates its
strength, stiffness and ability to fulfill its function.
Other areas of the design have been refined to try
and improve the aesthetic qualities of the bridge. The
tower has a tapered cross section refining it in a way
popular with the ancient Greeks. This stops it from
looking top heavy. At the base of the Y’s legs there is a
concrete detail designed to look like an Elephant’s foot.
I like this detail as it adds interest to the structure whilst
adding a sense of resistance from overturning at the
base of the slender tower. This detail draws inspiration
from nature satisfying several of Leonhardt’s criteria at
once. The detail also reflects Thai culture which was
particularly important to the designers as previous
structures have not been well received for having a too
‘clean European’ design.
Figure 4: Elephant Foot Detail
Figure 3: Bridge shows Good Structural Hierarchy [1]
A distinct amount of effort has been placed into
keeping a good sense of order within Rama VIII. This
reduces the amount of any unnecessary lines and edges
keeping the structure as simple as possible.
Elegant clean structural lines run throughout the
bridge keeping its order. The design has been refined so
that the fascia is carried uninterrupted from the west
anchorage to the east side of the river, minimizing
optical discomfort. This is done by hiding necessary but
protruding items such as corbels and stay anchorages
with the tower or bridge deck as required.
With cable stayed bridges it can be easy to break
order often unknowingly. As mentioned bridges are
primarily designed in elevation, but when viewed from
oblique angles cables can appear to cross destroying the
order of a bridge. This can be prevented to a certain
extent and methods of doing this have been adopted.
Firstly the stays supporting the main span are arranged
in a semi-fan configuration. This is a less structurally
efficient system than the optimum fan arrangement, but
the aesthetic benefits, particularly with respect to order
justify this. The design refinement of having an
inverted-Y tower where the pairs of stays converge and
meet at single point also helps with views from oblique
angles. On the anchor span there is only one plane of
cables so this problem is avoided.
Refinement has also been attempted through the
addition of the audacious Lotus inspired observation
tower and ornamental access piers (as seen in Fig. 3).
These items may help the bridge to be received locally,
but it is my opinion that they are a bit garish.
I also believe the bridge to be poorly integrated into
its environment. Cable-stayed bridges look good over
wide spans of water so the aesthetics are added to with
this, but the tall, linear concrete pylon looks completely
out of place compared with its small surroundings. One
tower may have been required so not to overwhelm
important buildings on the east side of the river but
resulted in creating a massive structure on the west.
Colour has been used within the structure to make it
seem more ‘jewel-like’. This has been done by painting
the stays gold and adding several gilded elements to the
tower (bands around the legs and the vertical stripe on
the Y). This can be seen especially well at night when
careful lighting upwards from the bridge deck is
reflected of the gold elements, creating what I believe to
be the best view of the bridge.
Finally Leonhardt said bridges have to have both
the closely linked properties of character and
complexity. These are somewhat achieved by having the
stays arranged in a double plane on the main span and in
a single plane on the anchor span. This creates a
particularly interesting effect when crossing the bridge
and makes the user think about why this change may be
occurring.
Character is a hard quality to define. I believe that
this bridge has it but I am unsure why. Possibly it is due
to the somewhat overpowering tower however badly
integrated it may be. The tower stands alone not being
rivaled in size or stature by anything around (see Fig. 2).
A true test of character is how the building is received
by the general public. Local Appreciation has been high
with the bridge becoming a notable tourist attraction and
even being featured on a banknote.
3 Structural Description
3.1 Structural Strategy
As is the case with asymmetric bridges, Rama VIII
has a long main span which acts as if to overturn the
pylon, developing bending moments within. Traditional
symmetrical cable-stayed bridges have spans of a
similar weight creating a balance and reduction of
bending in the pylons. As Rama VIII doesn’t have this,
moments need to be reduced in another way. Below is a
description of the structural strategy implemented in the
Rama VIII Bridge. This is by no means comprehensive
but does give an idea of the force transfer involved.
The main span (and loads upon it) is supported by
stays, with a regularly spacing of 10m. Load is carried
via tension in the stays to the pylon. This direct load
path is an advantage for cable-stay bridges (over
suspension) greatly stiffening up the structure. The stays
are in a semi-fan layout on the main span causing both a
horizontal and vertical force to act upon the pylon. The
vertical force places the pylon in compression.
Closely spaced main span stays reduce bending in
the deck allowing it to be kept light and slender. This
adds flexibility to the structure which is needed to cope
with seismic loading that may occur. Tension in the
stays also places horizontal compression within the
bridge deck, increasing with each stay towards the
pylon. The deck is designed carry both bending and
axial force.
The bridge is less structurally efficient than if a
complete fan system were used. Fan systems locate all
of the stays at one maximum eccentricity, meaning
greater cable inclinations and smaller horizontal
components of force acting on the pylon and in the
deck. This reduced deck compression then allows
smaller/lighter decks to be used, in turn reducing the
size of the stays needed.
As mentioned the stays place horizontal,
longitudinal loading upon the pylon. Fully anchored
backstays appose this force. The stays are the main
stabilizing element of this structure. The backstays are
tensioned so that under deadweight bending moments
within the pylon are reduced as much as possible.
