Concrete Box Girder Bridges - Jorg Schlaich

Historical Development 3 3, HISTORICAL DEVELOPMENT The first bridges of reinforced concrete were built as were their predecessors of stone, They were arch bridges with a gravel fill for

International Association for Bridge and Structural Engineering IABSE

Association Internationale des Ponts etCharpentes AIPC

FOREWORD

The box girder is today the most widely used superstructure in concrete bridge construction That fact

justifies the suggestion made by the Commission ill of the [ABSE that a comprehensive survey be

written concerning this particular bridge type The authors proceed from the assumption, however, that its contents will first be drawn upon when all possible design alternatives for the particular bridge pro- ject have been thoroughly examined, and the box girder has been proven appropriate Their aim is less that of encouraging the one-sided propagation of box-girder bridges but rather much more that of con- tributing to the improvement of the quality of such bridges They hope to contribute to this by exten- sively relieving the engineer of the study of today's hardly surveyable mass of literature on the subject

so that he can better devote that time to the actual design of the bridge That explains why this paper is kept short, why in particular cases the reader is referred to the literature, and why subjects not per- taining to the central theme are only touched upon and not handled exhaustively

For greater clearness, the survey follows the sequence of a practical bridge design process by dividing itself into three main parts, namely, “Design”, “Structural Analysis”, and “Dimensioning and Structural Detailing”; each section with its individual numbering and literature list

This survey directs itself especially to the design engineer, which manifests itself, for example, in the

fact that the construction methods are handled only briefly and in the section “Design”, because they decisively influence the design at the very beginning

Major contributions to Section il, “Structural Analysis”, were made by Prof Dr.-Ing Kurt Schafer, a col-

league of the authors in the Institut fiir Massivbau at the University of Stuttgart In this section the

attempt is made to portray the cafculation of the box-girder sectional! forces resulting from eccentric vehicle ioads with consideration of the folded plate action or profile deformation so comprehensively that it is not only easily understood but also rapidly applicable in the design office This thereby elimi- hates the often-discussed, controversial question as to whether the effort involved in the “exact” calcu- Jation of this loading case is actually worthwhile or whether an estimation of the transverse load distrib-

ution would not suffice

The authors would like to take this opportunity to thank Professors R Favre, Lausanne, and C Menn, Zirich, for their critical examination of the paper They are indebted to Mrs 1 Paechter and Mrs E Schnee for their conscientious preparation of the manuscript; and Mr E Kluttz for his empathetical translation of their German original into English

Stuttgart, January 1982

Copyright © 1982 by

International Association for Bridge and Structural Engineering

All rights reserved No part of this book may be reproduced in any form or by any means, electronic or mechanical, including photacopying, recording, ar by any information storage and retrieval system, without permission in writing from the publisher

41 Design Principles

4.1.1 The Role and Sequence of the Design Process ae

41.2 RemarksastoForm . - +22 eee eee

45,3 Foundations Lieratue -

5.4.1 Sectional Forces Acting on the Flanges 64.2 Analysis as a Frame

5.4.3 Transverse Bending

Direction .- Moments in the Haunch of Variable-Depth Girders

5.5 Folded PlateAction .-

55.1 Fundamental Concept

5.5.2 Solution by Means of the Analogy of a Seam on an Elastic Foundation

5.6 Multipfe-Cell Box Girders 5.7 Curved and Skew Box-Girder Bridges Computer-aided Analysis of th

6] Theory of Prismatie Folded Plates .-. -

le Superstructure

6.1.1 Hinged FoldedPlates Ặ QSnnÝ So 6.1.2 Folded Plates with Rigid Joints

6.2 finteStrips

63 Finite Elements

7 Abưtments ee wae 72

81 Loadings .- wae te sa " tae 72

83 Moments According to 2 Order Theory © 2-0 ee ee ng 74

3.1 The Level of Prestress cư

3.2 Tendon Profile in the Transverse Directi

33.2 In the Top and Bottom Flanges

3⁄4 Transfer of Concentrated Prestress Forces

3.5 Construction Joints and Coupling Joints

4 Dimensioning of the Top and Bottom Flanges

5 Dimensioning and Reinforcement of the Webs

5.1 Dimensioning for Shear, Torsion, and Transverse Bending " tee see

Abutments, Piers and Foundations "—=

Section If, 9.1

Part | DESIGN

1, TERMS, SYMBOLS

Terms, Symbols 1

Fig 1 Sections through a typical simple box-girder bridge

The Elements of a simple Box-Girder Bridge

columns, piers {with

2 or more hearings) breast wall wing walt back wall edge beam end diaphragm bridge seat support walls bridge seat beam access chamber bearing (can be fixed or

top slab (area between the webs)

top slab (cantilever section}

bottom slab fascia beam guard rail railing sealing membrane wearing surface drain inlet cross drain longitudinal drain

By and large the text and formulas use CEB or ISO symbols

to their indifference as to whether the bending moments are positive or ne- gative and to their torsional stiffness; from the point of view of economy, to their suitability for a factory-like construction sequence; and finally, from the point of view of form, to their sleek lines with which they fit into every landscape and surroundings

He, though, who expects a structure to reflect the flow of forces within it through ite outer shape will regret the above-mentioned neutral load-carrying behaviour of the box-girder bridges, especially those of today As a result

of the need to construct the bridges economically, the.development has tended towards bridges with constant depths, even for varying spans Box- girder bridges therefore deserve special care and attention with respect to pleasing proportions and conscientious shaping of their details

The above mentioned characteristics have made the concrete box-girder bridges the most widespread bridge type today, The fact that this develop- ment will continue for some time justifies this survey concerning a topic that

is certainly much too specialised for he who does not like to see his design possibilities restricted Therefore let one be reminded that the box girder

is only a part of the entire bridge structure and that the directly supported box girder continuous over the supports is only the standard case The box girder can also be found in portal frame bridges, arch and bow bridges, and cable-stayed and suspension bridges of all kinds {Fig 2)

