bridge calculus example

7/28/2019 Bridge Calculus Example

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European Union Brite EuRam III

Structural and economic

comparison of bridges made

of inverted T-beams

with topping

EuroLightCon

Economic Design and Construction with

Light Weight Aggregate Concrete

Document BE96-3942/R33, June 2000

Project funded by the European Union

under the Industrial & Materials Technologies Programme (Brite-EuRamIII)

Contract BRPR-CT97-0381, Project BE96-3942


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The European Union Brite EuRam III

Structural and economic comparison of

bridges made of inverted T-beams with topping

EuroLightCon



Document BE96-3942/R33, June 2000Contract BRPR-CT97-0381, Project BE96-3942


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Although the project consortium does its best to ensure that any information given is accurate, no liability or responsi-

bility of any kind (including liability for negligence) is accepted in this respect by the project consortium, the au-

thors/editors and those who contributed to the report.

Acknowledgements

This report is written by: Aleksandar Milenkovic (Spanbeton bv / CZ Civiele Techniek bv) and M.R. Trouw (Spanbeton

bv). The illustrations are made by C. v/d Ploeg (Spanbeton bv)

Information

Information regarding the report:

Spanbeton bv., Hoogewaard 209, 2396 AS Koudekerk aan den Rijn, The Netherlands;

Tel: +31 (0)71 3419115; E-mail [email protected]

Information regarding the project in general:

Jan P.G. Mijnsbergen, CUR, PO Box 420, NL-2800 AK Gouda, the Netherlands

Tel: +31 182 540620, Email: [email protected]

Information on the project and the partners on the internet:: http://www.sintef.no/bygg/sement/elcon

ISBN 90 376 02 68 1


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The European Union Brite EuRam III

Structural and economic comparison of

bridges made of inverted T-beams with topping

EuroLightCon



Document BE96-3942/R33, June 2000

Contract BRPR-CT97-0381, Project BE96-3942

Selmer ASA, NO

SINTEF, the Foundation for Scientific and Industrial Research at theNorwegian Institute of Technology, NO

NTNU, University of Technology and Science, NO

ExClay International, NO

Beton Son B.V., NL

B.V. VASIM, NL

CUR, Centre for Civil Engineering Research and Codes, NL

Smals B.V., NL

Delft University of Technology, NL

IceConsult, Lnuhnnun hf., IS

The Icelandic Building Research Institute, ISTaywood Engineering Limited, GB

Lias-Franken Leichtbaustoffe GmbH & Co KG, DE

Dragados y Construcciones S.A., ES

Eindhoven University of Technology, NL

Spanbeton B.V., NL


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Structural and economic comparison of bridges made of inverted T-beams with topping

BE96-3942 EuroLightCon 5

Table of Contents

PREFACE 7

SUMMARY 10

SYMBOLS 11

1. INTRODUCTION 17

2. GENERAL 20

2.1 Standards and starting points 20

2.2 Materials 20

2.3 Geometry 212.4 Loads 25

2.4.1 Permanent loads 25

2.4.2 Live loads 26

2.4.3 Loads combinations 29

2.5 Computer programs 30

2.5.1 Theory of shear force calculation 30

2.5.2 The Spreid program 32

2.5.3 The Span program 33

2.6 Superstructure calculation 33

2.6.1 Data obtained from computer programs 33

2.6.2 Beam 35

2.6.3 Topping 39

2.6.4 Composite structure 41

2.7 Substructure 48

3. COMPARISON 50

3.1 Quantities 50

3.1.1 Bridge with a span of 20 m 50



3.2 Costs per quantity 52

3.3 Project costs 53




4. CONCLUSIONS 55


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6 BE96-3942 EuroLightCon

APPENDIX: MIXTURE COMPOSITION 56


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PREFACEThe lower density and higher insulating capacity are the most obvious characteristics of Light-

Weight Aggregate Concrete (LWAC) by which it distinguishes itself from ordinary Normal

Weight Concrete (NWC). However, these are by no means the only characteristics, which jus-

tify the increasing attention for this (construction) material. If that were the case most of the

design, production and execution rules would apply for LWAC as for normal weight concrete,

without any amendments.

LightWeight Aggregate (LWA) and LightWeight Aggregate Concrete are not new materials.

LWAC has been known since the early days of the Roman Empire: both the Colosseum and thePantheon were partly constructed with materials that can be characterised as lightweight aggre-

gate concrete (aggregates of crushed lava, crushed brick and pumice). In the United States, over

100 World War II ships were built in LWAC, ranging in capacity from 3000 to 140000 tons and

their successful performance led, at that time, to an extended use of structural LWAC in build-

ings and bridges.

It is the objective of the EuroLightCon-project to develop a reliable and cost effective design and

construction methodology for structural concrete with LWA. The project addresses LWA manu-

factured from geological sources (clay, pumice etc.) as well as from waste/secondary materials

(fly-ash etc.). The methodology shall enable the European concrete and construction industry toenhance its capabilities in terms of cost-effective and environmentally friendly construction,

combining the building of lightweight structures with the utilisation of secondary aggregate

sources.

The major research tasks are:

L igh tweight aggregates: The identification and evaluation of new and unexploited sources spe-

cifically addressing the environmental issue by utilising alternative materials from waste. Further

the development of more generally applicable classification and quality assurance systems for

aggregates and aggregate production.

L ightweight aggregate concrete production: The development of a mix design methodology toaccount for all relevant materials and concrete production and in-use properties. This will include

assessment of test methods and quality assurance for production.

L ightweight aggregate concrete properties: The establishing of basic materials relations, the

influence of materials characteristics on mechanical properties and durability.

L ightweight aggregate concrete structur es: The development of design criteria and -rules

with special emphasis on high performance structures. The identification of new areas for appli-

cation.

The project is being carried out in five technical tasks and a task for co-ordination/management

and dissemination and exploitation. The objectives of all technical tasks are summarised below.


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Starting point of the project, the project baseline, are the results of international research work

combined with the experience of the partners in the project whilst using LWAC. This subject is

dealt with in the first task.

Tasks 2-5 address the respective research tasks as mentioned above: the LWA itself, production

of LWAC, properties of LWAC and LWAC structures.

Sixteen partners from six European countries, representing aggregate manufacturers and suppli-

ers, contractors, consultants research organisations and universities are involved in the Eu-

roLightCon-project. In addition, the project established co-operation with national clusters and

European working groups on guidelines and standards to increase the benefit, dissemination and

exploitation.

At the time the project is being performed, a Working Group under the international concrete

association fib(the former CEB and FIP) is preparing an addendum to the CEB-FIP Model

Code 1990, to make the Model Code applicable for LWAC. Basis for this work is a state-of-the-

art report referring mainly to European and North-American Standards and Codes. Partners in

the project are also active in the fibWorking Group.

