Slender box girders and/or less stirrups by applying HSC ...

Slender box girders and/or less stirrups by applying HSC or HSFRC

Master Thesis

Mathijs van den Hurk

4-12-2014

Graduation committee

Prof. dr. ir. D. A. Hordijk (TU Delft – Chairman)

Dr. ir. C. van der Veen (TU Delft)

Dr. M.H. Kolstein (TU Delft)

Ir. M.P.J. Pluis (Spanbeton)


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II

Preface This master thesis is written to finalize my study Civil Engineering at the department of Concrete structures at the University of Technology at Delft. The work is done from May 2014 until December 2014, at the office of Spanbeton. This report consists of 4 different sub reports. The first 2 reports are the results of a literature research to High Strength Concrete and to High Strength Fiber Reinforced Concrete, respectively. After that, the influence of HSC on the slenderness of box girders was investigated. The goal of this study is to increase the slenderness of SKK-girders (box-girder) by adjusting the cross section of the girders and by making use of higher concrete classes. The last, but not least, report contains the results of my research to the influence of steel fibers in HSFRC on the amount of stirrups in box girders. The goal of this study is to reduce the amount of stirrups that are needed in a box girder produced by Spanbeton. Without the help of others I would not have reached the results presented in this report. I would like to thank Spanbeton for offering the space and knowledge which was needed to provide this report. I want to thank all the employees of Spanbeton who contributed in any way, for their interest and helpful advices. In particular I would like to thank Math Pluis. First of all for his guidance provided during the research, but also for all the non-concrete related things we discussed. Furthermore I would like to thank my graduation committee for their input and scientific contribution to this master thesis. Mathijs van den Hurk Koudekerk aan den Rijn, December 2014


III

Summary In this report, the influence of High Strength (Fiber Reinforced) Concrete on precast box girders is investigated. The starting point was a box girder with a construction height of H=1300 mm, used for the Veerwegviaduct which has a span of approximately 40 meter. With the help of HSC, it is attempted to increase the slenderness, i.e. decrease the construction height, while keeping the span constant. This slenderness increase comes at a price. For example, more stirrups have to be applied to resist the increased shear stresses. However, when steel fibers are introduced inside the concrete mix, the shear capacity of the concrete itself will increase. With the design rules of the ModelCode 2010, the shear capacities of the concrete and the stirrups can be added. In this way, by adding fibers to the concrete, the number of stirrups can be reduced.

The first 2 parts of this report are literature researches in HSC and HSFRC, respectively. The properties of the different materials are described. HSC has, as the name reveals, a higher strength. This higher strength is achieved by using a lower water-cement ratio or by obtaining a higher packing density (this is done by adding more fines), while keeping the self-compacting characteristics of the concrete. The tensile strength does not increase as fast as the compressive strength. This gives an even smaller ratio of the tensile to compressive strength. The value of the end of the plastic strain trajectory (εcu) of HSC is smaller, which leads to a more brittle behavior. Another disadvantage is the higher material price, mainly caused by the higher content of fine materials.

To overcome the brittleness of HSC, fibers can be added. The (micro)cracks that arise in the concrete will be spanned by the steel fibers, which will transfer the tensile loads from one side of the crack to the other. In this way, a higher post-peak strength is achieved, leading to a more ductile behavior. Due to the fact that the cracks are bridged, new cracks can occur. In this way, a more evenly distributed crack pattern will occur with smaller crack widths. It was found, by means of the French regulations, that adding 25 kg/m3 of fibers (fiber type RC-80/30-CP) would lead to a sufficient improved ductility. For the first research, the fibers will only be used to overcome the brittleness. In the second research, the fibers will also be used to increase the shear capacity of the concrete member. When the height of the girder is reduced, the section modulus W decreases even faster. With constant loads (except the dead load of the girder) and a lower section modulus, higher stresses will occur (σ=M/W). To overcome the tensile stresses, more prestressing needs to be applied. In this report, the construction height is gradually decreased to H=1200 mm, H=1100 mm and H=1000 mm. For the original girder (H=1300 mm), 62 prestressing strands were needed. For the more slender construction, 67 strands, 76 strands and 85 strands were needed, respectively. The high prestressing force, combined with a decreased section modulus, will lead to a higher camber. This camber could rise to unpractical values, especially for a construction height of H=1000 mm. Due to the increased slenderness, the shear stresses will increase significantly (up to 50% for a construction height of H=1000 mm). This will lead to high material and labor costs, because placing and adjusting the stirrups is labor intensive. When the fibers are used (25 kg/m3 for all girder configurations) to increase the shear capacity of the concrete member and one is allowed to calculate according to rules of the ModelCode2010, a practical stirrup distribution (Ø10-200 or Ø10-300) will in most cases be sufficient. Only close to the supports, where the highest shear loads will arise, some additional stirrups need to be applied. This is, among others, because the fatigue load is assumed to be not governing anymore. Instead, the static ULS load will become governing.


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Conclusions and recommendations

Conclusions The objectives of this report were to increase the slenderness of box girders by using higher strength concrete and reducing the amount of stirrups by adding steel fibers to the (high strength) concrete. It can be stated that both goals are achieved. The higher slenderness is achieved by adding more prestressing. Due to the lower construction height, more prestressing is needed in order to prevent tensile stresses from occurring. Due to additionally needed prestressing, higher compressive stresses will occur. High strength concrete can cope with these high compressive stresses, however the high prestressing forces will lead to higher camber, which can reach unpractical values. 24 additional prestressing strands need to be added for a construction height of H=1000 mm, next to the 62 strands that were already present for construction height H=1300 mm. This is approximately 40% more prestressing, for a slenderness increase of 30%. This slenderness increase came together with a dead load decrease of approximately 10%. Next to the governing bending moments and occurring stresses, the shear capacity of the girders is checked. The shear force is based on the fatigue load, using fatigue load model 4b. Usually this will be the governing load. For lower construction height, the internal lever arm is smaller. This reduces the shear capacity. This loss in shear capacity can be compensated for by applying more shear reinforcement in the girder. For a construction height of H=1000 mm, approximately 50% additional rebar is needed. This is close to the support, where the highest shear force will occur. The additional reinforcement can be reduced with the help of steel fibers. The main disadvantage of high strength concrete, is the increased brittleness of the material. This makes it a more dangerous material to work with. To reduce the risk, steel fibers can be added to give the material a more ductile behavior. The French recommendations and a test performed by Bekaert are used to determine the minimum dosage of the fibers. It was found that a dosage of 25 kg/m3 should be sufficient to give the concrete suitable ductility, in order to avoid sudden collapse of the girder. When the fibers, which are already inside the concrete to reduce the brittleness, are also used to increase the shear capacity of the concrete member, the number of additionally added stirrups can be reduced. This is done with the design rules of the ModelCode 2010. With these rules, it is allowed to add the shear capacity of the (cracked) concrete and the shear capacity of the stirrups together. The shear capacity of the cracked concrete will depend on (among others) the state of strain. The steel fibers inside the concrete will lead to a lower overall strain εx and will thus increase the shear capacity of the concrete. The addition of the fibers leads to a tensile strength which depends on the CMOD. Characteristic values (obtained from Bekaert) for the tensile strength were used and were kept constant for different concrete classes. After some investigation, it was assumed that the fatigue loading was no longer governing. Instead, the static ULS load is assumed to be governing. That is why the increase in ULS shear capacity is determined with fibers added. This is done using the “consistent” approach of the Modelcode, which uses the same approach as the rest of the Modelcode, with an additional term for the fiber capacity. With this, it turned out that many stirrups can be removed. Close to the support approximately half the number of stirrups could be omitted, further away from the support the reduction percentages increased to 90-100%. However, in this


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figure the practical stirrups are not included. Two practical stirrup distributions are taken into account, being Ø10-200 and Ø10-300. With the first (Ø10-200), no additional stirrups were needed besides the practical stirrups. For the latter (Ø10-300) only close to the support some additional stirrups need to be added, as can be seen in Figure 1. This figure gives the amount of stirrups that are needed for constructive reasons and the grey area is the amount that is needed for practical reasons. It can be seen that for a distance greater than 3 meters from the support, only practical shear reinforcement is needed. Furthermore, the original stirrup distribution is given.

Figure 1 - Amount of reinforcement for different construction heights and practical stirrups Ø10-300

It is clear that it is possible to reduce the number of stirrups by using steel fibers and the amount of reduction depends on the chosen practical stirrup distribution.

0

200

400

600

800

1000

1200

1400

0,5 2,5 4,5 6,5 8,5 10,5 12,5

Am

ou

nt

of

rein

forc

em

en

t p

er

we

b

[mm

2/m

]

Distance from support [m]

H=1300

H=1200

H=1100

H=1000

PracticalstirrupsOriginal


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Recommendations The advantages and disadvantages of the use of higher strength concrete is now known. It is possible, for this particular reference project, to have a construction height of H=1000 mm. But this high slenderness comes with a high camber. A camber of approximately 110 mm is calculated, for the load combination prestressing and 1,1 times the static load. This large camber will usually result in additional asphalt to follow the alignment of the road. This additional asphalt will in turn lead to a higher dead load. On top of this comes the fact that girders with the same construction height and same amount of prestressing will not experience the same camber. With more prestressing applied and a higher concrete class, the (absolute) differences will increase. Therefore it might be wise to use a construction height of H=1100 mm. The camber for this height is approximately 80 mm, which is 30 mm less than with a construction height of H=1000 mm. This is due to the fact that fewer additional prestressing strands are needed. Next to this, for a construction height of H=1100 mm, a concrete class of C90/105 is sufficient. The Eurocode is valid up to C90/105, so the current regulations can still be used. Next steps in the investigation of the utilization of HSFRC should include more tests with the fibers to determine the exact strength of the material. For now, use is made of characteristic values which were obtained from Bekaert. To obtain the exact material properties, tests should be done on mixes which will be used at Spanbeton. These tests should be done on different concrete classes. Other additional tests should include the lowered workability when the fibers are added and the best way to add the fibers (think about a conveyer belt). Besides this, the scatter of the fiber concrete should be determined. In this report, the assumption is made that the fatigue loads are not governing anymore. This was based on the assumption that the fatigue strength is 30% of the static ULS strength, so

The auteur thinks that this is a safe assumption, but this is not yet proven for this particular combination of fiber type and concrete composition of Spanbeton. Tests should be done to provide more information about the fatigue life of the HSFRC. In this report, only 1 type and amount of fibers is applied on one particular project (Veerwegviaduct). On the basis of this type and amount of fibers, the conclusions are drawn. That is why further investigations should be done on other types and amounts of fibers. It could be possible that when less fibers are used, a better optimization and lower material costs can be obtained. Use was made of a practical stirrup distribution, which (at certain places) did have a small constructive contribution. When less fibers are used, both materials could be used in a more effective way. Furthermore, other fiber types should be investigated. One could question the influence of the aspect ratio of the fiber on the shear capacity. Besides this, it should be checked if the drawn conclusions also hold for all other boundary conditions.


Properties of High Strength Concrete

Literature research - HSC


15-5-2014

Properties of High Strength Concrete (literature research - HSC)

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Summary This report is the result of the literature research regarding High Strength Concrete, which was conducted in preparation of the main study regarding the increase of the slenderness of SKK-beams (box girders) and the reduction of stirrups by the use of HSFRC. The SKK-beams are produced by Spanbeton. First of all, the mechanical properties of the material are qualitatively discussed. The positive and negative aspects are pointed out, as well as the effect of the changed aspects. The higher strength of the concrete mainly refers to the compressive strength of the concrete. This higher compressive strength can be achieved by a lower water-cement ratio or a higher packing density. Unfortunately, the tensile strength does not increase that much. This leads to the fact that High Strength Concrete is more brittle compared to Normal Strength Concrete. To be able to make calculations with HSC, the building codes and regulations are highlighted. For this, the Eurocode was not sufficient because this only concerns concrete classes up to C90/105. That is why the Model Code was used to achieve appropriate values for the mechanical properties. The last part which is discussed in this report is the reference project. As stated, the goal of the main study is to increase the slenderness of box girders. That is why a reference project was regarded, to compare the achieved improvements.


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Table of Content 1. Study to the properties of High Strength Concrete ........................................................................ 1

1.1. Mechanical properties of HSC ................................................................................................. 1

1.1.1. Positive properties........................................................................................................... 1

1.1.2. Negative properties ......................................................................................................... 2

1.1.3. Conclusion ....................................................................................................................... 3

1.2. Building codes and regulations ............................................................................................... 3

1.2.1. Compressive strength ...................................................................................................... 3

1.2.2. Tensile strength ............................................................................................................... 3

1.2.3. Shear strength ................................................................................................................. 4

1.2.4. Fatigue strength .............................................................................................................. 5

1.2.5. Modulus of Elasticity ....................................................................................................... 5

1.2.6. Stress-strain relation ....................................................................................................... 5

1.2.7. Shrinkage and creep ........................................................................................................ 6

1.2.7.1. Shrinkage ................................................................................................................. 6

1.2.7.2. Creep ....................................................................................................................... 7

1.3. Reference project .................................................................................................................... 8

1.3.1. A15 Veerwegviaduct ........................................................................................................ 8

1.3.2. Regulations ...................................................................................................................... 9

1.3.3. Slenderness ................................................................................................................... 10

List of references ............................................................................................................................... 11

Appendix A .............................................................................................................................................. A


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1. Study to the properties of High Strength Concrete The goal of this study is find the influence of High Strength Concrete (HSC) on the slenderness of beams produced by Spanbeton. The considered beams will be SKK-beams (Spanbeton Koker Konstructie), which are hollow rectangular tubes as shown in Figure 1. The range in height of the SKK-beams is from 700 mm up to 1600 mm.

Figure 1 - SKK-beam

To obtain the knowledge which is required to describe the mechanical properties of HSC, a systematic review is performed. The main parts of the information below is based on [1], [2] and [3].

1.1. Mechanical properties of HSC

1.1.1. Positive properties

Concrete is a composite material composed of water, coarse granular material (the fine and coarse aggregate or filler) embedded in a hard matrix of material (the cement or binder) that fills the space around the aggregate particles and glues them together. In normal strength concrete (NSC) the strength of the matrix is determining the strength of the concrete, because the strength of the aggregates is considered to have a higher compression strength. To increase the strength of the cement matrix, there are two possibilities:

Increase the strength of the cement paste

Increase the packing density To increase the strength of the cement paste, the main focus will be to increase the cement strength class (CEM I/ III 52,5 R) and to decrease the water/cement ratio (favorable values are w/c<0.3). The first statement will speak for itself, however the second statement needs a bit more elaboration. Reducing the w/c-ratio increases the strength of the cement paste, but there are limits to this method. This is due to the fact that the w/c-ratio also is the main factor influencing the workability of the cement paste. When the w/c-ratio is too low, the cement paste will become too dry and will not flow into the mold. To overcome this problem, a superplasticizer (e.g. Cugla HR) can be used. This superplasticizer avoids agglomeration of the fine aggregates by forming a thin film around these aggregates and hereby increasing the workability tremendously, with relatively low dosage (0.15-0.30% by cement weight). Furthermore, the negatively charged particles of the superplasticizer permits the absorption on the positively charged colloidal particles. Due to this, the zeta potential (electrokinetic potential) of the suspended particles change. This gives the possibility for the particles


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to exert repulsion forces (see Figure 2), which disperse the particles and avoid friction by distribution the particles evenly through the matrix. The other option to increase the strength of the cement matrix is to increase the packing density of the matrix, by increasing the amount of fines in the fine aggregates (e.g. adding silica fume). This decreases the amount of voids in the matrix, and thus reducing the amounts of weak spots in it. The increase in packing density also leads to an increase in durability, because it is harder for chemicals to penetrate the material. This has three potential advantages:

Increased durability leads to an increased expected service lifetime.

With increased durability, less maintenance is required. This gives less maintenance costs and less nuisance for the users during the lifetime of the constructions.

The high durability aspects could be used to decrease the concrete cover of reinforcement steel and prestress steel, because the risk of penetration of chemicals is lowered and thus the risk of corrosion is lowered. However, one should keep in mind that the cover is also used to transfer forces from the reinforcement and prestressings strands to the concrete. When this cover becomes too small, the risk of splitting occurs.

Other possibilities to increase the strength are based on better curing of the cement paste, however the improvements on the strength after 28 days will not be as significant as with the methods describes above. On the other hand, bad curing will lead to significant reduction of the concrete strength after 28 days. The influence on the strength within the time lapse of a day after casting can be significantly influenced, by for example heat treatment of cement paste. This has effect on the time when prestressing of the beam can start and be stopped. With Ultra High Strength Concrete (UHSC) the above is even more utilized, leading to compressive strengths which exceed 150 N/mm2. This material is outside the scope of this report.

1.1.2. Negative properties

With the information above known, is must be noted that only increase of the cement matrix is not always sufficient. When the strength of the cement matrix exceeds the strength of the coarse aggregates, the latter will become governing because cracks will go through the aggregates. In this case, also the strength of the course aggregates should be increased, which will lead to a raise in the material costs. This raise is on top of the raise due to the extra cement and fines needed. On the other hand, the extra costs are partly taken care of the by the fact that less material is needed. Another drawback of the use of HSC is the fact that it becomes more and more brittle when the compressive strength increases. A possibility to deal with this drawback is to add fibers to the matrix, which give the concrete a more ductile behavior. This ductile behavior is required to assure a save construction, without sudden failure. The possibility of using fibers to increase the ductility will be discussed extensively in the next part of this report. Due to the more fine material and the complexity of the mixing, the mixing time is increased, because it will take more time for HSC to obtain a workable mix. Furthermore, the hydration process of HSC is faster. This gives an early strength to the concrete, but also generates more heat inside the

Figure 2 - Repulsion forces


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concrete. This can lead to trouble when big parts of a construction are poured at once due to cracks induces by temperature differences. However, due to the high strength, big parts are a rare phenomenon in the HSC industry. Due to the thin character of the HSC plates, the cooling down is better. Next to this, according to literature [4], the most efficient total amount of cementitious material usually appears to be between 450 and 550 kg/m3. After this point, the extra cementitious material will mainly act as a filler. This all implies that, generally speaking, the amount of extra added heat is relatively little and can be dealt with, without extra measures. Except for big parts like the end of a beam (beam head), which are often designed robustly.

1.1.3. Conclusion

Summarizing all the above said, HSC can be a good building material when one has the wish of a slender construction. The material is more durable than NSC, which gives it the opportunity to be used in harmful environments. The use of HSC will leads to higher production and material costs. Especially the new added materials (fine aggregates, superplasticizer) will increase the costs in comparison with the costs of NSC. This can be partly recouped by the fact that less material is needed.

1.2. Building codes and regulations According to literature, a concrete mixture is considered to be of high strength concrete when the (cube) compression strength of a certain concrete mixture is at least 65 MPa, so for concrete classes C53/65 and higher. To be able to do calculations with these HSC-classes, it should be known how one should do the calculations according to the regulations. The Eurocode ( [5]), is valid for concrete classes up to C90/105. For higher concrete classes [3] is used, which is a Model Code and is valid for concrete classes up to C120/140 but it is assumed that it can also be used for the concrete class C150/170. Below, an overview of the most important additions of the Model Code (in addition to the Eurocode) is given.

1.2.1. Compressive strength

The characteristic compressive strength fck is defined as the strength below which 5% of all possible strength measurements for the specified concrete may be expected to fail. It is based on the uniaxial compressive strength of cylinders. Thus fck of C90/105 will be 90 MPa. The mean value of the compressive strength fcm may be estimated by according to both the Eurocode (EC) and the Model Code (MC)

1.2.2. Tensile strength

In the Eurocode, the tensile strength of concrete is defined as a function of the compressive strength. However, with increasing compressive strength the ratio of tensile strength over compressive strength decreases. In other words, the tensile strength becomes only a small amount higher for higher concrete classes. The tensile strength may be estimated by

(

)

(

)


4

1.2.3. Shear strength

Regarding the shear strength of a concrete member, the (up to now) considered Model Code [3] is not a helping tool because the shear strength is not discussed in here. The EuroCode [5] does give design formulae regarding the shear capacity. However, the maximum shear capacity should not exceed

Where it holds that ν is a reduction factor dependent on the concrete class

(

)

So when using higher concrete classes (up to C150/170), the reduction factor ν becomes more dominant. This dominance is less for concrete classes up to C90/105 (the maximum design class for the EuroCode). For this reason another Model Code [6] is used. The design shear force must in general be determined for control sections at a location d from the face of supports. In [6] is stated that the shear resistance of a web consists of the shear resistance attributed to the concrete and the design shear resistance provided by shear reinforcement:

With

Where θ denotes the inclination of the compressive stress field (20°+1000εx≤θ≤45°). The strength reduction factor kc is defined as kc=kεηfc, with

(

)

⁄

This reduction factor is much more “high-strength friendly”. For C150/170, the reduction factors become ν=0.24 (EuroCode) and ηfc=0.58 (Model Code). Regarding the shear resistance attributed to the concrete, it holds that

√

[

(

)]

√ should not exceed 8. This limitation is due to the larger observed variability in shear strength of members with higher strength concrete. Furthermore, when the maximum aggregate particles do not exceed 16 mm, kdg can be taken as kdg=1.0. For further definitions, see Figure 3.

When the demand for minimum shear reinforcement is fulfilled ( √

), the shear

resistance provided by the shear reinforcement is

Together, the shear contributions of the concrete and shear reinforcement must be higher than the design value of the shear force.

Figure 3 – Definitions [6]


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1.2.4. Fatigue strength

When structures are exposed to frequently varying stresses, they are subjected to fatigue. The fatigue behavior of structures made of high strength concrete has rarely been investigated. This is due to the fact that not all structures are subject to fatigue. As a preliminary conclusion it is stated [3] that the specific values obtained from fatigue tests on HSC are of the same magnitude as obtained from tests on normal strength concrete as long as the specific values are referred to particular values obtained in static tests.

1.2.5. Modulus of Elasticity

The modulus of elasticity Eci is defined as the tangent modulus of elasticity at the origin of the stress-strain diagram. It can be estimated by

(

)

(

)

The value of αE is depending on the type of aggregate Table 1 - Effect of type of aggregate on modulus of elasticity [3]

Aggregate type αE

Basalt, dense limestone aggregates 1.2

Quartzitic aggregates 1.0

Limestone aggregates 0.9

Sandstone aggregates 0.7

1.2.6. Stress-strain relation

Figure 4 shows the stress-strain relations for concrete grades C12 up to C120 [3]. As can be seen from here, the values of εc3 (strain at maximum compressive stress) and εcu3 (maximum strain) becomes more close to each other for increasing concrete classes.

Figure 4 - Stress-strain diagram for different concrete strengths (mean values) [3]

Values for the different strains are given in Table 2.


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Table 2 - εc3 and εcu3 for various concrete grades [3]

Concrete grade

C12 C20 C30 C40 C50 C60 C70 C80 C90 C100 C110 C120

εc3 [‰] 1.90 2.07 2.23 2.37 2.48 2.58 2.67 2.76 2.83 2.90 2.97 3.0

εcu3 [‰] 3.5 3.5 3.5 3.5 3.4 3.3 3.2 3.1 3.0 3.0 3.0 3.0

It can be seen that from concrete class C120/140 both the strains are equal. This implies that the softening branch of the concrete is completely disappeared. The fact that the difference between the values of the abovementioned strains becomes smaller indicate the brittle behavior of HSC, which was mentioned above.

1.2.7. Shrinkage and creep

The time-dependent behavior of HSC is somewhat different compared to NSC. In here, the shrinkage and creep will be discussed. The different strain components are indicatively shown in Figure 5.

1.2.7.1. Shrinkage

The total shrinkage of the concrete consist of the autogenous shrinkage and drying shrinkage:

According to [3], it can be stated that:

The autogenous shrinkage significantly increases

The drying shrinkage significantly decreases From [3] is concluded that the total shrinkage is somewhat lower, but it is assumed to be equal for calculations which will be made according this research. This assumption is also justified by [7], which states that the difference in total shrinkage between NSC and HSC is rather small from a practical point of view. The main reason for this changes is the lower w/c-ratio. The time development of the shrinkage is indicatively shown in Figure 6 for NSC and HSC. The autogenous shrinkage can be predicted by using the following formulae

Where it holds that:

εcas=the autogenous shrinkage

εcds=the drying shrinkage

εcaso=notional autogenous shrinkage coefficient

εcdso=notional drying shrinkage coefficient

βas=function to describe the time-development of autogenous shrinkage

βRH=coefficient to take into account the effect of relative humidity on drying shrinkage

Figure 5 - Individual strain components of creep and shrinkage [3]

Figure 6 - Time development of shrinkage in NSC and HSC [3]


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βds=function to describe the time-development of drying shrinkage

t=concrete age [days]

ts=concrete age at the beginning of drying [days]

t-ts=duration of drying [days] The different components and coefficients may be estimated by

( ⁄

⁄)

√

[ (

⁄ )

]

[ (

)

]

√

⁄

Where it holds that h=2Ac/u=notional size of member in mm and the coefficients αas, αds1 and αds2 are dependent on the type of cement, see Table 3. Table 3 - coefficients dependent on type of cement

Type of cement according to EC 2 αas αds1 αds2

SL 800 3 0.13

N, R 700 4 0.12

RS 600 6 0.12

Due to the fast en relatively high autogenous shrinkage of HSC, combined with the drying shrinkage, pouring a concrete layer on top of an earlier poured layer will lead to complications. Even if the difference is as little as 2 hours between the different times of pouring [8]. Due to the cooling of the older layer, avoiding cracks is almost impossible. This brings some practical issues, regarding the SKK-beams. The pouring of a SKK-beam can be done in two different ways, being in one or two phases. One way (two phases) is with (inner) formwork inside the walls. When the concrete is hard enough, this formwork is removed and the deck will be poured on a slab of Polystyreen. The formwork can be used again for other beams, in contract to the other way. The other way (one phase) is to place a much bigger Polystyreen block inside the outer formwork, which will be there for the rest of its lifespan. In this method, the whole beam is poured in once. With HSC, only the last method is available, because the first method will probably lead to cracks between the different layers.

1.2.7.2. Creep

Creep deformation is the ongoing deformation of the concrete with constant stress. The total creep of concrete consists of the basic creep and the drying creep. According to [3], it can be stated that:

the basic creep is comparable for NSC and HSC

the drying creep is reduces for HSC compared to NSC

creep rate is significantly lower for HSC

the shape of the time-development function of the total creep deformation of HSC is similar to that of basic creep of NSC.


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From the above is, similar to the shrinkage deformation, assumed that the total creep deformation is equal for HSC and NSC. The creep coefficient ϕ(t,t0) may be written as:

Where ϕ0 is the notional creep coefficient and βc(t,t0) is the coefficient to describe the development of creep with time. They may be determined by

With

( ⁄

√ ⁄

)

√ ⁄

where

(

)

and

(

)

with

[ ( ⁄ )

] ⁄

and

(

)

(

)

(

)


t = age of concrete [days] at the moment considered

t0 = age of concrete at loading

t0,T = age of concrete at loading adjusted according to the concrete temperature

α = coefficient which depends on the type of cement; α-1 for slowly hardening cement, α=0 for rapidly hardening cement and α=1 for rapidly hardening high strength cement

1.3. Reference project With all the changed properties of HSC compared to NSC, it would be good to compare the dimensions and costs of the girders needed for a certain application in practice. To do this, a reference project will be discussed. In this reference project, concrete class C60/75 is used. To compare the dimensions, the bridge will also be designed in other concrete classes, being C90/105, C120/140 and C150/170. This will be done with the codes as mentioned above. The outcomes of the calculations will be compared to the corresponding values of the reference project.

1.3.1. A15 Veerwegviaduct

In 1938, the overpass Veerwegviadcuct was build. The Veerwegviaduct crossed the motorway A15 near Papendrecht. The main construction was made of 2 arches, with the slab of the bridge hanging to it. Due to changed regulations, which involves a higher traffic load, the Veerwegviaduct does not


9

comply anymore. Also advanced degradation due to chloride attacks were a reason of the abolition of the Veerwegbrug. That is why the old Veerwegviaduct will be removed and replaced by a new overpass. The new overpass will be called the “Witte brug Papendrecht” and will be constructed of SKK1300-beams. The construction will be statically determined and have a span of 41 m, as shown in Figure 7 and Figure 8. As can be seen, non-constructive arches will be build, which are esthetically comparable with the arches of the Veerwegviaduct.

Figure 7 - Longitudinal cross section of the Witte brug Papendrecht

Figure 8 - Transverse cross section of the Witte brug Papendrecht

1.3.2. Regulations

For the calculations of the Witte brug Papendrecht, the following building codes and regulations are used: Eurocode 0 – Basis of structural design - NEN-EN 1990 + NB Eurocode 1 – Actions on structures - NEN-EN 1991-1-1 + NB - NEN-EN 1991-1-2 + NB - NEN-EN 1991-1-3 + NB


10

- NEN-EN 1991-1-4 + NB - NEN-EN 1991-1-5 + NB - NEN-EN 1991-2 + NB Eurocode 2 – Design of concrete structures - NEN-EN 1992-1-1 + NB - NEN-EN 1992-1-2 + NB - NEN-EN 1992-2 + NB Additional regulations and documentation - ROK 1.2 - NEN 8005 - NEN 2889 - NEN 6722 - NEN-EN 1337-3 Other assumptions that were made:

Environmental class o Topside deck: XC4/XD3/XF4 o Left/right side deck: XC4/XD3/XF2 o Lower side deck: XC4/XD1/XF2

Time of reference: 100 year

Safety class: CC3

Humidity RV: 75%

Final camber due to 1.1*dead load: 1/2000 *L

Evenly distributed temp. component: maximum change -35/+30° C The used materials are

Concrete (after 28 days): C60/75

Concrete Joint: C35/45

Rebars: B500

Prestress steel FeP1860 Regarding the different stiffness’s in different directions, the following is used:

Longitudinal stiffness: uncracked composed beam

Transverse stiffness: uncracked joint (prestressed) and cracked walls

Torsional stiffness: 75% of uncracked stiffness beam

Transverse deformation: cross section prefab beam and joint For further assumptions, one is referred to Appendix A, which is the starting specification for this project.

1.3.3. Slenderness

As stated, the length of the Witte brug will be 41 meter and the construction will be built with SKK-1300 beams, which have a construction height of 1300 mm. This gives a slenderness of 31,5. The aim is to increase this slenderness by the use of HSC. Or in other words to decrease the construction height, but still be able to cope with the loads and associated deformations, both in SLS and ULS. Regarding the loads, they will remain the same. That is, the live loads will remain the same. The dead load can change, due to the changes dimensions of the construction.


11

List of references

[1] C. van Welij, "Prefab kokerbalken in voorgespannen vezelversterkt hogesterktebeton

(Vooronderzoek)," 2007.

[2] M. Pluis and K. Papampouklis, "High strength fibre cocnrete; influence of fibre content on tensile

strength," Koudekerk aan den Rijn, 2009.

[3] International Federation for Structural Concrete (fib), Constritutive modelling of high strength /

high performance concrete, 2008.

[4] BCA Sustainable Construction, "Design Guide of High Strength Concrete to Singapore Standard CP

65," 2008.

[5] NEN, Eurocode 2: Design of concrete structures - Part 1-1: General rules and rules for buildings,

2011.

[6] International Federation for Structural Concrete (fib), fib Model Code for Concrete Structures

2010, 2013.

[7] H. S. Müller, I. Anders, R. Breiner and M. Vogel, "Concrete: treatment of types and properties in

fib Model Code 2010," Structural Concrete, no. Volume 14, pp. 320-334, December 2013.

[8] VOBN, "Bruggen en viaducten in hogesterktebeton," Veenendaal, 2005.


A

Appendix A In this appendix, the starting specifications are included. In the starting specifications, all the made assumptions for the reference project are summarized and explained.

