Analysis of Bridge Decks – Part 1
Supplementary Notes SN1: Matrix equations
Bridge Engineering : Analysis of Bridge Decks – Part 1
©2024 S Y Chan
Supplementary Notes SN1
• Matrix equation for nodal forces for a 2-D beam element (shear deformation ignored):
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Bridge Engineering : Analysis of Bridge Decks – Part 1
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Supplementary Notes SN1
• Matrix equation for nodal forces for a grillage element (shear deformation and warping
ignored):
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Supplementary Notes SN1
• Matrix equation for nodal forces for a shear-flexible 2-D beam element:
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Bridge Engineering : Analysis of Bridge Decks – Part 1
©2024 S Y Chan
Supplementary Notes SN1
• Matrix equation for nodal forces for a shear-flexible grillage element (warping ignored):
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Bridge Engineering : Analysis of Bridge Decks – Part 1
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Analysis of Bridge Decks – Part 1
Supplementary Notes SN2: Prestress End Block
Bridge Engineering : Analysis of Bridge Decks – Part 1
©2024 S Y Chan
SN2: Prestress End Block
• Contents:
1) Introduction
2) Primary bursting
3) Spalling
4) Equilibrium (vertical, horizontal)
5) Secondary bursting
6) Secondary equilibrium
7) Intermediate anchorage (recess, external rib)
8) Curved prestress tendon
9) Inclined prestress tendon
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Bridge Engineering : Analysis of Bridge Decks – Part 1
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SN2: Prestress End Block: Introduction
• For post-tensioned prestressed concrete bridge deck, large concentrated forces are
transferred from the prestress anchorages to the concrete deck. The prestress forces would
spread out from the anchorages to the whole cross section of the bridge deck, creating high
local stresses on the way.
• The region in which this spread occurs is known as the anchorage zone and that part of the
structure within this zone is known as the anchor block, or prestress end block. This is
basically a D-region where a plane cross-section does not remain plane when subject to the
prestress forces.
• A similar zone occurs as a result of any locally applied concentrated load or reaction (e.g.
at bearing supports, in which case the part of the structure within the D-region is
sometimes called the bearing end block).
• The limit of the D-region is where the spread of the prestress stresses is completed and the
plane cross-section would remain plane under the prestress forces. This is usually taken at
a distance h from the loaded surface of the end block, where h is the depth of the end
block.
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SN2: Prestress End Block: Introduction
• For the case of a rectangular concrete block
subject to a single applied load, the stress pattern
is like this shown. Thick solid and hidden lines
indicate compressive and tensile stress
trajectories respectively.
• The curved compressive stress trajectories may
be considered as struts each carrying part of the
total prestress load. Due to the curvature of the
struts, there are radial resultant forces.
(Figure from CIRIA Guide 1)
• When the curved struts are concave towards the centre line of the end block, the radial
forces are acting outwards, trying to split the end block. The splitting stresses are called
the bursting stresses, and reinforcement should be provided to resist the stresses.
• It should be noted that near the loaded surface, the curved struts are concave outwards thus
causing compressive stresses towards the centre line of the end block and within this zone
there is no need to provide such reinforcement.
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Bridge Engineering : Analysis of Bridge Decks – Part 1
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SN2: Prestress End Block: Introduction
• The distribution of lateral stresses along the centre line of the end block is shown below
(tensile stress positive, compressive stress negative):
(Figure from CIRIA Guide 1)
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SN2: Prestress End Block: Introduction
• The spread of forces occurs on both axes, as
illustrated in the isometric view of a
prismatic prestress end block showing the
measured transverse surface strains on
axially loaded prism:
(Figure from CIRIA Guide 1)
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Bridge Engineering : Analysis of Bridge Decks – Part 1
©2024 S Y Chan
SN2: Prestress End Block: Introduction
(Figure from CIRIA Guide 1)
ft
End block
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Bridge Engineering : Analysis of Bridge Decks – Part 1
Linear stress distribution
• In addition to the bursting stresses, it is
observed that tensile stresses are found at
the loaded surface and also at the side faces
of the end block in the vicinities of the
loaded surface. These stresses would cause
spalling of the concrete surfaces and
therefore reinforcement should be provided
to resist the spalling stresses and to limit
the surface crack width.
