2005:248 CIV MASTER'S THESIS - DiVA portal1025325/FULLTEXT01.pdf2005:248 CIV MASTER'S THESIS Optimized Design of Integral Abutments for a Three Span Composite Bridge Gabriela Tlustochowicz

2005:248 CIV

M A S T E R ' S T H E S I S

Optimized Design of Integral Abutmentsfor a Three Span Composite Bridge

Gabriela Tlustochowicz

Luleå University of Technology

MSc Programmes in Engineering

Department of Civil and Environmental EngineeringDivision of Steel Structures

2005:248 CIV - ISSN: 1402-1617 - ISRN: LTU-EX--05/248--SE

Optimized design of integral abutmentsfor a 3 span composite bridge.

Gabriela T ustochowicz

List of contents

Master’s Thesis: ”Optimized design of integral abutments for a 3 span composite bridge”

List of contents:

Preface … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … .. IAbstract … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … ... IIISummary … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … . IV.I. Part1.0 Introduction … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … 1

1.1 What are integral bridges … … … … … … … … … … … … … … … … … … … … .… … … 11.2 Advantages of integral abutment bridges … … … … … … … … … … … … … … … … … 21.3 Problems and uncertainties … … … … … … … … … … … … … … … … … … … … … … .. 3

2.0 Literature review … … … … … … … … … … … … … … … … … … … … … … … … … … … ... 52.1 Types of piles … … … … … … … … … … … … … … … … … … … … … … … … … … … . 52.2 Piles configuration … … … … … … … … … … … … … … … … … … … … … … … … … . 52.3 Pile orientation … … … … … … … … … … … … … … … … … … … … … … … … … … ... 62.4 Pileabutment connection … … … … … … … … … … … … … … … … … … … … … … ... 82.5 Length limits for integral bridges … … … … … … … … … … … … … … … … … … … .. 92.6 Behaviour of piles supporting abutments … … … … … … … … … … … … … … … … .. 9

3.0 Practice … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … . 113.1 USA experience … … … … … … … … … … … … … … … … … … … … … … … … … … . 113.2 Swedish experience from a new solution … … … … … … … … … … … … … … … … .. 133.3 Poland … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … 153.4 United Kingdom … … … … … … … … … … … … … … … … … … … … … … … … … … .163.5 Germany … … … … … … … … … … … … … … … … … … … … … … … … … … … … … 173.6 Canada … … … … … … … … … … … … … … … … … … … … … … … … … … … … … ... 18

4.0 Design models and methods … … … … … … … … … … … … … … … … … … … … … … … . 194.1 General issue … … … … … … … … … … … … … … … … … … … … … … … … … … … .. 194.2 Calculation methods … … … … … … … … … … … … … … … … … … … … … … … … .. 19

4.2.1 Equivalent cantilever method … … … … … … … … … … … … … … … … … … 194.2.2 Finite Element Method … … … … … … … … … … … … … … … … … … … … .. 204.2.3 The method of py curves … … … … … … … … … … … … … … … … … … … . 20

5.0 Theoretical background: Subgrade reaction modulus … … … … … … … … … … … … … .. 215.1 Winkler soil model … … … … … … … … … … … … … … … … … … … … … … … … … 215.2 Subgrade modulus concept … … … … … … … … … … … … … … … … … … … … … … 245.3 Horizontal subgrade reaction modulus … … … … … … … … … … … … … … … … … .. 25

6.0 Simplified (hand) calculation of piles … … … … … … … … … … … … … … … … … … … .. 296.1 Global analysis … … … … … … … … … … … … … … … … … … … … … … … … … … .. 296.2 Ultimate limit state … … … … … … … … … … … … … … … … … … … … … … … … … 296.3 Calculation of the steel piles supporting integral abutment … … … … … … … … … . 31

6.3.1 Data … … … … … … … … … … … … … … … … … … … … … … … … … … … ... 316.3.2 Ultimate limit capacity … … … … … … … … … … … … … … … … … … … … . 326.3.3 Serviceability Limit State … … … … … … … … … … … … … … … … … … … . 346.3.4 Conclusions … … … … … … … … … … … … … … … … … … … … … … … … ... 36

II Part1.0 Genaral data … … … … … … … … … … … … … … … … … … … … … … … … … … … … … .. 37

1.1 Location … … … … … … … … … … … … … … … … … … … … … … … … … … … … … . 371.2 Soil conditions … … … … … … … … … ..… … … … … … … … … … … … … … … … … . 381.3 Material properties … … … … … ...… … .… … … … … … … … … … … … … … … … … . 381.4 General characteristics of the bridge … … … … … … … … … … … … … … … … … … . 38

2.0 Initial assumptions and calculations comments… … … … … … … … … … … … … … … … . 41

List of contents

Master’s Thesis: “Optimized design of integral abutments for a 3 span composite bridge”

2.1 Design assuptions and calculation comments ..… … … … … … … … … … … … … … . 412.1.1 Bridge model … … … … … … … … … … … … … … … … … … … … … … … … . 412.1.2 Pile model … … … … … … … … ...… … … … … … … … … … … … … … … … ... 412.1.3 Earth pressure … ..… … … … … ...… … … … … … … … … … … … … … … … ... 42

2.2 Calculations of forces acting on piles … … … … … … … … … … … … … … … … … … 422.3 Calculations of initial imperfections of the piles … … … … … … … … … … … … … ... 442.4 Calculations of stresses … … … … … … … … … … … … … … … … … … … … … … … .. 46

2.4.1 Piles crosssections … … … … … … … … … … … … … … … … … … … … … .... 472.4.2 Calculations … … … … … … … … … … … … … … … … … … … … … … ........... 48

2.5 Calculations of stresses with the use of simplified method ..… … … … … … … ......... 562.5.1 Ultimate Limit Capacity … … … … … … … … … … … … … … … … … ............ 572.5.2 Serviceability Limit State … … .… … … … … … … … … … … … … … … ......... 61

2.6 Comparison of stresses … … … … … … … … … … … … … … … … … … ........… … … … 653.0 Actions to lower the stresses in the piles … … … … … … … … … … … .. … … … … ........... 67

3.1 Elimination of horizontal displacements induced during casting … … … … … .......... 673.2 Lower the height of abutment … … … .. … … … … … … … … … … … … … … … ......... 673.3 Use softer material at the pile top … … .… … … … … … … … … … … … … … … … … . 673.4 Construction of a hinge … … … … … … .… … … … … … … … … … … … … … … … … . 70

4.0 Analysis with program SOFiSTiK … … … … … … … … … … … ..… … … … … … … … … .. 734.1 Numerical model… … … … .… … … … … … … … … … … … … … … … … … … … … ... 73

4.1.1 Types of elements… … … .… … … … … … … … … … … … … … … … … … … .. 734.1.2 Elements not included and simplifications … … … … … … … … … … … … … 73

4.2 Calculations… … .… … … … .… … … … … … … … … … … … … … … … … … … … … .. 734.2.1 Design assumptions… … .… … … … … … … … … … … … … … … … … … … ... 734.2.2 Calculations … … … … … … … … … … … ..… … … … … … … … … … … … … . 73

5.0 Summary and conclusions … … … … … … … … … … … .… … … … … … … … … … … … ... 83References … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … .. 83

Appendixes

A. Appendix Calculations of forces and displacements ..… … … … … … … … … … … … … 85B. Appendix: Geometry of the bridge.............................................................................. 117C. Appendix: Calculation of pile and soil stiffnes............................................................ 121D. Appendix: Loads ........................................................................................................ 133E. Appendix: Indata files for caculations of inner forces in bridge members and forcesacting on the abutment ...................................................................................................... 139F. Appendix: Indata files for piles calculations .............................................................. 143G. Appendix: Explanation of commends used in program CONTRAM ........................... 149

Preface

Master’s Thesis: ”Optimized design of integral abutments for a 3 span composite bridge”I

PREFACE

The thesis is performed for a company Ramböll Sverige AB in Luleå as a part ofreasearch on development of integral abutment bridges and their wider application in Sweden.

I would like thank company Ramböll Sverige AB on Luleå for giving me the opportunity to carryout my thesis work at the company and for making me feel so welcome.

Especially I would like to thank my supervisor Professor Peter Collin for his great help, supportand good will. I would also like to thank very much Hans Pétursson for his guidance during my workand for helping me with all the difficulties.

I would like to thank very much my family and friends for their support, help and belief in me.

Luleå, 20050921

Gabriela T ustochowicz

List of contents

Master’s Thesis: “Optimized design of integral abutments for a 3 span composite bridge”II

Abstract

Master’s Thesis: ”Optimized design of integral abutments for a 3 span composite bridge”III

ABSTRACT

The aim of the thesis is to analyse the foundation piles supporting the bridge over DalälvenRiver in the middleeast Sweden, which is designed as an integral abutment bridge. The analytical partof the work includes the checking of stresses in piles supporting integral abutments. The piles that areconsidered are steel piles with three different crosssections: pipe pile with outer diameter equals219.1 mm and 12.5 mm thick and two different crosssections of X piles (200x30mm and 180x24mm), which are the Swedish innovation in the field of integral abutments bridges. The piles analysedare loaded with vertical force and subjected to horizontal displacement caused by contracting andexpanding under influence of temperature changes, but also by breaking and accelerating of vehicleson the bridge and shrinking and creeping of a concrete bridge deck. The particular attention is paid tothe influence of displacements perpendicular to the longitudinal axis of the pile for the pile’sbehaviour. In this analysis the behaviour of pile depends a lot on soil surrounding the pile. Inconnection with this fact the author paid also attention to modelling behaviour of different types of soilin the process of analysing and designing. In the thesis the possible solutions enabling reduce thestresses in piles are also considered.

The analysis of the structure is done with the help of two computer programs using FiniteElement Method and with the help of simplified method. In the Swedish program named CONTRAMconsidered structure is analysed as a flat frame (twodimensional model), in the program SOFiSTiKthe bridge is modelled as a threedimensional structure, however the simplified analysis concernedonly the vertical piles loaded with a vertical axial force and subjected to lateral and rotationaldisplacements at the pile top. The methods and models used are described and compared.

Furthermore, rather an extensive review of available literature related to designing of integralbridges is included in the thesis. In the thesis technological solutions applied in integral abutmentbridges and advantages (especially from economical point of view) and disadvantages of thesestructures are discussed. Examples of application of the integral abutment concept in a few countries,where the widest experience belongs to United States of America, are presented. Information aboutparticular objects is at times rather poor with regard to not bad availability in the literature concerningthe subject.

The problems and uncertainties applied for designing integral bridges and the attempts ofsolving them are discussed. The methods and models available in the literature used for analysis offoundation piles subjected to mentioned influences were described. One of the models, beam on elasticfoundation (or on Winkler’s foundation) is discussed more in detail because of the widespread usageof this model. Also in connection with this model, researches and analyses that had been carried out todefine elasticity of different types of soil, which created the theoretical base concerning the consideredsubject are also presented.

List of contents

Master’s Thesis: “Optimized design of integral abutments for a 3 span composite bridge”IV

SUMMARY

Part I

Chapter 1 Introduction introduces integral and semiintegral bridges as structures offeringnumerous advantages comparing to traditional bridges, especially from economical point of view.However this type of structure has also disadvantages limiting its applications and those are alsodiscussed.

Chapter 2 Literature review has been done to recognise the current state of knowledge concerningintegral abutment bridges around the world with a special interest in following areas: types of piles,pile orientation, pileabutment connection, length limits for integral bridges and behaviour of pilessupporting abutments.

Chapter 3 Practice presents the gained information about a few countries and their experience indesigning and building integral bridges.

Chapter 4 Design models and methods describes problems and uncertainties connected withdesigning integral bridges and the attempts to solve them. Different methods available in the literatureare presented with their advantages and disadvantages.

Chapter 5 Theoretical background includes a theoretical basis for the methods of analysing pilesunder lateral loads. This chapter is focused on the soil response, soil modelling and researchconsidering this subject.

Chapter 6 Simplified calculations of piles presents the simplified calculations for the vertical pilessubjected to vertical force, horizontal displacement and rotation at the pile top. There is also included atheoretical basis for the calculations.

Part II

Chapter 1 General data includes all the data and information necessary for designing bridge overDalälven.

Chapter 2 Initial calculations and stresses analysis includes the analysis of the whole bridge andthe foundation piles. The bridge is considered as supported on the piled integral abutments. Thischapter also compares behaviour of piles with three different crosssections used for integralabutments. There are made calculations of forces and displacements acting on piles caused by appliedloads. Stresses in piles are calculated in two states according to Swedish norm.

Chapter 3 Actions to lower stresses presents calculations of stresses in piles for different optionspossible to decrease stresses in piles.

Chapter 4 Analysis in program SOFiSTiK presents modelling and analysing bridge over Dalälvenas a three dimensional structure.

Chapter 5 Summary and conclusions presents final results and compares all the methods used inthe thesis.

PART I1. Introduction

Master’s Thesis: ”Optimized design of integral abutments for a 3 span composite bridge”1

PART I1.0 Introduction

1.1 WHAT ARE INTEGRAL BRIDGES?

Development of traffic, which happens nowadays in many countries, results in building andmodernization roads and highways. This requires building a great number of small and medium spanbridges. In many countries as Great Britain, Canada and USA these objects are very often built asintegral bridges.

Integral bridges are bridges where the deck is continuous and connected monolithically with theabutment with a momentresisting connection. As an effect we obtain a structure acting as one unit.

The terminology varies in different sources, so sometimes the bridges which just do not havedilatations are called jointless bridges. These structures still have bearings, so the structure still canmove in the horizontal plane (but these movements are limited).In polish literature, there are manydefinitions used with regard to discussed structures: bridges with spans connected with supports withnohinged connection (with regard to the way of supporting spans on supports), frame bridges (withregard to static scheme of construction), bridges supported on piles (with regard to the type offoundation), etc. However, there is no definition which describes all the features of integral structures(a material, foundation type, static scheme and cooperation with surrounding soil).

There exists also a design variant called the semiintegral abutment bridge, which is acombination of conventional and integral abutment bridge. The semiintegral abutment is similar tothe fully integral abutment, except for a lateral joint forming a rotational hinge above the top of thepiles. To prevent shear displacements between the top and bottom sections of the abutment, a dowelpasses through this joint [1].

The use of semiintegral abutments is recommended to eliminate passive pressure belowbridge seats and also for longer bridges to inhibit foundation restraint to longitudinal movement.

Abutment

Pile

Girder

DowelJoint filler

Pile cap

Pile

Abutment

Girder

Figure 1

Enlarged details of fully integral bridge and semiintegral bridge.

The advantage of using semiintegral abutments is that the superstructure behaviour isindependent of the foundation type. Therefore, large spread footings or stiff pile groups can be used.

As the superstructure of the bridge expands and contracts under cyclic movements induced bytemperature variations and traffic (influences from second order effects: creep, shrinkage, thermalgradients, differential settlements, differential deflections and earth pressure also should beconsidered), a series of interactions takes place. We can observe interactions between the abutmentand the approach fill, between the approach fill and the foundation soil, between the abutment and the

PART I1. Inroduction

Master’s Thesis: “Optimized design of integral abutments for a 3 span composite bridge”2

piles supporting it, and between the piles and the foundation soil. Understanding those interactions isimportant for effective design and satisfactory performance of integral bridges.

The concept of integral abutment bridges is based on the theory that the flexibility of the pilingallows transferring thermal stresses to the substructure by the way of a rigid connection between thesuperstructure and substructure. Assumptions are made that concrete abutment contains sufficient bulkto be considered as a rigid mass. The positive moment connection with the ends of the beams orgirders is provided by rigidly connecting the beams or girders and by encasing them in reinforcedconcrete. This provides for full transfer to temperature variations and live load rotational displacementto the abutment piling. The crucial problem concerning piles supporting integral bridges is theirbehaviour under cyclic lateral pile movements induced by temperature variations and traffic (trafficacceleration, breaking and turning) and also by rotations of the superstructue. These bridges do nothave expansion joints so the structure has to withstand moves back and forth when subjected torepeated cyclic loading. However, the possibility of deflections is limited by structural integrity and itcauses formation of additional inner forces that structure has to withstand. This problem is alsoessential for development and wider application of integral bridges and to find out which pile typeperforms in best way. There is a necessity of finding a reasonably good estimation of the forcesgenerated in the abutments for design purposes to ensure satisfactory performance of the integralbridges through their life service.

The integral abutment bridges are usually built as one, two or three span structures. The simplifiedgeometry of one span integral abutment bridge is shown on the Fig. 2.

Foundation Foundation

Abutment Abutment

Superstructure

Bridge systemApproach system

Pevement Approach slab Approach slab Pavement

Sleeperslab

BackfillBackfill

Sleeperslab

Approach slabs and sleeperslabs are optional elements

Figure 2

Simplified geometry of an integral abutment bridge.

Integral abutment bridges have numerous attributes and few limitations. Detailed discussion ofthose is presented below.

1.2 ADVANTAGES OF INTEGRAL BRIDGES

Primarily, integral bridges eliminate the problem associated with movement joints andbearings. The reduction of initial cost is associated with elimination of expensive deck joints, anchorbolts, bearings and their time and money consuming assembling. We can also observe reduction oflong term maintenance costs. The maintenance costs reduction appears due to reduced corrosion (noleakage onto critical structural elements) and reduced material degradation. For this reason integratedbridges are becoming attractive options in cold climates such as northern United States, Canada andnorthern Europe. The integrated structures can eliminate jointrelated damage caused by the use ofdeicing chemicals and restrained growth of rigid movement. In conventional bridges, much of the costof maintenance is related to repair of damage of joints. Even waterproof joints will leak over time,allowing water (saltleaden or otherwise) to pour through the join accelerating corrosion damage togirder ends, bearings and supporting reinforced concrete substructures. The dirt, rocks and trash areaccumulating in the elastomeric glands and leading to failure.

PART I1. Introduction


The absence of deck joints has also advantage for bridge users, which should be quiteimportant factor. The smooth structure without joints provides improved vehicular riding quantity anddiminishes vehicular impact stress level.

Bearings are especially expensive to replace. Over time, steel bearings may tip over and/orseize up due to loss of lubrication or build up of corrosion. Elastomeric bearing can split due tounanticipated movements, or ratchet out of position. Avoiding joints and bearing we can eliminate amajor source of bridges maintenance problems [2].

Integral bridges are also more favourable with a structural point of view. They have increasedreserve load capacity and load distribution, resulting in higher resistance to damaging effects of illegaloverloads. There is also observed reduction of number of foundation piles.

The use of integral abutments allows also avoiding the risk of abutments instability andprovides substantial reserve capacity to resist potentially damaging overloads, by distributing loadsalong the continuous and fulldepth diaphragm at bridge ends.

Structural integrity has additional advantage, which is simplicity of design. An integral bridgemay, for analysis and design purposes, be considered as a continuous frame with a single horizontalmember and two or more vertical members. This eliminates separate design process for superstructureand foundations. On the other hand, integral bridges present a challenge for load distributioncalculations because the bridge deck, piers, abutments, embankments and soil must all be consideredas a single compliant system. There are also some more complicated interactions which are difficult tomodel in design process.

The article [3] presents that the concept of integral abutment bridges can be appliedsuccessfully for new designed and built bridges, also with skewed alignments, as well as forstrengthening existing bridges. In addition, since the simple design of the integral abutments lendsitself to simple structural modifications, future widening or bridge replacement becomes easier.

1.3 PROBLEMS AND UNCERTAINTIES

Despite the significant advantages of integral abutment bridges, there are some problems anduncertainties associated with them.

The article written by John S. Horvath [4] suggests that integral abutment bridges problemsare fundamentally geotechnical in the nature and they can manifest themselves both structurally andgeotechnically any time in the life of an integral abutment bridge.

Many articles, however mention, that the main problem connected with integral abutmentbridges are consequences of temperature variations and traffic loads, which cause horizontal bridgemovements. Horizontal movements and rotations of the abutment cause settlement of the approach fill,resulting in a void near abutment if the bridge has approach slabs.

Effects of lateral movements of integral abutments under cyclic loadings are obvious problemwhich demands solving, but positive aspect in this case is that temperature induced displacements inthe traditional bridge is over twice bigger than displacement at the end of (considering objects with thesame span length) integrated structure because of symmetrical nature of the thermal effects asillustrated on the Fig. 3 [5].

(a) freely supported (b) continuous

TT

< /2 < /2

Figure 3

Thermal displacements of the load carrying structureFor the reason of temperatureinduced displacements, concrete bridges are regarded as more

suited for integral bridge constructions as they are less sensitive to temperature variations andrecommended especially in cold climates.

The other uncertainties connected with designing and performance of integral abutment bridges are:

PART I1. Inroduction


The elimination of intermediate joints in multiple spans results in a structural continuity thatmay induce secondary stresses in the superstructure. These forces due to shrinkage, creep, thermalgradients, differential settlement, differential deflections, and earth pressure) can cause cracks inconcrete bridge abutments. Wingwalls can crack due to rotation and contraction of the superstructure.

Some sources recommend integral abutments for skewed bridges, but the design process forthis type of structure should be careful and approximate methods should not be used. Most of thesemethods do not include the influence of torsional moments arising in integral skewed bridges. Thebehaviour of skewed integral bridges differs from straight bridges. Under the influence of cyclicchanges in earth pressures on the abutment, the skewed integral bridges tend to rotate [6]. In USA thedesign guideline recommends that the skew angles for integral bridges should be less than 20 degrees.

Bridge abutment can be undermined due to water entering into the approach fills at the bridge ends.

The piles that support the abutments may be subjected to high stresses as a result of cyclicelongation and contraction of the bridge structure. These stresses can cause formation of plastic hingesin the piles and may reduce their axial load capacities.

The application of integral bridge concept has few other limitations. Integral bridges can notbe used with weak embankments or subsoil, and they can only be used for limited lengths, althoughthe maximum length is still somewhat unclear. Integral bridges are suitable if the expectedtemperature induced moment at each abutment is certain value specified by suitable authorities inevery country, and somewhat larger moments can be tolerable.

PART I2. Literature rewiev


2.0 Literature review

The objectives of literature review are:1) to recognize the current state of knowledge concerning integral bridges around the world,2) to review available pile types and solutions used in steel and composite bridges with integral

abutments,3) to synthesize the information available on the general behaviour of integral bridges.

The results of literature review and obtained information were organized according to followingareas of interest:

§ Types of piles§ Pile configuration§ Pile orientation§ Pileabutment connection§ Length limits for integral bridges§ Behaviour of piles supporting the abutment

2.1 TYPES OF PILES (AND PILES SIZE)

Literature review made in [6] revealed that there was found limited number of publishedpapers in the subject area. These publications concerned behaviour of integral bridges (survey of fiveexisting bridges: The Cass Country Bridge, The Boone River Bridge, The Maple River Bridge, abridge in Rochester (Minnesota), Route 257 overpass on I81 . All these bridges were supported by Hpiles, which were able to withstand the loads, including those induced by temperature variations. Nosign of damage was reported. Author suggests that steel Hpiles can withstand cyclic loading as longas the maximum stresses remain equal to or less than the nominal yield stress of the pile material.

After testing three types of piles, which were steel Hpile, steel pipe pile and concrete prestressedpile the author of [6] drew following conclusions and recommendations.

For a given pile width pipe piles have significantly higher flexural stiffness than steel Hpiles isweak axis bending. This is why for a given displacement in an abutment supported by pipe piles thestresses will be higher then in an abutment supported by steel Hpiles oriented in weak axis bending.In other words, the abutment will be more severely loaded if stiff pipe piles are used. Therefore, stiffpipe piles are not recommended for support of integral bridges.

Concrete piles are not recommended for integral bridge support, because under lateral loadstension cracks progressively worsen and significantly reduce the vertical load carrying capacity ofthese piles.

It is also worth mentioning that the strongly recommended abutment type is stub abutment(abutments with a length ~1.0 m below the deck soffit), because the use of this type of abutmentreduces the detrimental effects of thermalinduced movements on the components of the bridge.

2.2 PILE CONFIGURATION

The only recommendation given by Tennessee Department of Transportation in [7], but also byDepartments of Transportation in many states, is to use one row of piles driven vertically. Orientingpiles vertically causes that the abutment can move in the longitudinal direction and greater amount offlexibility is achieved to accommodate cyclic movements.

The Swedish innovation in integral abutment bridges is the use of Xshaped piles. Piles aresupposed to be located in one row vertically. The piles are rotated 45 degrees from the line of supportin order to minimise the bending stresses from traffic load (Fig. 4). [8]’

PART I2. Literature review


1 1

45°

900 900 900 1500

Figure 4

Pile configuration in bridge over Fjällån.

2.3 PILE ORIENTATION

A survey taken in 1983 [9] demonstrated that states in USA differ in opinion and practice withregard to pile orientation. Fifteen states orient piling so that the direction of thermal movement causesbending about the strong axis of the pile. Thirteen others orient the piling so that the direction ofmovement causes bending about the weak axis of the pile. Both methods have proven to besatisfactory to the respective agencies. Orienting the piling for weakaxis bending offers the leastresistance and facilitates pilehead bending for fixed head conditions. However, due to the potentialfor flange buckling, the total lateral displacement that can be accommodated is more limited thanwhen the piling is oriented for strongaxis bending. However the most often recommendation is tofacilitate the bending about weak axis of the pile, which means that the web of the H piles should beperpendicular to centreline of the beams regardless of the skew.

From the comparative analysis of two sizes of Hpiles (HP 310x125 and HP 250x85) presentedin [10] it was concluded that the axis of bending has only a negligible effect of the displacementcapacity of integral bridges with stub abutments. This may not be true for bridges with larger abutmentheight.

According to [11] it is observed that at small abutment displacements where the backfill and thefoundation soil remains within elastic limits, the size and orientation of the piles do not have aremarkable effect on the magnitude of the bending moment and shear forces in the abutment.However, at larger displacements, as the size of pile increases, the maximum bending moment and theshear force in the abutment increases as well.

2.4 PILEABUTMENT CONNECTION

The abutmentpile connection detail is believed to have a significant influence on the pile stresses[12].

Anchorage of beams to pile cap Steel beams according to [13] should be connected to the pile caps with anchor bolts prior to makingintegral connections.

There are two solutions of pile – abutment connection proposed in [2]:− Placing beams on ¼ in. plain elastomeric pads, anchor bolts pass from the abutment pile cap

through both the pad and the bottom flange of the beam or girder ( Fig. 5);



21

ELASTOMERIC PAD

4'' minimum6'' typical

ELASTOMERIC PAD


21

APPROACH SLAB

typical deckreinforcement

Figure 5

− Usage of taller projecting anchor bolts equipped with double nuts, one above and one below theflange; this method provides better control over the grade of the beam and requires lessprecision in preparing the bridge seats of the pile cap (Fig. 6).

21


ANCHOR BOLTW/ DOUBLE NUTS

typical deckreinforcement

APPROACH SLAB

21


RF BAR

ANCHOR BOLTW/ DOUBLE NUTS

Figure 6

The connection between the abutments and the superstructure shall be assumed to bepinned for the superstructure’s design and analysis. The superstructure design shall include a check forthe adverse effects of fixity. [14]

The typical detail used in Scotch Road Bridge over Route I95, showed on Fig. 7, is theother possible solution for pile – abutment connection detail, which insures full moment transfer.



Figure 7

The detail of pileabutment connection used in Scotch Road, I95 Integral Abutment Bridge

The alternate jointless bridge detail is proposed in the article [15] and showed on the Fig. 8 Inthis option the beams are rigidly connected to pear caps and abutments, and a continuous reinforcedconcrete or asphalt wearing surface is provided. When steel sections are used, for example, shearconnectors are welded to beam ends and encased in reinforced concrete pier caps and abutments.Shear connectors are also welded to the top flanges to develop the composite action with a reinforcedconcrete deck slab. These methods have been extensively used in New Zealand and Australia in lengths up to 160 feet.

Figure 8

Alternate joint less bridge detail for steel beam bridge.

2.5 LENGTH LIMITS

Reasons for length limitations for integral bridges: As the length of integral bridges increases, the temperatureinduced lateral cyclic displacements

in steel piles supporting construction become larger as well. As a result, the piles may experiencecyclic plastic deformations. This may result in the reduction of their service life due to lowcyclefatigue effects. Thus, the lengths of integral bridges should be limited to minimize such determineeffects.

The ability of piles to accommodate lateral displacements is a significant factor in determining themaximum possible length bridges, because temperature induced displacements are proportional tobridge length. The way to build the longer bridges is to keep the stresses in piles low [16].



Maximum length for steel integral bridges recommended in United States range between 80 and145 m in cold climates, and between 125 to 220 m in moderate climates [17]. Sometimes thelimitations are not in force and there are built longer bridges. For example Tennessee Department ofTransportation recommends maximal length for steel bridges with integral abutments – 120 m and forconcrete bridges 240 m. The newer data available in article [17] considering length limits for integralabutment bridges from various state departments of transportation for comparison purposes arepresented in Table 2.1. The longest bridges with integral abutments are: steel bridge – 152m andconcrete bridge – 352 m. In Sweden and Great Britain the recommended length for integral abutmentbridges is 60 – 70 m [18].

Despite some recommendations, universal guidelines to determine the maximum length of integralbridges do not exist. Generally, bridge designers, especially in USA, depend on the performance ofpreviously constructed integral bridges to specify the maximum lengths for their new designs.

According to [19] the most of the problems connected with temperature induced movements doesnot have substantial influence on the work of construction with the total length shorter than 60m. Inthe case of longer bridge there must be carried out researches to estimate approach fill movements, butthis kind of necessity do not exist very often, because in most of countries the percentage of new builtlong bridges is very small.

Table 2.1: Maximum length limits for integral bridges.Department ofTransportation

Steel bridgeslength [m]

Concrete bridgeslength [m]

Colorado 195 240Illinois 95 125New Jersey 140 140Ontario, Canada 100 100Tennessee 152 244Washington 91 107

It is noteworthy that concrete bridges are more recommended than steel bridges as integralstructures. Assuming the same length and localization, the seasonal thermalinduced displacements insteel integral bridge are about 20% bigger than displacements induced in concrete bridge. The dailytemperature induced displacements for steel bridge can be around three times bigger than for concretebridge [19].

2.6 BEHAVIOUR OF PILES SUPPORTING THE ABUTMENTS

While designing integral bridges, designers have to pay special attention on piles supportingabutments. One of the not finally solved problems is their behaviour under influence of climatic,meteorological and topographic factors. In integral bridges the thermal deformations are considered asthreedimensional and their scale and directions depend on: geometry of the bridge, length of spans,height of the supports, type of crosssection, deck/supports stiffness ratio and the material, that thestructure is made of.

The number and magnitude of factors cause that this is not possible to accurately estimate valuesof thermal displacements and deformations, so also we can observe not expected behaviour of thebridge.This is why there are limitations in application of integral bridges [19].

The ability of foundation piles to carry the vertical load may be reduced when piles aresubjected to lateral displacements. Piles can fail when the induced lateral loads are higher than theelastic buckling load. The effective designing of piles should assure the low level of stresses indesigned piles. However this may be difficult, because of a big number of parameters that influencethe magnitude of strains in the piles, e.g. changes of temperature, number of the trucks that pass thebridge and their weight, span length, stiffness of soil surrounding the pile, stiffness of the bridge deckand the height of the abutment wall.



One of used methods to decrease stresses in piles is using predrilled oversized holes filled withloose sand after pile drilling, but this is a good practice when the stiffness of removed soil is higherthan that of the loose sand, this mean for very stiff soil [16].

The Figure 9 shows the installation of the sleeved HP piles within crushed stoned backfill. Thegap between the sleeving is filled with sand to facilitate the movement of the piles as subjected tolateral displacements transferred from the superstructure (applied for The Scotch Road Bridge, locatedin Trenton, New Jersey). In USA there are similar recommendations to use prebored holes filled withgranular material as one of the solutions to make the abutment more compatible with longitudinalmovements [20].

Figure 9

Installation of the sleeved HP piles within crushed stoned backfill.

The opinions about behaviour of piles under vertical loads and influences of lateral movementsdiffer. But most probable opinion scenario is that although a section in steel pile may reach yieldstresses, this does not imply that the ultimate load is reached. The further load increase is possible,because the bending moment along the pile can be redistributed. The more advanced tools at presentallow for analysis based on plastic design. If the elastic theory is used to design the piles, the momentredistribution and effects of plastic behaviour of the pile can not be taken into account [21].

The behaviour of piles supporting integral abutments depends, between others, on stiffness ofsoil which is adjacent to the piles. The research described in [22] revealed that piles driven in stiffersoils will experience moment magnitudes greater than those experienced by piles driven in softer soil.The models with less stiff soil are capable to withstand a larger axial load than those in stiffer soil.However it should be noticed that to big reduction of soil stiffness may result buckling of pilesbecause of lack of lateral support. As described above, there are many factors that have an influence on behaviour of piles supportingintegral abutment bridges and this is the reason why it is very difficult to suggest design rules that arevalid for all bridges with integral abutment.

PART I3. Practice


3.0 Practice

Integral abutment bridges are not commonly used in Europe but the researches and observationsare going on in many countries. Lack of experience in designing bridges with integral abutmentsmakes it time consuming. Also people from roads administration have a little experience andknowledge in this field and therefore demand vary detailed analysis. The increased demand of verydetailed analysis makes the design process very expensive. The costs saved in construction stage maybe consumed in designing stage to make the offer satisfactory for everyone. Despite these problems,we can observe progress in this field in many countries.

3.1 UNITED STATES OF AMERICA

In the USA integral abutment bridges have been built since the 1960’s and are increasinglybeing used for replacement structures. The concept of integral abutment bridges has been proved to becompetitive in this country and it is believed to be so in most countries, if only given the chance bycontractors and authorities. Tennessee with more than 2 400 bridges with integral abutment isprobably the state with the widest experience in this field.

The example of attempts to improve the integral abutment idea can be built in Tennessee StateBridge carrying Route 50 over Happy Hollow Creek (Fig. 10) at a total length of 1,175 ft. (358 m),which is the longest jointless integral abutment bridge in the country.

Figure 10

Happy Hollow Creek

The other examples of integral abutment bridges built in USA are:

v Big East River Bridge, 63.4m long and 13.96m wide.

Figure 11

Big East River Bridge.

PART I3. Practice


v Highway 518 Parry Sound one span bridge with the length of 47.4 m supported on pilesHP310x310.