Imposed loading placed upon the main span is resisted
by tensile forces in the backstays, keeping pylon
bending to a minimum.
Torsion produced by unsymmetrical loading on
slender decks is a possible problem. The inverted-Y
pylon allows the stays to meet, increasing the bridges
structural performance. With cables spanning down to
either side of the main span a closed section is created,
increasing the torsional stiffness of the bridge.
3.2 Pylon Design Features
The pylon is the primary load bearing element of
any cable-stayed bridge, carrying compression applied
by vertical force from the stays. Rama VIII’s pylon is
built of reinforced concrete with sections of posttensioning. The use of concrete was a specified design
criterion for aesthetics but provides structural benefits.
The pylon has a rectangular cross section
throughout of sufficient size to provide the required
stiffness along the length of the tall tower.
Longitudinally the pylon has a constant width of 7m.
Along the upper section of the pylon the transverse
width tapers from 5 to 7.5m. This increase is necessary
to cope with high transverse bending demands at the
interface with the legs. The legs also taper with a width
of 5.4m at the interface down to 4m at the base. This
reduction in width minimizes the amount of bending
attracted to the base of the legs [2].
The tower legs are not tied together by the deck
causing thrust at the base. This is resolved by an 8m
wide, 1m deep beam between under each leg.
Two diaphragms are in place at the upper
section/leg interface. These tie the structure together
aiding the transfer of lateral force. This adds a great deal
of rigidity to the pylon and is especially important in the
ability of the pylon to resist wind/seismic loading.
Usually stays are anchored into the side of a pylon
facing the span in which they are placed, requiring tie
elements to transfer tension across the structure. In
Rama VIII the upper 14 of the 28 sets of stays are all
anchored into the main span wall. This is structurally
efficient as it allows forces to directly oppose each
other. Some bending is generated in the main span wall
but small amounts of post-tensioning can solve this [1].
Corbels are cast into the tower to support bearing
loads from the deck. Horizontal and vertical potbearings are placed here. The horizontal bearings allow
longitudinal movement which is important for affects
such as those due to temperature. The vertical bearings
carry transverse seismic/wind forces out of the flexible
deck into the much stiffer pylon [2].
3.3 Deck Design Features
Figure 5: Force Distribution within the Bridge
Transverse loading upon the bridge from actions
such as wind are resisted solely by bending of the pylon
about its transverse axis.
Usually backstays are anchored into the ground. A
different approach was taken on Rama VIII as they are
anchored into the ‘anchor span’. This is a purposely
heavy section of deck to stop uplift from the stays. In
turn uplift from the stays is used to support the deck.
Three different types of deck are used throughout
the structure, however the deck has still been design as
one continuous structural element.
The main span is a steel-concrete composite deck,
used for a reduction in selfweight. The deck is 29.2m
wide accommodating two lanes of traffic and a sidewalk
in each direction.
Two primary steel girders, 1.6m deep, run
longitudinally along the main span. 1.3m deep
floorbeams span between these at 5m centres creating a
steel grid [1]. Precast concrete panels (250mm deep)
span between the floor beams. The benefit to using
precast panels is the ease of installation and assured
build quality.
Composite action is achieved through cast-in-place
infill strips connecting shear studs (welded to the girder)
to the slabs via its reinforcement. The integration of
composite action has a positive affect on the design of
the bridge. Composite action allows the concrete to
participate in bending. This along with the concrete
helping to carry axial compression in the deck (from
stays), reduces the size of the steel required in the main
span.
A further size reduction of the steel was obtained
through designing the webs in accordance with BS 5400
[1]. This allows web buckling to occur, providing
account is taken of axial load shed to boundary elements
(i.e. the concrete deck). Concretes compression carrying
ability again proves a benefit.
Figure 6: Section of the Main Span Deck
The anchor span consists of a 10m wide, 9m deep
post-tensioned box spine. Ribs are placed at 5.4m
centers along the length of the span to provide the
required width to the deck. Precast concrete panels span
between the ribs and match those in the main span deck.
The uplift of the stays is resisted by the self weight
of this span along with some extra ballast. All of the
weight couldn’t be initially placed in the span as it
would have governed the pile design. To solve this,
reducing the size of the foundations, the box was filled
with concrete during main span construction allowing it
to act as a counterbalance.
The two 50m back spans are similar in construction
to the anchor span, but as no stays are anchored in this
span the central spine is only 2.5m deep.
4.1 Pylon Foundations
A group of 18, 1.5m diameter, 55m deep bored
piles are placed under each leg. The two groups are tied
together by an 8m wide, 1m deep tie-beam.
The main function of the piles is to carry the large
compressive load at the base of the tower into the
ground. Wind, seismic and asymmetric imposed loading
can cause bending to develop within the pylon in both
the longitudinal and transverse directions. The pylon
must be connected to the pile group with full moment
and shear connections to transfer these forces into the
ground. With this the pile group can resist any lateral
loads, overturning moments or uplift that may occur.
The ultimate capacity of each pile has been
calculated as 31MN [2]. As the soil is poor in end
bearing it only provides 5MN of the resistance. The
majority of resistance comes from skin friction along
the length of the piles (26MN). Skin friction resists both
downwards and upwards loading by the same degree.
