the power of prestressing j. strasky

The power of prestressingJ. Strasky

The idea of prestressing—a product of the twentieth century—has announced the single most significant new

direction in structural engineering of any period in history. It put into the hands of the designer an ability to control

structural behaviour and, at the same time, it enabled the designer—or forced thedesigner—to think more deeply

about the construction. Moreover, the idea of prestressing opened up new possibilities for a form that influences

the general culture. To focus on that fact, and to narrow the scope, the paper will consider bridges only, even

though prestressing has broad applications to all kinds of buildings. However, the idea of prestressing arose out of

bridge design, and its most impressive forms, from a purely engineering viewpoint, have appeared in bridges.

Introduction

While reinforced concrete combines concrete

and steel bars by simply putting them together

and letting them act together as they may

wish, prestressed concrete combines high-

strength concrete with high-strength steel in

an active manner. The prestressing allows us

to balance the load, change boundary condi-

tions and create supports within the structure.

Prestressing is really a revolution. Prestressing

is a radical step from passive reinforcement to

creative thinking and development.

Modern concrete structures combine rein-

forced concrete with different levels of post-

tensioning in order to obtain the most appro-

priate behaviour of structures, both for service

and ultimate load.1 In this way, so-called

‘structural concrete’ is developed.

By post-tensioning structures, we can redis-

tribute internal forces within the structure and

achieve any stage of stress. But we have to be

careful. In contrast to steel structures, the cho-

sen stage of stress is redistributed in time by

the creep of the concrete to the natural stage

of concrete structures. And, of course, the

alignment of prestressing tendons is influ-

enced by the requirements on the ultimate

capacity and the ductility of the structures.

This paper focuses on some problems that

are connected with finding the correct struc-

tural solution and the corresponding arrange-

ment of prestressing steel. In the examples of

several structures, the possibilities of post-ten-

sioning are presented and they serve to remind

us of the outstanding structures that use pre-

stressing in a non-traditional way.

The paper includes some structures where

the author worked on the design, and these

show the author’s approach to the design of

structures, which is developed from an

attempt to understand the structural beha-

viour and to find the most appropriate solu-

tion.

Load balancing

The design of structures is based on the full

understanding of the function of post-tension-

ing, both during the post-tensioning service

and in the ultimate limit state. During the

post-tensioning, the structure is loaded by an

equilibrium of forces. Owing to the creep of

concrete, the original stage of stress can

change significantly in time. The importance

of this phenomenon is presented in the follow-

ing example.

Figure 1 shows a simple beam with a span

length of 12 m, which was, after 14 days of

curing, suspended at mid-span on a very stiff

1464^4177 � 2003 Thomas Telford and fib

Jiri StraskyTechnical University ofBrno, and Strasky Hustyand Partners, Brno,Czech Republic

Figure 1 Redistribution of bending

moments in a two-span beam "

stay cable (EA¼ 1). Before suspending, a

force S was created at the cable. The value

of force S was S¼ 0, S¼ R and S¼ 2R,

where R is a reaction at the intermediate sup-

port of a continuous beam of two spans

2� 6 m.

The time-dependent analysis was per-

formed for the old Morch and CEB-FIP creep

function. In the course of time, a significant

redistribution of the bending moments

occurred for S¼ 0 and S¼ 2R. The course of

the bending moments is changing towards the

course of the bending moments of a two-span

beam. Concrete is a natural material and,

therefore, the structure tries to behave natu-

rally—as a continuous beam. In this case, a

redistribution of stresses is larger for the old

Morch creep function.

It is important to realise that for the force

S¼ R, there is no redistribution of stresses in

time for both creep functions. The structure

keeps its shape and the stresses are constant

in time. Their values do not depend on the

adopted creep function.

Since it is difficult to design a structure in

which the stresses are changing in time, it is

very important to design an initial stage in such

a way that the redistribution of stresses is mini-

mal. That means that the geometry and forces

in the internal prestressing tendons or external

cables (situated inside or outside the perimeter

of the deck) have to be determined in such a

way that their effects, together with the dead

load, create zero deflection at deviators (see

Figure 2). It means that the dead load should

be balanced by prestressing. Then the struc-

ture that is loaded only by a normal force

keeps its shape in time. This approach, which

was developed by Professors F. Leonhardt2

and T. Y. Lin,3 simply guides us to use partial,

limited or full prestressing. The importance of

the load balancing was again proved by Pro-

fessor R. Favre.4

If the deck is suspended on arches or

pylons, the initial forces in the stay or suspen-

sion cables have to be determined from the

condition of zero deflection of the deck at

the anchor points—see Figure 3.