General information on the EuroLightCon-project, including links to the individual project part-

ners, is available through the web site of the project:

http://www.sintef.no/bygg/sement/elcon/

At the time of publication of this report, following EuroLightCon-reports have been published:

R1 Definitions and International Consensus Report. April 1998

R1a LightWeight Aggregates Datasheets. Update September 1998

R2 LWAC Material Properties State-of-the-Art. December 1998

R3 Chloride penetration into concrete with lightweight aggregates. March 1999

R4 Methods for testing fresh lightweight aggregate concrete, December 1999

R5 A rational mix design method for lightweight aggregate concrete using typical UK mate-

rials, January 2000

R6 Properties of Lytag-based concrete mixtures strength class B15-B55, January 2000

R7 Grading and composition of the aggregate, March 2000

R8 Properties of lightweight concretes containing Lytag and Liapor, March 2000

R9 Technical and economic mixture optimisation of high strength lightweight aggregate con-

crete, March 2000

R10 Paste optimisation based on flow properties and compressive strength, March 2000

R11 Pumping of LWAC based on expanded clay in Europe, March 2000

R12 Applicability of the particle-matrix model to LWAC, March 2000

R13 Large-scale chloride penetration test on LWAC-beams exposed to thermal and hygral

cycles, March 2000

R14 Structural LWAC. Specification and guideline for materials and production, June 200

R15 Light Weight Aggregates, June 200

R16 In-situ tests on existing lightweight aggregate concrete structures, June 200

R17 Properties of LWAC made with natural lightweight aggregates, June 2000

R18 Durability of LWAC made with natural lightweight aggregates, June 2000


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R19 Evaluation of the early age cracking of lightweight aggregate concrete, June 2000

R20 The effect of the moisture history on the water absorption of lightweight aggregates,

June 2000

R21 Stability and pumpability of lightweight aggregate concrete. Test methods, June 2000

R22 The economic potential of lightweight aggregate concrete in c.i.p. concrete bridges, June

2000

R23 Mechanical properties of lightweight aggregate concrete, June 2000

R24 Prefabricated bridges, June 2000

R25 Chemical stability, wear resistance and freeze-thaw resistance of lightweight aggregate

concrete, June 2000

R26 Recycling lightweight aggregate concrete, June 2000

R27 Mechanical properties of LWAC compared with both NWC and HSC, June 2000

R28 Prestressed beams loaded with shear force and/or torsional moment, June 2000

R29 A prestressed steel-LWAconcrete bridge system under fatigue loading

R30 Creep properties of LWAC, June 2000

R31 Long-term effects in LWAC: Strength under sustained loading; Shrinkage of High

Strength LWAC, June 2000

R32 Tensile strength as design parameter, June 2000

R33 Structural and economical comparison of bridges made of inverted T-beams with top-

ping, June 2000

R34 Fatigue of normal weight concrete and lightweight concrete, June 2000

R35 Composite models for short- and long-term strength and deformation properties of

LWAC, June 2000

R36 High strength LWAC in construction elements, June 2000

R37 Comparison of bridges made of NWC and LWAC. Part 1: Steel concrete composite

bridges, June 2000

R38 Comparing high strength LWAC and HSC with the aid of a computer model, June 2000

R39 Proposal for a Recommendation on design rules for high strength LWAC, June 2000

R40 Comparison of bridges made of NWC and LWAC. Part 2: Bridges made of box beams

post-tensioned in transversal direction, June 2000

R41 LWA concrete under fatigue loading. A literature survey and a number of conducted

fatigue tests, June 2000

R42 The shear capacity of prestressed beams, June 2000

R43 A prestressed steel-LWA concrete bridge system under fatigue loading, June 2000


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SUMMARYLightweight aggregate concrete (LWAC) contains certain properties that could be of influence

upon the total project costs. A possible negative influence can be found in the higher material

costs of LWAC compared to the material costs of NDC, while a possible positive influence can

be found in the lower density, which can reduce the sub-, superstructure-, transport- and assem-

bling costs.

To find the influence of the application of LWAC (instead of NDC) on the total project costs,

this research is done with two variable factors: the change in application of LWAC in the beam

and topping, and the change in bridge span (20m, 30m and 40m).

The height of the beams is chosen in relation with the span of the bridge. To comply to fatigueregulations, the beam and the topping height are further assumed variable.

The width of the bridge is 18m, realised by 15 inverted T-beams with a structural topping of 210

mm.

The calculations are based on two regulations used for bridge calculations:

The Dutch standard V.B.C. 1995, calculation methods and structural demands for concreteapplication.

The Dutch standard V.B.B. 1995, calculation methods and structural demands for bridges

The load spreading calculation of the bridge is based on the theory of Guyon and Massonnet.

The bending and torsional moments of inertia, in both directions, are based on the theory of elas-

ticity.


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SYMBOLSGreek symbols

torsion factor used in loads spreading calculationangle for shear calculations.

factor used in fatigue calculationf loading factorm material factorsd safety factor for calculating design values fictive height, used in the theory of Timoshenko for stiffness calculation

max maximal shrinkage value dependent on the fckand the relative humidityc basic shrinkage dependent on the relative humidityrtopping representative creep value of the toppingrbeam representative creep value of the beam stiffness factor used in the loads spreading calculation ratio of bond strength of pre-stressing steel and high bond reinforcing steel. Poissons ratio density of the concrete [kg/m3]perm stress due to permanent loadss representative tensile stress in the reinforcement

bmd mean compressive stress due to the normal force with inclusion of thepre-stress load of Nd / Ab

s;107;rep representative value of the fatigue limit of the reinforcement at 107 cycless;n;rep representative value of the fatigue limit of the reinforcementc;max maximum compressive stress at a fibre under the frequent combinations of

actions

s;d;max design value of the tensile stress of the reinforcements;d;min minimal design value of the tensile strength in the reinforcements;u(n) ultimate tensile stress in the reinforcement at n cycles

b;90 compressive stress at 90 mm from the bottom of the beamtemp representative stress at the bottom caused by temperature influences1 limit value of the shear stress without shear reinforcement2 limit value of the shear stress with shear reinforcementd design value of the shear stressn part of the normal force in the shear capacityn+1 limit value of the shear stress without shear reinforcement with inclusion of

the pre-stress force

red reduced d due to the vertical component of the pre-stress steel forcebeam calculated creep factor of the beam

topping calculated creep factor of the topping


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max maximal creep values diameter of reinforcementkm diameter of the top reinforcementof the topping


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Latin lower case symbols

a half of the theoretical span of the bridge

b half of the effective width of the bridge

b half of the real width of the bridge

b1 fictive width of the topping (part 1) used in the theory of Timoshenko

b2 fictive width of the web (part 2) used in the theory of Timoshenko

b3 fictive width of the flange (part 3) used in the theory of Timoshenko

bt real width of the topping

bw width of the web

c coverage of the reinforcement, dependent on the environment classification

ctop coverage of the top reinforcement of the topping

dbeam useful height of the beam

dend distance between the centre of gravity of the reinforcement and the bottom

of the beam in the end section.

dmiddle distance between the centre of gravity of the reinforcement and the bottom

of the beam in the middle section.

fb design value of the compressive strength of the concrete

fbuv(n) see Su(n)

fck characteristic compressive strength of the concrete

fb design value of the tensile strength of the concrete

fbrep representative value of the tensile strength of the concrete

fs design value of the tensile strength of the reinforcement

h construction height

hf height of the flange

hm fictive thickness of the section

ht height of the topping

hw height of the web

i moment of inertia in longitudinal direction

io torsion moment of inertia in longitudinal direction

j moment of inertia in transversal direction

jo torsion moment of inertia in transversal direction

k1, k2, k3 cracking factors

kb shrinkage factor dependent on the factor fck

kc creep factor dependent on the relative humidity

kd creep factor dependent on the age of the concrete

kh shrinkage factor dependent on (hm).

kp shrinkage factor dependent on the amount of reinforcement

kt shrinkage factor dependent on the age of the concrete

l1 spacing between the two considered beams

m factor dependent ofs;107;repn number of load cycles

n1 number of beams

pd design value of the equally divided live load


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prep representative value of the equally divided live load

qd design value of the line load

qrep representative value of the line load

s spacing of the reinforcement bars in the cracking calculation

wb the fictive width of the topping used in the calculation of i

x the deformation of the beam due to the pre-stress force

xu height of the compressive zone in the cross section

y the deformation of the beam due to the self weight of the beam and topping

and the permanent loads

z internal distance between the compressive force and the tensile force

zb distance between centre of gravity and the top of the beam.

zo distance between centre of gravity and the bottom of the beam.