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SN2: Prestress End Block: Introduction
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Bridge Engineering : Analysis of Bridge Decks – Part 1
(Figure from CIRIA Guide 1)
ft
End block
Linear stress distribution
• When the prestress force is applied
eccentrically or when there are several
prestress anchorages, two distinct
distributions of stress occur, firstly near
the loaded face and secondly over the
whole cross section of the prestress end
block. The sketch illustrates the principal
stress trajectories in a prestress end block
with three prestress anchorages:
• At a distance from the loaded face
approximately equal to the distance
between the anchorages, the compressive
stress trajectories are parallel. This
location marks the end of the first stress
distribution.
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SN2: Prestress End Block: Introduction
• In this example, the second distribution is
not very pronounced, but generally it is
necessary to check the overall equilibrium of
the end block because the stress pattern at
the end of the first distribution is not yet a
linear stress distribution across the whole
cross section of the end block, and the
second distribution is required to achieve
this. The reinforcement which is required
for the overall equilibrium of the prestress
end block is called the equilibrium
reinforcement.
(Figure from CIRIA Guide 1)
• In a similar way in considering vertical equilibrium of the end block, the overall
horizontal equilibrium of the top and bottom flanges of a flanged deck cross section
should also be considered.
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SN2: Prestress End Block: Introduction
• For non-rectangular anchor blocks,
engineering judgment has to be
exercised. In a flanged member in which
the anchorages are located in the web
only, there is, in addition to the
distribution of stresses in the vertical
plane, a horizontal distribution of stress
in the flange from its intersection with
the web (ref. CIRIA Guide 1 Section
4.3). This is secondary bursting.
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Bridge Engineering : Analysis of Bridge Decks – Part 1
× flange thickness
(Figures modified from CIRIA Guide 1)
©2024 S Y Chan
SN2: Prestress End Block: Introduction
• Sometimes, near the prestress anchorages, the bridge deck cross section is strengthened
to take the high prestress stresses and/or the high support reactions. This may involve
converting a voided cross section to a solid section. When this is the case, there will be
further stress distribution due to the geometric change, and we have to consider:
1) secondary equilibrium for anchor block spanning vertically between top and bottom
flanges (ref. CIRIA Guide 1 Section 4.2) and/or
2) secondary equilibrium for anchor block spanning horizontally between anchorages as
necessary.
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Bridge Engineering : Analysis of Bridge Decks – Part 1
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SN2: Prestress End Block: CIRIA Guide 1
• The following design approach for prestress end block reinforcement design (similarly
applicable to bearing end block design) is based on CIRIA Guide 1 “A guide to the design
of anchor blocks for post-tensioned prestressed concrete” (June 1976). Please refer to the
document for further details.
• There are, however, departures from the recommendations of CIRIA Guide 1 in:
1) Section 3.3 of CIRIA Guide 1: The reduction factor K is not adopted as in most cases,
the tendons of a tendon group are not stressed simultaneously.
2) Section 3.3 of CIRIA Guide 1: In line with BS5400 Part 4, the strain limitation of
0.001 is only adopted in spalling reinforcement but not in bursting reinforcement
(unless such reinforcement is close to concrete surface like spalling reinforcement)
3) Section 4.3 of CIRIA Guide 1: ‘flange thickness’ is added to the equation for Pf
4) Section 4.4 of CIRIA Guide 1: The amount of longitudinal reinforcement at the edges
of anchorage pocket is based on 0.25Pk instead of 0.5Pk (ref. IABSE SED1 ‘Concrete
Box Girder Bridges’, page 91)
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SN2: Prestress End Block: Primary Bursting
• The first step in design for primary bursting is
determination of dimensions of primary prisms.
• Each of the two orthogonal planes (vertical and
horizontal) of a prestress anchorage in a
rectangular prestress end block should be
considered in turn. For the plane under
consideration, the dimension 2yo of the primary
prism should be taken as twice the smaller of
the two following dimensions:
1) the distance from the line of action of the force to
the nearest concrete side face
2) half the distance between the line of action of the
force and the line of action of its nearest neighbour
(for the case of multiple prestress anchorage on the
same loaded face of the end block)
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Bridge Engineering : Analysis of Bridge Decks – Part 1
(Figures from CIRIA Guide 1)
©2024 S Y Chan
SN2: Prestress End Block: Primary Bursting
• As the stressing sequence of the prestress anchorages may vary on site, it is prudent to
consider all possible scenarios during the stressing of the anchorages, when some
anchorages have not yet been stressed and these unstressed anchorages should be ignored
in the consideration of the dimension of the primary prism of an already stressed
anchorage.