TTT 7N EELV, Atmadh,

mT Wy „im gg»

Fig 2 Bridges with the box girder as main structural element

Historical Development 3

3, HISTORICAL DEVELOPMENT

The first bridges of reinforced concrete were built as were their predecessors

of stone, They were arch bridges with a gravel fill for the road surface between the two bridge parapets over the arch, Later the gravel fill was replaced by a transverse roadway slab, and the transition to a box girder was achieved

The world’s first reinforced concrete bridge, ari arch bridge, was built in

1875 t1 Probably the first box-girder bridge was Hennebique’s

Rigor gimento Bridge in 1911, a 3-hinged arch (see Fig 3)

Due to improvements in the quality of concréte and steel as well as a better

understanding of the material behaviour of reinforced concrete, the arch lost

more and more on importance as a load-carrying system to that of the beam loaded in bending The longest span simply reinforced bridge to-date was

puilt in 1939 at Ville-Neuve-St George, a three -celled, thin-walled, vary-

ing-depth box girder of three spans with a 78 m middle span

Fig 3 Risorgimento Bridge

It was only with the development of high-strength prestressing steel that it became possible to span longer distances, The first prestressed concrete

bridges, most of 7 or j-cross-section, were built towards the end of the

1920’s, The great breakthrough was achieved only after 1945, The Sclayn bridge over the river Maas, which was built by Magnel in 1948, was the first continuous prestressed box-girder bridge with 2 spans of 62, 70 m(see Fig 4)

In the following years the ratio of wages to material costs climbed sharply This thereby shifted the emphasis of development to the construction method,

4 Dasign

Important development stages were the following:

- cantilever construction in situ: the bridge over the river Rhine at Worms

in 1953 with a main span of 114 m, the Hamana bridge in Japan in 1978 with a main span of 230 m, the cable-stayed Brotonne bridge in 1978 with

a main span of 320 m

- cantilever construction with precast elements: the Chillon Viaduct in 1969 with a main span of 104 m, the cable-stayed bridge over the Columbia River

in the USA in 1980 with a’main span of 300 m

- construction with a travelling scaffolding: in situ (bridge on the Kettiger

Hang in 1959, with equal spans of 39 m each) or precast (Rio Niteroi Bridge

in 1974 with equal spans of 80 m)

- incremental launching method: Rio Caroni Bridge in 1962 with equal spans

of $6 m and the Taubertal Bridge in 1965 with spans of 54 and 60 m

The box-girder cross-section evolved structurally from the hollow cel] deck bridge or'the T-beam bridge The widening of the compression zone that be- gan as a structural requirement at the central piers was in the end extended throughout the entire length of the bridge because of the advantageous trans- verse load-carrying characteristics

The first box-girder cross-sections possessed deck slabs that cantilevered

out only slightly from the box portion (see Fig 5, a - e) With prestressed

concrete, the length of the cantilever could be increased, The high form- work costs caused a reduction in the number of cells (see Fig 5, f and g)

In order to reduce the construction loads to the minimum possible or to

require only one longitudinal girder in the working state even with multiple

traffic-lanes, the one-celled built-up cross-section constructed in modular

fashion emerged as the last development (see Fig, 5h ) This allowed the Semorile Viaduct to be built by first incrementally launching the U-shaped

portion of the box girder and adding the deck slab afterwards by means of

precast elements and insitu concrete infilling (see Fig 6) Some precast elements were built in before launching to provide stiffness In the case of the Eschachtal Bridge (Fig 7), the closed box girder was first constructed with only short cantilever deck slabs using the balanced cantilever method with erection girder In the follow-up stage of constructions, the main can- tilever deck portion was added in insitu concrete and supported by precast concrete struts, The Kochertal Bridge and the Liesertal Bridge were simi-

larly constructed, In the case of the West Gate Bridge in Melbourne however,

the cantilevered portion was built entirely of precast elements which were covered later with only a thin concrete topping A further reduction in the construction loads was only possible by dividing the bridge longitudinally as done for the Hammersmith Flyover in London (Fig 8)

Fig 8 Hammersmith Flyover Fig 9 Brotonne Cable-Stayed

in London {1} Bridge with centerline

cable attachment [5]

6 Design

The concrete box girder with streamlined cross-section has also been success- ful recently in the case of cable-stayed bridges, Its high dead load favorably influences the dynamic stress amplitudes of the cables and the necessary long- itudinal prestressing steel A torsionally stiff box girder is required to handle the torsional moments incurred by attaching the cables to the bridge’ s centerline (see Fig 9) Attaching the cables to both sides allows a much- reduced section depth A case.in point was the Columbia River Bridge where the side cells of the approach span cross-section (Fig 10 ) were only requi- red in the area near the cable-stayed portion of the bridge, and transverse diaphragms were added only where the cables were attached to the cross- section

A further area of application for box girders arose from noise and automobile emissions control for inner city elevated highways (Fig 11)

Fig 10 Columbia River Bridge [6]: a) cable-stayed bridge, b) approach span

glazed openings for natural lighting

Fig 11 Closed box girder for inner city elevated highways (7

Even though the structural development of the box girder cross-section is prob-

ably close to an end, it will continue to retain its firm place in bridge con- struction for some years to come