Figure 12

Highway 518 Parry Sound

v Duffin Creek Bridge

Figure 13

Duffin Creek Bridge

For bridges presented above there has been found no data about their performance. However inUSA there is a big number of bridges with integral abutments. For example authors of article [1]present results of studies on behaviour of integral abutment bridges. Investigated bridges were:

v The Cass Country Bridge in Fargo, in Dakota, which is six spans concrete bridge. Total lengthof the bridge is 137 m and width 9.7 m. The bridge consists of six spans, 22.9 m each. TheBoone River Bridge, in central Iowa, which is also concrete bridge with prestressed concretegirders. The bridge is 98.9m long with four continuous spans and 12.2 m, with a skew of 45º.

v The Maple River Bridge located in northwest Iowa and consists of a composite concrete deckand steel girders. Total bridge has three spans and is 97.5 m long. The bridge is 9.75 m wide,with a skew of 30º.

v The unnamed concrete bridge located in Rochester, Minnesota, built in 1996. The bridge is 66m long with 3 equal spans, 22m each and 12 m wide.

All of those bridges are supported on H piles oriented in weakaxis bending under abutments. Thefirst of mentioned bridges has also integral piers but supported on H piles oriented in strongaxis

PART I3. Practice


bending. For three out of four examined bridges, the foundation piles were installed in predrilledboreholes. Even though the departments of transportation in many states recommend for integralabutments one row of vertical piles, the Boone River Bridge and the Maple River Bridge havefoundation piles battered in the movement direction of the bridge. During the monitoring period of theCass Country Bridge, the strain gauges failed. However with analytical methods it was found that themaximal stresses in piles were around the yield stress. For two other bridges monitoring periodrevealed that stresses in piles are around 6075% of the nominal yield stress. For the last mentionedbridge the highest stresses in piles were slightly above the nominal yield stress of the piles. In all ofthose bridges the foundation piles were able to tolerate the expansioncontraction cycle withoutdamage.

3.2 SWEDEN

In Sweden the concept of integral abutment bridges becomes more popular, but there is a needto adapt wide American experience in this field to Swedish conditions. To develop the technology andsolutions used in designing and building integral bridges the Division of Steel Structures at LuleåUniversity of Technology realised a postgraduate project – the licentiate thesis of Hans Pètursson[23].

The thesis included static testing of Xpiles, Swedish innovation in integral abutment bridgestechnology. The piles tests simulated forces, to which piles are subjected in real conditions: normalforces and lateral displacements corresponding to displacements induced by temperature movementsat the ends of the bridge. Of course, as it was said before, not only temperature induced expansion andcontraction, but also by changes of air moisture, traffic, second order effects, etc. The effects ofmentioned influences were also analysed with help of computer simulations.

v Bridge over Fjällån

The new technology was put into practice while building the bridge crossing over the FjällånRiver [8].

Bridge is located in the Swedish province Västerbotten. This is a single span composite bridgewith a span of length of 37.15 m. The bridge is supported by eight X piles (180x24 mm) for eachabutment. The piles were rotated 45 degrees from the line of support in order to minimise the bendingstresses.

Figure 14

Bridge over Fjällån after completion

PART I3. Practice


v Bridge over Hökvik River

The bridge is located in the central part of Sweden. This is an arch bridge with the span length 42m.The idea of integral abutment bridge was used in this case to replace the old concrete bridge.

The construction works were completed in September 2004. The advantage of using integral abutmentbridge technology for the new bridge was that the foundation of the old bridge was left in place andthe piles of the integral abutments were driven just behind the old abutment (visible on the Fig. 15).The choice of integral abutments had time saving benefit, because the old abutment did not have to beremoved.

Figure 15

Bridge W1299 over Hökviksån in Linghed.

There was also used technology which allows decrease the stresses in piles caused by lateralmovements. The steel tubes were placed over the piles and the loose sand was filled around the piles.This action should minimise the pressure against the piles, when they deform due to translation androtation. The piles supporting abutments are steel cross shaped piles (Fig.16) with width (b) equals 200mmand thickness (t) equals 30 mm. Under each abutment was placed one row of eight piles. Six of themwere driven vertically and two the outermost are inclined (4:1) to take counteract transverse horizontalloads, which are wind and transverse component of vehicle brake force.

h

t

b

a

Figure 16

Cross section of X pile.

v One span, concrete, monolithic flyover showed on the Fig. 17 can be described as an exampleof the simplest integral flyover.

The type of integral bridge shown on the Fig.17 has been one of the most common types ofbridges in Sweden for over 70 years. In this country at least 8 000 out of 14 000 bridges owned by TheSwedish Road Administration are of the type shown above [24].

.

PART I3. Practice


Figure 17

The example of integral structure monolithic concrete frame flyover .Integral slab frame bridge

One of the main reasons why integral abutment bridges have not become common in Swedenis the difficulty with analysing them.

3.3 POLAND

In Poland there is also visible interest in integrated load carrying system and socalled smalland medium bridges are built as integral bridges. Unfortunately many designers did not include in thedesign process interactions between structure and surrounding soil while temperature inducedmovements. Many solutions did not appear favourably because proper draining devices were notapplied. These facts brought about that many solutions did not function properly [5].

According to Wojciech Trochymiak [6], the integral structures supported on piles are not, byno means, a novelty. They were built already before the II World War, but then called bridges onFerro concrete piles.

There were for example built:v In 1930’s the bridge over Tarczynka River in Tarczyn,

Figure 18

v The bridge over the Srebrna River in Mi sk Mazowiecki,

Figure 19

PART I3. Practice


v The one span composite integral fly over in Wyszogród

Figure 20

The built ring road of Ostrowia Mazowiecka crosses the singletrack railway line, so there wasa need to design two similar flyovers with a big angle of skew (130.29 between the longitudinal axisof the road and the longitudinal axis of the railway line). The integral abutment solution was chosenfor these purposes because of few reasons. The main reasons are: less expected maintenance costscompared to a traditional solution and the big skew of the flyovers that would cause the necessity ofvery complicated bearings and dilatations.

Figure 21

One of the flyovers on the Ostrowia Mazowiecka ring road.

Even though the interest in integral abutment bridges arises, nowadays in Poland there areneither length limitations nor recommendations for integral bridges. This is why designers almostnever choose integral structures [19].

3.4 UNITED KINGDOM

The one of the first integral bridges in UK was The North Shotton overbridge (Fig. 22) on theA1 Trunk Road in Numberland. The bridge was designed by Northumberland County CouncilTechnical Services Consultancy on behalf of the Highways Agency using recommendations containedin a draft version of the design standard which was later issued as BA & BD 57 and with the help ofLUSAS Bridge analysis. The bridge is two spans continuous bridge with four steel plate girders and areinforced concrete deck. The abutments are supported on steel H piles oriented in weak axis bending.

PART I3. Practice


Figure 22

The North Shotton over bridge.

In this country, the Highways Agency Departmental Standard, BD57, "Design for Durability",requires designers to consider designing all bridges with lengths of up to 60 metres and skew angles ofless than 30 degrees as integral bridges. This advice is intended to prevent all the maintenanceproblems connected with transition joints.

3.5 GERMANY

v Berching South Bridgev Nesselgrund Bridgev Schwabachtal Bridgev Rednitztal Bridge (These bridges were built for the Deutsche Bahn AG)

3.6 CANADA

The examples of steel integral bridges supported on piled foundation type:

v Browns River BridgeThe bridge has steel Igirders and the span of length 15+60+15=90m. The bridge is 22.4 m

wide.

v Forbidden Plateau UnderpassThe bridge is one span with the length of 42 m and 22.4 m wide. Bridge has steel box girder.

PART I3. Practice


PART I4. Design models and methods

Master’s Thesis: ” Optimized design of integral abutments for a 3 span composite bridge”19

4.0 Design models and methods.

Integral abutments have been successfully used for over 50 years, but their implementation(especially in USA) has been anything but an exact science, but rather a matter of intuition,experimentation and observation. Despite the lack of proper analytical tools, engineers have beenpushing the envelope by constructing longer and longer integral bridges, thus building on the lessonslearned. Since the age of the computer started, the tools have been developing and nowadays there is abig number of possible methods. The design process demands prediction of behaviour of the wholestructure, but especially problematic for integral abutment bridges is the behaviour of the pilessupporting abutments. The problems and uncertainties connected with designing integral bridges havebeen discussed in point 1.0. Here are presented chosen methods to analyse the piles under lateral loadsand also the whole structure, suggested in the literature as the most widely used.

4.1 GENERAL ISSUE

As we consider case when the soil along the pile length is not changing and the soil stiffness isconstant, the calculation of foundation piles is not complicated. In point 6.0 there is the example ofcalculating the ultimate limit capacity and the plastic stresses in three types of piles. In more realcases, when the soil along the pile length varies, the common practice is to model the soil byspecifying a series of spring supports along a pile. In this way we can approximate the soil behaviour,when the structural load effects are the main item of interest. When the soil movement is of interestcontinuum models are used instead [21].

In designing steel piles supporting integral abutments there is no need to consider lateraltorsionalbuckling or global buckling instability, because piles are laterally supported by the surrounding soil.However, the width to thickness ratios of the flanges and the web for steel H piles (the mostlyrecommended piles in most of states in USA) must be limited to allow for large plastic deformationswithout local buckling.

4.2 CALCULATION METHODS

The literature review in [7] presents various methods to calculate laterally loaded piles such as theMethod of py Curves Differential Equation, Closed Form Formula, Approximate Solution Methods,Empirical Methods and Equivalent Cantilever Method. These methods for solving laterally loadedpile problems are mostly empirical since the soil modulus is not a unique soil property. Numericalmethods such as finite difference and finite element methods provide very accurate results if the soilpressure is appropriately represented.

4.2.1 Equivalent cantilever method.

The equivalent cantilever method is a quite commonly used method and this is a simplified modeloffered by Abendorth. The soilpile system is modelled as an equivalent length of horizontallyunsupported cantilever beamcolumn (the model showed on Fig. 23). The method is based onanalytical and finite element studies and introduces an equivalent cantilever column to replace theactual pile. In other words, the soilpile system is reduced to an equivalent cantilever column. Themethod provides two alternatives involving both elastic and plastic behaviour. Finite elementsimulations indicated that both alternatives are conservative. Both alternatives are concerned with thevertical load carrying capacity of piles under lateral displacements induced by temperature changes,traffic and secondary forces. This method does not consider the effects of the abutmentapproach fillinteractions [16].



A bu tm ent

Pile

Le

M om en td iagram

Figure 23

Equivalent cantilever concept.

4.2.2 Finite Element Method

Finite Element Method nowadays is probably the most often used method to analyseconstructions. There is a great number of computer programmes, which allow defining the structure,creating model and apply the loads. Proper analysis is mostly a matter of defining a model as near toreal conditions as possible.

There are researches going on the proper integral bridge mode. Khodair and Hassiotis present intheir report [13] that there is a possibility to model integral abutment bridges with the use of finiteelement method model and obtain results very similar to experimental data (results were measured bydata acquisition system connected to fully instrumented bridge).

For FEM analysis the most usual case is laterally loaded piles modelled as elastic beamcolumnand the soil as a series of uncoupled “Winkler” springs (more about the Winkler soil model in point5.0) . The most proper representation of laterally loaded pile seems to be the 3Dmodel. The problemis threedimensional, because apart from vertical force acting on the pile, lateral loading causes lateraldisplacements on planes perpendicular to the vertical axis of the pile.

4.2.3 The Method of py Curves

The py curve method is a widely used empirical method in the subject area and it considers thefact that the soil pressure (p) and the pile deflection (y) are nonlinear. The essential of the method isto introduce a series of py curves to represent the true behaviour of soils by considering the nonlinearity of the soil modulus. The main purpose of the method is to obtain a representative value of kh– modulus of horizontal subgrade reaction for the desired depth and deflection values. This isaccomplished through an iterative process by assuming a deflection and calculating the value of kh.The iterations are continued until the assumed and calculated deflections are the same within atolerance limit. When representative py curves are used, the method is capable of reflecting the realdeflection behaviour of the pile and the moment distribution along the pile. The challenge is to obtaina representative set of py curves for each site.

The most crucial point of the solution is the proper representation of the soil modulus throughp(x). If p(x) is assumed to be linear, then a system of linear equations is obtained. The solutionbecomes trivial with matrix solvers. It is a well known fact that p(x) is a function of the lateraldeflection, which leads to a set of nonlinear equations. For nonlinear p(x), the solution is obtained byiterative procedures by assuming deflections for each node and thereby calculating p(x) and solvingfor qj (nodal unknowns) until the assumed and the calculated nodal unknowns are the same within atolerance range. The Newton and the Modified Newton methods are mostly used for iteration.



The py curve method is related to Subgrade Reaction Approach, which is also one of the mostoften used methods to analyse the behaviour of piles loaded laterally. In this work piles are analysedwith the use of Subgrade Reaction Approach and this method and its assumptions will be discussedmore detailed in Chapter 4: Theoretical background.

Most of methods to solve laterally loaded pile problems are empirical, since the soil modulus isnot a unique soil property. According to Arsoy Sami [7] numerical methods such as finite differenceand finite element methods provide very accurate results if the soil pressure is appropriatelyrepresented. The equivalent cantilever method does not consider the effects of the abutment/approachfill interactions.



PART I:5. Theoretical backround


5.0 Theoretical background: Horizontal Subgrade Reaction Modulus.

The aim of this part is introduce theoretical basis used in designing foundations, in considered inthis work case: piles subjected to vertical loads and lateral displacements.

5.1 THE WINKLER SOIL MODEL

The Winkler soil model (1867) treats foundation as a beam on the elastic foundation (Fig. 24 above), but the elastic medium is replaced by a series of infinitely closely spaced independent andelastic springs. The model for this soil idealization is showed below on Fig. 24 [25].

W

beam of EI

reaction dependent on deflection ofindividual springs only

beam of EI

Figure 24

Beam on the elastic foundation (above), Winkler’s idealization (below)

For vertical piles there can be made similar idealization and the predicted behaviour of thelaterally loaded piles according to Winkler’s idealization is showed on Fig. 25. Unfortunately, the realsoilreaction deflection relationship is nonlinear and the Winkler’s idealization would requiremodification.

P

y

x

p=kxyx

Pile, EI

Pile beforeloading

Pile beforeloading

MQground surface

x

ground surface

M

Elastic springskh=p/y

Qy

P

Figure 25

Laterally loaded pile in soil (on the left), laterally loaded pile on springs (right).

PART I5. Theoretical background


In the Winkler’s soil idealization the soil is represented by springs. For the design purposethere is a need to determine the soil stiffness – spring constants. The stiffness of those springs can beexpressed with the use of modulus of horizontal subgrade reaction:

= 2length

forceypkh

wherep – the soil reaction at a point on the pile per unit of the length along the pile,y – the pile deflection at this point .

In some sources [25] it is claimed that the determination of deflections and moments of pilessubjected to lateral loads and moments based on the theory of subgrade reaction is unsatisfactory,because the continuity of the soil mass is not taken into account.

5.2 SUBGRADE MODULUS CONCEPT

The analysis of laterally loaded piles can be done generally in two ways. The first way is to findthe allowable lateral load by dividing the ultimate load by an adequate factor of safety. The othermethod consists in finding the allowable lateral load that is corresponding to an acceptable lateraldeflection. Those two ways determine two groups of methods of analysing piles subjected to lateralloads.

In the analysis done in this work, there is used programme CONTRAM in which the soil isassumed to act as series of independent linearly elastic springs (Winkler’s soil idealization). For thisreason, the discussion in this chapter will be limited to method called in [25] Modulus of SubgradeReaction Approach (Reese and Matlock, 1956), which also treats a laterally loaded pile as a beam onelastic foundation.

In 1961 Vesic extended Biot’s work concerning a flexible beam supported on an elastic half space.He assumed piles as a long relatively flexible member and showed that the error in computations ofbending moments based on the subgrade reaction modulus is no more than few percent comparing tothe solution based on the theory of plasticity.

Therefore, the subgrade modulus concept has a reasonable theoretical foundation and has beenused in practice for a long time. This is quite commonly used method for computing response of pilesunder lateral loads. The advantage of this method is a relative simplicity and this method canincorporate factors such as nonlinearity, variation of subgrade reaction with depth and layeredsystems. On the other hand this method has also disadvantages such as: not considering continuity ofthe soil and the use of modulus of subgrade reaction, which is not a unique soil property but dependson the foundation size and deflection.

The behaviour of a laterally loaded pile can be analysed by using the equation of a beam on theelastic foundation. For the case, when the modulus of subgrade reaction (kh) varies with depth and canbe expressed as a function of deflection (y) kh = f(y), the equation for the beam is following:

0)(4

4

=+EI

yyfdx

yd

For the more simple case, when the subgrade reaction modulus (kh) is assumed as constant with thedepth, the equation for the beam on the elastic foundation can be rewritten:

04

4

=+EI

ykdx

yd h

5.3 HORIZONTAL SUBGRADE REACTION MODULUS

In point 4.0 there has been described the py curve method, which is connected with the subgradereaction modulus concept. Fig. 26 shows a typical soil reaction versus deflection curve (py curve) forsoil surrounding laterally loaded piles.



Deflection, y

Soil

reac

tion,

pSecant

modulus

p vs y

Tangentmodulus

Figure 26

Soil reaction versus deflection for soil surrounding a pile.

For soil reactions less than one third to one half of the ultimate soil reaction, the py relationship can be expressed adequately by a tangent modulus. The slope of the line is the coefficient of horizontal subgrade reaction for the pile, kh.

For soil reactions exceeding approximately one third to one half of the ultimate soil reaction, the secant modulus should be considered. The horizontal subgrade modulus becomes a function of the deflection.

Many researchers tried to find the actual variation of the subgrade modulus with depth and theresults of some of those can be found in [25].

The investigations considered different types of soil and the example results are as follows:

Uniform preloaded cohesive soils

Terzaghi (1955) [25] recommended that for this type of soil the kh can be assumed as constantwith depth (k = const) as shown on the Fig. 27 with the dashed line. However, because ofdeformations of the soil at the ground surface, there is more realistic variation of the subgrade reactionmodulus showed at the same figure by the solid line.

h

x

Assumedk = const

Probablereal

Figure 27

Variation of subgrade modulus with depth for preloaded cohesive soils.



§ Granular soils [25]

For these soils Tarzaghi (1995) recommended that subgrade modulus can be considered as directlyproportional with the depth, so the variation of kh would look as shown on the Fig. 28 by the dashedline. According to his recommendations the sub grade reaction modulus can be expressed with thefollowing formula:

znk hh =where:nh – the constant of the horizontal sub grade reaction [units of force/length3],z – depth.However the actual variation of kh with depth is indicated schematically by the solid line on

the Fig. 27.In 1962 Parkash demonstrated on the model scale that both the Terzaghi’s recommendation

for sands and the schematic variation presented with the solid line on the figure beneath are realistic.

Probablereal

xAssumedk = const

kh

Figure 28

Variation of subgrade modulus with depth for granular soils , normally loaded silts and clays.

The values of the coefficient of subgrade reaction nh were proposed for example by Davisson(1970) on the basis on simple soil tests and they can be regarded as reasonable. The estimated valuesof nh are presented in the Table 5.1.

Table 5.1 Estimated values of coefficient of subgrade reaction modulus after Davisson, 1970.

Soil type Values

Granular nh ranges from 0.408 to 54.4 MN/m3, is generally in the range from 2.72 to 27.2 MN/m3, and is approximately proportional to relative density

Normally loadedorganic silt nh ranges from 0.1088 to 0.816 MN/m3

Peat nh is approximately 0.0544 MN/m3

Cohesive soils kh is approximately 67 Cu, where Cu is undrained shear strength of the soil

In subgrade reaction approach the distribution of subgrade reaction modulus has beenproblematic and also has been a subject of many investigations. Between many distributions that havebeen employed, the most widely used is that developed by Palmer and Thompson (1948), which is ofthe form:



n

Lh Lzkk

=

where:kL – value of kh at the pile tip (z = L),L is pile’s length,z – any point along the pile depth,n – empirical index equal to or greater than zero.

The most common assumptions are that:n = 0 – when the modulus is constant with depth, that can be used for clay,n = 1 – when the modulus increases linearly with the depth, that can be assumed for granular

soil [26]. For the case n=1, it is convenient to reexpress the variation of kh as follows:

=

dznk hh

where:nh – coefficient of subgrade reaction (units of force/length3),d –pile’s diameter,z – depth below the surface.

This formula is used in the Swedish code.

According to M. Dicleli and S.M. Albhaisi [17] the subgrade reaction modulus can be represented byformulas summarized in Table 5.2.

Table 5.2 Modulus of horizontal subgrade reaction, kh.

Soil type kh

Soft clay and stiff clay 9Cu/2.5 50

Very stiff clay 9Cu/4 50

Sand kz

Where:Cu – undrained shear strength of the clay [kPa],

50 – the soil strain at 50% of the ultimate soil resistance,k coefficient of subgrade reaction (units of force/length3),kh – subgrade constant of the soil [kN/m3], (nh – mentioned above),z – depth below the ground surface [m].



PART I:6. Simplified calculations


6.0 Simplified Calculation of piles

Presented calculation is done according to simplified design method described in [12]. Thismodel includes the reduction in vertical loadcarrying capacity of the piles due to lateral movement asan important parameter in designing the piles. According to author of the article [12] the resultsreceived from the simplified model were compared to results from a nonlinear finite element programand shown to be conservative with respect to the finite element model.

6.1 GLOBAL ANALYSIS:

The calculations for integral bridges can be done with the use of different methods andtools. The best way to design those bridges seems to be designing with help of computer programsusing Finite Element Method. This allows modelling the interaction between piles and the bridge deckand pilesoil interaction in a realistic manner. Unfortunately FEM nonlinear calculations are usuallyvery time consuming and not wide spread among engineers. For wider integral abutment bridgesapplication there is a need for a simpler method.The global analysis can be made with the use of programs where the bridge model can be built of 2Dbeam elements. The pile top connection can be regarded as pinned. It can be also assumed that girderextraction/contraction moves take place without resistance. Comparing to the stiffness of the girder,the stiffness of the pile is very low and can be neglected.

To include the normal force and moment of the earth pressure against the back wall, springelements can be used. The springs should have different properties in tension and compression toaccount for passive and active earth pressure.

The closest to reality static scheme of integral bridge seems to be frame structure. Unfortunately,with the use of this scheme, the influence of the earth pressure acting on construction that changeswithin the time and also the influence of cooling soil on the bridge supports are not included inanalysis.

The static strength analysis of integral structures is usually done as for frame scheme treated asconsisting of beam elements. This analysis usually does not include influences of generated in thestructure deflections or forces on backfill, as it is for a frame scheme.

Considering the structuresoil interactions, makes the analysis much more complicated and itcauses more difficulties with finding satisfying solutions. Then, the problem appears to modelproperly backfill [19].

6.2 ULTIMATE LIMIT STATE.

According to Greimann and WoldeTinsae [28] the reasonable and conservative approximatecalculation of the ultimate load can be obtained using the Rankine equation which combines bothgeometric and material instabilities.

If the only collapse consideration was a geometric instability, the ultimate load would equalthe elastic buckling load (Ncr), i.e. the perfectly elastic case showed on the Figure 29a. If thegeometrical instability was not considered, and the only reason to collapse was assumed due to plasticeffects, the ultimate load (Vp) would occur when a plastic hinge forms and produces a plasticmechanism. The Figure 29b illustrates the rigidperfectly plastic case.

PART I6. Simplified calculations


Ncr Np

a. b.

h h

Figure 29

a: perfectly elastic behaviour of the pile, b: rigidperfectly plastic behaviour of the pile.

Rankine equation: 0.1=+pl

u

cr

u

NN

NN

Nu – ultimate load,Npl – plastic capacity,Ncr – elastic buckling load,

Elastic buckling load can be calculated with the use of following formulas depending onboundary conditions of the pile top and soil conditions.

Elastic bucklingload Ncr

Hinged piletop

Fixed piletop

Constant soilstiffness

Linearly varyingsoil stiffness ( ) ( )2

553

3.2 hnEI⋅ ( ) ( )257

32.4 hnEI⋅

Where:kh – the initial stiffness of the soil,nh – constant of subgrade reaction, J/1,35.

If the soil stiffness varies in a more complicated way, there can be calculated equivalentstiffness of the soil and formulas given above still can be used.

Plastic capacityof the pile

Hinged piletop

Fixed piletop

Npl

h

plM∆

⋅ '2

h

plM∆

⋅ '4

M’pl – reduced plastic moment capacity,h – the lateral displacement of the pile top.

However, to handle more complicated cases, where the soil stiffness varies with the depth,equivalent soil stiffness can be assumed.

EIkh5,2EIkh⋅0,2



r

w

Nu

L

6.3 CALCULATIONS OF STEEL PILES SUPPORTING INTEGRAL ABUTMENTS.

The aim of this part is to show the example of calculation of stresses in piles subjected tovertical force, horizontal and rotational displacement at the pile top with the help of one of thesimplified methods.

The calculation process is based on the theory of beam supported on elastic foundation that isdiscussed in [30].

6.3.1 Data

Length of the pile: L=10[m]

Loads: Nu =1 [MN] normal force, w = 0,015 [m] lateral displacement, r = 0,005 [] rotational displacement,

Type of soil: Loose sandSteel grade: S355

MPaf yk 345= characteristic yield strength of the steel,

nm

ykyd

ff

γγ ⋅= (16<t 40mm) – designed yield strength of the steel,

0,1=mγ [] partial coefficient, depending on structure’s safety class,2,1=nγ [] partial coefficient, depending on pile’s crosssection,

MPaf yd 5,2872,10,1

345=

⋅=

Figure 30

Pile model for simplified calculations.

Considered types of piles:

The piles, which are considered in this comparative analysis are of two types: steel X piles (X200and X180) and steel pipe pile (Ø219.1x12.5) supplied by Rautaruukki Sverige AB.

20030 180

24

12,5

219,1

Figure 31

Piles crosssections.Dimensions are given in [mm].



bt

h

6.3.2 Ultimate limit capacity

The calculations of ultimate limit capacity of the pile are done with the use of Rankine equationand with assumptions that soil stiffness is constant with the depth and that pile is considered with fixedconditions.

Ultimate Limit State equation:

0.1=+pl

u

cr

u

NN

NN

where:Ncr elastic buckling load, calculated from formula:

( ) ( )52

73

2.4 hcr nEIN ⋅⋅= for linearly varying soil stiffness,kh the initial lateral stiffness of the soil,

zkh ⋅= 66 [kPa] (for loose sand according to [12]),z depth from soil surface [m],Assuming that the stresses in pile are the highest at the top, the following values are taken: z = 2.0 m kh = 0.132 [MPa]E Young's modulus of the steel [GPa],I moment of inertia of pile crosssection [m4].

Npl plastic capacity, calculated from formula, symbols Npl and Np are used iinterchangeably,

h

plpl

MN

∆=

'4

however plastic capacity can not be higher than AfN ydpl ⋅=max,

A – area of pile crosssection [m2],Mpl plastic moment capacity [MNm],

ZfM ypl ⋅= (assumption Mpl’=Mpl)

h lateral displacement of a pile top [m],

Formulas used in calculations:

* Moment of inertia of inclined rectangle:

12

2bthI =

* Moment of inertia of Xshaped crosssection:

22 bhhb =⇒=

( )61212

2122

2

122

122

4322

2

22 ttbtttbb

tttbthI −=⋅⋅

−⋅⋅

⋅

=⋅⋅

−=

* Static moment of crosssection:

222424

2tbbthhtbZ ==⋅⋅⋅=



b

t

* Section modulus of the pile:

2hIW =

PILE: X 200 (the crosssection is schematically presented on the figure below)

I= 0,0000199 [m4]

A= 0,0111 [m2]Z= 0,000424264 [m3]

Nu= 1 [MN] normal force,x= 0,015 [m] horizontal displacement,

Ncr= 2,614 [MN]Mpl= 0,122 [MNm]Npl= 32,527 [MN] > Npl,max= 3,191 [MN]

Hence Np = Npl,max

0.1696.0313.0383.0191.30.1

614.20.1

<=+=+=+p

u

cr

u

NN

NN

PILE: X 180I= 0,00001162 [m4]

A= 0,008064 [m2]Z= 0,00027492 [m3]

Nu= 1,0 [MN] normal forcex= 0,015 [m] horizontal displacement,


Hence Np = Npl,max

0.1913.0431.0482.0318.20.1

075.20.1

<=+=+=+p

u

cr

u

NN

NN

PILE: Ø219.1x12.5I= 0,000043446 [m4]

A= 0,008113 [m2]Z= 0,0003966 [m3]

Nu= 1,0 [MN] normal forcex= 0,015 [m] horizontal displacement,

Ncr= 3,652 [MN]



Mpl= 0,114 [MNm]Npl= 30,406 [MN] > Npl,max= 2,332 [MN]

Hence Np = Npl,max

0.1703.0429.0274.0332.20.1

652.30.1

<=+=+=+p

u

cr

u

NN

NN

6.3.3 Serviceability Limit State

Calculations of stresses in Serviceability Limit State are done as for the beam on elasticfoundation according to Timoshenko’s theory that can be found in [30].

][355 MPafWM

AN

yk =≤+=σ

x – given horizontal displacement [m],

xLEIP

EILP

xb

xbx ⋅=⇒

⋅= 3

3 88 α

α

][0.1 −=α

γ⋅⋅

=4

bxx

LPM

0.1=γ [] – for maximal bending moment, r – given rotational displacement [],

rLEIM

EILMr

br

br

δδ =⇒=

Total bending moment:rx MMM +=

Lb – a buckling length of the pile, defined as the depth below which the displacements and bendingmoments at the pile head have little effect,

4 4h

b kEIL ⋅=

PILE: X 200I= 1,99045E05 [m4]

A= 0,0111 [m2]W= 0,00028126 [m3]

L= 3,355 [m]

x= 0,015 [m] horizontal displacement,r= 0,005 [] rotation at the pile top,

8EI/ L3= 0,886Px= 0,01328 [MN]

Mx= 0,01114 [MNm]



EI/ L= 1,24597Mr= 0,00623 [MNm]

M= 0,01737 [MNm]

][355854.151108126.2

01737.0008113.0

0.14 MPaf yk =<=

⋅+=

−σ

PILE: X 180I= 0,00001162 [m4]

A= 0,008064 [m2]W= 0,000182668 [m3]

L= 2,932 [m]


8EI/ L3= 0,774Px= 0,01161 [MN]

Mx= 0,00851 [MNm]

EI/ L= 0,83214Mr= 0,00416 [MNm]

M= 0,01267 [MNm]

][355][390.19310827.1

01267.0008064.0

0.14 MPafMPa yk =<=

⋅+=

−σ

PILE: Ø219.1x12.5

I= 0,000043446 [m4]A= 0,008113 [m2]W= 0,0003966 [m3]

L= 4,078 [m]


8EI/ L3= 1,07651Px= 0,01615 [MN]

Mx= 0,01646 [MNm]

EI/ L= 2,23746Mr= 0,01119 [MNm]



M= 0,02765 [MNm]

][355][973.19210966.3

02765.0008113.0

0.14 MPafMPa yk =<=

⋅+=

−σ

6.3.4 Conclusions:

The stresses in piles under the same vertical load and given rotational and vertical displacements:− Pile X 200

= 151.854 [MPa]− Pile X 180

= 193.390 [MPa]− Pile Ø219.1x12.5 = 192.973 [MPa]

The calculation with the use of simplified method showed that the level of stresses can be lover if weuse the suitable crosssection of piles supporting integral abutment. The stresses in piles X180 and apipe pile Ø219.1x12.5 are comparative, but with using bigger Xshaped pile we decreased the stressesabout 30 % (comparing to stress level in pipe piles). Probably the deciding factor can be the argument connected with costs.

PART II:1. General data


PART II

The aim of this part is to present some parts of design process for an integral abutment bridgewith particular attention to analysis of behaviour of piles supporting abutments. In this work were useddata from projecting Bridge over Dalälven as a traditional structure with bearings and transition joints(made by Håkan Tornberg, Ramböll AB, Luleå). This part contains comparison of different types ofpiles in the matter of stresses caused by applied loads and their behaviour in integrated abutments.

1.0 General data

1.1 LOCATION

Analysed bridge is to be located in the middleeast Sweden in city Torsång over the river Dalälve.

Torsång over Dalälven

Figure 32

Location of the bridge.

PART II1. General data


1.2 SOIL CONDITIONS

The soil has been assumed as very low compacted soil and ground over the level of ground waterand the parameter which is characterising the soil is the coefficient of horizontal subgrade reactionnh=2.5MN/m3 . The value of nh was taken from Table 1 Swedish norm considering bridges Bro 2004.The maximal value of the subgrade reaction modulus for sand is 12 [MN/m2] (according to Table 2).In calculations the soil is replaced by series of springs, which are characterized with the springconstants (a subgrade reaction modulus). The calculations of subgrade modulus values were done accordig to Swedish norm Bro 2004: Tables1 and 2 and the Appendix 34. The subgrade reaction modulus is assumed to change linearly with the depth, proportionally to thecoefficient of horizontal subgrade reaction of the soil(nh), what is expressed with formula:

]/[5,2 2mMNzznk hh ⋅=⋅= .

1.3 MATERIAL PROPERTIESConcrete K 40

Ec= 32 [Gpa] modulus of elasticity of concrete,f= 1,2 [] safety factor,

Ec,eff=Ec/ f= 26,67 [Gpa] effective modulus of elasticity of concrete,

Ec, =Ec,eff/3= 8,89 [Gpa] modulus of elasticity of concrete in long term loading,

SteelEs= 210 [Gpa] modulus of elasticity of steel,

girders: S420MS355J2G3other

elements: S355NHpiles: S355

1.4 GENERAL CHARACTERISTICS OF THE BRIDGE

Designed bridge is a three span bridge with spans lengths equal 38.5, 47 and 38.5 m, totallength of the bridge is equal 124m.

4738,5 38,5

5

Figure 33

Bridge scheme.

Girders are made of welded Isections placed at a nominal distance 5600 mm. Height of thegirders vary between 1250 and 2500 mm.



5600

2.5% 2.5% 2.5%

500 6500250

2750

total width of the bridge 10000 mm

Figure 34

One of bridge crosssecrions

Designed bridge is assumed to have integral abutments. Abutments are assumed to be single rowsof eight vertical piles. The outer piles are inclined in direction perpendicular to longitudinal axis of thebridge (inclination 1:4). All the calculations have been done for three considered pile types: X 180, X200 and Ø219.1x12.5. The abutment is 3.5 m high and 10 m wide, made of concrete.

10000

18002700

36004500

1:4

3500

Figure 35

Abutment schetch.