• For the plane under consideration, the design bursting force Fbst in the primary prism of an
anchorage can be determined from the following table (from CIRIA Guide 1):
ypo / yo
≤0.3
0.4
0.5
0.6
≥0.7
Fbst / Pk
0.23
0.20
0.17
0.14
0.11
where 2ypo is the length of the side of the loaded area of the anchorage and Pk is equal
to the highest load which will be applied to the anchorage (usually this is taken as 1.10
times the jacking load, to allow for any over-stressing on site).
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Bridge Engineering : Analysis of Bridge Decks – Part 1
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SN2: Prestress End Block: Primary Bursting
• For circular anchorages or bearing plates, the value of 2ypo can be obtained from an
equivalent square having the same loaded area.
• Intermediate values of Fbst/Pk are obtained by interpolation from the table values.
• When groups of anchorages are used, the bursting force may be reduced by a factor.
However, in usual cases this is ignored as the prestress forces in the anchorages are not
applied simultaneously.
• Effectively bonded reinforcement should be provided to resist the bursting force at a stress
of 0.87fy. The reinforcement should be distributed in a region extending from 0.2yo to 2yo
from the loaded face.
• The above exercise should be repeated for the other orthogonal plane. As the situation
may be different in the two planes, the greater steel requirement in both planes is usually
taken for the reinforcement design to simplify detailing.
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SN2: Prestress End Block: Primary Bursting
• It has been found that helical reinforcement or
closed rectangular links made up into box cages
are more efficient in taking the bursting stresses
than mat reinforcement placed at right-angles to
the axis of the prestress force. For rectangular
links, they should have internal bend radii of 5
times bar size and should be closed with full
tension lap. The size of the spiral or link should be
at least 50 mm greater than the size of the loaded
area of the anchorage in order to be effective.
• When the bursting reinforcement bars are not
placed at right angles to the axis of the prestress
force (for example, vertical links are provided but
the prestress force is inclined), the steel area may
have to be adjusted accordingly when the
deviation is significant.
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Example of rectangular links against bursting
Bridge Engineering : Analysis of Bridge Decks – Part 1
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SN2: Prestress End Block: Spalling
• The primary prism for bursting
design is always a symmetrical
prism, as the prism dimension 2yo is
taken as twice of the smaller of:
1)
2)
the distance from the line of action of the
force to the nearest concrete side face
half the distance between the line of action
of the force and the line of action of its
nearest neighbour (for the case of multiple
prestress anchorage on the same loaded face
of the end block)
(Figure modified from CIRIA Guide 1)
• Spalling design, however, takes a slightly different approach for the prism size. The edge
of prism at one side of the line of action of the force is determined by either 1) or 2),
whichever is applicable. The prism may, therefore, be unsymmetrical as indicated in red
outlines above.
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SN2: Prestress End Block: Spalling
• Effectively bonded reinforcement bars should be provided near the loaded face of the end
block to withstand a basic spalling force of 0.04Pk in either orthogonal direction.
• In addition, if the configuration of the anchorages is such that the prestress force acts on an
unsymmetrical prism, additional reinforcement should be provided to resist the additional
spalling force due to unsymmetrical prism when d1>2d2 where d1 and d2 are the larger and
smaller dimensions from the line of action of the force to the boundaries of the nonsymmetrical prism, equal to 0.2[(d1 – d2) / (d1 + d2)]3 Pk
• In order to limit the crack width at the concrete surface, the steel strain should not exceed
0.001. For reinforcement bars with a modulus of elasticity of 200kN/mm2, this is
equivalent to a steel stress limit of 200MPa. The reinforcement area is therefore obtained
by dividing the spalling force (basic + additional due to unsymmetrical prism where
appropriate) with 200MPa.
• Again, all possible scenarios of the stressing of the prestress anchorages should be
considered in checking for unsymmetrical prisms.
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SN2: Prestress End Block: Vertical Equilibrium
• The previous section on primary bursting only deals with the stresses in the primary
prisms. It is also necessary to consider the overall equilibrium of the end block and to
provide additional reinforcement as required.