Design Principles T7

4 OVER ALL DESIGN

4,1 Design Principles

4,1.1 The Role and Sequence of the Design Process

The over-all structural and architectural design is the most important and, for its designer, the most stimulating and beautiful stage in the creation ofa structure Problems during detailed analysis and-design and during construc- tion as well as defects arising during its use canbe traced in most cases to

a faulty overall design Design entails finding an optimum’ compromise among

the particular objective and subjective boundary conditions of an individual

structure That is why no bridge, even a box-girder one, can be like another

Much latitude remains for creative fantasy and considerations of quality and responsibility, The design engineer must be conscious at all times of the fact that he is irrevocably changing an area’s environment with his bridge Therefore, not only considerations of stability, serviceability, and economy count, but of equal importance are the bridge shape, the bridge’ s harmoni- zation with the surrounding landscape, and its impact on the preservation of

the quality of life of man and nature, `

The optimum solution, always and exclusively a subjective evaluation, can only be found through the comparison of many alternative solutions with a different assessment of the individual boundary conditions in each case, The entire planning process from the sketched design to the planning of the con- struction is a cyclical process of increasing refinement (Fig 12) It is to

be emphasized that the development of the structural details should be inclu- ded in the earliest phase of the design process, whereas the computer calcu- lations range at its end and should confirm only whether the roughly deter- mined dimensions suffice, Construction is carried out according to drawings,

not calculations Above all, it would be a great mistake to believe that the

computer could relieve the engineer of the design of a bridge

4.1.2 Remarks as to form

In contrast somewhat to arch, suspension, or cable-stayed bridges, the box-

girder bridge fits into almost every surrounding, be it varied or monotonous {8] Just because of its simplicity, the observer finds every imbalance in its proportions and uncleanness in its lines to be disturbing

Realizing well enough that, fortunately, it is not possible and perhaps even detrimental to put forth generally valid rules for aesthetics, a few remarks

on the subject will nevertheless be hazarded here, It has served its purpose well if the fact that a separate section in this paper is devoted to architectural design and form promotes the sharpening of the consciousness among engineers with respect to this subject That will even be achieved in the event that the reader finds the following guidelines or orientation aids to be false and in this manner critically grapples with the questions of form (Compare especially

[9, 10, 11] as well as [8, 12, 131):

Fig 12 Planning: a continuous refining process

- Order in the structural system: Retain the selected structural system (beam, arch, frame, suspension or cable~stayed) and only combine it with another system if the topografical boundary conditions change signi- ficantly along the length of the bridge (e.g widened river bed or approach)

- Harmony: Strive for balanced proportions among the length of the spans, the construction depth, and the depth of the valley; and between the

supporting and supported structural elements, The span/depth ratio , 1/d,

alone is no guaranty for a light and elegant appearance (Fig 13)

- Order in the lines: Restrict the characteristic lines to a few directions and avoid their intersecting A straight line should merge smoothly into a

Design Principles 9

Fig 13 Although 1/4, is greater than L/4, , (b) appears lighter than (a)

- Simplicity and clearness: Allow the function of the structural element and the necessity of the material to be perceived, and avoid unnecessary frills

- Integration into the environment: Either subordinate the bridge to its

surroundings; or, if the landscape is monotonous or the surroundings are

disorderly built up, make a feature of the bridge

- Pay attention to the order of scale between the bridge and its surroundings and the bridge and the individual person A long bridge, especially iftit passes through hilly terrain, should never be set out in a straight alignment but harmonically pick up the movement of the terrain and the lay-out of the

curves of the highway

An odd number of spans which decrease in length in the direction of the abut- ments are found to‘be pleasin (Figs 14a, “e and i) Veryirreguier-spen-—- lengtli® produce a feeling of uneasiness (Pig 14 b), Many spans of equal length produce a boring effect, and the valley appears to be walled in (Figs 14¢ and d), although a design in the form of Figure 14d with very slender in- dividual piers can be a viable solution The harmonic division of a line accord-

ing to the "golden section" commonly used in antiquity is limited by various

hindrances and the soil conditions and therefore can only seldom be realised

10 Design-

Should the bridge gradient follow a trough or a crest, i.e the upper charac- teristic line is curved, then a satisfying appearance can be best achieved by means of a constant depth, d, of the box-girder for the entire bridge

Especially for inner city elevated highways, the depth should be as small as

possible and the corresponding reduction in the lengths of the spans be

7 STs

Fig, 15 Shadow effect caused by Fig 16 Fascia Beam: the form (b)

the cantilevered deck slab causes the bridge to appear

sleeker than (a) The length,a,of the cantilevered deck slab and the form given to the fascia beam and railing determine the side view of the bridge as follows:

- For a/d< 1 no shadow effect is created, but for a/d> 3 the shadow is

very noticeable, and for a/d >2 it can be usefully employed as an element

of form (Fig 15), For varying bridge depths, however, the shadow should not be allowed to extend beneath the soffit of the box girder

- A deep, if necessary white-painted, fascia beam reduces the perceived depth of the box girder (Fig 16), Suitable values are the following [ 8, 10}:

d/d =1/5 to 1/4 but always < 1/3 d/l “ 1/20 to 1/80 for long bridges

4d, > 200 mm

An inclined fascia beam appears even lighter because of the angle at which the light falls on it (Fig 17) In addition, the wind is also deflected to ad-

vantage, In the case of bridges near residential areas, the fascia beams

can be placed higher to act as noise barriers (Fig 18), Varying inclina- tion cause light-dark effects that give the bridge a sleeker appearance With an appropriate design such deep fascia beams can be used as load- bearing members together with the box-girder

