1 Robert M. Foster – [email protected]
A CRITICAL ANALSIS OF THE NESCIO BRIDGE, AMSTERDAM
R M Foster1
1Department of Architecture and Civil Engineering, University of Bath
Abstract: The Nescio Bridge (Nesciobrug) is a self-anchored mono cable pedestrian suspension bridge
located near Amsterdam. This paper will seek to provide a comprehensive critical analysis of the Nescio.
The analysis will include a critique of the aesthetic, structural and construction solutions employed in the
design of this unusual bridge. A number of simple hand calculations are presented in order to evaluate the
performance of the bridge under various Ultimate Limit State and Serviceability Limit State conditions.
Although the concrete approach ramps are discussed where relevant, this paper is principally an analysis
of the steel main-span and foundations.
Keywords: Nescio, suspension bridge, mono-cable, self-anchored.
1 General Introduction
The Nescio Bridge (Nesciobrug) is a self-
anchored mono cable pedestrian suspension bridge
with a main span of 171m. Completed in 2006 on a
budget of only !12.2million, Nescio is the first
suspension bridge to have been built in the Netherlands
and has received several national and international
awards. The bridge connects existing pedestrian and
cycle routes across the Amsterdam-Rhine canal
(Rijnkanaal) and eliminates a 40-minute detour
between Oost-watergraafsmeer in the city of
Amsterdam and its Ijburg suburb.
Figure 1: Location plan of the Nescio Bridge.
Close collaboration was required between
Wilkinson Eyre, Arup and Grontmij to develop a
design that fulfilled the City of Amsterdam’s brief for a
bridge that would ‘demonstrate its commitment to
design quality, and sensitivity to the environment’, Ref.
[1]. Additional constraints on the design included
limited flexibility regarding the positioning of the
approach-ramps, stringent requirements for non-
interruption of the canal and the requirement to clear
the canal in a single span.
The main span is fabricated entirely from steel
while the long approach ramps are concrete cast in-
situ. The unusual bifurcated end design allows separate
pedestrian and cycle access. A winding steel stair
provides pedestrian access to the bridge, while cyclists
ascend a 275m concrete approach ramp to gain the
9.3m of elevation required to clear river traffic.
2 Aesthetics
2.1 Critical Method
The aesthetic critique conducted here is
undertaken principally with reference to Fritz
Leonhardt’s ten principles of bridge aesthetics. It is not
clear whether Leonhardt’s principles were deliberately
employed in the design process, but it is certain that
aesthetic considerations were fundamental to the
design.
2.2 Fulfillment of Function
The manner in which each component of the Nescio
fulfills its function is expressed with great clarity. The
composition of the bridge structure reflects Arup
Proceedings of Bridge Engineering 2 Conference 2009 April 2009, University of Bath, Bath, UK
Director Angus Low’s response to the challenge of
bridge design, expressed in his 2008 Milne Lecture,
Ref. [2], that ‘…despite their size they have relatively
few components to design. There are usually more
design criteria to satisfy than there are components to
shape. It follows that each component is serving
several functions and so there is a complex interaction
between all the design requirements, and the different
ways they can be satisfied.’ An illustration of this
challenge is the bridge’s deck that is required to act as
a long span beam during erection and an
aerodynamically stable, low radar profile, torsion
resisting, compression deck in the final condition.
Despite this, the arrangement of components that
comprise the Nescio is sufficiently simple that it is
clear, even to the lay bridge user, how the bridge
achieves its stability and span. Confidence in the
bridge’s stability is enhanced by the clearly expressed
role of the bifurcated ends of the bridge in providing
lateral stability. Similarly, the twin backstay cables at
each end of the span reassure the bridge user that the
slender pylons are securely restrained. The positioning
of the pylons between the legs of the bridge allows a
separation of elements that leaves no doubt that the
deck is suspended from the cable arrangement rather
than gaining direct support from the pylon, Fig. [2].
Figure 2: Clear separation of pylon and deck.
The deck section is principally governed by
structural requirements, with smooth curves
interpolated by the architect between critical sections
determined by the engineer, Ref. [3]. However, the
critical section at mid-span reflects the construction
requirement that the deck be erected as a single
component, simply supported at two points. In this
sense, it can be argued that the form does not represent
the honest fulfillment of the bridges functional
requirements in the final condition. The author would
not regard this as a fair criticism for the simple reason
that a bridge is not a solution to a single well-defined
problem or final load case. A bridge is a response to the
complete set of issues encountered in spanning a void,
from beginning to end, not just the final state
requirements. Therefore, a form that reflects an elegant
solution to the manifold of functional considerations,
including those of constructability, can be said to
express the fulfillment of its function rather more
honestly than a structure that purports to have been
designed solely for its final condition.