• The method is to isolate the end block
(which is a square having the length equal
to the depth), with anchorage forces
acting on the loaded face and a linear
stress distribution acting at the other face,
and obtain the bending moment M and
shear force Vh acting on the horizontal
cross sections of the end block, as
illustrated:
(Figure from CIRIA Guide 1)
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Bridge Engineering : Analysis of Bridge Decks – Part 1
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SN2: Prestress End Block: Vertical Equilibrium
(Figure from CIRIA Guide 1)
• The concept is more easily visualized by rotating the whole
end block 90 degrees so that the face with linear stress
distribution is on top and the loaded face with anchorage
forces is at the bottom; the linear stresses now become the
“loads” and the anchorages become the “supports”.
• Since the prestress anchorages are stressed sequentially, and
also the stressing order may be varied on site, checks should
be carried out for all possible scenarios to obtain the most
critical values of M and Vh.
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Prestress end block
ft
fb
• The design approach is the same for prestress end block with multiple anchorages:
Linear stress
distribution
ft
End block
Linear stress
distribution
End block
fb
(Figure from CIRIA Guide 1)
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SN2: Prestress End Block: Vertical Equilibrium
• After the critical bending moments and shear forces are obtained, reinforcement in the
form of effectively anchored links are provided within the regions (either 0.25h from
loaded face, or 0.5h from back of end block) illustrated below, depending on whether the
bending moment is “hogging” or “sagging”, as illustrated:
(Figures modified from CIRIA Guide 1)
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SN2: Prestress End Block: Vertical Equilibrium
• The reinforcement area required to resist the moment M is obtained by assuming that the
lever arm of the resisting couple is equal to half the length of the end block (i.e. 0.5h). The
reinforcement area should not be less than 0.3% of the horizontal cross section over the
full length of the block. The reinforcement should be in the form of closed links running
the full height of the end block.
• The reinforcement area required to resist the shear force Vh is obtained by checking the
horizontal shear stress against (2.25 + 0.65ρ fy) MPa, where ρ = As/bh and As is the total
area of effective reinforcement crossing the plane under consideration.
• The same bar may be counted both in checking for moment M and also in checking for
shear Vh.
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SN2: Prestress End Block: Secondary Bursting
• For the purpose of designing the end block reinforcement for the horizontal flow of prestress stress
into flanges (sometimes called secondary bursting),
consider the total force Pf flowing into the flange
[Pf = bt(fct+fcb)/2 where b and t are flange width
and thickness respectively, and (fct+fcb)/2 is average
stress in flange at distance b from loaded face], and
assuming that the force acts on a width bw at the
loaded end of the flange. The reinforcement
should be distributed over the region between 0.1b
and b measured from the loaded face. If the overall
depth of the flanged member, h, is greater than b,
then the reinforcement should extend to a distance
h from the loaded end. The reinforcement should
be in the form of horizontal bars provided at the
top and bottom faces of the flange.
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Bridge Engineering : Analysis of Bridge Decks – Part 1
× flange thickness
(Figures modified from CIRIA Guide 1)
(extend the
computed
reinforcement
to a distance h
from the loaded
end if h>b)
©2024 S Y Chan
SN2: Prestress End Block: Secondary Equilibrium
• Anchor block spanning vertically between top and
bottom flanges (ref. CIRIA Guide 1 Section 4.2): For
flanged structure which has a solid anchor block, such
as rectangular anchor block at the end of an I-beam,
or solid end diaphragm at the end of a cellular deck,
lateral tensile stresses occur near the change of
section. This is because the majority of the prestress
load on the anchor block is carried by the flanges and
the block effectively acts as a deep beam spanning
vertically between the top and bottom flanges.
When designing the vertical reinforcement for this secondary vertical equilibrium, either a
deep beam approach or a strut-and-tie approach may be adopted. When the steel
requirement is less than that obtained from the equilibrium check in Vertical Equilibrium,
no additional reinforcement is required. Otherwise, additional steel should be provided,
again in the form of vertical links running the full height of the block, and uniformly
distributed over a distance of 0.2h from the interface with the flanged section.
