Concrete Hinge

Steffen Marx, Gregor Schacht

CONCRETE

HINGES

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DEVELOPMENT

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Steffen Marx, Prof. Dr.-Ing. , Inst. of Concrete Structures, Techn. Univ. Dresden, Germany Gregor Schacht, Dipl.-Ing., Inst. of Concrete Structures, Techn. Univ. Dresden, Germany ABSTRACT

Articulated connections consisting of concrete have existed since 1880, when Claus Köpcke first used saddle bearings in a natural stone-arched bridge. Further developments were made in France at the beginning of the 20 th century. While Mesnager used reinforcement to carry the loads of his Mesnager hinges, Freyssinet developed an unreinforced hinge that transmits loads only through the concrete. All hinges work on the same principle – the centering of compression stresses in a very small zone (the throat of the hinge). Concrete hinges have also been used in Germany, in the USA and, particularly, in Switzerland. In the 1960’s, the work of Fritz Leonhardt (Germany), E.O. Fessler (Switzerland) and G.D. Base (Great-Britain), which define the international state-of-the-art until today, led to a renaissance of concrete hinges. The existing design rules are half-empirical and disallow the proper construction of concrete hinges up to the state-of-the-art. Investigations of the existing experiences and design rules were carried out. The design rules given by Leonhardt have been assigned to allow an appropriate design of unreinforced Freyssinet hinges which conform to current code. Keywords:

concrete hinge, Freyssinet hinge, tri-axial compression stress state, Mesnager hinge, saddle bearing,

INTRODUCTION

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Concrete hinges are characterized by an enormous load-bearing capacity and deformability. They are nearly maintenance-free and have a high durability if designed and constructed properly. Concrete hinges are perfectly suited to control the flow of forces and to efficiently reduce constraints. The first massive hinges were developed by Claus Köpcke (Dresden) in 1880 1 and successfully used in several construction projects. The fabrication of these hinges was difficult since the contact-surfaces had to be extremely level. In an effort to correct this problem, von Leibbrand (Stuttgart) developed an alternative type of hinge by arranging thin plumb-plates between the adjacent concrete blocks 2. The break-through in the development of durable and easily casted hinges was first accomplished by Augustin Mesnager in 1908 3. Inspired by his research on confined concrete columns, he developed a “spring-hinge” (semi-articulation), which was similarly used in steel construction. Adjacent concrete blocks are connected by intersecting steel bars. These steel bars transmit the entire force of the hinge-bodies. The concrete only serves to provide corrosion protection and – together with the confining reinforcement – to avoid the buckling of the steel bars. In 1910, Freyssinet was able to prove that reinforcement through the throat is unnecessary, and axial forces are only transmitted by the partially loaded area and an adequate confinement of the hinge4. The rotation of the hinge is secured by the elastic and plastic deformability of the concrete and with larger rotations a crack through the throat of the hinge occurs. In Germany these unreinforced concrete hinges are closely associated with Fritz Leonhardt who developed the commonly used design rules for this type of concrete hinge 5. In the course of recent research, various existing design-models for unreinforced concrete hinges were analyzed and compared6. Figure 1 shows a classification of the different types of hinges.

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Fig. 1: Classification of concrete hinges SADDLE BEARINGS

SADDLE BEARINGS, HINGE-BODIES AND THEIR LOAD BEARING BEHAVIOUR Saddle bearings are two adjacent cubes of stone, comprised of either concrete or reinforced concrete with cylindrical surfaces that allow a rolling motion. In 1880, Köpcke first used these hinges for an arched stonebridge for the Pirna-Berggießhübler Eisenbahn near Langenhennersdorf (Germany) to avoid cracking during settling while stripping away the structure’s formwork1. The hinges were filled with concrete after removal of the formwork. The positive results from the use of these simple hinges led to a large number of saddle bearing hinges in practice. A considerable basis for the use of these hinges was increased knowledge in the material strength of partially loaded areas. By 1869, 12 years before Hertz published his Hertzian stress equations, Köpcke presented an initial theoretical solution to describe the contact between two cylinders7. The first experimental investigations on these saddle bearings were done by Krüger in 1894 for the construction of the Marien Bridge in Dresden (Germany) 8. Krüger detected that the biggest tensile strains and stresses appeared in the middle of the hinge-bodies. These tensile stresses were distributed parabolically and the transverse tensile force was about 28% of the surcharge. The experiments of Bach with sandstone- and granitehinges showed that the failure of the hinges was always caused by tensile stresses rectangular to the pressure. All hinge specimens failed with a big crack in the middle of the hinge-bodies. The detection of the actual cause of failure led to the use of reinforced concrete saddle 3


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bearings (Friedrich-August-Bridge in Dresden, bridge in Rothenburg, Emsbridge Rheda – all Germany) (Fig. 2).

Fig. 2: Reinforced saddle bearings 9 In 1924, Mörsch developed the first theoretical solution for hinge-bodies 10. He used the conditions of distortion as a simple mechanical model to deduce the orthogonal tensile stresses and simplified the representation of these stress fields into a strut-and-tie-model that allowed the determination of the size of the tensile force depending on the surcharge (Fig. 3).