PART II2. Initial calculations and stresses analysis


kz

kx kr

2.0 Initial calculations and stresses analysis

2.1 DESIGN ASSUMPTIONS AND CALCULATION COMMENTS.

2.1.1 Bridge modelThe bridge has been modelled as a structure composed of beam elements. To model abutments

in program CONTRAM, the rows of piles have been replaced by three spring supports (visible on theFig.33 ).

2.1.2 Pile model:The spring constants were calculated in the way presented below with the help of program

CONTRAM. The piles have been defined as beams supported on series of springs representing soilresponse. The CONTRAM indata files and results of those calculations are presented in Appendix Band the calculation of spring constants representing piles supporting integral abutments is presentedbelow.

In order to do the calculations for the whole bridge in program CONTRAM, the piles areidealized by three sets of springs: a lateral spring, a vertical spring and a point spring. To obtain theconstants for those springs there were done calculations for a single pile modelled as a beam supportedon elastic foundation and the soil was replaced by the series of springs.

The spring constants were calculated with the use of a simple formula:

∆=

Fk [MN/m], [MNm/radian]

whereF – is an axial force, when calculating vertical and horizontal spring constant and a bending moment

for a rotational spring constant, [MN], [MNm], – a displacement related with acting load, adequately horizontal dispalacement [m], vertical

displacement [m] or rotation [radian].

Springs supporting a pile, representing the soil response are characterized with the spring constant(a subgrade reaction modulus. The calculations of subgrade modulus values were done accordig toSwedish norm Bro 2004: Tables 1 and 2 and the Appendix 34. The subgrade reaction modulus isassumed to change linearly with the depth, proportionally to the coefficient of horizontal subgradereaction of the soil(nh), what is expressed with formula: ]/[5,2 2mMNzznk hh ⋅=⋅= . The value of nh

was taken from Table 1 (Bro 2004), for very lowly compacted soil, the ground over the level ofground water. The maximal value of the subgrade reaction modulus for sand is 12 [MN/m2] (accordingto Table 2).



20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1kh

Table 2.1 Values of spring constants for considered pile.

Node z [m] kh[MN/m]2 0,5 0,7031253 1,0 1,254 1,5 1,8755 2,0 2,56 2,5 3,1257 3,0 3,758 3,5 4,3759 4,0 5

10 4,5 5,62511 5,0 6,2512 5,5 6,87513 6,0 7,514 6,5 8,12515 7,0 8,7516 7,5 9,37517 8,0 1018 8,5 10,62519 9,0 11,2520 9,5 11,875

Figure 36

Pile CONTRAM model.

Results:

Springconstant

Pile

Verticalkz

[MN/m]

Horizontalkx [MN/m]

Rotationalkr [MNm]

Pile X200 232,02 3,12 5,55Pile X180 168,92 2,52 3,61

Pile Ø219.1x12.5 169,78 4,27 10,40

2.1.3 Earth pressure:

On the special attention deservs the earth pressure which has very big influence on piles ingroud. There has been made assumption that the passive earth pressure only partly counteractsdisplacements caused by other loads. Final displacements of bridge ends have been calculated in afollowing way: Final displacement of the bridge end: pcalc ∆−∆=∆Where:

calc – displacement caused by all the loads, except for earth pressure,p – displacement from earth pressure that can be taken into consideration,

passivepCONTRAMp p

p⋅∆=∆

pCONTRAM – displacement from earth pressure calculated in programe CONTRAM,activepassive ppp −=



2.2 CALCULATIONS OF FORCES ACTING ON PILES.

Calculations of inner forces in bridge members have been done in the programmeCONTRAM. Applied loads are calculated in point 7.1. The analysis of inner forces in particular pileshas been done according to Swedish norm BRO 2004. There have been considered two loadscombinations: IVA and VA.

Load combination IV:A is the main load case for the Ultimate Limit State. In this loadcombination the number of variable loads that are taken into account is limited to four variable loadsthat have the most disadvantageous influence. The most disadvantageous variable loads have thehighest value of load coefficient . Remaining variable loads have lower coefficients.

Load combination V:A is the main load case for Serviceability Limit State.

The loads coefficients are taken according to Swedish norm: BRO 2004, Chapter 2:Lastförutsättningar, Table 221: Lastkoefficient för respektive lastkombination.

In order to obtain the highest possible value of vertical load acting on the pile, traffic load hasbeen taken as a dominant load. For maximal and minimal displacements (minimal in this case meansthe extreme value of displacement at the end of the bridge in opposite direction that it is considered formaximal displacement) the temperature loads have been taken as dominant loads.

Calculation procedure of forces acting on particular foundation piles and comments about theway of calculation are presented in Appendix A.

Results of calculations.

PILE X200Combination IV:A

Node 1 Node 10 Node 1 Node 10Case N [MN] N [MN] x [m] r [] x [m] r []

Maximal force 0,7796 0,604365 0,0589 0,016 0,05992 0,01261Maximal displacement 0,63 0,58 0,0693 0,0185 0,06459 0,01317Minimal displacement 0,51 0,509344 0,02578 0,0094 0,0244 0,00617

Combination V:ANode 1 Node 10 Node 1 Node 10

Case N [MN] N [MN] x [m] r [] x [m] r []Maximal force 0,6413 0,605566 0,0589 0,016 0,06018 0,01247

Maximal displacement 0,55 0,55 0,0675 0,0185 0,06485 0,01303Minimal displacement 0,47 0,467107 0,02578 0,0094 0,0193 0,00635

PILE X180Combination IV:A






[MN] N [MN] N [MN] x [m] r [] x [m] r []Maximal force 0,7241 0,60378 0,0603 0,016 0,06011 0,01248


PILE Ø219.1x12.5Combination IV:A

Node 1 Node 10 Node 1 Node 10Case N [MN] N [MN] x [m] r [] x [m] r []Maximal force 0,7847 0,603169 0,0479 0,0153 0,057674 0,011907Maximal displacement 0,70 0,58 0,0568 0,0153 0,066804 0,010432Minimal displacement 0,49 0,435704 0,04253 0,0145 0,03397 0,011701


Case N [MN] N [MN] x [m] r [] x [m] r []Maximal force 0,7267 0,604321 0,0475 0,0152 0,057881 0,011753Maximal displacement 0,67 0,60 0,0591 0,0174 0,06962 0,01154Minimal displacement 0,49 0,435704 0,04325 0,0093 0,03438 0,006363

2.3 CALCULATIONS OF INITIAL IMPERFECTIONS OF THE PILE.

The effects of piles initial imperfections and second order moments are considered in loadcombination IV. The initial imperfections of piles are calculated according to “Pålkommissionensrapport 98” chapter 5.2.6.

The total value of initial imperfection consists of dimension value and fictitious imperfection.The X shaped piles belong to the first stresses group and pipe piles belong to group 2, according toPålkommissionens rapport table 5.2.5 b.

Total value of initial imperfection: fd δδδ +=0 ’kf l⋅= 0003,0δ a fictitious imperfection for piles in group 1, according to Pålkommissionens

rapport 98 Tabel 5.2.5a,kf l⋅= 0013,0δ a fictitious imperfection for piles in group 2, according to Pålkommissionens

rapport 98 Tabel 5.2.5a,

600k

dl

=δ dimensioning value of geometrical imperfection according to Pålkommissionens rapport

98 chapter 4.3.1,

59.08.1

hk n

EIl ⋅⋅= buckling length of a pile,

E=210 [GPa] – Young’s modulus for steel, reduction of this modulus is recommended for compressedsteel members,nh=2,5 [MN/m3] – horizontal subgrade reaction coefficient,I – moment of inertia of pile crosssection [cm4].



Pile X200I = 1990.454 [cm4]

mn

IElh

k 953.15.2

10454.19902100009.08.18.1 58

5 =⋅⋅⋅

⋅=⋅

⋅=−

mll kkdf 00384.0

6000003.00 =+⋅=+= δδδ

Pile X180I=1166.4 [cm4]

mn

IElh

k 791.15.2

104.11662100009.08.18.1 58

5 =⋅⋅⋅

⋅=⋅

⋅=−

mll kkdf 00352.0

6000003.00 =+⋅=+= δδδ

Pile Ø219.1x12.5I=4344.6 [cm4]

mn

IElh

k 332.25.2

106.43442100009.08.18.1 58

5 =⋅⋅⋅

⋅=⋅

⋅=−

mll kkdf 00692.0

6000013.00 =+⋅=+= δδδ

Values of initial imperfections of piles:0[m]

Node z[m]X200 X180 Ø219.1x12.5

kh[MN/m]

1 0 0 0 0 02 0,1 0,000625 0,000614 0,000929 0,253 0,2 0,001233 0,00121 0,001842 0,54 0,3 0,00181 0,001768 0,002721 0,755 0,4 0,00234 0,002272 0,003551 16 0,5 0,002809 0,002706 0,004317 1,257 0,6 0,003206 0,003058 0,005004 1,58 0,7 0,003521 0,003315 0,005601 1,759 0,8 0,003744 0,003471 0,006096 2

10 0,9 0,003871 0,00352 0,00648 2,2511 1 0,003897 0,003461 0,006748 2,512 1,1 0,003823 0,003296 0,006893 2,7513 1,2 0,003651 0,00303 0,006913 314 1,3 0,003384 0,002671 0,006808 3,2515 1,4 0,003029 0,002229 0,006579 3,516 1,5 0,002597 0,00172 0,006231 3,7517 1,6 0,002097 0,001157 0,005771 418 1,7 0,001544 0,000559 0,005205 4,2519 1,8 0,00095 5,6E05 0,004546 4,520 1,9 0,000332 0,00067 0,003804 4,7521 2 0,00029 0,00126 0,002993 522 2,1 0,00091 0,00182 0,002128 5,2523 2,2 0,00151 0,00231 0,001224 5,524 2,3 0,00207 0,00274 0,000298 5,75



0[m]Node z[m]

X200 X180 Ø219.1x12.5kh[MN/m]

25 2,4 0,00257 0,00308 0,00063 626 2,5 0,00301 0,00333 0,00155 6,2527 2,6 0,00336 0,00348 0,00244 6,528 2,7 0,00364 0,00352 0,00329 6,7529 2,8 0,00382 0,00345 0,00408 730 2,9 0,0039 0,00328 0,00479 7,2531 3 0,00387 0,003 0,00542 7,532 3,1 0,00375 0,00263 0,00595 7,7533 3,2 0,00354 0,00219 0,00637 834 3,3 0,00323 0,00167 0,00668 8,2535 3,4 0,00284 0,0011 0,00686 8,536 3,5 0,00237 0,0005 0,00692 8,7537 3,6 0,00184 0,000111 0,00685 938 3,7 0,00127 0,000723 0,00667 9,2539 3,8 0,00066 0,001313 0,00636 9,540 3,9 3,8E05 0,001863 0,00593 9,7541 4 0,000587 0,002356 0,0054 1042 4,1 0,001197 0,002776 0,00477 10,2543 4,2 0,001776 0,003111 0,00405 10,544 4,3 0,00231 0,003351 0,00326 10,7545 4,4 0,002783 0,003488 0,00241 1146 4,5 0,003185 0,003517 0,00152 11,2547 4,6 0,003504 0,003439 0,0006 11,548 4,7 0,003733 0,003255 0,000335 11,7549 4,8 0,003866 0,002972 0,001261 1250 4,9 0,003898 0,002597 0,002163 1251 5 0,003831 0,002142 0,003026 12

The calculations of inner forces in piles subjected to vertical force, horizontal displacementand rotational displacement acting at the pile top are made in programme CONTRAM with taking intoconsideration the second order effects (Appendix E). The values of force and displacements are takenfrom IV:A and V:A loads combinations.

2.4 CALCULATION OF STRESSES

Equation for stresses checking in Ultimate Limit State:

00,10

≤+

Rd

Sd

Rd

Sd

MM

NN

γ

where:NSd – acting normal force,NRd – normal force resistance,MSd – acting bending moment,MRd – bending moment resistance,

20 xηγ =

In considered crosssections: yx ηη = and depends on class of crosssection.

Equation for stresses checking in Serviceability Limit State:

ydfWM

AN

≤+=σ



b t b t

t

D

h

r

h

where:N – normal force [MN],A – area of pile crosssection [m2],M – bending moment [MNm],W – second moment of area of pile crosssection [m3],

2.4.1 Piles crosssections

Figure 37

Used piles crosssections.

Class of crosssections (according to “Dimensionering av stålkonstruktioner K18” Torsten Höglund )

fyk= 345 [MPa]

fyd= 287,5 [MPa]

Ek= 210 [GPa]

Pile X 200:b= 200 [mm]t= 30 [mm]

A= 111 [cm2]

W= 281,264 [cm3]

Z= 424,264 [cm3]

mmtbb f 852

302002

=−

=−

=

mmtt f 30==

f pl– limit flange’s slenderness,

][402,7345

2100003,03,0 −===yk

kfpl f

Eβ

f – flange’s slenderness,

⇒=⟨=== 402,783,23085

fplf

ff t

bββ crosssection class 1

Pile X 180:b= 180 [mm]



t= 24 [mm]

A= 80,64 [cm2]

W= 182,67 [cm3]

Z= 274,92 [cm3]

mmtbb f 782

241802

=−

=−

=

mmtt f 24==

][402,7345

2100003,03,0 −===yk

kfpl f

Eβ

⇒=⟨=== 402,725,32478

fplf

ff t

bββ crosssection class 1

Pile Ø219.1x125D= 219,1 [mm]t= 12,5 [mm]

A= 81,13 [cm2]

W= 396,6 [cm3]

Z= 396,6 [cm3]

⇒==<== 26,18345

21000003,003,0528,165,126,206

yk

k

fE

tr

crosssection class 1

For the crosssections in the class 1:

WZ

=η

The crosssection resistances should be calculated according to following formulas:

ydRd fAN ⋅= [MN] – normal force crosssection resistance,

ydRd fWM ⋅⋅= η [MNm] – bending moment crosssection resistance,

2.4.2 Calculations

Steel S355

fyk= 345 [MPa]

fyd= 287,5 [MPa]

Ek= 210 [GPa]

mmtDr 6,2065,121,219 =−=−=



PILE X200

Combination IV:A (Ultimate Limit State)Node 1 Node 10 Node 1 Node 10



ForceNSd [MN]

MomentMSd[MNm]

Maximal force 0,7801 0,2871Maximal displacement 0,6306 0,3365Minimal displacement 0,5103 0,03422

= 1,50841914 []

0= 2,27532829 >2,0 0=2,0 []

NRd= 3,19125 [MN]

MRd= 0,1219759 [MNm]

* maximal force

0.1413.23533.20598.0122.02871.0

19125.37801.0 20

>=+=+

=+

RD

Sd

RD

Sd

MM

NN

γ

NOT OK

* maximal bending moment

0.1797.27582.20391.0122.03365.0

19125.36306.0 20

>=+=+

=+

RD

Sd

RD

Sd

MM

NN

γ

NOT OK

* minimal bending moment

0.14404.02805.01599.0122.0

03422.019125.35103.0 20

<=+=+

=+

RD

Sd

RD

Sd

MM

NN

γ

OK

Node 1 Node 10Case x [m] r [] x [m] r []

total 0,05886 0,01603 0,059917 0,012613castings 0,03931 0,01271 0,039314 0,009553

Maximalforce

% 66,8 79,3 65,6 75,7total 0,06934 0,01854 0,064588 0,013175castings 0,03931 0,01271 0,039314 0,009553Maximal

displacement% 56,7 68,5 60,9 72,5



Displacements at the pile top without including casting caused displacements:


Maximal force 0,7796 0,566213 0,0195 0,0033 0,020603 0,00306Maximal displacement 0,63 0,51 0,03 0,0058 0,025274 0,003622

ForceNSd [MN]

MomentMSd[MNm]

Maximal force 0,7799 0,0861Maximal displacement 0,6302 0,1268

* maximal force

0.1765.07057.00597.0122.00861.0

19125.37799.0 20

<=+=+

=+

RD

Sd

RD

Sd

MM

NN

γ

OK


0.1081.1039.1.10416.0122.01268.0

19125.36302.0 20

>=+=+

=+

RD

Sd

RD

Sd

MM

NN

γ

NOT OK

Combination V:A (Serviceability Limit State)



Inner forces in piles:Force

NSd [MN]Moment

MSd[MNm]Maximal force 0,6413 0,2905

Maximal displacement 0,55 0,3338Minimal displacement 0,47 0,03446

A= 0,0111 [m2]

W= 0,00028149 [m3]

Stresses in piles:* maximal force

][355783.1089008.1032775.57108149.2

2905.00111.06413.0

4 MPaf yk =>=+=⋅

+=−

σ NOT OK


][355383.1235833.1185550.49108149.2

3338.00111.055.0

4 MPaf yk =>=+=⋅

+=−

σ NOT OK




][355762.164420.122342.42108149.2

03446.00111.047.0

4 MPaf yk =<=+=⋅

+=−

σ OK


total 0,05894 0,01603 0,060179 0,012471castings 0,04128 0,01334 0,04128 0,010031

Maximalforce


displacement% 61,2 71,9 63,7 77,0




ForceNSd [MN]

MomentMSd[MNm]



][355529.325754.267775.57108149.2

07537.00111.06413.0

4 MPaf yk =<=+=⋅

+=−

σ OK


][355169.470619.420550.49108149.2

1184.00111.055.0

4 MPaf yk =>=+=⋅

+=−

σ NOT OK

PILE X180

Combination IV:A (Ultimate Limit State)Node 1 Node 10 Node 1 Node 10



ForceNSd [MN]

MomentMSd[MNm]




= 1,505 []

0= 2,2652 >2,0 0=2,0 []

NRd= 2,3184 [MN]

MRd= 0,079 [MNm]

* maximal force

0.1698.2581.21173.0079.0

2039.03184.27824.0 20

>=+=+

=+

Rd

Sd

Rd

Sd

MM

NN

γ

NOT OK


0.1769.2724.204469.0079.0

2152.03184.26603.0 20

>=+=+

=+

Rd

Sd

Rd

Sd

MM

NN

γ

NOT OK


0.1174.1136.10378.0079.0

08975.03184.24506.0 20

>=+=+

=+

Rd

Sd

Rd

Sd

MM

NN

γ

NOT OK


total 0,06006 0,01597 0,059837 0,012616castings 0,0398 0,01283 0,039799 0,009707

Maximalforce

% 66,3 80,3 66,5 76,9total 0,06479 0,01581 0,067939 0,010967

castings 0,0398 0,01283 0,039799 0,009707Maximaldisplacement

% 61,4 81,2 58,6 88,5




ForceNSd [MN]

MomentMSd[MNm]


* maximal force

0.1907.0793.01139.0079.0

06265.03184.27822.0 20

<=+=+

=+

Rd

Sd

Rd

Sd

MM

NN

γ

OK


0.1013.19315.00811.0079.0

07359.03184.26601.0 20

>=+=+

=+

Rd

Sd

Rd

Sd

MM

NN

γ

NOT OK



Combination V:A (Serviceability Limit State)

Node 1 Node 10 Node 1 Node 10[MN] N [MN] N [MN] x [m] r [] x [m] r []



NSd [MN]Moment


Maximal displacement 0,55 0,2166Minimal displacement 0,48 0,07949

A= 0,00806 [m2]

W= 0,00018267 [m3]


][355300.1197462.1107839.89108267.1

2023.000806.07241.0

4 MPaf yk =>=+=⋅

+=−

σ NOT OK


][355813.1253745.1185069.68108267.1

2166.000806.0

55.04 MPaf yk =>=+=

⋅+=

−σ NOT OK


][355950.495156.435794.60108267.1

07949.000806.0

48.04 MPaf yk =>=+=

⋅+=

−σ NOT OK


total 0,06027 0,01597 0,060114 0,012476castings 0,04233 0,01365 0,042327 0,010317Maximal

force% 70,2 85,4 70,4 82,7


displacement% 63,4 85,2 59,3 84,7



Maximal force 0,7241 0,603784 0,0179 0,0023 0,01779 0,00216

Maximal displacement 0,55 0,55 0,0242 0,0023 0,02866 0,00184




NSd [MN]Moment


Maximal displacement 0,55 0,0673


][355644.372805.282839.89108267.1

05166.000806.07241.0

4 MPaf yk =>=+=⋅

+=−

σ NOT OK


][355662.436424.368238.68108267.1

0673.000806.0

55.04 MPaf yk =>=+=

⋅+=

−σ NOT OK

PILE Ø219.1x12.5

Combination IV:A (Ultimate Limit State)

Node 1 Node 10 Node 1 Node 10Case N[MN] N [MN] x [m] r [] x [m] r []Maximal force 0,7847 0,603169 0,0479 0,0153 0,057674 0,011907Maximal displacement 0,70 0,58 0,0568 0,0153 0,066804 0,010432Minimal displacement 0,49 0,488274 0,04253 0,0145 0,03397 0,011701

Force [MN]

Moment[MNm]


= 1 []

0= 1 []

NRd= 2,332488 [MN]

MRd= 0,114023 [MNm]

* maximal force

0.1442.51053.53369.01140.0582.0

3325.27858.0 10

>=+=+

=+

Rd

Sd

Rd

Sd

MM

NN

γ

NOT OK


0.1568.52675.53005.01140.06005.0

3325.27012.0 10

>=+=+

=+

Rd

Sd

Rd

Sd

MM

NN

γ

NOT OK




0.1808.05976.02104.01140.006813.0

3325.24908.0 10

<=+=+

=+

Rd

Sd

Rd

Sd

MM

NN

γ

OK



force% 57,5 79,2 65,1 75,7


displacement% 48,5 79,0 56,2 86,4




ForceNSd [MN]

MomentMSd[MNm]


* maximal force

0.10613.37146.23367.0114.0

3106.03325.27853.0 10

>=+=+

=+

Rd

Sd

Rd

Sd

MM

NN

γ

NOT OK


0.12307.39263.23044.0114.0

3336.03325.27006.0 10

>=+=+

=+

Rd

Sd

Rd

Sd

MM

NN

γ

NOT OK

Combination V:A (Serviceability Limit State)Node 1 Node 10 Node 1 Node 10

Case N [MN] N [MN] x [m] r [] x [m] r []Maximal force 0,7267 0,604321 0,0475 0,0152 0,057881 0,011753Maximal displacement 0,67 0,60 0,0591 0,0174 0,06962 0,01154Minimal displacement 0,49 0,488274 0,04325 0,0093 0,03438 0,006363

ForceNSd [MN]

MomentMSd[MNm]




A= 0,008113 [m2]W= 0,0003966 [m3]


][355757.1140185.1051572.8910966.3

4169.0008113.07267.0

4 MPaf yk =>=+=⋅

+=−

σ NOT OK


][355108.1350524.1267584.8210966.3

5027.0008113.0

67.04 MPaf yk =>=+=

⋅+=

−σ NOT OK


][355042.401645.340397.6010966.3

1351.0008113.0

49.04 MPaf yk =<=+=

⋅+=

−σ OK.


total 0,04753 0,01522 0,057881 0,011753castings 0,02893 0,01271 0,039431 0,009459

Maximalforce


displacement% 48,9 73,3 56,6 82,0





NSd [MN]Moment


Maximal displacement 0,67 0,2115


][355290.409718.319572.8910966.3

1268.0008113.07267.0

4 MPaf yk =>=+=⋅

+=−

σ NOT OK


][355867.615283.533584.8210966.3

2115.0008113.0

67.04 MPaf yk =>=+=

⋅+=

−σ NOT OK



2.5 CALCULATION OF STRESSES WITH THE USE OF SIMPLIFIED METHOD

Steel grade: S355

MPaf yk 345=

MPaf yd 5,287=][210 GPaE = Young's modulus of the steel ,

2.5.1 Ultimate Limit CapacityUltimate Limit State equation:

0,1=+p

u

cr

u

NN

NN

where:Ncr elastic buckling load, calculated from formula:

( ) ( )52

73

2.4 hcr nEIN ⋅⋅= for linearly varying soil stiffness,kh the initial lateral stiffness of the soil,

zkh ⋅= 5.2 [MPa] (for loose sand),z depth from soil surface [m],Assuming that the stresses in pile are the highest at the top, the following values are taken: z = 0.1 m kh = 0.25 [MPa]I moment of inertia of pile crosssection [m4].

Np plastic capacity, calculated from formula:

h

plp

MN

∆=

'4

however plastic capacity can not be higher than AfN ydpl ⋅=max,

A – area of pile crosssection [m2],Mpl plastic moment capacity [MNm],

ZfM ypl ⋅= (assumption Mpl’=Mpl)

h lateral displacement of a pile top [m],

PILE: X 200

Case N[MN] x [m] r []Maximal force 0,7796 0,0589 0,016Maximal displacement 0,63 0,0693 0,0185Minimal displacement 0,51 0,0258 0,0094

I= 1,99E05 [m4]A= 0,0111 [m2]Z= 0,0004243 [m3]



* maximal forceNu= 0,7796 [MN] normal force,

x= 0,0589 [m] horizontal displacement,

Ncr= 0,579 [MN]


Np = Npl,max

0.159.1 >=+p

u

cr

u

NN

NN

* maximal displacementNu= 0,63 [MN] normal force,



Np = Npl,max

0.1285.1 >=+p

u

cr

u

NN

NN

* minimal displacementNu= 0,51 [MN] normal force,



Np = Npl,max

0.1040.1 >=+p

u

cr

u

NN

NN

PILE: X 180Case N[MN] x [m] r []Maximal force 0,7821 0,0601 0,016Maximal displacement 0,66 0,0648 0,0158Minimal displacement 0,45 0,05141 0,0099

I= 1,162E05 [m4]A= 0,008064 [m2]Z= 0,0002749 [m3]





Ncr= 0,460 [MN]


Np = Npl,max

0.1032.2 >=+p

u

cr

u

NN

NN




Np = Npl,max

0.1719.1 >=+p

u

cr

u

NN

NN




Np = Npl,max

0.1172.1 >=+p

u

cr

u

NN

NN

PILE: Ø219.1x12.5Case N[MN] x [m] r []Maximal force 0,7847 0,0479 0,0153Maximal displacement 0,7 0,0568 0,0153Minimal displacement 0,49 0,04253 0,0145

I= 4,345E05 [m4]A= 0,008113 [m2]Z= 0,0003966 [m3]





Ncr= 0,809 [MN]


Np = Npl,max

0.1306.1 >=+p

u

cr

u

NN

NN




Np = Npl,max

0.1165.1 >=+p

u

cr

u

NN

NN




Np = Npl,max

0.1815.0 <=+p

u

cr

u

NN

NN

2.5.2 Serviceability Limit State

][355 MPafWM

AN

yk =≤+=σ

x – given horizontal displacement [m],

xLEIP

EILP

x xx ⋅=⇒

⋅= 3

3 88 α

α

][0.1 −=α



γ⋅⋅

=4

LPM x

x

0.1=γ [] – for maximal bending moment, r – given rotational displacement [],

rL

EIMEI

LMr rr

δδ =⇒=

Total bending moment:rx MMM +=

L – buckling length of the pile, defined as the depth below which the displacements and bending moments at the pile head have little effect,

4 4hk

EIL ⋅=

PILE: X 200

Case N[MN] x [m] r []Maximal force 0,6413 0,0589 0,016Maximal displacement 0,55 0,0675 0,0185Minimal displacement 0,47 0,0258 0,0094

I= 1,99E05 [m4]A= 0,0111 [m2]W= 0,0002813 [m3]L= 2,860 [m]



8EI/ L3= 1,430Px= 0,0842186 [MN]

Mx= 0,0602103 [MNm]

EI/ L= 1,4616653Mr= 0,0233866 [MNm]

M= 0,0835969 [MNm]

][355][998.354 MPafMPaWM

AN

yk =≤=+=σ

* maximal momentNu= 0,55 [MN] normal force,




r= 0,0185 [] rotation at the pile top,

8EI/ L3= 1,430Px= 0,0965154 [MN]

Mx= 0,0690016 [MNm]

EI/ L= 1,4616653Mr= 0,0270408 [MNm]

M= 0,0960424 [MNm]

][355][021.391 MPafMPaWM

AN

yk =>=+=σ

* minimal momentNu= 0,47 [MN] normal force,


8EI/ L3= 1,430Px= 0,0368903 [MN]

Mx= 0,0263739 [MNm]EI/ L= 1,4616653

Mr= 0,0137397 [MNm]

M= 0,0401136 [MNm]

][355][963.184 MPafMPaWM

AN

yk =<=+=σ

PILE: X 180Case N[MN] x [m] r []Maximal force 0,7821 0,0601 0,016Maximal displacement 0,66 0,0648 0,0158Minimal displacement 0,45 0,05141 0,0099

I= 1,162E05 [m4]A= 0,008064 [m2]W= 0,0001827 [m3]L= 2,500 [m]



8EI/ L3= 1,250Px= 0,0751157 [MN]



Mx= 0,0469415 [MNm]

EI/ L= 1,6721846Mr= 0,026755 [MNm]

M= 0,0736965 [MNm]

][355][482.332 MPafMPaWM

AN

yk =>=+=σ

* maximal momentNu= 0,7 [MN] normal force,


8EI/ L3= 1,738Px= 0,0987167 [MN]

Mx= 0,0857833 [MNm]

EI/ L= 2,6248037Mr= 0,0401595 [MNm]M= 0,1259428 [MNm]

][355][556.503 MPafMPaWM

AN

yk =>=+=σ

* minimal momentNu= 0,49 [MN] normal force


8EI/ L3= 1,738Px= 0,0739159 [MN]

Mx= 0,0642318 [MNm]

EI/ L= 2,6248037Mr= 0,0380597 [MNm]

M= 0,1022914 [MNm]

][355][531.328 MPafMPaWM

AN

yk =<=+=σ

PILE: Ø219.1x12.5Case N[MN] x [m] r []Maximal force 0,7847 0,0479 0,0153Maximal displacement 0,7 0,0568 0,0153Minimal displacement 0,49 0,04253 0,0145



I=4,345E05 [m4]A=0,008113 [m2]W=0,0003966 [m3]L=3,476 [m]

* maximal forceNu=0,7847 [MN] normal force

x=0,0479 [m] horizontal displacement,r=0,0153 [] rotation at the pile top,

8EI/ L3=1,738Px=0,0832488 [MN]

Mx=0,0723419 [MNm]

EI/ L=2,6248037Mr=0,0401595 [MNm]

M=0,1125014 [MNm]

][355][386.380 MPafMPaWM

AN

yk =>=+=σ

* maximal momentNu=0,7 [MN] normal force


8EI/ L3=1,738Px=0,0987167 [MN]

Mx=0,0857833 [MNm]

EI/ L=2,6248037Mr=0,0401595 [MNm]

M=0,1259428 [MNm]

][355][838.403 MPafMPaWM

AN

yk =>=+=σ

* minimal momentNu=0,49 [MN] normal force


8EI/ L3=1,738Px=0,0739159 [MN]



Mx=0,0642318 [MNm]

EI/ L=2,6248037Mr=0,0380597 [MNm]

M=0,1022914 [MNm]

][355][319.318 MPafMPaWM

AN

yk =<=+=σ

2.6 COMPARISON OF STRESSED IN PILES (CASE INCLUDING CASTINGS) OBTAINED FROMCONTRAM RESULTS AND FROM THE SIMPLIFIED METHOD ( SERVICEABILITY LIMIT STATE).

F219.1x12.5 X 200 X 180Case Methods [MPa] s [MPa] s [MPa]

CONTRAM 1089,783 1197,300 1140,757Maximal force SM * 354,998 332,482 380,386

CONTRAM 1235,383 1253,813 1350,108Maximaldisplacement SM 391,021 503,556 403,838

CONTRAM 164,762 495,950 401,042Minimaldisplacement SM 184,963 328,351 318,319 * SM simplified method

The table with results presented above shows that results obtained from two used methods focalculations of stresses in steel piles differ a lot. This may suggest that at least one of those methodsgives not very probable and reliable results.



PART II3. Actions to lower the stresses in piles


H

r

1

0

3.0 Actions to lower the stresses in piles

3.1 ELIMINATION OF HORIZONTAL DISPLACEMENTS INDUCED DURING CASTING.

It was shown in point 7.3.2 that the big portions of displacements are caused during casting,when the beam is not very stiff. For cases with maximal force and maximal displacement the stressesexceed the acceptable level. The elimination of those displacements can be done during bridgeerection by constructing temporary hinge at the beamabutment connection that the horizontaldisplacements and rotations will not influence the abutment. This operation can allow decreasingstresses in piles. In all stresses checking the calculations are done for both cases: with and withoutdisplacements caused during casting.

3.2 LOWER THE HEIGHT OF ABUTMENT

Displacement at the pile top:Hr ⋅+∆=∆ 01

where:1 – displacement at the pile top [m],0 – displacement at the end of the girder [m],

r – rotation at the end of girder [],H – height of the abutment [m],

The conclusion seems to be obvious that if the height of the abutment will be lower, the horizontaldisplacement at the pile top will be smaller and at the same time the stresses in pile will decrease.

3.3 USE A SOFTER MATERIAL AT THE PILE TOP

The example how can stresses decrease with the softer material around the pile top is presented belowfor Pipe pile.