2.3 Proportion
Figure 3: Elevation of the Nescio Bridge.
The height of the masts and the parabolic curve
described by the main suspension cable are elegantly
proportioned relative to the length of the main span and
the height of the deck above the water. However, it
could be argued that the 2m depth of the deck at mid-
span is greater than might be considered ideal for a
suspension bridge.
The abruptness of the end of the pedestrian deck
at the stairs is disconcerting from some angles. The
composition would appear more balanced if a long
ramp where employed here, as at the end of the cyclist
deck. The designers were no doubt concerned that a
long ramp would be an inefficient method of ascent
and might frustrate pedestrians.
Figure 4: Plan of the Nescio Bridge.
Despite the unusual curvature of the bridge on
plan, it is symmetrical about the mid-span axis and
conforms to a constant radius of curvature of 300m,
Fig. [3]. This lends a sense of deliberateness to the
proportions of what might have otherwise seemed an
arbitrary freeform design. The curvature on plan also
echoes the vertical curve of the main cable engendering
a sense of converging trajectories, in different planes,
to the path of the bridge. In conjunction with the
bifurcated ends that come together mid-span, this
reinforces the image of the bridge as a unifying and
connecting structure. Bringing the main cable down to
connect with the deck might have made this imagery
more striking and would have had the added effect of
stiffening the deck.
2.4 Order
The principal reason for not attaching the main
cable to the bridge deck was to avoid disturbing the
order of the bridge. The designers felt it important to
ensure ‘visual continuity of the curtain of hangers…
For the same reason the hangers were spaced at the
relatively close spacing of 5m’ Ref. [3]. Connecting the
two components would have also undermined Low’s
desire for ‘a clear separation of parts’ Ref. [2].
A number of elements disturb the otherwise
disciplined order of the bridge. The steel end columns
are positioned too close to the adjacent concrete
column, disrupting the rhythm established by the ramp
supports. This breaking-of-step is no doubt required to
achieve additional stiffness at the end of steel structure
by tying any laterally induced differential forces
between the bifurcated deck-ends directly into the
torsion box of the foundations. However, aesthetically
this is a disappointing solution.
The steel connectors, shown in Fig. [5], that are
used to tie the otherwise un-hung pedestrian deck to
the suspended cycle deck after the point of bifurcation
undermine the order of the soffit in this area. Although
relatively unobtrusive, these connectors give the
impression of ad hoc rather than integral design
elements. Some thought has gone into the aesthetic
design of these components to alleviate this impression
but this author feels that further stiffening the
pedestrian deck to negate the need to reduce the
effective span would have been a better solution
aesthetically. Presumably, additional stiffening was
found to be a less materially efficient solution and so
the connector was chosen.
Figure 5: Hangar connection plate at bifurcation.
2.5 Refinement
A number of refinements contribute significantly
to the aesthetic appeal of the bridge. The fluent
changes in section of the bridge deck and the clean
lines of the soffit emphasise the sinuous form of the
bridge and alleviate the sense of heaviness that might
have arisen from the substantial depth of the deck at
mid-span.
The end taper of the pylons lends a sense of
elegance and lightness to these strong vertical
components of the composition. The length of the
taper, combined with the inclination of the pylons at
2.8° off vertical, helps convey the initial architectural
conception of the vertical elements as ‘backward
raking cocktail sticks’, Ref. [3].
2.6 Integration into the Environment
In elevation the bridge is sensitively proportioned
with the pylons high enough to allow the main cable to
achieve a graceful and efficient parabolic curve without
being so tall as to overbear the surrounding tree line.
The scale and slenderness of the pylons is also
reminiscent of a ship’s mast while the soffit of the deck
conjures images of a ship’s hull – indeed, the deck
steelwork was constructed in local shipyards using a
number of boat building techniques. Therefore, the
form of the bridge can be said to have been very much
a product of its environment, both in terms of
fabrication and of the sweeping plan geometry that was
required by the site constraints.
2.7 Texture
The glossy texture of the painted steel deck edges
and soffit is unusual but conveys a feeling of sleek
newness, rather like the brilliant-white hulled yachts
that leave the nearby shipyards.
2.8 Colour
Figure 6: Deck edge as illuminated ribbon.
The choice of an all-white soffit and pylons
reinforces the sense that this bridge is a showpiece and
harbinger of modernity and regeneration for the area.