Spanbeton B.V. Ingenieursbureau Opdrachtnummer: 1306805 Omschrijving: Papendrecht, Veerwegviaduct over de A15 Documentnaam: B01 Pagina 2 van 13

Tabel 1: documenthistorie

Versie Status Datum Wijzigingen Opm. op drachtgever / hoofdconstructeur

1 Ter controle 21-01-2014

2 Definitief 31-03-2014 - Dikte schampkanten aangepast

- Belasting uit boogconstructie toegevoegd

Spanbeton B.V. Ingenieursbureau Opdrachtnummer: 1306805 Omschrijving: Papendrecht, Veerwegviaduct over de A15 Documentnaam: B01 Pagina 3 van 13 Inhoudsopgave

1. Algemeen 4

1.1 Opdrachtgever 4

1.2 Doel van het document 4

1.3 Opbouw van het document 4

1.4 Basis documenten 5

2. Omschrijving van de constructie 6

2.1 Geometrie van de dekken 6

3. prefab gerelateerde uitgangspunten 7

3.1 Fabricage 7

3.2 Mallen 7

3.3 Transport. 7

3.4 Montage en bouwfase. 7

3.5 Oplegmaterialen. 7

3.6 Detaillering 7

3.7 Programma’s t.b.v. berekening 7

3.8 Tekeningen 7

4. Normtechnische bepalingen 8

5. Uitgangspunten berekening 9

5.1 Gevolgklasse en partiële factoren 9

5.2 Milieuklasse 9

5.3 Materiaaleigenschappen 9

5.4 Schematisering en krachtsverdeling 10

5.5 Permanente belasting. 10

5.6 Veranderlijke belasting. 10 5.6.1 Verkeer 10 5.6.2 Temperatuur 11 5.6.3 Rem- en aanzetbelasting 11 5.6.4 Windbelasting 11 5.6.5 Aanrijdbelasting 11 5.6.6 Veranderlijke belasting tijdens montage 11

5.7 Vervormingen. 12

6. Overige uitgangspunten 13

6.1 Engineeringsoverzicht 13 6.1.1 Berekeningen 13 6.1.2 Tekeningen 13

6.2 Aandachtspunten en openstaande zaken 13


1. Algemeen

1.1 Opdrachtgever

Volker InfraDesign Postbus 525 3440 AM Woerden Tel.: 0348 – 435100 Fax.: 0348 – 435111 1.2 Doel van het document

Dit document heeft als doel de uitgangspunten vast te leggen voor de berekeningen en tekeningen van de liggers van het veerwegviaduct over de A15. Deze uitgangspunten zijn gebaseerd op de bestekstekeningen etc. (zie tabellen 1 en 2) die voor deze brug van toepassing zijn. Tevens zullen eventuele afspraken in de opdrachtbevestiging in dit document vermeld worden, aangevuld met prefab beton gerelateerde aandachtspunten. Het gaat om het vastleggen van: • dwarsdoorsnede dek: waaruit doorsnede type en hoeveelheid liggers worden afgeleid.

(zie hoofdstuk 2 “omschrijving van de constructie”). • Langsdoorsnede /plattegrond dek: overspanningen/ kruisingshoeken/wegindelingen etc.

(zie hoofdstuk 2 “omschrijving van de constructie”). • Belastingen + belasting situaties (normtechnisch opgelegd en/of voortkomend uit bestek) • Materialen van onderdelen van de bruggen. 1.3 Opbouw van het document

In paragraaf 1.4 worden de basisdocumenten genoemd die op dit werk van toepassing zijn. Dit kunnen bestekken, nota van inlichtingen, bestektekeningen etc. zijn. In hoofdstuk 2 volgt een korte omschrijving van de constructie: vastlegging van vorm, afmeting etc. In hoofdstuk 3 worden prefab gerelateerde aandachtspunten vermeld. Dit zijn punten die niet zozeer omschreven zijn in het bestek, maar wel voor prefab van toepassing zijn. Men kan hierbij denken aan fabricage, gebruik van mallen, transport, detaillering, gebruik van reken programma’s etc. In hoofdstuk 4 worden nadere bepalingen en eventuele afwijkingen genoemd ten aanzien van de van toepassing zijnde normen en/of bestek. Ten slotte zullen in hoofdstuk 5 punten behandeld worden die nog niet behandeld zijn in voorgaande hoofdstukken, extra aandacht verdienen of gemeld worden omdat daarover nog aanvullende informatie moet worden verstrekt. In bijlage 2 wordt een overzicht gegeven van de engineering criteria, waarin werkzaamheden en verantwoordelijkheden worden vastgelegd.

Spanbeton B.V. Ingenieursbureau Opdrachtnummer: 1306805 Omschrijving: Papendrecht, Veerwegviaduct over de A15 Documentnaam: B01 Pagina 5 van 13 1.4 Basis documenten

tabel 1: Documenten Documentnr. Omschrijving Versie Datum 4275-VWV-VGO-ON-001 Ontwerpnota Vergunningontwerp

Veerwegviaduct 2.0 12-12-2013

tabel 2: Tekeningen Tekeningnr. Omschrijving Versie Datum 4275-WHV-DO-TEK-020 Bovenaanzicht, lengteprofielen en situatie 1.0 22-11-2013 4275-WHV-DO-TEK-021 Dwarsprofielen en details 1.0 22-11-2013 4275-WHV-DO-TEK-022 Bovenaanzicht, vooraanzichten en

doorsneden 1.0 26-11-2013

4275-WHV-DO-TEK-023 Details 1.0 26-11-2013 4275-WHV-DO-TEK-024 Palenplan en fundatie 1.0 22-11-2013


2. Omschrijving van de constructie

- Het brugdek van het Veerwegviaduct bestaat uit 1 overspanning met een breedte van ca. 16,48 m. en een theoretische overspanning van ca 40,7 m. - De opleggingen zijn scharnierend; het dek is statisch bepaald. - Elementen: 9 stuks SKK middenliggers, afm. 1480/1300 mm, lang 41200 mm. 2 stuks SKK randliggers, afm. 1480/1300 mm, afschuining 980/500 mm, lang 41200 mm. - De kruisingshoek bedraagt 100g, 900 (haakse kruising). - De boogconstructie boven het dek werkt niet constructief mee. 2.1 Geometrie van de dekken

Dwarsdoorsnede

A B

Bovenaanzicht


3. prefab gerelateerde uitgangspunten

3.1 Fabricage

De liggers zijn voorgespannen met voorgerekte strengen. Productie volgens het zogenaamde lange bank systeem. 3.2 Mallen

De liggers zullen worden geproduceerd in een standaardmal uit het mallenbestand van Spanbeton. 3.3 Transport.

De verschillende situaties van “handling” tijdens ontkisten (incl. ontspannen), transport en montage worden beschouwd en zijn daarmee bepalend voor de keuze van de zwaarte en plaats van de hijsvoorzieningen. 3.4 Montage en bouwfase.

Tijdelijke voorzieningen t.b.v. de montage van de diverse elementen worden vastgelegd in de legplannen en in het montageplan. 3.5 Oplegmaterialen.

Oplegmaterialen worden berekend conform alle van toepassing zijnde voorschriften. In principe bestaat het oplegmateriaal uit staalplaat gewapende rubber oplegblokken. 3.6 Detaillering

Spanbeton zal zoveel mogelijk gebruik maken van de daartoe ontwikkelde standaarddetaillering van verbindingen tussen de diverse prefab elementen. 3.7 Programma’s t.b.v. berekening

Voor de berekeningen van de liggers wordt onder meer gebruikt gemaakt van: • Rekenprogramma Scia-engineer gebaseerd op de Eindige Elementen Methode t.b.v.

belastingspreiding. • Rekenprogramma ALP voor de liggerberekening van de elementen en voor bepaling

van de lange termijninvloeden. • Rekenprogramma Dbet voor de doorsnedeberekening van de elementen. • Rekenprogramma van Spanbeton in Excel t.b.v. prognose van vervormingen van de

voorgespannen liggers. • Rekenprogramma’s van Spanbeton in Excel voor detailberekeningen.

3.8 Tekeningen

Voor de elementtekeningen van de liggers zal zoveel mogelijk gewerkt worden vanuit de standaards van Spanbeton. Het tekenwerk wordt gedaan met behulp van AutoCAD en/of Tekla.

Spanbeton B.V. Ingenieursbureau Opdrachtnummer: 1306805 Omschrijving: Papendrecht, Veerwegviaduct over de A15 Documentnaam: B01 Pagina 8 van 13 4. Normtechnische bepalingen

De volgende normen zijn bij dit project van toepassing: Eurocode 0 - grondslagen - NEN-EN 1990 + NB Grondslagen van het constructief ontwerp Eurocode 1 – Belastingen op constructies - NEN-EN 1991-1-1 + NB Volumieke gewichten, eigengewicht en opgelegde

belastingen voor gebouwen - NEN-EN 1991-1-2 + NB Belasting bij brand - NEN-EN 1991-1-3 + NB Sneeuwbelasting - NEN-EN 1991-1-4 + NB Windbelasting - NEN-EN 1991-1-5 + NB Thermische belasting - NEN-EN 1991-2 + NB Verkeersbelasting op bruggen Eurocode 2 – Ontwerp en berekening van betonconstru cties - NEN-EN 1992-1-1 + NB Algemene regels en regels voor gebouwen - NEN-EN 1992-1-2 + NB Ontwerp en berekening van constructies bij brand - NEN-EN 1992-2 + NB Betonnen bruggen – Regels voor ontwerp, berekening

en detaillering Aanvullende normen en documenten - ROK 1.2 Richtlijnen Ontwerp Kunstwerken - NEN 8005 Nederlandse invulling van NEN-EN 206-1 - NEN 2889 Betonelementen. Maximaal toelaatbare maatafwijkingen

aangevuld met BELTON-toleranties. - NEN 6722 VB Uitvoering - NEN-EN 1337-3 Opleggingen voor bouwkundige en civieltechnische

toepassingen – Deel 3: opleggingen van elastomeren.

Spanbeton B.V. Ingenieursbureau Opdrachtnummer: 1306805 Omschrijving: Papendrecht, Veerwegviaduct over de A15 Documentnaam: B01 Pagina 9 van 13 5. Uitgangspunten berekening

5.1 Gevolgklasse en partiële factoren

Gevolgklasse volgens NEN-EN 1990 Bijlage B tabel B.1 NB: CC3 Ontwerplevensduur: 100 jaar Partiële factoren en combinatieregels volgen uit de tabellen in NEN-EN1990 bijlage A1. 5.2 Milieuklasse

Bovenzijde dek: XC4, XD3, XF4 Zijkant dek: XC4, XD3, XF2 Onderzijde dek: XC3, XD1, XF2 5.3 Materiaaleigenschappen

De volgende materialen worden in dit werk gebruikt : Zie Tabel 3 t/m Tabel 6.

Tabel 3 ; materiaaleigenschappen beton Beton Beton 1 Beton 2

Plaats materiaal prefab ligger voeg Sterkteklasse C60/75 C35/45

Cement Hoogovencement CEM III/B 52,5R

Hoogovencement CEM III/B 42,5 LH HS

W.C.F. 0,45 0,45 Poissonverhouding 0,15 0,15

Het standaard mengsel voor ‘Beton 1’ voldoet aan alle eisen die worden gesteld in CUR aanbeveling 89 (tweede, herziene uitgave): “Maatregelen ter voorkoming van betonschade door ASR”. Tabel 4: materiaaleigenschappen betonstaal. Betonstaal Betonstaal 1 Betonstaal 2 Betonstaal 3 Staalsoort B500B B500B B500B Toepassingsgebied Langswapening Beugelwapening Niet constructieve

wapening Tabel 5: materiaaleigenschappen voorspanstaal. Voorspanstaal Voorspanstaal 1 Voorspanstaal 2 Voorspanstaal 3 Staalsoort Y 1860 S7 Y 1770 C Y 1860 S7 Staaltype Streng Draad Streng Kenmiddellijn [mm] 15.7 4 12.5

Tabel 6; Toegepast materiaal Onderdeel Beton Betonstaal Voorspanstaal Prefab liggers 1 1/2/3 1 Overige gewapende beton 2 1

Op de materialen zijn de gestelde eisen in NEN-EN 1992 van toepassing al dan niet aangevuld met besteksmatig omschreven eisen.

Spanbeton B.V. Ingenieursbureau Opdrachtnummer: 1306805 Omschrijving: Papendrecht, Veerwegviaduct over de A15 Documentnaam: B01 Pagina 10 van 13 5.4 Schematisering en krachtsverdeling

De liggers worden geschematiseerd als statisch bepaalde liggers op twee steunpunten. De krachtenverdeling volgt uit een EEM berekening waarbij het dek als orthotrope plaat wordt ingevoerd. 5.5 Permanente belasting.

De volgende permanente belastingen worden in rekening gebracht. • Eigen gewicht constructie: ρ = 25 kN/m3 • Asfalt / afwerklaag: pEk = 1,1 · 0,17 · 23 = 4,3 kN/m2

(+10% onvoorzien) • Schampkant: pEk = 1,1 · 0,3 · 25 = 8,25 kN/m2

(+10% onvoorzien) • Leuning: qEk = 0,75 kN/m • Randelementen: qEk = 5,0 kN/m • Boogconstructie (4x): FEk,vert = 95 kN verticaal

FEk,hor = 171 kN horizontaal

5.6 Veranderlijke belasting.

5.6.1 Verkeer

• De veranderlijke verkeersbelasting op het rijdek wordt gevormd door de aanwezigheid van laststelsels volgens onderstaand schema, belastingmodel 1 uit NEN-EN 1991-2.

Verklaring (1) rijstrook nummer 1 : Q1k = 300 kN ; q1k = 9 kN/m2

(2) rijstrook nummer 2 : Q2k = 200 kN ; q2k = 2,5 kN/m2

[C1] (3) rijstrook nummer 3 : Q3k = 100 kN ; q3k = 2,5 kN/m2; tussenafstand assen in tandemstelsel = 1,2 m * Voor wl = 3,00 m


Positie Tandemstelsel TS Gelijkmatig verdeelde belasting (GVB)

Aslast Qik (kN) qik (of qrk) (kN/m2)

Rijstrook nummer 1 300 9 Rijstrook nummer 2 200 2,5 Rijstrook nummer 3 100 2,5 Overige rijstroken 0 2,5

Resterende oppervlakte (q rk )

0 2,5

• Oppervlakte contactvlak: 400x400 mm • De laststelsels worden geplaatst op de meest ongunstige plaats voor de liggers • αQ1 = 1,0, αq1 = 1,15, αqi =1,4 • Voor de indeling van de rijstroken wordt de volledige dagmaat tussen de leuningen

gebruikt, met een maximale afstand tot de rand van het brugdek van 1,4 m. • Voor locale effecten kan belastingmodel 2 uit NEN-EN 1991-2 maatgevend zijn. • Voor vermoeiing wordt uitgegaan van een hoeveelheid zware voertuigen van

0,125·106 per jaar (verkeerscategorie 3).

5.6.2 Temperatuur

• Gelijkmatige temperatuurcomponent met een wisseling van –25/+30 °C volgens NEN-EN 1991-1-5

• Temperatuurverschilcomponent volgens NEN-EN 1991-1-5, welke een opgelegde kromming in het brugdek tot gevolg heeft.

5.6.3 Rem- en aanzetbelasting

• Belasting volgens NEN-EN1991-2, art. 4.4.1 5.6.4 Windbelasting

• Belasting volgens NEN-EN1991-1-4 5.6.5 Aanrijdbelasting

• Een aanrijdbelasting wordt voor dit brugdek in rekening gebracht volgens NEN-EN1991-1-7, art 4.3.2

5.6.6 Veranderlijke belasting tijdens montage

• In de montagefase wordt gerekend met een veranderlijke belasting op de elementen van 1,0 kN/m2.

5.6.7 Veranderlijke belasting uit boogconstructie

De belasting die vanuit de boogconstructie op het dek wordt uitgeoefend is overgenomen uit de DO-berekening (nota 4275-VWV-DO-ON-001), bijlage CON-D


• Verticaal UGT perm+ver: FEd = 139 kN BGT perm+ver: FEk ≈ 139 / 1,35 = 103 kN Veranderlijk: FEk = 103 – 95 = 8 kN

• Horizontaal UGT perm+ver: FEd = 396 kN BGT perm+ver: FEk ≈ 396 / 1,35 = 293 kN Veranderlijk: FEk = 293 – 171 = 122 kN

NB. De horizontale belasting in dwarsrichting (tov het dek) komt voort uit de windbelasting op de boogconstructie en wordt in de berekening van het dek meegenomen door - in de berekening van de windbelasting - de constructiehoogte met 2m te vergroten. 5.7 Vervormingen.

• Opbuiging onder 1,1 · permanente belasting: minimaal 1/2000 · lth


6. Overige uitgangspunten

De hieronder genoemde punten zijn in het voorafgaande deel niet genoemd of worden nogmaals vermeld, vanwege hun belang of het zijn nog openstaande punten waarover nog aanvullende informatie door de opdrachtgever dient te worden verstrekt. 6.1 Engineeringsoverzicht

6.1.1 Berekeningen

• Krachtverdelingsberekening van het dek m.b.v. een eindige elementenprogramma Scia Engineer.

• Ligger- en doorsnedeberekeningen van alle te leveren prefab betonelementen en maatgevende doorsneden.

• Bepaling voorspanning in dwarsrichting. • Bepaling van de beugel- en langswapening behorende bij uitkomst van de

liggerberekening, • Berekenen van het benodigde oplegmateriaal.

6.1.2 Tekeningen

De volgende tekeningen zijn in de engineering inbegrepen: • Legplannen inclusief de details en oplegblokken • De vorm- en wapeningstekeningen van alle te leveren prefab elementen.

6.2 Aandachtspunten en openstaande zaken

- De boogconstructie heeft enkel een esthetische functie en werkt niet constructief mee in de krachtswerking van het brugdek.


Properties of High Strength Fiber Reinforced Concrete

Literature research - HSFRC


28-5-2014

Properties of High Strength Fiber Reinforced Concrete (literature research - HSFRC)

i


ii

Summary This report is the result of the literature research regarding High Strength Fiber Reinforced Concrete, which was conducted in preparation of the main study regarding the increase of the slenderness of SKK-beams (box girders) by the use of HSFRC. The SKK-beams are produced by Spanbeton. First of all, the mechanical properties of the material are qualitatively discussed. Due to the addition of fibers, the mechanical properties improve, in particular the tensile and shear behavior. The fibers will span the cracks and thus lead to a higher ultimate tensile stress or higher tensile strain capacity (ductility), depending on the fiber length and type which is used. Furthermore, the durability aspects are improved. To obtain the quantitative values of the mechanical properties, tests should be run to measure them directly. They cannot be obtained from other tests, due to the high variety of materials and the associated scatter and uncertainty. The tests methods are partly described in this report, for the remaining part one is referred to the relevant parts of the French regulations. A lot of different fiber types are available, in even more dimensions. The influence of these differences are discussed. The influence of the length determines the pre- and post-peak behavior. Short fibers will mainly cross the micro-cracks and thus leading to an improved pre-peak behavior, while longer fibers will mainly cross the macro-cracks and thus leading to an improved post-peak behavior. The latter will result in a more ductile material. The failure of the fibers can take place in two ways, being the pullout of the fibers and the rupture of the fibers. Rupture of the fibers is a brittle failure mechanism, in contrast to the pullout of fibers which is therefore the favorable failure mechanism. Pullout is prevented by two mechanisms, being the adhesion of fibers to the matrix and by friction of the fibers when they are gradually pulled out. When hooked ends are applied, the hooks have to be plastically deformed in order to be pulled out, leading to a higher pullout strength in comparison to “unhooked” fibers. The workability of the cement paste is negatively influenced by the addition of fibers. The main factors of the fibers which influence the workability are the percentage by volume of the fibers Vf and the aspect ratio of the fibers, being the length/diameter ratio. The fiber orientation in the cement paste can be influenced by the way of pouring. Fibers tend to align with the flow of the cement paste and, in certain areas, with the formwork. When calculations will be made, this fiber orientation should be taken into account. This is done by means of the K-factor, which should be determined from suitable test.


iii

Table of Content

Study to the properties of High Strength Fiber Reinforced Concrete ..................................................... 1

1. Introduction ................................................................................................................................. 1

2. Mechanical properties ................................................................................................................. 2

2.1. Building codes and Regulations ........................................................................................... 2

2.2. Safety factors ....................................................................................................................... 2

2.3. Compressive strength .......................................................................................................... 2

2.4. Tensile strength ................................................................................................................... 3

2.5. Shear strength ..................................................................................................................... 6

2.6. Young’s modulus ................................................................................................................. 7

2.7. Fatigue strength .................................................................................................................. 7

2.8. Creep and shrinkage ............................................................................................................ 8

2.9. Durability ............................................................................................................................. 9

3. Fiber type and properties .......................................................................................................... 11

3.1. Differences in fiber type .................................................................................................... 11

3.2. Fiber length ........................................................................................................................ 12

3.3. Pullout behavior ................................................................................................................ 12

4. Production aspects .................................................................................................................... 15

4.1. Workability ........................................................................................................................ 15

4.2. Dosing of the fibers ........................................................................................................... 15

4.3. Compacting ........................................................................................................................ 16

4.4. Fiber orientation ................................................................................................................ 16

4.5. K-factor .............................................................................................................................. 17

5. Conclusion ................................................................................................................................. 19

List of figures and tables.................................................................................................................... 20

List of references ............................................................................................................................... 21


1

Study to the properties of High Strength Fiber Reinforced Concrete In addition to the already performed study to the properties of High Strength Concrete (HSC), this study will focus on the material properties and other aspects of High Strength Fiber Reinforced Concrete (HSFRC). This material is sometimes referred to as High Performance Fiber Reinforced Concrete, due to its high overall performances, besides the strength. As an example of this high performance, the durability of the material can be used. In this report however, it is referred to as HSFRC.

1. Introduction As can be read in the already mentioned study, HSC has a cube compressive strength of at least 65 MPa. This has great advantages, but also comes with some disadvantages. One of the disadvantages is the brittle behavior of the material. This brittle behavior is caused by the fact that the values of the strains εc0d and εcud are close to each other, see Figure 1. εc0d will become somewhat higher, where εcud will become smaller. This can also be explained by means of the factor β, which is the ratio of the height of the net force divided by the total height of the stress diagram. This factor is for NSC the well-known 0.389, for HSC this becomes smaller (for C90/105 it holds that β=0.337). This makes sudden failure of the structure possible. This should be avoided at all times, so the material needs to be given more ductility. To give the material more ductility, fibers can be used. The fibers will be mixed with the other materials in the concrete mixer to form the cement paste. So the fibers are already inside the cement paste at the time of pouring. Approximately 1-2% of volume fibers will be added. HSFRC is not that new, there are already different types of HSFRC currently marketed:

the different kinds of Ductal® concrete, including RPC (reactive powder concrete), resulting from joint research conducted by Bouygues, Lafarge and Rhodia, and marketed in France by Lafarge

BSI/CERACEM® concrete developed jointly by Eiffage and Sika

BCV® concrete developed by the cement manufacturer Vicat and Vinci construction consortium.

CEMTEC-multiscale® concrete developed by LCPC (now IFSTTAR, the national highways laboratory in France) and used for a number of construction projects in Switzerland, Slovenia and Canada

CRC concrete manufactured by Aalborg Portland Cement (Densit) in Denmark.

Figure 1 - Stress-strain diagram for NSC (upper) and HSC (lower)


2

2. Mechanical properties So the material needs more ductility, to achieve a safe structure. Ductility is defined as the physical property of a solid material which measures how much strain it can withstand before rupturing. When the first cracks appear in the concrete and fibers are added and distributed over the cement paste, the fibers will span this first cracks. The fibers have a much bigger ductility, so the fibers are able to deform over a greater distance and still be able to transfer the tensile forces. In this way, the first, small, cracks will not grow with increasing force, but other small cracks will form at other places. In this way, the structure can cope with a bigger tensile load. Eventually, when the fibers are ruptured or pulled out, the structure will fail. But this is at a bigger tensile force and after a longer time of cracking. The elongation will be bigger, so the warning given by the structure will be bigger. In this way, a safe structure will be created.

2.1. Building codes and Regulations

When dealing with HSFRC, the Eurocode is not a helping tool. This is due to the fact that in the Eurocode fibers are not included, so no calculations are included concerning the added fibers. So other regulations will have to be used. A possibility of other regulations are the French regulations [1]. These regulations are based on more than fifteen years of experience in using structural HSFRC in real-life structures, and twenty years of laboratory research. In the French regulations, HSFRC is defined as follows: “Ultra High Performance Fibre-Reinforced Concrete are materials with a cement matrix and a characteristic compressive strength of more than 150 MPa and a maximum of 250 MPa” Most of the definitions and statements are based on [1], so in order not to be repetitive, the references are left out in this part.

2.2. Safety factors

In order to take into account disparity in fiber orientation due to placement, the design formulae given below include an “orientation coefficient” or the “factor” 1/K. For every application it should be checked whether the local or global value is to be taken into account. If the placement methods are validated by test results obtained for a representative model of the actual structure, the K-coefficient is determined using the same results but with a minimum value of 1. A K-value of less than 1 would assume that a beneficial preferential orientation effect in a given direction would be taken into account. The resistance of the structure in all the other directions in which the K values are generally greater than 1 (negative fiber orientation effect) would then need to be validated even if the said directions do not correspond to those of the principal loads. Before implementing the validation process, the designer can begin with the following K values:

Kglobal = 1.25 for all loading other than local effects

Klocal = 1.75 for local effects A partial safety factor, γcf, for fiber-reinforced concrete under tension has been introduced in ULS verifications in order to take manufacturing defects into account. The value is (AFREM rules) γcf=1.3.

2.3. Compressive strength

An indicative σ-ε relationship for HSFRC is given in Figure 2. The changed post-cracking behavior is clear to see. In compression, HSFRC exhibits elastic behavior over a large strain range. They then reach a maximum (fcm in mean stress, fck in characteristic stress). As for all concretes, after the peak,


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the strain is no longer uniform and the decrease in the stress observed after the peak corresponds to a structural effect. The decrease can be extremely sudden and dispersed if the fiber content is less than the recommended minimum. The design formulae given below include Ecm, which is shown in Figure 1. αcc is the coefficient that takes into account the long-term effects on the compressive strength and the negative effects resulting from the way in which the load is applied. The recommended value if αcc=0.85.

⁄

⁄

⁄

The following value of εcud can be used:

[ (

⁄ )]

Where fctfm is the maximum mean post-cracking stress in tension (which will be discussed in section 2.5) and fcm is the maximum mean stress in compression. The coefficient multiplying εc0d results from the analysis of numerous tests on fiber-reinforced HSC, based on the most pessimistic results.

2.4. Tensile strength

Like ordinary concretes, HSFRC exhibits elastic linear tensile behavior up to a limit value of fct,el

(mechanical resistance of the cement matrix modified to a greater or lesser degree by the presence of fibers), with the Young’s modulus being the same in both traction and compression. However, unlike ordinary concrete, the stress does not become nil after reaching this limit, due to the effect of the fibers. The tensile strength balanced by the fibers is translated into a stress σf, which is the force of all the fibers combined over the concrete area of the cross section. When the crack widens, the fibers gradually pull out, which decreases the apparent stress. In general their ultimate strength is reached due to lack of bonding and not because of fibers break, due to the high steel grade of fibers. The amount of fibers, their length and the aspect ratio (lf/df) lead to different types of tensile constitutive laws. Short fibers will mainly cross micro-cracks and thus influence the pre-peak behavior. When longer fibers are used, the post-cracking is influenced because these fibers will transfer tensile forces when the concrete is (visually) cracked, see Figure 3. The influence of the aspect ratio is harder to see at first sight. That is why it is explained by means of an example, where two different aspect ratios are used: (lf/df)1=100 (e.g 13/0.13) and (lf/df)2=10 (e.g. 30/3,which is extreme, but in this way the example is more clear). For 1 kg/m3 of fibers, 1.63*107 fibers are needed with aspect ratio 100. This amount is only 1.63*105 for aspect ratio 10. So with aspect ratio 100 there are a factor 100 more fibers inside the cement paste, however the total weight of the fibers does not change.

Figure 2 - Experimental compressive constitutive law of a HSFRC [1]


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Figure 3 - Function of long and short fibers [2]

So the constitutive laws depend on the amount of fibers, their length and the aspect ratio. However, each law is characterized by:

A linear elastic stage limited by a stress value fct,el

A post-cracking stage generally characterized by a stress-crack width σf-w law or a stress-strain σf-ε law. The stress σf is conventionally equal to the tensile stress of all the fibers combined divided by the surface area of the concrete.

Although sufficient mixing time and fairly traditional placement conditions ensure low scatter of the yield strength fct,el, the post-cracking strength contributed by the fibers, σf, depends to a large extent on the placement process of the HSFRC. This is mostly incorporated in the K-factor. For more information, see section 4.5. As stated, the fiber aspects influence the constitutive laws, especially the post-cracking behavior of the material. To indicate this graphically, Figure 4 is added. This figure gives indicative stress-crack opening diagrams. From now on, three types of HSFRC are distinguished (depending on the material, but also on the placement method using the K-factor):

Type 1: strain-softening fiber-reinforced concrete

Type 2: low strain-hardening fiber-reinforced concrete

Type 3: high strain-hardening fiber-reinforced concrete Type 1 corresponds to HSFRC whose average constitutive law is strain-softening. This type of material is characterized by the fact that the crack localized once the matrix strength is reached, when a tensile force is applied. It thus obeys an σf(w) law. Type 2 corresponds to HSFRC whose constitutive law is strain-hardening, but in terms of characteristic law and the K-factor taken into account, their constitutive law is strain-softening. Most of the HSFRCs currently on the market correspond to this type. For material characterization and design purposes, these HSFRCs will be treated like strain-softening HSFRCs. Type 3 corresponds to HSFRC whose characteristic constitutive law is strain-hardening, even after taken into account the K-factor. This is, the post-cracking peak remains higher than fct,el, which can only be achieved by a high fiber content. For this type, a mean strain constitutive law can be assumed rather than a crack width law. Characterization and tensile constitutive laws differ depending on whether the elements are thick or thin, where the limit between them is at thickness e=3·lf. For this report, only thick elements will be treated (e>3 lf). To find the constitutive laws (σ-ε relations), several tests should be performed for each type of HSFRC. This is, for now, outside the scope of this report. For the test methods and designs, one is referred to [1], annex 3 and 4.


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Figure 4 - constitutive law of HSFRC (strain-hardening on the left, low strain-hardening in the middle and strain-softening on the right)

For the sake of completeness, the σ-ε diagrams are shown, see Figure 5 and Figure 6. As stated, the values in the diagrams follow from tests.

Figure 5 - SLS (left) and ULS (right) laws for strain softening [1]

Figure 6 - SLS (left) and ULS (right) laws for strain hardening [1]

In here, the following relations hold:

at SLS

at ULS

at SLS

at ULS


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In here, w1%=0.01H with H being the height of the prims tested under flexure corresponding to the thickness of the structure. Furthermore, it holds that lc is called the characteristic length, lc=2/3h. To end and punctuate the above described, Table 1 is given which is obtained from [3]. In here, it is

clear to see the increments in the different strengths.

Table 1 gives the results of tests where the fiber volume was varied and compressive strength, splitting tensile strength and modulus of rupture was investigated. The compressive strength and splitting tensile strength were measured on cylindrical specimens of 150x300 mm. The modulus of rupture was investigated on a 150x150x530 mm beam. Table 1 - Strength test results and strength-effectiveness on HSFRC and HSC [3]

Fiber volume

fraction (%)

Compressive strength Splitting tensile strength Modulus of rupture

Measured (MPa)

Strength-effectivenessa

Measured (MPa)


Measured (MPa)


0 85 - 5.8 - 6.4 -

0.5 91 7.1 6.9 19.0 8.2 28.1

1.0 95 11.8 8.7 50.0 10.1 57.8

1.5 98 15.3 10.8 86.2 12.3 92.2

2.0 96 12.9 11.5 98.3 14.5 126.6 a Strength-effectiveness =

2.5. Shear strength

The following formula is used in the Eurocode for the maximum shear capacity:

which are the shear resistance of the plain concrete and the shear resistance of the shear reinforcement. In the case of HSFRC, the resistance of the fibers should be added:

The design value for the part of the shear capacity VRd,f provided by the fibers is given by


Afv=area of fiber effect (bw*z, with z being the inner lever arm)

σRd,f=the residual tensile strength of the fiber reinforced cross section

θ=the angle between the principal compression stress and the beam axis, where a minimum value of θ=30° is recommended

The value of σRd,f depends on the post-cracking behavior:

for strain-softening or low strain-hardening (type 1 and type 2) it holds

∫ ( )

where wlim=max(wu,wmax). wu is the ultimate crack width attained at the ULS for bending combined with axial forces, on the outer fiber, under the moment exerted in the section. wmax is the maximal admissible crack width.