PILE Ø219.1x12.5

Assuming that until depth 2,0m the ground is less stiff (loose sand), the spring stiffness are following:][066.0][66 MPazkPazkh ⋅=⋅=

Node z[m] kh[MN/m]

1 0 02 0,1 0,00663 0,2 0,01324 0,3 0,01985 0,4 0,02646 0,5 0,0337 0,6 0,03968 0,7 0,04629 0,8 0,0528

10 0,9 0,059411 1 0,066



Node z [m] kh[MN/m]

12 1,1 0,072613 1,2 0,079214 1,3 0,085815 1,4 0,092416 1,5 0,09917 1,6 0,105618 1,7 0,112219 1,8 0,118820 1,9 0,125421 2 0,132


Acting force and displacements (extremal fof node 1):Node 1 Node 1

Case N [MN] x [m] r []Maximal force 0,7821 0,0601 0,016

Maximal displacement 0,66 0,0648 0,0158Minimal displacement 0,45 0,05141 0,0099

= 1 []

0= 1 []

NRd= 2,332488 [MN]

MRd= 0,114023 [MNm]

For weaker soil close to the pile top (with castings):Force [MN]

Moment[MNm]


Stresses in piles:

* maximal force

0.14511.4114.43371.0114.04690.0

3325.27862.0 10

>=+=+

=+

Rd

Sd

Rd

Sd

MM

NN

γ

NOT OK

* maximal bending moment`

0.15345.42342.43003.0114.0

4827.03325.27005.0 10

>=+=+

=+

Rd

Sd

Rd

Sd

MM

NN

γ

NOT OK


0.1629.04192.02102.01140.0

04779.03325.24904.0 10

<=+=+

=+

Rd

Sd

Rd

Sd

MM

NN

γ

OK



For weaker material (without castings):

Force [MN]

Moment[MNm]



0.1359.1023.1337.0114.0

1166.03325.2785.0 10

>=+=+

=+

Rd

Sd

Rd

Sd

MM

NN

γ

NOT OK


0.1642.1342.13003.0114.0153.0

3325.27005.0 10

>=+=+

=+

Rd

Sd

Rd

Sd

MM

NN

γ

NOT OK

Combination V:A

A= 0,008113 [m2]W= 0,0003966 [m3]

For weaker soil close to the pile top (with castings):Force [MN]

Moment[MNm]



][355145.951573.861572.8910966.3

3417.0008113.07267.0

4 MPaf yk =>=+=⋅

+=−

σ NOT OK


][355884.1117300.1035584.8210966.3

4106.0008113.0

67.04 MPaf yk =>=+=

⋅+=

−σ NOT OK


][35509.286693.225397.6010966.3

08951.0008113.0

49.04 MPaf yk =<=+=

⋅+=

−σ OK

For weaker material close to the pile top (without castings):

Force [MN]

Moment[MNm]

Maximal force 0,7267 01007Maximal displacement 0,67 0,1687



Stresses in piles:

* maximal force

][355480.343908.253572.8910966.3

1007.0008113.07267.0

4 MPaf yk =<=+=⋅

+=−

σ OK


][355950.507366.425584.8210966.3

1687.0008113.0

67.04 MPaf yk =>=+=

⋅+=

−σ NOT OK

3.4 CONSTRUCTION OF A HINGE

Constructing a hinge at the pile top we can also decrease stresses in the pile, rotations do notinfluence the abutment piles and do not cause additional bending moments. The example how the stresses can change when constructing hinge are shown on the example ofpipe pile. Assuming hinged conditions at the pile top, the rotations acting on the pile top are not takenunder consideration.

PILE Ø219.1x12.5

Forces and displacements acting on the pile top (pile Ø219.1x12.5):


Acting force and displacements (extremal fof node 1):Node 1 Node 1

Case N [MN] x [m] r []Maximal force 0,7821 0,0601 0

Maximal displacement 0,66 0,0648 0Minimal displacement 0,45 0,05141 0

= 1 []

0= 1 []

NRd= 2,332488 [MN]

MRd= 0,114023 [MNm]

For the hinge at the pile top (with castings):Force [MN]

Moment[MNm]



0.1139.1802.0337.0114.0

0914.03325.27849.0 10

>=+=+

=+

Rd

Sd

Rd

Sd

MM

NN

γ

NOT OK




0.1235.1934.03003.0114.01065.0

3325.27002.0 10

>=+=+

=+

Rd

Sd

Rd

Sd

MM

NN

γ

NOT OK


0.1858.0648.02102.01140.00739.0

3325.24906.0 10

<=+=+

=+

Rd

Sd

Rd

Sd

MM

NN

γ

OK

For the hinge at the pile top (without castings):

Force [MN]

Moment[MNm]



0.1697.0361.0336.0114.00411.0

3325.27848.0 10

<=+=+

=+

Rd

Sd

Rd

Sd

MM

NN

γ

OK


0.1797.0497.0300.0114.0

05671.03325.27001.0 10

<=+=+

=+

Rd

Sd

Rd

Sd

MM

NN

γ

OK

Combination V:A

A= 0,008113 [m2]W= 0,0003966 [m3]

Extreme forces acting on the pile (for the node 1):Node 1 Node 1

[MN] N [MN] x [m] r []Maximal force 0,7241 0,0603 0

Maximal displacement 0,55 0,0659 0Minimal displacement 0,48 0,04663 0

For hinge at the pile top (with castings):Force [MN]

Moment[MNm]





][355625.304053.215572.8910966.3

08529.0008113.07267.0

4 MPaf yk =<=+=⋅

+=−

σ OK


][355655.355071.273584.8210966.3

1083.0008113.0

67.04 MPaf yk =>=+=

⋅+=

−σ NOT OK


][355481.258084.198397.6010966.3

07856.0008113.0

49.04 MPaf yk =<=+=

⋅+=

−σ OK

For the hinge at the pile top (without castings):

Force [MN]

Moment[MNm]



][355637.176065.87572.8910966.3

03453.0008113.07267.0

4 MPaf yk =<=+=⋅

+=−

σ OK


][355331.226747.143584.8210966.3

05701.0008113.0

67.04 MPaf yk =>=+=

⋅+=

−σ NOT OK

PART II4. SOFiSTiK analysis


4.0 Analysis with program SOFiSTiK

4.1 NUMERICAL MODEL

To analyse considered construction with the help of program SOFiSTiK there has been done athreedimensional numerical model. This model was used to realise computations with the use ofFinite Element Method. The model consists of 6648 nodes 7498 elements and was analysed accordingto linear theory..

Used program enables also simulation of movement of traffic loads recommended for designpurposes by Swedish norm BRO 2004.

4.1.1 Types of elements used in MES analysis:§ QUAD – plane element, used to represent all the concrete elements of the bridge ( abutments

and deck)§ BEAM – beam elements, used to represent elements made of steel (girders and foundation

piles).

Figure 38

Bridge model.

4.1.2 Elements not included and simplifications.

§ The transverse beams at the middle supports were just modeled as steel beams. Theirgeometry does not have big influence on the structure, but their presence does, to assuresuitable stiffness of the whole structure.

§ The load from used and later taken off formwork was not included in a model because of lowmagnitude of its influence.

§ The loads from barriers were also not included for the same reason.

4.2 CALCULATIONS

4.2.1 Design assumptions.§ Materials and all the loads have been taken as for the calculations in program CONTRAM.§ The loads acting on the bridge were taken according to Swedish bridge norm BRO 2004 (as

for calculations in program CONTRAM).The structure was modelled as in original projectwith a crossroads at the southern end of the bridge, thus the abutment at this end is wider. It

§ has influence on the whole structure, but the analysis is on socalled safe side. The onlydifference is that instead of temperature gradients considered in program CONTRAM(temperature differences +10 and –5 degrees) there have been considered gradientsrecommended by Polish norm for concrete structures. Considered seasonal temperaturechanges are +30 and –15 degrees.



Figure 39

The view for the bridge deckgeometrl.

§ Concrete deck was modelled as a plate with constant thickness taken as mean value of realdimensions equals 27 cm.

§ The soil surrounding piles was modelled with the use of spring supports with suitable stiffnesrepresenting soil response.

Figure 40

SOFiSTiK pile model.

§ The middle supports were defined as movable. The more detailed specification wasnot necesarry for the sake of thesis purposes.

§

Figure 41

Middle supports model.The soil behind the abutments (backfill) was modelled with the use of series of spring

supports. Spring stiffnesses were assumed in the similar way as for springs representing soilaround the foundation piles.



4.2.2 Calculations

The model is three dimensional, so demanded more detailed geometical data than 2DCONTRAM model.

Similarly as for CONTRAM calculations there were taken into considerations three situations:maxinal axial load in pile and corresponding displacements (causing bending moments), and extremaldisplacements with corresponding loads (axial forces and bending moments). All the values weretaken for the tops of piles, where the piles are loaded in the most unfavourable way.The numbers of elements that are objects of an intrest at the piles’ tops are visible on figures 42 and43.

Figure 42

Wide abutmentwith numbers of important elements.

Figure 43

Narrow abutmentwith numbers of important elements..The stresses analysis in is done only in Ultimate Limit State. The main purpose of thesecalculations is to compare results from using different models (flat and three dimentional) andbecause of different temperature loads to compare influences from this kind of load.



PILE Ø219.1x12.5

0.11

≤+

=

Rd

Sd

Rd

Sd

MM

NN

α

NRd=2.3325 [MN] – axial force capacity of the pile,MRd=0.114 [MNm] – bending moment capacity of the pile,

Stresses in piles for the maximal axial forces in piles:(wide abutment)

max NSd corresp. MSd max minNumber of pile

Numberof element [MN] [MNm] [] [MPa] [MPa]

1 60301 0,152 0,110 1,034 262,60 300,052 60201 0,301 0,110 1,098 244,48 318,643 60101 0,385 0,110 1,131 233,43 328,324 60001 0,500 0,005 0,257 222,75 345,955 60401 0,896 0,111 1,361 173,43 394,356 60501 1,009 0,110 1,400 156,60 405,417 60601 1,115 0,111 1,450 145,20 420,038 60701 0,571 0,111 0,727 353,46 212,72

(narrow abutment)max NSd corresp. MSd max minNumber

of pileNumber

of element [MN] [MNm] [] [MPa] [MPa]1 61701 0,459 0,302 2,450 818,040 705,0202 61601 0,921 0,309 3,104 665,940 892,8603 61501 0,853 0,309 3,073 673,680 884,0204 61401 0,775 0,308 3,037 682,640 873,7805 61001 0,503 0,307 2,912 723,920 837,9106 61101 0,425 0,307 2,877 722,840 837,6407 61201 0,358 0,307 2,846 730,550 818,7908 61301 0,179 0,299 2,701 733,040 777,240

On the basis of results presented above and knowing the characteristics of loads acting on thebridge it can be concluded that that always two piles are subjected to the mostly disadvantageousloads. For this reason there is no point in presenting results for all the piles.

Extremal stresses for these piles in both abutments for the case with extremal axial force inpile are presented on the Fig.44 (pile number 7 in the wider abutment on the left side of the figure 44and pile number 2 in the narrow abutment – on the right side of the figure).

Figure 44

Graphical illustration of extremal stresses in elements number 60601 left and 61601 –right in the mostly loadedpiles for case with maximal axial force.



It is worth mentioning that negative normal forces in the piles mean that the piles are compressed.

Maximal displacement: pile number 2 in narrow abutment (element number 61601)LC x [mm] r [mrad] N M 1 [MPa] 2 [MPa]1 1,504 1,227 0,253 0,047 0,521 87,51 149,92 0,481 0,404 0,082 0,014 0,161 26,08 46,29

200 2,066 1,006 0,352 0,023 0,353 17,59 104,36301 0,05 3,062 0,009 0,034 0,305 85,53 87,63501 0,037 1,357 0,006 0,233 2,045 386,38 587,94

4,138 1,782 0,702 0,3516 3,3854 603,09 976,12

Minimal displacement: pile number 7 in wider abutment (element number 60601)LC x [mm] r [mrad] N M 1 [MPa] 2 [MPa]1 2,164 2,35 0,365 0,062 0,699 200,98 110,92 0,791 0,558 0,135 0,016 0,196 57,12 23,91

101 2,104 1,129 0,359 0,024 0,368 108,56 20,18301 0,057 1,418 0,010 0,041 0,361 104,05 101,64

5,116 2,619 0,868 0,14267 1,6238 470,71 256,63

Below the tables the values of particular displacements, forces and stresses are summed.

Explanation of LC(load cases):§ 1 – own weight of the bridge,§ 2 – traffic load, the part equally distributed,§ 101,200 – trucks (cases the mostly disadvantegous for particular abutments),§ 301 – temperature load,§ 501 – earth pressure load.

The results of extremal stresses in piles for cases with maximal and minimal displacement arepresented only for two piles. Analysed structure is unsymetrical, which means that one of theabutments is wider than the other, so the bridge has a tendency to move in one direction. Analysis ofall the loads acting on the bridge showed that assumed tendency is probable, so the results presented inmentioned way are sufficient for purposes of this work.

The result of analysis:§ the extremal stresses in the pile (wide abutment) in the case when loads combination causes

extremal axial force are –892,860 MPa§ the extremal stresses in the pile in the case when loads combination causes extremal

displacement at the pile top are –976,12 MPa

PILE X 200

0.12

≤+

=

Rd

Sd

Rd

Sd

MM

NN

α




Stresses and forces in piles for the maximal axial forces in piles:

Element number 60601:N = 1,1737 MNM = 0,08313 MNm

1 = 257,71 MPa2 = 469,19 MPa


1 = 828,44 MPa2 = 1001,13 MPa


101 1,623 1,219 0,378 0,016 0,146 112,25 44,1301 0,038 1,277 0,009 0,030 0,244 126,65 119,04

3,912 3,137 0,9076 0,0497 1,598 499,92 330,39


200 1,593 1,111 0,371 0,016 0,143 43,05 109,96301 0,036 2,895 0,009 0,028 0,227 111,13 112,66501 0,009 0,536 0,002 0,223 1,828 681,81 682,2

3,138 0,383 0,7274 0,3092 2,56 977,7 1108,77

Figure 45







PILE X 180

0.12

≤+

=

Rd

Sd

Rd

Sd

MM

NN

α


Stresses and forces in piles for the maximal axial forces in piles:Element number 60601:N = 1,1499 MNM = 0,06623 MNm

1 = 308,88 MPa2 = 594,07 MPa


1 = 970,28 MPa2 = 1202,42 MPa

Figure 46



101 2,183 1,259 0,370 0,012 0,173 137,8 46,13301 0,047 1,185 0,008 0,023 0,292 143,2 141,23

5,252 3,416 0,886 0,072 0,9682 585,63 365,84




200 2,147 1,164 0,008 0,012 0,147 46,88 137,07301 0,046 2,775 0,364 0,023 0,312 139,14 141,07501 0,011 0,216 0,008 0,001 0,008 812,93 812,7

4,221 0,291 0,718 0,066 0,8866 1156 1331,83




PART II5. Summary and conclusions


5.0 SUMMARY AND CONCLUSIONS

Summary of the results:The Ultimate Limit State is checked according to following equation: ( ) ( ) αγ =+ RdSdRdSd MMNN // ,where should fulfil a condition that 0.1≤α .

In the table presented below given are values of for particular considered cases in analysis of steelpipe pile (Ø219.1x12.5).

Case Maximal axialforce

Maximaldisplacement

Minimaldisplacement

CONTRAM with castings 5,422 5,568 0,808 without castings 3,061 3,231 Softer soil around pile top(CONTRAM) with castings 4,451 4,535 0,629 without castings 1,359 1,642 Hinge at the pile top(CONTRAM) with castings 0,907 1,013 without castings 0,697 0,797 Simplified method (SM) 1,306 1,165 0,815SOFiSTiK 3,104 3,385 1,624

General conclusion from piles analysis is that from all considered cases the highest stresses wereobtained for a case when loads combination gives maximal displacement at the pile top.

For the analysis in swedish program CONTRAM there were used data from earlier analysis ofbridge over Dalälven when it was designed as a traditional structure. The designer assumed the orderof deck castings that could have a very disadventageous influence on the integral structure. Thisinfluence does not have to be considered in this analysis, because it can be eliminated in erectionprocess. However the first analysis assumed mentioned castings order, thus all the calculations werealso done without including displacements induced during deck castings.

In most of obtained results in CONTRAM analysis, calculations with simplified method and inanalysis done in a program SOFiSTiK the stresses in piles are over acceptable level. From this fact itcould probably concluded that the piles used to support the bridge foundations are not numerousenough, have not suitable crosssection or assumed material is not resistant enough. It is noteworthythat in most of cases the axial load carrying capacity of the piles is not exceeded. Very high stresses inpiles are caused by bending moments induced by horizontal displacements at the piles’ tops.

However one of purposes of this thesis was to examine possible kind of technological solutionsthat can be applied to decrease stresses in Piles supporting integral bridges.

Firstly decreasing of stresses in piles can be obtained by using softer soil close to the pile top(actions described in point 2.6 , for instance: sleeves filled with sand or prebored holes filled withgranular material), as shown in point 4.3 in part II.

Another way to lower stressed in piles is to use piles with hinged conditions at the top. Thecalculation example is presented in point 3.3 in part II and shows that this action can significantlydecrease the stresses in piles. On the other hand this option demands constructing the hinge, whichincreases the costs of building.

In case of considered piles it is noteworthy that the piles crosssections are in class one(according to Swedish norm) and there is possible distribution of stresses (bending moments). The lastoption that can be taken into consideration is to use the higher strength steel for piles.



One of the aims of researshers dealing with analysing and designing integral bridges is to findrelatively simple, convinceing and efficient method.

References


REFERENCE

[1]Duncan J.M., Arsoy S.: Effect of bridgesoil interaction on behaviour of Piles supportingIntegral Bridges. Transportation Research Record 1849, Paper no. 032633

[2] Integral abutments for steel bridges. Vol.II, Chap. 5. Highways Structure Design Handbook(American Iron and Steel Institute,1996)

[3] R.Jajaraman, PB Merz and MvLellan Pte Ltd :Integral Bridge Concept Applied to Rehabilitatean existing bridge and construct a dualuse bridge. Singapore

[4] Horvath John S.: Integralabutment bridges: geotechnical problems and solutions usinggeosynthetics and ground improvement. Conference article, march 2005

[5] Ho owaty Janusz : O mo liwo ciach zwi kszenia trwa ci ma ych mostów na etapieprojektowania. V Krajowa Konferencja NaukowoTechniczna: Problemy projektowania,budowy oraz utrzymania mostów ma ych i rednich rozpi to ci, Wroc aw, December 2004

[6] Trochymiak W., Dobrowolski L., Jarominiak W., Szurowski T., PROFIL Sp. z o.o., Warszawa :O projekcie integralnego, sko nego, elbetowego wiaduktu drogowego.

[7]Arsoy Sami : Experimental and analytical investigations of piles and abutments of integralbridges. PhD Diploma, date of defence: 15122000

[8] Petursson Hans, Collin Peter : Composite Bridges with Integral Abutments Minimizing LifetimeCosts. IABSE Symposium Melbourne 2002

[9] WoldeTinsae A.M., Greimann D.M., Young, P.S.: Skewed bridges with integral abutments.Transportation Research Record 903; TRB, National Research Council, WashingtonD.C.;1983; pp.6472

[10] Dicleli M., Ph.D., P.Eng., M. ASCE; Suhali M. Albhais: Maximum length of integral bridgesbased on the performance of steel Hpiles at the abutments.

[11] Dicleli M., Albhaisi S. M.: Performance of abutmentbackfill system under thermal variationsin integral bridges built on clay. Department of Civil Engineering and Construction, BradleyUniversity

[12] Diceli M.: Simplified model for computeraided analysis of integral bridges. ASCE, Journal ofBridge Engineering 5 3 (2000), pp. 240248

[13] Khodair Yasser A.; Hassiotis Sophia : Analysis of pile soil interaction. Department of Civil,Environmental and Ocean Engineering, Stevens Institute of Technology, Hoboken, N.I.

[14] NJDOT Design Manual for Bridges and Structures, Section 15: Integral Abutment Bridges.[15] WoldeTensae, A., Klinger, J. : Integral Abutment Bridge Design and Construction.University

of Maryland, FHWA/MD – 87/07[16] Sami Arsoy, Baker Richard M. Ph.D., Duncan J. Michael Ph.D., The Charles E. Via,Jr. : The

behaviour of integral abutment bridges. ( The final contract report), VIRGINIATRANSPORTATION RESEARCH COUNCIL, Nov. 1999

[17] Dicleli Murat, Albhaisi Suhail M.: Effect of cyclic thermal loading on the performance of steelHpiles in integral bridges with stubabutments. Journal of Constructional Steel Research,Nov. 2003

[18] Hickman R., P.: Bridge Construction and Maintenance in The United Kingdom. An OverView“Prace IBDiM, nr 34, 1999; Sundquist H., Recutanu G.: Swedish Experiences of IntegralBridges. IABSE Symposium – Rio de Janeiro, August 2527, 1997.

[19] Zobel Henryk : Naturalne zjawiska termiczne w mostach. Wydawnictwa Komunikacji Iczno ci,2003, ISBN:8320615054

[20] Xanthakos Petros P. : Bridge Superstructure and Foundation Design. Prentice Hall PRT, NewJersey,1995, ISBN: 0133006174

[21] Pètursson Hans, Collin Peter: Swedish solutions for integral abutments.[22] Earl E. Ingram, Edwin G. Brudette, David W. Goodpasture, J. Harold Deatherage, and Richard

M. Bennett: Behavior of steel Hpiles supporting integral abutments.[23] Pètursson Hans: Broar med integrerade landfästen. Thesis 2000[24] Sundquist, H., Racutanu, G., Swedish Experiences for Integral Bridges. Proc. IABSE Symp.

STRUCTURES FOR THE FUTURE – THE SEARCH FOR QUALITY. Rio de Janeiro,1999, s. 5051



[25] Prakash S., Sharma H.D.:Pile Foundations in Engineering Practice. A WileyIntersciencePublikation, 1999, USA, ISBN: 0471616532

[26] Poulous H. D., Davis E. H. : Pile Foundation Analysis and Design. John Wiley & Sons Inc.,ISBN 047102084

[27] Kurman S., Lalvani L: Lateral LoadDeflection Response of Drilled Shafts in Sand. SouthernIllinois UniversityCarbondale, Carbondale, IL, USA, June 2002

[28] Greimann L., WoldeTinsae A. M.: Design Model for Piles in Jointless Bridges.1988, Journalof Constructional Engineerig, Vol. 114, No 6, pp. 13541371, ISSN 07339445/88/00061345

[29] BRO 2004[30] Timoshenko S. : Strength of materials, Part II: Advanced Theory and Problems, 1958,Van

Nostrand Reihnold Company Ltd., Toronto Melbourne

Appendix A


A. APPENDIX

Calculations of forces and displacements acting on particular foundationpiles.

General load acting on tha whole abutment can be treated as a vertical force acting with eccentricity, because of traffic loads.

V

Oe

To calculate forces acting on particular abutment piles there have been considered two separate cases: vertical force acting in thecentre of gravity of the abutment and bending moment acting at the same point.

O

MV

O

Vertical force acting in the centre of gravity influences equally all the piles, so the froce in each pile can be caqlculated with the use ofsimple formula:

nVVPi =)(

where:P(V) – force acting on the single pile;i number of the pile,V – vertical force acting on the whole abutment,n – number of piles.

Forces in particular piles from bending moment acting on the abutment can be calculated according to following formula:

∑⋅

= 2)(xxM

MP ii

where:P(M) – force acting on the single pile;M – bending moment acting on the whole abutment,xi distance of the pile axis from the centre of gravity (as shown on the figure below).

Appendix A


P 7

x2

x3

P 4P 3P 2

x7

x6

x5

P 5x4 P 6

M

O

P 1

P 8

x 1

x8

For all three types of piles the calculations are done in the same way, so only for one type of piles (X 200) the full calculations arepresented. For two remaining pile types there are only presented forces and displacements acting on the whole abutment (obtained fromCONTRAM) and final forces in particular piles.

CALCULATIONS OF FORCES AND DISPLACEMENTS ACTING ON PARTICULAR ABUTMENTPILES. PILE X200.

MAXIMAL FORCEFor this case the traffic load is considered as a dominant load.

Support reactions Displacements

Node 1 Node 10Loadcase

Descriptionof load case

Node 1[MN]

Node 10[MN] Hirizontal

[m]Rotational

[]Hirizontal

[m]Rotational

[]

Case 1 Own weight of steel beams 1,52 1,52 0,003188 0,0013 0,00459 0,0013

Case 2 Casting stage 1 1,31 0,112 0,031 0,0156 0,031 0,00195

Case 3 Casting stage 2 0,32 0,229 0,0163 3,49E03 0,0163 0,00573Case 4 Casting stage 3 0,0111 0,00991 0,000679 0,000135 0,000679 0,00025Case 5 Casting stage 4 0,127 1,21 0,0258 0,0009 0,0258 0,0137Case 6 Casting stage 5 0,0158 0,00939 0,000507 0,00017 0,000507 0,000117Case 7 Earth pressure 0,157 0,157 0,0248 0,00299 0,0248 0,00298

Case 21 Taking off the formwork+railings 0,116 0,115 0,00161 0,000459 0,00161 0,000451Case 22 Pavement 0,341 0,337 0,00471 0,00135 0,00471 0,00132Case 23 Shrinkage 0,201 0,203 0,00693 0,0028 0,00693 0,00278Case 31 Temperature gradient 5º 0,0329 0,0329 0,000751 0,000211 0,000751 0,000211Case 32 Temperature gradient 10º 0,0656 0,0656 0,0015 0,000422 0,0015 0,000422Case 33 Temp gradient 10º,higher steel temp 0,207 0,208 0,00505 0,000147 0,00505 0,00016Case 34 Temp gradient 10º,lower steel temp 0,207 0,208 0,00505 0,000147 0,00505 0,00016

Case Traffic load 1,3439 0,42072 0,006611 0,002299 0,006382 0,0020754

Node 1 Node 10Traffic load resultsx [m] Fz [MN] r [] x [m] Fz [MN] r []

NK 1 0,005748 0,5751 0,002916 0,003969 0,1389 0,001114NK 2 0,00474 0,3279 0,001334 0,002046 0,07175 0,0005757Max Fx

0,010488 0,903 0,00425 0,001923 0,21065 0,0005383NK 1 0,003969 0,1395 0,00112 0,002046 0,07176 0,0005759NK 2 0,002046 0,07175 0,0005757 0,00474 0,3279 0,001334Min Fx

0,006015 0,21125 0,0016957 0,002694 0,25614 0,0007581

Appendix A


Node 1 Node 10Traffic load resultsx [m] Fz [MN] r [] x [m] Fz [MN] r []

NK 1 0,003793 0,1467 0,001184 0,003793 0,1467 0,001184NK 2 0,002046 0,07175 0,0005757 0,002046 0,07176 0,0005759Max Fz

0,005839 0,21845 0,0017597 0,005839 0,21846 0,0017599NK 1 0,001871 1,016 0,0009656 0,001642 0,09282 0,0007414NK 2 0,00474 0,3279 0,001334 0,00474 0,3279 0,001334Min Fz

0,006611 1,3439 0,0022996 0,006382 0,42072 0,0020754

Loads combinations:

Combination IV:A

Combination V:ALoads coefficients Loads Combination loads

Long term loads: max min Node 1 Node 10 Node 1 Node 10own weight 1,05 0,95 2,7261 2,7087 2,862405 2,844135pavement 1,15 0,8 0,201 0,337 0,23115 0,38755earth prerssure 1,1 0,9 0,116 0,157 0,1276 0,1727shrinkage 1,0 0,0 0,0329 0,203 0 0castings 1,05 0,95 1,0901 1,0737 1,144605 1,127385Variable loads:traffic 1,0 0,0 1,3439 0,42072 1,3439 0,42072temperature gradient 0,6 0,0 0,207 0,208 0,1242 0,1248

Calculation of forces acting on piles:

1) Case with three line loadsV= 545,385 [kN]M= 1195,319 [kNm]

e= 2,19 [m] ( eccentricity concerns traffic load)

Figure 47Sketch for forces in piles calculations (three line loads)

Loads coefficients Loads Combination loadsLong term loads: max min Node 1 Node 10 Node 1 Node 10own weight 1,0 0,9 2,7261 2,7087 2,7261 2,7087pavement 0,9 0,8 0,341 0,337 0,3069 0,3033earth prerssure 1,1 0,9 0,116 0,157 0,1276 0,1727shrinkage 1,0 0,0 0,0329 0,203 0 0castings 1,0 0,9 1,0901 1,0737 1,0901 1,0737Variable loads:traffic 1,5 0,7 1,3439 0,42072 2,01585 0,63108temperature gradient 1,5 0,6 0,207 0,208 0,1242 0,1248

100005600

3 kN/m2

A

RA

500 2000

4 kN/m2

RB

B

2 kN/m2

170 kN250 kN

1000 2000

Appendix A


NODE 1 Combination VI:A Combination V:AForces in piles:1) from dead loads

VLT= 3160,6 [kN] VLT= 2758,855 [kN]n= 8 [] n= 8 []P= 395,075 [kN] P= 344,857 [kN]

2) from shrinkageVshrinkage= 0 [kN] Vshrinkage= 0 [kN]

n= 8 [] n= 8 []P= 0 [kN] P= 0 [kN]

3) from temperature gradientVT= 124,8 [kN] VT= 124,8 [kN]

n= 8 [] n= 8 []PT= 15,6 [kN] PT= 15,6 [kN]

Force in pile from central loadP(V)= 410,675 [kN] P(V)= 360,457 [kN]

5) from trafficSuperposition of two stages:I) vertical load from traffic applied at the centre of gravity

Vp= 2015,85 [kN] Vp= 1343,9 [kN]n= 8 [] n= 8 []

Pp= 251,9813 [kN] Pp= 167,9875 [kN]

II) bending moment induced by traffic load M= 1195,319 [kNm]

ipile xi[m] x2 x2 Pi(M)Pile 1 0 0 0,000Pile 2 3,6 12,96 91,595Pile 3 2,7 7,29 68,696Pile 4 1,8 3,24 45,798Pile 5 1,8 3,24 45,798Pile 6 2,7 7,29 68,696Pile 7 3,6 12,96 91,595Pile8 0 0

46,98

0,000

Forces in piles:Combination IV:A

Pilenumber

Pi(V)[kN]

Pi(Vtraffic)[kN]

Pi(M)[kN]

Pi[kN]

1 423,31 259,74 0,00 683,052 423,31 259,74 91,60 774,653 410,68 251,98 68,70 731,354 410,68 251,98 45,80 708,455 410,68 251,98 45,80 616,866 410,68 251,98 68,70 593,967 423,31 259,74 91,60 591,468 423,31 259,74 0,00 683,05

Combination V:A

Pilenumber

Pi(V)[kN]

Pi(Vtraffic)[kN]

Pi(M)[kN]

Pi[kN]

1 371,55 173,16 0,00 544,712 371,55 173,16 91,60 636,303 360,46 167,99 68,70 597,144 360,46 167,99 45,80 574,245 360,46 167,99 45,80 482,656 360,46 167,99 68,70 459,757 371,55 173,16 91,60 453,118 371,55 173,16 0,00 544,71

Appendix A


NODE 10Forces in piles: Combination VI:A Combination V:A1) from dead loads

VLT= 3184,7 [kN] VLT= 3404,385 [kN]n= 8 [] n= 8,000 []P= 398,088 [kN] P= 425,548 [kN]


n= 8 [] n= 8 []P= 0 [kN] P= 0 [kN]


n= 8 [] n= 8 []PT= 15,6 [kN] PT= 15,6 [kN]


4) from traffic

Superposition of two stages:I) vertical load from traffic applied at the centre of gravity

Vp= 631,08 [kN] Vp= 420,72 [kN]n= 8 [] n= 8 []

Pp= 78,885 [kN] Pp= 52,590 [kN]



46,98

0,00


Pilenumber

Pi(V)[kN]

Pi(Vtraffic)[kN]

Pi(M)[kN]

Pi[kN]

1 426,42 81,31 0,00 507,732 426,42 81,31 91,60 599,333 413,69 78,89 68,70 561,274 413,69 78,89 45,80 538,375 413,69 78,89 45,80 446,776 413,69 78,89 68,70 423,887 426,42 81,31 91,60 416,148 426,42 81,31 0,00 507,73

Combination V:A

Pilenumber

Pi(V)[kN]

Pi(Vtraffic)[kN]

Pi(M)[kN]

Pi[kN]

1 454,73 54,21 0,00 508,932 454,73 54,21 91,60 600,533 441,15 52,59 68,70 562,434 441,15 52,59 45,80 539,545 441,15 52,59 45,80 447,946 441,15 52,59 68,70 425,04

Appendix A


Pilenumber

Pi(V)[kN]

Pi(Vtraffic)[kN]

Pi(M)[kN]

Pi[kN]

7 454,73 54,21 91,60 417,348 454,73 54,21 0,00 508,93

2) Case with two line loadsV= 518,124 [kN]M= 1261,057 [kNm]e= 2,43 [m] eccentricity from traffic load,

170 kN

3 kN/m2

560010000RA

2000500

4 kN/m2

A

250 kN

RB

B

1000 2000

Figure 48

Sketch for forces in piles calculations (two line loads)




n= 8 [] n= 8 []P= 0 [kN] P= 0 [kN]


n= 8 [] n= 8 []PT= 15,525 [kN] PT= 15,525 [kN]



Vp= 2015,85 [kN] Vp= 1343,9 [kN]n= 8 [] n= 8 []

Pp= 251,9813 [kN] Pp= 167,9875 [kN]


Appendix A


ipile xi[m] x2 x2 Pi(M)Pile 1 0 0 0Pile 2 3,6 12,96 96,63Pile 3 2,7 7,29 72,47Pile 4 1,8 3,24 48,32Pile 5 1,8 3,24 48,32Pile 6 2,7 7,29 72,47Pile 7 3,6 12,96 96,63Pile8 0 0

46,98

0

Forces in pilesCombination IV:A

Pilenumber

Pi(V)[kN]

Pi(Vtraffic)[kN]

Pi(M)[kN]

Pi[kN]

1 423,24 259,74 0,00 682,972 423,24 259,74 96,63 779,613 410,60 251,98 72,47 735,064 410,60 251,98 48,32 710,905 410,60 251,98 48,32 614,266 410,60 251,98 72,47 590,117 423,24 259,74 96,63 586,348 423,24 259,74 0,00 682,97

Combination V:A

Pilenumber

Pi(V)[kN]

Pi(Vtraffic)[kN]

Pi(M)[kN]

Pi[kN]

1 371,47 173,16 0,00 544,632 371,47 173,16 96,63 641,263 360,38 167,99 72,47 600,844 360,38 167,99 48,32 576,695 360,38 167,99 48,32 480,056 360,38 167,99 72,47 455,897 371,47 173,16 96,63 448,008 371,47 173,16 0,00 544,63




n= 8 [] n= 8 []P= 0 [kN] P= 0 [kN]


n= 8 [] n= 8 []PT= 15,6 [kN] PT= 15,6 [kN]



Vp= 631,08 [kN] Vp= 420,72 [kN]n= 8 [] n= 8 []

Pp= 78,885 [kN] Pp= 52,590 [kN]II) bending moment induced by traffic load M= 1 261,057 [kNm]

Appendix A



46,98

0,00

Forces in piles:

Combination IV:A

Pilenumber

Pi(V)[kN]

Pi(Vtraffic)[kN]

Pi(M)[kN]

Pi[kN]

1 426,42 81,31 0,00 507,732 426,42 81,31 96,63 604,363 413,69 78,89 72,47 565,054 413,69 78,89 48,32 540,895 413,69 78,89 48,32 444,266 413,69 78,89 72,47 420,107 426,42 81,31 96,63 411,108 426,42 81,31 0,00 507,73

Combination V:A

Pilenumber

Pi(V)[kN]

Pi(Vtraffic)[kN]

Pi(M)[kN]

Pi[kN]

1 454,73 54,21 0,00 508,932 454,73 54,21 96,63 605,573 441,15 52,59 72,47 566,214 441,15 52,59 48,32 542,055 441,15 52,59 48,32 445,426 441,15 52,59 72,47 421,267 454,73 54,21 96,63 412,308 454,73 54,21 0,00 508,93

Final forces in piles:

Combination IV:ANode 1 Node 10

Pilenumber

3 lane loads

2 lane loads

3 lane loads

2 lane loads

1 683,050 682,973 507,732 507,7322 774,646 779,606 599,327 604,3653 731,353 735,056 561,269 565,0474 708,454 710,898 538,370 540,8895 616,859 614,265 446,775 444,2566 593,960 590,107 423,876 420,0987 591,455 586,340 416,137 411,0998 683,050 682,973 507,732 507,732

Combination V:ANode 1 Node 10

Pilenumber

3 lane loads

2 lane loads

3 lane loads

2 lane loads

1 544,708 544,631 508,934 508,9342 636,303 641,263 600,529 605,5663 597,141 600,844 562,435 566,2134 574,242 576,686 539,536 542,0545 482,647 480,053 447,940 445,422

Node 1 Node 10

Appendix A


Pilenumber

3 lane loads

2 lane loads

3 lane loads

2 lane loads

6 459,748 455,895 425,042 421,2647 453,113 447,998 417,338 412,3018 544,708 544,631 508,934 508,934

DISPLACEMENTS CORRESPONDING WITH MAXIMAL FORCES IN PILES

Displacements combinations corresponding with loads:

Combination IV:ADisplacements [m] Displacements from loads combination

Loads coefficients Node 1 Node 10 Node 1 Node 10Long term loads: max min Horizontal Rotational Horizontal Rotational Horizontal Rotational Horizontal Rotationalown weight 1,0 0,9 0,0441115 1,45E02 0,045514 0,011304 0,0441115 0,014464 0,045514 0,011304pavement 0,9 0,8 0,00471 0,00135 0,00471 0,00132 0,004239 0,001215 0,004239 0,001188earth pressure 1,1 0,9 0,0248 0,00299 0,0248 0,00298 0,02728 0,003289 0,02728 0,003278shrinkage 1,0 0,0 0,00693 0,0028 0,00693 0,00278 0 0 0 0castings 1,0 0,9 0,039314 0,012705 0,039314 0,009553 0,039314 0,012705 0,039314 0,009553Variable loads:traffic 1,5 0,7 0,006611 0,0022996 0,006382 0,0020754 0,0099165 0,0034494 0,009573 0,0031131temperature gradient 1,5 0,6 0,00505 0,000147 0,00505 0,00016 0,00303 0,0000882 0,00303 0,000096

Displacements 0,061297 0,0192166 0,062356 0,0157011

Combination V:ADisplacements from loads combination Displacements from loads combination

Loads coefficients Node 1 Node 10 Node 1 Node 10Long term loads: max min Horizontal Rotational Horizontal Rotational Horizontal Rotational Horizontal Rotationalown weight 1,05 0,95 0,0441115 0,014464 0,045514 0,011304 0,046317 0,0151872 0,0477897 0,0118692pavement 1,15 0,8 0,00471 0,00135 0,00471 0,00132 0,005417 0,0015525 0,0054165 0,001518earth pressure 1,1 0,9 0,0248 0,00299 0,0248 0,00298 0,02728 0,003289 0,02728 0,003278shrinkage 1,0 0,0 0,00693 0,0028 0,00693 0,00278 0 0 0 0castings 1,05 0,95 0,039314 0,012705 0,039314 0,009553 0,04128 0,0133403 0,0412797 0,0100307Variable loads:traffic 1,0 0,0 0,006611 0,0022996 0,006382 0,0020754 0,006611 0,0022996 0,006382 0,0020754temperature gradient 0,6 0,0 0,00505 0,000147 0,00505 0,00016 0,00303 0,0000882 0,00303 0,000096

Displacements 0,061375 0,0191275 0,0626182 0,0155586

Temperature induced displacement:Tmin= 35 [ºC]Tmax= 40 [ºC]

Temperature gradient:T= 75 [ºC]

Length of half of the bridge: L = 62 [m]

Temperature coefficient (for steel and concrete):

t= 0,00001 [1/ºC]

Tmax= 37,5 [ºC]

maxTtt L ∆⋅⋅=∆ α

t,max= 0,02325 [m]

Appendix A


Final displacements:


calc 0,084547 0,085606

pCONTRAM 0,02728 0,02728

p 0,02569 0,02569 [m] 0,05886 0,05992

r [] 0,01603 0,01261


calc 0,0846246 0,0858682

pCONTRAM 0,02728 0,02728

p 0,02569 0,02569 [m] 0,05894 0,06018

r [] 0,01603 0,01247

MAXIMAL DISPLACEMENTFor this case temperature loads are dominant.