The attempt to limit the redistribution of

stresses caused by the creep of concrete forces

us to design a correct structural system and

prevents us from designing fancy structures

that are very common in steel at present. In

~ Figure 2 Balancing of the dead load in a two-span beam: (a) by internal tendons;

(b) by external cables situated within the perimeter of the cross-section; and (c) by

external cables situated outside the perimeter of the cross-section. g= uniform dead

load; G = resultant of the dead load; P= prestressing force; r= uniform radial forces from

prestressing; Rp = radial force from prestressing at support; R= radial force from

prestressing

~ Figure 3 Balancing of the dead load: (a) arch structure; (b) cable-stayed structure;

(c) suspension structure; and (d) equivalent continuous beam. G= resultant of the dead

load situated between two cables; S= force in the cable; HL = resultant of the horizontal

forces left to the pylon; HP = resultant of the horizontal forces right to the pylon

26 Strasky

Structural Concrete� 2003 � 4�No 1

contrast to steel structures, we are not able to

design the structures in which a beam is

suspended on stay cables, stressed to a small

or large force, and so create an un-

natural structural system developed by an

architect.

The following subsections demonstrate

how a full understanding of prestressing

enables us to solve the problems of finding

the best structural solution that is inherent in

the site and which best fulfils the function of

bridging the site.

Hoechst Bridge, Frankfurt, Germany

The Hoechst Bridge, which was designed and

built by Dywidag, is one of the first modern

concrete cable-stayed bridges (Figure 4).5 It

was built across the River Main close to Frank-

furt and carries a railway and a motorway. The

deck, which is formed by a box girder with

large overhangs, is suspended on a single

pylon situated on one bank of the river and

it is stiffened by a low concrete wall situated

above the pier on the other bank. A hinge is

created between these two parts of the deck

(Figure 5).

The forces in the stay cables are designed in

such a way that they exactly balance the dead

load of the deck in the length between the

neighbouring stays. Similarly, the prestressing

of the wall is designed so that it balances the

dead load (see Figure 5). By a clever combina-

tion of the external prestressing created by the

stay cables and the internal prestressing of the

wall, it was possible to reduce the length of

the suspended portion of the deck and the

height of the pylon. The solution opened up

the view onto the river and created an

impressive structure that fits into nice sur-

roundings.

Viaduct near a shopping centre inHradec Kralove, Czech Republic

Swiss engineers have developed a strip post-

tensioning of flat slabs. The prestressing ten-

dons that are arranged in the support strips

create support strips of zero deflection in the

structure. A similar approach can also be used

in bridges. An advantage of this arrangement

has been demonstrated in a recently com-

pleted bridge built in the Czech Republic.

The bridge, 238 m long, is formed by a

continuous deck slab of 13 spans, which

range in length from 12 to 19 m. The deck

slab, which is 0.90 m deep and varies in

width from 12.30 to 14.30 m, is supported

by two pot bearings situated on narrow piers

(Figure 6).

Owing to the difficulties in obtaining the

building permission, the bridge had to be

designed and built within 15 weeks. There-

~ Figure 4 Hoechst Bridge, Frankfurt, Germany

~ Figure 5 Hoechst Bridge—balancing of the dead load (units in m)

The power of prestressing 27


fore, a traditional span-by-span construction,

which requires progressive casting and post-

tensioning of each span, was impossible. The

deck had to be cast in a few stages only, and

progressive longitudinal post-tensioning of the

deck had to be substituted by reinforcement

using reinforcing bars.

To allow a very simple reinforcement

formed by uniformly distributed straight rebars

and stirrups, a transverse post-tensioning of

the structure above the piers was designed.

The concept of the transverse post-tensioning

came from the idea of the post-tensioning of

the flat slab. The transverse post-tensioning

was created in such a way that there was no

deformation in the transverse strips above the

support.6 From Figure 7 it is evident that the

transverse post-tensioning can create a similar

distribution of longitudinal bending moments,

as it is supported by several bearings in the

structure.

Sunniberg Bridge, Switzerland

Sunniberg Bridge, whose concept was devel-

oped by Professor Menn, is one of the clever-

est structures ever built. The bridge has five

spans, ranging in length from 59 to 134 m,

and a plan curvature with a radius R= 503 m

(see Figures 8 and 9(b)).7,8 The slender deck,

running at 60 m above the grade, is suspended

on pylons protruding 15 m above the deck.