Any uplift that may arise can be resisted through this.
As mentioned it is possible for both longitudinal
and transverse moments to need to be resisted by the
piles. An effort has been made to minimize these,
reducing the required pylon size. Firstly the centre of
mass of the pile groups and tower legs have been offset,
counteracting dead load moments [1]. As previously
mentioned the legs of the pylon have been tapered
reducing the moment attracted to the foundations.
Piles within soils consisting of layers of soft clays
and sands have an increased risk of settlement. This is
due to the pressure from the piles causing consolidation
in the soil. Settlement levels must be checked as
significant amounts may possibly have a catastrophic
affect on the stability of the bridge. The equivalent raft
method can used to estimate pile settlement.
4.2 Pier Foundations
The system of cable stays is constructed using 1770
MPa prestressing strands. The closest main span stays
are constructed using 11 strands increasing to 65 for the
longest backstays [3]. On each side of the pylon 28
stays (or pairs of) are anchored along its height.
Dampers are fitted on all stays to minimize
problems due to vibrational affects. Two types of
dampers are used. Standard neoprene dampers are used
for all backstays and the first 10 main span stays. On the
longer main span stays where the deck is more
susceptible to vibrational affects specially developed
shear dampers are provided.
The bridge is also supported at piers 39, 41, 42, and
45 (Fig. 1) which each have their own smaller
foundation. Each of these foundations consists of 4,
1.5m diameter piles (55m deep under P39/41, 41m deep
under P42/45).
The piers have a relatively simple engineering role
primarily being required to carry vertical loads from the
deck to the foundations. They also need to provide the
necessary torsional restraint to the deck and resist any
horizontal loads applied to it. Connections of the deck to
the piers are either fully pinned or on longitudinal
bearings so no moments are carried from the deck to the
piers. This along with any loading upon them being
significantly smaller than that of the pylon has led to the
design of much smaller foundations.
4 Foundations
5 Bearings and Expansion Joints
Rama VIII has several groups of pile foundations
along it length, the main of which are under the pylon.
Bangkok is situated upon a floodplain with underlying
strata consisting of soft clays and sands to depths of
1000m so expansive foundations are required.
Pot bearings have been used to connect the bridge
deck to the piers/pylon. Bridge bearing are used to
transfer loads and movements from the deck into the
piers (and pylon) then foundations. Primarily they allow
rotation at the joints in order for the connections to be
considered as pinned.
3.4 Cable-Stay Design Features
Varying temperatures cause a bridge to expand/
contract. This movement needs to be allowed so not to
induce large thermal stresses within the bridge deck.
Expansion joints have been placed at Piers 39 and 45 to
accommodate for any movement.
The bearings at piers 39, 41 and the pylon allow the
horizontal movement required by temperature changes.
Longitudinal fixity is achieved at pier 42 where no
horizontal movement can occur [2].
anchorages were pre-welded to the top of the girders.
For the majority of the segments a typical erection
sequence was used and repeated until the main span
(and the bridge) was complete.
However the first two girder sections were installed
differently. The first stay only provides support at the
end of the second segment so temporary falsework was
used to provide support during construction for the first
segments. Great care was taken to align these correctly.
6 Construction
The first step in the construction process was to
cast the pile foundations. This was done using the
Continuous Flight Auger (CFA) process. A hollow
stemmed auger is bored to the required depth in the
ground. Once reached, high slump concreted is pumped
through the centre of the auger, as it is withdrawn. Soil
is also removed during withdrawal. Upon withdrawal
reinforcement cages are placed into the piles aided by
the use of a vibrator. CFA piles are effective for use on
soft ground as they cause minimal ground disturbance.
Following this the pylon and piers were
constructed, none of which are situated within the
channel of the river. This saved a substantial amount of
time and money as no cofferdams were required during
construction. The reinforced concrete piers were built
using the common technique of casting within timber
formwork. It is likely that this will have been built on
site, possibly being reused for several piers.
The pylon was jump-formed. This involved
concrete being poured into formwork which got jacked
further and further up the pylon as the concrete
hardened below. The steel reinforcement and
prestressing was continuously erected and the pylon got
taller. Concrete was poured, and the formwork raised in
4m lifts. As Fig. 7 shows two sets of formwork were
used on the inclined legs. These merged into one along
the upper section of the pylon. Once the pylon was
complete there was a period of time before stays were
attached. It is this period of time that is likely to have
governed its structural design. Strong wind/seismic
forces could have induced bending within the pylon that
the stays would help resist once installed.
Next the decks were constructed, with the anchor
and back spans before the main. These are pre-cast,
post-tensioned sections which were craned into place.
As previously mentioned concrete ballast is placed
inside the anchor spans to provide a downwards force to
resist uplift from the stays. This was not originally
placed in the anchor span but pumped in gradually
during construction to counteract the weight of the main
span. If all the ballast were all in place initially it would
have governed the design of the foundations [2].
As with a large number of cable-stayed bridges,
Rama VIII’s main span was constructed using the
suspended cantilevered method. This allowed the deck
to be built progressively out from the pylon.