Latin upper case symbols

Abot bottomreinforcement of the topping

Ac cross-section surface of the beam

As cross-section surface of reinforcement by tensile force

As cross-section surface of reinforcement by compressive force

Atop top reinforcement of the topping

Atot total fictive area used in the theory of Timoshenko

Bv load length factor

C factor for calculating the dynamic factor

Ebeam modulus of elasticity of the beam

Etopping modulus of elasticity of the topping

Es modulus of elasticity of the reinforcement

Fpw pre-stress force

Fwheel the wheel load

G sliding modulus

L loads

Lb beam length

LC loads combination

Lth theoretical span of the bridge

M1 / M2 moments used in fatigue calculationMb moment due to compressive stress in the concrete

Md design moment

Md;l decisive moment of Mfirst and Msecond obtained from load spreading

calculation

Mfirst moment caused by the first load system

Msecond moment caused by the second load system

Mneg;rep negative moment due to the local wheel load (topping reinforcement)

Mperm moment due to the permanent loads

Mpos;rep positive moment due to the local wheel load and global q-load

Mpre-stress moment due to the pre-stress force

Ms

moment due to the increasing tensile stress in the reinforcement, caused by


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cycle load

Msw;beam moment due to the self weight of the beam

Msw;topping moment due to the self weight of the topping


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Ms moment due to the increasing compressive stress in the top reinforcement,

caused by cycle load

Mu ULS moment

Nb compressive force in the concrete

Ns compressive force in the reinforcement due to the compressive stress in the

concrete

Q factor for traffic type

R ratio of minimum and maximum relative stress (R = c;min / c;max )S dynamic factor

Sc;d;max general fatigue quantity

Su(n) design value of the material strength in fatigue at n cycles

Vd;vertical design shear force (summation of the shear forces due to the self weight of

the beam, topping, permanent and live loads).

Vd;horizontal design shear force (summation of shear forces due to permanent and

live loads).

VRd1 design shear resistance

Vred shear force due to the vertical pre-stress force

Vrep shear resistance.

Vrep;max maximum representative shear force due to dead load, pre-tensioning and

maximum of the variable actions;

Wbeam;top moment of resistance in the top of the beam

Wbeam;bot moment of resistance in the bottom of the beam

Wcs moment of resistance in the composite structure


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1. INTRODUCTIONThis sub-task is set up in the EuroLightCon project, to find the economical consequences of the

application of Light Weight Aggregate Concrete (LWAC) compared to Normal Density Con-

crete (NDC) in a bridge structure.

Two concrete compositions, two compressive strengths and three different spans are used to get

a clear view in the relation of total strength, stiffness, material- and project costs.

The bridge consists of 15 standard VIP beams (inverted T-beams) with a concrete of C45/55

strength, and a topping of 210mm height and C30/37 strength.

Such a choice of bridge structure produces four material combinations: One with a reference bridge configuration completely executed in ordinary NDC The other three with an individual application of LWAC in the beam, topping or both.Spans of 20, 30 and 40 m are used in this research, with respectively VIP 700, VIP 1100 and

VIP 1600 beams.

The figures given in this document are based on a bridge span of 30m, unless me n-

tioned otherwise.

Superstructure

Length (of the beams) :30.35 mWidth : 18.00 m

Theoretical span : 30.35m - 2 * 0.30 = 29.75 m (fig. 1 and 3).

Beams : 15 VIP 1100 beams with an individual width of 1.18m and

15 joints of 20 mm

Transversal end beams : at both bridge ends with a size of 0.55 m * 1.325 m (fig. 3 )

Topping : 210 mm

Figure 1 Longitudinal section of the superstructure of the bridge

Beam length = 30350 mm

Lt = 29750 mm


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The topping and the edge beams are made in-situ after placing the inverted T-beams at the sub-

structure. The edge beams are made at the supports to connect the inverted T-beams in trans-

versal direction.

The width of the bridge is big enough to place four different lanes and two pedestrian strokes.

Although the bridge design could be interpreted as suitable for situations where side collision can

occur, it is omitted by this research due to the large difference in the international regulations.

Figure 2 Cross section of the bridge.

To calculate the spreading of permanent and live loads, the representative stresses and the de-formations of the beam two computer programs are used:

Spreid to calculate the spreading of permanent- and live loads over the bridge construction. Span , to calculate the representative stresses and deformations by the use of static quanti-

ties obtained from the load spreading calculation

Substructure (fig 3)

The substructure is divided in two land abutments and a number of piles.

Land abutment

The shape of the land abutment is designed to enable optimal support of the inverted T-beamsand the dynamic plate, as well as the accomplishment of the transitional joint.

Piles

The size of the piles is chosen at 250x250 mm2

with a length of 15 m. The piles are placed in

groups of two and equally divided over the land abutment. To take the horizontal force which is

caused by the breaking forces of the live loads, the piles are placed in the ground at a slight an-

gle.

15*1180 [VIP.1100] + 15*20 [joint] = 18000 [mm]


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Dynamic plate

Transitional joint

Structural topping

Transversal end beam

Inverted T-beam

Land abutment

Piles

Figure 3 Detail of the joint between the super- and substructure of the bridge


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2. GENERALThe used calculation procedures are based on real bridge calculations, while the project only

concerns a fictive bridge.

2.1 Standards and starting pointsIn structural bridge calculations the following standards and starting points are used:

Standards

V.B.C. 1995. (Dutch standard for calculation methods and structural demands by the con-crete application)

V.B.B. 1995. (Dutch standard for calculation methods and structural demands for bridges)

Starting points

Environmental class 3 (Moist surrounding in combination with thaw minerals). Relative humidity of 75%. Due to the ground configurations in the Netherlands, piles of 15m are used in the substructure

calculation.

2.2 MaterialsThe materials comply with the materials used in the real bridges. In such a way a realistic

comparison between LWAC and NDC is obtained.

Beams concrete strength by releasing the tension 30 N/mm2

(prefabricated) concrete strength (28 days) B55 (C45/55)

pre-stressing steel (VIP 700 and 1100) FeP (fp) 1860 , 12,5 mm,

with Ap = 93 mm2

(VIP 1600) FeP (fp) 1860 , 15,7 mm,

with Ap = 150 mm2

reinforcement: FeB (fy) 500

Topping (in-situ) concrete strength B35 (C30/37)reinforcement: FeB (fy) 500

Transversal end concrete strength b 35 (C30/37)beam (in-situ) reinforcement: FeB (fy) 500

Land abutment concrete strength B35 (C30/37)(in-situ) (normal density)

piles 250 x 250 mm2 B45 (C35/45)(prefabricated) (normal density)


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2.3 GeometryThe geometry of the beam is expressed in four static quantities:

i = moment of inertia in longitudinal direction [mm4

/mm1

] j = moment of inertia in transversal direction [mm4/mm1] i0= torsion moment of inertia in longitudinal direction [mm4/mm1] j0 = torsion moment of inertia in transversal direction [mm4/mm1]

The moment of inertia in longitudinal direction is obtained confirm the theory of elasticity of the

composite structure. The torsion moments of inertia are calculated by the theory of Bredt and

the membrane theory.

To obtain comparable stiffnesses for calculating the -factor and the -factor, the moments ofinertia in longitudinal direction are multiplied by the modulus of elasticity of the beam, and the

moments of inertia in transversal direction are multiplied by the modulus of elasticity of the top-

ping.

Figure 4 Cross section of the composite structure (VIP 1100 and topping)

Moment of inertia in longitudinal direction ( i )

This moment of inertia is calculated of the composite structure. Due to the E-modulus difference

between the beam and topping, the width of the topping (wb) changes, based on the following

formula:

This results in a change of the moment of inertia when LWAC applied

in the beam, topping or both.w bE

Eb ttopping

beam

=


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Moment of inertia in transversal direction ( j )

In this section only the topping is present, therefore this moment of inertia only is based on the

height of the topping.

j

b h

bh

t t

t

t= =

1

12 1

12

3

3[mm4/mm1]

Torsion moment of inertia in longitudinal direction ( i 0 )

The calculation of the torsion moment of inertia is based on the Timoshenko theory of elasticity

and is an approximation of the real cross section by three rectangles (figure 5).