The stiffness of the structure comes from

the plan curvature of the deck, which is fixed

at the abutments (Figure 9(a)). While in the

traditional multi-span cable-supported struc-

tures, vertical deflection of the deck has to

be controlled by intermediate anchor piers or

by the bending stiffness of the deck, in this

bridge the vertical deformation of the deck is

controlled by the transverse stiffness of the

curved deck. Any vertical load causes the

horizontal movement of the deck, which

acts in the horizontal plane as an arch. The

transverse movement of the deck creates sig-

nificant transverse moments in the piers form-

ing transverse frames (Figure 10(c)). Non-

traditional post-tensioning of the pylon legs

and diaphragms (Figure 11) eliminates these

stresses.

~ Figure 6 Viaduct near the shopping centre in Hradec Kralove, Czech Republic

~ Figure 7 Viaduct near the shopping centre in Hradec Kralove, Czech Republic: (a) deck

supported by three bearings; (b) deck supported by one bearing; (c) transversely post-

tensioned deck supported by one bearing; and (d) distribution of longitudinal bending

moments above the support. P= prestressing force; Mx = longitudinal bending moment

28 Strasky


3 Figure 8 Sunniberg Bridge, Switzerland (courtesy of Christian

Menn)

~ Figure 9 Sunniberg Bridge, Switzerland: (a) calculation model; and (b) cross-section of the deck (courtesy of Christian Menn)



Vranov Lake pedestrian bridge,Czech Republic

The deck (252 m long) of the suspension

pedestrian bridge across the Swiss Bay of the

Vranov Lake is suspended on suspension

cables that are supported by A-shaped con-

crete pylons (Figure 12).9 In order to create a

uniform architectural expression of all the

structural members and to visually soften the

structure, the pylons have slightly curved legs

(Figure 13).

~ Figure 10 Sunniberg Bridge, Switzerland—pylon: (a) cross-section; (b) longitudinal

section; (c) transverse bending moments; and (d) longitudinal bending moments

(courtesy of Christian Menn)

~ Figure 11 Sunniberg Bridge,

Switzerland—post-tensioning of the pylon

(courtesy of Christian Menn)

~ Figure 12 Vranov Lake pedestrian bridge, Czech Republic—suspension cables

supported by A-shaped concrete pylons

~ Figure 13 Vranov Lake pedestrian

bridge, Czech Republic

30 Strasky


The pylons were cast horizontally and then

lifted into the design position. To resist signifi-

cant bending stresses that originated in the

pylon’s legs during its lifting, it was necessary

to post-tension them. This post-tensioning

was utilised in the completed structure as

well. The layout of the prestressing tendons

was designed in such a way that it exactly

balanced the bending moment due to the

dead load (Figure 14).

Bridges across the River Elbe andVrsovice railway station, CzechRepublic

The cable-stayed bridge across the River Elbe

(Figure 15) has three spans of lengths

61.60 m, 123.20 m and 61.60 m, and the

cable-stayed bridge across the Vrsovice railway

station has nine spans of lengths 26.40 m,

4� 35.00 m, 44.00 m, 101.20 m, 48.40 m

and 33.00 m.10 The last three spans are sus-

pended on one single pylon. Single piers, situ-

ated in the bridge axis, support the approach

spans (Figure 16).

Both bridges have similar decks formed by

a spine box girder and additionally cast over-

hangs that are supported by precast struts. The

load from the girder’s webs is transferred into

the stay cables situated on the bridge axis by

internal ties formed by prestressed concrete

members (Figure 17(a)). This arrangement,

which was developed by a French engineer in

~ Figure 14 Vranov Lake pedestrian bridge, Czech Republic: (a) transverse bending

moments due to the dead load; (b) layout of prestressing tendons and equivalent radial

forces; and (c) transverse bending moments due to prestressing. P= prestressing force;

r= uniform radial forces from prestressing

~ Figure 15 Bridge across the River Elbe, Czech Republic

~ Figure 16 Bridge across the Vrsovice

railway station, Czech Republic—inter-

mediate support

~ Figure 17 Bridges across the River Elbe

and across the Vrsovice railway station,

Czech Republic—suspension of the deck:

(a) on stay cables; and (b) on external

cables



the design for the Broton Bridge, allows the

transfer of the dead load shear directly into

the pylon. However, in the non-suspended

part of the structure, the shear has to be

resisted by webs.