The main span consists of 29, 10m long girder
segments, each consisting of; 2 primary longitudinal
girders, 2 floorbeams 5m apart, and a steel sidewalk
attached to the side of each girder. These were formed
offsite and delivered by barge. The main stay
Figure 7: Jump-Formed Pylon, Girder Section Lifting
The first stage of the erection sequence was to
install and fully stress the anchor stay opposing the
stays supporting the section of main span being
installed. The stays are placed into pre-assembled
anchor bodies in the pylon and decks. Next the girder
was lifted by cranes to deck level off its delivery barge.
The section was aligned and bolted together through
splice plates.
Following this the front stays were installed, again
into pre-installed anchor points. They were initially
stressed to a level known as stage 0. If at any point
during construction the level of stress in the stays
dropped below 20kN construction was stopped as they
provided insufficient counter-balance loads [3].
Lifting pre-cast deck panels into place on top of the
floorbeams was the next step. To account for this extra
weight the stays were then stressed to an intermediate
level, stage 1. To connect the deck and girder segments
the concrete infill strips were then cast. Finally the
cables were stressed to their final level finishing the
erection sequence.
The underside of the main span is enclosed by fiber
reinforced concrete panels. These give the bridge a
clean aesthetic and create an access area for
maintenance and inspection. They also shield the steel
from the aggressive Bangkok environment. The
installation of these panels was several segments behind
that of the girder.
7 Loading
This paper analyses loads in accordance with BS
5400-2:2006. BS 5400 considers the main loads that
may act upon a bridge such as Dead, Super-Imposed
Dead, Live, Wind and Temperature then groups them
into 5 combinations (as set out later in this section).
Bridges need to be designed under both Ultimate
Limit State (ULS) and Serviceability Limit State (SLS)
conditions. The requirements for each are distinctly
different and this needs accounting for. Varying partial
safety factors γfl and γf3 as set out in BS 5400 help do
this. γfl is a partial load factor whilst γf3 accounts for
inaccuracies in the bridge analysis. Through stipulating
an elastic bridge analysis γf3= 1.10 at ULS and 1.00 at
SLS will be used throughout, whilst γfl varies with the 5
load combinations.
With Rama VIII having three decks, three different
sets of deck loading need to be analyzed. As the main
span is the only section of deck directly supported by
stays loading will be analyzed for this section alone.
7.1 Dead Load
Dead loads are those of permanent structural
elements that are unlikely to be replaced over the life of
a bridge. The weight of the main span girder (steel and
concrete) and pylon will be assessed. The weight of the
stays is neglected for the assessment.
The pylon is a reinforced concrete box with a
maximum Cross-Sectional Area (CSA) equal to 24.8m2.
Assuming this doesn’t alter and that the weight of
concrete =24kNm-3 the dead-loads can be calculated:
Pylon Dead-Load = 595 kNm-1 height
The 29.2m wide deck is constructed of girder
sections (as described in section 3.3). The main beams
have a top flange 700mm wide and 30mm thick, a
bottom flange 1300mm wide and 100mm thick and a
14mm thick web [2] giving a CSA = 0.172m2. The
transverse beams are smaller with a CSA = 0.06 m2.
With the weight of steel taken as 77kNm-3 the following
loads were calculated:
Main Beams
= 26 kNm-1 length
Transverse Beams = 22 kNm-1 length
Concrete Deck
= 138 kNm-1 length
Total Dead Load Main Span Girder Section
= 186 kNm-1 length
Dead load is constant for all load cases so we can
always take γfl= 1.15 at ULS and 1.00 at SLS. 1.15 is
used at ULS as such a large percentage of the total load
is due to concrete.
particularly heavily loaded. The design brief states that
1.3 times the loading suggested by design codes should
be used, this will be considered.
BS 5400 uses the concept of notional horizontal
lanes. Rama VIII has an approximately 8.7m wide
carriageway in each direction, corresponding to 3
notional lanes each 2.9m wide (clause 3.2.9.3.1). Two
main traffic loads (HA and HB loading) act upon
highway bridges.
HA loading is a uniformly distributed load applied
over a bridge. Clause 6.2.1 states that for bridges with a
length between 50 and 1600m that HA loading is equal
to:
1
W = 36( ) 0.1
L
= 20.35kNm-1 x 1.3
(1)
-1
= 26.5kNm length per notional lane
A Knife-Edge Load (KEL) of 120kN must also be
applied to each notional lane. This is a point load placed
at one location along the length of a lane where it will
cause the worst effect. Full HA and KEL are applied to
two of the notional lanes whilst 1/3 of the value is
applied to the rest of the lanes (placed to create the most
onerous effect).
HB loading represents an abnormal truck load on
the bridge. Clause 6.3.1 states that each truck axel
represents a 10kN point load for each unit of HB
loading, with full loading being 45 units i.e. 450kN per
axel. The inner axel spacing can be varied depending
upon what causes the worst effect as Fig. 8 shows. In
this instance it varies between 6 and 11m dependant
upon whether hogging or sagging is being considered,
6m for sagging (all in one span) and 11m for hogging
(spread equally over a support).