Fig. 3: Strut-and-tie-model of Mörsch 10 Almost half a century after Köpcke first successfully used his saddle bearings, Bortsch published his solution to calculating the stresses in hinge-bodies 11. For a cut out slice of a hinge-body Bortsch used an approximation of a cosine function for the load and applied it to a 4


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cross-section of a hinge-body before breaking down the cosine function into three separate components and solving the “Airy stress function”. He subsequently superposed the three resulting ratios and provided a solution for different geometric variations of the hinge-bodies. These theoretical solutions provided a means by which to calculate the stresses within these hinge-bodies. SPECIAL SADDLE BEARINGS The primary problem with using saddle bearings was the difficulty of creating accurate convex and concave surfaces. The smallest amount of unevenness from processing led to large stress-concentrations. Hence von Leibbrand (Stuttgart) developed a different type of hinged connection by placing small plumb-plates between the cubes allowing rotation from plumb deformation 2. These plates also provided an equalizing layer between the cube surfaces. Plumb hinges have been used successfully for a long time. Even so, in the 1960’s, engineers stopped using them since they had discovered that the plumb plates were worn down after numerous rotations even if the angles of rotation were small12. In 1933, Burkhardt presented a new development, concrete saddle bearings armored with steel plates13. It was thought that these would abolish the disadvantage of the uneven concrete surfaces. The first bridge with these hinges was built over the shipping channel near Obereßlingen (Germany). Experimental investigations at the MPA Stuttgart (Testing Laboratories Stuttgart) proved the enhanced bearing capacity of the armored saddle bearings. DEFORMATION HINGES

SPRING HINGES ACCORDING TO MESNAGER AND CONSIDÈRE At the beginning of the 20th century, French engineers intensively researched the new material, reinforced concrete. At the ‘École des Ponts et Chaussées’ Augustin Mesnager and Armand Considère carried out investigations on confined concrete columns. Based on these experiments, Mesnager developed a “semi-articulation” for reinforced concrete similar to the spring hinges used in steel construction. In 1908, Mesnager described experimental investigations he had made that proved his theoretical ideas3 (Fig. 4).

Fig. 4: Specimen of Mesnager’s experimental investigations3 The concrete in the throat of the hinge was only used for corrosion protection of the intersecting steel bars. In experiments, the failure of the hinges always occurred through concrete spalling at the hinge blocks near the throat followed by buckling or slipping of the steel bars. The intersecting bars must be rigidly confined, as close as possible to the throat of the hinge, to avoid this failure. Mesnager’s hinges have been used successfully in many projects such as the arching of the channel Saint-Martin in Paris, the Amélie-les-Bains Bridge 5


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(Fig. 5), the Carnon Bridge over the Canal du Midi in Montpellier, a suspended deck arch bridge in Mestre (Italy), the Pont sur la Noce and several airship hangars that were constructed as three-hinged arches.

Fig. 5: Three-hinged arch-bridge Amélie-les-Bains 6 The Swiss engineer, Robert Maillart, is particularly known for his use of Mesnager hinges. For instance, he used these hinges in: his famous bridge over the Salginatobel (Fig. 6), the Rossgraben Bridge, the Thur Bridge near Felsegg and the Arve-Bridge in Vessy-Geneve. The Mesnager hinges were also used in Germany for such structures as the arching of Huckarder Street in Dortmund. Emil Mörsch provided several examples of halls that were constructed with these hinges in14.

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Fig. 6: Salginatobel Bridge of Robert Maillart The first report on the experimental investigations of Mesnager’s hinges was published in Germany in 1930. Jesinghaus and Bieligk discovered that the load-bearing behavior of these spring-hinges is similar to that of saddle bearings and that the concrete in the throat is triaxially compressed and, therefore, able to withstand much higher levels of stress15. Jesinghaus experimented with various forms of reinforcement and assessed the necessity to use rigid, confining, stirrup reinforcement. In the USA Moreell16 designed a ship-model testing plant for the U.S. Navy in which the three-hinged arch roof was built with Mesnager hinges. Experimental testing was conducted to insure the adequate performance of these hinges. Parson and Stang implemented investigations with 7 hinge specimens and developed a calculation model to design Mesnagerhinges. They were extremely concerned with confinement of the longitudinal bars and tested the shear force bearing capacity of the hinges. The Universities of Maryland and Illinois set about confirming the calculation model of Parson and Stang and to expand these findings to add information about dynamic loading and the influence of concrete creep. In the early 1950’s, Jeske and Kammüller rediscovered the Mesnager-hinges and published their findings in 1957 in 17. They searched for the ultimate shape for the notch using analytical and experimental techniques, as well as providing theoretical solutions for the distribution of the elastic stresses in the hinge. In Switzerland, Mesnager hinges were used for highway bridges in Encublens and for the Hardturm-Viaduct, accompanied by extensive experimental investigations, by the EMPA Zürich (Swiss National Laboratories Zürich)18. These hinges successfully carried millions of alternating rotations and withstood even extreme angles of rotation without any sign of failure (Fig. 7).