The unusual section of the bridge has the effect of
shading the soffit while the shallow side plates are
illuminated by sunlight, appearing as a thin white
ribbon snaking across the canal, Fig. [6]. This reduces
the apparent depth of the bridge, lightening the deck
and restoring the hierarchical supremacy of the main
cable over the bridge deck. The choice of a steely
coloured and permeable parapet reinforces this effect.
Figure 7: Use of colour and spacing in column
design.
The steel columns at the ends of the bifurcated
deck are coloured dark grey in a rather unsuccessful
attempt to diminish their presence. Figure [7] illustrates
both the colouring, and the cramped spatial relationship
between the steel column and its concrete neighbour as
highlighted in Section [2.4].
2.9 Character
The distinctive character of the Nescio Bridge
derives principally from its combination of a bifurcated
deck, pronounced curvature and skew on plan, and its
single main suspension cable. This combination has led
to a number of unusual features, such as the ‘parting
curtain’ that occurs when the hangers switch sides to
accommodate the curvature of the deck, Ref. [3].
2.10 Complexity
Although complex in its actions, and constantly
varying in its geometry, the Nescio manages to achieve
an admirable degree of visual simplicity. While some
may consider visual complexity to be an indicator of
intelligent design, this author regards it, generally, as
indicative of a designer’s failure to find a simple
formal solution to the set of problems encountered.
Mies van der Rohe’s famous assertion that ‘less is
more’ seems particularly apt for bridge design and it is
clear that this is the approach taken, with some success,
by the Nescio’s designers.
2.11 Incorporation of Nature
The creation of the wetland habitat in the area of
the winding approach ramp has led to the use of the
ramp by ornithologists and as a nature walk by local
people. The success of this aspect of the design raises
the question as to whether a long approach would
really have been inappropriate for pedestrians or
whether the stairs may have been unnecessary.
Trees break up the continuity of the concrete
approaches in a pleasing manner. This reduces the
apparent mass of the approach structure and increases
the sense of drama as the main span sweeps out from
the treeline and across the water.
3 Loading
3.1 Analytical Approach
The following analysis of loading conditions is
informed by the Limit State approach that will be taken
in Section [4] to evaluate the design strength of the
bridge. The load factors !fl applied in this section will
be those for Ultimate Limit State design unless
otherwise specified. Serviceability conditions are
discussed in Section [5]. Temperature, creep and wind
loading effects are discussed in Sections [8, 9&10].
3.2 Dead Load
The dead load (DL) of the bridge is taken as the
self-weight of the super structure, principally the steel
box section that comprises the deck. Due to the varying
section geometry of the deck over the length of the
span and the bifurcation of the deck towards the ends, a
value for DL per metre can been obtained by first
averaging the estimated cross sectional steel areas as
shown in Table [1]:
Table 1: Steel deck cross-sectional areas.
Midspan 0.201m2
At bifurcation 0.224m2
Footpath end 0.097m2
Cycle-path end 0.129m2
Footpath/Cyclepath ends combined 0.226m2
Average value 0.217m2
Taking the average cross sectional area obtained
in Table [1] and multiplying by the weight of steel, an
average deck weight can be estimated as 17kN/m.
Factoring by !f3 of 1.1 for steel, and !fl of 1.05
(appropriate for all adverse combinations), a uniform
dead load (UDL) due to the deck is obtained as
19.6kN/m.
The main cable is a 140mm steel cable weighing
1.13kN/m. Hangers are spaced every 5.5m with an
average length of 14.2m and a typical diameter of
36mm. This gives a suspension steelwork weight of
2.0kN/m on plan. Factored by !f3 and !fl as before, this
gives a DL of 2.3kN/m.
Summing these loads gives the total DL of the
structure as 21.9kN/m.
3.3 Superimposed Dead Load
There appears to be little topping material to the
bridge deck, simply an unidentified high friction finish
to avoid slips. Consequently the superimposed dead
load (SiDL) due to this topping is considered to be
negligible.
The lightweight, predominantly wire mesh,
parapet, provides little additional load. The SiDL due
to lighting and electrical cabling is uncertain, although
it is not thought that any other services are carried.
Consequently, the total weight of these components is
conservatively estimated at 1kN/m.
Additionally, the 130kN of tuned mass dampers
are to be considered as SiDL. It is possible that these
dampers may be altered, or most critically, added to, at
a future time in the bridge’s design life. The large !fl of
1.75 for SiDLs allows this possibility to be
accommodated more conservatively. Although the
dampers act as point loads at the mid and quarter span
positions, they will be taken here as a uniformly
distributed 0.8kN/m load across the main-span of
171m. This simplification is made because the actual
distribution of the total load of 130kN is unknown.