7.2 Super-Imposed Dead Load
These are dead loads acting upon a structure from
objects which do not serve a structural purpose. Objects
of this type are likely to change several times over a
bridges life. This gives rise to a tendency for layers of
road surface to be built up. Also, the possibility of fill
becoming saturated and objects possibly being replaced
with something of a different weight make superimposed dead loads difficult to predict. This is reflected
by high values of γ fl= 1.75 at ULS and 1.20 at SLS. A
200mm layer of hardcore fill (density = 1920kgm-3) and
a 100mm layer of asphalt (density = 2300kgm-3) have
been assumed, along with an allowance of 1.0kNm-2 for
services and street furniture.
Total Super-Imposed Dead Load
= 205 kNm-1 length
7.3 Primary Live Loads
Primary live loads are vertical loads from traffic
and pedestrians upon the bridge. In Thailand trucks are
Figure 8: Variable Axel Width
HA
HA
HA
HA
1/3HA
1/3HA
1/3HA
1/3HA
Figure 9: HA and HB Load Distribution
As the notional lane width is less than 3.5m the HB
load straddles two lanes. This gives the load distribution
for HA and HB loading as shown on plan above. For
both HA and HB loading γfl and γf3 vary dependant
upon the load combination.
Rama VIII has a 5.3m walkway in each direction so
pedestrian loads must also be considered. For bridges in
excess of 36m length the pedestrian load is equal to k x
5.0kNm-2:
k=
( HAUDL × 10) = 0.36
( L + 270)
(2)
Pedestrian Load = 9.5 kNm-1 length walkway
As the walkway has both foot and cycle access and
is wider than 2m the pedestrian load can be reduced by
15% for the first meter over a 2m width and by 30% for
any width over this. For simplicity an average load over
the width of each walkway can be calculated (2
walkways in total).
Av. Pedestrian Load = 8.0 kNm-1 length per walkway
7.4 Secondary Live Loads
Various secondary live loads can also arise due to
traffic. Centrifugal loads must be applied to bridges
with a radius of curvature less than 1000m. The curve
on Rama VIII is shallow so this is ignored.
Longitudinal loads due to braking/acceleration
forces need considering. BS 5400 Clause 6.10.1 states
that for the HA load type a nominal load of 8kNm-1
along the loaded length +250kN or a maximum load of
750kN must be applied longitudinally. The maximum is
exceeded in this instance so a value of 750kN is used.
For the HB load type breaking/acceleration loading is
taken as 25% of the nominal HB loading, applied
between 8 wheels of two axels. As the HB load is taken
as 450kN per axel a longitudinal force of 225kN is
applied along the bridge.
7.5 Wind Loading
As Rama VIII is outside of the UK and has a span
greater than 200m, wind loadings obtained from BS
5400 are not strictly applicable. However they still can
be used to give an idea of the loads upon the bridge. In
situations such as this the aerodynamic stability of the
bridge would be confirmed though wind tunnel testing.
Through information obtained by wind tunnel
testing the fiber-reinforced composite panels, placed
upon the underside of the deck, were designed to make
it as aerodynamic as possible, relieving the load it feels.
Reduced wind loading is another benefit of having a
slender deck. This is primarily due to the wind having a
smaller area to act over but also through the reduction of
a decks coefficient of drag. As mentioned it is likely
that wind loading upon the pylon during the
construction stage would have played a large part in its
structural design.
Wind loading in accordance with BS 5400 is based
upon 120 year wind speeds at a height of 10m above the
ground. Wind loads acting upon both the pylon and
deck must be considered. The first step in finding wind
loads is to calculate the wind gust speed (vc) acting upon
a bridge. The mean hourly wind speed (v) for Bangkok
was not readily available therefore has been
conservatively assumed as 30ms-1. The height of the
deck above ground ≈ 15m, but the pylon height alters.
For simplicity an average pylon height of 80m will be
used. For a 300m long bridge the wind coefficient (K1)
= 1.39/1.71 (Deck/Pylon), funneling factor (S1) =
1.00/1.00 and gust factor (S2) = 1.07/1.42:
vc = v K1 S1 S2 = 44.6 ms-1(Deck)
(3)
= 72.8 ms-1(Pylon)
The transverse wind load (Pt) acting at the centroid
of the element under consideration, is a function of
Pressure Head (q), area (A) and coefficient of drag (CD).
As the deck is 2.4m deep it has an approximate area of
720m2 along its length. The 29.2m wide deck has a d/b
= 12.1, corresponding to a CD = 1.00. The pressure
head is found using Eq. (4):
q = 0.613vc2 = 1219 Nm-2 (Deck)
(4)
The transverse wind load is then calculated using:
Pt = q A1 CD = 878kN
(5)
-1
Transverse Deck Wind Load = 2.9 kNm length
Both transverse and longitudinal (PL) wind loads
act upon the pylon. With tapering sections in both
directions finding accurate wind loads can become
complicated. As the section is almost square a worst
case wind loading will be calculated an applied in both
directions. If the 161m high pylon is assumed to have a
7m width in both directions, an area of 1200m2 and CD
= 1.90 a value for pressure head can be calculated:
q = 0.613vc2 = 3248 Nm-2 (Pylon)
PT/L = q A1 CD = 7408kN
(6)
-1
Pylon Wind Load = 46.0 kNm height
Wind can also cause uplift or a downwards force to
act over a bridge deck. This force is calculated using the
plan area of the deck (= 8760m2) and a lift coefficient
(CL = 0.25) as shown below:
Pv = q A3 CL = 2670kN
(7)
-1
Vertical, Deck Wind Load = 8.9 kNm length
Wind loads are combined in the following ways; Pt
alone, Pt with ± Pv, PL alone, 0.5Pt with PL ±0.5Pv.