Figure 5 Torsion stiffness calculation by the method of Timoshenko

Where:

Part 1(topping) 2(web) 3(bottom flange)

b bt x 0.5 x (Et / Eb) bw bt -10 mm

H ht hw + 0.25ht + 0.175 hf hf

db 2 xb1-b2 2 x b2 2 x b3-b2

A h1 x b1 h2 x b2 h3 x b3

bt

bt

0.175

0.65

0.175


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db is the second fictive width used in the calculation


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To calculate the torsion moment of inertia (io) these data are used in the following formula:

iw

Adb

h

h dbb

tot

t w f

t w f0

2

1 2 3

31 2 31 4 13= +

, ,, ,

, , , , or: i wAdb

h

h dbb

tot

t w f

t w f0

2

1 2 3

31 2 31 4 13= +

, ,, ,

, , , ,

This formula is composed of the theory of Bredt (first part) and the Membrane theory (second

part)

Torsion moment of inertia in transversal direction (j0)

The torsion moment of inertia is calculated taking in account only the present height of the top-

ping.

j

b h

bh

t t

t

t0

3

3

1

6 1

6= = [mm4/mm1]

Review of the moments of inertia and the torsion moments of inertia

Combinations

Topping-beam

i [mm4/mm1] j [mm4/mm1] i0

[mm4/mm1]

j0

[mm4/mm1]

NDC-NDC 129.2E+6 771.8E+3 5.36E+6 1.54E+6 0.162 1.118

LWAC-NDC 113.6E+6 771.8E+3 5.03E+6 1.54E+6 0.177 1.163NDC-LWAC 145.8E+6 771.8E+3 5.79E+6 1.54E+6 0.152 1.073

LWAC-LWAC 129.4E+6 771.8E+3 5.36E+6 1.54E+6 0.162 1.119

where:

=b

a

i

j24 and

( ) =

+

G i j

E i j

0 0

2=

( )0 2 0 0, i ji j

+

( v = 0,2)

Review of the stiffness

Combinations:Topping-beam

Modulus of elastic-ity

(topping-beam)

stiffness(EI): i

Stiffness(EI): j

torsionstiffness

(EI) :i0

torsionstiffness

(EI): j0

NDC NDC 31000-36000 4650E+9 23.9E+9 192.9E+9 47.85E+9

LWAC NDC 23276-36000 4088E+9 18.0E+9 181.2E+9 35.93E+9

NDC LWAC 31000-27030 3941E+9 23.9E+9 156.6E+9 47.85E+9

LWAC LWAC 23276-27030 3487E+9 18.0E+9 144.9E+9 35.93E+9


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2.4 LoadsThe representative loads are divided into permanent and live loads

2.4.1 Permanent loads

Figure 6 Detail of the location of the loads at the side and at the middle of the bridge

The next permanent loads (L) are determined:

L1: Railing

L2: Crash barriers at both sides of the bridge

L3: Crash barrier at the middle of the bridge

L4: Side element at both sides of the bridge

L5: Dump in the middle and at both sides of the bridge

L6: Asphalt layer

The railing and the side element are placed directly at the side of the bridge. The crash barriers are placed in the middle and at 1400 mm from the sides of the bridge.

The dump is present between 500 and 1200 mm from the side of the bridge. The asphalt layer is present from 1200 mm form the side of the bridge.


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Figure 7 Detail of the place and size of the permanent loads

2.4.2 Live loads

Live loads can be divided into an equally divided square load and axle pressures of two loads

systems. The representative forces of these live loads are obtained from following table:

Mobileclass

subscription equal dividedsquare load

three axlepressures

axle pressuredivided over:

60 Bridges admitted in roads

where the traffic cannot be

diverted.

Prep = 4 kN/m2

Frep= 200kN 4 wheels

These loads are multiplied with the dynamic factor to include the impact of the entering vehicles

at the bridge.

Dynamic factor for load spreading calculation, S CL

h L

th

th= +

+1

100( )

For NDC (C = 0.7) : 1 + 0.7 * 29.75 / (1.325 * 129.75) = 1.12

For LWAC (C = 0,8) :1 + 0.8 * 29.75 / (1.325 * 129.75) = 1.14

Review of the dynamic factors that are calculated by different spans and concrete composi-

tions.

Span / material NDC LWAC

20 m 1.12 1.14

30 m

40 m

1.12

1.11

1.14

1.12


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First load system Second load system

The next live loads (L) are determined:

L7: Equal divided mobile load is present from 1200 mm of both sides of the bridge

Loads 8 and 9 are obtained from the load spreading calculation, based on the most unfavourable

positions.

L 8: Simple load system. (position of the first load system in figures 8a and 9)

L 9: Double load system is used to calculate the moment in longitudinal direction according

to figures 8a and 9

Loads 10 and 11 have standard positions.

L10: Double load system is used to calculate the negative moment in transversal

direction(simple load system at both sides of the bridge, fig 9).

L11: Second load system is used to calculate the fatigue and an extreme loading

case (second load system in figures 8a and 9)

L12: Extreme loading case (wheel directly at the side of the bridge, in case of an accident),

figure 8b.

Figure 8a Wheel configurations of two load systems in SLS

Figure 8b Wheel configuration of two load systems in ULS

Figure 8c Wheel configurations that are causing the largest bending moment in longitu-


31/59



dinal direction

Lth

Figure 9 Place of the traffic loads with regard to the load combinations

2.4.3 Loads combinations

The next load combinations are used for calculation of the representative moment:

LC 1: L1 + L2 + L3 + L4 + L5 + L6 (Permanent load)

LC 2: LC1 + L7 + L8 (Simple load system)

LC 3: LC1 + 0.8 L7 + 0.8 L9 (Double load system, longitudinal

direction)

LC 4: LC1 + 0.8 L7 + 0.8 L10 (Double load system, transversal

direction)

LC 5: LC1 + L7 + 1.2 L12 (Extreme loading case, simple load

system)

LC 6: LC1 + 0.8 L7 + 0.8 L11 + 1.2 L12 (Extreme loading case, double load

system)

When two load systems are applied at the same time (in LC3, LC4 , LC6), the result of bothload systems are then multiplied with = 0.8, according to Dutch regulations.

L 12 (included in LC5 and LC6) is multiplied with 1,2 according to Dutch regulations


32/59



2.5 Computer programsThe shear forces, caused by the live loads, are calculated in paragraph 2.5.1.

The other calculations in this report are based on two computer programs, which calculate thespreading of the loads, the representative moments and shear forces (the Spreid program) and

the representative stresses and deformations in the elements (the Span program).

2.5.1 Theory of shear force calculation

The representative decisive shear force is calculated in two live loading situations:

1. Simple loading case where only one load system placed at the bridge.

2. Double loading case where two load systems is placed at the bridge.

The largest shear force is chosen in those two loading cases

Simple load system:

Vrep.

1

Lth

Lth

a 5000

X3

Lth

a 1000

X2

Lth

a

X1

=

+

+

axle load +

1

2 P S lrep th

Figure 10 Simple load system

Where:

( )x a c1 22

3= +

( )x a c2 2 10002

3= + +

( )x a c b3 50002

3= + + +

Where:a = 500 mm

b = 1400 mm

c = 1750 mm

Load system

B

X1X2

X3

a 1000 4000

Lth

b

c

=tan23


33/59




34/59



Double load system

V axle load1

Lth

Lth

a 9500

X6

Lth

a 5500

X5

Lth

a 500

X4

Lth

a 5000

X3

Lth

a 1000

X2

Lth

a

X1

rep. =

+

+

+

+

+

4

0,8 +1

20 8 p S lrep th. ,

Where:

( )x a c1 22

3= +

( )x a c2 2 10002

3= + +

( )x a b c3 5000

2

3= + + +

( )x a c4 2 45002

32 1000= + + +

( )x a c5 2 55002

31000= + + +

( )x a b c6 95002

32 1000= + + + +

a = 500 mm

b = 1400 mm

c = 1750 mm

Figure 11 Double load system

2.5.2 The Spreid program

This computer program is based on the theory of Guyon & Massonnet. The calculations of the

representative moments and shear forces are done with this theory for every composite beam

structure individually, in longitudinal direction and every joint in transversal direction.For practical reasons, the beam with the governing moments and shear forces is representative

for all the beams. Therefore all other beams are equally pre-stressed and reinforced.