Thus the total factored SiDL is found to be
1.8kN/m.
3.4 Live Load
Live load for pedestrian and cycle bridges
spanning in excess of 36m can be taken as 5kN/m2
multiplied by a factor k, Ref. [5]. The factor k is
defined in Eq. (1), where HA is the nominal HA
uniformly distributed load for the loaded length in
kN/m, and L is the loaded length in metres.
!
k =HA "10
L + 270 (1)
Considering L as the main span and obtaining HA
from Eq. (2):
!
HA = 36" 1/L( )0.1
kN /m. (2)
A value for k is obtained in Eq. (3):
!
k =21.53"10
171+ 270= 0.5 (3)
This gives a value of 2.5kN/m2, indicating an
average unfactored live load of 13.8kN/m. Factoring by
!f3 and !fl for load combinations 1, 2 and 3 gives values
for Ultimate live load (ULL) shown in Table [2].
Table 2: Live loads for Loading Combinations 1, 2&3.
Combination 1 2 3
!f3 1.1 1.1 1.1
!fl 1.5 1.25 1.25
ULL [kN/m] 20.7 17.3 17.3
Although reductions for pedestrian bridges greater
than 2m wide are permissible, these will not be applied
as it is foreseeable that the bridge might be fully loaded
with crowds watching events on the river.
Bollards preventing motor vehicle access to the
approach ramps mean that accidental vehicular loading
does not require consideration.
3.5 Parapet Load
Parapet loads are required to resist a notional
design load of 1.4kN/m acting at the top of the parapet.
Scaling off drawings indicates the parapet height is
1.120m and the vertical supports are spaced at 1.940m.
Taking !f3 as 1.1 and !fl as 1.5, a factored design
moment, requiring resistance by each vertical support
is obtained as 5kNm.
4 Strength
4.1 Arrangement of Forces
Combination 1 loading is carried by the structure
as indicated in Fig. [8].
Figure 8: Simplified schematic indicating arrangement
of forces under Combination 1 loading.
The relatively uniform plan loading of the bridge
deck carried by the hangers causes the main cable to
form a parabolic curve, rather than the catenary that
would form if the cable were to hang under its own
self-weight. Unlike most suspension bridges, Nescio is
self-anchored. This means that the deck acts in
compression to carry the large horizontal forces
exerted by the backstay cables, rather than transferring
these forces into the foundations.
4.2 Hangers
The 36 hangers are 36-42mm Macalloy 460 type
bars spaced at 5m centres. This indicates that, from the
loadings calculated in Section [3], each hanger carries
an ultimate load of:
!
5" 21.9+ 3.5+ 20.7( ) = 230.5 kN .
The ultimate capacity of the smaller 36mm bars
can be estimated as:
!
460000" 0.0182" #
1.05= 445.9 kN .
Since 445.9>230.5, the hangers are safe and
perhaps a little conservatively sized.
4.3 Main cable
The maximum tension in the main cable will
occur at the pylons and can be determined by resolving
forces at the pinned connection to the pylon top. The
vertical force component V can be taken as the load on
half the span, amounting to 4.1MN. The horizontal
force component H can be found using Eq. (4), where
w is the [Combination 3] load per unit length on plan, l
is the span and s is the depth of the parabola.
!
H =wl
2
8s=46.1"171
2
8" 20.8= 8.1 MN . (4)
Having found H and V, the maximum cable
tension Tmax can be obtained:
!
Tmax
= H2
+V2
= 4.12
+ 8.12
= 9.1 MN .
The main cable is specified as a 140mm fully
locked vvs-3 Pfeiffer cable. The manufacturer’s tables,
Ref. [6], indicate a limit tension for this cable of
12.1MN. Since 12.1>9.1MN, this cable is safe.
4.4 Deck
4.4.1 Compression
Assuming that the foundations take no significant
horizontal forces, the force component H obtained in
Eq. (4) must be tied back into the superstructure by the
backstay cables in the form of a longitudinal
compression of the bridge deck. Taking the cross
sectional area A of the deck at mid-span an axial
compressive stress "c, ignoring bending effects, is
obtained in Eq. (5):
!
"c
=H
A=8100000
201000= 40.3 N /mm
2. (5)
Clearly "c is acceptable for a steel deck.
4.4.2 Buckling
In its action as a relatively slender compression
member the deck must be checked for susceptibility to
buckling. Lateral buckling is unlikely as stiffness in
this plane is enhanced by the end bifurcations. Lateral
torsional buckling is unlikely in a torsionally stiff
closed section. Therefore, it is buckling in the vertical
plane, about the x-x axis that must be checked. The
critical force for buckling, Pcrit, is found in Eq. (6),
where E is the Young’s Modulus of steel and Ixx is the
second moment of area about the x-x axis at mid-span.