Fig 17 An inclined fascia beam Pig 18 Fascia beam as noise barrier Great care should be employed with the shape and structural details of the guard rail Sufficient protection for the pedestrian plus an unhindered

view for the driver of the motor vehicle are achieved with a hefty cross-

beam mounted onto slender vertical standards placed at intervals of

approximately 150 mm

FETs

Design Principles 11

Especial care should also be taken with the proportions of the piers with

respect to the bridge superstructure, If the piers are too slender, the super- structure will appear too heavy, especially if the bridge cross-section is increased in depth from a minimum at mid-span to a maximum over the piers There the piers should never be any narrower than the box- girder bottom flange which they support Round piers appear boring compared with prismatic ones with at least six sides, The abutments should be placed high in the

embankment and be only marginally exposed,

In order to assess the appearance of the bridge, it is important to compose a

“picture' of it This means making sketches at first and later drawings to

scale, Along with a plan view, cross-section, and elevation, at least one per- spective drawing is necessary in order to obtain an impression of the bridge in its surroundings With an inclined view one can best determine if the super-

structure and substructure are in harmony with each other, Of great help in

this respect is the photomontage, which is really not so costly, or a model The model must include a sufficient portion of the surroundings Not only should one not attempt to evoke a favourable impression of the structure by choosing

an unrealistic standpoint from which to observe the bridge,but one should design

a bridge that is found to be harmonically proportioned even when viewed from

the worst possible perspective

4.1,3 Costs

In letting the contract for a bridge one should not overlook the fact that the total costs include not only the costs of construction but also the follow-up costs of maintenance and the ensuring of proper functioning of the bridge for

at least 50 years Unfortunately, even in the rich industrialized nations of the world, bridges are predominantly let on the basis of the lowest bid One

is seldom prepared to pay a bit more for a good architectural design and form and tong-lasting quality

The growth of costs shown in Fig, 19 are valid for Central Europe, Depending upon the regional construction materials at hand, the qualifications of the wor-

kers, the ratio of wages to material costs, the extent of mechanization of the

construction industry, and the climate; the particular cost analysis yields dif- fering results, The course of costs over time portrayed in Fig 20 shows that

an economical solution is only achieved today if the labour-intensive work is li-

mited through repetition of the same operations or construction under factory conditions Cost optimizations with specification of the most favourable span length or the like, as is so often found in papers are questionable for the most part, because they can never take every possible parameter into consideration They often only consider material expenditure.Only if the ratio of labour costs

to material costs is less than 1 do savings of material gain significance

One can observe from Fig, 19 that inflated calculations of savings of mild steel

reinforcement, approximately half of which is required as minimum reinforce- ment anyway, do not change the total cost of the bridge to any great extent Lar-

ge savings are only achieved if an element of the design is changed, such as a less expensive foundation or a less labour intensive construction method,

17 typical examples (from [14] ) : industrialized ‘nations For a bridge with average span lengths and a span/depth ratio, 1/d © 18, one

can proceed from the following values for the superstructure (from [14]):

prestressing steel for the case of predominantly

continuous prestressing tendons © ( 4,5 + 0, 5-] [m] hee /m 3} }

- average cost of falsework and formwork = 60 % of the expenditure for

concrete and steel,

4.2 Construction Methods

The method of construction influences the design and its details in both the

longitudinal and transverse direction, In the laSt 20 years construction me-

thods have experienced a stage of rapid development They appear today,

however, to have reached the end of this stage Box-girder bridges are con-

structed today on stationary falsework (Fig 21), if at all, only in the extreme

ease of a small number of spans or when the superstructure is not at a great

height above the ground For some of the large bridges highly mechanized

constructions methods are used, By means of construction rhythms and many

repetitive construction operations, these methods reduce construction time

and formwork (Figs, 22 and 23),

For the foreseeable future one can expect that long bridges will be construc-

ted using either launching girders or segmental cantilever construction, For

medium -length bridges between 200 m and 500 m the incremental launching

method and classical balanced cantilever method or cantilever method with

launching gantry will be predominantly used

“tk At=35-som |

ce) cantilever construction with launching gantry ( Siegtal Bridge )

d) launching girder ( Krahnenberg Bridge )

E°%s tà

~~ flourching jock f ~

Al =10.0-25.0m e) incremental launching method ( Taubertal Bridge )

Fig 22 Construction methods

Fig 23 Classification according to construction method, span length, total

bridge length, and construction progress (from { 151) 4,3 Superstructure

4.3.1 General

The box girder often is more advantageous than say aTT -beam due to

- its high bending stiffness combined with a low dead load, yielding a

favorable ratio of dead load to live load;

- its high torsional stiffness which allows freedom in the selection of both the supports and bridge alignment; and

- the possibility of utilizing the space inside the box girder

Several of the following aspects apply to both the box girder and 1 -beam,

The superstructure should always pe designed as a complete entity, However,

in order to provide a better overview, the longitudinal and transverse direc- tion are handled separately here

4.3.2 Longitudinal Direction

Because of excessive bending deformations even under constant loads and in order to avoid cracking under repeated Joading, most box- girder pridges are prestressed, As short a span a8 20 m is more economical and possesses more favorable load-carrying characteristics when partially prestressed than

if it were simply reinforced, Under 20 m is a box-girder cross-section no longer sensible anyhow, The limit for mild steel reinforced bridges of a single span lies at approximately 35 m; for more than one span at a maximum of 60 m Today practically all box-girder bridges are prestressed

The selection of the span lengths should mainly follow from aesthetic aspects (compare with Section 4.1.2) From the structural point of view, the span length ratio of end span to its neighboring inner span should be lp /ly = 0,75 but not < 0.40 so as to avoid uplift at the end span supports Most end spans with in/y = 0.5 do not look good

Sup ture

Especially important for the form and the dimensioning of the bridge is the selection of the bridge depth Up to a span length of about 90 m, a constant bridge depth is sensible [16, 17}, whereby beginning with a span length of approximately 50 m it is expedient to increase the thickness of the bottom flange over the piers on the inside of the box girder where this can not be seen from the outside For span lengths, 1, in the middle range and constant bridge depth, d, the following ratios are normally used:

- mild steel reinforced: single span 1/d“~ 17

multiple spans 1/d“ 18

- prestressed: single spans 1/4 ~ 31

multiple spans 1/d = 25

If not done earlier for aesthetic reasons, it is structurally and economically

advantageous to vary the bridge depth in the longitudinal direction beginning with span lengths of about 60 m onwards For span lengths over 150-m this cannot be avoided, According to [18], the depth, dg, over the piers should vary so that it is about 3 times as jarge as at mid-span, dyn The depth of the box girder should vary in the longitudinal direction between the piers and mid-span in such a way that the forces in the tensile and compressive chords increase linearly and therefore the shear forces in the webs remain roughly constant throughout the span Suitable ratios are:

1/dy = 33 to 50

dg ~ 12 to 20

Should the bridge be placed high above the valley, aesthetics dictate that, de- pending upon the width of the piers, the ratio dg /dg is better chosen some- what smaller than the structural analysis indicates as the optimum

Much larger slenderness ratios can be achieved in the case of suspension and cable-stayed bridges, as the depth of the main girder is not determined by the total span length but by the spacing of the hangers, which act as spring supports For small hanger or cable intervals of from 6 m to 15 m, which also prove suitable for the free cantilever construction of cable-stayed bridges, the depth

of the main girder when suspended from both sides is in principle determined only by its strength in the transverse direction, When the girder is suspen- ded from the center,the necessary torsional strength or torsional stiffness plays a decisive role as well

Skewed single celled box- girder bridges with g = 15° (Fig, 24) can be designed

as if they were orthogonal bridges For larger B the angle of skew must be

is sufficient to calculate M, as for a straight bridge and My for the curved bridge, i.e to neglect the coupling effect of the two upon each other (e g

(21, 22})

4.3.3 Transverse Direction

Figure 26 portrays the factors influencing the cross-sectional form

are all approximately of the same importance, They

USE

-pedestrian -automobile strain

PROPORTIONS -length of cantilever -web inclination -dimensions

BRIDGE FINISHES + FORM fascia beam

~guard rail

in,

- ie -web inclination -view from below

DESIGN OFA BOX -GIRDER CROSS-SECTION

POSSIBLE CROSS-SECTIONS -single-cetl

~mulfiple - cel!

sconstant or varying -wlth/without diaphragms

CONSTRUCTION METHOD

~astationary falaework -incremental launching -farrawork girder

SUPPORTS

=pler wall with multiple bridge bearings -several individual piers -eingte middle pier

~euspended from bridge centerline -suepended from both sides

Fig 26 Influences on the design in the transverse direction

The use to which the cross-section is put determines its form, especially the width of the top slab No standards exist for the necessary width of foot- bridges That must be determined according to the expected number of pedestrians for the particular location in question {23} In order to provide ample space for at least 2 baby carriages plus one pedestrian and to impart a feeling of safety and well-being to pedestrians, a minimum width of 3.5 m between the hand rails should be provided Should the bridge possess light, open balustrades or carry pedestrians over major traffic arteries, the width should be chosen expecially liberally

For railway bridges, the railway clearance profile (in western Europe

as in Fig 27) determines the width of the upper flange and the distance bet- ween the webs, as the loads should act on the box girder as near to the webs

as possible (Fig 29) Should the rail traffic be transferred to the inside of the box girder , the railway clearance profile would-then determine the width

Fig 27 Railway clearance Fig 28 Double-track railway:

Place the webs as nearly as possible underneath the paths

of the loads

and height of the box girder as well (Fig 29) The details of the slab carry- ing the tracks depend in addition upon whether the ballast bed is continued over

the bridge or whether the sleepers are placed on vibration-absorbing pada

sitting directly on the structure

For highway bridges the bridge should maintain the normal highway cross-section (e.g Fig 30) Should later widening of the highway be planned, the additional lanes should be constructed for the initial bridge stage and the areas not planned for initial commissioning blocked off, This avoids expen- sive reworking of the bridge in the future

+ omlem—mmberok

Pig 29 Design of the Metro in Lyon Fig 30 Typical cross-section

(from [24]) of a 4-lane Autobahn (R Q 29)

18 = Design

The box-girder cross-section shown in Fig 31 has proven itself with regard

to its form and structural characteristics Many variations of this “standard cross-section " are possible

Fig 31 Typical single-cell box-girder cross-section (1/d © 20;see Fig 43)

If the available depth of the girder,d;is greater than from 1/6-to 1/5 of the

bridge width ,boay (© roadway slab width), a single-cell box girder is in order, If a/b lab < 1/6, a 2-cell or multiple-cell box girder is more sen- sible (Fig sah 25 ¥or wider bridges the vehicle loads acting on the canti- jever slab can be distributed longitudinally by means of a pronounced edge

beam, enabling the cantilever length to be increased (Fig 33)

Fig 32 Double-cell box girder with Fig 33 Load-distributing edge

support in the middle beam The number of cells should be kept as small as possible even for wider bridges with a small depth in order to minimize problems in construction As can be seen in Fig 34, no substantial improvement in the transverse load distribu-

tion is achieved with 3 cells and beyond, For economic reasons, today more

than 2 cells are rare

If 2 or more box girders are placed next to each other it is advantageous to connect their top and bottom flanges in order to achieve a better transverse load distribution (Fig 35 b) If only the top flanges are connected, they will

be hightly stressed due to bending moments in the transverse direction with-

out being able to effectively distribute the stresses in this direction (Fig 35 a)

It is then better to separate the two box girders

Fig 34 Longitudinal bending stresses o at mid-span in relation to the number

of cells; (example for 1/d 18 from [26])