In the case of the cable-stayed bridge

across the River Elbe, the bending moments

in the non-suspended portion of the deck

were balanced by short straight cables situated

at the top slab. The shear was resisted by the

shear capacity of the widened webs (Figure

18(a)).

In the case of the Vrsovice Bridge, the shear

in the non-suspended parts of the deck (close

to the pylon and in the approaches) is trans-

ferred into the pylon or single supports directly

by the external cables situated like the stay

cables in the bridge axis. These cables are

draped in blisters situated at the bottom slab.

The vertical component of the prestressing

force balances the shear forces that are trans-

ferred into the middle of the top slab by ties

(see Figures 17(b) and 18(b)). The middle of

the top slabs are connected by short compres-

sion struts (Figure 19).

In 2000, a similar structural arrangement

and a similar layout of external cables was

used in the construction of the Santarem

cable-stayed bridge in Portugal.11

Cable-stayed bridge across the RiverOdra, Czech Republic

At present, many clients prefer motorway

bridges in which there is an independent struc-

ture for each direction of the motorway to

allow easy repair works by transferring all the

traffic onto one structure when repairing the

other. The following structure shows the pos-

sible solution for a cable-supported bridge.

Freeway D47 crosses the River Odra and

Antosovice Lake on a 589 m long bridge. The

span across the River Odra is suspended on a

single pylon situated on the bridge axis (Figure

21). The deck on each structure is formed by a

continuous box girder. The girders, which are

2.20 m deep, are assembled out of precast

match-cast segments and additionally cast

top slab (see Figures 20 and 21). The segments

have an open cross-section formed by a central

web and curved bottom slab. The segments,

3 Figure 18 Bridges across

the River Elbe and across the

Vrsovice railway station,

Czech Republic: (a) balancing

of the bending moments by

straight tendons; and (b) bal-

ancing of the shear forces and

bending moments by draped

external cables. W= resultant

of the dead load situated

between two cables; S= force

in the cable; PV = vertical com-

ponent of the prestressing

force; M = bending moment;

V = shear force; DL = dead

load; P = prestressing

~ Figure 19 Bridges across the River Elbe and across the Vrsovice railway station, Czech

Republic—testing of the external cables

32 Strasky


together with the top slab, form two cell box

girders without any traditional overhangs.

In the suspended spans, the segments are

connected by a continuous deck slab and by

single precast struts erected between the seg-

ments. These struts are fabricated together

with stay anchor blocks (Figure 21).

The transverse connection of the segments

is relatively simple and creates a clear truss

structural system. The shear forces from the

central webs are transferred by post-tensioned

inclined webs into the stay cable’s anchor

blocks. The transverse bending of the structure

is resisted by a tension capacity of the trans-

versally prestressed deck and by a compression

capacity of the struts (Figure 22).

A similar arrangement can be easily used in

the design of an arch or suspension structure.

Bridge across the River Svratka,Czech Republic

A relatively small cable-stayed bridge with a

span length of 50 m has been built across

the River Svratka in the small city of Zidlocho-

vice.12,13 The adjacent roads leave little space

on the banks, therefore the deck is suspended

on one side by an inclined pylon (Figure 23).

3 Figure 20 Cable-stayed bridge across

the River Odra, Czech Republic—structural

solution of the approaches


the River Odra, Czech Republic—structural

solution of the main span



(a)


the River Odra, Czech Republic—trans-

verse connection: (a) structural arrange-

ment; and (b) static function. G= dead

load; S= force in the inclined webs;

T= tension in the deck slab;

C= compression in the strut

3 Figure 23 Bridge across the River

Svratka, Czech Republic

34 Strasky


The deck of the bridge, 18.60 m wide and only

0.70 m deep, is formed by two longitudinal

precast edge girders and transverse solid slab

members connected by longitudinal and trans-

verse post-tensioning (Figure 24).

The structure was erected progressively

(see Figure 24). Initially, the edge girders

were erected and suspended on the stay

cables (see Figures 24(a) and (b)), then the

transverse solid members were placed on the

edge girders (see Figure 24(c)). To eliminate

the torsion of the longitudinal girders, caused

by their eccentric loading by the transverse

members, an eccentric transverse post-ten-

sioning was created (Figure 25).