L’ is the effective length of the deck, taken as 0.5L for
the fixed ended condition. L is the total unrestrained
length of the steel deck, 205m.
!
Pcrit
=" 2EI
xx
( # L )2
!
=3.14
2" 200"10
9" 0.032
(0.5" 205)2
= 6.0 MN . (6)
Since 6.0<8.1MN from Eqs. (4, 6) indicates
Pcrit<H, the deck does not appear to be safe for
buckling. However, the value of Ixx used in Eq. (6)
assumes the section as a simple triangular hollow
section and neglects the longitudinal stiffeners that can
be seen in Fig. [9].
These longitudinal stiffeners appear to be 25mm
steel plate and provide the additional stiffness to
prevent the global buckling effect identified above.
Transverse stiffeners, also identifiable in Fig. [9],
contribute to the section’s resistance to local plate
buckling effects.
4.4.3 Torsion
Figure 9: Mid-span deck section.
The main cable passes over the mid-line of the
overall bridge structure, switching sides as the deck
curves on plan, preventing any net overturning effect.
However, at various points, notably mid-span, there are
significant torsional moments generated by the
asymmetric support provided by the hangers, as shown
in Fig. [10].
Figure 10: Deck supported on one side at mid-span,
inducing torsion in the deck.
The distributed Combination 1 load on the bridge
acts as a 46.1kN/m load at a lever arm of 2.5m. This
induces a moment of 115.3kNm/m in the deck that
must be resisted as a torsionally induced shear stress in
the deck section.
If the length of deck that is asymmetrically
supported as in Fig. [10] is taken as the 71m portion
between the bifurcations, then the total moment M to
be resisted is 3.3MNm. The trapezoidal deck section at
each end of the span considered can be assumed to
carry half of this moment. The maximum torsional
stress # can be approximated using Bredt’s formula,
Ref. [7], shown in Eq. (7), where A0 is the area
enclosed by the section and t is the plate thickness:
!
" =M
2A0t=
(3.3/2) #106
2# [(5+ 2.5) /2]#1.7# 0.012
!
= 10.8"106
N /m2
= 10.8 N /mm2. (7)
Despite the asymmetric support arrangement the
torsional shear stress in the section is acceptable.
5 Serviceability
Consideration of the issues affecting the
serviceability of a bridge is a crucial aspect of bridge
design. This is particularly true of pedestrian bridges
where users travel slowly and expect to be provided
with a positive experience rather than simply a viaduct.
Detailed modeling that is beyond the scope of this
paper is required to conduct Serviceability Limit State
checks to any meaningful degree of accuracy.
Deflection in the span should be limited to 1:240, but
checking this requires an analysis of the stiffness of the
structural as a whole, which is not feasible by hand.
Issues of vibration, durability and intentional damage
are considered in Sections [11, 12&13].
A governing serviceability consideration for the
structure was the slope of the bicycle approach ramp to
achieve the necessary 9.3m clearance over the
waterway. This rise is accommodated by the 275m
concrete ramps, giving a slope of 3.4% and eliminating
the need for landings. Allowing space for these ramps
was an important consideration during the initial
design process.
The estimated 1.120m high parapets are below the
minimum height of 1.400m suitable for a cycle bridge.
If this estimated height is accurate then these parapets
are not serviceable and should be replaced.
6 Construction
Construction method was determined by two main
considerations: a requirement to close the canal for no
more than 12 hours, and the need to self anchor the
main cable. Both of these problems were solved by the
decision to design the deck as a single component,
sufficiently stiff to span with only two temporary
intermediate supports.
Figure 11: Deck lifted into place by crane barges.
This allowed the deck to be lifted into position by
two crane barges, Fig. [11], and the ends secured to the
main cable in a single 10-hour shift. The deck then
spanned, without impeding river traffic, in its
temporarily supported state while the hangers were
connected over a much longer period, Fig. [12].
Figure 12: Deck supported at ends and two
intermediate positions during construction.
The deck is fabricated by a ‘coffin construction’
welding technique used for box girders that are too
small to weld from the inside, Ref. [1]. Basically, a box
is constructed and then the lid is welded on from the
outside. Careful welding is necessary to avoid locking
thermal stresses into the welded plates.
Deck sections were fabricated in local shipyards
before being assembled and floated down the canal in a
single piece.