Fig 35 The coupling of box girders

The combination of extremely wide roadway decks with slender piers can be accomplished with a box girder by supporting the cantilevers with precast struts (Fig 36) This is also advantageous for the construction,

At the inner supports of continuous long span bridges it is usually necessary to increase the thickness of the bottom flange to take the compression stresses (Fig 37) The center of gravity is thereby lowered towards the bottom flange,

80m ————+|

Fig 36 Kochertal Bridge at Geislingen Fig, 37 Thicker bottom flange

for a 4-lane Autobahn (from (27) Valley Creek Bridge, over the support (Pine

from (28])

The bottom flange should be gradually thickened over a distance of 1/10 times

the span on both sides of the inner support,

With varying bridge depth and inclined webs, the box-girder soffit is wider in the span than over the supports (Fig 38) In order to simplify the formwork

in this case, vertical webs are therefore often selected (Fig 39)

Fig 38 Felsenau Bridge, single- Fig 39 Oléron Bridge with ver-

celled box girder with tical webs and two sepa-

‘ inclined webs rate box girders Especially in the case of inner city elevated highways, exit lanes often begin

on the bridge, requiring a widening of the bridge top slab If the widening is not too great, it can be handled by extending the length of the cantilever por-

tion (Fig 40a), Its soffit must however be carefully designed (Fig 41) If the

widening of the roadway is not symmetric, an equal cantilever length for both sides of the box girder can be achieved by offsetting the center line of the box girder (Fig 40b), The torsional moments are thereby reduced as well, The formwork costs are substantially increased however

In extreme cases (Fig, 42) the distance between the webs or the number of celis can be increased, The possible position of supports thereby influences the number of webs more in most cases than the maximum cantilever length

of the top slab or the maximum span of the top slab between the webs,

a) symmetrical widening b) unsymmetrical widening;

equal cantilevers achieved through a curved alignment

of the box section Fig 40 Widening of top slab

Superstructure 21

a) simple design but too b) extensive formwork but in

stubby in the normal region return a well-proportioned

cantilever slab in the normal region

Fig 41 Extension of the cantilever slab

- aesthetic and structural suggestions

are intended to facilitate the preliminary design but should in no way restrict

the scope of the design possibilities (Fig 43)

tae

8pecia] form for the coup- ling of prestressing tendons Fig 43 Design aids for the cross-sectional dimensions

< tr ngg

launch! ‘stab = 0.2 (to simplify the formwork, a value of

launch! ‘s1ab = 0,5 is recommended)

- tity = from 1:2 to 1:3

(This also applies for tạ},

- minimum dimensions: deck slab ty = 200 mm; ti 2 200 mm

webs ty > 300 ram or (200 + 2-Banet? bottom slab ts 2 150 mm

(with the utmost of care in construction, e.g pre~

cast elements, these values can be decreased by

as much as 50 mm)

The ratio 1,:1, shown in Fig 43 is very much dependent upon the transverse bending stiffness of the slabs and the webs as well as the maximum possible eccentricity of the vehicle loading as “defined by the sidewalk For normal cross-sectional dimensions, 80 % to 90 % of the fixed-end moment of-the can-

tilever slab is transmitted into the web and 20 % to 10 % into the deck slab

between the webs The optimum cantilever length 1, lies between 2,0m and 3.5m 1, should be so selected that no negative moments in the span occur

in the deck slab between the webs

In order to minimize the width of the pier and the span length of the bottom

slab between webs, the webs should be given an inclination of from 4: 1 te

3:1 for a constant bridge depth The transverse tensile forces in the deck slab must be accepted thereby

In order to facilitate rainwater run-off, the roadway should be transversely inclined as follows:

for a straight alignment: 2 2.5%

for curves, depending upon the

radius of curvature 2.5% to 6 %,

For narrow bridges the transverse gradient can be achieved by varying the road surfacing thickness In general though, the deck slab should be given

a gradient itself The possibilities to achieve this are shown in Figure 44,

a} rotation of the b) a rhombic cross- ce) differing web cross-section section with vertical heights and a about the axis webs of equal height horizontal bottom

Fig 44 Transverse gradient of the roadway (from [14])

The other elements and structural details of the bridge finishes are handled

in Section III,9,

Comptete System and Supports 23

Diaphragms hinder the construction of box- girder bridges in most cases They are sensible in the span only for the case of very long spans, if then Over the piers they can take the form shown in Figs 45 and 46, depending upon how the cross-section is supported They can be omitted if the bridge bearings are placed directly underneath the w his makes it more difficult to replace

2

section 11 a) most common form; b) for a central support e) for very stiff

with access opening box girders lotally

thickened webs suffice

Fig 45 Diaphragms over the piers

the bridge bearing

4.4 Complete System and Supports

The superstructure is acted upon by both horizontal and vertical loads which

must be carried into the foundation by way of the bearings, piers, and abut- ments (Fig 47)

‘Transverse horizontal forces acting on the superstructure and piers include

mainly wind but also earthquake forces, In exceptional cases, impact forces

from vehicles or ships and ice pressure should be considered,

Longitudinal horizontal forces include forces from vehicle acceleration and braking, resistance to deformation of the supports or piers, and earthquake forces For very long bridges, longitudinal wind forces should also be borne

in mind as well as the dead-load components of bridges with longitudinal’ gra- dients, as long as the bridge bearings are positioned with the same inclination

structural! system for tronsverse horizontal toads what

+ FF Ap : : wide box on piers

twin columns necessary every = 100m of the bridge

{because of torsional moments)