Node 1[MN]


[m]Rotational

[]Hirizontal

[m]Rotational

[]




Case 21 Taking off the formwork+railings 0,116 0,115 0,00161 0,000459 0,00161 0,000451Case 22 Pavement 0,341 0,337 0,00471 0,00135 0,00471 0,00132Case 23 Shrinkage 0,201 0,203 0,00693 0,0028 0,00693 0,00278Case 31 Temperature gradient 5º 0,0329 0,0329 0,000751 0,000211 0,000751 0,000211Case 32 Temperature gradient 10º 0,0656 0,0656 0,0015 0,000422 0,0015 0,000422Case 33 Temp gradient 10º,higher steel temp 0,207 0,208 0,00505 0,000147 0,00505 0,00016Case 34 Temp gradient 10º,lower steel temp 0,207 0,208 0,00505 0,000147 0,00505 0,00016


Node 1 Node 10Traffic load resultsx Fz r x Fz r

NK 1 0,005748 0,5751 0,002916 0,003969 0,1389 0,001114NK 2 0,00474 0,3279 0,001334 0,002046 0,07175 0,0005757Max Fx

0,010488 0,903 0,00425 0,001923 0,21065 0,0005383NK 1 0,003969 0,1395 0,00112 0,002046 0,07176 0,0005759NK 2 0,002046 0,07175 0,0005757 0,00474 0,3279 0,001334Min Fx

0,006015 0,21125 0,0016957 0,002694 0,25614 0,0007581NK 1 0,003793 0,1467 0,001184 0,003793 0,1467 0,001184NK 2 0,002046 0,07175 0,0005757 0,002046 0,07176 0,0005759Max Fz

0,005839 0,21845 0,0017597 0,005839 0,21846 0,0017599NK 1 0,001871 1,016 0,0009656 0,001642 0,09282 0,0007414NK 2 0,00474 0,3279 0,001334 0,00474 0,3279 0,001334Min Fz

0,006611 1,3439 0,0022996 0,006382 0,42072 0,0020754

Appendix A


Loads combinations:

Combination IV:ALoads coefficients: Loads Combination loads

Long term loads: max min Node 1 Node 10 Node 1 Node 10own weight 1,0 0,9 2,7261 2,7087 2,7261 2,7087pavement 0,9 0,8 0,341 0,337 0,3069 0,3033earth pressure 1,1 0,9 0,157 0,157 0,1413 0,1413shrinkage 1,0 0,0 0,201 0,203 0 0castings 1,0 0,9 1,0901 1,0737 1,0901 1,0737traffic 1,5 0,7 0,903 0,42072 0,6321 0,294504temperature gradient 1,5 0,6 0,207 0,208 0,3105 0,312

Combination V:ALoads coefficients: Loads Combination loads

Long term loads: max min Node 1 Node 10 Node 1 Node 10own weight 1,05 0,95 2,7261 2,7087 2,862405 2,844135pavement 1,15 0,8 0,341 0,337 0,39215 0,38755earth pressure 1,1 0,9 0,157 0,157 0,1413 0,1413shrinkage 1,0 0,0 0,201 0,203 0 0castings 1,05 0,95 1,0901 1,0737 1,144605 1,127385Variable loads:traffic 1,0 0,0 0,903 0,42072 0 0temperature gradient 0,6 0,0 0,207 0,208 0,1242 0,1248

Calculation of forces acting on piles:1) Case with three line loads (illustration in case with maximal force)

V= 545,385 [kN]M= 1195,319 [kNm]e= 2,19 [m]




n= 8 [] n= 8 []P= 0 [kN] P= 0 [kN]


n= 8 [] n= 8 []PT= 38,8125 [kN] PT= 15,525 [kN]


4) from trafficSuperposition of two stages:

I) vertical load from traffic applied at the centre of gravityVp= 632,1 [kN] Vp= 0 [kN]

n= 8 [] n= 8 []Pp= 79,0125 [kN] Pp= 0 [kN]


Appendix A



46,98

0,000


Pilenumber

Pi(V)[kN]

Pi(Vtraffic)[kN]

Pi(M)[kN]

Pi[kN]

1 449,01 81,44 0,00 530,452 449,01 81,44 91,60 622,053 435,60 79,01 68,70 583,314 435,60 79,01 45,80 560,415 435,60 79,01 45,80 468,816 435,60 79,01 68,70 445,927 449,01 81,44 91,60 438,868 449,01 81,44 0,00 530,45

Combination V:A

Pilenumber

Pi(V)[kN]

Pi(Vtraffic)[kN]

Pi(M)[kN]

Pi[kN]

1 453,55 0,00 0,00 453,552 453,55 0,00 91,60 545,143 440,01 0,00 68,70 508,704 440,01 0,00 45,80 485,805 440,01 0,00 45,80 394,216 440,01 0,00 68,70 371,317 453,55 0,00 91,60 361,958 453,55 0,00 0,00 453,55




n= 8 [] n= 8 []P= 0 [kN] P= 0 [kN]

3) from temperature gradientVT= 312 [kN] VT= 124,8 [kN]

n= 8 [] n= 8 []PT= 39 [kN] PT= 15,6 [kN]



Vp= 294,504 [kN] Vp= 0 [kN]n= 8 [] n= 8 []

Pp= 36,813 [kN] Pp= 0,000 [kN]


Appendix A



46,98

0,00

Forces in piles:

Combination IV:A

Pilenumber

Pi(V)[kN]

Pi(Vtraffic)[kN]

Pi(M)[kN]

Pi[kN]

1 446,49 37,95 0,00 484,442 446,49 37,95 91,60 576,033 433,16 36,81 68,70 538,674 433,16 36,81 45,80 515,775 433,16 36,81 45,80 424,186 433,16 36,81 68,70 401,287 446,49 37,95 91,60 392,848 446,49 37,95 0,00 484,44

Combination V:A

Pilenumber

Pi(V)[kN]

Pi(Vtraffic)[kN]

Pi(M)[kN]

Pi[kN]

1 450,68 0,00 0,00 450,682 450,68 0,00 91,60 542,273 437,22 0,00 68,70 505,924 437,22 0,00 45,80 483,025 437,22 0,00 45,80 391,436 437,22 0,00 68,70 368,537 450,68 0,00 91,60 359,088 450,68 0,00 0,00 450,68

2) Case with two line loads (illustration in case with maximal force):V= 518,124 [kN]M= 1261,057 [kNm]e= 2,43 [m]




n= 8 [] n= 8 []P= 0 [kN] P= 0 [kN]


n= 8 [] n= 8 []PT= 38,8125 [kN] PT= 15,525 [kN]


4) from traffic

Appendix A


Superposition of two stages:

I) vertical load from traffic applied at the centre of gravityVp= 632,1 [kN] Vp= 0 [kN]

n= 8 [] n= 8 []Pp= 79,0125 [kN] Pp= 0 [kN]


ipile xi[m] x2 x2 Pi(M)Pile 1 0 0 0Pile 2 3,6 12,96 96,63Pile 3 2,7 7,29 72,47Pile 4 1,8 3,24 48,32Pile 5 1,8 3,24 48,32Pile 6 2,7 7,29 72,47Pile 7 3,6 12,96 96,63Pile8 0 0

46,98

0

Forces in piles:

Combination IV:A

Pilenumber

Pi(V)[kN]

Pi(Vtraffic)[kN]

Pi(M)[kN]

Pi[kN]

1 449,01 81,44 0,00 530,452 449,01 81,44 96,63 627,083 435,60 79,01 72,47 587,094 435,60 79,01 48,32 562,935 435,60 79,01 48,32 466,306 435,60 79,01 72,47 442,147 449,01 81,44 96,63 433,828 449,01 81,44 0,00 530,45

Combination V:A

Pilenumber

Pi(V)[kN]

Pi(Vtraffic)[kN]

Pi(M)[kN]

Pi[kN]

1 453,55 0,00 0,00 453,552 453,55 0,00 96,63 550,183 440,01 0,00 72,47 512,484 440,01 0,00 48,32 488,325 440,01 0,00 48,32 391,696 440,01 0,00 72,47 367,537 453,55 0,00 96,63 356,928 453,55 0,00 0,00 453,55




n= 8 [] n= 8 []P= 0 [kN] P= 0 [kN]


n= 8 [] n= 8 []

PT= 39 [kN] PT= 15,6 [kN]

Appendix A




Vp= 294,504 [kN] Vp= 0 [kN]n= 8 [] n= 8 []

Pp= 36,813 [kN] Pp= 0,000 [kN]II) bending moment induced by traffic load M= 1 261,057 [kNm]


46,98

0,00

Forces in piles:

Combination IV:A

Pilenumber

Pi(V)[kN]

Pi(Vtraffic)[kN]

Pi(M)[kN]

Pi[kN]

1 446,49 37,95 0,00 484,442 446,49 37,95 96,63 581,073 433,16 36,81 72,47 542,454 433,16 36,81 48,32 518,295 433,16 36,81 48,32 421,666 433,16 36,81 72,47 397,507 446,49 37,95 96,63 387,818 446,49 37,95 0,00 484,44

Combination V:A

Pilenumber

Pi(V)[kN]

Pi(Vtraffic)[kN]

Pi(M)[kN]

Pi[kN]

1 450,68 0,00 0,00 450,682 450,68 0,00 96,63 547,313 437,22 0,00 72,47 509,704 437,22 0,00 48,32 485,545 437,22 0,00 48,32 388,916 437,22 0,00 72,47 364,757 450,68 0,00 96,63 354,058 450,68 0,00 0,00 450,68



Pilenumber

3 lane loads

2 lane loads

3 lane loads

2 lane loads

1 530,450 530,450 484,440 484,4402 622,046 627,083 576,035 581,0723 583,309 587,087 538,672 542,4504 560,410 562,929 515,773 518,2925 468,815 466,296 424,178 421,6596 445,916 442,138 401,279 397,5017 438,855 433,818 392,844 387,8078 530,450 530,450 484,440 484,440

Appendix A



Pilenumber

3 lane loads

2 lane loads

3 lane loads

2 lane loads

1 453,549 453,549 450,679 450,6792 545,144 550,181 542,275 547,3123 508,703 512,481 505,920 509,6984 485,805 488,323 483,021 485,5395 394,209 391,691 391,425 388,9076 371,310 367,532 368,527 364,7497 361,953 356,916 359,084 354,0478 453,549 453,549 450,679 450,679

DISPLACEMENTS

Displacements combinations (corresponding to lads combinations):

Combination IV:ADisplacements [m] Displacements from loads combination

Loads coefficients Node 1 Node 10 Node 1 Node 10Long term loads: max min Horizontal Rotational Horizontal Rotational Horizontal Rotational Horizontal Rotationalown weight 1,0 0,9 0,0441115 0,014464 0,045514 0,011304 0,0441115 0,014464 0,045514 0,011304pavement 0,9 0,8 0,00471 0,00135 0,00471 0,00132 0,004239 0,001215 0,004239 0,001188earth pressure 1,1 0,9 0,0248 0,00299 0,0248 0,00298 0,02232 0,002691 0,02232 0,002682shrinkage 1,0 0,0 0,00693 0,0028 0,00693 0,00278 0 0 0 0castings 1,0 0,9 0,039314 0,012705 0,039314 0,009553 0,039314 0,012705 0,039314 0,009553Variable loads:traffic 1,5 0,7 0,010488 0,00425 0,006382 0,0020754 0,015732 0,006375 0,009573 0,0031131temperature gradient 1,5 0,6 0,00505 0,000147 0,00505 0,00016 0,00303 0,0000882 0,00303 0,000096

Displacements 0,0671125 0,0221422 0,062356 0,0157011

Combintion V:ADisplacements [m] Displacements from loads combination

Loads coefficients Node 1 Node 10 Node 1 Node 10Long term loads: max min Horizontal Rotational Horizontal Rotational Horizontal Rotational Horizontal Rotationalown weight 1,05 0,95 0,0441115 0,014464 0,045514 0,011304 0,0463171 0,0151872 0,0477897 0,0118692pavement 1,15 0,8 0,00471 0,00135 0,00471 0,00132 0,0054165 0,0015525 0,0054165 0,001518earth pressure 1,1 0,9 0,0248 0,00299 0,0248 0,00298 0,02232 0,002691 0,02232 0,002682

shrinkage 1,0 0,0 0,00693 0,0028 0,00693 0,00278 0 0 0 0

castings 1,05 0,95 0,039314 0,012705 0,039314 0,009553 0,04128 0,0133403 0,0412797 0,0100307

Variable loads:traffic 1,0 0,0 0,010488 0,00425 0,006382 0,0020754 0,010488 0,00425 0,006382 0,0020754temperature gradient 0,6 0,0 0,00505 0,000147 0,00505 0,00016 0,00303 0,0000882 0,00303 0,000096

Displacements 0,0652516 0,0210779 0,0626182 0,0155586

Temperature induced displacement:Tmin= 35 [ºC]Tmax= 40 [ºC]


Length of half of the bridge: L = 62 [m]

Temperature coefficient (for steel and concrete):

t= 0,00001 [1/ºC]Tmax= 37,5 [ºC]


t,max= 0,02325 [m]

Appendix A




calc 0,0903625 0,085606

pCONTRAM 0,02232 0,02232

p 0,02102 0,02102 [m] 0,06934 0,06459

r [] 0,01854 0,01317


calc 0,0885016 0,0858682

pCONTRAM 0,02232 0,02232

p 0,02102 0,02102 [m] 0,06748 0,06485

r [] 0,01854 0,01303

MINIMAL DISPLACEMENTIn this case temperature loads are dominant.




Node 1[MN]


[m]Rotational

[]Hirizontal

[m]Rotational

[]



Case 3 Casting stage 2 0,32 0,229 0,0163 3,49E03 0,0163 0,00573Case 4 Casting stage 3 0,0111 0,00991 0,000679 0,000135 0,000679 0,00025Case 5 Casting stage 4 0,127 1,21 0,0258 0,0009 0,0258 0,0137Case 6 Casting stage 5 0,0158 0,00939 0,000507 0,00017 0,000507 0,000117Case 7 Earth pressure 0,157 0,157 0,0248 0,00299 0,0248 0,00298Case 21 Taking off the formwork+railings 0,116 0,115 0,00161 0,000459 0,00161 0,000451Case 22 Pavement 0,341 0,337 0,00471 0,00135 0,00471 0,00132Case 23 Shrinkage 0,201 0,203 0,00693 0,0028 0,00693 0,00278Case 31 Temperature gradient 5º 0,0329 0,0329 0,000751 0,000211 0,000751 0,000211Case 32 Temperature gradient 10º 0,0656 0,0656 0,0015 0,000422 0,0015 0,000422Case 33 Temp gradient 10º,higher steel temp 0,207 0,208 0,00505 0,000147 0,00505 0,00016Case 34 Temp gradient 10º,lower steel temp 0,207 0,208 0,00505 0,000147 0,00505 0,00016


Node 1 Node 10Traffic load resultsx Fz r x Fz r

NK 1 0,005748 0,5751 0,002916 0,003969 0,1389 0,001114NK 2 0,00474 0,3279 0,001334 0,002046 0,07175 0,0005757Max Fx

0,010488 0,903 0,00425 0,001923 0,21065 0,0005383NK 1 0,003969 0,1395 0,00112 0,002046 0,07176 0,0005759NK 2 0,002046 0,07175 0,0005757 0,00474 0,3279 0,001334Min Fx

0,006015 0,21125 0,0016957 0,002694 0,25614 0,0007581NK 1 0,003793 0,1467 0,001184 0,003793 0,1467 0,001184NK 2 0,002046 0,07175 0,0005757 0,002046 0,07176 0,0005759Max Fz

0,005839 0,21845 0,0017597 0,005839 0,21846 0,0017599NK 1 0,001871 1,016 0,0009656 0,001642 0,09282 0,0007414NK 2 0,00474 0,3279 0,001334 0,00474 0,3279 0,001334Min Fz

0,006611 1,3439 0,0022996 0,006382 0,42072 0,0020754

Appendix A


Loads combnations:

Combination IV:ALoads coefficients Loads Combination loads

Long term loads: max min Node 1 Node 10 Node 1 Node 10own weight 1,0 0,9 2,7261 2,7087 2,45349 2,43783pavement 0,9 0,8 0,341 0,337 0,2728 0,2696earth pressure 1,1 0,9 0,157 0,157 0,1727 0,1727shrinkage 1,0 0,0 0,201 0,203 0,201 0,203castings 1,0 0,9 1,0901 1,0737 0,98109 0,96633Variable loads:traffic 1,5 0,7 0,21125 0,21846 0,147875 0,152922temperature gradient 1,5 0,6 0,207 0,208 0,3105 0,312

Combination V:ALoads coefficients Loads Combination loads

Long term loads: max min Node 1 Node 10 Node 1 Node 10own weight 1,05 0,95 2,7261 2,7087 2,589795 2,573265pavement 1,15 0,8 0,341 0,337 0,2728 0,2696earth pressure 1,1 0,9 0,157 0,157 0,1727 0,1727shrinkage 1,0 0,0 0,201 0,203 0,201 0,203castings 1,05 0,95 1,0901 1,0737 1,035595 1,020015Variable loads:traffic 1,0 0,0 0,21125 0,21846 0,21125 0,21846temperature gradient 0,6 0,0 0,207 0,208 0,1242 0,1248

Calculations of forces acting on piles:

1) Case with three line loads (illustration in case with maximal force):

V= 545,385 [kN]M= 1195,319 [kNm]e= 2,19 [m]




n= 8 [] n= 8 []

P= 25,125 [kN] P= 25,125 [kN]

3) from temperature gradient

VT= 310,5 [kN] VT= 124,2 [kN]

n= 8 [] n= 8 []

PT= 38,8125 [kN] PT= 15,525 [kN]Force in pile from central load

P(V)= 426,311 [kN] P(V)= 389,012 [kN]


I) vertical load from traffic applied at the centre of gravityVp= 147,875 [kN] Vp= 211,25 [kN]

n= 8 [] n= 8 []Pp= 18,4844 [kN] Pp= 26,40625 [kN]


Appendix A



46,98

0,000

Forces in piles:

Combination IV:A

Pilenumber

Pi(V)[kN]

Pi(Vtraffic)[kN]

Pi(M)[kN]

Pi[kN]

1 439,43 19,05 0,00 420,382 439,43 19,05 91,60 511,973 426,31 18,48 68,70 476,524 426,31 18,48 45,80 453,625 426,31 18,48 45,80 362,036 426,31 18,48 68,70 339,137 439,43 19,05 91,60 328,788 439,43 19,05 0,00 420,38

Combination V:A

Pilenumber

Pi(V)[kN]

Pi(Vtraffic)[kN]

Pi(M)[kN]

Pi[kN]

1 400,98 27,22 0,00 373,772 400,98 27,22 91,60 465,363 389,01 26,41 68,70 431,304 389,01 26,41 45,80 408,405 389,01 26,41 45,80 316,816 389,01 26,41 68,70 293,917 400,98 27,22 91,60 282,178 400,98 27,22 0,00 373,77




n= 8 [] n= 8 []P= 25,375 [kN] P= 25,375 [kN]


n= 8 [] n= 8 []PT= 39 [kN] PT= 15,6 [kN]



I) vertical load from traffic applied at the centre of gravityVp= 152,922 [kN] Vp= 218,46 [kN]

n= 8 [] n= 8 []Pp= 19,115 [kN] Pp= 27,308 [kN]


Appendix A



46,98

0,00Forces in piles:

Combination IV:A

Pilenumber

Pi(V)[kN]

Pi(Vtraffic)[kN]

Pi(M)[kN]

Pi[kN]

1 437,45 19,70 0,00 417,752 437,45 19,70 91,60 509,343 424,39 19,12 68,70 473,974 424,39 19,12 45,80 451,075 424,39 19,12 45,80 359,486 424,39 19,12 68,70 336,587 437,45 19,70 91,60 326,158 437,45 19,70 0,00 417,75

Combination V:A

Pilenumber

Pi(V)[kN]

Pi(Vtraffic)[kN]

Pi(M)[kN]

Pi[kN]

1 346,31 28,15 0,00 318,162 346,31 28,15 91,60 409,763 335,97 27,31 68,70 377,364 335,97 27,31 45,80 354,465 335,97 27,31 45,80 262,876 335,97 27,31 68,70 239,977 346,31 28,15 91,60 226,578 346,31 28,15 0,00 318,16

2) Case with two line loads (illustration in case with maximal force):

V= 518,124 [kN]M= 1261,057 [kNm]e= 2,43 [m]




n= 8 [] n= 8 []P= 25,125 [kN] P= 25,125 [kN]


n= 8 [] n= 8 []PT= 38,8125 [kN] PT= 15,525 [kN]


4) from traffic

Appendix A



Vp= 147,875 [kN] Vp= 211,25 [kN]n= 8 [] n= 8 []

Pp= 18,4844 [kN] Pp= 26,40625 [kN]


ipile xi[m] x2 x2 Pi(M)Pile 1 0 0 0Pile 2 3,6 12,96 96,63Pile 3 2,7 7,29

46,98

72,47ipile xi[m] x2 x2 Pi(M)Pile 4 1,8 3,24 48,32Pile 5 1,8 3,24 48,32Pile 6 2,7 7,29 72,47Pile 7 3,6 12,96 96,63Pile8 0 0

46,98

0

Forces in piles:

Combination VI:A

Pilenumber

Pi(V)[kN]

Pi(Vtraffic)[kN]

Pi(M)[kN]

Pi[kN]

1 387,64 19,05 0,00 368,582 387,64 19,05 96,63 465,213 376,06 18,48 72,47 430,054 376,06 18,48 48,32 405,895 376,06 18,48 48,32 309,266 376,06 18,48 72,47 285,107 387,64 19,05 96,63 271,958 387,64 19,05 0,00 368,58

Combination V:A

Pilenumber

Pi(V)[kN]

Pi(Vtraffic)[kN]

Pi(M)[kN]

Pi[kN]

1 400,98 27,22 0,00 373,772 400,98 27,22 96,63 470,403 389,01 26,41 72,47 435,084 389,01 26,41 48,32 410,925 389,01 26,41 48,32 314,296 389,01 26,41 72,47 290,137 400,98 27,22 96,63 277,138 400,98 27,22 0,00 373,77




n= 8 [] n= 8 []P= 25,375 [kN] P= 25,375 [kN]


n= 8 [] n= 8 []PT= 39 [kN] PT= 15,6 [kN]

Appendix A



4) from traffic


Vp= 152,922 [kN] Vp= 218,46 [kN]n= 8 [] n= 8 []

Pp= 19,115 [kN] Pp= 27,308 [kN]

II) bending moment induced by traffic load M= 1 261,057 [kNm]


46,98

0,00


Pilenumber

Pi(V)[kN]

Pi(Vtraffic)[kN]

Pi(M)[kN]

Pi[kN]

1 385,14 19,70 0,00 365,442 385,14 19,70 96,63 462,073 373,64 19,12 72,47 427,004 373,64 19,12 48,32 402,845 373,64 19,12 48,32 306,216 373,64 19,12 72,47 282,057 385,14 19,70 96,63 268,808 385,14 19,70 0,00 365,44

Combination V:A

Pilenumber

Pi(V)[kN]

Pi(Vtraffic)[kN]

Pi(M)[kN]

Pi[kN]

1 398,62 28,15 0,00 370,472 398,62 28,15 96,63 467,113 386,72 27,31 72,47 431,894 386,72 27,31 48,32 407,735 386,72 27,31 48,32 311,106 386,72 27,31 72,47 286,947 398,62 28,15 96,63 273,848 398,62 28,15 0,00 370,47

Final forces in piles:Combination IV:A

Node 1 Node 10

Pilenumber

3 lane loads

2 lane loads

3 lane loads

2 lane loads

1 420,378 368,582 417,749 365,4372 511,974 465,215 509,344 462,0703 476,523 430,051 473,972 427,0014 453,625 405,893 451,074 402,8425 362,029 309,261 359,478 306,2106 339,130 285,102 336,580 282,0517 328,783 271,949 326,154 268,8048 420,378 368,582 417,749 365,437

Appendix A



Pilenumber

3 lane loads

2 lane loads

3 lane loads

2 lane loads

1 373,765 373,765 318,163 370,4752 465,361 470,398 409,758 467,1073 431,302 435,080 377,360 431,8884 408,403 410,922 354,461 407,7295 316,808 314,289 262,865 311,0976 293,909 290,131 239,967 286,9397 282,170 277,133 226,567 273,8428 373,765 373,765 318,163 370,475

DISPLACEMENTS

Displacements combinations (corresponding to lads combinations):

Combination IV:A

Displacements [m] Displacements from loads combinationLoads

coefficients: Node 1 Node 10 Node 1 Node 10

Long term loads: max min Horizontal Rotational Horizontal Rotational Horizontal Rotational Horizontal Rotational

own weight 1,0 0,9 0,0441115 0,014464 0,045514 0,011304 0,0397004 0,0130176 0,0409626 0,0101736

pavement 0,9 0,8 0,00471 0,00135 0,00471 0,00132 0,003768 0,00108 0,003768 0,001056

earth pressure 1,1 0,9 0,0248 0,00299 0,0248 0,00298 0,02728 0,003289 0,02728 0,003278

shrinkage 1,0 0,0 0,00693 0,0028 0,00693 0,00278 0,00693 0,0028 0,00693 0,00278

castings 1,0 0,9 0,039314 0,012705 0,039314 0,009553 0,0353826 0,0114345 0,0353826 0,0085977

Variable loads:

traffic 1,5 0,7 0,006015 0,0016957 0,005839 0,001760 0,0042105 0,0011870 0,004087 0,001232temperature gradient 1,5 0,6 0,00505 0,000147 0,00505 0,00016 0,007575 0,0002205 0,007575 0,00024

Displacements 0,00252715 0,0122011 0,001142 0,0092597

Combination V:ADisplacements [m] Displacements from loads combination

Loads coefficients Node 1 Node 10 Node 1 Node 10Long term loads: max min Horizontal Rotational Horizontal Rotational Horizontal Rotational Horizontal Rotationalown weight 1,05 0,95 0,0441115 0,014464 0,045514 0,011304 0,0419059 0,0137408 0,0432383 0,0107388pavement 1,15 0,8 0,00471 0,00135 0,00471 0,00132 0,003768 0,00108 0,003768 0,001056earth pressure 1,1 0,9 0,0248 0,00299 0,0248 0,00298 0,02728 0,003289 0,02728 0,003278shrinkage 1,0 0,0 0,00693 0,0028 0,00693 0,00278 0,00693 0,0028 0,00693 0,00278castings 1,05 0,95 0,039314 0,012705 0,039314 0,009553 0,0373483 0,0120698 0,0373483 0,00907535Variable loads:traffic 1,0 0,0 0,006015 0,0016957 0,005839 0,001756 0,006015 0,0016957 0,005839 0,0017599temperature gradient 0,6 0,0 0,00505 0,000147 0,00505 0,00016 0,00303 0,0000882 0,00303 0,000096

Displacements 0,0024189 0,0125479 0,0039273 0,0094409Temperature induced displacement:

Tmin= 35 [ºC]Tmax= 40 [ºC]


Length of half of the bridge: L = 62 [m]Temperature coefficient (for steel and concrete):

t= 0,00001 [1/ºC]

Tmax= 37,5 [ºC]


t,max= 0,02325 [m]

Appendix A




calc 0,02577715 0,0243917

pCONTRAM 0,02728 0,02728

p 0,02569 0,025690,02578 0,02439

r 0,00945 0,00617


calc 0,02083108 0,0193227

pCONTRAM 0,02728 0,02728

p 0,02569 0,025690,02083 0,01932

r 0,00945 0,00635

CALCULATIONS OF FORCES AND DISPLACEMENTS ACTING ON PARTICULAR ABUTMENTPILES. PILE X180.





Node 1[MN]


[m]Rotational

[]Hirizontal

[m]Rotational

[]




Case 21 Taking off the formwork+railings 0,116 0,115 0,00161 0,000461 0,00161 0,000452Case 22 Pavement 0,34 0,336 0,00471 0,00135 0,00471 0,00132Case 23 Shrinkage 0,2 0,203 0,00694 0,0028 0,00694 0,00278Case 31 Temperature gradient 5º 0,0329 0,0329 0,000765 0,000216 0,000766 0,000216Case 32 Temperature gradient 10º 0,0656 0,0656 0,00153 0,000432 0,00153 0,000432Case 33 Temp gradient 10º,higher steel temp 0,206 0,208 0,00506 0,000152 0,00505 0,000165Case 34 Temp gradient 10º,lower steel temp 0,206 0,208 0,00506 0,000152 0,00506 0,000165Case 35 Traffic load 1,3411 0,4196 0,006535 0,0022553 0,006384 0,0020814



Pilenumber

3 lane loads

2 lane loads

3 lane loads

2 lane loads

1 685,499 685,499 505,994 505,9942 777,094 782,131 597,589 602,6273 733,728 737,506 559,583 563,3614 710,829 713,348 536,684 539,2035 619,234 616,715 445,089 442,5706 596,335 592,557 422,190 418,4127 593,903 588,866 414,399 409,3618 685,499 685,499 505,994 505,994

Appendix A



Pilenumber

3 lane loads

2 lane loads

3 lane loads

2 lane loads

1 627,48 627,48 507,15 507,152 719,08 724,11 598,75 603,783 677,44 681,22 560,71 564,484 654,54 657,06 537,81 540,335 562,95 560,43 446,21 443,696 540,05 536,27 423,31 419,537 535,88 530,85 415,56 410,528 627,48 627,48 507,15 507,15

DISPLACEMENTS corresponding with maximal forces in piles



calc 0,0861665 0,08594

pCONTRAM 0,02772 0,02772

p 0,02610 0,02610 [m] 0,06006 0,05984

r [] 0,01597 0,01262


calc 0,0863685 0,08621745

pCONTRAM 0,02772 0,02772

p 0,02610 0,02610 [m] 0,06027 0,06011

r [] 0,01597 0,01248

MAXIMAL DISPLACEMENTFor this case temperature loads are dominant.