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Bridge Engineering : Analysis of Bridge Decks – Part 1
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SN2: Prestress End Block: Secondary Equilibrium
• Anchor block spanning horizontally between anchorages: This is also for flanged structure
which has a solid anchor block (as above), but this time, the anchor block is assumed to be
spanning horizontally between the anchorages, whereas the forces in the flanges are
considered as the “loads” acting on the anchor block. Horizontal reinforcement are
provided at the two vertical faces of the anchor blocks to resist the “hogging” or “sagging”
moments.
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SN2: Prestress End Block: Intermediate Anchorage
• When a prestress anchorage is not located at the end of a bridge deck but somewhere along
the deck length, local recess or blister has to be formed in the deck cross section to
accommodate the prestress anchorage. In the vicinity of the recess or blister, special
reinforcement has to be provided to resist the local high stresses, as illustrated in the
following slides (ref. CIRIA Guide 1 Section 4.4).
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Bridge Engineering : Analysis of Bridge Decks – Part 1
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SN2: Prestress End Block: Intermediate Anchorage
• For anchorage in a recess, tensile stresses are
produced in the prestressing direction
immediately beside the recess. If the overall
compression due to prestressing of the deck is
adequate such that the net stress is
compressive, then there is no need to provide
special longitudinal reinforcement.
• Nevertheless, it is recommended to provide
some additional longitudinal reinforcement
which is capable of carrying at least 0.25Pk
and should be fully anchored, in addition to
the usual reinforcement against bursting.
(Figures from CIRIA Guide 1)
• The amount of lateral reinforcement against bursting should be determined as for an endloaded prism. It can be in the form of a spiral (helical reinforcement), with additional
lateral reinforcement to transfer the load to the longitudinal bars.
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SN2: Prestress End Block: Intermediate Anchorage
• For anchorage on an external blister, similar
longitudinal reinforcement is required.
However, because the tendon is now curved,
there is a lateral component of load which
must be resisted by additional reinforcement
anchored back into the main body of the
(Figure from CIRIA Guide 1)
structure.
• A detailed strut-and-tie model analysis of a prestress blister is given in CEB Bulletin No.
150 “Detailing of concrete structures” (written in German)
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Bridge Engineering : Analysis of Bridge Decks – Part 1
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SN2: Prestress End Block: Intermediate Anchorage
(Figures from CEB Bulletin No. 150 ‘Detailing of Concrete Structures’)
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SN2: Prestress End Block: Curved prestress tendon
• A curved prestress tendon gives rise to radial force of P/R kN/m, where P kN is the
prestress force and R m is the radius of curvature. This is nothing new, as it has been
discussed in Leonhardt’s “Prestressed Concrete Design and Construction” in 1964.
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Bridge Engineering : Analysis of Bridge Decks – Part 1
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SN2: Prestress End Block: Curved prestress tendon
• The radial force is seldom a concern when the curvature is gentle as the magnitude of the
radial force is inversely proportional to the radius of curvature.
• For prestress tendon with sharp curvature, such as the curvature introduced to bring the
tendon inside a web to meet an anchorage, special reinforcement in the form of horizontal
shear links across web thickness [As = (P/R)/(0.87fy)] is needed to avoid concrete cracking.
Horizontal tendon profile with S-curve comprising two arcs
(this type of profile is also suitable at anchorage coupling)
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SN2: Prestress End Block: Curved prestress tendon
• This shows an alternative horizontal tendon profile using a single arc instead of a S-curve
consisting of two arcs as shown in the previous example. With a single arc, the radius is
increased and the radial force is reduced. However, the main reason of using a single arc
is to reduce the large friction loss associated with a S-curve. With this alternative
arrangement, the anchorage has a horizontal inclination to the concrete end face.
Alternative horizontal tendon profile with single arc
(This type of profile is unsuitable at anchorage coupling)
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SN2: Prestress End Block: Inclined Prestress Tendon
• When the anchorage of a prestress tendon is not set perpendicular to the concrete end face,
apart from the ‘normal’ component of the prestress force which has been adequately
covered in CIRIA Guide 1, there is a ‘shear’ component which acts along the concrete
face.
• In a similar way as transmission of horizontal bearing load through horizontal
reinforcement bars placed in the vicinity of the bearing base (ref. BS5400 Part 4 Clause
7.2.3.4), it is suggested that reinforcement bars should be provided near the concrete end
face for the transmission of the ‘shear’ component of prestress force to the concrete.