Fig 47 Typical longitudinal and transverse support schematic for a medium-

"length (L* 300 m) box-girder bridge with short or medium high piers

Up to a bridge of medium length, the fixed point should’be at one of the abut- ments, as the abutment is heavy anyway and can take the horizontal forces more economically than the piers In this case the bridge also needs only one expansion joint (Figs 47 and 48a) For long bridges it can be more advantage- ous to place the point of fixity somewhere near the middle of the bridge in order

to halve the horizontal movements to be accomodated by the bearings on the piers and by the two expansion joints at the bridge ends (Figs 48b and c), This point of fixity should lie at a pier with a large vertical load in the case of short _piers For.a bridge with tall piers, several piers near the middle ofthe bridge may be monolithically connected with the superstructure, yielding a floating -support,The stability of the entire system should, however, be examined,

Piers constructed integrally with the superstructure are not only advantageous

because the vulnerable bearing can be done away with,but also because they

then possess the shortest effective Euler buckling length (Fig 49) One should therefore take advantage of the deformability of tall:piers —

————————_—_—_.SSsSBS T

If the final fixed points are not located at the abutments or the bridge construc-~ tion is advanced from both abutments, the fixed points must be moved during the construction (Fig 50) This requires a careful determination of the initial

set-up positons of the bearings (see Section IJI,8 )

Fig 49 Influence of end restraint on the

effective Euler buckling length đà

For extremely long bridges it can be more economical to provide intermediate joints in the superstructure and therefore several fixed points, as the bearings become more complex and costly the heavier the loads they are required to handle and the larger the movements they are required to accomodate sirnul-

taneously, i.e the higher and wider the "trees" of Fig, 51 for the particular

bridge

temperature- induced movement

Fig 51 Load vs movement depending upon the support condition in the lon-

gitudinal direction (from [29])

>> TTR ST To increase the number of joints

because of an unsubstantiated fear

of differential settlements to the point that the effect of continuity is lost (Fig 52) should, however, be rejected The best detailed expan- sion joint will always be much worse than the continuous superstructure

In addition, the structural reserves

of the continuous system are lost by the multiple-span statically deter- minate system

Fig 52 Superfluous arrangement

of joints

Complete System and Supports 27

The torsionally stiff box girder enables the_ skewed abutment and pier walls to

be avoided for the case that the bridge must cross over an obstruction at a

Torsionally stiff box-girder bridges built on sharp horizontal curves and d_sup-

Ported by at least 3 individual columns located under the middle of the cross-

section are stable even without the bridge ends being fixed (Fig 54), This permits very transparent support systems, which are especially welcomed in

the inner city, Nevertheless, in order to be able to use the normal expansion

jeints, the bridge ends are fixed torsionally stiff

alternative

ixed Fig 54 Support of sharply curved box-girder bridges

In the case of long lightly curved bridges, the columns can be alternatingly placed off-center to the bridge axis (Fig 55a) if the bending stiffness of one

or all of the columns is not to be utilized (Fig 55b), Of course a fixed end

as shown in Fig 53 suffices for short bridges

Fig 55 Support system for long lightly curved box-girder bridges

28 Design

As curved bridges experience horizontal deformations due to prestressing and creep parallel to the bridge axis and deformations due to shrinkage and tempe- rature radially from the fixed point, bearings capable of accomodating move- ment in any direction are to be preferred over roller bearings,

This requirement of freedom of movement in any direction produces difficul- ties for the free bridge ends Therefore in most cases the movements there are restricted to one direction, and the piers or abutments are designed for the unavoidable restraint stresses (Fig 56)

_

w ~- — 0 N , ahs

Vy Fig 56 Longitudinal movement in the direction of the bridge axis can be

brought about by horizontal restraint forces (from [9))

For bridges with transverse or longitudinal gradients the bearings can be placed as shown in Figs 57 and 58 The transverse diaphragms should be placed vertically Beginning with radients g greater than 3°, the gradient

must be considered Ốc ¬

Fig 57 Placement of Fig 58 Placement of bearings for a longitu-

bearings for a dinal gradient avoiding horizontal transverse gra- forces on the piers

dient (from [14])

In Fig 1, two abutment types are sketched For small bridges the spill- through abutment is sufficient A box abutment large enough for access ingide

is normally provided for large bridges The earth fill behind the abutment should be well compacted As the abutments even for small bridges possess

large dimensions, they should be covered as much as possible by the slope or

embankment, The sloped area underneath the superstructure ends should be covered with dark paving stones, as no plants will grow there, The view into the access chamber, where the bearings and any drainage lines are located, should be concealed by the end diaphragm The end diaphragm should, how- ever, leave a gap of approximately 100 mm between it and the soffit of the

box girder,

4,5,2 Piers

For low bridges, especially those for elevated highways, two individual

columns are more transparent and therefore more advantageous than pier walls, It can be more aesthetically pleasing to set the columns back somewhat from the outside edge of the bridge cross-section (Fig 59b) and to forego” the more efficient carrying of the loads directly from the webs into the columns (Fig 59a).In any case, good uniform soil conditions are necessary

in order to prevent differential settlement between the columns standing so

close to each other Otherwise a common foundation should be provided, on

piles if necessary Should it not be necessary to handle any torsion moments,

a single column underneath the middle of the cross-section appears more ele-

gant than two (Figs 59c to e), However, this is only sensible for one or two-

celled cross-sections (Fig 59d), By-inclining the webs more a smaller

bottom slab is thereby possible (Fig 59e) The single columns should be de-

signed sufficiently robust, as columns that are too slender do not convey a feeling of safety underneath a large box-girder (Fig 59f) Round, elliptic,

or octagonal cross-sections should be preferred above square or rectangular ones because of their better appearance (Fig 60a) Even for extremely wide, multiple-celled cross-sections, not more than 3 individual columns together

should be used, as the skewed view through them produce an unsettling effect

Massive pier walls (Fig 60b and 61) should only be used for low bridges By breaking up the walls or varying their width, the squat shape produced can be lightened,