7.6 Temperature Loading
Varying temperatures will cause a bridge to
expand/contract in both the longitudinal and transverse
directions. Usually this movement is allowed through
expansion joints and bearings along the bridge. If these
get blocked they can restrain the deck from movement,
inducing thermal stresses with it. Bridges are designed
to 120 year return temperatures.
Two effects of temperature change need to be
considered, the first being when one temperature acts
uniformly over the whole bridge. It is also possible for
there to be a variation in temperature between the top
and bottom of the deck inducing bending stresses
within. In this section I will analyze the stress induced
longitudinally along the deck by a constant temperature.
Through looking at the climate data for Bangkok I
believe it acceptable to assume a temperature range of
+5 to +40°C. If there is a temperature change of ±20°C
the change in length of the bridge will be:
ε = α ∆T where α = 12x10-6°C-1 for steel/conc (8)
ε = 240µε
δ=εL
(9)
δ = 0.072m = 72mm
As the bridge is designed to act compositely a
thermal stress will be induced in both the steel and
concrete. Assuming full restraint of the bridge deck the
stresses induced in the main section (either tension or
compression) along its length are:
σ C/T = ε x E
(10)
C/T
-2
Thermal Stress - Steel, σ
= 48Nmm
Thermal Stress - Concrete, σ C/T = 7.2Nmm-2
7.7 Seismic Loading
Bangkok is an area of low-to-moderate seismicity
with approximately 20 earthquakes being recorded over
the last 200 years. No record of any significant damage
occurring during any of these quakes exists. However
the soft soils and deep pile foundations cause the design
spectral input to increase to such a level that seismic
effects need to be considered [2]. As the UK is not a
seismic area British Standards have no guidance on
seismic loading. If a full analysis of the Rama VIII
Bridge were to be conducted provisions from a design
code such as AASHTO would need to be used.
7.8 Fatigue Loading
It is likely that the concrete pylon will undergo
some degree of creep caused by sustained periods of
stress. Creep occurs over a significant period of time
(20-30 years), but it is estimated that 75% occurs within
the first year. Consequences of creep include increased
deflections, a reduction in prestress and redistribution of
internal forces. Creep and shrinkage of a composite
deck as used in Rama VIII would lead to axial load
being redistributed from the concrete into the main steel
girder beams. To combat this the precast deck panels
were stored for 90 days before being installed [1].
Steel is not susceptible to creep but is to stress
relaxation, particularly in stays and steel prestressing
tendons. Stress relaxation in the stays will causes them
to lengthen. This is only likely to cause serviceability
issues (i.e. increased deflections) but in extreme
circumstances could cause the pylon to become
destabilized. Elastomeric dampers are placed upon the
stays in Rama VIII to compensate for this [3]. If the
affects of stress relaxation become too large the stays
will need to be re-tensioned or possibly replaced.
Prestressing tendons also loose prestress during
loading. Both concrete creep and stress relaxation play a
part in this, along with the shrinkage of concrete and
other possible causes under special circumstances. The
initial tensioning stress can be reduced by up to 30% so
needs to be considered and accounted for during the
design process.
7.9 Load Combinations
BS 5400 groups the previously described loads into
5 combinations which need to be checked at both ULS
and SLS. These are shown below:
1. Permanent Loads plus Primary Live Loads
2. Combination 1, plus Wind and temporary
erection loads (if any)
3. Combination 1, plus Temperature and temporary
erection loads (if any)
4. Permanent Loads, Secondary Live Loads and
associated Primary Live Loads
5. Permanent Loads, plus loads due to friction at
supports
Section 8 (Strength Analysis) uses the appropriate
safety factors γfl and γf3 to combine the loads and form
the most onerous effects on various parts of the bridge.
The loads obtained are used to check the capacity of the
structure.
8 Strength
This section aims to analyze the strength of several
parts of the Rama VIII Bridge using the ULS
philosophy. A worst case set of forces is obtained from
the loadings in section 7 (Note: γf3= 1.10 at ULS).
8.1 Strength of the Deck
Whilst in operation a bridge deck will be subject to
axial force, bending and torsion. For the purpose of this
analysis several assumptions have been made. Firstly
the main girder beams are continuous with rigid support
provided from stays at every 10m. The stays would
actually provide elastic support so the stresses in reality
would be slightly larger than those obtained here.
Secondly it is assumed that the two main girder beams
will carry all of the longitudinal bending in the main
span. Fig. 10 shows a simplified cross section of the
main span deck that will be used for analysis purposes.