Node 1[MN]


[m]Rotational

[]Hirizontal

[m]Rotational

[]



Case 3 Casting stage 2 0,319 0,227 0,0166 3,55E03 0,0166 0,00584Case 4 Casting stage 3 0,0111 0,00984 0,000689 0,000137 0,000689 0,000254Case 5 Casting stage 4 0,125 1,2 0,0261 0,000986 0,0261 0,0138Case 6 Casting stage 5 0,0157 0,00357 0,000512 0,000171 0,000512 0,000119Case 7 Earth pressure 0,158 0,159 0,0252 0,00309 0,0252 0,00309Case 21 Taking off the formwork+railings 0,116 0,115 0,00161 0,000461 0,00161 0,000452Case 22 Pavement 0,34 0,336 0,00471 0,00135 0,00471 0,00132Case 23 Shrinkage 0,2 0,203 0,00694 0,0028 0,00694 0,00278Case 31 Temperature gradient 5º 0,0329 0,0329 0,000765 0,000216 0,000766 0,000216Case 32 Temperature gradient 10º 0,0656 0,0656 0,00153 0,000432 0,00153 0,000432Case 33 Temp gradient 10º,higher steel temp 0,206 0,208 0,00506 0,000152 0,00505 0,000165Case 34 Temp gradient 10º,lower steel temp 0,206 0,208 0,00506 0,000152 0,00506 0,000165Case 35 Traffic load 1,3488 0,011969 0,007465 0,0015072 0,011969 0,0010606

Appendix A




Pilenumber

3 lane loads

2 lane loads

3 lane loads

2 lane loads

1 567,772 567,772 443,841 443,8412 659,368 664,405 535,436 540,4743 619,516 623,295 499,285 503,0644 596,618 599,136 476,387 478,905

Node 1 Node 10

Pilenumber

3 lane loads

2 lane loads

3 lane loads

2 lane loads

5 505,022 502,504 384,791 382,2736 482,124 478,345 361,892 358,1147 476,177 471,140 352,246 347,2088 567,772 567,772 443,841 443,841


Pilenumber

3 lane loads

2 lane loads

3 lane loads

2 lane loads

1 450,61 450,61 448,99 448,992 542,21 547,24 540,58 545,623 505,85 509,63 504,28 508,064 482,96 485,47 481,38 483,905 391,36 388,84 389,79 387,276 368,46 364,68 366,89 363,117 359,02 353,98 357,39 352,368 450,61 450,61 448,99 448,99

DISPLACEMENTS



calc 0,0861435 0,0892963

pCONTRAM 0,02268 0,02268

p 0,02136 0,02136 [m] 0,06479 0,06794

r [] 0,01581 0,01097


calc 0,0872985 0,0918025

pCONTRAM 0,02268 0,02268

p 0,02136 0,02136 [m] 0,06594 0,07045

r [] 0,01581 0,01204

Appendix A






Node 1[MN]


[m]Rotational

[]Hirizontal

[m]Rotational

[]




Case 21 Taking off the formwork+railings 0,116 0,115 0,00161 0,000461 0,00161 0,000452Case 22 Pavement 0,34 0,336 0,00471 0,00135 0,00471 0,00132Case 23 Shrinkage 0,2 0,203 0,00694 0,0028 0,00694 0,00278




Node 1[MN]


[m]Rotational

[]Hirizontal

[m]Rotational

[]

Case 31 Temperature gradient 5º 0,0329 0,0329 0,000765 0,000216 0,000766 0,000216Case 32 Temperature gradient 10º 0,0656 0,0656 0,00153 0,000432 0,00153 0,000432Case 33 Temp gradient 10º,higher steel temp 0,206 0,208 0,00506 0,000152 0,00505 0,000165Case 34 Temp gradient 10º,lower steel temp 0,206 0,208 0,00506 0,000152 0,00506 0,000165




Pilenumber

3 lane loads

2 lane loads

3 lane loads

2 lane loads

1 359,958 308,419 378,869 326,5582 451,553 405,051 470,465 423,1903 417,907 371,685 436,254 389,2824 395,008 347,526 413,355 365,1245 303,412 250,894 321,760 268,491

Node 1 Node 10

Pilenumber

3 lane loads

2 lane loads

3 lane loads

2 lane loads

6 280,514 226,736 298,861 244,3337 268,362 211,786 287,274 229,9258 359,958 308,419 378,869 326,558


Pilenumber

3 lane loads

2 lane loads

3 lane loads

2 lane loads

1 392,902 393,044 368,310 420,6222 484,498 489,677 459,906 517,2553 449,868 453,783 426,010 480,5384 426,969 429,625 403,111 456,3805 335,374 332,992 311,516 359,7476 312,475 308,834 288,617 335,5897 301,307 296,411 276,715 323,9898 392,902 393,044 368,310 420,622

Appendix A


DISPLACEMENTS


calc 0,0253041 0,0252898

pCONTRAM 0,02772 0,02772

p 0,02610 0,02610 [m] 0,05141 0,05139

r [] 0,00988 0,00647


calc 0,02052695 0,020522

pCONTRAM 0,02772 0,02772

p 0,02610 0,02610 [m] 0,04663 0,04663

r [] 0,00988 0,00685

Calculations of forces and displacements acting on particular abutment piles. PileØ219.1x12.5.





Node 1[MN]


[m]Rotational

[]Hirizontal

[m]Rotational

[]



Case 3 Casting stage 2 0,322 0,231 0,0157 0,00334 0,0157 0,00549Case 4 Casting stage 3 0,0112 0,01 0,000655 0,000129 0,000655 0,000239Case 5 Casting stage 4 0,129 1,21 0,0248 0,000741 0,0248 0,0132Case 6 Casting stage 5 0,0158 0,00946 0,000492 0,000164 0,000492 0,000112Case 7 Earth pressure 0,153 0,154 0,0243 0,00281 0,0243 0,00281Case 21 Taking off the formwork+railings 0,116 0,115 0,00155 0,000439 0,00155 0,000431Case 22 Pavement 0,341 0,338 0,00453 0,00129 0,00453 0,00126Case 23 Shrinkage 0,201 0,204 0,00683 0,00281 0,00683 0,0028Case 31 Temperature gradient 5º 0,0327 0,0327 0,000741 0,000207 0,000741 0,000207Case 32 Temperature gradient 10º 0,0653 0,0653 0,00148 0,000413 0,00148 0,000413Case 33 Temp gradient 10º,higher steel temp 0,209 0,209 0,00498 0,000127 0,00498 0,000127Case 34 Temp gradient 10º,lower steel temp 0,209 0,209 0,00498 0,000127 0,00498 0,000127


Final forces in piles:Combination IV:A

Node 1 Node 10

Pilenumber

3 lane loads

2 lane loads

3 lane loads

2 lane loads

1 688,030 688,030 506,536 506,5362 779,626 784,663 598,131 603,1693 736,184 739,962 560,108 563,8864 713,285 715,804 537,210 539,7285 621,690 619,171 445,614 443,0966 598,791 595,013 422,715 418,9377 596,435 591,398 414,940 409,9038 688,030 688,030 506,536 506,536

Appendix A



Pilenumber

3 lane loads

2 lane loads

3 lane loads

2 lane loads

1 630,107 630,107 507,688 507,6882 721,702 726,740 599,283 604,3213 679,990 683,768 561,226 565,0044 657,091 659,610 538,327 540,8465 565,496 562,977 446,732 444,2136 542,597 538,819 423,833 420,0557 538,512 533,474 416,093 411,0558 630,107 630,107 507,688 507,688

DISPLACEMENTS corresponding with maximal forses in piles



calc 0,0730655 0,082845

pCONTRAM 0,02673 0,02673

p 0,02517 0,02517 [m] 0,04789 0,05767

r [] 0,01530 0,01191

Combination V:ANode 1 Node 10x [m] x [m]

calc 0,0726987 0,08305165

pCONTRAM 0,02673 0,02673

p 0,02517 0,02517 [m] 0,04753 0,05788

r [] 0,01522 0,01175

MAXIMAL DISPLACEMENTFor this case temperature loads are dominant




Node 1[MN]


[m]Rotational

[]Hirizontal

[m]Rotational

[]



Case 3 Casting stage 2 0,322 0,231 0,0157 0,00334 0,0157 0,00549Case 4 Casting stage 3 0,0112 0,01 0,000655 0,000129 0,000655 0,000239Case 5 Casting stage 4 0,129 1,21 0,0248 0,000741 0,0248 0,0132Case 6 Casting stage 5 0,0158 0,00946 0,000492 0,000164 0,000492 0,000112Case 7 Earth pressure 0,153 0,154 0,0243 0,00281 0,0243 0,00281Case 21 Taking off the formwork+railings 0,116 0,115 0,00155 0,000439 0,00155 0,000431Case 22 Pavement 0,341 0,338 0,00453 0,00129 0,00453 0,00126Case 23 Shrinkage 0,201 0,204 0,00683 0,00281 0,00683 0,0028Case 31 Temperature gradient 5º 0,0327 0,0327 0,000741 0,000207 0,000741 0,000207Case 32 Temperature gradient 10º 0,0653 0,0653 0,00148 0,000413 0,00148 0,000413Case 33 Temp gradient 10º,higher steel temp 0,209 0,209 0,00498 0,000127 0,00498 0,000127Case 34 Temp gradient 10º,lower steel temp 0,209 0,209 0,00498 0,000127 0,00498 0,000127


Appendix A




Pilenumber

3 lane loads

2 lane loads

3 lane loads

2 lane loads

1 624,232 599,996 479,962 479,9622 715,827 696,628 571,557 576,5953 674,290 654,556 534,328 538,1064 651,391 630,398 511,429 513,9485 559,796 533,765 419,834 417,3156 536,897 509,607 396,935 393,1577 532,636 503,363 388,367 383,3298 624,232 599,996 479,962 479,962


Pilenumber

3 lane loads

2 lane loads

3 lane loads

2 lane loads

1 570,103 570,103 498,822 498,8222 661,698 666,736 590,417 595,4553 621,778 625,556 552,625 556,4034 598,879 601,398 529,726 532,2455 507,284 504,765 438,131 435,6126 484,385 480,607 415,232 411,4547 478,508 473,470 407,227 402,1898 570,103 570,103 498,822 498,822

DISPLACEMENTS



calc 0,0773987 0,0873987

pCONTRAM 0,02187 0,02187

p 0,02059 0,02059 [m] 0,05680 0,06680

r [] 0,01533 0,01043


calc 0,0797147 0,0902147

pCONTRAM 0,02187 0,02187

p 0,02059 0,02059 [m] 0,05912 0,06962

r [] 0,01735 0,01154

Appendix A






Node 1[MN]


[m]Rotational

[]Hirizontal

[m]Rotational

[]



Case 3 Casting stage 2 0,322 0,231 0,0157 0,00334 0,0157 0,00549Case 4 Casting stage 3 0,0112 0,01 0,000655 0,000129 0,000655 0,000239Case 5 Casting stage 4 0,129 1,21 0,0248 0,000741 0,0248 0,0132Case 6 Casting stage 5 0,0158 0,00946 0,000492 0,000164 0,000492 0,000112Case 7 Earth pressure 0,153 0,154 0,0243 0,00281 0,0243 0,00281

Case 21 Taking off the formwork+railings 0,116 0,115 0,00155 0,000439 0,00155 0,000431Case 22 Pavement 0,341 0,338 0,00453 0,00129 0,00453 0,00126Case 23 Shrinkage 0,201 0,204 0,00683 0,00281 0,00683 0,0028Case 31 Temperature gradient 5º 0,0327 0,0327 0,000741 0,000207 0,000741 0,000207Case 32 Temperature gradient 10º 0,0653 0,0653 0,00148 0,000413 0,00148 0,000413Case 33 Temp gradient 10º,higher steel temp 0,209 0,209 0,00498 0,000127 0,00498 0,000127Case 34 Temp gradient 10º,lower steel temp 0,209 0,209 0,00498 0,000127 0,00498 0,000127Case 35 Traffic load 0,21442 0,21373 0,007687 0,0014503 0,008317 0,0014458



Pilenumber

3 lane loads

2 lane loads

3 lane loads

2 lane loads

1 360,798 309,002 358,269 305,6992 452,394 405,635 449,864 402,3323 418,722 372,250 416,268 369,0464 395,823 348,092 393,370 344,8885 304,228 251,459 301,774 248,2566 281,329 227,301 278,875 224,0977 269,203 212,369 266,674 209,0678 360,798 309,002 358,269 305,699


Pilenumber

3 lane loads

2 lane loads

3 lane loads

2 lane loads

1 394,308 394,450 339,072 339,0722 485,903 491,083 430,667 435,7043 451,231 455,147 397,644 401,4224 428,333 430,989 374,746 377,2645 336,737 334,356 283,150 280,6326 313,839 310,198 260,251 256,4737 302,713 297,817 247,476 242,4398 394,308 394,450 339,072 339,072

Appendix A


DISPLACEMENTS



calc 0,0361002 0,0275412

pCONTRAM 0,00683 0,00683

p 0,00643 0,00643 [m] 0,04253 0,03397

r [] 0,01454 0,01170


calc 0,01807459 0,0092046

pCONTRAM 0,02673 0,02673

p 0,02517 0,02517 [m] 0,04325 0,03438

r [] 0,00934 0,00636

Appendix B


B. APPENDIX

Geometry of the bridge

The bridge over Dalälven is a three span bridge with the lengths of spans: 38.5 m and47 m.Total length of the bride equals 124m (L = 38.5 + 47 +38.5 m). Girders are made of welded Isectionsplaced at a nominal distance 5600 mm. Height of the girders vary between 1250 and 2500 mm.

Integrated abutments (single rows of vertical piles) for calculations purposed have beenreplaced with three sets of springs: horizontal, vertical and point spring. Spring constants have beencalculated in the way to represent response of abutments and soil surrounding them. Calculation ofspring constants is presented in point 1.5 and Appendix C.

Figure 49

Schematic geometry of the bridge.Beams 2 and 7

Length: 18300 mmAmount Profile Thickness Width Length

Upper flange 1 PL 25 600 17800Web 11771198 1 PL 17 1188 18300Bottom flange 1 PL 49 825 18300

Beams 3 and 6Length: 27000 mm

Amount Profile Thickness Width LengthUpper flange 1 PL 25 600 15000Upper flange 1 PL 34 600 12000Web 12041949 1 PL 18 1576 15000Web 1 PL 21 2426 12000Bottom flange 1 PL 42 825 15000Bottom flange 1 PL 40 825 12000

Beams 4 and 5Length: 17000 mm

Amount Profile Thickness Width LengthUpper flange 1 PL 25 550 17000Web 11771198 1 PL 17 1532 17000Bottom flange 1 PL 49 825 17000

47

1

1

number of the element,

number of the node,

38,5

2

1

1 2

543

3 4 5

38,5

8

876

6 7

9

5

10

9

Appendix B


• Elements (nodes coordinates)

Figure 50

Schematic geometry of the bridge with the length of elements .

No a node b node Xa Za Xb Zb1 1 2 0 5 0 02 2 3 0 0 30 03 3 4 30 0 38.5 04 4 5 38.5 0 49.5 05 5 6 49.5 0 74.5 06 6 7 74.5 0 85.5 07 7 8 85.5 0 94 08 8 9 94 0 124 09 9 10 124 0 124 5

• Supports

Node x z y4 0 1 07 0 1 0

• Springs

Springconstant

Pile

Verticalkz

[MN/m]

Horizontalkx [MN/m]

Rotationalkr [MNm]

Pile X200 232,02 3,12 5,55Pile X180 168,92 2,52 3,61

Pile Ø219.1x12.5 169,78 4,27 10,40

• Stiffness of elements [m4]en ria rib x1 ri1 x2 ri2 x3 ri31 0.0587 0.05872 0.0308 0.0794 0.566 0.0308 0.567 0.0362 0.700 0.04123 0.0794 0.2154 0.353 0.1048 0.354 0.1322 0.588 0.15984 0.2154 0.0640 0.136 0.1950 0.318 0.1598 0.499 0.12225 0.0640 0.0640 0.140 0.0492 0.300 0.0396 0.500 0.0356

number of the element,

number of the node,

1

Z

1

2

11 2

43 5

3 4 5

876

6 7 8

9

10

9

X

2500011000850030000 30000850011000 5000

Appendix B


ria ribrikri2ri1

x1*lx2*l

xk*l

l

en ria rib xl ri1 x2 ri2 x3 ri36 0.0640 0.2154 0.273 0.0832 0.500 0.1048 0.501 0.13227 0.2154 0.0794 0.176 0.1950 0.412 0.1598 0.646 0.13228 0.0764 0.0308 0.100 0.0612 0.200 0.0492 0.300 0.04129 0.0587 0.0587

en x4 ri4 x5 ri512 0.800 0.0492 0.900 0.06123 0.824 0.19504 0.500 0.1048 0.727 0.08325 0.700 0.0396 0.860 0.04926 0.628 0.1598 0.864 0.19507 0.647 0.10488 0.433 0.0362 0.434 0.03089

• Stiffness of elements after casting particular parts of the bridge.Stages of casting:stage 1 casting element 2stage 2 casting element 5stage 3 casting elements 3,4stage 4 casting element 8stage 5 casting elements 6,7

After stage 1:ria rib x1 ri1 x2 ri2

Element 2 0.0776 0.1774 0.566 0.0776 0.567 0.0904

x3 ri3 x4 ri4 x5 ri50.700 0.1008 0.800 0.1172 0.900 0.1416


Element 5 0.1470 0.1470 0.140 0.1172 0.300 0.0974

x3 ri3 x4 ri4 x5 ri50.500 0.0890 0.700 0.0974 0.860 0.1172


Element 3 0.0794 0.2154 0.353 0.1048 0.354 0.1322Element 4 0.2154 0.0640 0.136 0.1950 0.318 0.1598

x3 ri3 x4 ri4 x5 ri50.588 0.1598 0.824 0.19500.499 0.1222 0.500 0.1048 0.727 0.0832

Appendix B



Element 8 0.1774 0.0776 0.100 0.1416 0.200 0.1172

x3 ri3 x4 ri4 x5 ri50.300 0.1008 0.433 0.0904 0.434 0.0776


Element 6 0.1242 0.3464 0.273 0.1564 0.500 0.1920Element 7 0.3464 0.1500 0.176 0.3162 0.412 0.2640

x3 ri3 x4 ri4 x5 ri50.501 0.2224 0.628 0.2640 0.864 0.31620.646 0.2224 0.647 0.1920

Appendix C


kz

kx kr

C. APPENDIX

Calculation of pile and soil stiffnes.

In order to do the calculations for the whole bridge in program CONTRAM, the piles areidealized by three sets of springs: a lateral spring, a vertical spring and a point spring. To obtain theconstants for those springs there were done calculations for a single pile modelled as a beam supportedon elastic foundation and the soil was replaced by the series of springs.

The spring constants were calculated with the use of a simple formula:

∆=

Fk [MN/m], [MNm/radian]

whereF – is an axial force, when calculating vertical abd horizontal spring constant and a bending moment

for a rotational spring constant, [MN], [MNm], – a displacement related with actin load, adequately horizontal dispalacement [m], vertical

displacement [m] or rotation [radian].

To simplify the calucations the piles are subjected to unit loads or displacements: Vertical force Fz=1MN Horizontal displacement x=0,01 m Rotational displacement r=0,001 rad

The second component of the formula was taken from the CONTRAM results (presented at the end ofthis appendix).

Springs supporting a pile, representing the soil response are characterized with the springconstant (a subgrade reaction modulus).The calculations of subgrade modulus values were doneaccordig to Swedish norm Bro 2004: Tables 1 and 2 and the Appendix 34. The subgrade reactionmodulus is assumed to change linearly with the depth, proportionally to the coefficient of horizontalsubgrade reaction of the soil(nh), what is expresseb with formula: ]/[5,2 2mMNzznk hh ⋅=⋅= . Thevalue of nh was taken from Table 1 (Bro 2004), for very lowly compacted soil, the ground over thelevel of ground water. The maximal value of the subgrade reaction modulus for sand is 12 [MN/m2](according to Table 2).

Subgrade reaction modulus:

Node x [m] kh[MN/m] Node x [m] kh[MN/m]1 0 0 11 5,0 6,252 0,5 0,703125 12 5,5 6,8753 1,0 1,25 13 6,0 7,54 1,5 1,875 14 6,5 8,1255 2,0 2,5 15 7,0 8,756 2,5 3,125 16 7,5 9,3757 3,0 3,75 17 8,0 108 3,5 4,375 18 8,5 10,6259 4,0 5 19 9,0 11,25

10 4,5 5,625 20 9,5 11,875

Appendix C


20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1kh

PILE X200

1) Vertical stiffness

CONTRAM METER MNPiles for integral abutment bridge (Fz=1 MN)Vertical stifness, X200 pile

GEOM 1 20 1 0 0 0 10RAND 1 1 1 1 0 1/ 20 20 1 0 1 0

Add 2 2 1 0.703 0 0/ 3 3 1 1.25 0 0/ 4 4 1 1.875 0 0/ 5 5 1 2.5 0 0/ 6 6 1 3.125 0 0/ 7 7 1 3.75 0 0/ 8 8 1 4.375 0 0/ 9 9 1 5.0 0 0/ 10 10 1 5.625 0 0/ 11 11 1 6.25 0 0/ 12 12 1 6.875 0 0/ 13 13 1 7.5 0 0/ 14 14 1 8.125 0 0/ 15 15 1 8.75 0 0/ 16 16 1 9.375 0 0/ 17 17 1 10 0 0/ 18 18 1 10.625 0 0/ 19 19 1 11.25 0 0/ 20 20 1 11.875 0 0

ELEM 1 19 1 1 2 1 111.0E4 19.9E6 2.1E5 1.0E5 0.08endg

LAST 3 US3 Vertical forceEGENT Z 1.0LASTK 1 1 1 0 1.0 0RESULT 3 3PRTL 3 3 3 3 1 1 1

Figure 51LAST 13 Horizontal displacementTVDEF 1 0.00 0 0

LAST 14 Rotational displacementTVDEF 1 0 0 0.000RESULT 13 14PRTL 13 14 13 14 1 1 1SLUT

RESULTS

PROGRAM CONTRAM Ramböll Sverige AB, LuleåPiles for integral abutment bridge (Fz=1 MN)Vertical stifness,X200 pile

***RESULTAT FÖR LASTFALL NR. 3: US3 Vertical force

******APPLICERAD LASTVEKTOR******* ***BERÄKNAD DEFORMATIONSVEKTOR**** (calculated deformations)NOD XKRAFT ZKRAFT YMOMENT XFÖRSKJ. ZFÖRSKJ. YROT. 1 0.000E+00 0.100E+01 0.000E+00 0.000E+00 0.431E02 0.000E+00 2 0.000E+00 0.467E03 0.000E+00 0.000E+00 0.408E02 0.000E+00 3 0.000E+00 0.467E03 0.000E+00 0.000E+00 0.386E02 0.000E+00 4 0.000E+00 0.467E03 0.000E+00 0.000E+00 0.363E02 0.000E+00 5 0.000E+00 0.467E03 0.000E+00 0.000E+00 0.341E02 0.000E+00 6 0.000E+00 0.467E03 0.000E+00 0.000E+00 0.318E02 0.000E+00 7 0.000E+00 0.467E03 0.000E+00 0.000E+00 0.295E02 0.000E+00 8 0.000E+00 0.467E03 0.000E+00 0.000E+00 0.273E02 0.000E+00 9 0.000E+00 0.467E03 0.000E+00 0.000E+00 0.250E02 0.000E+00 10 0.000E+00 0.467E03 0.000E+00 0.000E+00 0.227E02 0.000E+00

Appendix C


11 0.000E+00 0.467E03 0.000E+00 0.000E+00 0.205E02 0.000E+00 12 0.000E+00 0.467E03 0.000E+00 0.000E+00 0.182E02 0.000E+00 NOD XKRAFT ZKRAFT YMOMENT XFÖRSKJ. ZFÖRSKJ. YROT. 13 0.000E+00 0.467E03 0.000E+00 0.000E+00 0.159E02 0.000E+00 14 0.000E+00 0.467E03 0.000E+00 0.000E+00 0.136E02 0.000E+00 15 0.000E+00 0.467E03 0.000E+00 0.000E+00 0.114E02 0.000E+00 16 0.000E+00 0.467E03 0.000E+00 0.000E+00 0.910E03 0.000E+00 17 0.000E+00 0.467E03 0.000E+00 0.000E+00 0.683E03 0.000E+00 18 0.000E+00 0.467E03 0.000E+00 0.000E+00 0.455E03 0.000E+00 19 0.000E+00 0.467E03 0.000E+00 0.000E+00 0.228E03 0.000E+00 20 0.000E+00 0.234E03 0.000E+00 0.000E+00 0.000E+00 0.000E+00

2) Horizontal stiffness

CONTRAM METER MNPiles for integral abutment bridge (x=0,01 m)Horizontal stiffness, X 200

GEOM 1 20 1 0. 0. 0 10RAND 1 1 1 1 0 1/ 20 20 1 0 1 0Add 2 2 1 0.703 0 0/ 3 3 1 1.25 0 0/ 4 4 1 1.875 0 0/ 5 5 1 2.5 0 0/ 6 6 1 3.125 0 0/ 7 7 1 3.75 0 0/ 8 8 1 4.375 0 0/ 9 9 1 5.0 0 0/ 10 10 1 5.625 0 0/ 11 11 1 6.25 0 0/ 12 12 1 6.875 0 0/ 13 13 1 7.5 0 0/ 14 14 1 8.125 0 0/ 15 15 1 8.75 0 0/ 16 16 1 9.375 0 0/ 17 17 1 10 0 0/ 18 18 1 10.625 0 0/ 19 19 1 11.25 0 0/ 20 20 1 11.875 0 0

ELEM 1 19 1 1 2 1 111.0E4 19.9E6 2.1E5 1.0E5 0.08ENDG

LAST 3 US3 Vertical force from the bridgeEGENT Z 1.0LASTK 1 1 1 0 0 0RESULT 3 3PRTL 3 3 3 3 1 1 1ENDG

LAST 13 Horizontal displacementTVDEF 1 0.01 0 0LAST 14 Rotational displacementTVDEF 1 0 0 0.0RESULT 13 14PRTL 13 14 13 14 1 1 1SLUT

RESULTS

PROGRAM CONTRAM Ramböll Sverige AB, LuleåPiles for integral abutment bridge (x=0,01 m)Horizontal stiffness, X 200

***RESULTAT FÖR LASTFALL NR. 13: Horizontal displacement

***BERÄKNADE UPPLAGSREAKTIONER**** (support reactions)NOD XKRAFT ZKRAFT YMOMENT 1 0.312E01 0.000E+00 0.329E01 2 0.639E02 0.000E+00 0.000E+00 3 0.882E02 0.000E+00 0.000E+00 4 0.890E02 0.000E+00 0.000E+00

Appendix C


5 0.680E02 0.000E+00 0.000E+00 6 0.387E02 0.000E+00 0.000E+00 NOD XKRAFT ZKRAFT YMOMENT 7 0.123E02 0.000E+00 0.000E+00 8 0.521E03 0.000E+00 0.000E+00 9 0.130E02 0.000E+00 0.000E+00 10 0.136E02 0.000E+00 0.000E+00 11 0.102E02 0.000E+00 0.000E+00 12 0.590E03 0.000E+00 0.000E+00 13 0.236E03 0.000E+00 0.000E+00 14 0.188E04 0.000E+00 0.000E+00 15 0.746E04 0.000E+00 0.000E+00 16 0.883E04 0.000E+00 0.000E+00 17 0.656E04 0.000E+00 0.000E+00 18 0.349E04 0.000E+00 0.000E+00 19 0.771E05 0.000E+00 0.000E+00 20 0.164E04 0.000E+00 0.000E+00

3) Rotational stiffness

CONTRAM METER MNPiles for integral abutment bridge (r=0.001)Rotational stifness, X200

GEOM 1 20 1 0 0 0 10RAND 1 1 1 1 0 1/ 20 20 1 0 1 0Add 2 2 1 0.703 0 0/ 3 3 1 1.25 0 0/ 4 4 1 1.875 0 0/ 5 5 1 2.5 0 0/ 6 6 1 3.125 0 0/ 7 7 1 3.75 0 0/ 8 8 1 4.375 0 0/ 9 9 1 5.0 0 0/ 10 10 1 5.625 0 0/ 11 11 1 6.25 0 0/ 12 12 1 6.875 0 0/ 13 13 1 7.5 0 0/ 14 14 1 8.125 0 0/ 15 15 1 8.75 0 0/ 16 16 1 9.375 0 0/ 17 17 1 10 0 0/ 18 18 1 10.625 0 0/ 19 19 1 11.25 0 0/ 20 20 1 11.875 0 0

ELEM 1 19 1 1 2 1 111.0E4 19.9E6 2.1E5 1.0E5 0.08ENDGLAST 3 US3 Vertical force from the bridgeEGENT Z 1.0LASTK 1 1 1 0 0 0RESULT 3 3PRTL 3 3 3 3 1 1 1

LAST 13 Horizontal displacementTVDEF 1 0.00 0 0


RESULTS

PROGRAM CONTRAM Ramböll Sverige AB, LuleåPiles for integral abutment bridge (r=0.001)Rotational stifness, X200

Appendix C


***RESULTAT FÖR LASTFALL NR. 14: Rotational displacement

***BERÄKNADE UPPLAGSREAKTIONER**** (support reactions)NOD XKRAFT ZKRAFT YMOMENT 1 0.329E02 0.000E+00 0.555E02 2 0.254E03 0.000E+00 0.000E+00 NOD XKRAFT ZKRAFT YMOMENT 3 0.586E03 0.000E+00 0.000E+00 4 0.797E03 0.000E+00 0.000E+00 5 0.787E03 0.000E+00 0.000E+00 6 0.611E03 0.000E+00 0.000E+00 7 0.371E03 0.000E+00 0.000E+00 8 0.153E03 0.000E+00 0.000E+00 9 0.323E05 0.000E+00 0.000E+00 10 0.707E04 0.000E+00 0.000E+00 11 0.862E04 0.000E+00 0.000E+00 12 0.693E04 0.000E+00 0.000E+00 13 0.421E04 0.000E+00 0.000E+00 14 0.183E04 0.000E+00 0.000E+00 15 0.306E05 0.000E+00 0.000E+00 16 0.393E05 0.000E+00 0.000E+00 17 0.539E05 0.000E+00 0.000E+00 18 0.414E05 0.000E+00 0.000E+00 19 0.198E05 0.000E+00 0.000E+00 20 0.416E06 0.000E+00 0.000E+00

PILE X180


CONTRAM METER MNPiles for integral abutment bridge (Fz=1 MN)Vertical stifness, X 180 pile

GEOM 1 20 1 0 0 0 10RAND 1 1 1 1 0 1/ 20 20 1 0 1 0Add 2 2 1 0.703 0 0/ 3 3 1 1.25 0 0/ 4 4 1 1.875 0 0/ 5 5 1 2.5 0 0/ 6 6 1 3.125 0 0/ 7 7 1 3.75 0 0/ 8 8 1 4.375 0 0/ 9 9 1 5.0 0 0/ 10 10 1 5.625 0 0/ 11 11 1 6.25 0 0/ 12 12 1 6.875 0 0/ 13 13 1 7.5 0 0/ 14 14 1 8.125 0 0/ 15 15 1 8.75 0 0/ 16 16 1 9.375 0 0/ 17 17 1 10 0 0/ 18 18 1 10.625 0 0/ 19 19 1 11.25 0 0/ 20 20 1 11.875 0 0

ELEM 1 19 1 1 2 1 80.64E4 11.62E6 2.1E5 1.0E5 0.08endgLAST 3 US3 Vertical forceEGENT Z 1.0LASTK 1 1 1 0 1.0 0RESULT 3 3PRTL 3 3 3 3 1 1 1



Appendix C


RESULTS

***RESULTAT FÖR LASTFALL NR. 3: US3 Vertical force

******APPLICERAD LASTVEKTOR******* ***BERÄKNAD DEFORMATIONSVEKTOR****(calculated deformations)

NOD XKRAFT ZKRAFT YMOMENT XFÖRSKJ. ZFÖRSKJ. YROT. 1 0.000E+00 0.100E+01 0.000E+00 0.000E+00 0.592E02 0.000E+00 2 0.000E+00 0.340E03 0.000E+00 0.000E+00 0.561E02 0.000E+00 3 0.000E+00 0.340E03 0.000E+00 0.000E+00 0.530E02 0.000E+00 4 0.000E+00 0.340E03 0.000E+00 0.000E+00 0.499E02 0.000E+00 5 0.000E+00 0.340E03 0.000E+00 0.000E+00 0.468E02 0.000E+00 6 0.000E+00 0.340E03 0.000E+00 0.000E+00 0.437E02 0.000E+00 7 0.000E+00 0.340E03 0.000E+00 0.000E+00 0.406E02 0.000E+00 8 0.000E+00 0.340E03 0.000E+00 0.000E+00 0.375E02 0.000E+00 9 0.000E+00 0.340E03 0.000E+00 0.000E+00 0.343E02 0.000E+00 10 0.000E+00 0.340E03 0.000E+00 0.000E+00 0.312E02 0.000E+00 11 0.000E+00 0.340E03 0.000E+00 0.000E+00 0.281E02 0.000E+00 12 0.000E+00 0.340E03 0.000E+00 0.000E+00 0.250E02 0.000E+00 13 0.000E+00 0.340E03 0.000E+00 0.000E+00 0.219E02 0.000E+00 14 0.000E+00 0.340E03 0.000E+00 0.000E+00 0.187E02 0.000E+00 15 0.000E+00 0.340E03 0.000E+00 0.000E+00 0.156E02 0.000E+00 16 0.000E+00 0.340E03 0.000E+00 0.000E+00 0.125E02 0.000E+00 17 0.000E+00 0.340E03 0.000E+00 0.000E+00 0.938E03 0.000E+00 18 0.000E+00 0.340E03 0.000E+00 0.000E+00 0.625E03 0.000E+00 19 0.000E+00 0.340E03 0.000E+00 0.000E+00 0.313E03 0.000E+00 20 0.000E+00 0.170E03 0.000E+00 0.000E+00 0.000E+00 0.000E+00


CONTRAM METER MNPiles for integral abutment bridge (x=0,01 m)Horizontal stiffness, X 180