30 Design

Fig 60 Cross-sectional shapes for piers (from [9] }

Fig 61 Comparison between pier and twin columns for multiple-celled

7722/7770

Hf Crear

a}

Fig 63 Box piers Fig 64 Pier design

The piers should be lightly tapered from the bottom upwards, at least for one dimension (Fig 64a) Stiffening diaphragms are not normally required or desired because of thermal stresses, The top of the pier (Fig 64b).should be designed compatible with the construction method of the superstructure, In the longitudinal direction of the bridge the width of the top of the pier depends upon the type of bearings selected, the span between the bearings, and the dimensions of the jacks necessary to replace the bearings It varies between

1,20 m and 2.0 m

4,5,3 Foundations

The simplest type is the shallow spread foundation which is used if good soil conditions are found at a shallow depth The foundation slab is constructed on top of an 0,1 m thick sub-base, The slab thickness should be so chosen that shear and punching reinforcement can be avoided, The bottom of the founda- tion must lie below the level of frost penetration

Should adequate soil conditions be found only at lower levels, an excavated pile foundation or one on drilled or driven piles should be selected In gene- ral this type of foundation is provided with a pile cap with which the pier is connected Depending upon the loads to be carried, the piles are either dri-

ven (for loads up to * 1 000 KN) or drilled (up to * 9 000 KN) In the case of

pile foundations for single columns, it is better to carry the forces directly into the foundation by means of large drilled piles or wells rather than for-

cing them to travel a roundabout way through a pile cap on top of several small individual piles and its complicated reinforcing arrangement

(Fig 65)

If unfavourable soil conditions are encountered

or the foundations are into a hillside, it can be necessary to carry out open excavations down

to a suitable soil layer or to sink caissons,

The pier can then either be placed directly on Fig 65 (a) is more the bottom of the excavation or on top of the

favourable than (b) excavation or caisson wall

34 Structural Analysis

understand The detailed explanation included herein should alleviate this

difficulty Formulae are derived which are not only suitable for hand cal-

culation but also for small computer programs, With enough experience so

gathered in this area, one can later on appropriately estimate the effect of

this loading and forego the exact calculation,

2, LOADS and EXTERNAL INFLUENCES

Those loads to which a bridge is subjected in the structural analysis are

generally specified in the applicable code of practice for a particular country,

As the design loads should not be given consideration independent of their

respective safety concept and as the live loads vary greatly indeed from country

to country (Fig 1), only the general basis for the consideration of loadings is given here as follows:

Fig 1 Comparison of various loading assumptions (from [ 1)

- Dead loads of the structure, gy: normal reinforced eqnerete Yo = 25 KN/m?3,

lightweight reinforced concrete Yrg™ 16 to 2l kN/m

~ Dead loads of the inishes, go: roadway surfacing (asphalt) y * 22 kN/mŠ,

concrete) y* 25 kN/m3, bridge railing * 0.22 KN/m,

guard railing ~ 0,25 - 0.35 kN/m

~ Live loads: In most codes a single-vehicle loading with a series of wheel

foads,Q,,and a uniformly distributed load , q; (main lane, secondary lanes),

is given Railway bridges are loaded with the appropriate loading configura- tion for each track (e.g UIC 71 [ 2]) Impact is considered by increasing portions of the live loads by means of system-dependent impact factors The machinery employed in constructing the bridge should also be included as

live loads In contrast to the assumed vehicle loadings however, these loads act with 100 % of their actual magnitude, a fact to be taken into account in the safety concept for the design

specifications), horizontal loads act upon the box~girder bottom flange and the piers

Loads and External Influences

Fig 2 Notation used for the determination of wind load from Figure 3

W_ in kN/m M_in kNm/m factors "from without live load 2 ty q-h 2O,°q-b - cụ = Fig 3b

Bo = ‘wa cwab oh 3c

5 # =%4-cwq [h+h HE =-icug:b ch cự =Fig 3b

ø ithout live load -

: 2 without live loa = cựq ch = cụ-q :b th cự = ig af

8 £ [with live load Cy =Fig 3f

z BA i = Rey 2'cewgtn+ lh+h) = 08-q-b -h q Xz = Fig 3f = Fi

direction of force region position w_in kN/m^ factors Cp from

cantilever Luff = Spa Fig 31

36 ‘Structural Analysis

- Wind loads: With the cross-sectional dimensions (Fig 2) and the dynamic pressuré,

q, obtained from the wind velocity, v {m/sec], according to

the formula q [kN/m?] ws v2/1600, the wind loads, W and M, on the entire cross-section can be determined from Figures 3a to f and the localized

wind loads, w, from Figures 3 g toi Information concerning the maximum

wind velocity can be taken from the applicable Code or obtained from a local weather station If constant contact is maintained with the weather station during construction the design wind loads for the erection phase can be re- duced, depending upon the expected duration of the particular erection,any-

where from 0.2 max W(< 1 day) to0.7 max W(>3 days),

The critical wind velocity causing such vortex-shedding phenomena as flutter’ or galopping vibrations can be estimated with Figure 4 and the formula (from [4])

An = SECTION & vibration for the

tunnel tests a* factor from Fig 4

derived from wind tunnel tests

A more exact analysis requires wind tunnel tests in most cases, Bridges of normal dimensions continuous over fixed supports are generally not critical Suspension or cable-stayed box girders could be, however,

(According to the German Code, Fy * 3/20-L+ b

but Fy is at least = 0.3 - Q ) roadway [EN] (1 £200 m),

heavy vehicle’

~ Temperature: A uniformly distributed heating or cooling of the super- structure from its mean temperature at the time of construction only affects the movements to be accommodated by the bearings and possibly the sub- structure, The magnitude of such temperature changes can be taken