7 Foundations & Geotechnics
Very soft ground to a depth of around 20m meant
that horizontal forces from the backstay cables had to
be tied into the superstructure, discussed in Section
[4.4.1], rather than into the ground. Similarly, force
differentials, due to lateral wind loading, between the
deck ends acting at the top of the steel end columns can
cause moments to be induced in the foundations. The
netting out of these moments is achieved by the use of
reinforced concrete torsion box that effectively
prevents moments being transferred into the piles. The
box acts as a torsionally stiff ground beam and pile cap
that ties the legs of the superstructure together. Figure
[13] clearly shows this push-pull effect on the pairs of
end columns.
Figure 13: Arup model of first deformation mode
under lateral wind loading.
The steel end columns have fixed moment bearing
base connections, necessitating the use of the torsion
box. The pylon bases are nominally pinned, using a
50mm thick, 420mm diameter steel disk as a simple
rocker bearing. This connection prevents significant
moments developing, allowing a slender mast-like
pylon to be designed and meaning that moments in the
underlying raked pile groups are minimal.
8 Temperature
Making the reasonable assumption that thermal
conditions near coastal Amsterdam are similar to
conditions on the English coast at the same latitude:
Table 3: Values for calculating thermal stresses.
Maximum Minimum
120-year 33°C -14°C
50-year 31°C -12°C
50-year[group1] 31°C -10°C
Since footbridges may be designed to 50-year
return temperatures, a design range $T, adjusted for
group 1 construction type, can be taken as 41°C. For a
205m continuous steel deck this entails a maximum
thermal expansion/contraction e of:
!
e ="L#T
= 12$10%6$ 205$ 41= 0.101 m.
If the deck were initially restrained at the median
of the range, this expansion would induce a maximum
stress in the deck "T of:
!
"T
=±eE
L=
±0.051# 200#109
205
!
= ±50"106
N /m2
= ±50 N /mm2.
This stress entails an additional [Combination 3]
compressive force of 14.2MN in the deck. In addition
to the [Combination 3] 7.5MN compressive force
obtained similarly to Section [4.4.3], this gives a total
of 21.7MN and a clear risk of failure through buckling.
It is likely that it is for this reason that the steel deck
end is not connected to the concrete approaches,
allowing for independent movement. The steel end
columns, being less stiff than the deck, will elastically
deform to allow end movement and avoid the buildup
of these stresses.
Differential heating across the section is unlikely
to be significant as the section is relatively small and
the inclined soffit likely to receive some sun along with
the top of the deck.
9 Creep
Creep effects in steel are negligible in the range of
temperatures experienced by bridge components.
10 Wind
Wind conditions are assumed to be similar to
conditions on the English coast at the same latitude.
Thus the maximum wind gust vc, reduced for
footbridges at Nescio’s height of approximately 10m
above ground, can be found in Eq. (8). The value v
denotes the mean hourly wind speed, K1 is a wind
coefficient and S2 is the gust factor. Funneling effects
are unlikely at this site so a funneling factor S1 of 1 is
used.
!
vc
= 0.8vK1S1S2
!
= 0.8" 28"1.37"1"1= 30.7 m / s. (8)
The horizontal wind load Pt and the vertical wind
load Pv are calculated in Eqs. (9, 10). The value q is the
dynamic pressure head, A1 A3 are the characteristic
areas, and CD CL are coefficients of drag and lift. CD is
taken here as the minimum value of 2 for a footbridge.
However, Nescio’s relatively aerodynamic deck profile
is likely to exhibit a lower CD value even when the
additional 1.25m of live load height is considered.
!
q = 0.613Vc2
= 0.613" 30.72
= 577 N /m2
!
Pt = qA1CD
!
= 577" 3.15" 2 = 3.6 kN /m. (9)
!
Pv = qA3CL
!
= 577" 5" 0.4 = 1.2" kN /m. (10)
The longitudinal wind loading Pl is insignificant.
Therefore, the most onerous design combination of
wind loads is Pt±Pv. Factored for Combination 2
loading, Pv contributes only 1.5kN/m while other live
load is reduced by 3.4kN/m from Combination 1 to
Combination 2. Consequently, Combination 1 can be
seen as the governing vertical load case.
Figure 14: Plan. Arrangement of forces in legs due to
wind load.
The bifurcated deck causes Pt to induce a tension
in the upwind leg and compression in the down wind
leg, Fig. [14]. The factored Pt load of 5.5kN/m for half
the structure can be simplified as acting as force F1.
This allows forces T1, C1 to be estimated by statics as
±641kN. Due to the heavy compression exerted on the
deck [4.4.1] by the self-anchored arrangement of the
backstay cables, T1 will not lead to a net tension in the
deck. However, the ±641kN reactions in the line of
each leg of the deck acting at over 10m above the top
of the foundations will generate a pair of opposing
moments in the order of 7MNm each. This necessitates
the use of the torsion boxes discussed in Section [7].