The theory uses the following equations for the calculation of the spreading of the loads:

= 0 2.

=b

a

i

j24 with b

n

nb=

1

1 1'

( )

=+

G i j

E i j

0 0

2with

( )G

E=

+2 1

( ) =

+

0 2 0 0, i j

i j

Load system

Load system

c

c

Lth


35/59



2.5.3 The Span program

This computer program is based on the theory of elasticity and calculates i.e. the geometry, the

representative stresses and deformations of the composite structure.

The program checks the cross-sections of the beam in SLS and ULS.

2.6 Superstructure calculationBoth computer programs and the spreadsheet for live shear force are used in this calculation.

2.6.1 Data obtained from computer programs

The used data in the calculations are obtained from the computer programs and are divided into:

The moments and shear forces due to self-weight of the topping and the beam. The moments and shear forces due to permanent loads and the moments due to live loads. The shear force due to live loads.

2.6.1.1 Moments and shear forces due to self weight

The moments and shear forces caused by self-weight are obtained from the representative

stresses and deformations calculation.

Combinations topping-beam Moments (kNm) Shear force (kN)

beam Topping beam topping

NDC-NDC 1080 683 145 92

LWAC-NDC 1080 530 145 71

NDC-LWAC 837 683 113 92

LWAC-LWAC 837 530 113 71

2.6.1.2 Data due to loads spreading calculationThe moments caused by the permanent and live loads, and the shear forces caused by the per-

manent loads, are obtained from the loads spreading calculation and are divided into longitudinal

and transversal direction. In longitudinal direction the moments and shear forces are calculated in

the beam; in transversal direction the moments and shear forces are calculated in the topping.The shear force caused by the live loads in longitudinal direction is calculated using the theory of

paragraph 2.5.1.

Longitudinal direction

The moments and shear forces, given in the following table, are used for the stress and deforma-

tion calculation of the beam. The dynamic factor is included in the results.


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Combinations

topping-beam

Moment (kNm) Shear force (kN)

permanent loads live loads Permanent loads live loads

NDC-NDC 578 1395 80 290

LWAC-NDC 585 1412 80 295

NDC-LWAC 573 1463 80 295

LWAC-LWAC 578 1420 80 295

Transversal direction

This calculation can be divided into two situations: overall and local.

Overall situationA car is placed at both sides of the bridge, by which, theoretically, the bridge bends upwards in

transversal direction. This loading situation is resulting in the following moments.

Combinations

topping-beam

Decisive moment

normal situation;

positive (LC 1-4)

normal situation;

negative (LC 1-4)

extreme situation;

negative (LC 5,6)

NDC-NDC 33 -11 -21

LWAC-NDC 31 -9 -19

NDC-LWAC 34 -13 -23

LWAC-LWAC 34 -11 -21

Local situationThe wheel load of a vehicle causes an extra positive moment in the topping, when standing pre-

cisely between the two beams (the most unfavourable position). These moments are used to cal-

culate the topping reinforcement.

Mneg;rep : Fwheel

qd

l1 l1 l1

Mpos;rep

M q lpos rep d; =1

24 12

( = 0.3 kNm)

M q lneg rep d ; =1

12 12

( = 0.6 kNm)

M F lpos rep wheel; =1

8

1 (= 6.4 kNm)


37/59



Shear calculations

The shear calculations are done in the web of the beam (vertical direction) and in transitional

zone between beam and topping (horizontal direction, due to the deformation of the construc-

tion). This horizontal stress is present near the top of the stirrup and therefore influences the stir-

rup composition at the top. A standard stirrup composition is used with three sections at the top

(according to fig 14).

The vertical component caused by the pre-stress force (fig 12) is used to reduce the shear force

in the web (vertical direction).

Vd;vertical = design shear force (summation of shear forces due to self weight beam, topping,

permanent and live loads).

Vd;horizontal = design shear force (summation of shear forces due to only permanent and live

loads).

Combinations

Topping-beamVertical Vd

(kN)

vertical component

pre-stress force

(kN)

horizontal Vd (kN)

NDC-NDC 607 -75 370

LWAC-NDC 592 -74 376

NDC-LWAC 579 -65 375

LWAC-LWAC 559 -63 375

2.6.2 Beam

2.6.2.1 Pre-stress steel calculationThe numbers of pre-stress strands are determined full filling all demands in ULS and SLS, in the

transitional (assembling) phase of the construction as well as at the end stage.

In this case, deformations of the beam were decisive.

The exact place of the strands in the beam is based on the application of fig 12 and 13.

Two strands are needed at the top of the beam for the application of the stirrups. The position of the strands in the cross section is chosen to cover as good as possible the ex-

pecting moments of the beam under all the loadings.

Cross section B Cross section A

dmiddle dend

3/8 x Lth

Lth

Vertical component of

the pre-stress force


38/59



Figure 12 Position of the centre of gravity of the pre-stress strands over the beam length

Topping

Beam

Cross section A Cross section B

Figure 13 Details of the place of the pre-stress strands in the cross section

The deformation of the beam is calculated in the several development stadiums: from the time

the beam is fabricated, until the moment when the beam is loaded by live loads (period of 12

months)

The deformation is checked in agreement with specific regulations, based on the next formula:

x - 1,1 y > 1 where: 1 = Lth / 2000 [mm]

2.6.2.2 Check in extreme loading caseThe moment in extreme loading case is checked at the maximum moment, with the formula:

M M M M Mu extremeloadingcase sw beam sw topping prestress + + +; ;

Where:

( )( )M LC LC LC LCextreme loadingcase = + + + 1 0 1 0 8 7 11 1 0 12, , ,

Mu, Msw;beam , Msw;topping and Mprestress , are obtained from the representative stresses and deforma-

tions calculations

2.6.2.3 ShearThe shear reinforcement is first calculated in the beam and then checked with the horizontal

shear in the transitional zone between the beam and topping.

a) The shear force in the web of the beam


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The shear force is divided into live and permanent part.

Live part

The shear in the beam is calculated with a simple and double load system, according to the fig-

ures 10 and 11.

Permanent part

The representative shear force is obtained from the loads spreading calculation.

The shear reinforcement is calculated by the following figure which is based on Dutch stan-

dards.

dd

w

V

b d=

d = h-c ; where: d

c(bottom)=30 mm d;red.

c(top) = 40 mm 0,2d(n+1)

n bmd = 0 15, ; Where bmdpw

c

F

A= 1

n n+ = +1 1 200 - 1300

1 0 4= , b ;Whereff f

b

brep

m

ck= = +

0 7 1 05 0 05

1 4

, ( , , ' )

,

2 = 0 2, ' f k kb n ;Where f bf ck

'. '

,=

0 72

1 2; k

fnbmd

b

=

5

31 10

'

'. ; k = 10.

redred

w

V

b d=

; WhereV

d d

L

Fredend middle

th

pw=

3

8

(based on the following figure)

dmiddle dend

3/8 x Lth

Lth

When LWAC applied, certain factors are changing:

2 =

0 2 1, ' f k k kb n

k1 0 4 0 6 2300= + , .