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for strain-hardening (type 3) it holds

∫ ( )

where εlim=max(εu,εmax). εu is the ultimate strain attained at the ULS for bending combined with axial forces, on the outer fiber, under the moment exerted in the section. εmax is equal to εlim.

The value of both the integrals should be obtained from suitable tests, representative for the designed structure.

2.6. Young’s modulus

The material property that relates the amount of stress to the occurring strain is called the Young’s modulus. Materials with a high Young’s modulus deform little for high stresses. [1] states that there is no simple formula that links the Young’s modulus to the compressive strength and tests should be run to measure it directly. The fact that there is no simple formula linking the compressive strength and the Young’s modulus implies that there is a high influence of the different materials. Compared to NSC, HSFRC has a lot more materials, each with their own influences on the final material. A good and obvious example are the fibers, which come in numerous types. Each unique fiber type has a unique influence. Also the type of aggregate will play a significant role for the Young’s modulus.

2.7. Fatigue strength

Fatigue is a possible failure mechanism of a material when it is subjected to repeated loading. Fatigue cracks can be easily recognized in metals. However, unlike in metals, fatigue cracks cannot be distinguished from other types of concrete cracks. Therefore, fatigue of concrete was not recognized as a possible failure mode until the 70s [4], when damage was observed at a number of prestressed concrete bridges that was eventually attributed to fatigue. Since then, fatigue of concrete has been a research topic and fatigue models and design verifications have been proposed and implemented into concrete codes. According to [5], p119 and further, the fatigue resistance should be checked in case the structure is subjected to repeated loadings. These checks should be done for the concrete and rebars independently. The calculations should be based on a cracked cross section (no tensile stresses transferred by the concrete), but with compatibility of the different strains. The way of testing the designed values is via the well-known S-N curves. According to the national annex of [5], the following material factors should be used when calculating the fatigue strength of structural parts:

γc,fat=1.35 for concrete

γc,fat=1.15 for rebars

γc,fat=1.1 for prestressing strands

The design fatigue strength thus becomes

.

In the case of parts subject to fatigue, according to [1] the stress must be limited to min(fctm,el, fctfm) under frequent combinations, being the mean limit of elasticity under tension and the mean maximal post-cracking stress. In [4], the fatigue behavior of 4 HSFRC mixtures has been tested. The tests showed that there is a clear relation between the workability on the one hand and the scatter in static and fatigue behavior on the other hand. This highlights the effect of the fresh state properties on the material behavior in


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the hardened state. Moreover, it shows that it is not by definition the material with the highest material strength in static loading that will also have the best resistance in fatigue loading. A fiber count showed that even though a direct relation was found between the number of fibers in the critical cross-section and the flexural strength of the beam in static loading, such a clear relation was not found in fatigue loading. More parameters than the fibers alone are responsible for fatigue failure. Also, while in plain concrete the static load-displacement curve has been reported to function as an

envelope curve for fatigue displacements, this was not valid for the flexural tests of this study. Only

the mixture with the best workability showed an improved fatigue resistance in comparison with

plain concrete, while the other two mixtures had a comparable fatigue performance with plain

concrete. This shows that a good workability, which improves the homogeneity in the fiber

alignment, can significantly reduce the scatter in fatigue results. Due to the better fiber alignment,

the fatigue resistance is improved. A general conclusion derived from the fatigue tests of the

mixtures in this study, is that the fatigue regulations, as used for NSC, remain suitable for a safe

fatigue design with high and ultra-high strength concretes.

In [6], which is a research also done accompanied by Spanbeton, the following values for the fatigue strength have been used:

With

2.8. Creep and shrinkage

Creep and shrinkage are depending significantly on the curing of the cement paste, especially the heat treatment.

2.8.1. Heat treatment

The main effects of heat treatment are as follows:

Faster development of the concrete (compressive and tensile strength)

Reduction of delayed shrinkage and creep effects once the heat treatment is finished

Improvement of durability Two kinds of heat treatment are distinguished and can be applied independently of one another:

The first type is applied during the first few hours. Its aim is to anticipate the moment at which the HSFRC starts to set and accelerate the initial hardening. It is carried out at a moderate temperature. Experience shows that a temperature of less than 65° C avoids the risk of delayed ettringite formation.

The second type is applied when the concrete has hardened. Its aim is to develop new hydrates in order to further increase the mechanical strength of the cement matrix and reduce the delayed deformations. For this type of heat treatment, the components are taken to a relatively high level temperature (about 90° C) and to moisture content close to saturation a few hours after the concrete has set. In this case, the durability characteristics are improved and there is a significant decrease in the delayed deformations.


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The main effect of type two heat treatment are as follows:

The heat-treated components have reached their final maturity and can therefore be used without waiting 28 days or more as is the case with ordinary concretes.

The compressive and tensile strength after heat treatment is about 10% higher than the 28-day strength with storage in water.

Total shrinkage after heat treatment is zero.

Creep is significantly reduced: the creep coefficient is 0.2 instead of 0.8 without heat treatment.

Durability is improved due to a reduction in the porosity.

2.8.2. Shrinkage

In HSFRC, shrinkage is mainly endogenous, provided there is adequate moist curing during setting. Heat treatment, as described above, can be used to fasten up the process of shrinkage. In the case of a heat treatment of the first type, shrinkage partly occurs during heat treatment. In the case of heat treatment of the type 2, it is considered that there will be no further shrinkage once the treatment is finished. To illustrate this, Figure 7 is added.

Figure 7 - Example of shrinkage of a HSFRC with and without heat treatment [1]

2.8.3. Creep

The creep behavior of HSFRC is similar to the creep behavior of HSC, if there is no treatment. Heat treatment of the second type could considerably reduce the creep. In Appendix 7 of [1], a few examples are given from test results, with and without treatment of the second type. These examples show the positive influenced described above. Generally speaking, for structures sensitive to creep, a quantitative identification of the time-dependent deformation must be carried out according to the HSFRC chosen and its maturity during loading under representative conditions for the structure.

2.9. Durability

As stated, curing is of more importance for HSFRC compared to NSC. Special attention should be paid to the curing of HSFRC because of its very low or even non-existent bleeding. Construction joint should be systematically cured, particularly in order to prevent the concrete drying out before setting and micro-cracking during setting. When curing, among others, is done in a proper way the durability of HSFRC can be higher than NSC.


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According to [1], the durability of HSFRC structures or concrete structures in general depends on the following:

the transfer properties (porosity, permeability, diffusivity)

internal reactions relating to the specific components of the material which can develop not only within the material over the course of time, but also affect more subjective aspects such as appearance.

That is why the following four durability indicators have been kept:

water voids

permeability to oxygen

diffusion coefficient of chloride ions

portlandite content To determine the magnitudes of the above mentioned indicators, measurement methods are recommended or are the subject of standards, see [1]. In here, also measurements ranges are given. The results confirm that HSFRC have “very high” durability potential in relation to corrosion risks. This can be explained by their particular non-porous structure characterized by an absence of capillary porosity and non-interconnected porosity on a very small scale. As described in the study to HSC, the increased durability of the concrete have several advantages and can for example be used to decrease to concrete cover on rebars and prestressing strands.


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3. Fiber type and properties As extensively discussed, the fibers increase the mechanical properties of the concrete. But there are various types of fibers, all with different material properties. First thing to be noted here is that only steel fibers will be discussed. Besides the steel fibers, mineral, glass, polypropylene, basalt, carbon and more materials can be used. However, steel fibers are still most widely applied for concrete structures. The amount of fibers added is approximately 1-2% of volume. When more fibers are added, the workability of the mix will decrease rapidly. Fibers will agglomerate, leading to less flowability, fibers sticking around rebars and some parts of the beam will not have any fibers at all. So to avoid all these problems, limits should be set to the maximum amount of fibers. On the other hand, when an insufficient amount of fibers is added, the function of the fibers will disappear as well.

3.1. Differences in fiber type

The steel fibers are manufactured in different types. The main properties in which fibers differ to each other are:

the cross-sectional shape (circular, rectangular, square, see Figure 8 obtained from [7])

the length and diameter (see also the example in section 2.4)

the surface pattern (smooth, indented, crimped, with end hooks, see Figure 9 obtained from [7]).

Figure 8 - Cross-sectional shapes [7]

Figure 9 - Surface patterns [7]

Despite the wide variation, the fiber types that are distinguished more in the current literature are the short, straight, smooth fibers and the long, with end hooks, smooth fibers. An example of the first type is OL 13/.20. The O stands for straight shape, L for loose form of delivery and 13/.20 represents the aspect ratio (lf/df) which is the most important parameter with respect to the concrete’s properties, as discussed in the example in section 2.4.


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An example for the second type of fibers (long with end hooks) are the Dramix® products. The 3D, 4D and 5D differ from each other by the amount of end hooks or kinks, see Figure 10. The 3D-type has only 2 kinks, the 4D-type has 3 kinks and 5D has 4 kinks. The latter is designed in such a way that pullout of the fibers is not governing anymore, but rupture of the fibers is.

Figure 10 - Pullout test of the 3 different types of Dramix® [8]

3.2. Fiber length

As mentioned above, there are two main types of fibers; the short and straight fibers and the longer and hooked fibers. The short fibers will mainly cross the micro-cracks and thus influence the pre-peak behavior of the concrete, the longer fibers will cross the macro-cracks and thus influence the post-cracking behavior of the concrete. For this, see again Figure 3 for the differences schematically displayed in the concrete. A different way to look at this is by comparing the energy needed to bring the beam to failure. This energy can be calculated by determining the area below the stress-strain diagram. The short fibers give a higher peak in this diagram and thus increasing the energy needed to bring the beam to failure. However, the longer fibers give the beam a strain-softening or even strain-hardening behavior, leading to a much bigger increase in energy needed, due to the much higher strain at failure. To even further depict this, see Figure 11. The lower dashed line represent the type 1 and type 2 defined in section 2.4, the upper dashed line represent type 3.

3.3. Pullout behavior

When the tensile stresses in a fiber-reinforced concrete beam increase, cracks will form (comparable to NSC). Before this point, the added fibers will play no role in the transmission of forces. At the crack-formation stage, this will change. The fibers will cross the micro-cracks, thus when the micro-cracks form and increase in size, the tensile forces in the fibers will increase. These tensile forces have to be transmitted to the concrete matrix. This is done with two mechanisms:

Adhesion of fibers to the matrix

Friction of fibers when the fibers are gradually pulled out The pullout strength of the fibers depends on both mechanisms and both mechanisms can be increased separately of each other. At the start of loading the fiber is fully bonded with the surrounding concrete, so the adhesion is the only mechanism which will transfer the tensile force.

Figure 11 - σ-ε relation with different fibers amounts


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This adhesion bond is highly dependent on the quality of the material in the vicinity of the interface. As the pullout force increases, micro-cracks propagate along the fiber-matrix interface causing debonding. Actually, the debonding process occurs not directly on the surface of the fiber, but in a very small distance from the fiber. This follows from the fact that the strain energy is absorbed from the matrix, resulting from the accumulation of a weak calcium-hydroxide layer at the interface, due to inefficient packing of the cement particles [7]. When the adhesion strength is overcome, the only mechanism which prevents the fiber from being pulled out is the friction between the fibers and the matrix. This friction force can be increased in two ways:

increasing the roughness of the fibers (comparable to ribbed rebars)

adding hooks to the end of the fibers Increasing the roughness of the fibers leads to more friction between the matrix and the fibers. This is, as stated above, comparable to ribbed rebars. The use of ribbed rebars, compared to smooth rebars, leads to a smaller anchorage length, due to the higher friction between rebar and cement matrix. For fibers this leads to a higher pullout strength, for the same fiber length. Regarding the hooked ends, one is again referred to Figure 10, where the 3D, 4D and 5D fibers are shown of Dramix®. The pullout stresses are also shown, which clearly shows the influences of the differences between the types. 3D has only 2 kinks at each end, so only 2 places where plastic deformation should take place to overcome the mechanical interlock of the hook. With increasing type, the amount of kinks increase and thus the places where plastic deformation must occur before pullout will take place (assumed that rupture will not take place). So with every extra hook, the pullout strength increases significantly. Another failure mode is rupture of the fibers. This should be avoided, because it is a brittle failure mode. In high strength concrete, the higher matrix strength and the improved interfacial bond may lead to decreased toughness due to sudden fiber rupture rather than continuous frictional pullout. The way to avoid this brittle failure mode is to make sure that the pullout strength of the fibers is less than the rupture strength of the fibers. In this way, first pullout will occur, before the rupture of the fibers can take place. It must be noted here that the 5D type can be used when, on the contrary, pullout should be avoided and rupture should be the governing failure type. This is possible because another type of steel is used for the 5D type, with higher ultimate strength and higher toughness. For the sake of understanding the material and the act of forces, Figure 12 [2] is added regarding short fibers and Figure 13 [9] regarding long and hooked fibers. In Figure 12, the stresses in the fiber and concrete are shown. At the crack, the concrete tensile stress is obviously zero and the tensile stress in the fiber is at maximum. Further to the sides, the tensile stress in the fiber decreases, where the tensile stress of the concrete increases back to its original stress before cracking. This is, again, comparable to rebars, where such a stress pattern is also obtained at cracks. The shear stresses along the fiber-concrete interface are at the crack zero, and maximum just aside of the crack. This shear stresses transfer the tensile stress of the fiber to the concrete, by means of bond.

Figure 12 - Stresses in different parts near a crack [2]


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Figure 13 displays a typical fiber pullout curve for hooked fibers. Firstly, a very short debonding phase between fiber and surrounding matrix takes place. It is followed by a relatively longer phase during which plastic deformation in both curved parts (1 and 2 of stage a, see Figure 14) at the end of the fiber takes place. After that, the first part (1) is straightened and it moves in the mortar channel. The second part (2) has to be bent another time, at the place where part 1 used to be in the beginning (stage c). This corresponds to the second peak on the pullout curve, this time of course with relatively lower value of the pullout force. Afterwards, the hook is almost completely straightened, so the fiber can move through the original channel without much resistance, generating constant frictional stresses on the contact with the surrounding matrix (stage d).

Figure 14 - stages in the plastic deformation of the fiber hook [9]

In [9], which is the report of a single fiber pullout test from hybrid fiber reinforced concrete, the combination of long and short fibers is discussed. An increase of 40% of the average single fiber pullout forces was introduced by adding 4% by volume of short fibers OL 6/.16. The short fibers will cross the micro-cracks surrounding the long fibers and hereby increase the matrix strength in the vicinity of the long fibers. An additional 2% of OL 13/.20 did not result in any further improvement, due to the unsatisfactory workability.

Figure 13 - Typical fiber pullout curve [9]


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4. Production aspects Sufficient mixing time and fairly traditional placement conditions ensure low scatter in the properties of NSC and to a little lesser extent of HSC. Adding fibers to the concrete increases the possible scatter. However, there are possibilities to limit this scatter.

4.1. Workability

As already described in the study to the properties of HSC, the workability of concrete can be modified by various aspects:

the water/cement-ratio (or the water/binder-ratio)

the usage and amount of superplasticizer

types of aggregates used The w/c-ratio, among others, determines the strength of the matrix. Less water gives a higher strength, but less flowability of the cement paste. That is why for HSC superplasticizer is used, which increased the flowability by forming a film around the fine aggregates to prevent them from agglomerating. The flowability can also be increased by the usage of different aggregates. Round aggregates (e.g. fly ash) increase the workability the same way as ball-bearings do, due to their round profile. Another advantage of the fly ash is the fact that it gives a latent hydraulic reaction, which is a reaction that is very slow, thus not increasing the strength of the concrete after 28 days, but after various months. The maximum diameter of the aggregates also influences the workability. When the maximum diameter of the aggregates is small, a better workability and packing density is reached. This is the same for fibers. In [4], a value for the maximum fiber factor is obtained, for Dmax=4 mm:

This corresponds to for instance Vf=4.0% for aspect ratio 6/0.16. When this criteria is met, there are no big differences in workability. From this formula can also be seen that the amount of fibers influence the workability, due to the volume of fibers Vf. A higher amount of volume percentage must be accompanied with reduced length of the fiber Lf or increased fiber diameter Df. As already explained, better workability will lead to less scatter in the material properties. Furthermore, in [4] a direct relation is found between the workability of the cement paste and the fatigue behavior. This al leads to the obvious conclusion that the material properties of the viscous-liquid and solid phase are clearly related to each other.

4.2. Dosing of the fibers

The mixing of HSFRC is for the biggest part done in a conventional way. First dry mixing of aggregate and cement after which most of the water and the fine fillers are added. To increase the workability, the superplasticizer is added. So far the conventional way. After obtaining a flowable mix, the fibers are added. It is important to add the fibers in a meticulously way and to make sure that the fibers are not sticking together, but are loose from each other. This can be done by the use of a vibrating conveyer belt (e.g. Dramix® Booster, see Figure 15). Controlled adding of loosely vibrated fibers leads to an evenly distribution of fibers trough the matrix. After the fibers are added, the cement paste is mixed for an additional 2-3 minutes, to guarantee a homogeneous distribution of the fibers.


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Figure 15 - Dramix® Booster adding the fibers in a controlled way

4.3. Compacting

Compacting of concrete is conventionally done with industrial vibrators. The vibrators consolidate freshly poured concrete so that trapped air and excess water are released and the concrete settles firmly in place in the formwork. So the flowability is increased by means of vibrating the concrete. Vibration tables can also be used. Consequently, no industrial vibrators have to be used and thus the amount of labor is reduced. Another way of compacting concrete is by means of self-compacting concrete. For this type of concrete, the flowability is significantly higher, allowing the concrete to flow to the difficult to reach places by means of the self-weight. For HSFRC the compacting issues are even more important, because insufficient compacting leads to agglomeration of fibers around the rebars. In this way, the concerned fibers will not contribute. But perhaps even worse is the fact that due to the agglomeration of the fibers around the rebars, the bond of the rebars will be significantly reduced, leading to reduced efficiency of the rebars. Generally, more compacting is needed for HSFRC. This is due to the fact that the fibers need more compacting to evenly distribute around the matrix.

4.4. Fiber orientation

Any flow during concrete placement tends to align fibers in the direction of flow, due to the natural behavior of fibers in the viscous-liquid phase of concrete before setting. According to [4], this can be divided into the primary and secondary flow (see Figure 16 and Figure 17), which will not be further discussed here.

Figure 16 - Illustration of the fiber alignment due to primary and secondary flow [4]


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Figure 17 - Fracture surface of a tested beam and schematic representation of the fiber alignment in the cross section [4]

Fibers near formwork walls are naturally aligned parallel to the formwork. This only occurs when the distance from the formwork is less than or equal to the length of the fiber [1]. Thus, the closer the thickness of the structure to the dimension of the fibers, the greater the effect on the effective tensile strength of the parts will be. Preferential gravitational orientation can sometimes occur. In this light, it is useful to look at the SKK-beam and the pouring method. The pouring of the SKK-beam is done in the following way:

first the “bottom flange ” is poured, until the cement paste just rises above the bottom side of the inner formwork or PS-block. This is done for the whole beam.

after this, both the webs are poured simultaneously. During this process it is made sure that the cement paste of the bottom flange is in little movement. Otherwise, different layers could occur in the beam, leading to a weak spot in the concrete.

After this, the top flange is poured. Depending on the method, this is done directly after the pouring of the webs or a few hours later. For HSFRC this will most likely be the first method, because different layers are disastrous for HSFRC.

With this known, it is conceivable that the fibers in the bottom flange will be generally aligned in longitudinal direction. However, in the webs the fibers will be generally random or even also longitudinal, where it would be desirable to have a generally vertical aligned orientation.

4.5. K-factor

So the fiber orientation is influenced by the pouring direction. Fiber orientation is taken into account by the use of the K-factor. K-factors enable to represent distribution and orientation of fibers in the real structure, compared to a theoretical model where fibers would be randomly equally distributed and with an isotropic orientation. For thin plates or thick beams, it is necessary to determine the different global and local values of the K-factor. At the stage of suitability tests, the K-factors taken into account in the design stage of a project must be verified experimentally. In order to do this, several samples have to be taken from a mock-up at full scale, sufficiently representative of the structure and fabricated with the same material in the same conditions (in terms of formwork and casting process). Despite the fact that no general K-factor can be given here (because it should be obtained from tests), the edge effect can be discussed. Several effects can influence more or less the fiber orientation or the anchoring of the fibers located in the vicinity of the edge of a structure. The main edge effects are linked to the presence of a formwork, to the effect of a sawing or to the presence of a notch.


18

The fibers in the middle of a tested prism are not disturbed by the formwork. They are assumed to be distributed isotropically in 3D. The fibers located in the vicinity of a formed face (see Figure 18 [1]), that is to say these whose center of gravity is inside a lf/2 wide band along this formed face, are subjected to this edge or wall effect. A comparable phenomena is obtained for a sawn surface. Again, the fibers in the middle of a prism are not disturbed by the sawing and are assumed to be distributed isotropically in 3D. The fibers whose center of gravity is located inside a lf/2 wide band along the sawn surface are also distributed isotropically in 3D, but their length has been reduced by the sawing. It is therefore considered that a fiber whose center of gravity is on the sawn face is no longer anchored. Anchoring becomes fully effective only for fibers whose center of gravity is at lf/2 from the face. In the interval area [0; lf/2], it is assumed that the fibers are 50% effective.

An example of sawn specimens to determine the K factor in different directions is shown in Figure 19. This example is obtained from [1], where in Annex 6 more is explained about the determination of the K factor.

Figure 19 - Example of sawn specimens to determine the K-factor in different directions [1]

Figure 18 - Effect of formed surface and of a sawn surface [1]


19

5. Conclusion In this report, a literature research is done regarding High Strength Fiber Reinforced Concrete. This was done to prepare for the main study regarding the increase of the slenderness of SKK-beams produced by Spanbeton. In this report, the main mechanical properties of HSFRC are described, being the different design strengths and mechanical behavior (which follow from the French regulations). Due to the high uncertainty and scatter of the material, tests should be done to figure out the numerical values of the mentioned material properties. The way the tests should be done are partly described and partly one is referred to the relevant parts of the French regulations. The different types and associated mechanical properties of fibers are described. The most common type of fibers are the long, hooked fibers and the short, smooth fibers. The short fibers are mostly used to increase the pre-peak strength, in contrast to the long fibers which are used to increase the ductility of the material by increasing the strain capacity. This is due to the fact that the short fibers mainly cross the micro-cracks and the longer fibers will cross the macro-cracks. The act of forces at the moment of cracking is described, giving the different stresses of different parts. The tensile stress will, in the post-cracking stage, be transferred from the fibers to the concrete by means of adhesion and friction. It should be kept in mind that pullout of fibers is a ductile failure mechanism and thus preferable to the rupture of the fibers. The production aspects are influenced by the fibers. Addition of fibers will lead to a decrease in workability. To overcome this, additional superplasticizer can be added. Furthermore, longer mixing times are indicative for HSFRC. The fiber orientation inside the matrix is taken into account by means of the K-factor, which should be determined by suitable tests. By adjusting the pouring method, the fiber orientation can be influenced. The fiber orientation is also influenced by the surrounding formwork (so this only influences the fibers in the outer layers of the beam). Inside the area of a Lf/2 wide band, formwork alignment is to be expected. Last, but not least, the financial aspects of HSFRC are discussed. The aspects which increase the total costs of the HSFRC in comparison to NSC and HSC are described, partly based on the experiences of the Spanbeton staff. There are also positive influences on the costs. Moreover, the environmental impact of HSFRC is better than the environmental impact of NSC. The results of this report can be used to perform the main study, which will be the next step in the development of the total report. Particularly the mechanical properties will be of importance when calculations should be performed regarding HSFRC.


20

List of figures and tables Figure 1 - Stress-strain diagram for NSC (upper) and HSC (lower) .......................................................... 1

Figure 2 - Experimental compressive constitutive law of ....................................................................... 3

Figure 3 - Function of long and short fibers [2] ....................................................................................... 4

Figure 4 - constitutive law of HSFRC (strain-hardening on the left, low strain-hardening in the middle

and strain-softening on the right) ........................................................................................................... 5

Figure 5 - SLS (left) and ULS (right) laws for strain softening [1] ............................................................. 5

Figure 6 - SLS (left) and ULS (right) laws for strain hardening [1] .......................................................... 5

Figure 7 - Example of shrinkage of a HSFRC with and without heat treatment [1] ................................ 9

Figure 8 - Cross-sectional shapes [7] ..................................................................................................... 11

Figure 9 - Surface patterns [7] ............................................................................................................... 11

Figure 10 - Pullout test of the 3 different types of Dramix® [8] ............................................................ 12

Figure 11 - σ-ε relation with different fibers amounts .......................................................................... 12

Figure 12 - Stresses in different parts near a crack [2] .......................................................................... 13

Figure 13 - Typical fiber pullout curve [9] ............................................................................................. 14

Figure 14 - stages in the plastic deformation of the fiber hook [9] ...................................................... 14

Figure 15 - Dramix® Booster adding the fibers in a controlled way ...................................................... 16

Figure 16 - Illustration of the fiber alignment due to primary and secondary flow [4] ........................ 16

Figure 17 - Fracture surface of a tested beam and schematic representation of the fiber alignment in

the cross section [4] .............................................................................................................................. 17

Figure 18 - Effect of formed surface and of a sawn surface [1] ............................................................ 18

Figure 19 - Example of sawn specimens to determine the K-factor in different directions [1] ............ 18

Table 1 - Strength test results and strength-effectiveness on HSFRC and HSC [3] ................................. 6


21

List of references

[1] AFGC/SETRA, "Bétons fibrés à ultra-hautes performances – recommandations (Edition révisée),"

2013.

[2] I. Marković, "High-Performance Hybrid-Fibre Concrete; Development and Utilisation," 2006.

[3] P. Pong and S. Hwang, "Mechanical properties of hihg-strength steel fiber-reinforced concrete,"

ACI construction and Building Materials Journal, 2004.

[4] E. Lappa, C. Braam and J. Walraven, "High Strength Fibre Reinforced Concrete; Static and Fatigue

Behaviour," 2005.


2011.

[6] C. van Welij, "Prefab kokerbalken in voorgespannen vezelversterkt hogesterktebeton

(Vooronderzoek)," 2007.

[7] M. Pluis and K. Papampouklis, "High strength fibre cocnrete; influence of fibre content on tensile

strength," Koudekerk aan den Rijn, 2009.

[8] Bekaert, Brochure Dramix®; De toekomst versterken, Zwevegem, 2012.

[9] I. Markovich, J. van Mier and J. Walraven, "Single fiber pullout from hybrid fieber reinforced

concrete," Delft, 2001.

[10] Bekaert, Dramix® Booster; The safest and most productive way to dose Dramix® steel fibres,

Zwevegem, 2010.

[11] N. Nieuweboer, "Marktkansen van staalvezelbeton in prefab beton," 2011.


Increasing the slenderness of box girders by using HSFRC

Main Study


5-9-2014


i


ii

Table of Content 1. Introduction ..................................................................................................................................... 1

2. Slenderness reduction ..................................................................................................................... 2

2.1. Method of calculation ............................................................................................................. 2

2.1.1. SPAN-sheet ...................................................................................................................... 2

2.1.2. Assumptions .................................................................................................................... 3

2.1.3. Paradox ............................................................................................................................ 5

2.2. Constant section modulus ....................................................................................................... 6

2.2.1. Theory .............................................................................................................................. 6

2.2.2. Tables ............................................................................................................................... 6

2.2.3. Conclusions ...................................................................................................................... 8

2.3. Variable flange heights ............................................................................................................ 9

2.3.1. Unity checks..................................................................................................................... 9

2.3.2. H=1300 mm ................................................................................................................... 10

2.3.3. H=1200 mm ................................................................................................................... 11

2.3.4. H=1100 mm ................................................................................................................... 12

2.3.5. H=1000 mm ................................................................................................................... 13

2.3.6. Further decrease of construction height ....................................................................... 13

2.4. Conclusion ............................................................................................................................. 15

3. Shear force .................................................................................................................................... 16

3.1. Theory .................................................................................................................................... 16

3.1.1. Shear resistance ............................................................................................................ 16

3.1.2. Design force ................................................................................................................... 18

3.2. Method of calculation ........................................................................................................... 24

3.2.1. SPAN-sheet .................................................................................................................... 24

3.2.2. Loads .............................................................................................................................. 24

3.2.3. Checks performed ......................................................................................................... 24

3.3. Reference project .................................................................................................................. 26

3.3.1. Fatigue loading, cross-section at 0,5 m ......................................................................... 26

3.4. Configurations ....................................................................................................................... 28

3.4.1. H=1200 mm ................................................................................................................... 28

3.4.2. H=1100 mm ................................................................................................................... 29

3.4.3. H=1000 mm ................................................................................................................... 29

3.5. Conclusions ............................................................................................................................ 30


iii

4. Fibers ............................................................................................................................................. 32

4.1.Minimum ductility ....................................................................................................................... 32

4.2.French recommendations ........................................................................................................... 32

4.3.Test results .................................................................................................................................. 32

5. Conclusions and recommendations .............................................................................................. 35

5.1. Conclusions ............................................................................................................................ 35

5.2. Recommendations................................................................................................................. 35

List of reference ..................................................................................................................................... 37

List of figures and tables........................................................................................................................ 38

Appendix A .............................................................................................................................................. A

Appendix B .............................................................................................................................................. B

Appendix C............................................................................................................................................... C


1

1. Introduction This report builds on the already performed literature research to High Strength Concrete (HSC). It is performed during an internship at Spanbeton and serves (partly) as Master thesis, to finalize my study Civil Engineering at the department of concrete structures at the University of Technology of Delft. The goal of this study is to increase the slenderness of SKK-girders (box-girder) by adjusting the cross section of the girders and by making use of higher concrete classes. The reduction in construction height is achieved by decreasing the height of the web. The flange heights will be kept the same or will even be increased. The first chapter describes the way of how the slenderness reduction is achieved. First it was tried to decrease the construction height but at the same time keeping the same section modulus. This turned out not to be the right approach, so a different approach is used. The flange heights are increased in a piecemeal manner or are kept the same. By adding more prestressing it was made sure that no tensile stresses should occur. With this approach, an increase in slenderness is obtained. In the first chapter, shear force is not taken into account. This is done in the second chapter. The shear capacity of a girder will reduce when the construction height is reduced. This is due to the smaller internal lever arm z, which is approximately 0,9d for a box-girder, d is the effective depth of a cross-section. On the other hand, higher concrete classes and more prestressing will lead to a higher shear

capacity, but this is only for uncracked concrete. According to the Eurocode (Chapter 6.2) [1], for

cracked concrete the shear capacity of the concrete will reduce to nil and the stirrups must be

designed on the full load.

Higher concrete classes have one main disadvantage: they will become more brittle. This brittle behavior is dangerous, because brittle failure is a sudden failure. In other words, the construction will not give any warning before failure. To overcome the brittleness and give the concrete more ductility, steel fibers will be added to the concrete. This is described in chapter 4. Due to the added fibers, cracks will be bridged, so the first crack will not lead to failure. In this way, a higher level of safety is achieved. Note that the fibers can also be used to achieve other mechanical properties of the concrete, but this is not done in this report.


2

2. Slenderness reduction In this chapter, it is tried to reduce the slenderness of the girders by using a higher strength class. Shear capacity is not yet taken into account.

2.1. Method of calculation The calculations which are done to support this section are performed with SPAN-sheet, which is described below. The reduced slenderness will be compared to the slenderness of the girders of the already described reference project “A15 Veerwegviaduct”. In here SKK1300 girders (box girder with a construction height H=1300) were used to span 40,7 meter. This gives a slenderness of 31,3. These girders are calculated with the software of Alp and Dbet.