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SN2: Prestress End Block: Example of rebar detailing
• This shows the rebar detailing
of a prestress end block of a
prestressed multicellular bridge
deck constructed in the 80’s.
Noting that there is room for
improvement in the detailing, it
is shown here solely to illustrate
the provision of bursting and
spalling reinforcement and also
the reinforcement for curved
tendon.
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SN2: Prestress End Block: Worked Examples
• Please refer to CIRIA Guide 1 Section 8.
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SN2: Prestress End Block: Designs to Eurocode 2
• Please refer to BS EN 1992-2:2005 Section 8.10 “Prestressing tendons” and Annex J. The
principle of using strut and tie model (or other appropriate representation) for the analysis
of the end block region remains the same but there are some changes in the design
parameters.
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Bridge Substructures
Bridge Engineering : Bridge Substructures
©2024 S Y Chan
Introduction
• The usual types of bridge substructures include the following:
1) Abutment
2) Pier
3) Pile cap and piles
4) Spread footing
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Bridge Engineering : Bridge Substructures
©2024 S Y Chan
Introduction
• The following sketches (extracted from SED 1e ‘Concrete Box-Girder Bridges’ - Schlaich
& Scheef) illustrate the various typical components of a bridge:
Foundation (also part
of Substructure)
1 spread footing
2 pile cap
3 bored piles
4 driven piles
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Bridge Engineering : Bridge Substructures
Substructure
Superstructure
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
box abutment
spill-through abutment
column, pier
breast wall
wing wall
back wall
edge masking wall
front masking wall
bridge seat
support wall
bridge seat beam
access chamber
bearing (fixed or sliding)
deck movement joint
diaphragm
box-girder web
top slab
top cantilever slab
bottom slab
fascia beam
guard rail, safety fence
railing
waterproofing system
deck surfacing
drainage gully
cross drain
longitudinal drain
©2024 S Y Chan
Abutment
• Abutment is usually provided at the boundaries between the elevated and ground level
portions of a road/railway; the elevated portions are the bridges and the ground level
portions are the at-grade roads.
• Since the construction and maintenance costs of an earth embankment of reasonable height
is much cheaper than that of a bridge of the same elevation, it is generally more costeffective to place abutments in such locations so as to minimize the length of the bridge
superstructure.
• Broadly speaking, there are two types of bridge abutment: wall abutments and open
abutments.
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Bridge Engineering : Bridge Substructures
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Abutment
• A wall abutment is in fact a retaining wall that
supports the bridge deck (usually through
bearings) in addition to retain soil behind the wall.
• An open abutment is designed to mainly support
the bridge deck but is not normally expected to
retain soil. Stability of earth embankment at the
open abutment is usually maintained by a well
compacted slope.
• The above sketches were extracted from Building Research Establishment Report ‘Bridge
foundations and substructure’ by Dr E C Hambly, which contains detailed discussions on
the various types of wall abutments and open abutments.
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Bridge Engineering : Bridge Substructures
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Abutment Design
• The front wall of an abutment that is supporting a bridge
deck via pot bearings should be checked for the local
stress effects in a similar manner as a prestress end
block, in addition to the normal checking for lateral earth
and water pressures as a typical retaining wall.
• Also, it is important
that adequate
reinforcement is
provided for
horizontal bearing
loads.
• An example of
reinforcement
details of abutment
wall is shown.
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Bridge Engineering : Bridge Substructures
©2024 S Y Chan
Abutment Design
• Run-on slab (also known as ‘transition slab’, ‘approach slab’) has been provided in the
past as a transition between the relatively rigid bridge deck and the earth embankment
behind the abutment wall, to span across any differential settlement of the carriageway
there.
• This sketch shows an
exposed type, with only
road surfacing on top.
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Bridge Engineering : Bridge Substructures
©2024 S Y Chan
Abutment Design
• However, the run-on slabs are often damaged and maintenance of a run-on slab is usually
difficult, especially when it lies on a busy road. The current practice in Hong Kong is to
provide run-on slab only for concrete pavement but not for flexible pavement.
• This sketch shows an
exposed type, with only
road surfacing on top.