Torsion is developed from asymmetric loading. Open
sections (as often is the case in cable-stayed bridges)
have a low torsional rigidity. As Rama VIII’s cables
converge this is increased but torsion may still be an
issue. However torsion has been neglected in this
analysis.
Figure 10: Approximated Main Girder Section
As the deck is continuous both sagging and
hogging moments will form within it. Steels properties
are isotropic so it can carry both equally well but they
each need to be assessed to find which has the greatest
magnitude. Load combination 1 is likely to induce the
greatest moments in the deck. Here Permanent and
primary live loads are considered. Fig. 11/12 shows how
loads would be arranged within each span to induce the
greatest moments.
Figure 11: Load Distribution for Maximum Sagging
Figure 12: Load Distribution for Maximum Hogging
Load patterns as seen in Fig. 9 are complex and
would be analyzed using a computer. However the deck
can be analyzed with relative ease if no HB loading is
applied and the two lanes of full HA loading are
arranged symmetrically about the deck. It is for this
variation of load case 1 that the bridge deck will be
analyzed. Using the loads shown in Table 1 and the
unfactored dead load = 186 kNm-1 the moments in the
deck can be found.
Table 1: Loads – Case 1
Load:
γfL
Factored Load
Dead
1.15
213 kNm-1
Super – Imposed Dead
1.75
359 kNm-1
Live: Full HA (2 Lanes)
1.5
39.8 kNm-1
1/3 HA (4 Lanes)
1.5
13.3 kNm-1
Pedestrian
1.5
24 kNm-1
Total:
729 kNm-1
A factored knife edge load (180kN and 60kN)
must also be applied in each notional lane at one point
along the length of the bridge.
The results obtained give a maximum sagging
moment = 7.96 MNm and hogging moment = 8.10
MNm. From this the bending stress within the section
can be found using Eq. 11:
My = 54Nmm-2
(11)
σ=
I
Transverse wind loading acting upon the main span
would cause bi-axial bending within the deck. This
would be checked using load case 3.
The maximum force in the stays and ultimately the
maximum compression in the deck is found when the
full factored load is placed over the whole length of the
bridge rather than in selected spans. The vertical
reaction at each of the 28 sets of supports can be taken
as 7290kN. The inclination of the stays changes along
the length of the bridge but through taking the angle of
the central most stay and applying it to them all a fair
approximation of the compression in the deck can be
obtained. With the angle of the central stay taken as
37.5° the compressive force from a single pair of stays =
9500kN, making the total compressive force in the deck
= 266MN. If we make the assumption that the load has
spread out equally over the complete area of
concrete/steel section we can obtain a value for the level
of compressive stress in the deck as shown in equation
(12). The C.S.A. for the section is 7.65m2:
F
-2
(12)
σ = = 34.8 Nmm
A
By totaling the stresses we can find the total level
of stress within the deck. Thermal stresses are included
with a factor of γfL = 1.3 applied (note that live loads
would have a smaller safety factor when temperature is
considered so the stresses obtained are conservative).
Total Stress - Steel,
σ = 151.2Nmm-2
Total Stress - Concrete, σ = 44.2Nmm-2
Extra stress due to torsion, transverse wind etc. will
need to be added to these totals. Concrete with a
cylinder strength of 55Nmm-2 and S355 steel [2] have
been used so the stresses obtained show an understressed deck for this load case.
8.2 Strength of the Stays
The maximum tensile force is induced within the
stay with the smallest angle of inclination. This is the
stay that spans the longest from the pylon.
This stay hits the deck at an approximate angle of
27.3° and supports an ≈ 7290kN reaction, making the
tension in the stay = 15890kN. Ref. [3] states that each
strand has an ultimate tensile strength of 265.5kN. The
longest stays each contain 73 strands, giving a tensile
strength = 19382kN, with two stay supporting each
section of deck. Equation (13) shows that the level of
stress within each stay is at an acceptable value.
Unity Factor =
15890 =0.41
( 2 × 19382)
(13)
8.3 Strength of the Pylon
The compression within the pylon can be found
using an average value of 11975kN for the level of
tension within each stay, and 595kNm-1 height for the
unfactored dead load of the pylon. To check the
capacity of the pylon bending within it will need to be
analyzed under all loading conditions, including wind
and seismic in every direction.
9 Serviceability
Designing bridges to comply with SLS criteria is as
equally important as for ULS conditions. Excessive
deflections may not pose a threat to the stability of a
bridge but is likely to put people off wanting to use it.
Deflections of cable-stayed bridges due to permanent
loads can be controlled through tension in the stays.
Equation (14) shows an approximate value for the
level of deflection within a 10m span between stays. It
has been assumed that the girder sections are simply
supported between the stays for conservatism. Using the
same load case as in section 8 the SLS load long the
length of the bridge = 495 kNm-1 with a 120kN KEL
load placed at the centre of the span.
5wL4
PL3 = 2.7 + 0.1 = 2.8mm
(14)
δ=
+
384EI 48EI
The level of deflection obtained is minimal for a
300m long bridge and would not be noticed. Once again
this value may be lower than what would realistically
occur due to the distance between rigid supports being
300m and the intermediate stay supports being elastic.
However the value is so small the actual deflections are
still unlikely to cause an issue.