2.1.1. SPAN-sheet

SPAN-sheet is an Excel-program which is used to calculate the different girders of Spanbeton. It is based on the current regulations, being the Eurocode. The cross section of the girder must be given as input by the user. In order to do so, the girders is divided in different layers. For each different layer, the width and height must be given. When this is done correctly, SPAN-sheet produces and displays the cross section, see Figure 1.

Figure 1 - Cross section girder produces by SPAN-sheet

The strength class of the concrete must be specified by the user. The original SPAN-sheet is limited up to concrete class C90/105. The slenderness of girders can be reduced by, among others, increasing the concrete class. In order to do calculations with higher concrete classes, the concrete classes C120/140 and C150/170 are added. The different structural properties of these concrete classes are shown in Table 1. These properties are obtained from the already performed literature research to HSC. Table 1 - Mechanical properties of the added concrete classes

fck,cyl fck,cube fcm Ecm fctm fctk;0,05 fctk;0,95 εc2 εcu2 εc3 εcu3 α β

Concrete class

[MPa] [MPa] [MPa] [GPa] [MPa] [MPa] [MPa] [‰] [‰] [‰] [‰] [-] [-]

C120/140 120 140 128 48 6,71 4,70 8,73 3,00 3,00 3,00 3,00 0,500 0,333

C150/170 150 170 158 51 7,55 5,29 9,82 2,90 2,90 2,90 2,90 0,500 0,333


3

The loads on the girders are also input in SPAN-sheet. These loads, and the governing bending moments, are calculated with an FEM-method, e.g. SCIA Engineer. The loads and governing bending moments are assumed to be equal for changing cross sectional properties. An exception to this is of course the dead load of the structure. Due to the changed cross section, the amount of concrete changes and thus the dead load of the structure changes. Besides the input described above, more input can be given. Examples are the cement strength class, the used aggregates, the applied cover and the relative humidity. All the values of this mentioned input are kept constant compared to the reference project. The last part of the input is the amount of prestressing strands, including the distance from the bottom fiber zp. The amount of straight strands should be specified, with the associated height. Furthermore, also the amount of kinked strands should be specified, with the associated height and the associated places of the deviators. When all the input is given, SPAN-sheet will do calculations as prescribed in the regulations. The cross sectional properties (moment of inertia, center of gravity) are calculated, the losses in prestressing (e.g. relaxation) and losses due to creep and shrinkage are calculated. After this, checks are done regarding the different time moments (during pouring and tensioning of the prestressing strands, during storage and during the usage of the structure) and limit states (serviceability limit state and ultimate limit state). The checks are regarding the bending moment, associated stresses, the occurring camber and checks regarding the fatigue life of the girder. This latter check also takes account of the crack width control.

2.1.2. Assumptions

Regarding the calculations which are done with SPAN-sheet, assumptions were made. Some of these assumptions need elaboration. Assumptions have been made regarding the loads on the structure, regarding the mechanical properties and regarding the prestressing and reinforcement.

2.1.2.1. Loads on the structure

The different loads which are considered are:

Dead load of the girder

Dead load of the concrete topping

Static load

Variable load

Fatigue load The cross section of a typical SKK-girder is discontinuous. Every 5 to 6 meter, there is a part of the girder which has a solid cross section. But SPAN-sheet can only take into account one cross section, so a continuous cross section. In order to account for this, the density of the concrete have been multiplied by a factor 1,2, from ρc=24 kg/m3 to ρc=28,8 kg/m3. In this way, the dead load of the girder and the associated bending moment calculated with SPAN-sheet corresponds better to the dead load calculated by Alp (used for the calculations of the reference project). For changing cross sections, SPAN will now calculate the associated dead load, taking into account the solid cross section every 5 to 6 meter. However, the dead load of the concrete topping will also increase in this way because it is calculated with the same density. This is not correct, because the cross section of the concrete topping is continuous and thus does not need the increment by a factor 1,2. However, this load is significantly lower than the dead load of the girder, so this minor error is accepted.


4

The other loads are considered to be constant, despite changing cross sections. The loads are already calculated for the reference project, using a FEM-program. The values of the loads and associated bending moments are given below, see Table 2. To calculate the bending moments, an effective width of 1500 mm is considered. Note that the values in Table 2 are characteristic values. Table 2 - Used loads

Load [kN/m] Bending moment [kNm]

Static 7,08 2199

Variable 9,88 3069

Fatigue 4,77 1482

2.1.2.2. Mechanical properties

The concrete classes C120/140 and C150/170 are added. These concrete classes have different stress-strain relations, as is described in the literature research to HSC. The values for the strain at maximum compressive stress (εc3) and the maximum strain (εcu3) are equal. According to [2], the value is εc3=εcu3=3,00‰ for C120/140. Due to absence of values in literature for C150/170, this value is assumed to be εc3=εcu3=2,90‰. The time-dependent influences (creep and shrinkage) are assumed to be equal for the different concrete classes. Both the creep and the drying shrinkage will decrease slightly for higher concrete classes. However, note that the autogenous shrinkage can increase significantly. For this report, it is assumed that the total change in time-dependent influences is negligible. Also the increase in density is assumed to be negligible. For increasing strength classes, the density increases slightly. For example, the difference between C30/37 and C120/140 is 150 kg/m3

(ρc=2400 kg/m3 for C30/37 and ρc=2550 kg/m3 for C120/140 [2]). This increase is mainly due to the lower w/c-ratio.

2.1.2.3. Prestressing and reinforcement

Spanbeton only works with pre-tensioned prestressing. SPAN-sheet gives the possibility to include the prestressing strands in the calculation. To do so, the diameter of the strands and the height of the strands have to be specified. Kinked prestressing strands are also possible. However, unbonded strands are not possible. In the reference project, some unbonded strands are used. The main reason to use unbonded strands is when the tensile stress due to prestressing will become too high. This can happen close to the supports. Due to the prestressing strands, mostly located at the lower side of the girder, a negative bending moment leads to tensile stresses at the upper side of the girder, which can lead to cracks. These tensile stresses can be reduced by using unbonded strands, leading to a lower (negative) bending moment close to the supports. Further away from the support, the positive bending moment due to dead load will cause compressive stresses in the upper side of the girder, decreasing the risks of cracks due to tensile stresses. When unbonded strands are used for calculations in this report, one will be referred to this fact. When more prestressing strands are needed in order to meet the requirements, the height of the lower flange should be increased by 20 mm. In this extra amount of concrete, a third row of strands can be placed. The first row is at a height of 65 mm from the bottom fiber, the second row at 90 mm from the bottom fiber and the newly added row will be at 115 mm from the bottom fiber. In this way, the minimum cover requirements are met. SPAN-sheet also gives the possibility to add reinforcement in longitudinal direction. These reinforcement bars will be located in the upper flange, to distribute the axle load of vehicles. The reinforcement will be in compression, but due to the higher Young’s modulus it will contribute a little


5

bit when the moment capacity is considered. However, this positive influence is not used in the calculation. Transverse reinforcement is not possible in the used SPAN-sheet. To calculate the shear capacity, other programs are used. This will be the next step in this study, to perform shear checks.

2.1.3. Paradox

As stated, the reference project is calculated with Alp and Dbet. From these calculations followed a certain composition with a construction height of 1300 mm, an upper flange height of hu= 170 mm, a lower flange of hl=140 mm and 62 prestressing strands. When the exact same input is used for SPAN-sheet, the unity check for the bending moment capacity is 1,04, so it does not meet the requirements. When the calculation was regarded in detail, it turned out that the bending moment capacity was reduced. This follows from [1], which states (6.1 [C1]): “In parts of cross-sections which are subjected to approximately concentric loading (e/h < 0,1), such as compression flanges of box girders, the mean compressive strain in that part of the section should be limited to εc2 (or εc3 if the bilinear relation of Figure 3.4 is used).” However, the stated programs (Alp and Dbet), also make use of these regulations if the input is correctly given. So it could be possible that the input was not correctly given. On the other hand, Alp and Dbet are using more detailed calculations. Therefore it may be possible that the used configuration does meet the requirements. For the upcoming calculations regarding other configurations, different unity checks were done. When a unity check was higher than 1, the girder was assumed to be not sufficient.


6

2.2. Constant section modulus In this section it is tried to increase the slenderness, but keeping the section modulus constant.

2.2.1. Theory

When the height of the girder is decreased, the moment of inertia decreases even faster, according to the following formula

When more material is located at the outer sides of the cross section, the moment of inertia increases according to the Steiner-theorem. So by increasing the height of the flanges, the moment of inertia can be kept constant for lower construction heights. The limit for this approach gives a solid cross section instead of a box girder. The stress in the outer fiber of a cross section due to a bending moment, can be determined when the section modulus is known. The section modulus can be calculated by dividing the moment of inertia by the distance of the outer fiber to the center of gravity. So one cross section has two section moduli, Wupper and Wlower. The stress in the outer fiber can now be calculated using the following formula

So when the loads are constant and the section modulus is constant (despite the lower construction height), the stresses are constant and the concrete classes thus meet the requirements.

2.2.2. Tables

So in order to have a constant section modulus, the height of the flanges are increases for decreasing construction height. There are three possibilities:

Wupper is kept constant

Wlower is kept constant

Wupper and Wlower is kept constant Below a few tables are given for different construction heights. The height of the flanges are given, the moment of inertia, the different section moduli and the cross sectional area Ab. The latter is important for the weight of the girder. Higher weight brings higher transportation costs, besides the higher costs for more concrete. On the following line in the tables, the percentages of the different properties are given, compared to the original. This “original” is referring to the reference project, the properties of this girder are given in Table 3. Table 3 - Mechanical properties of original girder

Construction height [mm]

Height lower flange [mm]

Height upper flange [mm]

I [mm4]

Wlower [mm3]

Wupper [mm3]

Cross sectional area Ab [mm2]

1300 140 170 1,77E+11 2,64E+08 2,82E+08 7,73E+05

100% 100% 100% 100% 100% 100% 100%

2.2.2.1. H=1200 mm

The following three tables are concerning a construction height of 1200 mm. In these tables can be seen by how much the height of the flanges should be increased in order to keep a constant section modulus. For instance, for a construction height of 1200 mm and to have a constant upper section modulus Wupper, the height of the upper flange should be increased by 60 mm, which corresponds to an increase of 135%


7

Table 4 - H=1200 mm and Wlower constant




I [mm4]

Wlower [mm3]

Wupper [mm3]


1200 190 170 1,56E+11 2,65E+08 2,54E+08 8,01E+05

92% 136% 100% 88% 100% 90% 104%

Table 5 - H=1200 mm and Wupper constant




I [mm4]

Wlower [mm3]

Wupper [mm3]


1200 140 230 1,53E+11 2,35E+08 2,78E+08 8,09E+05

92% 100% 135% 86% 89% 99% 105%

Table 6 - H=1200 mm and both Wupper and Wlower constant




I [mm4]

Wlower [mm3]

Wupper [mm3]


1200 175 213 1,60E+11 2,59E+08 2,75E+08 8,31E+05

92% 125% 125% 90% 98% 98% 107%

2.2.2.2. H=1100 mm

These tables are also given for a construction height of 1100 mm.

Table 7 - H=1100 mm and Wlower constant




I [mm4]

Wlower [mm3]

Wupper [mm3]


1100 280 170 1,33E+11 2,65E+08 2,23E+08 8,75E+05

85% 200% 100% 75% 100% 79% 113%

Table 8 - H=1100 mm and Wupper constant




I [mm4]

Wlower [mm3]

Wupper [mm3]


1100 140 510 1,28E+11 2,05E+08 2,72E+08 1,09E+06

85% 100% 300% 72% 78% 96% 141%

Table 9 - H=1100 mm and both Wupper and Wlower constant




I [mm4]

Wlower [mm3]

Wupper [mm3]


1100 245 340 1,47E+11 2,57E+08 2,77E+08 1,02E+06

85% 175% 200% 83% 97% 98% 132%

2.2.2.3. H=1000 mm

These tables are also given for a construction height of 1000 mm.

Table 10 - H=1000 mm and Wlower as high as possible




I [mm4]

Wlower [mm3]

Wupper [mm3]


1000 560 170 1,06E+11 2,36E+08 1,91E+08 1,17E+06

77% 400% 100% 60% 89% 68% 151%

Table 11 - H=1000 mm and Wupper as high as possible




I [mm4]

Wlower [mm3]

Wupper [mm3]


1000 140 510 9,97E+10 1,78E+08 2,27E+08 1,06E+06

77% 100% 300% 56% 67% 80% 137%


8

Table 12 - H=1000 mm and both Wupper and Wlower as high as possible




I [mm4]

Wlower [mm3]

Wupper [mm3]


1000 455 545 1,21E+11 2,44E+08 2,39E+08 1,44E+06

77% 325% 321% 68% 92% 85% 186%

For a construction height of H=1000 mm, it is not possible to modify the cross section in such a way that constant section moduli are found. As can be seen from Table 12, for a solid cross section the values of Wlower=92% and Wupper=85% are reached.

2.2.3. Conclusions

As can be seen from the last column of the tables above, the cross sectional area Ab increases rapidly for lower construction height and constant section modulus. For example, for a construction height of H=1100 mm and constant upper section modulus Wupper, the cross sectional area Ab increases with 41%, from 7,73·105 mm2 to 1,09·106 mm2. As stated, it is not possible to keep the section modulus constant for a construction height of H=1000 mm. However, even when it is possible to keep the section moduli constant, the girders do not meet the requirements. This is due to the fact that the dead load of the girder is responsible for almost 50% of the total load on the girder. So when the dead load, or in other words the cross sectional area Ab, increases with 10%, the total load increases with 5%. In most of the cases this already leads to insufficient bearing capacity of the girder. This is the reason why it is chosen not to continue with constant section moduli. Instead, lower section moduli with lower dead loads are chosen. This is elaborated in the next section.


9

2.3. Variable flange heights It is found in the previous section that the flanges should not be increased too much. A big increase in flange height leads automatically to a big increase in dead weight, which leads to too high bending moments. Therefore it is chosen to experiment with flange heights in SPAN-sheet. It is determined, for different configurations, whether the girder meets the requirements or not. Or in other words: if all the unity checks are less than 1. When they are not, the concrete class is increased to determine the influence of this on the unity checks. The new concrete classes which are checked are:

C90/105

C120/140

C150/170

These higher concrete classes have, as explained in literature research to HSC, a much higher compressive strength. Due to this fact, a higher prestressing force can be applied. This is necessary to overcome the tensile stresses, which should (mostly) be avoided, because the tensile strength does not increase proportionally to the compressive strength. In the original girder, some tensile stresses did occur. The way the tensile stress is checked at SPAN is by means of a limit which is set for the maximum increase in tensile stress at the height of the prestressing strands. For this project, the requirement was that no tensile stresses did occur at the height of the prestressing strands for the SLS load combination (dead load, static load and the live load multiplied with a transient load factor of 0,8). This implies that little tensile stresses can occur at the lowest fiber, but these stresses will not be higher than the tensile strength of the concrete. By adding more prestressing strands, this requirement can be met for lower construction heights. Due to lower construction heights, the tensile stress will increase. To overcome these tensile stresses, more prestressing strands will be added. On the other hand will the compressive stresses also for lower construction height, and adding more prestressing force will only increase it further. This is where the increased compressive strength proves to be useful.

2.3.1. Unity checks

SPAN checks various aspects of the girder. First of all, it is made sure that the requirement on tensile stress, as described above, is met. Next check which is made is the bending moment capacity in the ultimate limit state. The governing load combination (ULS) gives a certain bending moment. If this bending moment is lower than the bending moment capacity of the girder, the unity check will be less than 1. These checks are performed for different configurations (flange heights, concrete class) and different construction heights:

H=1200 mm

H=1100 mm

H=1000 mm

After the bending moment capacity, the compressive stresses at 2 different load combinations are checked, which are both SLS checks. First combination is at the instance when the prestressing force is applied, which is after 16 hours of casting. The concrete does not have its full strength yet, but the full prestressing force is applied and the dead load will also lead to compressive stresses in the upper part of the girder. It is made sure that the compressive stress in this stage does not exceed 0,70*fckp ( [1], 5.10.2.2 of EC 2), with fckp=40 MPa for all concrete classes. This is not correct, because for higher concrete classes the strength after 16 hours will be (much) higher. The other load combination is when all the loads are applied. At this combination, the governing


10

compressive stress will be in the top fiber. At this time, the compressive strength of the concrete is fully developed. Besides the stresses, the camber of the girder is checked. According to [3], the camber due to the prestressing force and 1,1 times the static load should at least be 1/2000 of the span, so at least 20,4 mm. Due to the increased prestressing force, the camber increases so this check will not lead to problems. However, due to the increased prestressing force, the camber can become unpractical high when no loads are applied. That is why the camber is checked at the moment when the concrete topping is not yet applied (approximately after 60 days, when the camber will be at its highest point). It should be noted here that the assumed strength at the instance of prestressing (fck=40 MPa) also influences the camber. A higher concrete class at the time of prestressing will lead to lower camber, because of the higher Young’s modulus that is already present. So again, the fck=40 MPa is a conservative approach. During the research, it was found that the fatigue life of the girder is never governing for the applied loads. In every configuration which was tested, the fatigue life was abundantly sufficient. This is, when the rules of the Eurocode are extrapolated to higher strength classes. As stated in the literature research to HSC, not much is known about the fatigue life of HSC. However, as a preliminary conclusion it can be stated that the specific values obtained from fatigue tests on HSC are of the same magnitude as obtained from tests on normal strength concrete, as long as the specific values are referred to particular values obtained in static tests. Because the fatigue life was abundantly sufficient with extrapolated rules, the check for the fatigue life is left out of the results, but this does not mean that this check was not performed. Summarizing, the following checks are performed for different configurations:

U.C. on bending moment

U.C. compressive stress for different stages

Highest and final camber is checked and the latter should not be less than 20,4 mm

2.3.2. H=1300 mm

As already described, the original cross section does not meet the requirements, i.e. does not have all unity checks less than 1. This can be seen from Table 13. In here, U.C. compressive stress 1 represents the stage after 16 hours, and U.C. compressive stress 2 represents the stage when all the loads are applied.

Table 13 - Unity checks original girder

Concrete class

U.C. bending moment

U.C. compressive stress 1


Final camber [mm]

Maximum camber [mm]

C60/75 1,06 0,75 0,70 48,8 134,5

The original amount of prestressing strands is 62 strands with diameter 15,7 mm. This gives a total area of prestressing steel of Ap=9300 mm2. 22 of those strands are at height zp=65 mm (measured from the bottom fiber) and 24 strands are at height zp=90 mm (measured from the bottom fiber). The other 16 strands are kinked, Table 14 gives the different heights of the kinked strands at the support and at midpoint. The distance between the deviators is set on 18250 mm.


11

Table 14 - zp of kinked strands

Amount of strands

zp,support [mm]

zp,midpoint [mm]

2 500 122

2 550 145

2 600 185

2 650 220

2 700 255

2 750 290

2 800 325

2 850 360

When not much additional prestressing strands are needed (this holds for construction height H=1200 mm), the additional prestressing strands will fit in the lower flange. When more prestressing strands have to be added (construction heights H=1100 mm and H=1000 mm), 20 mm of concrete will be added to the lower flange in order to be able to fit the prestressing strands in the lower flange. This gives a lower flange of 160 mm and the additional prestressing strands will be located at height zp=115 mm. To be able to do this, 20 mm of concrete will be added to the lower flange, so the height of the lower flange will be 160 mm.

2.3.3. H=1200 mm

In Section 2.2 was found that the height of the flanges should not be increased too much. That is why for the construction height of H=1200 mm 3 different configurations are checked. The first configuration with both flange heights the same height (hl=140 mm and hu=170 mm), the second configuration has an increased lower flange (hl=154 mm and hu=170 mm) and the third configuration has an increased upper flange (hl=140 mm and hu=187 mm). 5 additional prestressing strands should be applied in order to achieve no tensile stresses. The results of the considered configurations can be found in Appendix A. The first configuration did not meet all the requirements with concrete class C60/75. The bending moment capacity has lowered somewhat. This is due to the reduction in construction height of 100 mm, which goes to the power 3, as explained. On the other hand, not much concrete has been removed, so the dead load does not change that much. Furthermore, the mean compressive strain in the upper flange should be limited to εc2, according to 6.1 (5) of [4], as is discussed in Section 2.1.3. The compressive stress at the time the prestressing force is applied is sufficient. Because only 5 additional strands are applied, not that much additional compressive stress is initiated. However, when the concrete class is increased to C90/105, the girder does meet the requirements, as can be seen from Table 15. For higher concrete classes, εc2 goes up, so a higher mean compressive strain in the compression zone is applied. In this way a higher bending moment capacity is obtained. Table 15 - Unity Checks for hl=140 mm and hu=170 mm

Concrete class

U.C. bending moment



Final camber [mm]

Maximum camber [mm]

C60/75 1,20 0,85 0,78 62,1 166,5

C90/105 0,85 0,85 0,52 74,2 173,4

C120/140 0,78 0,85 0,39 74,0 167,3

C150/170 0,75 0,85 0,32 71,5 160,3


12

The use of even higher concrete classes lead to a lower unity check on bending moment (ULS) and compressive stress in the final stage (U.C. compressive stress 2, SLS). U.C. on compressive stress 1 does not become lower because the fckp=40 MPa is used for all concrete classes, as stated in Section 2.3.1. From Appendix A can be seen that increasing the lower flange will not lead to a higher bending moment capacity, but increasing the upper flange does increase the bending moment capacity because this gives a bigger area for the compression zone. Increasing the lower flange leads to lower compressive stresses, because the prestressing force can be divided over a bigger area. An increase in lower flange height leads to a lower camber, where an increase in upper flange height gives a higher camber. Both give a higher dead load, which should lead to a lower camber. But increasing the upper flange height brings the center of gravity upwards. Due to this, the bending moment due to the prestressing increases, which leads to a higher camber. The opposite holds for increasing the lower flange height. From the previous can be concluded that:

The unity check on bending moment can be lowered by increasing the height of the upper flange and by increasing the concrete class.

The unity check on maximum occurring compressive stress in the lower flange (due to prestressing and dead load only) can be lowered by increasing the height of the lower flange.

The occurring camber can be decreased by increasing the lower flange height.

2.3.4. H=1100 mm

Also for a construction height of H=1100 mm, 3 different configurations are checked. The first configuration has a lower flange of hl=160 mm (20 mm additional concrete in order to fit the additional prestressing strands) and an upper flange height of hu=170 mm. The second configuration has a lower flange height of hl=175 mm and an upper flange height of hu=170 mm and the third configuration has a lower flange hl=160 mm and an upper flange height of hu=187 mm. 14 additional prestressing strands should be added in order to avoid tensile stresses, which will be located at height zp=115 mm from the lowest fiber. The results of the considered configurations can be found in Appendix B. The first configuration has just enough bending moment capacity with concrete class C90/105, as can be seen from Table 16. The compressive strength is also sufficient (U.C=0,94), but again, the strength assumed at this time moment is 40 MPa. It can be seen that the unity check on compressive stress 2 decreases rapidly for higher concrete classes. This makes sense, because this stress is measured to the 28-days strength of the concrete. The same amount of prestressing strands were used for the different concrete classes. The camber is increased, compared to a construction height of H=1200 mm. This is due to the lower moment of inertia. Table 16 - Unity Checks for hl=160 mm, hu=170 mm

Concrete class

U.C. bending moment



Final camber [mm]

Maximum camber [mm]

C60/75 1,39 0,94 0,89 69,6 195,6

C90/105 0,94 0,94 0,60 83,7 203,5

C120/140 0,80 0,94 0,45 83,2 195,8

C150/170 0,75 0,94 0,36 80,1 187,3


13

For the influence of both flange heights holds the same as discussed in Section 2.3.3. A higher upper flange leads to a higher bending moment capacity, but also to a higher camber. A higher lower flange leads to a lower unity check on compressive stress and also to a lower camber.

2.3.5. H=1000 mm

Also for a construction height of H=1000 mm, 3 different configurations are checked. The first configuration has a lower flange of hl=160 and an upper flange height of hu=170 mm. The second configuration has a lower flange height of hl=175 mm and an upper flange height of hu=170 mm and the third configuration has a lower flange hl=160 mm and an upper flange height of hu=187 mm. 23 additional prestressing strands should be added in order to avoid tensile stresses. These additional strands will be located at height zp=115 mm from the lowest fiber. The results of the considered configurations can be found in Appendix C. For all 3 configurations, a concrete class of at least C120/140 was needed to achieve an unity check lower than 1 for bending moment. The unity check on compressive stress 1 is not sufficient, but this is with a compressive strength of 40 MPa. It is believed that concrete class C120/140 will have a higher compressive strength after 16 hours, so this unity check will also be below 1. From Table 17 can be seen that the camber will be high. The final camber, which is calculated for the loads prestressing and 1,1 times all the static loads (art. 16.9.3 of ROBK6 [3]). Table 17 - Unity Checks for hl=160 mm, hu=170 mm

Concrete class

U.C. bending moment



Final camber [mm]

Maximum camber [mm]

C60/75 1,65 1,10 1,02 97,9 257

C90/105 1,09 1,10* 0,68 114,9 266,3

C120/140 0,89 1,10* 0,51 113,2 255,5

C150/170 0,77 1,10* 0,41 108,3 243,9

*The assumed strength after 16 hours is 40 MPa. However, for higher concrete classes this will be (much) higher, so the unity checks will become below 1. When the camber is found to be too high for practical reasons, it can be lowered in 2 ways:

When the prestressing strands are higher, the camber due to the prestressing force will be lower. This can be achieved by placing the strands in the webs, whether or not kinked.

As found earlier, the camber can be reduced by using a higher lower flange. The additional weight ensures a lower camber. Besides that, the center of gravity lowers, so the bending moment introduces by the prestressing force will be lower, leading to a lower camber.

However, the abovementioned ways are no real solutions, because the bearing capacity of the girders will also reduce, along with the camber. For the influence of both flange heights holds the same as discussed in Section 2.3.3. A higher upper flange leads to a higher bending moment capacity, but also to a higher camber. A higher lower flange leads to a lower unity check on compressive stress and also to a lower camber. For comparison to Section 2.2, the section moduli (both upper and lower) of the configurations shown in Table 17 are around the 70% of the section moduli of the original configuration. This justifies the chosen changed approach.

2.3.6. Further decrease of construction height

Concluding from the above, the construction height can be reduced to 1000 mm instead of 1300 mm, when higher concrete classes are used and more prestressing is applied. The reached increase in


14

slenderness is 30% (from 31,3 to 40,7). The main advantage of this would be introduced by the boundary conditions of the project. When a big span and only a limited construction height could be used, more slender construction have to be used. Other advantages are introduced by the lower dead load, which results in lower hoisting power needed. Further decrease of the construction height is hardly possible. Due to the low construction height, there are many additional prestressing strands needed in order to achieve no tensile stresses in serviceability limit state. But due to these additional strands, the compressive stress at the instance that the prestressing is applied will become too high, also because the compressive strength is not that high after 16 hours. Next to the compressive stress which will not be sufficient, the occurring camber will become very high due to the additional prestressing strands. In this light, it should be mentioned that not every girder will experience the same camber. Even if the construction height and amount of prestressing are constant, different camber will be found for different girders. This has to do with the exact mix properties, exact time of prestressing, exact temperature conditions etcetera. When more prestressing is applied and thus a higher overall camber will be found, these (absolute) differences will also grow. On top of this will the use of HSC lead to bigger differences. With this known, it could be a conclusion that the camber, for a construction height of H=1000 mm, will become unpractical. Besides the practical issues, the costs aspects should be considered. When a lot of prestressing should be applied, a lot of steel is needed, which is expensive. Also higher concrete classes will lead to higher costs.


15

2.4. Conclusion Different tests and calculations have been carried out in order to find the influence of High Strength Concrete on the slenderness of SKK-girders. HSC has better mechanical properties compared to NSC, which allow higher compression stresses. Higher compression capacity is advantageous because more prestressing can be used before the maximum compressive stress is reached. The additional prestressing is needed in order to prevent tensile stresses to occur. First of all, it was tried to achieve a higher slenderness by reducing the web height, but at the same time increasing the heights of the flanges in order to keep a constant section modulus. This turned out not to be the right approach, because the increase in flange heights entails a too high increase in dead load. Due to this increases dead load, the constant section moduli were not sufficient anymore. Therefore it was tried to achieve a higher slenderness by increasing the height of the flanges in a piecemeal manner. The general conclusions for increasing the flange heights are:

The unity check on bending moment can be lowered by increasing the height of the upper flange.

The unity check on maximum occurring compressive stress in the lower flange (due to prestressing and dead load only) can be lowered by increasing the height of the lower flange.

A significant increase in slenderness was achieved. The slenderness of the original girder was 31,3 (40,7/1,3) and the highest slenderness was reached for a girder with construction height H=1000, so a slenderness of 40,7. This is an increase in slenderness of 30%. To achieve this increase, use should be made of higher concrete classes. For a construction height of H=1200 mm and H=1100 mm, concrete class C90/105 should be applied. For a construction height of H=1000 mm, concrete class C120/140 should be used. Furthermore, additional prestressing strands should be added, up to 23 additional strands for a construction height of H=1000 mm, see Figure 2. This is accompanied with a decrease in cross sectional area of almost 10%.

Figure 2 - Amount of prestressing for different construction heights

The bending moment is the governing failure mechanism. This is, among others, due to the limited mean compressive strain according to 6.1 [C1] of Eurocode 2. In this way, not enough compression force can be provided. In addition to the conclusions above, it should be noted that all the examined girders are not yet checked on shear capacity. This will be done in the next chapter.

6000

7000

8000

9000

10000

11000

12000

13000

14000

1300 1200 1100 1000Am

ou

nt

of

pre

stre

ssin

g A

p [m

m2 ]

Construction height H


16

3. Shear force In this section, the shear capacity of the “new” girders is discussed.

3.1. Theory When the design shear force VEd is less than the shear resistance, the girder will have sufficient shear capacity. The design shear force VEd consists of two parts: the pure shear force and the shear force due to torsion.

3.1.1. Shear resistance

In Eurocode 2, Chapter 6.2 [1] the following symbols are defined regarding the shear resistance of a concrete member:

VRd,c is the design shear resistance of the member without shear reinforcement.

VRd,s is the design value of the shear force which can be sustained by the yielding shear reinforcement.

VRd,max is the design value of the maximum shear force which can be sustained by the member, limited by crushing of the compression struts.

So when the design shear force VEd is less than VRd,c, no shear reinforcement is needed. The shear resistance of the concrete member without shear reinforcement can be calculated using

[ ( ) ]

With a minimum of

[ √ ]

Where coefficient taking into account longitudinal reinforcement, recommended value

aa ⁄

√

, Asl is the area of the tensile reinforcement and bw is the smallest width

of the cross-section in the tensile area coefficient taking into account prestressing, recommended value k1=0,15

⁄ , NEd is the axial force due to loading or prestressing

When the shear resistance of the concrete member alone is not enough, shear reinforcement should be applied. The design of members with shear reinforcement is based on a truss model, see Figure 3 [1].

Figure 3 - Truss model and notation for shear reinforced members [1]


17

In Figure 3 the following notations are shown: α angle between shear reinforcement and the beam axis perpendicular to the shear

force. θ angle between the concrete compression strut and the beam axis perpendicular to

the shear force. The value of θ should be limited: 21,8°≤θ≤45. z inner lever arm, as discussed in the Introduction.