= 0.9 (

= 1900 kg/m3)

Fpw

top surface


40/59



ff k f

b

brep

m

ck=

= + 1 0 7 1 05 0 05 0 9

1 4

, ( , , ' ) ,

,

Other agreements: The shear reinforcement is calculated at 200mm from the beam end. The transfer length, is estimated at 1500 mm from the beam end. The shear stress in the middle of the span, is estimated at 20 % of the calculated d The intersection between the d line and the n+1 line is calculated by the equality of triangles. The distance from the support to the intersection must be reinforced. This distance is sub-

divided into three equal distances in which:

Part 1 is calculated for: 5/9 of the total surface

Part 2 is calculated for: 3/9 of the top surface

Part 3 is calculated for: 1/9 of the top surface

The calculation of the shear reinforcement, is based on the next procedures:

1.Needed reinforcement surface is calculated by the above-described method.

2. The practical reinforcement is chosen (based on diameter and spacing) compared to the

needed reinforcement.

3. The maximum number of stirrups is calculated by :re orcement dis ce

spacing

inf tan

4. The optimisation of the reinforcement by choosing a second spacing, is based on the follow-

ing example :

End of a considered reinforcement part

8-100 assume a stirrup reinforcement witha spacing of 100 mm and that four stirrups

can be reduced at the end of the rein-

forcement section.

When a second spacing of 200 mm is used,

a distance of 800 mm is needed to get this

reduction.

8-200

In the more complex cases, this distance can be calculated by the formula below:

reduced stirrups

spacing first spacing

first spacing

spacingsec.

sec.


41/59



b) Shear force in transitional zone

The transitional zone between the beam and the topping must be reinforced because of the hori-

zontal shear stress occurring when the construction is under permanent and live load.

The shear stress in the transitional zone is calculated by the formulas below:

dd

w

V S

b I=

1 0 3= , 'f ck

The difference between dand 1 is reinforced. This length is divided into 5 parts by which the

first part is calculated by 9/25 part of the surface, the second part 7/25, the third part 5/25, the

fourth part 3/25 and the last part 1/25.The stirrup calculation in this zone is equal to the calculation procedure of the shear in the web.

3 sections in transitional zone

Figure 14 Detail of the stirrup composition in transitional layer between topping and

beam

2.6.3 Topping

The reinforcement is calculated in two loading situations:

1. The ultimate limit state (ULS)

2. The serviceability limit state (SLS)

In ULS, the positive and negative moments are calculated in normal (sd = 1,5) and extremesituation (

sd= 1,0). The representative moments in normal situations are divided into local and

topping

beam


42/59



overall moments. The representative moments in extreme situation exist only of a global mo-

ment.

The moments in overall situation are obtained from the load spreading calculation.

The moments in local situation are calculated by the figure below:

Mneg;rep : Fwheel

qd

l1 l1 l1

Mpos;rep

The total positive moment is based on a summation of the wheel- and q-load. The total negative moment is based only on the q load. The wheel load cannot occur in the

situation when each of two cars stands at the side of the bridge.

The necessary reinforcement in the topping in transversal direction is determined in ULS

In SLS, already chosen reinforcement is checked on cracking. This check is done according to

the Dutch regulation, which includes two methods:

Complete developed cracking pattern (M

Wf

rep

bm )

Incomplete developed cracking pattern ( MW

frep

bm )

Agreements by a complete developed cracking pattern according to the Dutch regula-

tions

One of the two agreements below has to be correct:

a) ss

k1

b) s k

s

100 132

,

Agreements by an incomplete developed cracking pattern according to the Dutch

regulations

( )

+

+km

ck

sr s sr s

k f kand

3

2

150

'

s

s


43/59



src r bm

s

A k f

A=

5 4. s s

rep

u

fcalculated mm

present mm

M

M=

2

2

kr = 0,9-0,5h2.6.4 Composite structure

2.6.4.1 Stresses due to shrinkage , creep and temperatureDue to the difference in the humidity and the temperature of the surroundings and the fresh con-

crete, a part of the mix water of the concrete can evaporate resulting in the shrinkage of the

concrete. Creep, however, depends only on the loading and loading time. Theoretically, the creep

reduces the shrinkage.

The differences of the temperature at the top and the bottom of the bridge also influences the

stresses in the construction.

Shrinkage

According to the Dutch standard, the shrinkage factor 'r(for NDC) is calculated by the

multiplication of several variable factors:

' ' 'maxr c b h p t k k k k =

Where:

kp =1

1 0 2+ , o

kt =t

t hm+ 0 043,

with t in days; and hm =2

2

+

( )

( )

L h

L h

When using LWAC:

' ' 'maxr c b h p t k k k k k = 5

k5 = : 1.2 for a strength fck > 25 N/mm2: 1.5 for a strength fck = 15 N/mm

2

strength values between 15 and 25 N/mm2

are linear interpolated

kt =t

t hm+with t in days

Creep

Creep factor is dependent on several variable factors:


44/59



= k k k k k c d b h t max

Where:

hm =

2

2

+

( )

( )

L h

L h

kt =t

t hm+ 0 043,

with t in days

Stresses due to shrinkage and creep

The shrinkage difference between the topping (fresh concrete) and the beam (aged concrete)

causes a horizontal force and moment which is given by the following figure and formulas:

------- F ( )F E Ar topping r beamtopping topping

= ' ; ' ;

M F hh

ztopping

o=

2

These two forces cause stresses in the construction, which are calculated using the next formu-

las:

F

Atopping

F

A

E

Etotal

topping

beam

( )M h z

W

h h z

total b

beam top

topping b

,

M

W

E

Ebeam top

topping

beam,

M

Wbeam top,

+ + =

F

Atotal

M

Wbeam bottom, ' , ,r beam bottom

The total stress at the bottom of the beam is calculated by the formulas below:

Topping

Beam

ht / 2

zo

h

M


45/59



beam bottom; = (creepreduction beam + creepreduction topping) x ', ,r beam bottom

Where:

Creep reduction of the beam = 1

ebeam

beam

Creep reduction of the topping =1

e topping

topping

' , ,r beam bottom= Stress caused by shrinkage

Temperature

The temperature of the surroundings causes extra stress in the construction. When certain tem-

perature on the top of the bridge is reached, an extra stress occurs at the bottom of the construc-

tion. This extra stress together with the present stress (due to loading) needs to be checked tothe maximal stress.

In this situation a tensile stress occurs at the bottom of the beam and therefore checked with the

present tensile stress.

The mean temperature Tmean is calculated by the next formula:

TA

T x b x dxmeanc x

x

= 1

1

2

( ) ( )

The temperature difference Tb is calculated by the formula:

Th

IT x b x x dxb

x

x

= ( ) ( )1

2

The temperature of the construction Te ( ) is calculated by the formula:

{ } T x T T x T xmean b e( ) ( ) ( ) + =

T x T T T xmean b e( ) ( ) =1

6

7

18

4

9

01

6

7

54

8

27 = T T T xmean b e ( )


46/59



01

6

7

18

2

9 = T T T xmean b e ( )

temperature beam beam bottomE T= ,

Where:

= -1.0 x 105

T beam bottom = 016

718

29

= T T T xmean b e ( )

The total extra stress (caused by shrinkage and creep differences and temperature influence) is

added to the present tensile stress (caused by permanent and live loading). And is given by the

following formula:

b admissible b present shrinkage creep temperature, , , + +

2.6.4.2 Fatigue

Fatigue in the construction is caused by the load cycles due to the passing traffic (live load).These load cycles are influencing in time the representative stresses. Such behaviour can cause

fatigue in the construction parts due to which the construction can collapse without exceeding

the maximum calculated stress.

Fatigue in longitudinal direction

The fatigue moment is calculated with the next formula:

M M Bfatigue d l v= ;

Where:


47/59



( )B Lv th= =0 8 20 0 004 0 839, , .

( ) = f Ke12

1 0.

f Lth1 0 01 0 15 0 4475= + =, , .