GEOM 1 20 1 0. 0. 0 10RAND 1 1 1 1 0 1/ 20 20 1 0 1 0Add 2 2 1 0.703 0 0/ 3 3 1 1.25 0 0/ 4 4 1 1.875 0 0/ 5 5 1 2.5 0 0/ 6 6 1 3.125 0 0/ 7 7 1 3.75 0 0/ 8 8 1 4.375 0 0/ 9 9 1 5.0 0 0/ 10 10 1 5.625 0 0/ 11 11 1 6.25 0 0/ 12 12 1 6.875 0 0/ 13 13 1 7.5 0 0/ 14 14 1 8.125 0 0/ 15 15 1 8.75 0 0/ 16 16 1 9.375 0 0/ 17 17 1 10 0 0/ 18 18 1 10.625 0 0/ 19 19 1 11.25 0 0/ 20 20 1 11.875 0 0

ELEM 1 19 1 1 2 1 80.64E4 11.62E6 2.1E5 1.0E5 0.08ENDG



Appendix C


RESULTS

PROGRAM CONTRAM Ramböll Sverige AB, LuleåPiles for integral abutment bridge (x=0,01 m)Horizontal stiffness, X 180


***BERÄKNADE UPPLAGSREAKTIONER**** (support reactions)NOD XKRAFT ZKRAFT YMOMENT 1 0.252E01 0.000E+00 0.239E01 2 0.625E02 0.000E+00 0.000E+00 3 0.816E02 0.000E+00 0.000E+00 4 0.750E02 0.000E+00 0.000E+00 5 0.493E02 0.000E+00 0.000E+00 6 0.205E02 0.000E+00 0.000E+00 7 0.677E04 0.000E+00 0.000E+00 8 0.109E02 0.000E+00 0.000E+00 9 0.123E02 0.000E+00 0.000E+00 10 0.908E03 0.000E+00 0.000E+00 11 0.480E03 0.000E+00 0.000E+00 12 0.151E03 0.000E+00 0.000E+00 13 0.241E04 0.000E+00 0.000E+00 14 0.779E04 0.000E+00 0.000E+00 15 0.671E04 0.000E+00 0.000E+00 16 0.375E04 0.000E+00 0.000E+00 17 0.130E04 0.000E+00 0.000E+00 18 0.121E06 0.000E+00 0.000E+00 19 0.463E05 0.000E+00 0.000E+00 20 0.532E05 0.000E+00 0.000E+00


CONTRAM METER MNPiles for integral abutment bridge (r=0.001)Rotational stifness, X180

GEOM 1 20 1 0 0 0 10RAND 1 1 1 1 0 1/ 20 20 1 0 1 0Add 2 2 1 0.703 0 0/ 3 3 1 1.25 0 0/ 4 4 1 1.875 0 0/ 5 5 1 2.5 0 0/ 6 6 1 3.125 0 0/ 7 7 1 3.75 0 0/ 8 8 1 4.375 0 0/ 9 9 1 5.0 0 0/ 10 10 1 5.625 0 0/ 11 11 1 6.25 0 0/ 12 12 1 6.875 0 0/ 13 13 1 7.5 0 0/ 14 14 1 8.125 0 0/ 15 15 1 8.75 0 0/ 16 16 1 9.375 0 0/ 17 17 1 10 0 0/ 18 18 1 10.625 0 0/ 19 19 1 11.25 0 0/ 20 20 1 11.875 0 0

ELEM 1 19 1 1 2 1 80.64E4 11.624E6 2.1E5 1.0E5 0.08

ENDGLAST 3 US3 Vertical force from the bridgeEGENT Z 1.0LASTK 1 1 1 0 0 0RESULT 3 3PRTL 3 3 3 3 1 1 1


LAST 14 Rotational displacement

Appendix C


TVDEF 1 0 0 0.001RESULT 13 14PRTL 13 14 13 14 1 1 1SLUT

RESULTS

PROGRAM CONTRAM Ramböll Sverige AB, LuleåPiles for integral abutment bridge (r=0.001)Rotational stifness, X180


******APPLICERAD LASTVEKTOR******* ***BERÄKNAD DEFORMATIONSVEKTOR**** (calculated deformations)NOD XKRAFT ZKRAFT YMOMENT XFÖRSKJ. ZFÖRSKJ. YROT. 1 0.529E01 0.000E+00 0.186E01 0.000E+00 0.000E+00 0.100E02 2 0.529E01 0.000E+00 0.928E02 0.345E03 0.000E+00 0.357E03 3 0.000E+00 0.000E+00 0.000E+00 0.420E03 0.000E+00 0.298E04 4 0.000E+00 0.000E+00 0.000E+00 0.351E03 0.000E+00 0.203E03 5 0.000E+00 0.000E+00 0.000E+00 0.233E03 0.000E+00 0.229E03 6 0.000E+00 0.000E+00 0.000E+00 0.123E03 0.000E+00 0.180E03 7 0.000E+00 0.000E+00 0.000E+00 0.466E04 0.000E+00 0.110E03 8 0.000E+00 0.000E+00 0.000E+00 0.508E05 0.000E+00 0.508E04 9 0.000E+00 0.000E+00 0.000E+00 0.107E04 0.000E+00 0.132E04 10 0.000E+00 0.000E+00 0.000E+00 0.123E04 0.000E+00 0.433E05 11 0.000E+00 0.000E+00 0.000E+00 0.849E05 0.000E+00 0.878E05 12 0.000E+00 0.000E+00 0.000E+00 0.417E05 0.000E+00 0.711E05 13 0.000E+00 0.000E+00 0.000E+00 0.126E05 0.000E+00 0.394E05 14 0.000E+00 0.000E+00 0.000E+00 0.102E06 0.000E+00 0.145E05 15 0.000E+00 0.000E+00 0.000E+00 0.467E06 0.000E+00 0.122E06 16 0.000E+00 0.000E+00 0.000E+00 0.385E06 0.000E+00 0.324E06 17 0.000E+00 0.000E+00 0.000E+00 0.204E06 0.000E+00 0.323E06 18 0.000E+00 0.000E+00 0.000E+00 0.674E07 0.000E+00 0.195E06 19 0.000E+00 0.000E+00 0.000E+00 0.633E08 0.000E+00 0.971E07 20 0.000E+00 0.000E+00 0.000E+00 0.464E07 0.000E+00 0.658E07


PILE Ø219.1x12.5


CONTRAM METER MNPiles for integral abutment bridge (Fz=1 MN)Vertical stifness, Ø219.1x12.5 pile

GEOM 1 20 1 0 0 0 10RAND 1 1 1 1 0 1/ 20 20 1 0 1 0

Appendix C


Add 2 2 1 0.703 0 0/ 3 3 1 1.25 0 0/ 4 4 1 1.875 0 0/ 5 5 1 2.5 0 0/ 6 6 1 3.125 0 0/ 7 7 1 3.75 0 0/ 8 8 1 4.375 0 0/ 9 9 1 5.0 0 0/ 10 10 1 5.625 0 0/ 11 11 1 6.25 0 0/ 12 12 1 6.875 0 0/ 13 13 1 7.5 0 0/ 14 14 1 8.125 0 0/ 15 15 1 8.75 0 0/ 16 16 1 9.375 0 0/ 17 17 1 10 0 0/ 18 18 1 10.625 0 0/ 19 19 1 11.25 0 0/ 20 20 1 11.875 0 0

ELEM 1 19 1 1 2 1 81.13E4 43.45E6 2.1E5 1.0E5 0.08endg

LAST 3 US3 Vertical forceEGENT Z 1.0LASTK 1 1 1 0 1.0 0RESULT 3 3PRTL 3 3 3 3 1 1 1



RESULTS

PROGRAM CONTRAM Ramböll Sverige AB, LuleåPiles for integral abutment bridge (Fz=1 MN)Vertical stifness, Ø219.1x12.5 pile

***RESULTAT FÖR LASTFALL NR. 3:US3 Vertical force ******APPLICERAD LASTVEKTOR******* ***BERÄKNAD DEFORMATIONSVEKTOR**** (calculated deformations)NOD XKRAFT ZKRAFT YMOMENT XFÖRSKJ. ZFÖRSKJ. YROT. 1 0.000E+00 0.100E+01 0.000E+00 0.000E+00 0.589E02 0.000E+00 2 0.000E+00 0.342E03 0.000E+00 0.000E+00 0.558E02 0.000E+00 3 0.000E+00 0.342E03 0.000E+00 0.000E+00 0.527E02 0.000E+00 4 0.000E+00 0.342E03 0.000E+00 0.000E+00 0.496E02 0.000E+00 5 0.000E+00 0.342E03 0.000E+00 0.000E+00 0.465E02 0.000E+00 6 0.000E+00 0.342E03 0.000E+00 0.000E+00 0.434E02 0.000E+00 7 0.000E+00 0.342E03 0.000E+00 0.000E+00 0.403E02 0.000E+00 8 0.000E+00 0.342E03 0.000E+00 0.000E+00 0.372E02 0.000E+00 9 0.000E+00 0.342E03 0.000E+00 0.000E+00 0.341E02 0.000E+00 10 0.000E+00 0.342E03 0.000E+00 0.000E+00 0.310E02 0.000E+00 11 0.000E+00 0.342E03 0.000E+00 0.000E+00 0.279E02 0.000E+00 12 0.000E+00 0.342E03 0.000E+00 0.000E+00 0.248E02 0.000E+00 13 0.000E+00 0.342E03 0.000E+00 0.000E+00 0.217E02 0.000E+00 14 0.000E+00 0.342E03 0.000E+00 0.000E+00 0.186E02 0.000E+00 15 0.000E+00 0.342E03 0.000E+00 0.000E+00 0.155E02 0.000E+00 16 0.000E+00 0.342E03 0.000E+00 0.000E+00 0.124E02 0.000E+00 17 0.000E+00 0.342E03 0.000E+00 0.000E+00 0.932E03 0.000E+00 18 0.000E+00 0.342E03 0.000E+00 0.000E+00 0.622E03 0.000E+00 19 0.000E+00 0.342E03 0.000E+00 0.000E+00 0.311E03 0.000E+00 20 0.000E+00 0.171E03 0.000E+00 0.000E+00 0.000E+00 0.000E+00


CONTRAM METER MNPiles for integral abutment bridge (x=0,01 m)Horizontal stiffness, Ø219.1x12.5

Appendix C


GEOM 1 20 1 0. 0. 0 10RAND 1 1 1 1 0 1/ 20 20 1 0 1 0Add 2 2 1 0.703 0 0/ 3 3 1 1.25 0 0/ 4 4 1 1.875 0 0/ 5 5 1 2.5 0 0/ 6 6 1 3.125 0 0/ 7 7 1 3.75 0 0/ 8 8 1 4.375 0 0/ 9 9 1 5.0 0 0/ 10 10 1 5.625 0 0/ 11 11 1 6.25 0 0/ 12 12 1 6.875 0 0/ 13 13 1 7.5 0 0/ 14 14 1 8.125 0 0/ 15 15 1 8.75 0 0/ 16 16 1 9.375 0 0/ 17 17 1 10 0 0/ 18 18 1 10.625 0 0/ 19 19 1 11.25 0 0/ 20 20 1 11.875 0 0

ELEM 1 19 1 1 2 1 81.13E4 43.45E6 2.1E5 1.0E5 0.08ENDG



RESULTS

PROGRAM CONTRAM Ramböll Sverige AB, LuleåPiles for integral abutment bridge (x=0,01 m)Horizontal stiffness, Ø219.1x12.5



Appendix C



CONTRAM METER MNPiles for integral abutment bridge (r=0.001)Rotational stifness, Ø219.1x12.5

GEOM 1 20 1 0 0 0 10RAND 1 1 1 1 0 1/ 20 20 1 0 1 0Add 2 2 1 0.703 0 0/ 3 3 1 1.25 0 0/ 4 4 1 1.875 0 0/ 5 5 1 2.5 0 0/ 6 6 1 3.125 0 0/ 7 7 1 3.75 0 0/ 8 8 1 4.375 0 0/ 9 9 1 5.0 0 0/ 10 10 1 5.625 0 0/ 11 11 1 6.25 0 0/ 12 12 1 6.875 0 0/ 13 13 1 7.5 0 0/ 14 14 1 8.125 0 0/ 15 15 1 8.75 0 0/ 16 16 1 9.375 0 0/ 17 17 1 10 0 0/ 18 18 1 10.625 0 0/ 19 19 1 11.25 0 0/ 20 20 1 11.875 0 0

ELEM 1 19 1 1 2 1 81.13E4 43.45E6 2.1E5 1.0E5 0.08

ENDGLAST 3 US3 Vertical force from the bridgeEGENT Z 1.0LASTK 1 1 1 0 0 0RESULT 3 3PRTL 3 3 3 3 1 1 1



RESULTS

PROGRAM CONTRAM Ramböll Sverige AB, LuleåPiles for integral abutment bridge (r=0.001)Rotational stifness, Ø219.1x12.5


***BERÄKNADE UPPLAGSREAKTIONER**** (support reactions)NOD XKRAFT ZKRAFT YMOMENT 1 0.524E02 0.000E+00 0.104E01 2 0.269E03 0.000E+00 0.000E+00 3 0.669E03 0.000E+00 0.000E+00 4 0.100E02 0.000E+00 0.000E+00 5 0.112E02 0.000E+00 0.000E+00 6 0.103E02 0.000E+00 0.000E+00 7 0.795E03 0.000E+00 0.000E+00 8 0.512E03 0.000E+00 0.000E+00 9 0.251E03 0.000E+00 0.000E+00 10 0.548E04 0.000E+00 0.000E+00 11 0.634E04 0.000E+00 0.000E+00 12 0.113E03 0.000E+00 0.000E+00 13 0.115E03 0.000E+00 0.000E+00 14 0.910E04 0.000E+00 0.000E+00 15 0.591E04 0.000E+00 0.000E+00

Appendix C


NOD XKRAFT ZKRAFT YMOMENT16 0.306E04 0.000E+00 0.000E+00 17 0.999E05 0.000E+00 0.000E+00 18 0.260E05 0.000E+00 0.000E+00 19 0.970E05 0.000E+00 0.000E+00 20 0.145E04 0.000E+00 0.000E+00

Calculation of spring constants:

The spring constants were calculated according to simple formulas:

stiffness of a vertical spring:z

zz

Fk∆

=

Fz – vertical force, equal 1 MN for simpler calculations,z – vertical displacement corresponding with acting force, [m]

kz – vertical spring constant, [MN/m]

stiffness of a horizontal spring:x

xx

Fk

∆=

x – given horizontal displacement equal 0.01 [m] for simpler calculations,Fx – horizontal force corresponding with acting pile deformation, [MN]kx– horizontal spring constant, [MN/m]

stiffness of rotational spring:r

rr

Fk∆

=

r– given pile top rotation, equal 0.001 [rad] for simpler calculations,M – bending moment corresponding with acting pile deformation, [MNm]kr– rotational spring constant, [MNm]

Vertical stiffness

Pile ForceFz [MN]

Displacementz [m]

Spring constantkz [MN/m]

Pile X200 1,0 0,00431 232,02Pile X180 1,0 0,00592 168,92

Pile Ø219.1x12.5 1,0 0,00589 169,78

Horizontal stiffness

Pile ForceFx [MN]

Displacementx [m]

Spring constantkx [MN/m]

Pile X200 0,0312 0,01 3,12Pile X180 0,0252 0,01 2,52

Pile Ø219.1x12.5 0,0427 0,01 4,27

Rotational stiffness

Pile MomentM [MNm]

Rotationr []

Spring constantkr [MNm]

Pile X200 0,00555 0,001 5,55Pile X180 0,00361 0,001 3,61

Pile Ø219.1x12.5 0,0104 0,001 10,40

Appendix D


D. APPENDIX

Loads

The crosssections in particular nodes for one beam:hw tw b1 tf1 b2 tf2 H

Node[mm] [mm] [mm] [mm] [mm] [mm] [mm]

2, 9 1177 17 600 25 825 48 12503, 8 1204 18 600 25 825 42 12714, 7 2426 21 600 34 825 40 25005, 6 1191 17 550 25 825 34 1250

Figure 52

Geometry of the girder.For both girders:

Asteel Ssteel ysteel esteelNode[mm2] [mm3] [mm] [mm]

2, 9 149218 64497257 432.2 817.83, 8 142644 67123836 470.6 800.44, 7 208692 230297076 1103.5 1396.55, 6 124094 60475923 487.3 762.7

The crosssection of concrete deck for longterm loads and shortterm loads is calculated according to

following formulas:s

effcconcrSTconcr E

EAA ,

, ⋅= for shortterm loads,

s

cconcrLTconcr E

EAA ∞⋅= ,

, for longterm loads,

Asteel Aconcr,ST A SST yST eSTNode[mm2] [mm2] [mm2] [mm3] [mm] [mm]

2, 9 149218 406349.21 555567.2 65015873 117.0 203.03, 8 142644 406349.21 548993.2 65015873 118.4 201.64, 7 208692 406349.21 615041.2 65015873 105.7 214.35, 6 124094 406349.21 530443.2 65015873 122.6 197.4

tf1

hwH

b2

tf2

ye

x1

x

b1

Appendix D


Asteel Aconcr,LT A SLT YLT ELTNode[mm2] [mm2] [mm2] [mm3] [mm] [mm]

2, 9 149218 135449.74 284667.7 255481384 897.5 672.53, 8 142644 135449.74 278093.7 260952407 938.4 652.64, 7 208692 135449.74 344141.7 590593372 1716.1 1103.95, 6 124094 135449.74 259543.7 251460050 968.9 601.1

Eccentricities:Node esteel [mm] eST [mm] eLT [mm]2, 9 817.8 203.0 672.53, 8 800.4 201.6 652.64, 7 1396.5 214.3 1103.95, 6 762.7 197.4 601.1

1) CastingArea of crosssection of concrete slab:

[ ]22.3 mAconcr =

Own weight of concrete slab:concrconcrconcr Ag γ⋅=

[ ]mMNg concr /08.0=

Own weight of formwork:[ ]mMNg form /0054.0=

2) Barriers[ ]mMNgbarriers /0014.0=

3) Pavement

Materials are taken from Swedish norm Bro 2004.Weight of pavement is 2.52 [kN/m2]

[ ]mMNg pavement /0252.0=

4) Shrinkage

[ ]GPaEc 89.8, =∞ modulus of elasticity of concrete for longterm loads,

][00025.0 −=εεσ ⋅= ∞,cshrinkage E

][22.2 MPashrinkage =σ

][11.72.322.2 MNAF concrshrinkageshr =⋅=⋅= σ

Node F etLT M2 7.111 0.673 4.7823 0.000 0.653 0.1414 0.000 1.104 3.067

Appendix D


Node F etLT M5 0.000 0.601 0.5086 0.000 0.601 0.5087 0.000 1.104 3.0678 0.000 0.653 0.1419 7.111 0.673 4.782

5) Earth pressureH= 3.5 [m] height of the abutment,D= 10 [m] width of the abutment,

Kp= 5.83 [] passive earth pressure coefficient,Ko= 0.34 [] active earth pressure coefficient,

= 18 [kN/m3] volumetric density of the soil,

HKp ppass ⋅⋅= γ][29.3675.31883.5 kPap pass =⋅⋅=

HKp oactive ⋅⋅= γ][42.215.31834.0 kPapactive =⋅⋅=

General data: L= 44.5 [m] length of the bridge,B= 13 [m] width of the bridge,

Eccentricities:H = 1.532 [m] the mean value,

32 Hetp ⋅=

etp = 1.021 [m]etp,LT = 0.673 [m]etp,ST = 0.203 [m]

Forces:5.0⋅⋅⋅= BHpF passpass

][428.6 MNFpass =

5.0⋅⋅⋅= BHpF activeactive

][375.0 MNFactive =

( )STtptppasspass eeFM ,−⋅=][258.5 MNmMpass =

( )LTtptpactiveactive eeFM ,−⋅=

][130.0 MNmMactive =

Appendix D


6) Temperature gradient 5ºC

875.1=bridgeH [m] – the mean value of the girders height,T = 5 [ºC] the temperature gradient,

bridgegrad H

TT =

Tgrad = 2.67 [ºC/m]

7) Temperature gradient +10ºC

875.1=bridgeH [m] – the mean value of the girders height,T = 10 [ºC] the temperature gradient,

bridgegrad H

TT =

Tgrad = 5.33 [ºC/m]

8) Temperature difference

Steel beams are 10ºC warmer then roadway.][10 CT o=∆ temperature difference,

][210 GPaE = Young’s modulus for steel,[ ]Co/100001.0=α thermal coefficient of expansion,

][21 MPaT −=∆σ

Calculation of forces from temperature difference:Asteel esteel eST Fnode Mnode

Node[m2] [m] [m] [MN] [MNm]

2 0.149218 0.818 0.203 3.13 1.933 0.142644 0.800 0.202 3.00 1.794 0.208692 1.396 0.214 4.38 5.185 0.124094 0.763 0.197 2.61 1.476 0.124094 0.763 0.197 2.61 1.477 0.208692 1.396 0.214 4.38 5.188 0.142644 0.800 0.202 3.00 1.799 0.149218 0.818 0.203 3.13 1.93

9) Traffic loads

The calculation of socalled "filfaktor"C= 5.6 [m] distance between girders,

Appendix D


FILFAKTOR is the number of axial loads (specified in calculated case) acting on one girder.

* filfaktor for axial loads 210 kN250 kN

4 kN/m2

2000

10000

500

5600RA

A

RB

B

2000

3 kN/m2

1000

170 kN

23004300

53007300

Figure 53

Sketch for filfaktor calculations [mm]0=Σ BM

06,5)5,08,2(170)7,06,5(250 =⋅−+⋅++⋅=Σ AB RM

kNRA 4,381210

3,31703,6250=

⋅+⋅=

filfaktor ][816,1210

4,381−=

* filfaktor for fatigue loads (150 kN and 180 kN)180 kN or 150 kN

4 kN/m2 3 kN/m2

5600

500 2000

A B

10000

53007300

RA RB

Figure 54

Sketch for filfaktor calculations [mm]

for force 150 kN0=Σ BM

06,5)7,06,5(150 =⋅−+⋅=Σ AB RM

kNRA 75,1686,5

3,6150=

⋅=


75,168−=

Appendix D


for force 180 kN

0=Σ BM06,5)7,06,5(180 =⋅−+⋅=Σ AB RM

kNRA 5,2026,5

3,6180=

⋅=


5,202−=

Appendix E


E. APPENDIX

Indata files for calculations of inner forces in bridge members and forcesacting on the abutments.PILE X 200

CONTRAM METER MNBridge over Dalälvenbeams Spv=38.5+47+38.5 m=124m,piles X200

GEOM 1 2 1 0 3.5 0 0/ 3 4 1 30. 0 38.5 0/ 5 6 1 49.5 0 74.5 0/ 7 8 1 85.5 0 94. 0/ 9 10 1 124 0 124 3.5RAND 4 4 1 0 1 0/ 7 7 1 0 1 0

ADD 1 1 1 3.12 232.02 5.55/ 4 4 1 0. 0. 1.E5/ 7 7 1 0. 0. 1.E5/ 10 10 1 3.12 232.02 5.55

!without cooperation

ELEM 1 1 1 1 2 1 4.4 1. 0.32E5 1.0E5 0.08/ 2 2 1 2 3 1 .14 1. 2.1E5 1.0E5 0.08/ 3 4 1 3 4 1 .20 1. 2.1E5 1.0E5 0.08/ 5 5 1 5 6 1 .14 1. 2.1E5 1.0E5 0.08/ 6 7 1 6 7 1 .20 1. 2.1E5 1.0E5 0.08/ 8 8 1 8 9 1 .14 1. 2.1E5 1.0E5 0.08/ 9 9 1 9 10 1 4.4 1. 0.32E5 1.0E5 0.08

STIF 1 .0587 .0578/ 2 .0308 .0794 .566 .0308 .567 .0362 .700 .0412 .800 .0492 .900 .0612/ 3 .0794 .2154 .353 .1048 .354 .1322 .588 .1598 .824 .195/ 4 .2154 .0640 .136 .1950 .318 .1598 .499 .1222 .500 .1048 .727 .0832/ 5 .0640 .0640 .140 .0492 .300 .0396 .500 .0356 .700 .0396 .860 .0492/ 6 .0640 .2154 .273 .0832 .500 .1048 .501 .1322 .682 .1598 .864 .1950/ 7 .2154 .0794 .176 .1950 .412 .1598 .646 .1322 .647 .1048/ 8 .0794 .0308 .100 .0612 .200 .0492 .300 .0412 .433 .0362 .434 .0308/ 9 .0587 .0587ENDGLast 1 US1 own weight of steel beams without cooperation *1.0egent Z 1.10 !10% additionally for stiffeners and crossbeams

Last 2 US2 casting slab stage 1 1*1.0Lastf 2 2 1 .08 0. 0. 1. !concrete slablastf 2 2 1 .0054 0. 0. 1. !formwork

RESULT 1 2PRTL 1 0 0 3 1 1

! casting 2

ELEM 2 2 1 2 3 1 .12 1. 2.1E5 1.0E5 0.08STIF 2 .0776 .1774 .566 .0776 .567 .0904 .700 .1008 .800 .1172 .900 .1416ENDG

LAST 3 US3 Casting slab stage 2 *1.0LASTF 5 5 1 .0800 0. 0. 1. !concrete slabLASTF 5 5 1 .0054 0. 0. 1. !formwork

RESULT 3 3PRTL 3 3 0 0 3 1 1

! casting 3

ELEM 5 5 1 5 6 1 .12 1. 2.1E5 1.0E5 0.08STIF 5 .1470 .1470 .140 .1172 .300 .0974 .500 .0890 .700 .0974 .860 .1172

Appendix E

Master’s Thesis:”Integral Abutments”140

ENDG


RESULT 4 4PRTL 4 4 0 0 3 1 1

! casting 4

ELEM 3 4 1 3 4 1 .14 1. 2.1E5 1.0E5 0.08STIF 3 .1500 .3464 .353 .1920 .354 .2224 .588 .2640 .824 .3162STIF 4 .3464 .1242 .136 .3162 .318 .2460 .499 .2224 .500 .1920 .727 .1564ENDG


RESULT 5 5PRTL 5 5 0 0 3 1 1

! casting 5

ELEM 8 8 1 8 9 1 .12 1. 2.1E5 1.0E5 0.08STIF 8 .1774 .0776 .100 .1416 .200 .1172 .300 .1008 .433 .0904 .434 .0776ENDG


RESULT 6 6PRTL 6 6 0 0 3 1 1

! Long term loads

ELEM 6 7 1 6 7 1 .14 1. 2.1E5 1.0E5 0.08STIF 6 .1242 .3464 .273 .1564 .500 .1920 .501 .2224 .682 .2640 .864 .3162STIF 7 .3464 .500 .176 .3162 .412 .2640 .646 .2224 .647 .1920ENDG

LAST 7 LT3 Earth pressureLASTK 2 2 1 6.053 0 5.128/ 9 9 1 –6.053 0 5.128RESULT 7 7PRTL 7 7 0 0 3 1 1

LAST 19 sum of own weight oif concrete slab form load cases 26LSUM 19 2 1. 3 1. 4 1. 5 1. 6 1.PRTL 19 19 1 1 3 1 1

LAST 21 US21 taking off formwork+railings *1.0LASTF 2 8 1 .014 0. 0 1 ! railings/ 2 8 1 .0054 0. 0 1 ! taking offRESULT 21 21PRTL 21 21 0 0 3 1 1

LAST 22 LT1 Pavement *1.0LASTF 2 8 1 .0252 0. 0. 1.RESULT 22 22PRTL 22 22 0 0 3 1 1

LAST 23 KR1 Shrinkage *1.0LASTK 2 2 1 7.11 0. 4.782/ 3 3 1 0. 0. 0.141/ 4 4 1 0. 0. 3.067/ 5 5 1 0. 0. 0.508/ 6 6 1 0. 0. 0.508/ 7 7 1 0. 0. 3.067/ 8 8 1 0. 0. 0.141/ 9 9 1 7.11 0. 4.782RESULT 23 23PRTL 23 23 0 0 3 1 1

Appendix E


LAST 25 OV1 Överhojning (LAST 16+2123)LSUM 25 1 1. 2 1. 3 1. 4 1. 5 1. 6 1. 21 1. 22 1. 23 1.PRTL 25 25 0 0 0 1 1

ELEM 1 1 1 1 2 1 4.4 1. 0.32E5 1.0E5 0.08/ 2 2 1 2 3 1 .48 1. 2.1E5 1.0E5 0.08/ 3 4 1 3 4 1 .42 1. 2.1E5 1.0E5 0.08/ 5 5 1 5 6 1 .48 1. 2.1E5 1.0E5 0.08/ 6 7 1 6 7 1 .42 1. 2.1E5 1.0E5 0.08/ 8 8 1 8 9 1 .48 1. 2.1E5 1.0E5 0.08/ 9 9 1 9 10 1 4.4 1. 0.32E5 1.0E5 0.08

STIF 2 .1024 .2402 .566 .1024 .567 .1222 .700 .1364 .800 .1586 .900 .1916/ 3 .2112 .4830 .353 .2706 .354 .3116 .588 .3692 .824 .4414/ 4 .4830 .1756 .136 .4414 .318 .3692 .499 .3116 .500 .2706 .727 .2206/ 5 .1990 .1990 .140 .1586 .300 .1318 .500 .1204 .700 .1318 .860 .1586/ 6 .1756 .4830 .273 .2206 .500 .2706 .501 .3116 .682 .3692 .864 .4414/ 7 .4830 .2118 .176 .4414 .412 .3692 .646 .3116 .647 .2706/ 8 .2402 .1024 .100 .1916 .200 .1586 .300 .1364 .433 .1222 .434 .1024ENDG

LAST 31 KT1 Temperature gradient 5 C deg *1.0LASTT 2 8 1 0. 2.67LAST 32 Temperature gradient +10 C deg * 1.0LASTT 2 8 1 0. 5.33LAST 33 KT2 Temperature difference 10 C deg higher steel temp * 1.0LASTK 2 2 1 3.13 0. 1.92/ 3 3 1 3.00 0. 1.79/ 4 4 1 4.38 0. 5.18/ 5 5 1 2.61 0. 1.48/ 6 6 1 2.61 0. 1.48/ 7 7 1 4.38 0. 5.18/ 8 8 1 3.00 0. 1.79/ 9 9 1 3.13 0. 1.92LAST 34 Temperature difference 10 C deg lower steel temperature * 1.0LKOMB 33 1RESULT 31 34 1PRTL 31 34 0 0 3 1

! UTMATTNINGSLAST

FILFAKT 1 0. 1.125 124. 1.125ENDGLSTGRP 1 AXELTRYCK 2*(150+180)*FILF*1.0LASTR 2 .180 0. 2./ 2 .150 8. 9.5LSTGRP 2 AXELTRYCK 2*(150+180)*FILF*1.0LASTR 2 .150 0. 1.5/ 2 .180 7.5 9.5LSTGRP 3 AXELTRYCK 2*(150+180)*FILF*1.0LASTR 2 .180 0. 2./ 2 .150 33. 34.5LSTGRP 4 AXELTRYCK 2*(150+180)*FILF*1.0LASTR 2 .150 0. 1.5/ 2 .180 32.5 34.5GRUPP 2000 7 0 0 1 10GRUPP 2000 7 0 1 2 10GRUPP 2000 7 0 1 3 35GRUPP 2000 7 0 1 4 35PRTMM 1 0 0 0 1 1 UTM Utmattningslast

! EKV.LAST 1

FILFAKT 1 0. 1.816 124. 1.816ENDGLSTGRP 1 AXELTRYCK 3*0.21*FILF*1.0LASTR 2 .210 0. 1.5/ 1 .210 7.5LSTGRP 2 AXELTRYCK 3*0.21*FILF*1.0LASTR 2 .210 0. 6./ 1 .210 7.5LSTGRP 3 AXELTRYCK 3*0.21*FILF*1.0LASTR 2 .210 0. 1.5/ 1 .210 34.5LSTGRP 4 AXELTRYCK 3*0.21*FILF*1.0

Appendix E


LASTR 2 .210 0. 33./ 1 .210 34.5GRUPP 2000 7 0 0 1 8GRUPP 2000 7 0 1 2 8GRUPP 2000 7 0 1 3 35GRUPP 2000 7 0 1 4 35PRTMM 1 0 0 0 1 1 NK1 AXELTRYCK 0.21*FILF*1.0

!FILLAST(??)

FILFAKT 1 0. 2.125 124. 2.125ENDGINTEGQ 2 8 0 .009PRTMM 2 0 0 0 1 1 NK2 FILLAST*FILF*1.0 MN/M

!MMSUM 0 0 0 0 1.5 1.5!PRTMM 3 0 0 0 1 1 TRAFIKLAST *1.5!SELECT 2 31 0 32 0 33 0 34 0!FKOMB 23 23 1 1!MMSUM 0 0 0 1 0 1!MMSUM 1 6 1.0 1 0 1!MMSUM 21 21 1.0 1 0 0!MMSUM 22 22 1.0 1 0 0!PRTMM 3 0 0 0 1 1 SUMMA LASTKOMBINATION IV:ASLUT

The main indata file is the same for all three pile types. The only difference are the values of constants of sringsupports.