The shear resistance of concrete members with vertical shear reinforcement is defined as

( )

Where: Asw cross-sectional area of the shear reinforcement s spacing of the stirrups fywd design yield strength of shear reinforcement However, VRd,s is limited by the value of VRd,max. VRd,max gives the shear force at which the compression struts will fail due to too high compressive stress. VRd,max is defined as:

( ) ( )

Where: αcw coefficient taking account of the state of stress in the compression chord ν1 strength reduction factor for concrete cracked in shear The recommended value of αcw is as follows: αcw =1 for non-prestressed structures

αcw =

⁄ for 0 ≤ σcp ≤ 0,25·fcd

αcw =1,25 for 0,25·fcd ≤ σcp ≤ 0,5·fcd

αcw = (

⁄ ) for 0,5·fcd ≤ σcp ≤ fcd

This indicates that adding prestressing results in an increase in VRd,max, so adding prestressing will help to prevent the concrete compressive strut to fail. However, αcw is not included in the formula of VRd,s, which will be (in most cases) the governing value of the shear resistance. Thus, adding prestressing will (in most cases) not result in a higher shear resistance. The recommended value of ν1 is:

[

]

With increasing strength class, ν1 decreases. For example, for fck=90 MPa ν1=0,384. At a certain point, the strength reduction due to ν1 will be bigger than the increase due to the higher concrete class. This point is around strength class C120/140, as can be seen from Figure 4. For concrete classes higher than C90/105, the Eurocode is not valid anymore. As described in previous parts of this report, the Model Code [5] will be used in this case. In here, VRd,max is defined as:

( ) ( )

Where the strength reduction factor kc consists of two parts: the state of strain in the webs of beams is taken into account by kε, the effect of more brittle behavior of concrete of strengths greater than 30 MPa is considered in ηfc. The latter is defined as:


18

( )

The influence of kc is also graphically shown in Figure 4, where kε=0,65 is used. It can be seen that the Model Code is, as earlier concluded, more “high strength friendly”.

Figure 4 - Influence of ν1 (EuroCode) and kc (Model Code)

3.1.2. Design force

As stated, the design shear force consists of two parts, being the pure shear force and the shear force introduced by torsion in the cross-section. Both individual parts should be summed to get to the design shear force.

3.1.2.1. Pure shear

All vertical loads on the girder will introduce shear forces. Distributed loads will lead to a linearly varying shear force diagram, while a “point load” gives jumps in the shear force diagram. Kinked tendons will also introduce a shear force. The shear force will be introduced at the deviators, where the kink of the tendon is located. The value of the shear force introduced at the deviator depends on the angle at the deviator and the value of the prestressing force Fpw.

3.1.2.2. Torsion

Torsion will also introduce shear forces in different parts of the box girder. The shear stress due to torsion depends on the value of the torsional moment and the area of the cross-section:

The shear force VEd,i in a wall i due to torsion is given by (see also Figure 5):

Where: τt,i torsional shear stress in wall i

tef,i effective wall thickness,

A total area of the cross-section within the outer circumference, including inner hollow areas

u outer circumference of the cross-section


19

TEd applied design torsion Ak area enclosed by the center-lines of the connecting walls, including inner hollow

areas zi side length of wall i defined by the distance between the intersection points with the

adjacent walls

Figure 5 - Notations and definitions concerning torsion [1]

The maximum resistance of a member subjected to torsion and shear is limited by the capacity of the concrete struts. In order not to exceed this resistance the following condition should be satisfied:

where TRd,max is defined as:

( ) ( )

With regard to the reduction factor the same holds as explained in Section 3.1.1. The reduction factor ν changes in the Model Code to kc, see again Figure 4.

3.1.2.3. Fatigue loading

Traffic running on bridges produces a stress spectrum which may cause fatigue. The stress spectrum depends on the geometry of the vehicles, the axle loads, the vehicle spacing, the composition of the traffic and its dynamic effects. No further fatigue checks need to be performed when the following criteria are met:

When

| |

| |

| |

| |

When

| |

| |

| |

| |

Where: VEd,max maximum shear force for frequent load combination

VEd,min minimum shear force for frequent load combination When the criteria above are not met, additional checks should be performed. In these checks, comparable to what is said above, only the capacity of the reinforcement should be taken into


20

account. In Eurocode 1 [6], 5 different fatigue load models are distinguished. Load models 1 and 2 are intended to check whether the fatigue life may be considered as unlimited when a constant stress amplitude fatigue limit is given. Load Models 3, 4 and 5 are intended for fatigue life assessment by reference to fatigue strength curves. In the reference project, fatigue load model 4 is used. That is why this model is further elaborated.

3.1.2.4. Fatigue load model 4

A traffic category on a bridge should be defined by:

the number of slow lanes

the number Nobs of heavy vehicles per year and per slow lane Indicative values for Nobs are given in Table 18 [6]. On each fast lane, additionally 20% of Nobs may be taken into account.

Table 18 – Indicative number of heavy vehicles expected per year and per slow lane [6]

Traffic categories Nobs per year and per slow lane

1 Roads and motorways with 2 or more lanes per direction with high flow rates of lorries

2,0·106

2 Roads and motorways with medium flow rates of lorries

0,5·106

3 Main roads with low flow rates of lorries 0,125·106

4 Local roads with low flow rates of lorries 0,05·106

Fatigue load model 4 consists of sets of standard lorries which together produce effects equivalent to those of typical traffic on European roads. A set of lorries appropriate to the traffic mixes predicted for the route as defined in Table 19 [7] (obtained from the (Dutch) ROK and comparable to Table 4.7 of Eurocode 1 [6]) and Table 20 [6] should be taken into account. Table 19 - Set of equivalent lorries [7]

Vehicle type Axle spacing Equivalent axle loads (kN)

Wheel type Amount per year

1 4,50

70 130

A B

750.000

2 4,20 1,30

70 120 120

A B B

600.000

3 3,20 5,20 1,30 1,30

70 150 90 90 90

A B C C C

600.000

4 3,20 1,30 4,40 1,30 1,30 1,30 1,30

70 90 70 70 70 70 70 70

A C A A A A A A

230.000

5 1,50 2,40

70 70

A A

66.000


21

1,30 9,50 1,30 1,30 1,30

170 160 70 70 70 70

B B A A A A

6 1,70 3,30 1,30 3,50 3,50 1,30

70 70

180 190 70

180 190

A A B B A B B

3.100

7 2,40 1,30 5,50 1,30 1,30

170 170 200 180 180 190

B B B B B B

500

8 2,50 1,30 5,20 1,30 1,30 1,30

130 160 170 220 200 70 70

B B B B B B B

200

9 1,40 2,60 1,30 6,10 1,90 1,90

130 130 180 180 220 220 220

B B B B B B B

100

10 2,40 1,30 1,30 9,50 1,30 1,30 1,30

90 90

240 220 200 180 190 200

C C B B B B B B

100


22

Table 20 - Definition of wheels and axles [6]

The calculations should be based on the following procedure:

The total number of vehicles per year to be considered for the whole carriageway ΣNobs should be defined, based on Table 18.

Each standard lorry is considered to cross the bridge in the absence of any other vehicle.

The stress range spectrum and the corresponding number of cycles from each fluctuation in stress during the passage of a set of lorries on the bridge should be taken into account by the Rainflow or the Reservoir counting method.

For every vehicle type of Table 19 the minimum and maximum shear force should be determined. With these values, the fatigue shear force can be determined:

( ) ( )

The associated torsion is accounted for by a magnification factor ξ, which is based on the ratio of shear-torsion in ULS:

With this, the assumption is made that the ratio shear-torsion for fatigue loading is the same as when the loading for ULS is concerned. This is a conservative assumption, because the part of torsion will reduce. This is due to the fact that the load system in fatigue will be spread over a bigger area because the load system will be longer for heavy lorries. The stress spectrum, introduces by ΔVfat, is determined by:

( )

Where Δϕfat amplification factor for dynamical effects.

ϕfat angle between the concrete compression strut and the beam axis perpendicular to the shear force. The value of θ should (for fatigue) be limited: 32,3°≤θ≤45, θ=32,3° is chosen


23

The damage done by one stress spectrum Δσs can be determined by using a S-N diagram, see Figure 6. The allowable stress spectrum ΔσR,sk should be divided by γs,fat=1,15.

Figure 6 - S-N diagram

The values for the S-N diagram can be determined by Table 21. Table 21 - Values for S-N diagram for reinforcement steel

Type of reinforcement

N* Stress exponent ΔσRsk (MPa) for N*

cycles k1 k2

Straight or bended bars

106 5 9 162,5

Welded bars 107 3 5 58,5

Joints 107 3 5 35

For this project, straight and bended bars are used. Ni can now be determined. Furthermore, ni should be determined by multiplying the values of Table 19 by 0,06. The values of Table 19 are based on traffic category 1. For the concerned construction, “the Witte brug”, the traffic category is 3, where the Nobs is 0,06 times lower compared to traffic category 1. Now the Miner rule can be used:

∑

Where it holds that: m number of intervals with constant amplitude. ni occurring number of cycles with constant amplitude in interval i. Ni maximum number of cycles with constant amplitude in interval i before failure.


24

3.2. Method of calculation Similar to the previous section (where the bending moment capacity of different girders is checked), the calculations to check the different girder configurations will be done with SPAN-sheet. An exception to this is the fatigue calculations, which will be calculated by hand. SPAN-sheet is an Excel-program which is used to calculate the different girders of Spanbeton. It is based on the current regulations, being the Eurocode (described above). However, new concrete classes are added. The Eurocode is valid for concrete classes up to C90/105, but the concrete classes C120/140 and C150/170 are added.

3.2.1. SPAN-sheet

To use the SPAN-sheet properly, the material- and constructive properties (e.g. allowable stresses, section moduli) should be determined and given as input. The material properties of the new concrete classes were already shown, see Table 1. The prestressing strands should also be specified, along with the residual capacity of the strands. The design shear force should be checked in different cross-sections. The shear force varies along the length of the girder. Also the cross-sectional properties of the girder vary along the length of the girder. For example, the first 0,5 meter of the girder has a solid cross-section. The different cross-sections which will be checked are:

0,5 meter (solid cross-section) from the support

0,5 meter (hollow cross-section) from the support

2,0 meter (hollow cross-section) from the support

Every 1,5 meter, until 12,5 meter from the support (all hollow cross-sections) When the material- and constructive properties are known, the effective width and height of every cross-section is determined. For the solid cross-section this is done by subtracting A/u from the height of the wall, for a hollow cross-section half of the thickness of the adjacent walls is subtracted from the height of the wall. So this means that the Ak will be bigger for the hollow cross-section.

3.2.2. Loads

As already stated, the box girder configurations which will be discussed in this study, will be compared to the original box girder which was designed for the “Witte Brug”. The box girder configurations should be able to fulfill the same requirements as this original girder. This holds for the loads and occurring deflections. That is why the loads will be adopted from the original design, with exception of the dead load of the girder. The amount of concrete Ab will change for different configurations, so the dead load of the girder will change with the same ratio. For example, when the amount of concrete decreases with 5%, it is assumed that the dead load will also decrease with 5%. The fatigue loading is also adopted. Vmax,fat and Vmin,fat are the maximum and minimum values (for all the different vehicle types taken into account) of the shear force in fatigue loading with respect to Load Model 4, see Section 3.1.2.4.

3.2.3. Checks performed

To obtain the design shear force VEd from both pure shear and torsion, the characteristic values of both the shear force and the torsional moment are multiplied with the load factors. This load factors depend on the governing situation, which can be situation 6.10a or 6.10b (Table A2.4(B) of [8]).


25

Now the shear capacity should be determined. The first check which is performed is the maximum shear force VRd,max. When the design shear force VEd is bigger than VRd,max the compression struts will fail. This cannot be avoided by adding stirrups, so the cross-section should be adapted. That is why this check is performed first. When VEd<VRd,max it is checked if the design shear force is less than the shear capacity of the concrete, i.e. if it holds that VEd<VRd,c. When this is true, the cross-section has sufficient shear capacity without stirrups, so there is no need to place constructive stirrups. For practical reasons it is chosen to always use at least practical stirrups (for example Ø10-250). As stated in Section 3.1.1, the amount of prestressing determines (among others) the shear resistance of the concrete cross-section. This value is adapted from Section 2, where this value is determined (including the (time-dependent) losses). When the shear capacity of the concrete cross-section is less than the design shear force (VRd,c<VEd), stirrups should be applied to achieve sufficient shear capacity. To determine the shear resistance of the cross-section with stirrups, the angle between the concrete compression strut and the beam axis θ should be chosen. The value of θ is limited: 21,8°≤θ≤45. The value θ=21,8° is chosen, because this gives the biggest shear resistance (more stirrups are crossed by the crack). In the case that VEd>VRd,max this value of θ can be increased (to increase VRd,max). When fatigue loading is concerned, the value of θ is chosen to be 32,3°. The amount of stirrups needed can now be determined. Depending on the diameter of the stirrups, the distance s between the stirrups is chosen. Generally speaking, the fatigue loading will be governing. This is because of the increased angle θ and the fact that the allowable stress in the stirrups is limited when fatigue loading is concerned, see Section 3.3.


26

3.3. Reference project As stated, the box girders used for the reference project had a construction height of H=1300 mm. The internal forces in the structure were determined using a FEM-program, SCIA Engineer. The loads were used as input for SCIA. All the load combinations are taken into account, and for every situation (ULS, SLS, fatigue) the governing loads are determined. For every situation it is determined whether the concrete member can cope with the loads. When this is not the case, stirrups should be applied. As stated before, when the concrete capacity alone was sufficient, still practical reinforcement is applied (Ø10-250). It was found that, when shear capacity is concerned, the fatigue loading is governing for the girders. To keep this report comprehensible and concise, only the results of the fatigue checks are presented here. Furthermore, only the first hollow cross-section is presented. The other checks, for all cross-sections, are done and an overview of the results is given in Table 24.

3.3.1. Fatigue loading, cross-section at 0,5 m

The cross-section at 0,5 meter from the support is the cross-section which will be loaded the most compared to the other cross-sections in shear, i.e. the shear force will be the highest in this cross-section. Table 22 gives the values that are needed to perform the calculations (discussed in Section 3.1.2.4) regarding the shear capacity of the cross-section. It can be seen that Ø10-125 is used here, which is a double-crossed stirrup per web of the box-girder. Table 22 - Shear capacity values

VEd,perm [kN]

ξ Asw

[mm2/m] z

[mm] cot(ϕfat) Δϕfat

154 1,34 1257 894 1,58 1,15

In the table below, the results of the fatigue calculation are presented. The ΔV is determined from the vehicle types of Table 19, from which the Δσs can be calculated. With the use of Figure 6 and Table 21 the Ni can be calculated. When these values are known, Σn/N is calculated. This value should always be below 1, in order to satisfy the fatigue capacity. For every vehicle type of Table 19, the second row in Table 23 represents the summation of the vehicle type in question and the combination “fast lane”. In 20% of the crossings of a vehicle of Table 19 on the slow lane, lorries are also present on a fast lane. This is reflected in the column ni/Ni. Table 23 – Shear capacity

Vehicle type Vmax,fat [kN]

Vmin,fat [kN]

ΔVfat [kN]

Δσs [N/mm2]

Ni ni ni/Ni

1 54,0 0 54 47 2,08E+10

45.000 1,73E-04

78,3 0 78 68 7,34E+08 1,23E-03

2 85,8 0 86 74 3,22E+08

36.000 8,96E-03

110,1 0 110 95 3,41E+07 2,11E-02

3 112,8 0 113 98 2,73E+07

36.000 1,05E-01

137,1 0 137 119 4,73E+06 1,52E-01

4 113,3 0 113 98 2,64E+07

13.800 4,19E-02

137,6 0 138 119 4,59E+06 6,01E-02

5 140,9 0 141 122 3,70E+06

3.960 8,56E-02

165,2 0 165 143 9,34E+05 8,48E-02

6 209,3 0 209 182 2,86E+05

186 5,21E-02

233,6 0 234 203 1,65E+05 2,26E-02


27

7 248,7 0 249 216 1,21E+05

30 1,99E-02

273,0 0 273 237 7,57E+04 7,93E-03

8 290,1 0 290 252 5,58E+04

12 1,72E-02

314,4 0 314 273 3,74E+04 6,42E-03

9 277,7 0 278 241 6,95E+04

6 6,90E-03

302,0 0 302 262 4,57E+04 2,62E-03

10 349,6 0 350 303 2,20E+04

6 2,18E-02

373,9 0 374 324 1,57E+04 7,64E-03

The summation for this situation of ni/Ni gives Σni/Ni=0,727, for the hollow cross-section at 0,5 meter from the support. For the other cross-sections the value of Σni/Ni is given in Table 24. Table 24 - Σni/Ni for different cross-sections

Cross-section Σni/Ni

0,50 1,47E-02

0,50 7,27E-01

2,00 2,61E-01

3,50 4,17E-01

5,00 2,96E-01

6,50 8,43E-02

8,00 8,55E-02

9,50 3,37E-01

11,00 6,77E-01

12,50 n/a

For the cross-section at 12,50 meter from the support, the concrete member did not need stirrups to be able to cope with the fatigue load.


28

3.4. Configurations In Section 2, the original girder was adapted in such a way the it did meet the requirements regarding bending moment, allowable stresses and deflections, and still had a lower construction height. The different heights were:

H=1300 mm

H=1200 mm

H=1100 mm

H=1000 mm By using a higher concrete class and adding more prestressing to the girder, it did still meet the requirements. For these different configurations, the shear force is checked here. These checks are based on the fatigue loading, because it is believed that this is the governing load configuration. The fatigue loads are kept the same. The dead load of the girder does not play a role for fatigue loading, so this does not need adjustment. The internal lever arm z is adjusted, along with the amount of reinforcement. It is endeavored to keep the value of Σni/Ni the same to be able to compare the values of different construction heights. The internal lever arm z is calculated by the following approximation:

Where dsp can be determined by

Where h construction height dpr distance of common center of gravity of the prestressing strands, measured from the

lowest fiber The value of dpr will increase when more prestressing is added. Besides the check on fatigue loading, the VRd,max is checked. The maximum shear force should not exceed this value. However, due to the higher concrete class, the checks on VRd,max are satisfied for all girder configurations. That is why this check is not further presented in this report.

3.4.1. H=1200 mm

For every cross-section, the fatigue loading is checked and when the capacity was not sufficient, additional stirrups were added. For a construction height of H=1200 mm, 5 additional prestressing strands were needed. They were added next to the original prestressing strands at a height op zp=90 mm. This means that dpr remains (almost) unchanged, however z will decrease due to the lower construction height. Some additional stirrups were needed, as can be seen in Table 25. The amount of additional stirrups is presented in percentage and in mm2/m, compared to the original girder. In here, practical issues (e.g. convenient spacing between stirrups) are not yet taken into account.


29

Table 25 - Amount of additional stirrups needed with H=1200 mm

Cross sections

Asw [mm2/m]

Σni/Ni

Additional stirrups

[%]

Additional stirrups

[mm2/m]

0,5 1414 0,684 13% 157

2,0 1382 0,276 10% 126

3,5 1152 0,423 10% 105

5,0 1152 0,292 10% 105

6,5 1152 0,084 10% 105

8,0 1152 0,082 10% 105

9,5 1152 0,315 10% 105

11,0 864 0,630 10% 79

3.4.2. H=1100 mm

For a construction height of H=1100 mm, 14 additional prestressing strands were needed, which will be placed 25 mm above the other prestressing strands. This give a somewhat higher value of dpr, leading to a relatively bigger decrease of z compared to H=1200 mm. Approximately 25-30% of additional stirrups were needed, see Table 26. Table 26 - Amount of additional stirrups needed with H=1100 mm

Cross sections

Asw [mm2/m]

Σni/Ni

Additional stirrups

[%]

Additional stirrups

[mm2/m]

0,5 1634 0,677 30% 377

2,0 1571 0,285 25% 314

3,5 1309 0,403 25% 262

5,0 1309 0,269 25% 262

6,5 1309 0,077 25% 262

8,0 1309 0,073 25% 262

9,5 1309 0,273 25% 262

11,0 982 0,550 25% 196

3.4.3. H=1000 mm

For a construction height of H=1000 mm, 23 additional prestressing strands were added. This gives, again, a relatively bigger decrease of z compared to H=1100 mm. Approximately 40-55% of additional stirrups were needed, see Table 27. Table 27 - Amount of additional stirrups needed with H=1000 mm

Cross sections

Asw [mm2/m]

Σni/Ni

Additional stirrups

[%]

Additional stirrups

[mm2/m]

0,5 1948 0,734 55% 691

2,0 1885 0,253 50% 628

3,5 1518 0,410 45% 471

5,0 1466 0,344 40% 419

6,5 1466 0,095 40% 419

8,0 1466 0,088 40% 419

9,5 1466 0,330 40% 419

11,0 1100 0,637 40% 314


30

3.5. Conclusions In this section, the shear capacity of different girder configurations is checked. The first configuration is based on the reference project and had a construction height of H=1300. The other configurations had a lower construction height. For decreasing construction height, the amount of stirrups that are needed to meet the requirements regarding the shear capacity, increases. This is due to the fact that the internal lever arm z decreases. When additional prestressing strands are, dpr increases and thus z decreases, relatively speaking, even more. In the figure below, Figure 7, the value of the internal lever arm z is plotted for different construction heights. It can be seen that the value of z does not decrease linear. Due to the additional prestressing strands (which are located above the original prestressing strands), the value of dpr becomes bigger and thus z becomes smaller.

Figure 7 - Internal lever arm z for different construction heights

Due to the lower z, the amount of stirrups increase. For H=1000 mm, approximately 50% of additional stirrups are needed, see Figure 8.


31

Figure 8 - Stirrups for different construction heights

These additional stirrups can be obtained by reducing the spacing s between the stirrups. Another option is to use bigger diameters for the stirrups.


32

4. Fibers In this section, steel fibers are used to increase the ductility of the concrete.

4.1.Minimum ductility Ductility is described as the material’s ability to (plastically) deform under tensile stress. When a concrete beam has adequate ductility, moment redistribution becomes possible and brittle failure is prevented, when tensile stress is regarded.

A possibility to give concrete a more ductile behavior is by adding fibers to the concrete. When plain concrete is considered, the first tensile crack will lead to brittle failure of the concrete specimen because the tensile force cannot be transferred from one side of the crack to the other. By adding fibers to the concrete, this first crack will be bridged by fibers. These fibers will transfer the tensile stress from one side of the crack to the other. When the tensile stress increases, the fibers will still transfer the force, but they will deform. In this way, more deformation is added to the concrete, before the specimen will fail. Or, in other words, the concrete has become more ductile. This is up to the point where the fibers will fail, due to fiber break or fiber pullout.

4.2.French recommendations According to the French recommendations [2], a minimum ductility check is not required when a strain-hardening fiber-reinforced concrete is considered. That is because a strain-hardening material has a higher tensile strength after the first crack, which guarantees a ductile behavior.

However, when a strain-softening material is considered, a minimum ductility check is required. In order to guarantee that the material will have adequate ductility in bending, the following criterion must be respected for strain-softening and low strain-hardening materials:

∫

( )

( )

where wlim can be chosen equal to 0.3 mm fctm,el is the mean elastic limit stress in tension σ(w) is the characteristic post-cracking stress

4.3.Test results Bekaert, one of the leading companies for the production of steel fibers, conducted various tests with steel fiber reinforced concrete. In most of these tests, the fiber dosage was rather high and thus not that representative for a minimum ductility test.

There is one test known, in where 25 kg/m3 of fibers were used. The fibers that were used in this test are of the type RC-80/30-CP, which are galvanized fibers, they have a length of 30 mm and an aspect ratio of 80, which gives a diameter of 0,38 m. The test was done according to EN14651 [9]. The test is a 3-points bending test on specimens of 150x150x550 mm, with a notch of 25 mm in the middle of the beam (see Figure 9). The mean compressive strength of the used concrete was 60,3 MPa. To determine the residual flexural strength, the following formula is used:

Where: fR,j residual flexural strength corresponding with CMOD=CMODj (j=1,2,3,4) [N/mm2] Fj load corresponding with CMOD=CMODj [N]


33

l span length [mm] b width of the specimen [mm] hsp distance between the tip of the notch and the top of the specimen [mm]

Figure 9 - Test setup for the EN 14651-test

The results of these test are shown in Table 28, where CMOD represents crack mouth opening displacement and fl represents the maximum load for CMOD<0,05 mm (in other words the cracking stress). Table 28 - Residual flexural strength for different CMOD

CMOD [mm]

Residual flexural strength [N/mm2]

fl 0,02 6,32

fR,1 0,5 4,91

fR,2 1,5 6,21

fR,3 2,5 6,35

fR,4 3,5 5,97

These results are put in a graph as shown in Figure 10.

Figure 10 - Residual flexural strength for different CMOD

0

1

2

3

4

5

6

7

0 0,5 1 1,5 2 2,5 3 3,5 4


34

When the mean value of the residual flexural strength over a CMOD of 0,3 mm is calculated, one finds the value of 5,50 N/mm2. These are characteristic values, so they should be divided by a K-factor of Kglobal=1,25. This gives a value of 4,58 N/mm2. This value should be equal or more than max(0,4 fctm,el,3 MPa). Since the values of Table 28 follow from a bending test, the value of fl gives the flexural tensile strength. fctm,el represents the pure tension strength. However, the pure tension strength is always lower than the flexural tensile strength, so when the found value of the residual flexural strength is higher than the flexural tensile strength, the requirement is always met. Max(0,4 fctm,el,3 MPa) will become 3 MPa, because 0,4*6,32 is less than 3 MPa. So the requirement is met, since 4,58>3 MPa. This means that with a fiber dosage of 25 kg/m3, the minimum ductility requirement is abundantly met. It is assumed that a fiber dosage of 25 kg/m3 is always sufficient to acquire enough ductility for the concrete member of concrete class up to C120/140.


35

5. Conclusions and recommendations

5.1. Conclusions The object of this report was to increase the slenderness of box girders by using higher strength concrete. By reducing the construction height of the box girder, but at the same time being able to cope with the loads on the structure, this slenderness is successfully increased. A box girder with construction height H=1300 mm and concrete class C60/75 can now be executed with a construction height H=1000 mm and concrete class C120/140. The higher slenderness is achieved by adding more prestressing. Due to the lower construction height, more prestressing is needed in order to prevent tensile stresses to occur. But due to additionally needed prestressing, higher compressive stresses will occur. High strength concrete can cope with these high compressive stresses. 24 additional prestressing should be added for a construction height of H=1000 mm, next to the 62 strands that were already present for construction height H=1300 mm. This is approximately 40% additional prestressing, for a slenderness increase of 30%. This slenderness increase came together with a dead load decrease of approximately 10%. Next to the governing bending moments and occurring stresses, the shear capacity of the girders is checked. The shear force is based on the fatigue load, being fatigue load model 4b. It is believed that this will be the governing load. For lower construction height, the internal lever arm is also smaller. Due to this, the shear capacity will reduce. This loss in shear capacity can be compensated for by putting more shear reinforcement in the girder. For a construction height of H=1000 mm, approximately 50% additional rebars are needed. This is close to the support, where the highest shear force will occur. Further away from the support, less vertical reinforcement is needed. The main disadvantage of high strength concrete, is the increased brittleness of the material. This makes it a more dangerous material to work with. To reduce the risk, steel fibers can be added to give the material a more ductile behavior. The French recommendations and a test performed by Bekaert are used to determine the minimum dosage of the fibers. It was found that a dosage of 25 kg/m3 should be sufficient to give the concrete a ductile enough behavior, in order to avoid sudden collapse of the girder.

5.2. Recommendations The advantages and disadvantages of the use of higher strength concrete are now known. It is possible, for this particular reference project, to have a construction height of H=1000 mm. But this high slenderness comes with a high camber. A camber of approximately 110 mm is calculated, for the load combination prestressing and 1,1 times the static load. When the asphalt will be put on top of the girder, a lot of asphalt is needed to realize a horizontal road. This additional asphalt will on its turn lead to a higher dead load. Besides the high camber, the differences in camber for different girders is a point of attention. All the girders will have different camber and when more overall camber will occur, the absolute differences between the different girders will also increase. This could lead to unpractical situations. Therefore it might be wise to use a construction height of H=1100 mm. The camber for this height is approximately 80 mm, which is 30 mm less than with a construction height of H=1000 mm. This is due to the fact that less additional prestressing strands are needed.


36

Next to this, for a construction height of H=1100 mm, a concrete class of C90/105 is sufficient. The Eurocode is valid up to C90/105, so the current regulations can still be used. Furthermore, there is presumable no need for fibers to guarantee a ductile behavior. Most of the work done for this report was theoretical. To achieve a higher certainty about the conclusions which are drawn in this report, (full-scale) tests should be performed. In this way, the ductility can be demonstrated, also for high strength concrete.


37

List of reference


2011.

[2] International Federation for Structural Concrete (fib), Constritutive modelling of high strength /

high performance concrete, 2008.

[3] RWS Bouwdienst, Richtlijnen voor het Ontwerpen van Betonnen Kunstwerken (versie 6), 2006.

[4] NEN, National Annex to Eurocode 2: Design of concrete structures - Part 1-1: General rules and

rules for buildings.


2010, 2013.

[6] NEN, Eurocode 1: Actions on structures - Part 2: Traffic loads on bridges, 2011.

[7] RWS Dienst Infrastructuur, Richtlijnen Ontwerpen Kunstwerken ROK 1.2, 2013.

[8] NEN, Eurocode: Basis of structural design, 2011.

[9] NEN, "EN 14651: Test method for metallic fibered concrete," 2007.


38

List of figures and tables Figure 1 - Cross section girder produces by SPAN-sheet ........................................................................ 2

Figure 2 - Amount of prestressing for different construction heights .................................................. 15

Figure 3 - Truss model and notation for shear reinforced members [1] .............................................. 16

Figure 4 - Influence of ν1 (EuroCode) and kc (Model Code) ................................................................... 18

Figure 5 - Notations and definitions concerning torsion [1] ................................................................. 19

Figure 6 - S-N diagram ........................................................................................................................... 23

Figure 7 - Internal lever arm z for different construction heights......................................................... 30

Figure 8 - Stirrups for different construction heights ........................................................................... 31

Figure 9 - Test setup for the EN 14651-test .......................................................................................... 33

Figure 10 - Residual flexural strength for different CMOD ................................................................... 33

Table 1 - Mechanical properties of the added concrete classes ............................................................. 2

Table 2 - Used loads ................................................................................................................................ 4

Table 3 - Mechanical properties of original girder .................................................................................. 6

Table 4 - H=1200 mm and Wlower constant .............................................................................................. 7

Table 5 - H=1200 mm and Wupper constant .............................................................................................. 7

Table 6 - H=1200 mm and both Wupper and Wlower constant .................................................................... 7

Table 7 - H=1100 mm and Wlower constant .............................................................................................. 7

Table 8 - H=1100 mm and Wupper constant .............................................................................................. 7

Table 9 - H=1100 mm and both Wupper and Wlower constant .................................................................... 7

Table 10 - H=1000 mm and Wlower as high as possible ........................................................................... 7

Table 11 - H=1000 mm and Wupper as high as possible ........................................................................... 7

Table 12 - H=1000 mm and both Wupper and Wlower as high as possible .................................................. 8

Table 13 - Unity checks original girder .................................................................................................. 10

Table 14 - zp of kinked strands .............................................................................................................. 11

Table 15 - Unity Checks for hl=140 mm and hu=170 mm ...................................................................... 11

Table 16 - Unity Checks for hl=160 mm, hu=170 mm ............................................................................ 12

Table 17 - Unity Checks for hl=160 mm, hu=170 mm ............................................................................ 13

Table 18 – Indicative number of heavy vehicles expected per year and per slow lane [6] .................. 20

Table 19 - Set of equivalent lorries [7] .................................................................................................. 20

Table 20 - Definition of wheels and axles [6] ........................................................................................ 22

Table 21 - Values for S-N diagram for reinforcement steel................................................................... 23

Table 22 - Shear capacity values ........................................................................................................... 26

Table 23 – Shear capacity ...................................................................................................................... 26

Table 24 - Σni/Ni for different cross-sections ........................................................................................ 27

Table 25 - Amount of additional stirrups needed with H=1200 mm .................................................... 29



Table 28 - Residual flexural strength for different CMOD ..................................................................... 33


A

Appendix A In here, the results of the calculations are shown for a construction height of H=1200 mm.


B

Appendix B In here, the results of the calculations are shown for a construction height of H=1100 mm.


C

Appendix C In here, the results of the calculations are shown for a construction height of H=1000 mm.