The transverse members have steel brack-

ets with nuts and screws located on the sur-

face close to their ends. After the transverse

members were erected, the screws were

drawn out until their heads touched the long-

itudinal girders. Then, the post-tensioning bars

were partially tensioned. The force couple act-

ing on the girder (under the screw’s head and

the bar’s anchor) created a moment that

balanced the torsion.

Ruck a Chucky Bridge, California

An excellent example of load balancing is

represented by the design of the Ruck a

Chucky Bridge by T. Y. Lin International.14

Although this bridge has not been built, its

design clearly demonstrates how all internal

forces can be balanced by an external prestres-

sing—by the arrangement of stay cables.

The bridge, with a span of 396.24 m,

crosses the reservoir in the plan curvature of

628 m (Figure 26). The deck is suspended on

~ Figure 24 Bridge across the River Svratka, Czech Republic—erection of the deck

~ Figure 25 Bridge across the River

Svratka, Czech Republic—static function of

the connection of the transverse and

longitudinal members. WTM = dead load of

the transverse members; PV = vertical

component of the stay force;

PH = transverse prestressing force;

H= compression force in the screw head;

MH = bending moment created by hori-

zontal forces PH and H; MV = bending

moment created by vertical forces PV and

WTM

3 Figure 26 Ruck a Chucky

Bridge, California (courtesy of

T. Y. Lin International)



the stay cables arranged in a hyperbolic para-

boloid formation to create an array of tensile

forces, which produce pure axial compression

in the curved deck. The vertical force compo-

nents of the cables balance the weight of the

deck (see Figure 27(a)). The horizontal compo-

nents are designed to reduce the horizontal

bending moments at critical points to zero

(see Figure 27(b)).

The design demonstrates how a pure engi-

neering approach can create a structure of

unbelievable beauty and elegance.

Pedestrian bridge, Kelheim,Germany

The design of the pedestrian bridge built in the

small city of Kelheim clearly proves that

science, not intuition, is the tool of creativity.

The structural solution was developed from a

deep understanding of the behaviour of

curved structures. The design was performed

by Professor Schlaich from Stuttgart.15

The bridge crosses the Mohan–Danube

canal in smooth curves, naturally connecting

the pedestrian traffic on both banks (Figure

28). The deck, which, in the plan curvature

has a radius from 18.89 to 37.79 m, is sus-

pended on one suspension cable situated

inside the plan curvature. Two inclined pylons,

situated on both banks, support the suspen-

sion cables with hangers. The geometry and

initial stresses in the cables were designed in

such a way that the vertical components of the

hangers’ forces balance the dead load (Figure

29). The horizontal components of the hanger

force, together with the radial forces from the

prestressing cables situated close to the top

fibre of the cross-section, create a moment

that balances a torsional moment caused by

vertical forces.

By fully understanding the prestressing,

and by clever arrangement of the suspension

cables, a true structure was developed. Again,

the design demonstrates how a pure engineer-

ing approach can create a structure of unbe-

lievable beauty and elegance.

Bridge across the River Vltava nearPrague, Czech Republic

At present, cantilever structures are being

designed for longer and longer spans. The sec-

tions above piers create unnatural barriers in

the countryside. A proposed bridge across the

River Vltava tries to solve this problem by

creating a light and transparent structure

(Figure 30).

The bridge is formed by a self-anchored

arch, in which a horizontal force due to the

dead load is resisted by external cables. The

structure has three spans of lengths 64 m,

114 m and 64 m. The arch is erected in sym-

~ Figure 27 Ruck a Chucky Bridge, California: (a) balancing of the vertical forces; and (b) balancing of the transverse forces (courtesy of

T. Y. Lin International)

3 Figure 28 Pedestrian bridge, Kelheim, Germany (courtesy of Schlaich,

Bergerman and Partners)

36 Strasky


metrical cantilevers starting from the piers,

using a temporary pylon and stays (Figure

31). After erection of the arches, the central

joint is to be cast and the external cables are to

be post-tensioned. Then the portion of the

deck above the piers is cast and post-ten-

sioned. Although the arches can be designed

as traditional reinforced concrete members,

they call for taking advantage of the high-

strength concrete.

Bridge across the River Odra, CzechRepublic

The bridge, 402 m long, is being built in an

area influenced by the effects of mining sub-

sidence. The structures have to resist the

effects caused by different deflections of the

supports and also the effects caused by their

horizontal movements and rotations. The

motorway bridge is formed by two parallel

structures comprised of composite box girders

of four spans, with lengths ranging from 49 to

102 m (Figure 32).