11 Natural Frequency
The natural frequency, f0, of the bridge can be
estimated using Eqn. (11) based on the Rayleigh-Ritz
method for beams, where m is the mass per unit length
and l the length of the beam considered.
!
f0
= "n l( )2EIxx /ml
4Hz. (11)
In order to apply this method to the Nescio, a
number of simplifying assumptions are required. It is
assumed that the deck is prismatic in section; not
curved on plan or elevation and does not bifurcate. It is
also assumed that only the bridge deck contributes to
stiffness. The section geometry chosen as indicative for
the purposes of this analysis is that at mid-span. The
value of
!
"nl( )2 is taken as that of a beam rigidly fixed
at both ends. Taking the values: (!nl)2 = 22.37, Ixx =
0.032, m = 1570kg and l = 170.690m, the value of f0
can be estimated as:
!
fo = 22.37200"10
9" 0.032
1570"170.6904
= 1.54 Hz. (12)
The value of f0 obtained in Eqn. (12) is
significantly below the guideline acceptable value of
f0>5Hz. Therefore, it is necessary to conduct a check
for the most adverse vertical acceleration, a. To be
considered acceptable, a must satisfy the requirement
that:
!
a < 0.5 f 0 m / s2. (13)
Substituting the value of f0 from Eq. (12) into Eq.
(13) it is clear that, in order to be considered acceptable
for vibration:
!
a < 0.5 1.54 = 0.62 m / s2. (14)
The value of a at a given position can be
determined by:
!
a = 4" 2 f0
2ysk# m / s
2.
Where ys is the vertical deflection at mid-span due
to a notional 0.7kN load, k is the span configuration
factor and " is the dynamic response factor due to the
dampening characteristics of the bridge materials. The
value of ys is obtained conservatively from the standard
deflection formula for a simply supported beam:
!
ys =700"170.690
3
48" 200"109" 0.032
= 0.011 m.
The value of " is obtained by extrapolation from
Ref. [5]. Taking the values: f0 = 1.54Hz, ys = 0.011m, k
= 1 and " = 20 in Eq. (15), the value of a mid-span
can be estimated as:
!
a = 4 " # 2 "1.542 " 0.011"1" 20
!
= 20.60 m / s2. (15)
The value of a obtained in Eq. (15) is
unacceptable according to the limiting value obtained
from Eq. (14) as 20.60>>0.62m/s2 and would clearly be
extremely dangerous for bridge users. However, in
obtaining this value of a, it has been assumed that the
bridge acts solely as a beam. In reality, of course, the
parabolic cable arrangement will limit downward
deflections of the deck at the hangar attachment points.
This will interfere with the vibration modes that have
led to the very high value of a, obtained in Eq. (15). If
a is recalculated with the span reduced to that of the
5.048m between hangers, taking " as 5 while f0
remains that for the overall span:
!
ys =700" 5.048
3
48" 200"109" 0.032
!
= 2.931"10#7
m / s2,
!
a = 4 " # 2 "1.542 " 2.931"10$7 "1" 5
!
= 1.37"10#4
m / s2
(16)
Clearly the value of a obtained in Eq. (16)
satisfies Eq. (14) as 0.000137<<0.62m/s2. The actual
value of a will fall between the values obtained in Eqs.
(15, 16). Obtaining a more accurate value of a is
beyond the scope of this paper, but would be necessary
to demonstrate the serviceability of the bridge.
It is worth noting that the value of 1.54Hz for f0
obtained in Eq. (12) is outside of the typical range of
1.6-2.4Hz for pedestrian motion indicated in Ref. [4].
This indicates that normal pedestrian motion may not
excite the bridge deck. However, forced vibration at
1.54Hz would be easy to achieve, making the bridge
susceptible to vandalism. This frequency is also a
concern for wind excitation.
The possibility of Synchronous Lateral Excitation
was also considered by the designers, as indicated in
Refs. [2, 3], and tuned mass dampers are utilized at the
half and quarter span positions to mitigate this effect.
12 Durability
As a steel bridge with concrete approaches,
Nescio’s deck is unlikely to face any particular
durability issues provided that regular maintenance and
repainting is undertaken. Hatches in the top of the deck
provide maintenance access to the void and electrical
cabling.
The structural round steel wires in the main cable
are hot-dip galvanised and the bundle permeated with
zinc paint. A triple layer of profiled and interlocking
outer wires is GALFAN coated to provide additional
corrosion resistance, Ref. [6].