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Bridge Engineering : Bridge Substructures
©2024 S Y Chan
Abutment Design
• Run-on slab design should aim to achieve its function: the length should be adequate to
span across the area susceptible to significant long-term settlement, the thickness and
reinforcement should be adequate to carry the design actions, and there should be a hinge
connection with the abutment to allow the run-on slab to rotate. Run-on slab can be either
exposed or buried. A buried type is less preferred as maintenance inspection and repair
will be difficult.
• This sketch shows an
exposed type, with only
road surfacing on top.
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Bridge Engineering : Bridge Substructures
©2024 S Y Chan
Abutment Design
• The assumed support conditions of an abutment wall under lateral loads must reflect the
actual situation. An abutment wall with monolithic wing walls set at right angles to the
abutment wall should not be considered as a free cantilever wall in the design as there will
be substantial horizontal bending moments due to the monolithic connection with the wing
walls.
Abutment wall
Wing wall
(Figure extracted from IASBE SED1)
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Abutment Design
• In the 90’s, in order to eliminate the maintenance and water seepage problems associated
with deck movement joints, integral abutment bridges (or integral bridges, or more
commonly called as jointless bridges in USA) have been introduced. Integral bridges have
monolithic connections between bridge superstructure and abutments. In UK, BD57/01
Section 2.3 requires that bridges with lengths not exceeding 60m and skews not exceeding
30° shall generally be designed as integral bridges (ref. BA42/96) except when such
integral construction is not appropriate, e.g. large differential settlements are anticipated.
(Extracted from BA42/96)
(Extracted from BD57/01)
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NOTE: BA42/96 has been
withdrawn and BD57/01 has been
superseded by CD 350 ‘The design
of highway structures’, which
contains similar requirement: ‘All
bridges with a skew angle up to 30
degrees or 60m length or less shall
be designed as integral bridge
structures’.
©2024 S Y Chan
Pier
• As contrary to abutments which are provided at the ends of a bridge deck, piers are
provided along the length of the bridge at suitable spacing to support the bridge deck.
• The bridge piers are usually provided with bearings at the top to permit lateral translations
of the bridge deck due to thermal contraction/expansion, shrinkage (for concrete deck)
and/or creep (for prestressed deck), and to allow adjustment of deck levels in case of
excessive settlement of bridge foundations. However, for tall and long span bridges
especially those constructed by balanced cantilever method, the piers are sometimes
designed to be monolithic with the bridge deck.
Standard 8-span module of
prestressed concrete viaduct of
Shenzhen Western Corridor
pier with sliding bearings & movement joint
pier with sliding bearings
pier monolithic with bridge deck
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Pier
• Examples of pier shapes:
Above figures are extracted from IABSE SED1
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Bridge Engineering : Bridge Substructures
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Pier Design
• In general cases, bridge pier with bearings at the bottom should be avoided:
1) The bearings, being at ground level, will be exposed to more aggressive environment
than if they are placed on top of piers. Sliding surfaces of bearings will be easily
damaged in the event of flooding of ground, when grits carried by flood water
penetrate the gap between the PTFE and stainless steel sliding plate.
2) For bridge pier with bearings at both ends (i.e. hinged at top and bottom), temporary
propping is necessary to maintain stability of the pier during construction and also
during bearing replacement in future.
3) For bridge pier with bearings at bottom and monolithic connection with the deck at top,
the usual methods for the design of bridge deck are not applicable due to frame action
of the pier and the deck. A 3-D structural model is needed.
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Pier Design
• For bridge piers located in drainage channels, the piers should generally be designed for
the least obstruction to water flow. But of course, the best solution is to span the bridge
across the drainage channel if this is practical.
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Pier Design
• For bridge piers located on or near navigation channels, the piers should either be designed
for the ship collision forces or protected by suitable collision protection measures.
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Bridge Engineering : Bridge Substructures
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Pier Design
• For bridge piers situated near road junctions or bends, the piers should be set back from
the carriageway to provide the minimum visibility sight distances as required in the
Transport Planning and Design Manual or other relevant design manuals. For examples:
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Pier Design
• The top end of pier under bearing loads should be designed in a similar manner as
prestress end block to cater for the load dispersion effects from the bearings, unless the
bearing contact pressure is comfortably low.
• For pier with two bearings (particularly for flared pier), adequate horizontal reinforcement
should be provided to resist the horizontal tension caused by the vertical bearing loads. In
addition, adequate horizontal reinforcement should be provided at the pier top surface for
any transverse and/or longitudinal bearing loads.