For pile X 180 the opart of indata file responsible for spring supports definition will look as follows:

ADD 1 1 1 2.52 168.92 3.61/ 4 4 1 0. 0. 1.E5/ 7 7 1 0. 0. 1.E5/ 10 10 1 2.52 168.92 3.61

For pile Ø 219.1x12.5 the opart of indata file responsible for spring supports definition will look as follows

ADD 1 1 1 4.27 169.78 10.4/ 4 4 1 0. 0. 1.E5/ 7 7 1 0. 0. 1.E5/ 10 10 1 4.27 169.78 10.4

Simplified bridge model in programme CONTRAM:

Figure 55

Simplified CONTRAM bridge model

Appendix F


F. APPENDIXIndata files for piles calculationsPILE X 200

Combination IV:A

CONTRAM METER MNPiles for integral abutment bridgePile X200, combination IV:AGEOM 1 1 1 0.0000 0/ 2 2 1 0.0006 0.1/ 3 3 1 0.0012 0.2/ 4 4 1 0.0018 0.3/ 5 5 1 0.0023 0.4/ 6 6 1 0.0028 0.5/ 7 7 1 0.0032 0.6/ 8 8 1 0.0035 0.7/ 9 9 1 0.0037 0.8/ 10 10 1 0.0038 0.9/ 11 11 1 0.0039 1/ 12 12 1 0.0038 1.1/ 13 13 1 0.0036 1.2/ 14 14 1 0.0034 1.3/ 15 15 1 0.0030 1.4/ 16 16 1 0.0026 1.5/ 17 17 1 0.0021 1.6/ 18 18 1 0.0016 1.7/ 19 19 1 0.0010 1.8/ 20 20 1 0.0004 1.9/ 21 21 1 0.0002 2/ 22 22 1 0.0009 2.1/ 23 23 1 0.0014 2.2/ 24 24 1 0.0020 2.3/ 25 25 1 0.0025 2.4/ 26 26 1 0.0029 2.5/ 27 27 1 0.0033 2.6/ 28 28 1 0.0036 2.7/ 29 29 1 0.0038 2.8/ 30 30 1 0.0038 2.9/ 31 31 1 0.0038 3/ 32 32 1 0.0037 3.1/ 33 33 1 0.0035 3.2/ 34 34 1 0.0032 3.3/ 35 35 1 0.0029 3.4/ 36 36 1 0.0024 3.5/ 37 37 1 0.0019 3.6/ 38 38 1 0.0013 3.7/ 39 39 1 0.0007 3.8/ 40 40 1 0.0001 3.9/ 41 41 1 0.0005 4/ 42 42 1 0.0011 4.1/ 43 43 1 0.0017 4.2/ 44 44 1 0.0022 4.3/ 45 45 1 0.0027 4.4/ 46 46 1 0.0031 4.5/ 47 47 1 0.0034 4.6/ 48 48 1 0.0037 4.7/ 49 49 1 0.0038 4.8/ 50 50 1 0.0039 4.9/ 51 51 1 0.0038 5

RAND 1 1 1 1 0 1/ 51 51 1 0 1 0ADD 1 1 1 0 0 0/ 2 2 1 0.025 0 0/ 3 3 1 0.05 0 0/ 4 4 1 0.075 0 0/ 5 5 1 0.1 0 0/ 6 6 1 0.125 0 0/ 7 7 1 0.15 0 0/ 8 8 1 0.175 0 0

/ 9 9 1 0.2 0 0/ 10 10 1 0.225 0 0/ 11 11 1 0.25 0 0/ 12 12 1 0.275 0 0/ 13 13 1 0.3 0 0/ 14 14 1 0.325 0 0/ 15 15 1 0.35 0 0/ 16 16 1 0.375 0 0/ 17 17 1 0.4 0 0/ 18 18 1 0.425 0 0/ 19 19 1 0.45 0 0/ 20 20 1 0.475 0 0/ 21 21 1 0.5 0 0/ 22 22 1 0.525 0 0/ 23 23 1 0.55 0 0/ 24 24 1 0.575 0 0/ 25 25 1 0.6 0 0/ 26 26 1 0.625 0 0/ 27 27 1 0.65 0 0/ 28 28 1 0.675 0 0/ 29 29 1 0.7 0 0/ 30 30 1 0.725 0 0/ 31 31 1 0.75 0 0/ 32 32 1 0.775 0 0/ 33 33 1 0.8 0 0/ 34 34 1 0.825 0 0/ 35 35 1 3 0 0/ 36 36 1 3 0 0/ 37 37 1 3 0 0/ 38 38 1 3 0 0/ 39 39 1 3 0 0/ 40 40 1 3 0 0/ 41 41 1 3 0 0/ 42 42 1 1.8 0 0/ 43 43 1 1.8 0 0/ 44 44 1 1.8 0 0/ 45 45 1 1.8 0 0/ 46 46 1 1.8 0 0/ 47 47 1 1.8 0 0/ 48 48 1 1.8 0 0/ 49 49 1 1.8 0 0/ 50 50 1 1.8 0 0/ 51 51 1 1.8 0 0

ELEM 1 50 1 1 2 1 111.0E4 19.9E6 2.1E5 1.0E5 0.08ENDG

LAST 1 10 mm förskjutningLASTK 1 0 0 0 0.600TVDEF 1 0.01

LAST 2 10 promille rotationLASTK 1 0 0 0 0.600TVDEF 1 0 0 0.01

LAST 3 Calculations according to II orders theory, max forceORD2LASTK 1 0 0 0 0.796TVDEF 1 0.0573 0 0.0159

LAST 4 Calculations according to II orders theory, maxdisplacementORD2LASTK 1 0 0 0 0.65 0TVDEF 1 0.068 0 0.0195

LAST 5 Calculations according to II orders theory, mindisplacementORD2LASTK 1 0 0 0 0.49 0TVDEF 1 0.02578 0 0.0122RESULT 1 5PRTL 1 5 0 0 2SLUT

Appendix F


Combination V:A

CONTRAM METER MNPiles for integral abutment bridgePile X200, combination V:AGEOM 1 1 1 0.0 0/ 2 2 1 0.0 0.1/ 3 3 1 0.0 0.2/ 4 4 1 0.0 0.3/ 5 5 1 0.0 0.4/ 6 6 1 0.0 0.5/ 7 7 1 0.0 0.6/ 8 8 1 0.0 0.7/ 9 9 1 0.0 0.8/ 10 10 1 0.0 0.9/ 11 11 1 0.0 1/ 12 12 1 0.0 1.1/ 13 13 1 0.0 1.2/ 14 14 1 0.0 1.3/ 15 15 1 0.0 1.4/ 16 16 1 0.0 1.5/ 17 17 1 0.0 1.6/ 18 18 1 0.0 1.7/ 19 19 1 0.0 1.8/ 20 20 1 0.0 1.9/ 21 21 1 0.0 2/ 22 22 1 0.0 2.1/ 23 23 1 0.0 2.2/ 24 24 1 0.0 2.3/ 25 25 1 0.0 2.4/ 26 26 1 0.0 2.5/ 27 27 1 0.0 2.6/ 28 28 1 0.0 2.7/ 29 29 1 0.0 2.8/ 30 30 1 0.0 2.9/ 31 31 1 0.0 3/ 32 32 1 0.0 3.1/ 33 33 1 0.0 3.2/ 34 34 1 0.0 3.3/ 35 35 1 0.0 3.4/ 36 36 1 0.0 3.5/ 37 37 1 0.0 3.6/ 38 38 1 0.0 3.7/ 39 39 1 0.0 3.8/ 40 40 1 0.0 3.9/ 41 41 1 0.0 4/ 42 42 1 0.0 4.1/ 43 43 1 0.0 4.2/ 44 44 1 0.0 4.3/ 45 45 1 0.0 4.4/ 46 46 1 0.0 4.5/ 47 47 1 0.0 4.6/ 48 48 1 0.0 4.7/ 49 49 1 0.0 4.8/ 50 50 1 0.0 4.9/ 51 51 1 0.0 5

RAND 1 1 1 1 0 1/ 51 51 1 0 1 0

ADD 1 1 1 0 0 0/ 2 2 1 0.025 0 0/ 3 3 1 0.05 0 0/ 4 4 1 0.075 0 0/ 5 5 1 0.1 0 0/ 6 6 1 0.125 0 0/ 7 7 1 0.15 0 0/ 8 8 1 0.175 0 0/ 9 9 1 0.2 0 0/ 10 10 1 0.225 0 0/ 11 11 1 0.25 0 0/ 12 12 1 0.275 0 0/ 13 13 1 0.3 0 0/ 14 14 1 0.325 0 0/ 15 15 1 0.35 0 0/ 16 16 1 0.375 0 0

/ 17 17 1 0.4 0 0/ 18 18 1 0.425 0 0/ 19 19 1 0.45 0 0/ 20 20 1 0.475 0 0/ 21 21 1 0.5 0 0/ 22 22 1 0.525 0 0/ 23 23 1 0.55 0 0/ 24 24 1 0.575 0 0/ 25 25 1 0.6 0 0/ 26 26 1 0.625 0 0/ 27 27 1 0.65 0 0/ 28 28 1 0.675 0 0/ 29 29 1 0.7 0 0/ 30 30 1 0.725 0 0/ 31 31 1 0.75 0 0/ 32 32 1 0.775 0 0/ 33 33 1 0.8 0 0/ 34 34 1 0.825 0 0/ 35 35 1 3 0 0/ 36 36 1 3 0 0/ 37 37 1 3 0 0/ 38 38 1 3 0 0/ 39 39 1 3 0 0/ 40 40 1 3 0 0/ 41 41 1 3 0 0/ 42 42 1 1.8 0 0/ 43 43 1 1.8 0 0/ 44 44 1 1.8 0 0/ 45 45 1 1.8 0 0/ 46 46 1 1.8 0 0/ 47 47 1 1.8 0 0/ 48 48 1 1.8 0 0/ 49 49 1 1.8 0 0/ 50 50 1 1.8 0 0/ 51 51 1 1.8 0 0

ELEM 1 50 1 1 2 1 111.0E4 19.9E6 2.1E5 1.0E5 0.08ENDG



LAST 3 Calculations, max forceLASTK 1 0 0 0 0.6577TVDEF 1 0.0573 0 0.0158

LAST 4 Calculations, max displacementLASTK 1 0 0 0 0.57 0TVDEF 1 0.0662 0 0.0184

LAST 5 Calculations, min displacementLASTK 1 0 0 0 0.48 0TVDEF 1 0.02083 0 0.0125RESULT 1 5PRTL 1 5 0 0 2SLUT

Appendix F


PILE X 180

Combination IV:A

CONTRAM METER MNPiles for integral abutment bridgePile X180,combination IV:AGEOM 1 1 1 0.0000 0/ 2 2 1 0.000614 0.1/ 3 3 1 0.001210 0.2/ 4 4 1 0.001768 0.3/ 5 5 1 0.002272 0.4/ 6 6 1 0.002706 0.5/ 7 7 1 0.003058 0.6/ 8 8 1 0.003315 0.7/ 9 9 1 0.003471 0.8/ 10 10 1 0.00352 0.9/ 11 11 1 0.003461 1/ 12 12 1 0.003296 1.1/ 13 13 1 0.00303 1.2/ 14 14 1 0.002671 1.3/ 15 15 1 0.002229 1.4/ 16 16 1 0.00172 1.5/ 17 17 1 0.001157 1.6/ 18 18 1 0.000559 1.7/ 19 19 1 0.000056 1.8/ 20 20 1 0.00067 1.9/ 21 21 1 0.00126 2/ 22 22 1 0.00182 2.1/ 23 23 1 0.00231 2.2/ 24 24 1 0.00274 2.3/ 25 25 1 0.00308 2.4/ 26 26 1 0.00333 2.5/ 27 27 1 0.00348 2.6/ 28 28 1 0.00352 2.7/ 29 29 1 0.00345 2.8/ 30 30 1 0.00328 2.9/ 31 31 1 0.003 3/ 32 32 1 0.00263 3.1/ 33 33 1 0.00219 3.2/ 34 34 1 0.00167 3.3/ 35 35 1 0.0011 3.4/ 36 36 1 0.0005 3.5/ 37 37 1 0.00011 3.6/ 38 38 1 0.000723 3.7/ 39 39 1 0.001313 3.8/ 40 40 1 0.001863 3.9/ 41 41 1 0.002356 4/ 42 42 1 0.002776 4.1/ 43 43 1 0.003111 4.2/ 44 44 1 0.003351 4.3/ 45 45 1 0.003488 4.4/ 46 46 1 0.003517 4.5/ 47 47 1 0.003439 4.6/ 48 48 1 0.003255 4.7/ 49 49 1 0.002972 4.8/ 50 50 1 0.002597 4.9/ 51 51 1 0.002142 5

RAND 1 1 1 1 0 1/ 51 51 1 0 1 0

ADD 1 1 1 0 0 0/ 2 2 1 0.025 0 0/ 3 3 1 0.05 0 0/ 4 4 1 0.075 0 0/ 5 5 1 0.1 0 0/ 6 6 1 0.125 0 0/ 7 7 1 0.15 0 0/ 8 8 1 0.175 0 0/ 9 9 1 0.2 0 0/ 10 10 1 0.225 0 0/ 11 11 1 0.25 0 0/ 12 12 1 0.275 0 0/ 13 13 1 0.3 0 0

/ 14 14 1 0.325 0 0/ 15 15 1 0.35 0 0/ 16 16 1 0.375 0 0/ 17 17 1 0.4 0 0/ 18 18 1 0.425 0 0/ 19 19 1 0.45 0 0/ 20 20 1 0.475 0 0/ 21 21 1 0.5 0 0/ 22 22 1 0.525 0 0/ 23 23 1 0.55 0 0/ 24 24 1 0.575 0 0/ 25 25 1 0.6 0 0/ 26 26 1 0.625 0 0/ 27 27 1 0.65 0 0/ 28 28 1 0.675 0 0/ 29 29 1 0.7 0 0/ 30 30 1 0.725 0 0/ 31 31 1 0.75 0 0/ 32 32 1 0.775 0 0/ 33 33 1 0.8 0 0/ 34 34 1 0.825 0 0/ 35 35 1 3 0 0/ 36 36 1 3 0 0/ 37 37 1 3 0 0/ 38 38 1 3 0 0/ 39 39 1 3 0 0/ 40 40 1 3 0 0/ 41 41 1 3 0 0/ 42 42 1 1.8 0 0/ 43 43 1 1.8 0 0/ 44 44 1 1.8 0 0/ 45 45 1 1.8 0 0/ 46 46 1 1.8 0 0/ 47 47 1 1.8 0 0/ 48 48 1 1.8 0 0/ 49 49 1 1.8 0 0/ 50 50 1 1.8 0 0/ 51 51 1 1.8 0 0

ELEM 1 50 1 1 2 1 80.64E4 11.62E6 2.1E5 1.0E5 0.08ENDG



LAST 3 Calculations according to II orders theory, max forceORD2LASTK 1 0 0 0 0.79367 0TVDEF 1 0.05845 0 0.01578


LAST 5 Calculations according to II orders theory, mindisplacementORD2LASTK 1 0 0 0 0.49 0TVDEF 1 0.010124 0 0.01301RESULT 1 5PRTL 1 5 0 0 2SLUT

Appendix F


Combination V:A

CONTRAM METER MNPiles for integral abutment bridgePile X180,combination V:AGEOM 1 1 1 0.0 0/ 2 2 1 0.0 0.1/ 3 3 1 0.0 0.2/ 4 4 1 0.0 0.3/ 5 5 1 0.0 0.4/ 6 6 1 0.0 0.5/ 7 7 1 0.0 0.6/ 8 8 1 0.0 0.7/ 9 9 1 0.0 0.8/ 10 10 1 0.0 0.9/ 11 11 1 0.0 1/ 12 12 1 0.0 1.1/ 13 13 1 0.0 1.2/ 14 14 1 0.0 1.3/ 15 15 1 0.0 1.4/ 16 16 1 0.0 1.5/ 17 17 1 0.0 1.6/ 18 18 1 0.0 1.7/ 19 19 1 0.0 1.8/ 20 20 1 0.0 1.9/ 21 21 1 0.0 2/ 22 22 1 0.0 2.1/ 23 23 1 0.0 2.2/ 24 24 1 0.0 2.3/ 25 25 1 0.0 2.4/ 26 26 1 0.0 2.5/ 27 27 1 0.0 2.6/ 28 28 1 0.0 2.7/ 29 29 1 0.0 2.8/ 30 30 1 0.0 2.9/ 31 31 1 0.0 3/ 32 32 1 0.0 3.1/ 33 33 1 0.0 3.2/ 34 34 1 0.0 3.3/ 35 35 1 0.0 3.4/ 36 36 1 0.0 3.5/ 37 37 1 0.0 3.6/ 38 38 1 0.0 3.7/ 39 39 1 0.0 3.8/ 40 40 1 0.0 3.9/ 41 41 1 0.0 4/ 42 42 1 0.0 4.1/ 43 43 1 0.0 4.2/ 44 44 1 0.0 4.3/ 45 45 1 0.0 4.4/ 46 46 1 0.0 4.5/ 47 47 1 0.0 4.6/ 48 48 1 0.0 4.7/ 49 49 1 0.0 4.8/ 50 50 1 0.0 4.9/ 51 51 1 0.0 5

RAND 1 1 1 1 0 1/ 51 51 1 0 1 0

ADD 1 1 1 0 0 0/ 2 2 1 0.025 0 0/ 3 3 1 0.05 0 0/ 4 4 1 0.075 0 0/ 5 5 1 0.1 0 0/ 6 6 1 0.125 0 0/ 7 7 1 0.15 0 0/ 8 8 1 0.175 0 0/ 9 9 1 0.2 0 0/ 10 10 1 0.225 0 0/ 11 11 1 0.25 0 0/ 12 12 1 0.275 0 0/ 13 13 1 0.3 0 0/ 14 14 1 0.325 0 0/ 15 15 1 0.35 0 0/ 16 16 1 0.375 0 0

/ 17 17 1 0.4 0 0/ 18 18 1 0.425 0 0/ 19 19 1 0.45 0 0/ 20 20 1 0.475 0 0/ 21 21 1 0.5 0 0/ 22 22 1 0.525 0 0/ 23 23 1 0.55 0 0/ 24 24 1 0.575 0 0/ 25 25 1 0.6 0 0/ 26 26 1 0.625 0 0/ 27 27 1 0.65 0 0/ 28 28 1 0.675 0 0/ 29 29 1 0.7 0 0/ 30 30 1 0.725 0 0/ 31 31 1 0.75 0 0/ 32 32 1 0.775 0 0/ 33 33 1 0.8 0 0/ 34 34 1 0.825 0 0/ 35 35 1 3 0 0/ 36 36 1 3 0 0/ 37 37 1 3 0 0/ 38 38 1 3 0 0/ 39 39 1 3 0 0/ 40 40 1 3 0 0/ 41 41 1 3 0 0/ 42 42 1 1.8 0 0/ 43 43 1 1.8 0 0/ 44 44 1 1.8 0 0/ 45 45 1 1.8 0 0/ 46 46 1 1.8 0 0/ 47 47 1 1.8 0 0/ 48 48 1 1.8 0 0/ 49 49 1 1.8 0 0/ 50 50 1 1.8 0 0/ 51 51 1 1.8 0 0

ELEM 1 50 1 1 2 1 80.64E4 11.62E6 2.1E5 1.0E5 0.08ENDG



LAST 3 Calculations, max forceORD2LASTK 1 0 0 0 0.73565 0TVDEF 1 0.05865 0 0.01578

LAST 4 Calculations, max displacementORD2LASTK 1 0 0 0 0.57 0TVDEF 1 0.06362 0 0.01565

LAST 5 Calculations, min displacementORD2LASTK 1 0 0 0 0.48 0TVDEF 1 0.01445 0 0.01326RESULT 1 5PRTL 1 5 0 0 2SLUT

Appendix F


PILE Ø219.1x12.5

Combination IV:A

CONTRAM METER MNPiles for integral abutment bridgePile PIPE, combination IV:AGEOM 1 1 1 0.0000 0/ 2 2 1 0.000929 0.1/ 3 3 1 0.001842 0.2/ 4 4 1 0.002721 0.3/ 5 5 1 0.003551 0.4/ 6 6 1 0.004317 0.5/ 7 7 1 0.005004 0.6/ 8 8 1 0.005601 0.7/ 9 9 1 0.006096 0.8/ 10 10 1 0.00648 0.9/ 11 11 1 0.006748 1/ 12 12 1 0.006893 1.1/ 13 13 1 0.006913 1.2/ 14 14 1 0.006808 1.3/ 15 15 1 0.006579 1.4/ 16 16 1 0.006231 1.5/ 17 17 1 0.005771 1.6/ 18 18 1 0.005205 1.7/ 19 19 1 0.004546 1.8/ 20 20 1 0.003804 1.9/ 21 21 1 0.002993 2/ 22 22 1 0.002128 2.1/ 23 23 1 0.001224 2.2/ 24 24 1 0.000298 2.3/ 25 25 1 0.00063 2.4/ 26 26 1 0.00155 2.5/ 27 27 1 0.00244 2.6/ 28 28 1 0.00329 2.7/ 29 29 1 0.00408 2.8/ 30 30 1 0.00479 2.9/ 31 31 1 0.00542 3/ 32 32 1 0.00595 3.1/ 33 33 1 0.00637 3.2/ 34 34 1 0.00668 3.3/ 35 35 1 0.00686 3.4/ 36 36 1 0.00692 3.5/ 37 37 1 0.00685 3.6/ 38 38 1 0.00667 3.7/ 39 39 1 0.00636 3.8/ 40 40 1 0.00593 3.9/ 41 41 1 0.0054 4/ 42 42 1 0.00477 4.1/ 43 43 1 0.00405 4.2/ 44 44 1 0.00326 4.3/ 45 45 1 0.00241 4.4/ 46 46 1 0.00152 4.5/ 47 47 1 0.0006 4.6/ 48 48 1 0.000335 4.7/ 49 49 1 0.001261 4.8/ 50 50 1 0.002163 4.9/ 51 51 1 0.003026 5

RAND 1 1 1 1 0 1/ 51 51 1 0 1 0

ADD 1 1 1 0 0 0/ 2 2 1 0.025 0 0/ 3 3 1 0.05 0 0/ 4 4 1 0.075 0 0/ 5 5 1 0.1 0 0/ 6 6 1 0.125 0 0/ 7 7 1 0.15 0 0/ 8 8 1 0.175 0 0/ 9 9 1 0.2 0 0/ 10 10 1 0.225 0 0/ 11 11 1 0.25 0 0/ 12 12 1 0.275 0 0/ 13 13 1 0.3 0 0

/ 14 14 1 0.325 0 0/ 15 15 1 0.35 0 0/ 16 16 1 0.375 0 0/ 17 17 1 0.4 0 0/ 18 18 1 0.425 0 0/ 19 19 1 0.45 0 0/ 20 20 1 0.475 0 0/ 21 21 1 0.5 0 0/ 22 22 1 0.525 0 0/ 23 23 1 0.55 0 0/ 24 24 1 0.575 0 0/ 25 25 1 0.6 0 0/ 26 26 1 0.625 0 0/ 27 27 1 0.65 0 0/ 28 28 1 0.675 0 0/ 29 29 1 0.7 0 0/ 30 30 1 0.725 0 0/ 31 31 1 0.75 0 0/ 32 32 1 0.775 0 0/ 33 33 1 0.8 0 0/ 34 34 1 0.825 0 0/ 35 35 1 3 0 0/ 36 36 1 3 0 0/ 37 37 1 3 0 0/ 38 38 1 3 0 0/ 39 39 1 3 0 0/ 40 40 1 3 0 0/ 41 41 1 3 0 0/ 42 42 1 1.8 0 0/ 43 43 1 1.8 0 0/ 44 44 1 1.8 0 0/ 45 45 1 1.8 0 0/ 46 46 1 1.8 0 0/ 47 47 1 1.8 0 0/ 48 48 1 1.8 0 0/ 49 49 1 1.8 0 0/ 50 50 1 1.8 0 0/ 51 51 1 1.8 0 0

ELEM 1 50 1 1 2 1 81.13E4 43.45E6 2.1E5 1.0E5 0.08ENDG



LAST 3 Calculations according to II orders theory, max forceORD2LASTK 1 0 0 0 0.8063 0TVDEF 1 0.0463 0 0.0151


LAST 5 Calculations according to II orders theory, mindisplacementORD2LASTK 1 0 0 0 0.48 0TVDEF 1 0.0361 0 0.0119

RESULT 1 6PRTL 1 6 0 0 2SLUT

Appendix F


Combination V:A

CONTRAM METER MNPiles for integral abutment bridgePile PIPE, Combination VA

GEOM 1 1 1 0.0 0/ 2 2 1 0.0 0.1/ 3 3 1 0.0 0.2/ 4 4 1 0.0 0.3/ 5 5 1 0.0 0.4/ 6 6 1 0.0 0.5/ 7 7 1 0.0 0.6/ 8 8 1 0.0 0.7/ 9 9 1 0.0 0.8/ 10 10 1 0.0 0.9/ 11 11 1 0.0 1/ 12 12 1 0.0 1.1/ 13 13 1 0.0 1.2/ 14 14 1 0.0 1.3/ 15 15 1 0.0 1.4/ 16 16 1 0.0 1.5/ 17 17 1 0.0 1.6/ 18 18 1 0.0 1.7/ 19 19 1 0.0 1.8/ 20 20 1 0.0 1.9/ 21 21 1 0.0 2/ 22 22 1 0.0 2.1/ 23 23 1 0.0 2.2/ 24 24 1 0.0 2.3/ 25 25 1 0.0 2.4/ 26 26 1 0.0 2.5/ 27 27 1 0.0 2.6/ 28 28 1 0.0 2.7/ 29 29 1 0.0 2.8/ 30 30 1 0.0 2.9/ 31 31 1 0.0 3/ 32 32 1 0.0 3.1/ 33 33 1 0.0 3.2/ 34 34 1 0.0 3.3/ 35 35 1 0.0 3.4/ 36 36 1 0.0 3.5/ 37 37 1 0.0 3.6/ 38 38 1 0.0 3.7/ 39 39 1 0.0 3.8/ 40 40 1 0.0 3.9/ 41 41 1 0.0 4/ 42 42 1 0.0 4.1/ 43 43 1 0.0 4.2/ 44 44 1 0.0 4.3/ 45 45 1 0.0 4.4/ 46 46 1 0.0 4.5/ 47 47 1 0.0 4.6/ 48 48 1 0.0 4.7/ 49 49 1 0.0 4.8/ 50 50 1 0.0 4.9/ 51 51 1 0.0 5

RAND 1 1 1 1 0 1/ 51 51 1 0 1 0

ADD 1 1 1 0 0 0/ 2 2 1 0.025 0 0/ 3 3 1 0.05 0 0/ 4 4 1 0.075 0 0/ 5 5 1 0.1 0 0/ 6 6 1 0.125 0 0/ 7 7 1 0.15 0 0/ 8 8 1 0.175 0 0/ 9 9 1 0.2 0 0/ 10 10 1 0.225 0 0/ 11 11 1 0.25 0 0/ 12 12 1 0.275 0 0/ 13 13 1 0.3 0 0/ 14 14 1 0.325 0 0/ 15 15 1 0.35 0 0

/ 16 16 1 0.375 0 0/ 17 17 1 0.4 0 0/ 18 18 1 0.425 0 0/ 19 19 1 0.45 0 0/ 20 20 1 0.475 0 0/ 21 21 1 0.5 0 0/ 22 22 1 0.525 0 0/ 23 23 1 0.55 0 0/ 24 24 1 0.575 0 0/ 25 25 1 0.6 0 0/ 26 26 1 0.625 0 0/ 27 27 1 0.65 0 0/ 28 28 1 0.675 0 0/ 29 29 1 0.7 0 0/ 30 30 1 0.725 0 0/ 31 31 1 0.75 0 0/ 32 32 1 0.775 0 0/ 33 33 1 0.8 0 0/ 34 34 1 0.825 0 0/ 35 35 1 3 0 0/ 36 36 1 3 0 0/ 37 37 1 3 0 0/ 38 38 1 3 0 0/ 39 39 1 3 0 0/ 40 40 1 3 0 0/ 41 41 1 3 0 0/ 42 42 1 1.8 0 0/ 43 43 1 1.8 0 0/ 44 44 1 1.8 0 0/ 45 45 1 1.8 0 0/ 46 46 1 1.8 0 0/ 47 47 1 1.8 0 0/ 48 48 1 1.8 0 0/ 49 49 1 1.8 0 0/ 50 50 1 1.8 0 0/ 51 51 1 1.8 0 0

ELEM 1 50 1 1 2 1 81.13E4 43.45E6 2.1E5 1.0E5 0.08ENDG



LAST 3 Calculations, max forceLASTK 1 0 0 0 0.7484 0TVDEF 1 0.046 0 0.015

LAST 4 Calculations, max displacementLASTK 1 0 0 0 0.68 0TVDEF 1 0.0578 0 0.0172

LAST 5 Calculations, min displacementLASTK 1 0 0 0 0.48 0TVDEF 1 0.01807 0 0.0123

RESULT 1 5PRTL 1 5 0 0 2SLUT

Appendix G


G. APPENDIX

Explanation of commends used in program CONTRAM.

Units: meter, MN.• Nodes

GEOM na nb incn xa za xb zb nc gl

na,nb,incn nodes na, na+incn,na+2incn… .nbxa,za coordinates of node na,xb,zb coordinates of node nb,

Graphical ilustration:

Z

Y Xnana+incn

na+2~incn

na+incnna

nb

nb

nc

na

na

• Supports

RAND na nb inc tx tz ty rot

na,nb,inc support conditions for nodes na, na+inc, na+2inc,… ,nb

tx=1 support in X direction,tx=0 no support,

tz=1 support in Z direction,tz=0 no support,

ry=1 support inry=0 no

rot rotation positiv around Yaxis relatively to global coordinate system for modes of local coordinate system,

Appendix G


• Spring supports

ADD na nb inc addx addz addr rot

na,nb,inc support conditions for nodes na, na+inc, na+2inc,… ,nbaddx spring constant for translation in Xdirection,addz spring constant for translation in Zdirection,addy spring constant for rotation around Yaxis,

rot rotation positiv around Yaxis relatively to global coordinate system for modes of local coordinate system,

• Elements

ELEM ea eb ince i j incn a tm emod alfaea,eb,inc elements ea,ea+ince,ea+2ince,… ,nb

i,j,incn element allot nodes (i,j),(i+incnc,j+incn),(i+2incn,j+2incn), etc.,a area of the crosssection,

tm moment of inertia,emod Young's modulus,

alfa thermal coefficient of expansion,

• Stiffness of elements

STIF en ria rib x1 ri1 x2 ri2 … . xk rik (kmax=15)en number of beam element,

ria, rib moment of inertia at the ends of beam element,x1, x2… xk local relative xcoordinators for intermediate points,

ri1..rik moments of inertia for intermediate points,

• Distributed loads

LAST load case: number and description,

LASTF ea eb ince p dp xa xb m dmea,eb,ince loaded elements ea,ea+ince,ea+2ince,… ,eb,

p intensity of the load which is acting in point xa,dp p+dp= intensity of the loas in point xb,xa relative distance from "inod" to the nearest load,xb relative distance from "inod" to the farest load,

ria ribrikri2ri1

x1*lx2*l

xk*l

l

Appendix G


m moment intensity in point xa,dm m+dm = moment intensity in point xb,

• Point loads

LASTK na nb inc px px myna,nb,inc loaded points na, na+inc,na+2inc,… ,nb,

px force in global X direction (or local x direction with rotated local coordinate system)pz force in global Z direction (or local z direction with rotated local coordinate system)

my moment around Y axis,

• Internal forces : sign convention

l

xb*l

Y

xa*l

pm m+dm

p+dp

X

Z

Y

Pz

MyX

Px Px My

Pz

Px My

Pz

N(+)

M(+) T(+) T(+) M(+)

N(+)

Appendix G


List of figures


List of figures:

Figure 1 Enlarged details of fully integral bridge and semiintegral bridge.......................................... 1Figure 2 Simplified geometry of an integral abutment bridge.............................................................. 2Figure 3 Thermal displacements of the load carrying structure ........................................................... 3Figure 4 Pile configuration in the bridge over Fjällån ......................................................................... 6Figure 5 Anchorage of a beam to the pile cap with an elastomeric pad............................................... 7Figure 6 Anchorage of a beam to the pie cap with duble nuts.............................................................. 7Figure 7 The detail of pileabutment connection used in Scotch Road Bridge ..................................... 8Figure 8 Alternate jointless bridge detail for steel beam bridge .......................................................... 8Figure 9 Installation of the sleeved HP piles within the crushed stoned backfill .................................10Figure 10 Happy Hollow Creek.........................................................................................................11Figure 11 Big East River Bridge........................................................................................................11Figure 12 Highway 518 Parry Sound.................................................................................................12Figure 13 Duffin Creek Bridge..........................................................................................................12Figure 14 Bridge over Fjällån after completion..................................................................................13Figure 15 Bridge W1299 over Hökviksån in Linghed........................................................................14Figure 16 Crosssection of X pile ......................................................................................................14Figure 17 The example of integral structure – monolithic concrete frame flyover ..............................15Figure 18 Bridge over Tarczynka River.............................................................................................15Figure 19 Bridge over Srebrna River .................................................................................................15Figure 20 Composite flyover in Wyszogród ......................................................................................16Figure 21 One of the flyovers on the Ostrowia Mazowiecka ring road ...............................................16Figure 22 The North Shotton Bridge .................................................................................................17Figure 23 Equivalent cantilever concept ............................................................................................20Figure 24 Beam on the elastic foundation and Winkler’s idealization ................................................23Figure 25 Laterally loaded pile in soil, laterally loaded pile on springs .............................................23Figure 26 Soil reaction versus deflection for soil surrounding a pile ..................................................25Figure 27 Variation of subgrade modulus with depth for preloaded cohesive soils .............................25Figure 28 Variation of subgrade modulus with depth for granular soils , normally loaded silts and

clays .........................................................................................................................................26Figure 29 Perfectly elastic and rigidperfectly plastic behaviour of the pile........................................30Figure 30 Pile model for simplified calculations ................................................................................31Figure 31 Piles crosssections............................................................................................................31Figure 32 Location of the bridge .......................................................................................................37Figure 33 Bridge scheme...................................................................................................................38Figure 34 One of bridge crosssections..............................................................................................39Figure 35 Abutment schetch..............................................................................................................39Figure 36 Pile CONTRAM model.....................................................................................................42Figure 37 Used piles crosssections. ..................................................................................................47Figure 38 BridgeSOFiSTiK model ....................................................................................................73Figure 39 The view for the bridge deck geometry..............................................................................74Figure 40 SOFiSTiK pile model........................................................................................................74Figure 41 Middle supports model ......................................................................................................74Figure 42 Wide abutment with number of important elements ...........................................................75Figure 43 Narrow abutment with number of important elements........................................................75Figure 44: Graphical illustration of extremal stresses in elements number 60601 left and 61601 – right in the mostly loaded piles for case with maximal axial force. … … … … … … … … … … … ..82Figure 45 Stresses in the mostly loaded piles (narrow abutmenton the left, wide abutment –on the

right side) for maximal axial force. ...........................................................................................78Figure 46 Sketch for forces in piles calculations (three line loads) .....................................................87Figure 47 Sketch for forces in piles calculations (two line loads) .......................................................90Figure 48 Schematic geometry of the bridge....................................................................................117Figure 49 Schematic geometry of the bridge with the length of elements .........................................118Figure 50 CONTRAM pile model ...................................................................................................122

List of figures


Figure 51 Geometry of the girder ....................................................................................................133Figure 52 Sketch for filfaktor calculations.......................................................................................137Figure 53 Sketch for filfaktor calculations.......................................................................................137Figure 54 Simplified CONTRAM bridge model..............................................................................142

Documents

2005:248 CIV MASTER'S THESIS - DiVA portal1025325/FULLTEXT01.pdf2005:248 CIV MASTER'S THESIS Optimized Design of Integral Abutments for a Three Span Composite Bridge Gabriela Tlustochowicz