The simplicity of the bearings at the base of the
pylons, discussed in Section [7], minimises the
maintenance required at this point. The complete
separation between the steel deck and the concrete
approaches eliminates many maintenance issues at this
movement joint. However, an issue could arise if the
8mm thick steel cover plate that prevents obstruction or
injury were to be removed or damaged by vandalism or
accident.
13 Intentional Damage
13.1 Graffiti
The concrete columns that support the approach
ramp are the components that would typically be most
vulnerable to defacement by graffiti. However, the
creation of the marshy wetland habitat in the area of
the approach ramp means that columns are typically
positioned in shallow water, discouraging vandals.
The pedestrian stairs at each end of the bridge do
appear to have been used as platforms from which to
graffiti the side of the bridge deck. However, the
painted steel surfaces are easily cleaned or repainted,
minimising the disruptive effect of such vandalism.
Figure 15: Vulnerability to graffiti at stairs.
13.2 Terrorist Action
In order to span efficiently Nescio has, like any
suspension bridge, very limited capacity for
redundancy. Therefore, serious damage to a principle
element such as one of its pylons or back-stay cables
would likely cause failure of the structure. However,
despite being something of a local showpiece, Nescio
is an unlikely target for terrorist action at present.
14 Future Changes
There are unlikely to be any changes to the design
in the foreseeable future. The bridge is relatively new,
having been completed in 2006, and was designed to
be compliant with Eurocodes. As a pedestrian and
cycle bridge, there is unlikely to be any need to
upgrade the capacity of the bridge to meet future
demand. If this were to be required, it is difficult to see
how this would be achieved using the existing
structure.
Tuned mass dampers have been utilised to
mitigate Simultaneous Lateral Excitation and could
presumably be retuned if such effects were found to
continue to occur. Consideration in [3.3] of the tuned
mass dampers as SiDL with !fl of 1.75 allows for
86.7kN of additional load if the dampers are
reclassified as DL with !fl of 1.05.
Addition of further masses would require detailed
analysis of the structure to check that there is sufficient
spare capacity.
15 Suggested Improvements
Overall, this design is a very successful response
to the challenges of the City of Amsterdam’s brief.
There are some, relatively minor, improvements that
this author can suggest could have made the design
even more successful.
Pulling the first concrete ramp-support column
back from the steel end column would relieve the
congestion of vertical components highlighted in Fig.
[7] and remove the need to forlornly ‘hide’ the column
by darkening its colour.
Removing the bifurcation support plate
highlighted in Fig. [5] would restore the order to this
area of the bridge. Compensatory stiffening to the
pedestrian deck would doubtless have been required, as
discussed in Section [2.4]. Nonetheless, the order of
the deck soffit, and lack of functional clarity in the
anomalous hanger detail, would be markedly
improved.
Acknowledgements
The author would like to express his gratitude to
Angus Low at Arup for providing a number of
technical drawings and journal articles without which
this paper would have been very much poorer. The
author would also like to thank Dr Mark Evernden for
his supervision in the preparation of this paper and
Professor Tim Ibell for his invaluable blue book. Any
errors of fact or analysis are doubtless attributable to
this author, while any insights should be credited to the
guidance of the gentlemen mentioned above.
References
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Amsterdam, The Structural Engineer, IStructE, 6th
March 2007, p.22.
[2] Low, A. M., 2008. The Milne Lecture: Designing
Bridges, The Structural Engineer, 87 (5), 3rd
March 2009, pp.26-31.
[3] Low, A., and Ichimaru, Y., 2007. Nesciobrug,
Amsterdam: A Symbol For A New Suburb,
inspirational and functional, Improving
Infrastructure Worldwide: IABSE Symposium –
Weimar 2007, No. 93, pp.242-245.
[4] Melchor Blanco, C., et al., 2005. Structural
Dynamic Design Of A Footbridge Under
Pedestrian Loading, 9th SAMTEC Users
Conference 2005, p.2. Available at:
http://mecanique.in2p3.fr/JUsamtech/proceedings/
02_11_ULB_Bouillard/02_11_ULB_Bouillard.pd
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[5] BD37/01: Loads For Highway Bridges. Design
Manual For Roads And Bridges, Vol. 1, Section 3,
Part 14, Appendix A: Composite Version Of
BS5400.
[6] Pfeiffer, 2007. Fully Locked Cable – GALFAN,
Cable Structures: Data Sheets.
[7] Blake, A., 1990. Practical Stress Analysis In
Engineering Design [2nd Ed.], CRC: Basel, p.24.