Reducing the amount of stirrups in box girders by using HSFRC

Main Study


1-12-2014


i


ii

Table of Content 1. Introduction ..................................................................................................................................... 1

2. Comparison of shear capacity according to EC and MC .................................................................. 2

2.1 Eurocode.................................................................................................................................. 2

2.2 Modelcode ............................................................................................................................... 2

2.2.1. Without fibers ................................................................................................................. 2

2.2.2. With fibers ....................................................................................................................... 3

2.3. Comparison codes ................................................................................................................... 5

2.3.1. Girder ............................................................................................................................... 5

2.3.2. VRd,max ............................................................................................................................... 6

2.3.3. VRd,c .................................................................................................................................. 7

2.3.4. VRd,c + VRd,s ........................................................................................................................ 9

2.3.5. VRd,f ................................................................................................................................. 10

2.4. Fatigue ................................................................................................................................... 11

3. Increased ULS shear capacity H=1100 mm ................................................................................... 15

3.1. ULS shear capacity ................................................................................................................. 15

3.2. Conclusions ............................................................................................................................ 17

4. Increased ULS shear capacity H=1300 mm, H=1200 mm and H=1000 mm .................................. 19

4.1 H=1300 mm ........................................................................................................................... 19

4.2 H=1200 mm ........................................................................................................................... 22

4.3 H=1000 mm ........................................................................................................................... 23

4.4 Conclusions ............................................................................................................................ 25

5. Influence on casting process ......................................................................................................... 28

5.1 Casting process ...................................................................................................................... 28

5.2 Conclusions ............................................................................................................................ 29

6. Early age strength .......................................................................................................................... 30

6.1 Properties young concrete .................................................................................................... 30

6.1.1 Regular concrete ........................................................................................................... 30

6.1.2 High strength concrete .................................................................................................. 33

6.2 Influence on casting process ................................................................................................. 34

6.2.1 Compressive stress ........................................................................................................ 34

6.2.2 Tensile splitting stress ................................................................................................... 35

6.2.3 Compressive strength .................................................................................................... 36

6.2.4 Tensile splitting strength ............................................................................................... 36


iii

7. Conclusions and recommendations .............................................................................................. 37

7.1 Conclusions ............................................................................................................................ 37

7.2 Recommendations................................................................................................................. 38

List of references ................................................................................................................................... 39

List of figures and tables........................................................................................................................ 40

Appendix A .............................................................................................................................................. A

Appendix B .............................................................................................................................................. B

Appendix C............................................................................................................................................... C

Appendix D .............................................................................................................................................. D


1

1. Introduction This report builds on the already performed literature research to High Strength Fiber Reinforced Concrete (HSC). It is performed during an internship at Spanbeton and serves (partly) as Master thesis, to finalize my study Civil Engineering at the department of concrete structures at the University of Technology of Delft. In a previous report, the slenderness of the box girders was increased. For this, a box girder with a construction height of H=1300 mm was considered as a reference project. By using higher strength concrete and increasing the prestressing force, the girder with lower construction height did still meet the requirements regarding occurring stresses. However, to meet the requirements regarding shear force, many additional stirrups had to be used (for a construction height of H=1000 mm, 50% of additional stirrups were necessary). When fibers are added, the additional stirrups could be minimized. The goal of this study is to reduce the amount of stirrups that are needed in a box girder. This is done by adding 25 kg/m3 of steel fibers (fiber type RC-80/30-CP) to the concrete. When the concrete cracks, the fibers will bridge these cracks. In this way, the (shear) force can still be transmitted despite the fact that the concrete is cracked. With this, the amount of vertical reinforcement does not have to be designed on the full shear load when the cross section is cracked, because the concrete shear capacity is not nil. The Eurocode does not allow this method of calculation, there are no design rules for fiber concrete. However, the Model Code 2010 does include the fibers in the calculations. That is why the calculations that are done for this report, are done according to rules of the Model Code 2010. In here, two different approaches are presented to calculate the shear capacity of fiber concrete: the consistent and the non-consistent approach. The formulae of the consistent approach are comparable to the formulae of the Model Code when no fibers are used. The formulae of the non-consistent approach are more comparable to the formulae of the Eurocode. The governing shear load for the girder of the reference project was the fatigue load. Although not much is known about the fatigue shear capacity of the fibers, it is believed that fiber concrete is insensitive to fatigue load. That is why the shear load of the “new” girders is based on the ULS load, instead of the fatigue load. The influences on the casting process are discussed. Is it possible to improve the casting process, when use is made of HSFRC? The final chapter of this report deals with early age concrete and their properties. Due to the higher prestressing forces that are needed, the risk of cracking due to compressive stresses or due to tensile (splitting) stresses increases. The properties of HSFRC can be advantageous in this respect.


2

2. Comparison of shear capacity according to EC and MC The shear capacity of a cross section can be determined according to different codes and regulations. First of all there is the Eurocode [1], where no fiber contribution is taken into account. Second, the Modelcode [2] can be used. In the Modelcode, there are two possibilities to take the shear contribution of the fibers into account. One possibility is when a formula is used which is consistent with the rest of the Modelcode. This is a different approach then used in the Eurocode, this approach makes use of the state of strain in the concrete. The other possibility is when the formula of the shear capacity of the Eurocode is modified in such a way that fiber contribution is taken into account For both codes is shortly expounded how the shear capacity can be taken into account. After this, one girder with construction height H=1100 mm is calculated and worked out according to the different codes and approaches. The fibers increase the shear capacity of the concrete in the following way:

Higher tensile strength of the concrete

Cracks propagation is slowed down

Crack distribution is better, leading to smaller cracks and thus higher shear capacity of the concrete

Higher residual capacity due to pullout and dowel action

2.1 Eurocode According to the Eurocode, the shear capacity of an (uncracked) cross section can be calculated by

[ ( ) ]

Where coefficient taking into account longitudinal reinforcement, recommended value

aa ⁄

√

, Asl is the area of the tensile reinforcement and bw is the smallest width

of the cross-section in the tensile area coefficient taking into account prestressing, recommended value k1=0,15

⁄ , NEd is the axial force due to loading or prestressing

Once the cross section is cracked, no concrete part can be taken into account regarding the shear capacity. That is why the shear capacity of the stirrups should be designed on the full shear load:

( )

As can be seen, no fiber contribution can be taken into account. That is because the Eurocode does not include any contribution of fibers.

2.2 Modelcode

2.2.1. Without fibers

The design shear resistance of a web or a slab without shear reinforcement is given by

√

The value of √ is limited to 8. This is “due to the larger observed variability in shear strength of members with higher strength concrete, particularly for members without stirrups such as slabs”.


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The value of kv depends, among others, on the state of the longitudinal strain εx. This state of strain is calculated as follows:

( )

(

)

If the value of εx is negative it must be taken as zero. To calculate kv, different Level of Approximation (LoA) are introduced. For this report, LoA III is used, where kv is described as

(

( )

)

This formula implies that the shear capacity of the concrete member depends on the ratio of the actual shear force and the maximum shear force VRd,max. This latter is calculated as given below:

( ) ( )

As can be seen, to calculate VRd,max, kc is needed. This strength reduction factor consists of two parts: again the state of strain taken into account by kε and the effect of more brittle failure behavior of concrete of strengths greater than 30 MPa, which is considered in ηfc:

(

)

The state of strain is taken into account by kε:

The principal strain ε1 is defined by Mohr’s circle of strains, as an adequate approximation, the negative principal strain ε2 may be taken as the concrete peak strain εc0=2‰. This gives

( ) ( )

The minimum inclination of the compressive stress field is:

In contrast to the Eurocode, in the Modelcode both shear capacities (plain concrete and stirrups) can be added to each other to obtain the total shear capacity, so VRd=VRd,c+VRd,s. The latter part, the stirrups part, is calculated in the exact same way as done in the Eurocode.

2.2.2. With fibers

Modelcode Section 5.6.3 (page 146) states that fiber reinforcement can substitute (also partially) conventional reinforcement at ultimate limit stage, if the following relationships are fulfilled:

fR1k/fLk>0,4

fR3k/fR1k>0,5 For the values of fR1k, fR3k and fLk, see below. As with the concrete without fibers, the shear capacities of the different parts can be added, so it holds that VRd=VRd,F+VRd,s. A recent model that follows the approach to shear as presented above, computes the term VRd,f as follows:

( √ ( ))

The value of fFtuk is the characteristic value of the ultimate tensile strength corresponding to the crack width at ultimate, wu=0,2+1000 mm. This value is determined on the basis of a (bending) test, according to [3]. This value is described in more detail below. The value of kf can be taken as 0,8. The other factors are already known, but for fiber concrete they change. The value of kv turns into


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so not dependent on the ratio of VEd and VRd,max. Furthermore, the value of the inclination changes. The minimum inclination θmin is defined as θmin=29°+7000εx. This approach is not yet fully validated. A remark that should be made here is that the approach is not fully consistent, because the kv in this approach is not dependent on the ratio of VEd and VRd,max. Another method described in the Modelcode to take into account the fibers when shear capacity is concerned, is more or less a modified method of the Eurocode. This approach is validated and is now reliable, but is not consistent with the approach as described above. The Modelcode modified the formula regarding shear capacity of the Eurocode in such a way that fiber contribution is taken into account:

[ ( (

) )

]

Where fFtuk = characteristic value of the ultimate residual tensile strength for FRC, by considering

wu=1,5 mm according to Eq 5.6-6 fctk = characteristic value of the tensile strength for the concrete without fibers

Eq 5.6-6 of the MC describes the ultimate residual strength and reads:

( )

Where fFts = represents the serviceability residual strength, defined as the post-cracking strength for serviceability crack openings. The following can be used: fFts=0,45fR1 CMOD3 =2,5 mm fR1 = residual flexural strength according to w=0,5 mm (according to EN14651)

fR3 = residual flexural strength according to w=2,5 mm (according to EN14651) The equation for fFtu is obtained by considering a linear constitutive law between points with abscissa CMOD1 and CMOD3, up to the point with abscissa wu, see Figure 1.

Figure 1 - Linear constitutive law between abscissa CMOD1 and CMOD3

The stress value corresponding to the crack opening CMOD1 is determined from equilibrium, with the assumption that the compressive stress distribution is linear and that the tensile behavior is elasto-plastic until a crack opening displacement corresponding to the serviceability limit state (CMOD1). The variability introduced in the numerical coefficient introduced by the elastic modulus is here neglected and a common value is assumed.


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Figure 2 - Linear compressive stress distribution and elasto-plastic tensile behavior

The stress value corresponding to the crack opening CMOD3 is determined from equilibrium, with the assumption that the compressive stress is applied on the extrados chord and that the tensile behavior is rigid-linear.

Figure 3 - Rigid-linear tensile behavior and compressive stress applied on the extrados

For the design of members with shear reinforcement, the separate contributions of the fiber concrete and stirrups can be summed, regardless of the cracked concrete. The minimum amount of conventional shear reinforcement is not required if the following condition is fulfilled:

√ This allows limiting the development and the diffusion of the inclined cracking and can ensure sufficient member ductility.

2.3. Comparison codes To compare the results obtained by the Eurocode and by the Modelcode, one girder with construction height H=1100 mm is calculated and discussed according to the different codes and approaches. Note that the loads are all for ultimate limit state (ULS), except when stated otherwise.

2.3.1. Girder

The girder which is considered, is obtained from the reference project, but is modified. This was done in a previous report, where the construction height of the girders was decreased and higher concrete classes were used. Some values of the considered girder are:

Span: l=40,7 m

Construction height: H=1100 mm

Concrete class: fck=90 - 120 MPa


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Amount of prestressing strands: 76 Ø15,7 mm

Amount of fibers: 25 kg/m3 RC-80/30-CP, leading to: o fLk = 6,32 N/mm2 o fR1,k = 4,91 N/mm2 o fR2,k = 6,21 N/mm2 o fR3,k = 6,35 N/mm2 o fR4,k = 5,97 N/mm2

When the latter values are presented in a graph (and linear lines are drawn between the various points), the following figure is obtained, see Figure 4. Note that these are bending stresses, performed on beams with the dimensions 150x150x550 mm3. Because of the limited height of the beam, the values give a somewhat too optimistic view, because no pure tensile stresses are reached at the bottom. When higher beams would be used, this phenomenon would have less influence.

Figure 4 - Residual flexural strength for different CMOD's

2.3.2. VRd,max

First of all, the maximum shear force is considered. The maximum shear force is limited by failure of the compressive struts. As can be seen from Figure 5, the Modelcode is somewhat more conservative about the maximum shear force resistance VRd,max, when the concrete class C90/105 is chosen. At 3,5 meters from the support, the VRd,max suddenly increases, according to the Eurocode. This is related to a rule in the Eurocode, which states that when the stress in the stirrups is below 0,8fyk, the reduction ratio ν1 can be chosen as 0,5 instead of ν1=0,6(1-fck/250) (formula 6.10bN of [1]). Is the case that σs<0,8fyk upward of 3,5 meters from the support, so Vrd,max increases from here. According to the Modelcode, the VRd,max increases suddenly at 8 meters from the support. The Modelcode takes into account state of strain in longitudinal direction εx. If the value of εx is negative it must be taken as zero. This is the case up to 9,5 meters from the support. The longitudinal strain εx is used to determine the minimum crack inclination θ. For εx is zero the θmin becomes 20°, for positive εx the θmin increases. This leads to an increase in VRd,max.

0

1

2

3

4

5

6

7

0 0,5 1 1,5 2 2,5 3 3,5 4

Re

sid

ual

fle

xura

l str

en

gth

[M

pa]

CMOD [mm]


7

Figure 5 - Maximum shear force Vrd,max with fck=90 MPa

For the sake of completeness, the design shear force VEd is also shown. It can be seen that this value is always lower than VRd,max, for both the Modelcode and Eurocode. This is not the case when concrete class C120/140 is chosen. The reduction factor according to the Eurocode (ν1) becomes too big in this case, leading to the fact that VEd>VRd,max at the cross-section 0,5 meters from the support. It must be noted here that the Eurocode is only valid up to concrete class C90/105. According to the Modelcode, which is valid up to C120/140, VEd<VRd,max for every cross section.

Figure 6 - Maximum shear force VRd,max with fck=120 MPa

2.3.3. VRd,c

The shear resistance of the plain concrete is also compared for the different codes. From the graph can be seen that the Eurocode gives a significant higher shear resistance of the plain concrete, see Figure 7. However, this gives an distorted image, because when it holds that VRd,c<VEd no shear resistance of the plain concrete can be calculated for according to the Eurocode. This is not true for the Modelcode, in here the VRd,c can be taken into account, even when it holds that VRd,c<VEd. The reason for the VRd,c to be so low according to the Modelcode has to do with the fact that the ratio of VEd and VRd,max is taken into account in the reduction factor kv:


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(

( )

)

Due to the low z and low chosen θ, the VRd,max will come close to VEd. This results in a near-zero value of kv. The value of θ can be chosen bigger, to increase the value of VRd,max. However, the same value of θ should be used for calculating the shear resistance of VRd,s. With a bigger value of θ, the value of VRd,s decreases, see further.

Additionally to this, the value of √ , which is used to calculate VRd,c with the Modelcode, is limited

to 8 MPa.

Figure 7 – Shear resistance of the plain concrete VRd,c with fck=90 MPa

That was the case when fck=90 MPa. When fck is increased to 120 MPa, the graph below holds. The increase in VRd,c according to the Eurocode is rather limited. The reduction factor ν1 increases when fck is increased and fck is to the power 1/3 in the formula of VRd,c. The increase in VRd,c according to the Modelcode is bigger. The value of VRd,max increases, leading to a lower ratio of VEd/VRd,max. This results in a higher kv, so a higher VRd,c.

Figure 8 - Shear resistance of the plain concrete VRd,c with fck=120 MPa


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2.3.4. VRd,c + VRd,s

When the total shear capacity is considered, the shear resistance of the Modelcode should always be higher or equivalent to the one of the Eurocode, due to the additional concrete term. Figure 9 shows the total shear resistance for the different codes, with fck=90 MPa. This is with the stirrup distribution as given in Table 1. Note here that this is the stirrup distribution per web, but Figure 9 is based on both webs. Table 1 - Stirrup distribution

The shear capacity according to the Eurocode is completely based on the capacity of the stirrups, VRd,s. This gradually increases from 3,5 meter to 9,5 meter from the support, while the Asw stays the same. The gradually increase is due to the internal lever arm z, which increases because the overall height of the prestressing strands decrease further away from the support. Close to the support, where it holds that VEd≈VRd,max, the values of VRd are almost equal according to both codes. This is because there is almost no contribution of the plain concrete to the shear capacity, VRd,c. Further away from the support, the ratio of VEd/VRd,max decreases, thus VRd,c increases (as was already stated). This gives an increase in VRd according to the Modelcode (however relatively small), because in this code both values can be added to each other.

Figure 9 - Shear capacity VRd with fck=90 MPa

When a higher concrete class is used, fck=120 MPa, the concrete contribution is somewhat bigger. VRd,max will increase with 33%, so the ratio VEd/VRd,max decreases with 25%. With this, the concrete contribution increases, thus the sum of VRd,c and VRd,s also increases, see Figure 10. Further away

Distance to support [m]

Asw/s [mm2/m]

Applied stirrups

0,5 2094 Ø10-150

0,5 1257 Ø10-125

2,0 1257 Ø10-125

3,5 1047 Ø10-150

5,0 1047 Ø10-150

6,5 1047 Ø10-150

8,0 1047 Ø10-150

9,5 1047 Ø10-150

11,0 785 Ø10-200

12,5 785 Ø10-200


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from the support this increase is less notable, because the ratio VEd/VRd,max was already significant below 1.

Figure 10 - Shear capacity VRd with fck=120 MPa

2.3.5. VRd,f

As stated, there is no strength contribution of fibers included in the Eurocode. In the Modelcode there are two different formulas to take into account the fiber contribution. From now on they are referred to as the “consistent approach” and “non-consistent approach”, following from the fact that one is consistent with the rest of the Modelcode and one is not. Note here that the non-consistent approach is, on its turn, consistent with the Eurocode. As can be seen in Figure 11 and Figure 12, the 2 different approaches results in comparable shear capacities VRd,f. At the moment the longitudinal strain εx becomes positive, the capacity of the consistent formula decreases somewhat, due to the increased inclination and decreased reduction factor kv.

Figure 11 - Shear capacity VRd,f with fck=90 MPa


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The same pattern is observed for a higher concrete class, see Figure 12. Both capacities (both the consistent and non-consistent approach) increase somewhat. The capacity of the consistent approach increases a little bit more, in the formula of this approach fck is to the power ½ and in the non-consistent approach it is to the power ⅓.

Figure 12 - Shear capacity VRd,f with fck=120 MPa

2.4. Fatigue Not much is known about the fatigue capacity of fiber concrete, it can be described as a “terra incognita”. Although the precise influence of the fibers to the fatigue strength of concrete is not (yet) known, the majority of researchers have, to a limited extend, found that the inclusion of fibers can benefit the fatigue performance of concrete [4]. As steel fibers usually bridge cracks at a non-perpendicular angle they will already be deforming and picking up load at small crack widths, see Figure 13 [5]. Local friction is increased and thus compressive stresses parallel to the crack surface are induced. As a consequence, the associated tensile stresses perpendicular to the crack can lead to secondary cracking.

Figure 13 - Secondary cracking [5]

To be able to say something about the increased fatigue capacity introduced by the addition of fibers to the concrete, the following assumption is made:

So the fatigue capacity is 30% of the capacity in ULS. This reduction is also observed with reinforcement steel when loaded in fatigue (e.g. ΔσRsk/fyk=162,5/500=0,325). This assumption is backed up by the findings of E.S. Lappa [6]. In her dissertation, she has tested HSFRC girders and


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found that when the flexural tensile strength remains lower than 50% of the static ULS strength, the girder will not collapse after 10 million stress cycles. In this light, the assumption of 30% is thus on the safe side. Another assumption that is made is that only the capacity of the fibers is taken into account, so not the concrete capacity. This is a conservative assumption, because the fibers and concrete will work together, a synergetic relation will most likely arise. This is, for now, not taken into account, only the fiber contribution is taken into account. Now it is time to determine the fiber capacity only. Above, the capacity of the fiber concrete is determined, not the fiber part only. The formulas for the fiber part only are:

( ( ))

[( (

) )

( ) ]

When these formulas are applied to the girder with a construction height of H=1100 mm and concrete class C90/105, the following graph is obtained, see Figure 14.

Figure 14 - Shear capacity of the fibers only, VRd,f with fck=90 MPa

It can be seen that the two different approaches give quite different values. The consistent approach give higher values for the shear capacity of the fibers only. With this approach, the fiber shear capacity varies between 420 kN and 480 kN, depending on the internal lever arm z and the crack inclination θ, which is in its turn depending on the state of longitudinal strain εx. The non-consistent approach mainly depends on the effective depth of the cross section d. So this values increases somewhat along the distance of the girder, because d increases somewhat. This is, as stated, due to the common center of gravity of the prestressing strands, which goes down along the distance of the girder. When a higher concrete class is used, the consistent approach does not change because it is not dependent on the compressive strength of the concrete. The non-consistent approach will increase slightly, but not significantly.


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As stated, when fatigue loads are considered, the assumption is made that the fatigue strength is only 30% of the ULS strength. On top of this comes a changed crack inclination θ when fatigue loads are considered. The following condition should be applied

( ) √ ( )

This leads to a higher crack inclination θ when fatigue loads are considered and thus a lower shear capacity of the fibers, when the consistent approach is applied. The non-consistent approach does not change, because the crack inclination is not taken into account with this approach. With both the reductions applied, Figure 14 changes into Figure 15. Note here that the shear capacity of the solid cross section is not taken into account, to give a better view. For the sake of completeness, the non-fatigue values are also shown in this figure.

Figure 15 - Fatigue shear capacity of the fibers, VRd,f,fat

It can be seen that the non-consistent approach is still more conservative than the consistent approach. The shear capacity according to the consistent approach is approximately two times higher than the non-consistent approach. From the above can be concluded that the approximated fatigue shear capacity is in the range of 50-100 kN. This value will be used in the calculations regarding the fatigue shear of the reference project, the “Veerwegviaduct”. The fatigue strength of the reference project was calculated using load model 4b of the Eurocode [7]. This load model consists of a set of standard lorries which together produce effects equivalent to those of typical traffic on European roads. For every vehicle type it is determined what the maximum shear force difference is, ΔVmax. When this ΔVmax is too high to be taken by the concrete, the stirrups should be designed on the full fatigue load. However, when fibers are used to reinforce the concrete, the stirrups will not have to be designed of the full fatigue load. For this report, it is assumed that the fatigue shear capacity of the fibers VRd,f can be subtracted from the fatigue load ΔVmax. So when the fatigue load of a certain lorry is ΔV=100 kN and the fatigue shear capacity VRd,f=50 kN, the design shear load for the stirrups is reduced to ΔV=50 kN. The stirrups should then be designed on the remaining shear force in fatigue, ΔVmax,remaining.

The different lorries have different fatigue loads because of the different axle loads of the lorries. The lorries with high axle loads induce high fatigue loads, but these lorries are not that frequent on the road. The lorries with lower axle load are more frequent. The loads of these lorries are in the range of VRd,f, leading to no fatigue damage of the stirrups because the design load of the stirrups will


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become close to zero. The fatigue loads of the heavier lorries will still hold (the absolute decrease is the same, however the relative decrease is much less). So they will lead to fatigue damage of the stirrups, but the amount of passages Nobs is much less. That is why these loads are also not that harmful for the stirrups. From this can be concluded that the fatigue load is not governing (anymore). Instead, the ULS shear load will become governing. So from now on, the girders with fiber concrete are, in this report, designed on the ULS shear load instead of the fatigue shear load. It should be kept in mind that the conclusion drawn above is based on some assumptions. The assumptions are listed below:

First assumption is that the fatigue capacity is 30% of the static ULS capacity, in formula this

gives

Second assumption is that only the fibers will contribute to the fatigue capacity, the fatigue capacity of the concrete itself is not taken into account

Third assumption is that the fatigue capacity (of the fibers only) can be subtracted from the fatigue load of every standard lorry. The stirrups should be designed on the remaining shear force.

The assumptions above model the reality in a tractable way. With these assumptions, calculations can be made and with these calculations it followed that the fatigue load was not governing anymore. However, the assumptions should be verified with suitable tests. This could be done in further research.


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3. Increased ULS shear capacity H=1100 mm To determine the increase in shear capacity for the ultimate limit state, the shear capacity is calculated according to the model code. The found value is compared to the value which was already found for the shear capacity according to the Eurocode. This is done for the girder with a construction height of H=1100 mm, because this was the recommendation of the previous report regarding the increased slenderness of box girders. The concrete class used here was C90/105. The shear capacity for other construction heights will be determined in the next chapter.

3.1. ULS shear capacity The increase in ULS load is rather limited for a construction height of H=1100 mm (when no fibers are considered), due to the ratio VEd/VRd,max. For this construction height, the VRd,max reaches a value which is close to VEd. In this way the shear capacity of the plain concrete is reduced close to zero. However, when fibers are considered this ratio does not play a role, because than the reduction factor kv does not depend on VEd/VRd,max, see Section 2.2.2. This is for both the consistent and non-consistent approach. This absence of the factor kv can be seen as a big plus for using the fibers. As can be seen in Figure 12, the additional shear capacity in ULS, introduced by the fibers, is approximately 1000 kN for this girder configuration. According to the Modelcode, this holds that the stirrups can be designed on a load which is approximately 1000 kN less than the original load. To attain a shear capacity of 1000 kN with stirrups, roughly 1150 mm2/m of stirrups are needed. This implies that roughly 1150 mm2/m less of stirrups are needed, when the fibers are added. Note that this is for both webs, so this means that roughly 575 mm2/m of stirrups could be omitted per web. This would be the case if the crack inclination would be constant at θ=21,8° and the internal lever arm z would be constant at z=800 mm. However, when fibers are used, the crack inclination should be changed. This crack inclination should be increased to θ=29°+7000εx≥29°. Furthermore, the internal lever arm z is not constant over the length of the girder. To see the influence of the fibers over the length of the girder, the following procedure is followed:

First the shear capacity VRd,f of the fiber concrete is determined at the position which is considered. This is done with the consistent approach (although the values of the non-consistent approach does not differ much)

This value is subtracted from the acting shear force VEd

The stirrups should be designed on the remaining acting shear force (VEd,rem=VEd-VRd,f). To obtain the stirrup distribution, the following formula is used:

( )

where θ should be determined from θmin=29°+7000εx

This value of Asw/s is subtracted from the original value of Asw/s. The value that remains is the amount of stirrups that could be omitted when the fibers are used, so that is the gain that is realized. Of course, one should bear in mind that for this gain 25 kg/m3 of fibers were needed.

The procedure described above is used to determine the reduction that can be obtained for a construction height of H=1100 mm. First, the shear capacity of the fiber concrete VRd,f is determined for every cross section. This value increases, because the internal lever arm increases. This is due to the kinked tendons that become lower further away from the support.


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However, further away from the support the bending moment will increase. This bending moment determines, among other (e.g. shear force), the strain in the cross section. The strain at the mid-depth of the effective shear depth is negative (so there is compression, note however that the minimum strain that can be used is 0) until 9,5 meters from the cross section. This strain is used in the calculation for VRd,f. As can be seen from Table 2, VRd,f decreases for cross section further away than 9,5 meters from the support, due to the strain εx. Table 2 – Shear capacity VRd,f,consistent for different cross sections and H=1100 mm

Cross section VRd,f,consistent [kN] 0,5 917

2,0 953

3,5 988

5,0 1008

6,5 1024

8,0 1037

9,5 1049

11,0 958

12,5 856

Now that the shear capacity of the fiber concrete is known per cross section, the remaining shear force can be determined per cross section. The original shear force can be seen in several figures above, for example Figure 10. When the values of Table 2 are subtracted from them, the remaining shear force is found, see Table 3. It can be seen that the remaining shear force decreases rapidly and even becomes zero for values up to 9,5 meter away from the support. This means that the fiber concrete can cope with the full ULS shear load at these points, so no (constructive) stirrups are needed anymore. Table 3 – Remaining shear force for different cross sections and H=1100 mm

Cross section VEd [kN] VEd - VRd,f [kN] 0,5 1791 874

2,0 1741 788

3,5 1547 559

5,0 1384 376

6,5 1242 218

8,0 1128 92

9,5 1020 0

11,0 910 0

12,5 800 0

The stirrup distribution of the girder with fiber concrete should be based on the values of Table 3. To determine the needed amount of stirrups per cross section, the internal lever arm z and the crack inclination ϴ is needed. These values are determined for the different cross sections, followed by the determination of the amount of stirrups Asw/s, see Table 4. Note that this is the amount of stirrups that are needed in the whole cross section, so in 2 webs combined.


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Table 4 - Needed amount of vertical reinforcement for different cross sections and H=1100 mm

Cross section z [mm] ϴ [°] Asw/s [mm2/m] 0,5 759 29,0 1469

2,0 789 29,0 1272

3,5 818 29,0 871

5,0 835 29,0 574

6,5 848 29,0 328

8,0 858 29,0 136

9,5 869 29,0 0

11,0 879 29,8 0

12,5 883 31,0 0

The amount of stirrups per web is thus half of the value obtained from Table 4. When this value is compared to the original amount of stirrups, which can be found in Table 1, the reduction of vertical reinforcement can be found for different cross sections. Note that this all is for a construction height of H=1100 mm, where the original construction height was H=1300 mm. From Table 5 can be seen that the reductions are significant. Table 5 - Reduction of vertical reinforcement for different cross sections and H=1100 mm

Cross section Asw/s per web

[mm2/m]

Original Asw/s per web [mm2/m]

Reduction of Asw/s [%]

0,5 734 1257 42%

2,0 636 1257 49%

3,5 436 1047 58%

5,0 287 1047 73%

6,5 164 1047 84%

8,0 68 1047 93%

9,5 0 1047 100%

11,0 0 785 100%

12,5 0 785 100%

Note that upward from the cross section at 11 meters from the support, no constructive stirrups were needed anymore for the ULS shear load of the original girder. The shear force in these cross sections could (also without fibers) be designed on the concrete capacity only. However, practical stirrups are placed (Ø10-200). Since this practical reinforcement is not necessary in a constructive way, the reduction percentages are not that relevant here. It must be noted here that the original stirrups were designed on the fatigue load. With the used stirrup distribution, the unity checks on shear load in ULS were around 0,8-0,9. This means that when fatigue is left out of the calculations, the original stirrup distribution would become somewhat smaller. This implies that the reduction percentages of Table 5 would also lower somewhat. In order words, the results have a little too optimistic character.

3.2. Conclusions From the tables above can be seen that the relevant reductions are between 42% (close to the support) to 93% (further away from the support). The latter value implies that almost all the stirrups can be omitted when the fibers are used. But also with a high shear force VEd, the possible reduction of the shear reinforcement is significant, being 42% of the original amount of stirrups. This is when it is compared to construction height of H=1300. So instead of an increase in stirrups due to a lower construction height, a significant amount of stirrups could be omitted because of the addition of fibers.


18

This is all when 25 kg/m3 of fibers are added to the concrete, fiber type RC-80/30-CP, and a construction height of H=1100 mm. The concrete class used was C90/105. The next goal is to obtain the values of the shear capacity for the other construction heights, which were H=1300 mm, H=1200 mm and H=1000 mm.


19

4. Increased ULS shear capacity H=1300 mm, H=1200 mm and

H=1000 mm Now it is time to determine the values of the shear capacities for other construction heights. The other construction heights that were used in the previous report were H=1200 mm and H=1000 mm. Next to this, the original girder had a construction height of H=1300 mm. The concrete classes were different for the different construction heights. The original girder with a construction height of H=1300 mm used a concrete class C60/75. The girders with lower construction heights used higher concrete classes; for a construction height of H=1200 mm and H=1100 mm concrete class C90/105 were used. When the construction height was even further decreased, a concrete class of C120/140 was necessary. Besides the concrete class, also the amount of prestressing strands did increase for lower construction heights. The original girder had 62 prestressing strands Ø15,7 mm. For a construction height of H=1200 mm, 5 additional strands were needed (so a total of 67 strands), for a construction height of H=1100 mm 14 additional strands were needed (so a total of 76 strands) and for a construction height of H=1000 mm 23 additional strands were needed (so a total of 85 strands). To be able to fit these in the box girder, the lower flange height is increased with 20 mm when needed.