KK

K Ke=

+1

1 2

KM

M

first

1 =max

KM

Mond

2 =sec

ma x

The load spreading calculation (LC8 and LC11) calculates Mfirst and Msecond

Mmax is calculated by the following figure:

Lth

x 1000 4000 y

Fwheel Fwheel Fwheel

Ra Rb

500

Schematical longitudinal section of the bridge

( )R

x F

Lbwheel

th

= + 3 6000

R y Fb wheel ma x ( )= + 4000 4000

Topping (longitudinal direction)

The representative stress caused by fatigue is checked by the maximal stress according to the

formulas below:

tot buv n u nf S =' ( )( ) ( )

Where:

tot perm fatigue= +

fatiguefatigue

c s

M

W=

;

( ) ( ) ( )S R n f u n bv= 1 0 1 1, log '

Where:

RM

M

bd

d

permanent= =

'

'

;min

;max max

middle of the span


48/59



n = 1,1 x 109

= 1.0

( )f fbvb rep k

m

'' , ,; ;= +

1

2 0 85 30 0 85 30

f fb rep k ck ' . '; ; = 0 85

m = 1 2,

Beam (longitudinal direction)

The representative stress caused by fatigue is compared with the maximal stress according to

the formulas below: tot buv n u nf S =' ( )( ) ( )

Where:

tot perm fatigue= +

fatiguefatigue

c s

M

W=

;

( ) ( ) ( )S R n f u n bv= 1 0 1 1, log '

Where:

RM

M

bd

d

permanent= =

'

'

;min

;max max

n = 1,1 x 109 = 1.0

( )f

f

bv

b rep k

m

'

' , ,; ;=

+ 1

20 85 30 0 85 30

f fb rep k ck ' . '; ; = 0 85

m = 1 2,

Tension in pre-stress steel

The tension leap is calculated by:

s rep s u; ;

Where:


49/59



s u s ds rep

m

m

n; ; ;min

; ;

= +

10

7

7

10

n = 1.1 x 108

m = 11,

s rep bn; =

n =E

Es

b0 6, b

fatigue

liveload

b mm

M

M=

;90

Transversal direction

The representative moment is checked by the chosen top and bottom reinforcement of the top-ping. It appeared in all cases that the earlier calculated bottom reinforcement was too small to

comply with the fatigue regulations, hence a new reinforcement had to be chosen. This new re-

inforcement is again checked on cracking.

M Mrep s. < (Tensile strength reinforcement)

M M Mrep b s. ' '< + (Compressive strength concrete and steel)

Where:

Mrep

= the decisive moment of M1

and M2

loadlocalMM vfirst +=2

11

loadlocalMM vond +=2

1sec2

Mfirst and Msecond are calculated in the spreading calculation in LC8 and LC11

Mpos;rep is calculated in paragraph 2.6.3

M z Ass n rep

m top=

; ;

10 6

Where:

s n rep s repm

n; ; ; ;=

10

7

7

10

m = 1.15z = d - 1/3 x

Mpos;rep

Mpos;rep


50/59



Where:

( ) ( )x n A A n A A n c A A dtop bot top bot top km top bot = + + + + + + 2

2

2 10001

2

and is obtained from the two equations:

N A E A Ed

xs s s s s s bs

' ' ' ' ''

= =

1 and

N A E A Ed

xs s s s s s bs= =

' 1

( )

M

x A S d x

b

top u n

' = 12

1000 13

106

( ) ( ) ( )S R n f u n bv= 1 0 1 1, log '

Where:

RM

M

bd

d

permanent= =

'

'

;min

;max max

n = 1,1 x 109

= 1.0

( )f

f

bv

b rep k

m

'

' , ,; ;=

+ 1

20 85 30 0 85 30

f fb rep k ck ' . '; ; = 0 85

m = 1 2,

M

A E cx

d c

s

top s bu

top km

top km

'

'

=

+

10 1

1

2 12

10

3

6

2.7 SubstructureA land abutment is placed in transversal direction under both bridge ends. Both land abutments

are supported by a number of piles, calculated according to the local (Dutch) ground regulations.

Land abutment


51/59



The height of the land abutment is related to the height of the beam, therefore by an increasing

span, the height of the beam and height of the land abutment increases. This results in a larger

volume according to the table below:

Span Volume land abutment

20 1.2 m3

/ m1

30 1.6 m3

/ m1

40 2.0 m3

/ m1

Piles

The piles are calculated by inclusion of the following loads:

Weight of the land abutment

Weight of the beams Weight of the topping The permanent loads of the individual bridge parts (railing, asphalt layer, etc.) Equally divided live loads Live loads (two cars standing directly at the support).The total weight per span changes only when the weight of the topping and beam are changed.

The reduction in piles can be found when LWAC is applied by different spans.

The size of the piles is 250 x 250 mm2. Assumed is a ground resistance of 10 N/mm2. This as-

sumption results in a maximum pile force of 625 kN.

The calculated number of piles is rounded to an even figure. In this way the piles can be appliedin groups of two, and equally divided over the length of the land abutment.


52/59



3. COMPARISONThe LWAC is variable applied in the beam as well as the topping. Also the spans of the bridge

are changed from 20, 30 up to 40 m. Combination of all this variables results in an reliable com-

parison. First have been calculated the material quantities for every combination. The total costs

are obtained multiplying the quantities by there costs. The total costs are excluding overhead and

engineering costs.

3.1 QuantitiesThe quantities are given in the tables with constant span and with variable LWAC application to

find the influence of LWAC on the construction.

Superstructure

The quantities of the superstructure are expressed per square meter bridge surface. The total

amount of concrete (C30/37) added in-situ consists of the topping layer and the two edge beams

(figure 3).

Substructure

The influence of the weight reduction on the superstructure is expressed in a smaller pile force

and where possible in reducing the number of piles. The volume of the land abutment is held

constant by each span.

3.1.1 Bridge with a span of 20 m

The inverted T-beam with height of 715mm (VIP 700) is chosen from tables in relation to the

span of the bridge.

Lth = 20 m

B = 18 m

Abridge = 20 x 18 = 360m2

Superstructure Combinations

topping-beam

Elements topping + 2 edge beams

concrete

(m3/m2)

pre-stressing

steel (kg/m2)

Reinforcement

(kg/m2)

concrete

(m3/m2)

reinforcement

(kg/m2)

NDC-NDC 0.27 18.1 6.0 0.25 14.9

LWAC-NDC 0.27 15.1 6.1 0.25 15.9

NDC-LWAC 0.27 12.7 7.4 0.25 16.5

LWAC-LWAC 0.27 12.1 7.2 0.25 17.2


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Substructure

Volume of the land abutment: 1,2 m3 / m1

Combination

Topping-beam

Present pile force [kN] Total number of piles

NDC-NDC 595 24

LWAC-NDC 567 24

NDC-LWAC 565 24

LWAC-LWAC 536 24


The VIP 1100 is chosen in relation to the span of the bridge.

Lth = 30 m

B = 18 m

Abridge = 30 x 18 = 540m2

In the combinations with NDC beams, the height of the beam is increased with approximately 50

mm due to fatigue regulations. This results in a difference of 0,01 m3/m2 compared to the other

combinations

Superstructure

Combinations

topping-beam

Elements topping + 2 edge beams

concrete

(m3/m2)

pre-stressing

steel (kg/m2)

reinforcement

(kg/m2)

concrete

(m3/m2)

reinforcement

(kg/m2)

NDC-NDC 0.34 25.4 6.8 0.254 21.9

LWAC-NDC 0.34 24.9 6.3 0.254 21.3

NDC-LWAC 0.33 22.5 7.5 0.254 24.7

LWAC-LWAC 0.33 21.9 7.5 0.254 26.3

Substructure


Combination

Topping-beam

Present pile force

[kN]

total number of piles

NDC-NDC 604 36

LWAC-NDC 580 36

NDC-LWAC 563 36

LWAC-LWAC 602 32


The VIP 1600 is chosen in relation to the span of the bridge.