(Extracted from IABSE SED1)
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Pier Design
• The lower part of the pier, where linear strain
condition is met, should be designed with
coexistent sets of P, Mx, My, Hx and Hy. For
bridge piers, the critical loading set is usually
the one with minimum P and maximum Mx,
My. (i.e. critical mode is failure in tension this is contrary to the columns of tall buildings
which would fail in compression). This is
illustrated in a typical column design chart
extracted from BS 8110-3:1985
• At the bottom part of pier where bending moment is highest, it is usually necessary to
avoid congestion of reinforcement by using couplers or staggering laps. Clear distance
between lapped bars should not be greater than 4∅ or 50mm for most effective lap [BS EN
1992-1-1:2004 Section 8.7.2].
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Pile Cap and Piles
• BS5400 (and Eurocode 2, BS EN 1992-1-1:2004 Section 9.8.1) allows pile cap design to
be based either on simple bending theory or strut-and-tie method. Strut-and-tie method
should be used whenever practical, since it is able to simulate the actual stress trajectories
in the pile cap more accurately than simple bending theory. However, for pile cap with
complicated pile configuration, the strut-and-tie method may be difficult to use and the
simple bending theory may be more convenient.
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Pile Cap and Piles
• For important pile caps, finite element analysis may be used. In the finite element model,
a sufficient height of the bottom part of pier which is within the ‘D’ region should be
included, in addition to the pile cap and the piles. Otherwise the analysis may produce
unreasonably high stresses in the pile cap near the pier/cap interface, resulting in overdesign of the pile cap.
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Bridge Engineering : Bridge Substructures
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Pile Cap and Piles
• Nowadays, the pile connection with pile cap is typically assumed to be monolithic and
capable of moment transfer. Lateral load acting on the pile cap is resisted by the frame
consisting of the pile cap and the piles, which can be all vertical piles without any raking
piles. The pile head details require special attention in this case, to ensure that the assumed
moment transfer between pile cap and pile can actually occur.
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Pile Cap and Piles
• Avoid noisy driven piles if the site is close to noise sensitive areas (e.g. hospital, school) or
otherwise temporary noise barriers should be installed. Some recent pile driving
equipment has built-in silencer or uses hydraulic hammer/press-in systems to address this
noise concern.
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Pile Cap and Piles
• Hand-dug caissons had been used extensively in Hong Kong in the past, due to the
technical and financial benefits associated with this construction method. However, high
accident rate and health hazards posed to workers have caused concerns and the method
has been generally banned from use in Hong Kong by Works Branch Technical Circular
No. 9/94 (now incorporated in Project Administration Handbook for Civil Engineering
Works, 2022 Edition, Chapter 4 Section 4.6.7), except where the use of hand-dug caissons
is the only practical solution or there is no safe engineered alternative and all necessary
precautionary measures are taken to safeguard workers against accidents and health
hazards.
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Pile Cap and Piles
• On restricted site, the limited space available may not be adequate for spread footing. In
such case, a pile cap with a small number of large diameter piles may be the only solution.
A pier supported on a single large diameter pile is not uncommon.
Example of pier supported on single pile without pile cap
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Pile Cap and Piles
• For pile design,
1) The vertical and horizontal capacities of pile are checked in turn.
2) In checking vertical load capacity, include positive/negative skin friction.
3) Horizontal load capacity is usually analysed by model beam on horizontal soil springs.
4) Adequate corrosion protection (by protective coating, sacrificial thickness, or cathodic
protection etc.) should be provided to the pile if the site is aggressive (e.g. high
sulphate content or low pH value). (Ref. GEO Publication No. 1/2006 “Foundation
Design and Construction” Section 6.14.)
5) Avoid raking pile whenever practical, as the installation of the pile would be difficult
and any ground settlement after pile construction will induce loading on the raking
pile.
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Spread Footings
• Spread footings are not popular in Hong Kong, probably because of the limited space
available for the foundation works, particularly when the site is located in the urban
districts.
• Also, the presence of water main in the vicinity of a spread footing could impose severe
threat to its long term stability as any leakage in the water main could erode the foundation
soil beneath the spread footing and cause bearing failure of the footing.
• Nevertheless, when space is adequate and when bed rock level is close to ground level,
spread footing is sometimes a good solution.
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