The design of the bridge was influenced by

two opposing requirements. On the one hand,

the structure had to be sufficiently stiff to be

able to resist the designed load and, on the

other hand, the structure had to be sufficiently

flexible to be able to resist the effects of the

subsidence. Since the relative different rota-

3 Figure 30 Bridge across the River

Vltava near Prague, Czech Republic—

rendering

~ Figure 31 Bridge across the River Vltava near Prague, Czech Republic—static function and erection

3 Figure 29 Pedestrian bridge, Kelheim,

Germany—balancing of the forces (cour-

tesy of Schlaich, Bergerman and Partners).

G= dead load; S= force in the suspender;

SV = vertical component of the suspender

force; SH = horizontal component of the

suspender force; PH = horizontal radial

forces from prestressing



tions of the supports decrease with the length

of the bridge, the points where rotations are

transferred into the deck were designed at the

longest possible distance—at the abutments.

On all the intermediate supports, the deck is

supported by single bearings situated on the

bridge axis.

The deck slab is stressed by bending and

shear stresses caused by a local load and also

by significant membrane stresses caused by

global bending and torsion (Figure 33). Since

the composite deck slab guarantees the integ-

rity of the structure, we tried to eliminate the

cracks. Therefore, the deck is post-tensioned

both in the transverse and longitudinal direc-

tion of the bridge. The transverse post-tension-

ing is created by traditional transverse deck

tendons, the longitudinal post-tensioning by

external cables situated inside the box (Figure

34). The level of the post-tensioning is

designed in such a way that after all losses,

and after the significant redistribution of stres-

ses caused by the creep and shrinkage of the

concrete, the principal stresses in the deck are

within the limits given for limited prestressing.

The application of post-tensioning in the com-

posite structure allows us to design a very sim-

ple and clear continuous bridge structure in an

area where only statically determined struc-

tures have been built so far.

Structures using tensionstiffening

Our experience with the design of stress ribbon

(Figure 35) and suspension structures (Figure

36) has confirmed that the static and dynamic

response of the prestressed concrete deck can

be significantly reduced by preventing the hor-

izontal movement of the deck at the sup-

ports.16–18 Figure 37(a) shows vertical

3 Figure 33 Bridge across the River Odra,

Czech Republic—deformation and stresses

in the deck


Czech Republic—structural arrangement

38 Strasky


deformations of the deck of the central span of

the Willamette River Bridge (see Figure 36),

which was completed in 2000 in Eugene,

Oregon, for loading situated on one-half of

the main span and for different values of the

horizontal springs modelling the flexible fixing

of the deck. Although a tension force stresses

the horizontally fixed deck, the resultant

normal stresses are much smaller than the

stresses in the structure with moveable sup-

ports.

A similar reduction of the deflection and

stresses is found for the load situated in the

main span in a chessboard pattern that caused

maximum distortions of the deck (Figure

37(b)). It explains the good behaviour of the

stress ribbon and suspension structures with a

prestressed concrete deck for pedestrian and

wind loading.

Since the segments of the stress ribbon and

suspension structures are suspended on the

bearing cables before the casting of the joints

between them (Figures 38 and 39), the dead


Czech Republic—layout of external cables

3 Figure 35 Pedestrian bridge across the

River Rough, Grants Pass, Oregon




River Willamette, Eugene, Oregon


River Willamette, Eugene, Oregon: (a)

vertical deformations of the deck for

loading situated on one half of the main

span; and (b) vertical deformations of the

deck for loading situated in a chessboard

pattern

40 Strasky


load of the structures is always balanced by

the forces in the cables.

Tension stiffening of the deck was also uti-

lised by Jean Muller in his proposal for long-

span cable-stayed structures, which he calls bi-

stayed bridges.19 The longest back stays are

anchored in abutments that serve as anchor

blocks as well. In this way, the longest stays,

anchored in the main span, create a tension

force in the deck and stabilise it (Figure 40).

It is well known that cables can stabilise

mats, pylons and arches (see Figure 41(a)).