Lth = 40 m

B = 18 m

Abridge = 40 x 18 = 720 m2


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In the combinations with NDC beams, the height of the beam is increased with 50 mm due to

fatigue regulations. This resulted in a difference of 0,01 m3/m2 compared to the other combina-

tions

Superstructure

Combinations

topping-beam

Elements topping + two edge beams

concrete

(m3/m2)

pre-stressing

steel (kg/m2)

reinforcement

(kg/m2)

concrete

(m3/m2)

reinforcement

(kg/m2)

NDC-NDC 0.48 36.1 7.6 0.258 17.2

LWAC-NDC 0.48 31.2 7.5 0.258 18.9

NDC-LWAC 0.47 26.3 8.8 0.258 19.3

LWAC-LWAC 0.47 26.3 8.5 0.258 21.8

Substructure


Combination

topping-beam

Present pile force [kN] total number of piles

NDC-NDC 620 52

LWAC-NDC 594 52

NDC-LWAC 612 48

LWAC-LWAC 583 48

3.2 Costs per quantityThe costs in the table below are average prices of spans 20, 30 and 40m and they are based on

mean Dutch prices.

Materials Units Material costs

(euros)

labour costs

(euros)

Topping NDC C30/37 m3 81 157

Topping LWAC C30/37 m3 79 157

Beam NDC C45/55 m3 118 91

Beam LWAC C45/55 m3

110 91The material costs exist of: The labour costs exist of:

- Concrete material - equipment costs

- Reinforcement - moulding

- Pre-stressing steel - assembling of prestress and reinforcing steel

- Maintenance and energy. - casting

- Small inserts - other


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Transport and assembling costs

The transport costs are obtained from the relation between the weight of the beam and the

needed lorry; given in the table below:

Weight of the beam costs per transport over 100 km

(euros)

0 - 350 kN 340

350 450 kN 795

450 600 kN 1248

The assembling costs are obtained from the relation between the weight of the beam and the

needed crane; given in the table below:

Weight of the beam costs per hour(euros)

0 - 480 kN 567

480 590 kN 681

Review transport and assembling costs

span Beam weight transport costs

(euros)

assembling costs (euros)

(2 beams / hour)

NDC LWAC NDC LWAC NDC LWAC

20m 162 kN 130 kN 2723*1 2723*1 4253 4253

30m 306 kN 238 kN 5106*2 5106*2 4253 425340m 576 kN 450 kN 18720*2 11913*2 5108 4253

*1 two beams per drive *2 one beam per drive

3.3 Project costsTo get a clear view of the costs per bridge part, the sub- and superstructure are divided into

parts. The costs of the land abutment are equally calculated as the costs of the topping (equal

concrete and reinforcement price).

The costs of the piles are assumed at 410 Euro / piece (all costs included).

3.3.1 Bridge with a span of 20 mL = 20 m

A = 20 x 18 = 360 m2

substructure

(euros/m2)

superstructure

(euros/m2)

total

(euros/m2)

topping-beam land

abutment

piles element topping transport assembling

NDC-NDC 25.8 27.3 56.8 59.2 7.6 11.8 188.5

LWAC-NDC 25.8 27.3 55.2 58.6 7.6 11.8 186.3

NDC-LWAC 25.8 27.3 53.7 59.6 7.6 11.8 185.8


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LWAC-LWAC 25.8 27.3 53.3 58.9 7.6 11.8 184.7


L = 30 m

A = 30 x 18 = 540 m2

substructure

(euros/m2)

superstructure

(euros/m2)

total

(euros/m2)

topping-beam land

abutment


NDC-NDC 23.4 27.3 72.7 61.5 9.5 7.9 202.3

LWAC-NDC 23.4 27.3 72.3 60.5 9.5 7.9 200.9NDC-LWAC 23.4 27.3 69.0 62.3 9.5 7.9 199.4

LWAC-LWAC 23.4 24.3 68.7 61.8 9.5 7.9 195.6


L = 40 m

A = 40 x 18 = 720 m2

substructure

(euros/m2)

superstructure

(euros/m2)

total

(euros/m2)

topping-beam landabutment


NDC-NDC 22.7 29.6 102.3 61.1 26 7.1 248.8

LWAC-NDC 22.7 29.6 99.6 60.7 26 7.1 245.7

NDC-LWAC 22.7 27.3 94.6 61.7 16.6 5.9 228.8

LWAC-LWAC 22.7 27.3 94.5 61.5 16.6 5.9 228.5


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4. CONCLUSIONSIt is very important to stress again that following conclusions are based, structurally on the Dutch

codes and regulations of concrete structures and economically on the average material and la-

bour prices in The Netherlands. As earlier mentioned engineering and overhead costs are in this

comparison excluded as well as the eventually investments.

Using LWAC in stead of NDC, in the structural parts of composite bridges made of inverted T

beams with topping, can reduce amount of needed pre-stressing steel in the elements for more

than 30 %.

On the other hand, amount of applied reinforcement in the LWAC elements and the topping will

increase up to 25 %.

LWAC used in the beams and the topping will reduce the total weight of the bridge. For the la r-

ger bridge spans this will lead to reducing of amount of needed piles in the substructure up to 11

%.

The material costs of new, within Euro- LightCon project developed, LWAC (C45 / 55) are

lower than standard NDC (C45 / 55) of some 4%. Also the material costs of LWAC (C30 / 37)

are lower than NDC (C30 / 37).

Especially for longer beams, the transport and assembling costs are in favour of LWAC ele-

ments of about 32%.

For bridges with a superstructure fully made of LWAC, the total project costs will decrease

from 2% for span of 20m up to 8% for span of 40m, in comparison with bridge with NDC super-

structure. The relative big costs reduction at the span of 40 m, is significantly influenced by the

lower transportation and assembling costs (about 4%)


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APPENDIX:MIXTURE COMPOSITIONMixture compositionsof Normal Density Concrete and LightWeight Aggregate Concrete withC30/37 and C45/55 strengths.

Mixture composition (Normal density concrete, NDC)

C45/55

(kg / m3)

costs

/ ton

Costs / m3

(euros)

C30/37

(kg / m3)

cost

s/

ton

costs /

m3

(euros)

Cem | 52.5 R 120 84.7 10.16 - - -Cem ||| A 52.5 245 81.1 19.87 320 81.1 25.95

Additive Cugla MO 20 6.5 499 3.24 - - -

Water 160 0.87 0.14 144 0.87 0.13

Sand 0-4 mm 775 8.5 6.59 885 8.5 7.52

Concrete granulate 0-16 135 10.6 1.43 140 10.6 1.48

Gravel 4-16mm 950 11.9 11.31 910 11.9 10.83

Total 2392 52.7 2399 45.9

Mixture composition (Light weight aggregate concrete, LWCA)

C45/55

(kg/m3)

cost

s/

ton

Costs /

m3

(euros)

C30/37

(kg/m3)

costs/

ton

costs /

m3

(euros)

Cem | 52.5 R 350 84.7 29.65 - - -

Cem | 32.5 R - - - 320 81.2 26.3

Additive Tillman ON2 1.75 454 0.79 - - -

Additive Tillman Oft3 2.45 454 1.11 - - -

Limestone 25 77.1 1.93 - - -

Water 151 0.87 0.13 150 0.87 0.13

Sand 0-2 mm 489 9.0 4.40 761 9.0 6.85

Lytag 0,5-4 mm 99 17.2 1.71 72 17.2 1.24

Lytag 0.5-6 mm 258 17.2 4.45 186 17.2 3.21

Lytag 6-12 mm 377 17.2 6.50 272 17.2 4.69

Total 1753*1 50.7 1761*

1 42.4

*1 This is the dry density of LWAC. When the LWA particles are fully saturated, a wet density


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of approximately 1900 kg/m3 is obtained.

bridge calculus example

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