4.1 H=1300 mm The stirrup distribution of this girder was, as stated before, designed on the fatigue load. The unity checks of the shear capacity in ULS were approximately 0,8-0,9. The stirrup distribution of this girder was already given, but for the convenience of the reader it is given again in Table 6. Table 6 - Stirrup distribution

Distance to support [m]

Asw/s [mm2/m]

Applied stirrups

0,5 2094 Ø10-150

0,5 1257 Ø10-125

2,0 1257 Ø10-125

3,5 1047 Ø10-150

5,0 1047 Ø10-150

6,5 1047 Ø10-150

8,0 1047 Ø10-150

9,5 1047 Ø10-150

11,0 785 Ø10-200

12,5 785 Ø10-200

To determine the amount of stirrups that could be reduced, the same systematic procedure (described in Section 3.1) is used. First of all, it is assumed that 25 kg/m3 of fibers are added and that the tensile strength will become the same as with other concrete classes. So with the addition of fibers, the tensile strength is independent of the concrete class. This is not correct, but will give sufficient accuracy for this report. This means that the values that are used for the calculations are:

fLk = 6,32 N/mm2

fR1,k = 4,91 N/mm2

fR2,k = 6,21 N/mm2

fR3,k = 6,35 N/mm2

fR4,k = 5,97 N/mm2 Now the shear capacity of the fiber VRd,f concrete is determined and this value is subtracted from the shear force VEd. The stirrups are designed on the remaining shear force and the amount of stirrups is


20

compared to the original amount of stirrups of Table 6. The shear capacity VRd,f is determined (again with the consistent approach) and the results are shown in Table 7. Table 7 - Shear capacity VRd,f,consistent for different cross sections and H=1300 mm


2,0 1022

3,5 1066

5,0 1090

6,5 1108

8,0 1103

9,5 949

11,0 873

12,5 805

When the values of Table 7 are compared to the values of Table 2 (which are the values of VRd,f for H=1100) the values of Table 7 are somewhat higher. This is not a factor 1300/1100=1,18 higher, as could be approximately expected when one sees the formula and knows that fFtuk is the same (because this is based on the frn,k which are the same):

( √ ( ))

However, for a construction height of H=1300 mm, a concrete class C60/75 is used, instead of C90/105 which was used for a construction height of H=1100. That is why the increase in VRd,f is less than a factor 1,18. The increase in VRd,f is now approximately 8%. With the values of Table 7, the remaining shear force can be determined, see Table 8. In here, it is taken into account that the dead load of the girder is higher for a construction height of H=1300 mm compared to a construction height of H=1100 mm. That is why the shear force VEd is higher for a construction height of H=1300 compared to a construction height of H=1100 (compare Table 8 with Table 3). The stirrups should be designed on the remaining shear force. This remaining shear force does not, in contract to the girder with a construction height H=1100 mm, become zero for any cross section that is considered. The shear force VEd increases with (approximately) a factor 1300/1100=1,18, but the shear capacity does “only” increase by approximately 8%. Due to this, there is a remaining shear force for all the cross sections that are considered. This implies that there should always be some stirrups, even from a constructive point of view. This is the results of the lower concrete class. In general, the remaining shear force is approximately the same for construction height H=1300 and H=1100. This is the net result of a higher VEd, a higher VRd,f. Table 8 – Remaining shear force for different cross sections and H=1300 mm


2,0 1835 813

3,5 1632 566

5,0 1462 372

6,5 1313 205

8,0 1192 89

9,5 1076 127

11,0 958 85

12,5 840 35


21

Now the amount of needed vertical reinforcement area can be determined, based on the values of Table 8. For this, the internal lever arm z and the crack inclination ϴ have to be known. The values of these parameters are given in Table 9, along with the total amount of stirrups that are needed to deal with the remaining shear force determined in Table 8. Note that this is the amount of stirrups that are needed in the whole cross section, so in 2 webs combined. It can be seen that the value of z can very well be predicted by multiplying the value of z, with a construction height of H=1100, by the factor 1300/1100. Table 9 - Needed amount of vertical reinforcement for different cross sections and H=1300 mm


2,0 894 29,0 1103

3,5 940 29,0 736

5,0 981 29,0 473

6,5 1003 29,0 256

8,0 1019 29,1 110

9,5 1032 30,7 165

11,0 1045 31,8 115

12,5 1058 33,0 50

Because the remaining shear force, i.e. the design force of the stirrups, stays approximately constant, but the internal lever arm z increases, the amount of stirrups that are needed are lower when compared to the case of H=1100 mm. This will lead to a higher reduction percentage, because the amount of stirrups are still compared to the original values of Table 6, as were the values of the case H=1100. The reduction percentages are shown in Table 10. Table 10 - Reduction of vertical reinforcement for different cross sections and H=1300 mm


[mm2/m]



0,5 652 1257 48%

2,0 551 1257 56%

3,5 368 1047 65%

5,0 237 1047 77%

6,5 128 1047 88%

8,0 55 1047 95%

9,5 83 1047 92%

11,0 58 785 93%

12,5 25 785 97%

From Table 10 follows that when the construction height is kept the same and 25 kg/m3 are added, the amount of stirrups could be substantially reduced. Close to the support, where the highest shear force will act, approximately 50% of stirrups could be removed. Further away from the support, almost all the stirrups could be removed. The reason for this is that the shear capacity of the fiber concrete will be approximately constant over the length of the girder, aside from the increase in internal lever arm z due to the changed center of gravity zp of the prestressing strands. Close to the support, this shear capacity VRd,f is about half the shear force VEd. But further away from the support, VRd,f comes close to the shear force VEd so here almost all the stirrups could be removed (when only the constructive matter is considered, so no practical stirrups).


22

Note that the values of the reduction percentages are a little too optimistic. The values of the original amount of stirrups are based on the fatigue load, not the ULS load. As stated, when fibers are added, the fatigue load is no longer governing but the ULS load will become governing. The unity checks on shear load is ULS were around 0,8-0,9 with the original stirrup distribution. This implies that the original amount of stirrups could be reduced to 80-90%. When these values are used, the reduction percentages lower somewhat.

4.2 H=1200 mm So now the values of the stirrup reductions are known for a construction height of H=1300 mm and H=1100 mm, when compared to the original girder with a construction height of H=1300 mm. It is to be expected that when a construction height of H=1200 mm is chosen, the values of the reduction percentages of the amount of stirrups will be in between the values of H=1300 mm and H=1100 mm. Also for the construction height of H=1200 mm the concrete class C90/105 was used. Furthermore, the amount of prestressing strands that were needed was 67 strands. To determine these values, the same procedure will be used. The shear capacity is determined when 25 kg/m3 of fibers (fiber type RC-80/30-CP) are added. This value is subtracted from the shear force VEd, the stirrups are designed on the remaining shear force. The shear capacity VRd,f of the girder with a construction height of H=1200 mm is given in Table 11. The values of VRd,f for a construction height of H=1200 mm are both higher than the same quantity with H=1100 and H=1300. It is higher than with H=1300 mm because the concrete class is increased (from C60/75 to C90/105). It is higher than with H=1100 mm because the internal lever arm is increased. Table 11 - Shear capacity VRd,f,consistent for different cross sections and H=1200 mm


2,0 1044

3,5 1087

5,0 1110

6,5 1129

8,0 1143

9,5 1019

11,0 923

12,5 841

The remaining shear force is thus expected to be lower when compared to a construction height of H=1300. The acting shear force VEd decreases (due to a lower dead load of the girder) and the shear capacity of the fiber concrete increases (see Table 11). The remaining shear force can be seen in Table 12. Indeed, the remaining shear force is lower, and even becomes zero again. This is for 12,5 meter from the support.

Table 12 – Remaining shear force for different cross sections and H=1200 mm


2,0 1789 744

3,5 1590 503

5,0 1424 313

6,5 1278 149

8,0 1161 18

9,5 1048 29

11,0 935 12

12,5 820 0


23

Now the amount of needed vertical reinforcement area can be determined, based on the values of Table 12. For this, the internal lever arm z and the crack inclination ϴ have to be known. The values of these parameters are given in Table 13, along with the total amount of stirrups that are needed to deal with the remaining shear force. Note that this is the amount of stirrups that are needed in the whole cross section, so in 2 webs combined. Table 13 - Needed amount of vertical reinforcement for different cross sections and H=1200 mm


2,0 864 29,0 1098

3,5 899 29,0 714

5,0 919 29,0 434

6,5 934 29,0 204

8,0 946 29,0 24

9,5 958 30,1 41

11,0 970 31,2 17

12,5 975 32,4 0

With the known values of Table 13, the reduction percentages for the box girder with a construction height of H=1200 mm can be determined. This is done in Table 14. The reduction percentages of this girder are comparable to the girder with a construction height H=1300 mm. Table 14 - Reduction of vertical reinforcement for different cross sections and H=1200 mm


[mm2/m]



0,5 650 1257 48%

2,0 549 1257 56%

3,5 357 1047 66%

5,0 217 1047 79%

6,5 102 1047 90%

8,0 12 1047 99%

9,5 20 1047 98%

11,0 8 785 99%

12,5 0 785 100%

As stated at the beginning of the section, the expectation was that the reduction percentages of a construction height H=1200 mm were between the values of those with the construction height H=1300 mm and H=1100 mm. However, as can be seen from Table 14, the values tend to be more close to the values with construction height H=1300. This is due to the interaction between concrete class and shear capacity on one side and the interaction between the internal lever arm and the shear capacity on the other side.

4.3 H=1000 mm The last girder configuration which is used in this report is the girder with a construction height of H=1000 mm. The amount of applied prestressing strands was 85, and the concrete class used was C120/140. And again, the same type and amount of fibers are used. The shear capacity VRd,f of the girder with a construction height of H=1000 mm is given in Table 15. Close to the support and up to approximately 8 meters from the support, the shear capacity of this configuration is lower compared to all other configurations (H=1300 mm, H=1200 mm and H=1100


24

mm), despite the higher prestressing force and the higher concrete class. For this, the internal lever arm has thus more influence on the shear capacity. Table 15 - Shear capacity VRd,f,consistent for different cross sections and H=1000 mm


2,0 932

3,5 963

5,0 983

6,5 998

8,0 1010

9,5 1022

11,0 1026

12,5 896

But due to the lower construction height, the dead load will again decrease. This leads to a lower design shear force VEd. The remaining shear force is given in Table 16. From this table can be seen that this girder configuration has the lowest remaining shear force. Table 16 – Remaining shear force for different cross sections and H=1000 mm


2,0 1645 713

3,5 1458 495

5,0 1304 321

6,5 1170 172

8,0 1064 54

9,5 963 0

11,0 861 0

12,5 759 0

This low remaining shear force could lead to a low needed amount of vertical reinforcement. However, due to the small internal lever arm the needed amount of vertical reinforcement will not become that low, see Table 17. The values are comparable to the values with a construction height H=1100 mm. This makes sense, because the internal lever arm decreases somewhat, but the concrete class increases. Both effects cancel each other out. Table 17 - Needed amount of vertical reinforcement for different cross sections and H=1000 mm


2,0 712 29,0 1276

3,5 736 29,0 858

5,0 750 29,0 546

6,5 762 29,0 288

8,0 771 29,0 89

9,5 781 29,0 0

11,0 790 29,1 0

12,5 794 30,2 0

With the known values of Table 17, the reduction percentages for the box girder with a construction height of H=1000 mm can be determined. This is done in Table 18. The reduction percentages of this girder are comparable to the girder with a construction height H=1100 mm.


25

Table 18 - Reduction of vertical reinforcement for different cross sections and H=1000 mm


[mm2/m]



0,5 735 1257 42%

2,0 638 1257 49%

3,5 429 1047 59%

5,0 273 1047 74%

6,5 144 1047 86%

8,0 44 1047 96%

9,5 0 1047 100%

11,0 0 785 100%

12,5 0 785 100%

Again, all the stirrups could be removed for a distance of 9,5 meter from the support and further, when no practical stirrups are needed.

4.4 Conclusions In this chapter, the results of shear reinforcement calculations are presented. This is done for different construction heights, which on their turn made use of different concrete classes and amount of prestressing strands. One value was kept constant: the amount of fibers per cubic meters of concrete was in every configurations 25 kg/m3 (fiber type RC-80/30-CP). It was assumed that, despite the different concrete classes, the tensile strength of the fiber concrete was also constant due to the constant amount and type of fibers. The addition of the fibers lead to an increase in shear capacity of the concrete cross section. When the construction height is kept the same as the reference project (H=1300 mm) the amount of stirrups could be significantly reduced. Close to the support this reduction is approximately 50% and further away from the support the stirrups could be completely omitted. For lower construction heights, the values of the reduction percentages do not differ that much. When the construction height decreases, the internal lever decreases and thus the shear capacity of the concrete cross section decreases. However, for lower construction heights the concrete class was increased. This leads to a higher shear capacity. Both effect cancel each other more or less out, as can be seen in Figure 16.

Figure 16 - Reduction percentages for different construction heights

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0,5 2,5 4,5 6,5 8,5 10,5 12,5

Re

du

ctio

n p

erc

en

tage

s [%

]


H=1300

H=1200

H=1100

H=1000


26

So, from a constructive point of view the stirrups could be completely omitted from a certain distance from the support. However, this is not possible from a practical point of view. Practical reinforcement is needed to, among others, make sure that the longitudinal reinforcement is kept in place. This is done by tightening the stirrups to the reinforcement nets with wire. When the stirrups are not present, the reinforcement nets will not have enough cover. In this section, this practical reinforcement is set to Ø10-200, so stirrups with a diameter of 10 mm, which are placed every 200 mm. When the amount of stirrups per construction heights are put in a graph, together with the minimum amount of stirrups for practical reasons, the graph of Figure 17 is obtained. In this graph, the area below the practical stirrups is made gray because these values are irrelevant, only the values above the gray area are relevant. This is because no values less than the practical stirrups can be used. From Figure 17 can be seen that all the values are in the “gray area” which means that in the whole girder, for every construction height, only practical stirrups are required.


With this known, it could be beneficial when it is possible to place less practical stirrups and still be able to tie the nets to the stirrups and obtain sufficient connections between the nets and the stirrups. When less practical stirrups are used (Ø10-300), the “gray area” in Figure 17 becomes lower, see Figure 18. With this, not all the stirrups in the girder are less than the practical stirrups. Close to the support, more stirrups are needed to be able to deal with the large shear forces in this area. For a distance of 3,5 meter from the support and further, the needed amount of stirrups is again less than the practical stirrups.

0

200

400

600

800

1000

1200

1400

0,5 2,5 4,5 6,5 8,5 10,5 12,5

Am

ou

nt

of

rein

forc

em

en

t p

er

we

b [

mm

2 /m

]


H=1300

H=1200

H=1100

H=1000

Practical stirrups

Original


27


0

200

400

600

800

1000

1200

1400

0,5 2,5 4,5 6,5 8,5 10,5 12,5

Am

ou

nt

of

rein

forc

em

en

t p

er

we

b [

mm

2/m

]


H=1300

H=1200

H=1100

H=1000

Practical stirrups

Original


28

5. Influence on casting process Every day, multiple girders of various types are produced at Spanbeton (e.g. composite beams, box girders). In this section, the casting process of the box girders is discussed, as well as the possible improvements that could be made when the girders are produced with high strength (fiber reinforced) concrete. With the current system, which is described in further detail below, one girder can be produced per day per prestressing bed. In here, the prestressing force is applied after 15-16 hours. This cannot be applied earlier, because the concrete strength is not yet developed enough to be able to withstand the prestressing force. In this section, it is (theoretically) tried to produce 2 girders per prestressing bed per day. For this, the prestressing should already be applied earlier.

5.1 Casting process For the casting of box girders, a certain sequence of different operations should be performed. First, the reinforcement cages (which are produced by another company, very close to Spanbeton) and Polystyrene blocks will be placed inside the (cleaned and oiled) formwork. The Polystyrene block will stay inside the box girder during its lifetime and is only used to divide the “hollow” part from the concrete. When the reinforcement and Polystyrene is placed, the prestressing strands will be placed. The strands that will be kinked, are fixed with deviators. When everything is in place, the prestressing stands are connected to the stressing jacks. When all the above mentioned operations are performed, the prestressing strands are stressed (Spanbeton makes use of pre-tensioned strands), after which the concrete is poured and covered with a plastic sheet (to keep the heat inside). Currently, the pouring is done in one batch. This is possible, because of the Polystyrene block which is left inside the girder. No measures have to be taken to get the Polystyrene block out, leading to the fact that the whole girder can be poured at once. Not so long ago, a method with an inner box (of steel, so no Polystyrene) was used. When this was done, the pouring was done in two batches, to be able to remove the inner box. But to remove the inner box takes time. In this time, the already poured concrete will start to harden. In this way, a strength differences occurs between the two (at different times poured) layers. When the pouring is done, one needs to wait until the concrete has sufficient strength before the prestressing can be released. This strength is needed to be able to cope with the prestressing forces. When the concrete has sufficient strength, the pre-tensioned prestressing strands are released, which leads to stresses in the girder. In the lower side of the girder, the stresses will be compressive stresses. But also tensile stresses will be introduced in some parts of the girder, which will be discussed in Section 6. When using the “standard strength” of C60/75, the release of the prestressing could be done after 16 hours of pouring. The compressive strength is then assumed to be 40 MPa. According to the code [1] (Eurocode 2 - 5.10.2.2 (5)), the compressive stress at the moment the prestressing is applied should not exceed 0,7*fck(t), so in this case 28 MPa. In normal situations (i.e. not very slender girders), this requirement is met. When using this “standard strength” girders, a scheme could be used of preparing, tensioning an pouring the girder in the afternoon. Then the concrete hardens overnight, so the next morning, the prestressing can be released and the formwork can be removed. The rest of the morning, a new girder can be prepared (cleaning and greasing the formwork, placing the reinforcement etc.). Then again, in the afternoon, the pouring is done. In this way, one girder can be produced per day, per prestressing bed. An (indicative) example of a casting schedule, as is described above, is given in Table 19. When the cycle is started 8.00 am, the pouring could start around 2.00 pm. Than at 6.00 am the next day, the


29

formwork could be removed and the prestressing could be applied. With this, the formwork would be ready for cleaning again at 8.00 am. Table 19 - Indicative casting schedule

Process Process time [h] Total time elapsed [h]

1. Cleaning formwork and applying

formwork oil 0,75 0,75

2. Placing reinforcement cages and

Polystyrene block 3,5 4,25

3. Placing prestressing (couplers etc.) 0,5 4,75

4. Tensioning prestressing strands 0,5 5,25

5. Checking reinforcement,

prestressing and formwork 0,5 5,75

6. Pouring of the concrete 2 7,75

7. Covering girder and hardening of

the concrete 15 22,75

8. Removal of the formwork 0,5 23,25

9. Release of the prestressing force 0,5 23,75

10. Hoisting girder 0,25 24

11. Checking of the girder 1 n.a.*

12. Finishing of the girder 1 n.a.*

*Is done in another place in the factory, so a new cycle can already start Note that the lower side of the girder is poured earlier than rest of the girder, so this section will already start to harden before the rest of the girder is poured. In this way, the section will already be hardened for one hour, leading to a hardening time before prestressing of 16 hours for this section. This is needed, because most of the prestressing strands are located in this section.

5.2 Conclusions From Table 19 can be concluded that a pouring two box girders per day per prestressing bed will not be able. This has some reasons:

When everything of Table 19 is kept constant except the hardening time and a whole cycle should be performed in half a day, the hardening time would become 3 hours. This is, even for high strength concrete, far too short.

Even when it was possible to apply the prestressing after 3 hours, it would not be possible for practical reasons. Spanbeton does not work overnight, this time is always used for the concrete to harden. When only a hardening time of 3 hours is used, this would not be possible.

Due the complexity of the reinforcement cages, it is not possible to win time in this part. Furthermore, the pouring of the concrete could take longer when fiber concrete is used.

On the other side, various types of girders are produced at Spanbeton. When more simple girders (less reinforcement, less prestressing strands) are produced, more girders could be produced per time interval. The faster hardening of the high strength concrete could be used here to increase the amount of girders produced per day per prestressing bed.


30

6. Early age strength From the previous section can be concluded that it is not possible to cast two box girders in one day. Nevertheless, in this section the increased early strength of concrete is discussed. In the early age, the girder will be faced with both compressive and tensile stresses. Both are increased compared to the original girder with a construction height of H=1300 mm and 62 prestressing strands. The compressive stresses are increased due to the higher prestressing force. The highest compressive force could occur in two places: close to the head of the beam (only prestressing force) or in the middle of the beam (prestressing force plus bending moment due to dead load). The tensile stresses, introduced as splitting stresses, are the effect of the prestressing force located in the lower side of the girder. Just above the prestressing strands, the tensile splitting stresses will occur. The kinked strands will compensate for some of the tensile splitting stresses, but not all of them. Moreover, the additional prestressing strands are all located in the lower flange (so no kinked strands are added), leading to higher tensile splitting force. For normal strength (prestressted) concrete girders, the head of the girders are mostly heavily reinforced. This reinforcement is placed to control the (splitting) cracks at the head of the girder, which are introduced by the prestressing. However, when fiber reinforced concrete is used, these fibers could be able to take up (part) of these tensile stresses. With this, the heavy reinforcement could be (partly) omitted. In this respect, another property of the early age concrete comes of importance, being the bond strength. The fibers will bridge the cracks and transfer the tensile stresses to the concrete by means of bond. So the bond strength must have a certain value already when the prestressing is applied, to be able to transfer the (tensile) stresses from the fiber to the concrete. The bond strength ,and thus also the early age bond strength, depends among others on the (early age) tensile strength of the concrete. Another parameter that is of importance for the bond strength is the aspect ratio of the fiber, which is defined as the ratio of the fiber length and the fiber diameter. In general it holds that the higher the aspect ratio, the better the bond properties [8]. This is mainly caused by the fact that there will be more fibers per kilogram fibers when a higher aspect ratio is used. This implies that there is more effective bond area per kg fibers.

6.1 Properties young concrete

6.1.1 Regular concrete

When water and cement are mixed, a thin layer of reaction products are formed at the surface of the cement particles (the so-called phase-boundary reaction). The precipitation of the reaction products initially slow down the reaction process. This period, without any observable reaction activity, is called the dormant stage and lasts for several hours up to more than twenty hours [9]. The total time can be influenced by means of reaction accelerators or retarders. After the dormant stage, the acceleration period follows where, in a relatively short time, a substantial part of the cement reacts with water. In this period, the layer of hydration products around the cement particles become thicker. Eventually, the particles come in contact with each other. A microstructure is formed, with unhydrated cement, hydration products and a (capillary) pore system, partly filled with water. After a certain period, the acceleration changes towards the “ceasing stage”. For an indicative figure of all the stages as a function of the degree of hydration αh(τ), see Figure 19. The degree of hydration is a direct measurement for the strength development of the concrete, as discussed later.


31

Figure 19 - Indicative view of different hydration stages [9]

The degree of hydration is defined as the ratio of the amount of hydrated cement to the total amount of cement. When it is assumed that the amount of liberated heat is proportional to the amount of cement that has reacted, the degree of hydration can be presented as

( ) ( )

with Q as the liberated heat. Qmax depends on the amount and type of cement. At Spanbeton, cement type CEM III/A 52.5N is used, which has a Qmax of approximately 450 J/g cement. Depending on the type of cement, a water-cement ratio (wcr) of about 0,4 is theoretically required to obtain complete hydration of all the cement present. In practice however, a wcr of 0,4 does not result in complete hydration. Figure 20 gives an impression of the maximum degree of hydration αh,max expected in practice as a function of the wcr.

Figure 20 - Practical values of the αmax as a function of the wcr [9]

As stated, the degree of hydration is a direct measurement for the strength development of the concrete. The relation between the degree of hydration and the compressive strength is a bi-linear


32

relationship. First, a certain degree of hydration should be reached to obtain any compressive strength. After this point, the increase in degree of hydration is linearly related to the increase in compressive strength. This can be seen in Figure 21, which provided an indicate view of the relation between the degree of hydration and the compressive strength, for different water cement ratios.

Figure 21 - Indicative view of compressive strength as a function of α [9]

A similar bi-linear relationship holds for the tensile splitting strength and the degree of hydration. Again, first a certain degree of hydration should be reached. After this, the tensile (splitting) strength starts to rise, linearly depending on the degree of hydration. In Figure 22, again an indicative view is given of the discussed bi-linear relationship. This is a results of a test performed by S.J. Lokhorst et al. [10], where 350 kg/m3 of Blast furnace slag cement CEM II was used.

Figure 22 - Indicative view of tensile strength as a function of α [10]

The same report provides indicative values of the early age values for the Young’s modulus, see Figure 23. Again, 350 kg/m3 of blast furnace slag cement CEM II was used. It can be seen that the Young’s modulus does not have a bi-linear relationship like the compressive and tensile strength. The Young’s modulus could be assumed to be depending on the root of the degree of hydration. Furthermore, again a certain critical degree of hydration should be reached, before any increments in the Young’s modulus are to be expected.


33

Figure 23 - Indicative view of Young's modulus as a function of α [10]

6.1.2 High strength concrete

Higher strength concretes have, among others, a lower water cement factor (wcf) compared to normal strength concrete. As can be seen from Figure 21 and Figure 22, this implies that at a lower degree of hydration the compressive and tensile strength already starts to grow, i.e. a lower critical degree of hydration is needed for the strengths to grow. This is caused by the fact that with a lower wcf, more cement is present and the cement particles are more close to each other. So when the cement particles react with the water, they will reach other (already reacted) particles earlier. This is the instance from where the strength will start to grow. Next to the fact described above, a higher cement content will lead to a higher amount of heat that is liberated by (and inside) the concrete. This heat will lead to a faster rate in degree of hydration. This can be seen in the following factor used in the Modelcode [2], which describes the strength development of the concrete in time for the first 28 days (and has its maximum of 1 after 28 days):

( √

)

where s depends on the strength class of the cement (for strength classes with fcm>60 MPa it holds s=0,20). The time t in days should be adjusted according to the following formula, which takes into account the temperature during curing:

∑

( )

Where: tT = the temperature-adjusted concrete age which replaces t in the formula of βcc [days] Δti = the number of days where a temperature T prevails [days] T(Δti) = the mean temperature during the time period Δti [°C] Compared to a temperature of 20° C, a concrete temperature of 40° C gives a tT which is a factor 2,4 higher. This implies that concrete, which is cured at 40° C for 1 day, would be a factor 1,5 stronger than concrete which is cured at 20° C for 1 days (when s is assumed to be 0,2). Curing at 60° C even leads to a value of tT which is 5,1 times higher, implying a 1,8 times stronger concrete.


34

Besides the heat that is liberated by the concrete itself, Spanbeton makes use of a heating system. Tubes are present along the formwork, through which hot water can flow. These tubes emit heat to the concrete girder. Furthermore, inside the formwork a thermal insulation sheet is present. In this way, the heat will stay inside the formwork and will thus effect the hardening process in a positive way (i.e. hardening will go faster). This temperature system is a measurement-regulated system. This means that the output of a constant temperature-measuring system controls the amount of heat that is applied to the heating system. In this way, it is made sure that every girder has a sufficient strength before the prestressing is applied. When it seems that a girder will not have had enough heat after 16 hours (so if the maturity is too low), the amount of heat applied to the heating system is increased, leading to a sufficient maturity before applying the prestressing force.

6.2 Influence on casting process The influence of the information presented above is still to be investigated. Does the compressive stress at the instance that the (increased) prestressing is applied overcomes the compressive strength at that instance? And how about the tensile splitting stresses? To investigate this, the stresses at the instance that the prestressing is applied are determined (with the help of various programs), together with the strength at the same instance.

6.2.1 Compressive stress

The maximum compressive stress during construction (so with still a low compressive strength) could occur in two places: in the head of the girder or in the middle of the girder. In the head of the girder, there is no bending moment present, so no tensile stress. This would lead to high compressive stresses, if the area was not that big. But in the head of the girder, the girder is solid, so the prestressing force could be divided over a bigger area. In the middle of the girder, the area is not that big. In the construction phase, the highest compressive stress would be in the lower side of the girder. This is introduces by the prestressing force (F/A+M/W), but it is partly compensated by the dead load of the girder (M/W). For a construction height of H=1000 mm, this stress will become approximately 31 MPa, as followed from the previous report. This is subdivided in 51 MPa of compression due to prestressing and 20 MPa of tension due to the dead load. This dead load will already work, even in the girder is still on the prestressing bed. Due to the prestressing, the girder will get a camber. Due to this camber, the girder is only supported at both ends. So in this way, the dead load will already lead to tensile stresses in the lower side of the girder. However, the maximum compressive stress at the (solid) head of the girder is not checked in the current SPAN-sheet. This will be done here roughly to get indicative values for a construction height of H=1000 mm. In this girder, 85 strands with a diameter of 15,7 mm are present of which 16 are kinked. The stress at the instance that the prestressing is applied will be 1470 MPa. When the initial losses (friction losses, elastic shortening) the stress will be approximately 1150 MPa. This gives a prestressing force of Fpi=14663 kN. The common center of gravity of the strands will be at 200 mm from the lowest fiber. The center of gravity of the girder itself will be somewhat lower than half the girder height. It would be in the middle of girder if the recesses (used for the joint) were not present. By means of Autocad, it followed that the center of gravity will be at 495 mm from the lowest fiber, the cross sectional area of the concrete here is 1,46*106 mm2 and the moment of inertia is 1,21*1011 mm4. Now the compressive stress in the lower side of the girder, due to the prestressing only (there is no bending moment due dead load at the head of the girder), will become:

( )

⁄


35

As can be seen, the initial stress at the head of the girder is somewhat less than (but comparable to) the stress in the middle of the girder.

6.2.2 Tensile splitting stress

The prestressing force is applied by means of various strands. In the reference project (construction height H=1300 mm) 62 strands were used and 16 of them were kinked. It was found in the previous report that for lower construction heights more prestressing was needed. The added prestressing strands were placed in the lower flange, so none of them were kinked. The amount of increased strands for the different construction heights were:

H=1200 mm: 5 additional strands, leading to a total of 67 strands (of which were 16 kinked)

H=1100 mm: 14 additional strands, leading to a total of 76 strands (of which were 16 kinked)

H=1000 mm: 23 additional strands, leading to a total of 85 strand s (of which were 16 kinked) As can be seen, the largest part of the prestressing force will be applied in the lower flange, especially for the lower construction heights. These large forces will lead, as stated above, to tensile splitting stresses just above the mean center of gravity of the prestressing strands. These tensile splitting stresses could lead to cracks. The kinked tendons could reduce the magnitude of the splitting stresses, because these strands introduce compressive stresses above the mean center of gravity of the strands. So by adding more kinked strands, this problem could be reduced. However, this is not done because there is no place in the webs to place more prestressing strands in here. To investigate the magnitude of the tensile splitting stresses, the four different girder configurations were used as input for a FEM-program (SCIA Engineer). The prestressing strands were modelled as a line load. The magnitude of the load depends on the actual force and the bond stress to the concrete. This bond stress can be calculated using formula 8.15 of Eurocode 2 [1]:

( )

Leading to a (lower bound) transmission length lpt of:

When the known values are substituted, a transmission length of 770 mm is found, which is used in all the models. When the formulae of the ModelCode 2010 would be used, a longer transmission length would be found. This would lead to lower tensile splitting stresses, that is why the formulae of the Eurocode are used here. The results of the calculations are found in Table 20. As can be seen, for a construction height of H=1000 mm, the tensile splitting stress would become 5,2 MPa, which is 63% higher compared to a construction height of H=1300 mm. The total results of the calculations with SCIA can be found in Appendix A (H=1300 mm), Appendix B (H=1200 mm), Appendix C (H=1100 mm) and Appendix D (H=1000 mm).