The stabilising effect of the cables for the

seismic load is proposed by Professor

Ikeda.20 The cables are tensioned in such a

way that they behave elastically for seismic

load. The tension force in the cables, which

is similar to stay cables, stabilises the columns

(see Figure 41(b)). A similar idea has also

been used recently in a design for the new

San Francisco–Oakland Bay Bridge, Califor-

nia.21

Conclusions

The structures presented in this paper clearly

demonstrate the power of prestressing. Pre-

stressing allows us to balance the load, change


River Rough, Grants Pass, Oregon—erec-

tion of a segment


River Willamette, Eugene, Oregon—erec-

tion of a segment



boundary conditions, and create supports

within the structures. Prestressing is really a

revolution—it is a radical step from passive to

creative thinking and development.

Prestressing allows the design of structures

that are of a high architectural value and that

have a minimum impact on the environment. It

is our responsibility to utilise prestressing and

to provide structures of architectural elegance,

beauty and charm.

Acknowledgement

This paper was prepared in conjunction with

the research project MSM 261100007 Theory,

reliability and mechanism of failure of statically

and dynamically stressed structures, granted by

the Ministry of Education of the Czech Repub-

lic.

References

1. Walther, R. Partial prestressing. Prestressed con-

crete of Switzerland. Proceedings of the 9th FIP

Congress, Stockholm, 1982.

2. Leonhardt, F. Spannbeton fur die Praxi. Verlag

Ernst und Sohn, Berlin, 1955.

3. Lin, T. Y. and Burns, N. H. Design of prestressed

concrete structures. Wiley, New York, 1981.

4. Favre, R. and Markey, I. Generalization of the

load balancing method. Prestressed concrete in

~ Figure 40 Bi-stayed bridge: (a) axonometric view; and (b) cross-section. DL = dead load; S= force in the cable; T= tension in the deck;

R= radial force; DL = dead load; P = prestressing

~ Figure 41 Tension stiffening: (a) pylons by stay cables; and (b) columns by external cables. EQ = horizontal force due to earthquake

42 Strasky


Switzerland 1990–1994. Proceedings of the 12th

FIP Congress, Washington DC, USA.

5. Festschrift Ulrich Finsterwalder—50 Jahre fur

Dywidag. Verlag G. Braun, Karlsruhe, 1973.

6. Strasky, J. Betonove mosty. CKAIT, Praha, 2001

(in Czech).

7. Menn, C. Sonnibergbrucke, Generelle Berech-

nung. Schweizerische Bauzeitung, 1998,

Oktober.

8. Banziger, D. J., Bacchetta, A. and Baumann, K.

Sonnibergbrucke, Statik und Konstruction.

Schweizerische Bauzeitung, 1998, Oktober.

9. Strasky, J. Design and construction of Vranov

Lake pedestrian bridge, Czech Republic. PCI

Journal, 1998, Nov.–Dec.

10. Strasky, J. Design and construction of cable-

stayed bridges in the Czech Republic. PCI

Journal, 1993, Nov.–Dec.

11. Bridge over the river Tagus, Santarem. Concrete

structures in Portugal. Proceedings of the 1st fib

Congress, Osaka, 2002.

12. Strasky, J. Progressive assembly of the deck of

the cable-stayed bridges. Proceedings of the

Symposium on Modern Prestressing Techniques

and their Application, Kyoto, Japan, 1993.

13. Strasky, J., Navratil, J. and Susky, S. Applications

of time-dependent analysis of the design of

hybrid bridge structures. PCI Journal, 2001,

July–Aug.

14. Ruck a Chucky Bridge. 26th annual P/A Awards.

Progressive Architecture, 1979, Jan.

15. Schlaich, J. and Bergermann, R.

Fußgangerbrucken. ETH Zurich, 1992.

16. Strasky, J. Stress-ribbon pedestrian bridges.

Proceedings of the International Bridge

Conference, Pittsburgh, 1999.

17. Strasky, J. and Rayor, G. Technical innovations of

the Willamette River pedestrian bridge, Oregon.

Proceedings of the International Bridge

Conference, Pittsburgh, 2000.

18. Strasky, J. Long-span, slender pedestrian bridges.

Concrete International, 2002, Feb.

19. Muller, J. Reflections on cable-stayed bridges.

Revue generale des routes et des aerodromes,

Paris, 1994.

20. Hishiki, Y. and Ikeda, S. Experimental study on

seismic performance of prestressed concrete col-

umns. Proceedings of the fib Symposium,

Prague, 1999.

21. Sun, J., Manzanarez, R., Nader, M. and Duxbury,

J. P. Anchoring the new San Francisco–Oakland

Bay Bridge main suspension span with pre-

stressed concrete. Proceedings of the 1st fib

Congress, Osaka, 2002.



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