The bridge will also deflect laterally from wind
blowing upon the side of the deck. The aerodynamic
shape of the underside of the deck will help to minimize
this.
10 Natural Frequency
Lessons have been learnt from past events and
dynamic effects due to vibrations are checked for all
bridges. Primarily this is a serviceability check to ensure
that no discomfort if felt (particularly by pedestrians)
when crossing a bridge. Both low and high frequency
vibrations can cause problems so a check is conducted
to ensure that a bridges natural frequency lies with an
acceptable range of 5 – 75 Hz. If a bridge vibrates at its
natural frequency it can cause large oscillations of the
bridge deck. It is at this point when a bridge has
serviceability issues and faces the risk of collapse. If the
natural frequency is below 5 Hz it is at risk of being
matched by people walking across the bridge or by wind
(if around 1 Hz). If this occurs consideration needs to be
placed into limiting the maximum acceleration of the
bridge to within limits set out it BS 5400. When above
75 Hz the frequency is unlikely to cause collapse but
may create unpleasant physiological effects.
The natural frequency of a bridge deck can be
calculated using Eq. (15). It calculates the frequency of
a section, taking into account its end conditions using a
coefficient kn. It is again assumed that the deck is
continuous over rigid supports (stays). The frequency
will be calculated for a 10m girder section between
stays. The support provided by the stays is considered to
be clamped. Two types of end conditions exist,
clamped-clamped between stays (kn = 22.37 [7]) and
clamp-pinned on the end spans (kn = 15.42 [7]). It is the
end spans that will have the lowest frequency. For the
girder section I = 0.120m4, m = 39.9x103kgm-1 and E =
200x109Nm-2:
k
EI
(15)
fn = n
2π mL4
f0 =27.6 Hz (clamped – clamped)
f0 = 19.0 Hz (clamped – pinned)
The values obtained lie within acceptable limits but
are higher than what would realistically be achieved.
The stays are not rigid supports but elastic allowing a
limited movement causing the deck/stay system to
vibrate as one.
11 Durability
Durability is a key concern for all bridges. As is the
norm for most bridges, Rama VIII has a design life of
120 years, set under the assumption of regular
maintenance. The enclosed space on the underside of
the main span provides access for maintenance, where
the girder section can be inspected for corrosion. The
enclosure also provides a dehumidified atmosphere and
reduced environmental exposure, greatly reducing the
risk of corrosion. The main span steel is still painted
with a protective coating to reduce this risk further.
Corrosion of steel cables is another concern. Four
barriers are used to protect the stays from the elements.
Firstly each strand within every stay is galvanized. They
are then waxed and coated in a protective layer of
polyethylene. Finally the stays are cased inside a HDPE
sheath. This allows replacement of individual strands if
required. The stays anchorages are one of the key areas
that require regular maintenance. In the anchor span
where the back stay anchorages are hidden from sight,
access can be achieved through the central spine beam
running along the said span. Inspection of movement
joints and bearings is also needed to ensure the do not
become blocked restraining deck movement.
12 Vandalism
Small scale vandalism is a problem in Bangkok.
This is in the magnitude of graffiti and not at a level
which would cause anything more than superficial
damage to the Rama VIII Bridge. It is not impossible to
imagine a vehicle being purposely being crashed into
one of the piers or the pylon. Both elements will have
been designed to be robust enough to withstand the
necessary impact loads. The threat of terrorism is
becoming more and more of an issue. Rama VIII is
fairly modern so it is likely that it will have been
designed to withstand some degree of blast loading.
13 Future Changes
As Rama VIII is effectively performing its required
task with no reported operational problems it is difficult
to suggest future changes. The increasing level of
congestion in Bangkok will require further capacity to
cross the Chao Phraya River at some point in the future.
Widening of Rama VIII is one solution to this problem.
The location of the pylon and where the stays meet the
deck make this difficult to do but there is precedence.
The likely way in which this would be done is to replace
the cantilevered walkway with a larger stiffer
cantilevered section. This solution is not realistic and
you can tell that the bridge was not designed to be
widened. The extra load would change the back staypylon-main span equilibrium resulting in further design
work. The most practical solution to the problem is
likely to be the construction of a new bridge at some
point along the river.
References
[1] Heidengren, C.R., 2003. Rama VIII – Regal
Crossing, Civil Engineering Magazine, Vol.73,
No.7, pp. 34-43.
[2] Torrejon, V.E., Berman, D.W., Design of Rama
VIII Bridge in Bangkok, Thai Engineering.com,
[Online].
[3] Lengweiller, R., Kaufmann, E., 2002. Rama VIII
Bridge in Bangkok: Construction and Stay Cable
System, JKR Seminar, Kuala Lumper Aug 2002,
[Online].
[4] BS 5400-2:2006, Steel, Concrete and Composite
Bridges – Part 2: Specification for Loads, BSI.
[5] Walther, R., 1999. Cable Stayed Bridges 2nd Ed.,
Thomas Telford Publishing.
[6] Leonhardt, F., 1982. Bridges, The Architectural
Press.
[7] Davison, B., Owens, G.V., 2003. Steel Designers
Manual 6th Ed., Blackwell Publishing.