Table 20 - Maximum tensile splitting stress

Construction height H [mm]

Maximum tensile splitting stress [MPa]

1300 3,2

1200 3,8

1100 4,5

1000 5,2


36

6.2.3 Compressive strength

It was found that the maximum compressive stress, at the instance of prestressing, would occur in the middle of the girder in the bottom flange. The stress would, according to the SPAN-sheet, become 31 MPa. With the rules of the Eurocode, the compressive stress at the time of prestressing should not exceed 0,7*fck(t). In this case, the minimum required fck after 16 hours should thus become 45 MPa. However, this stress would occur in the girder with a construction height of H=1000 mm. For this construction height, a concrete class of C120/140 was used. It is believed and assumed, without further calculations, that this concrete class will have a compressive strength after 16 hours which is higher than the 45 MPa.

6.2.4 Tensile splitting strength

As shown, the maximum tensile splitting stresses would become 5,2 MPa for a construction height of H=1000 mm. These maximum tensile splitting stresses were 3,2 MPa for a construction height of H=1300 mm. However, these stresses will not be uniaxial tensile stresses, it will be a (far) more complex state of stress at the head of the girder. Because of this complex state of stress, the exact influence of the fibers on the tensile splitting strength at the head of the girder is not yet known. To be able to say something about the required tensile splitting strength, which is needed because the tensile splitting stresses increase, rough calculations are done. In these calculations, the influence of the fibers is not taken into account. In this way, the amount of reinforcement in the head of the girder will increase in order to limit the crack widths. The calculations are done in another SPAN-sheet. The input needed are the stresses at various point in the cross section, the amount of prestressing steel together with the initial steel stress and the amount of reinforcement in the head of the girder. The output of the sheet is the crack width together with the tensile splitting force. Furthermore, the sheet indicates if this tensile splitting force can be taken up by the reinforcement or if more reinforcement is needed. When the known values are substituted for the different girder configurations, the additionally needed reinforcement in the head of the girder can be obtained. For the original girder (H=1300 mm), the needed amount of reinforcement in the head of the girder was:

6 vertical hairpins

24 stirrups The stirrups were divided over 6 layers, i.e. there were 4 stirrups in one layer. The center to center distance for the different layers was 65 mm. From the calculations followed that for a construction height of H=1000 mm, 16 additional stirrups were needed. This means that 10 layers were needed to be able to cope with the tensile splitting force. For now, the influence of the fibers is not taken into account because this is a very complex state of strain and the exact influence of the fibers to this state of strain is not known. However, it is to be expected that the introduction of the fibers will lead to a better distributed crack pattern and thus smaller crack widths. This would on its turn lead to less amount of reinforcement, as was obtained for the shear reinforcement. The exact influence should still be investigated. This could be done in further research.


37

7. Conclusions and recommendations

7.1 Conclusions In this report, the shear capacity of box girders produced by Spanbeton are investigated. This report is a sequel. In the previous report, the slenderness of the box girders were (successfully) increased. This increased slenderness led to higher shear stresses and thus to more stirrups. In this report, the high amount of stirrups is tried to be reduced by means of High Strength Fiber Reinforced Concrete. This is done with the design rules of the ModelCode 2010. With these rules, it is allowed to add the shear capacity of the (cracked) concrete and the shear capacity of the stirrups. The shear capacity of the cracked concrete will depend on (among others) the state of strain. The steel fibers inside the concrete will lead to a lower overall strain and will thus increase the shear capacity of the concrete. For this report, 25 kg/m3 of fiber type RC-80/30-CP were added. This led to a tensile strength which depends on the CMOD. Characteristic values (obtained from Bekaert) for the (flexural) tensile strength were used and were kept constant for different concrete classes. After some investigation, it was assumed that the fatigue loading was no longer governing. Instead, the static ULS load is assumed to be governing. That is why the increase in ULS shear capacity is determined when fibers are added. This is done using the “consistent” approach of the Modelcode, which uses the same approach as the rest of the Modelcode, with an additional term for the fiber capacity. With this, it turned out that much stirrups can be omitted. Close to the support approximately half the amount of stirrups could be omitted, further away from the support the reduction percentages increased to 90-100%, see Figure 24. However, in this figure the practical stirrups are not included. Two practical stirrup distributions are taken into account, being Ø10-200 and Ø10-300. With the first (Ø10-200), no additional stirrups were needed besides the practical stirrups. For the latter (Ø10-300) only close to the support some additional stirrups should be added.

Figure 24 - Reduction percentages for different construction heights

So it is clear that it is possible to reduce the amount of stirrups by using steel fibers and the amount of reduction depends on the chosen practical stirrup distribution.

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0,5 2,5 4,5 6,5 8,5 10,5 12,5

Re

du

ctio

n p

erc

en

tage

s [%

]


H=1300

H=1200

H=1100

H=1000


38

Higher strength concretes have a higher compressive strength, both in the final phase and at the instance that the prestressing is applied. Due to the latter, the higher prestressing force (for lower construction heights) will not lead to compressive failure. The compressive strength will already be high enough to be able to resist the high compressive stresses. The prestressing force will also lead to tensile (splitting) stresses, which also increase for a higher prestressing force. Due to these higher tensile splitting stresses, more reinforcement should be applied at the head of the girder. This increase is a factor 2 for construction height H=1000 mm, compared to a construction height of H=1300 mm. However, in here the influence of the fibers is not taken into account. To investigate the exact influence of the fibers on the complex state of strain, further research is necessary.

7.2 Recommendations On the basis of the presented report, some recommendations are presented to Spanbeton. Next steps in the utilization of HSFRC should include more tests with the fibers to determine the exact strength of the material. For now, use is made of characteristic values which were obtained from Bekaert. To obtain the exact material properties, tests should be done on mixes which are used at Spanbeton. These tests should be done on different concrete classes. Other additional tests should include the lowered workability when the fibers are added and the best way to add the fibers (think about a conveyer belt). Besides this, the scatter of the fiber concrete should be determined. In this report, the assumption is made that the fatigue loads are not governing anymore. This was based on some assumptions, one of them was that the fatigue strength is 30% of the static ULS strength, so

The auteur thinks that this is a safe assumption, but this is not yet proven for this particular fiber type and concrete composition of Spanbeton. Tests should be done to provide more information about the fatigue life of the HSFRC. This could be done in further research. In this report, only 1 type and amount of fibers is applied on one particular project (Veerwegviaduct). On the basis of this type and amount of fibers, the conclusions are drawn. That is why further investigations should be done to other types and amount of fibers. It could be possible that when less amount of fibers are used, a better optimization and lower material costs are obtained. Use was made of a practical stirrup distribution, which (at some places) did have only a small constructive contribution. When less fibers are used, both materials could be used in a more effective way. Furthermore, other fiber types should be investigated. One could question the influence of the aspect ratio of the fiber on the shear capacity. Besides this, it should be checked if the drawn conclusions also hold for other boundary conditions. In Section 5, the influence on the casting process is shortly discussed. It was concluded that the use of HSFRC did not lead to a faster casting process, it was not possible to produce 2 girders in one day due to practical reasons. One of the practical reasons is the time to prepare the formwork with the reinforcement and prestressing steel. However, when other girder types are used (for example SJP’s), the use of HSFRC could actually lead to a faster production process. This is still to be investigated.


39

List of references

[1] NEN-EN 1992-1-1, Eurocode 2: Design of concrete structures - Part 1-1: General rules and rules

for buildings + NA, 2011.


2010, 2013.

[3] NEN, "EN 14651: Test method for metallic fibered concrete," 2007.

[4] M. Lee and B. Barr, "An overview of the fatigue behaviour of plain and fibre reinforced

concrete," Elsevier, Cement & Concrete Composites, vol. 2004, no. 26, pp. 299-305, 2002.

[5] B. Gerhart Vitt, "Understanding steel fibre reinforced cocnrete: Dramix," 2011.

[6] E. Lappa, C. Braam and J. Walraven, "High Strength Fibre Reinforced Concrete; Static and Fatigue

Behaviour," 2005.

[7] NEN-EN 1991-1-1, Eurocode 1: Actions on structures - Part 2: Traffic loads on bridges + NA,

2011.

[8] N. V. Chanh, "Steel fiber reinforced concrete," 2004.

[9] R. Braam, K. van Breugel, C. van der Veen and J. Walraven, Imposed thermal and shrinkage

deformations, Delft, 2011.

[10] ,. S. e. a. Lokhorst, "Ontwikkeling van de mechanische eigenschappen: sterkte en stijfheid,"

CEMENT, 1995/1996.


40

List of figures and tables Figure 1 - Linear constitutive law between abscissa CMOD1 and CMOD3 .............................................. 4

Figure 2 - Linear compressive stress distribution and elasto-plastic tensile behavior ........................... 5

Figure 3 - Rigid-linear tensile behavior and compressive stress applied on the extrados ...................... 5

Figure 4 - Residual flexural strength for different CMOD's ..................................................................... 6

Figure 5 - Maximum shear force Vrd,max with fck=90 MPa ........................................................................ 7

Figure 6 - Maximum shear force VRd,max with fck=120 MPa ...................................................................... 7

Figure 7 – Shear resistance of the plain concrete VRd,c with fck=90 MPa ................................................. 8

Figure 8 - Shear resistance of the plain concrete VRd,c with fck=120 MPa ............................................... 8

Figure 9 - Shear capacity VRd with fck=90 MPa ......................................................................................... 9

Figure 10 - Shear capacity VRd with fck=120 MPa ................................................................................... 10

Figure 11 - Shear capacity VRd,f with fck=90 MPa ................................................................................... 10

Figure 12 - Shear capacity VRd,f with fck=120 MPa ................................................................................. 11

Figure 13 - Secondary cracking [5] ........................................................................................................ 11

Figure 14 - Shear capacity of the fibers only, VRd,f with fck=90 MPa ...................................................... 12

Figure 15 - Fatigue shear capacity of the fibers, VRd,f,fat ........................................................................ 13

Figure 16 - Reduction percentages for different construction heights ................................................. 25


............................................................................................................................................................... 26


............................................................................................................................................................... 27

Figure 19 - Indicative view of different hydration stages [9] ................................................................ 31

Figure 20 - Practical values of the αmax as a function of the wcr [9] ..................................................... 31

Figure 21 - Indicative view of compressive strength as a function of α [9] .......................................... 32

Figure 22 - Indicative view of tensile strength as a function of α [10] .................................................. 32

Figure 23 - Indicative view of Young's modulus as a function of α [10] ................................................ 33

Figure 24 - Reduction percentages for different construction heights ................................................. 37


41

Table 1 - Stirrup distribution ................................................................................................................... 9

Table 2 – Shear capacity VRd,f,consistent for different cross sections and H=1100 mm .............................. 16

Table 3 – Remaining shear force for different cross sections and H=1100 mm ................................... 16

Table 4 - Needed amount of vertical reinforcement for different cross sections and H=1100 mm ..... 17

Table 5 - Reduction of vertical reinforcement for different cross sections and H=1100 mm............... 17

Table 6 - Stirrup distribution ................................................................................................................. 19

Table 7 - Shear capacity VRd,f,consistent for different cross sections and H=1300 mm ........................ 20

Table 8 – Remaining shear force for different cross sections and H=1300 mm ................................... 20

Table 9 - Needed amount of vertical reinforcement for different cross sections and H=1300 mm ..... 21

Table 10 - Reduction of vertical reinforcement for different cross sections and H=1300 mm............. 21

Table 11 - Shear capacity VRd,f,consistent for different cross sections and H=1200 mm ...................... 22

Table 12 – Remaining shear force for different cross sections and H=1200 mm ................................. 22

Table 13 - Needed amount of vertical reinforcement for different cross sections and H=1200 mm ... 23


Table 15 - Shear capacity VRd,f,consistent for different cross sections and H=1000 mm ...................... 24

Table 16 – Remaining shear force for different cross sections and H=1000 mm ................................. 24

Table 17 - Needed amount of vertical reinforcement for different cross sections and H=1000 mm ... 24


Table 19 - Indicative casting schedule ................................................................................................... 29

Table 20 - Maximum tensile splitting stress .......................................................................................... 35

Project Afstuderen

Onderdeel H=1300 mm

Omschrijving -

Auteur MHU

A) 1

Appendix A Below, the coordinates of the prestressing strands at the head of the girder and in the midspan are given, for a construction height of H=1300 mm. The most right column gives the distances [mm] of debonding. It can be seen that 62 strands are applied here, of which 16 are kinked and 22 are debonded over various distances. Further assumptions that are made:

All strands had a diameter of 15,7 mm, so Ap=150 mm2

Working prestressing stress of all the strands is 1110 N/mm2

Transmission length, following from formula 8.15 of NEN-EN 1992-1-1, is kept lpt=770 mm.

streng coördinaten coördinaten onthechtingen

nr midden kop

x-

richt. y-

richt. x-

richt. y-

richt. links rechts

1 87 65 87 65 0 0

2 -87 65 -87 65 0 0

3 139 65 139 65 0 0

4 -139 65 -139 65 0 0

5 191 65 191 65 0 0

6 -191 65 -191 65 0 0

7 243 65 243 65 0 0

8 -243 65 -243 65 0 0

9 295 65 295 65 0 0

10 -295 65 -295 65 0 0

11 347 65 347 65 1000 1000

12 -347 65 -347 65 1000 1000

13 399 65 399 65 1000 1000

14 -399 65 -399 65 1000 1000

15 451 65 451 65 1000 1000

16 -451 65 -451 65 1000 1000

17 503 65 503 65 5000 5000

18 -503 65 -503 65 5000 5000

19 555 65 555 65 5000 5000

20 -555 65 -555 65 5000 5000

21 659 65 659 65 7000 7000

22 -659 65 -659 65 7000 7000

23 74 90 74 90 0 0

24 -74 90 -74 90 0 0

25 126 90 126 90 0 0

26 -126 90 -126 90 0 0

27 178 90 178 90 0 0

28 -178 90 -178 90 0 0

29 230 90 230 90 0 0

30 -230 90 -230 90 0 0

31 282 90 282 90 0 0

32 -282 90 -282 90 0 0

33 334 90 334 90 0 0

34 -334 90 -334 90 0 0

35 386 90 386 90 0 0

Project Afstuderen

Onderdeel H=1300 mm

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Auteur MHU

A) 2

36 -386 90 -386 90 0 0

37 438 90 438 90 3000 3000

38 -438 90 -438 90 3000 3000

39 490 90 490 90 3000 3000

40 -490 90 -490 90 3000 3000

41 542 90 542 90 3000 3000

42 -542 90 -542 90 3000 3000

43 594 90 594 90 3000 3000

44 -594 90 -594 90 3000 3000

45 646 90 646 90 3000 3000

46 -646 90 -646 90 3000 3000

47 663 122 642 500 0 0

48 -663 122 -642 500 0 0

49 642 145 642 550 0 0

50 -642 145 -642 550 0 0

51 642 185 642 600 0 0

52 -642 185 -642 600 0 0

53 642 220 642 650 0 0

54 -642 220 -642 650 0 0

55 642 255 642 700 0 0

56 -642 255 -642 700 0 0

57 642 290 642 750 0 0

58 -642 290 -642 750 0 0

59 642 325 642 800 0 0

60 -642 325 -642 800 0 0

61 642 360 642 850 0 0

62 -642 360 -642 850 0 0

Project Afstuderen

Onderdeel H=1300 mm

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Auteur MHU

A) 3

1.Belastingsgevallen Naam Actie type Lastgroep Belastingtype

#10-65 0 Permanent LG1 Standaard



#16-kink Permanent LG1 Standaard




The prestressing forces are applied as loads on the girder. #10-65 0 represents 10 strands at a distance of 65 mm from the lowest fiber, with a debonding length of 0 mm. In the same way, #6-65 1000 represents 6 strands at 65 mm from the lowest fiber and a debonding length of 1000 mm.

2.Combinaties

Naam Type Belastingsgevallen Coëff. [-]

Alle voorspanning

Omhullende - uiterst

#10-65 0 #6-65 1000 #14-90 0 #16-kink #4-65 5000 #2-65 7000 #10-90 3000

1,00 1,00 1,00 1,00 1,00 1,00 1,00

zonder gedrukte strengen


#10-65 0 #6-65 1000 #14-90 0 #4-65 5000 #2-65 7000 #10-90 3000

1,00 1,00 1,00 1,00 1,00 1,00

Project Afstuderen

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A) 4

3.Combinaties 3.1.Combinaties - Alle voorspanning


Alle voorspanning


#10-65 0 #6-65 1000 #14-90 0 #16-kink #4-65 5000 #2-65 7000 #10-90 3000

1,00 1,00 1,00 1,00 1,00 1,00 1,00

3.1.1.2D element - Spanningen; sigx-

3.1.2.2D element - Spanningen; sigy-

Project Afstuderen

Onderdeel H=1300 mm

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A) 5

3.2.Combinaties - zonder gedrukte strengen Naam Type Belastingsgevallen Coëff.

[-]



#10-65 0 #6-65 1000 #14-90 0 #4-65 5000 #2-65 7000 #10-90 3000

1,00 1,00 1,00 1,00 1,00 1,00



Project Afstuderen

Onderdeel H=1200 mm

Omschrijving -

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B) 1

Appendix B Below, the coordinates of the prestressing strands at the head of the girder and in the midspan are given, for a construction height of H=1200 mm. The most right column gives the distances [mm] of debonding. It can be seen that 67 strands are applied here, of which 16 are kinked and 22 are debonded over various distances. Further assumptions that are made:





nr midden kop

x-

richt. y-

richt. x-

richt. y-

richt. links rechts

1 87 65 87 65 0 0

2 -87 65 -87 65 0 0

3 139 65 139 65 0 0

4 -139 65 -139 65 0 0

5 191 65 191 65 0 0

6 -191 65 -191 65 0 0

7 243 65 243 65 0 0

8 -243 65 -243 65 0 0

9 295 65 295 65 0 0

10 -295 65 -295 65 0 0

11 347 65 347 65 1000 1000

12 -347 65 -347 65 1000 1000

13 399 65 399 65 1000 1000

14 -399 65 -399 65 1000 1000

15 451 65 451 65 1000 1000

16 -451 65 -451 65 1000 1000

17 503 65 503 65 5000 5000

18 -503 65 -503 65 5000 5000

19 555 65 555 65 5000 5000

20 -555 65 -555 65 5000 5000

21 659 65 659 65 7000 7000

22 -659 65 -659 65 7000 7000

23 74 90 74 90 0 0

24 -74 90 -74 90 0 0

25 126 90 126 90 0 0

26 -126 90 -126 90 0 0

27 178 90 178 90 0 0

28 -178 90 -178 90 0 0

29 230 90 230 90 0 0

30 -230 90 -230 90 0 0

31 282 90 282 90 0 0

32 -282 90 -282 90 0 0

33 334 90 334 90 0 0

Project Afstuderen

Onderdeel H=1200 mm

Omschrijving -

Auteur MHU

B) 2

34 -334 90 -334 90 0 0

35 386 90 386 90 0 0

36 -386 90 -386 90 0 0

37 438 90 438 90 3000 3000

38 -438 90 -438 90 3000 3000

39 490 90 490 90 3000 3000

40 -490 90 -490 90 3000 3000

41 542 90 542 90 3000 3000

42 -542 90 -542 90 3000 3000

43 594 90 594 90 3000 3000

44 -594 90 -594 90 3000 3000

45 646 90 646 90 3000 3000

46 -646 90 -646 90 3000 3000

47 663 122 642 500 0 0

48 -663 122 -642 500 0 0

49 642 145 642 550 0 0

50 -642 145 -642 550 0 0

51 642 185 642 600 0 0

52 -642 185 -642 600 0 0

53 642 220 642 650 0 0

54 -642 220 -642 650 0 0

55 642 255 642 700 0 0

56 -642 255 -642 700 0 0

57 642 290 642 750 0 0

58 -642 290 -642 750 0 0

59 642 325 642 800 0 0

60 -642 325 -642 800 0 0

61 642 360 642 850 0 0

62 -642 360 -642 850 0 0

63 0 90 0 90 0 0

64 696 90 696 90 0 0

65 -696 90 -696 90 0 0

66 746 90 746 90 0 0

67 -746 90 -746 90 0 0

Project Afstuderen

Onderdeel H=1200 mm

Omschrijving -

Auteur MHU

B) 3











2.Combinaties


Alle voorspanning


#10-65 0 #6-65 1000 #14-90 0 #16-kink #5-90 0 #4-65 5000 #2-65 7000 #10-90 3000

1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00

origineel (62 strengen)


#10-65 0 #6-65 1000 #14-90 0 #16-kink #4-65 5000 #2-65 7000 #10-90 3000

1,00 1,00 1,00 1,00 1,00 1,00 1,00



#10-65 0 #6-65 1000 #14-90 0 #5-90 0 #4-65 5000 #2-65 7000 #10-90 3000

1,00 1,00 1,00 1,00 1,00 1,00 1,00

Project Afstuderen

Onderdeel H=1200 mm

Omschrijving -

Auteur MHU

B) 4



Alle voorspanning


#10-65 0 #6-65 1000 #14-90 0 #16-kink #5-90 0 #4-65 5000 #2-65 7000 #10-90 3000

1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00



Project Afstuderen

Onderdeel H=1200 mm

Omschrijving -

Auteur MHU

B) 5

3.2.Combinaties - origineel (62 strengen) Naam Type Belastingsgevallen Coëff.

[-]



#10-65 0 #6-65 1000 #14-90 0 #16-kink #4-65 5000 #2-65 7000 #10-90 3000

1,00 1,00 1,00 1,00 1,00 1,00 1,00



Project Afstuderen

Onderdeel H=1200 mm

Omschrijving -

Auteur MHU

B) 6


[-]



#10-65 0 #6-65 1000 #14-90 0 #5-90 0 #4-65 5000 #2-65 7000 #10-90 3000

1,00 1,00 1,00 1,00 1,00 1,00 1,00



Project Afstuderen

Onderdeel H=1100 mm

Omschrijving -

Auteur MHU

C) 1

Appendix C Below, the coordinates of the prestressing strands at the head of the girder and in the midspan are given, for a construction height of H=1100 mm. The most right column gives the distances [mm] of debonding. It can be seen that 76 strands are applied here, of which 16 are kinked and 22 are debonded over various distances. Further assumptions that are made:





nr midden kop

x-

richt. y-

richt. x-

richt. y-

richt. links rechts

1 87 65 87 65 0 0

2 -87 65 -87 65 0 0

3 139 65 139 65 0 0

4 -139 65 -139 65 0 0

5 191 65 191 65 0 0

6 -191 65 -191 65 0 0

7 243 65 243 65 0 0

8 -243 65 -243 65 0 0

9 295 65 295 65 0 0

10 -295 65 -295 65 0 0

11 347 65 347 65 1000 1000

12 -347 65 -347 65 1000 1000

13 399 65 399 65 1000 1000

14 -399 65 -399 65 1000 1000

15 451 65 451 65 1000 1000

16 -451 65 -451 65 1000 1000

17 503 65 503 65 5000 5000

18 -503 65 -503 65 5000 5000

19 555 65 555 65 5000 5000

20 -555 65 -555 65 5000 5000

21 659 65 659 65 7000 7000

22 -659 65 -659 65 7000 7000

23 74 90 74 90 0 0

24 -74 90 -74 90 0 0

25 126 90 126 90 0 0

26 -126 90 -126 90 0 0

27 178 90 178 90 0 0

28 -178 90 -178 90 0 0

29 230 90 230 90 0 0

30 -230 90 -230 90 0 0

31 282 90 282 90 0 0

32 -282 90 -282 90 0 0

33 334 90 334 90 0 0

34 -334 90 -334 90 0 0

Project Afstuderen

Onderdeel H=1100 mm

Omschrijving -

Auteur MHU

C) 2

35 386 90 386 90 0 0

36 -386 90 -386 90 0 0

37 438 90 438 90 3000 3000

38 -438 90 -438 90 3000 3000

39 490 90 490 90 3000 3000

40 -490 90 -490 90 3000 3000

41 542 90 542 90 3000 3000

42 -542 90 -542 90 3000 3000

43 594 90 594 90 3000 3000

44 -594 90 -594 90 3000 3000

45 646 90 646 90 3000 3000

46 -646 90 -646 90 3000 3000

47 663 122 642 500 0 0

48 -663 122 -642 500 0 0

49 642 145 642 550 0 0

50 -642 145 -642 550 0 0

51 642 185 642 600 0 0

52 -642 185 -642 600 0 0

53 642 220 642 650 0 0

54 -642 220 -642 650 0 0

55 642 255 642 700 0 0

56 -642 255 -642 700 0 0

57 642 290 642 750 0 0

58 -642 290 -642 750 0 0

59 642 325 642 800 0 0

60 -642 325 -642 800 0 0

61 642 360 642 850 0 0

62 -642 360 -642 850 0 0

63 87 115 87 115 0 0

64 -87 115 -87 115 0 0

65 139 115 139 115 0 0

66 -139 115 -139 115 0 0

67 191 115 191 115 0 0

68 -191 115 -191 115 0 0

69 243 115 243 115 0 0

70 -243 115 -243 115 0 0

71 295 115 295 115 0 0

72 -295 115 -295 115 0 0

73 347 115 347 115 0 0

74 -347 115 -347 115 0 0

75 399 115 399 115 0 0

76 -399 115 -399 115 0 0

Project Afstuderen

Onderdeel H=1100 mm

Omschrijving -

Auteur MHU

C) 3











2.Combinaties


Alle voorspanning


#10-65 0 #6-65 1000 #14-90 0 #16-kink #14-115 0 #4-65 5000 #2-65 7000 #10-90 3000

1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00



#10-65 0 #6-65 1000 #14-90 0 #16-kink #4-65 5000 #2-65 7000 #10-90 3000

1,00 1,00 1,00 1,00 1,00 1,00 1,00



#10-65 0 #6-65 1000 #14-90 0 #14-115 0 #4-65 5000 #2-65 7000 #10-90 3000

1,00 1,00 1,00 1,00 1,00 1,00 1,00

Project Afstuderen

Onderdeel H=1100 mm

Omschrijving -

Auteur MHU

C) 4



Alle voorspanning


#10-65 0 #6-65 1000 #14-90 0 #16-kink #14-115 0 #4-65 5000 #2-65 7000 #10-90 3000

1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00



Project Afstuderen

Onderdeel H=1100 mm

Omschrijving -

Auteur MHU

C) 5


[-]



#10-65 0 #6-65 1000 #14-90 0 #16-kink #4-65 5000 #2-65 7000 #10-90 3000

1,00 1,00 1,00 1,00 1,00 1,00 1,00



Project Afstuderen

Onderdeel H=1100 mm

Omschrijving -

Auteur MHU

C) 6


[-]



#10-65 0 #6-65 1000 #14-90 0 #14-115 0 #4-65 5000 #2-65 7000 #10-90 3000

1,00 1,00 1,00 1,00 1,00 1,00 1,00



Project Afstuderen

Onderdeel H=1000 mm

Omschrijving -

Auteur MHU

D) 1

Appendix D Below, the coordinates of the prestressing strands at the head of the girder and in the midspan are given, for a construction height of H=1200 mm. The most right column gives the distances [mm] of debonding. It can be seen that 85 strands are applied here, of which 16 are kinked and 22 are debonded over various distances. Further assumptions that are made:





nr midden kop

x-

richt. y-

richt. x-

richt. y-

richt. links rechts

1 87 65 87 65 0 0

2 -87 65 -87 65 0 0

3 139 65 139 65 0 0

4 -139 65 -139 65 0 0

5 191 65 191 65 0 0

6 -191 65 -191 65 0 0

7 243 65 243 65 0 0

8 -243 65 -243 65 0 0

9 295 65 295 65 0 0

10 -295 65 -295 65 0 0

11 347 65 347 65 1000 1000

12 -347 65 -347 65 1000 1000

13 399 65 399 65 1000 1000

14 -399 65 -399 65 1000 1000

15 451 65 451 65 1000 1000

16 -451 65 -451 65 1000 1000

17 503 65 503 65 5000 5000

18 -503 65 -503 65 5000 5000

19 555 65 555 65 5000 5000

20 -555 65 -555 65 5000 5000

21 659 65 659 65 7000 7000

22 -659 65 -659 65 7000 7000

23 74 90 74 90 0 0

24 -74 90 -74 90 0 0

25 126 90 126 90 0 0

26 -126 90 -126 90 0 0

27 178 90 178 90 0 0

28 -178 90 -178 90 0 0

29 230 90 230 90 0 0

30 -230 90 -230 90 0 0

31 282 90 282 90 0 0

32 -282 90 -282 90 0 0

33 334 90 334 90 0 0

Project Afstuderen

Onderdeel H=1000 mm

Omschrijving -

Auteur MHU

D) 2

34 -334 90 -334 90 0 0

35 386 90 386 90 0 0

36 -386 90 -386 90 0 0

37 438 90 438 90 3000 3000

38 -438 90 -438 90 3000 3000

39 490 90 490 90 3000 3000

40 -490 90 -490 90 3000 3000

41 542 90 542 90 3000 3000

42 -542 90 -542 90 3000 3000

43 594 90 594 90 3000 3000

44 -594 90 -594 90 3000 3000

45 646 90 646 90 3000 3000

46 -646 90 -646 90 3000 3000

47 663 122 642 500 0 0

48 -663 122 -642 500 0 0

49 642 145 642 550 0 0

50 -642 145 -642 550 0 0

51 642 185 642 600 0 0

52 -642 185 -642 600 0 0

53 642 220 642 650 0 0

54 -642 220 -642 650 0 0

55 642 255 642 700 0 0

56 -642 255 -642 700 0 0

57 642 290 642 750 0 0

58 -642 290 -642 750 0 0

59 642 325 642 800 0 0

60 -642 325 -642 800 0 0

61 642 360 642 850 0 0

62 -642 360 -642 850 0 0

63 87 115 87 115 0 0

64 -87 115 -87 115 0 0

65 139 115 139 115 0 0

66 -139 115 -139 115 0 0

67 191 115 191 115 0 0

68 -191 115 -191 115 0 0

69 243 115 243 115 0 0

70 -243 115 -243 115 0 0

71 295 115 295 115 0 0

72 -295 115 -295 115 0 0

73 347 115 347 115 0 0

74 -347 115 -347 115 0 0

75 399 115 399 115 0 0

76 -399 115 -399 115 0 0

77 451 115 451 115 0 0

78 -451 115 -451 115 0 0

79 503 115 503 115 0 0

80 -503 115 -503 115 0 0

81 555 115 555 115 0 0

82 -555 115 -555 115 0 0

83 607 115 607 115 0 0

84 -607 115 -607 115 0 0

85 0 115 0 115 0 0

Project Afstuderen

Onderdeel H=1000 mm

Omschrijving -

Auteur MHU

D) 3











2.Combinaties


Alle voorspanning


#10-65 0 #6-65 1000 #14-90 0 #16-kink #23-115 0 #4-65 5000 #2-65 7000 #10-90 3000

1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00



#10-65 0 #6-65 1000 #14-90 0 #16-kink #4-65 5000 #2-65 7000 #10-90 3000

1,00 1,00 1,00 1,00 1,00 1,00 1,00



#10-65 0 #6-65 1000 #14-90 0 #23-115 0

1,00 1,00 1,00 1,00

Project Afstuderen

Onderdeel H=1000 mm

Omschrijving -

Auteur MHU

D) 4



Alle voorspanning


#10-65 0 #6-65 1000 #14-90 0 #16-kink #23-115 0 #4-65 5000 #2-65 7000 #10-90 3000

1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00



Project Afstuderen

Onderdeel H=1000 mm

Omschrijving -

Auteur MHU

D) 5


[-]



#10-65 0 #6-65 1000 #14-90 0 #16-kink #4-65 5000 #2-65 7000 #10-90 3000

1,00 1,00 1,00 1,00 1,00 1,00 1,00



Project Afstuderen

Onderdeel H=1000 mm

Omschrijving -

Auteur MHU

D) 6


[-]



#10-65 0 #6-65 1000 #14-90 0 #23-115 0 #4-65 5000 #2-65 7000 #10-90 3000

1,00 1,00 1,00 1,00 1,00 1,00 1,00




Date post:	16-Oct-2021
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Slender box girders and/or less stirrups by applying HSC ...

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