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Fig. 7: Mesnager hinges at the EMPA-test for Hardturm Viaduct 18 At the same time Mesnager developed his spring-hinge, the French engineer, Armand Considère, invented a hinge with a spiral confining reinforcement in the throat of the hinge. By 1902, he had already received a patent on spirally confined concrete. The first arched bridge that used the Considère hinge is the 1930 built Caveman Bridge near Grants Pass in Oregon (USA). Many more bridges in the USA have been built using the Considère hinges (Rogue River Bridge, Coos Bay Bridge / McCullough Memorial Bridge, Oregon) (Fig. 8). The use of this type of hinge in the USA is primarily associated with the engineer, Conde B. McCullough19.

Fig. 8: Spiral reinforced hinge – Considère19 8


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UNREINFORCED CONCRETE HINGES ACCORDING TO FREYSSINET A few years after Mesnager presented his Mesnager hinge, the French engineer, Eugène Freyssinet, used a similar shaped hinge for his bridge, ‘Pont du Veurdre’ and its two sisterbridges, Boutiron and Châtel de Neuvre 4. Freyssinet recognized that the tri-axial state of stress prevented the concrete from collapse and that the resulting compression strength of the concrete in the throat was significantly higher. Knowing this, he abandoned any reinforcement of the throat and assigned the entire load-bearing function only to the concrete in the throat.

Fig. 9: Luzancy Bridge of Eugène Freyssinet4 Initial experimental investigations of unreinforced concrete hinges were done by Riessauw and Passelecq at the University of Gent (Belgium)20. The specimens were able to bear rotations up to 0.02 rad without any signs of failure. The positive results from the use of these unreinforced concrete hinges led to the proliferation of their use in construction. The waterreservoir in Orleans, the Coudette Bridge and the six prefabricated, pre-stressed bridges over the Marne21 (France) are only a few examples of the widespread use of this type of hinge (Fig. 9, Fig. 10).

Fig. 10: Concrete hinges used at the base of six Marne Bridges, Photo: J.Mossot, www.structurae.de 9


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In Great-Britain, an alternative to using steel bearings was sought after to reduce the cost of the expansion of the highway network system. G.D. Base 22 carried out several experiments with Mesnager and Freyssinet hinges. His investigations on the shear force bearing-capacity of the hinges are worth noting. He proved that unreinforced concrete hinges are capable of transmitting enormous shear forces if the surcharge is sufficient enough. The results of these experimental investigations were transformed into a model for calculation by Sims and Bridle which has been used for the design of Freyssinet hinges since 1975 23. Freyssinet hinges were first been used in Germany in 1953 for a pre-stressed bridge over the Nidda. Fritz Leonhardt then used concrete hinges for the hinged columns of a motorway in Mannheim to allow small rotations and to avoid expansive steel bearings. Next, Dix24 in Karlsruhe and Leonhardt 5 in Stuttgart carried out experimental investigations to study and describe the load-bearing behavior of the Freyssinet hinges. In 1965, Leonhardt produced the first design- and construction rules for the practical use of unreinforced concrete hinges in Heft 175 DAfStb. In 1969, Mönnig and Netzel reworked these rules to provide for greater ease of use in practice. Finally, the rules for the design and construction of Freyssinet hinges were published in Vorlesungen über Massivbau25. Since then, these rules have been the basis for the design of many hinges in bridge constructions such as the Mainbrücke in Gemünden, the Valley Bridge Korntal-Münchingen, the Lockwitztal Bridge and the ElbeBridge in Mühlberg. The experimental investigations of Franz 26 showed that unreinforced concrete hinges are able to withstand 3 million alternating rotations without experiencing any problems. CALCULATION MODELS

GERMAN MODEL ACCORDING TO FRITZ LEONHARDT While Freyssinet designed and constructed his hinge only by sense and experience, Fritz Leonhardt was able to develop a model from his experimental investigations. In the 1960’s it wasn’t yet possible to describe the results of the tests with proper mechanical models so he used empirical terms to describe the load-bearing behavior. Additionally, Leonhardt’s model is based on the safety concept of allowable stresses. These design rules, according to Leonhardt, were assigned to actual code based on a research project. This assignment assures proper design and construction of unreinforced concrete hinges. In 25 Fritz Leonhardt defined the nomenclature for concrete hinges which remains unchanged to date (Fig.11).

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Fig. 11: Nomenclature of concrete hinges from Fritz Leonhardt For plane systems and loading conditions at the ultimate limit state, hinges are subjected to axial loads N d and rotation around the axis of rotation α d . An overstraining of the concrete in the throat of the hinge, due to axial loads or rotation, is theoretically possible but has never been detectable in any experimental investigation. Failure occurred in all tests in members adjacent to the hinges due to the yielding of reinforcement. The transmission of the axial forces through the throat of the hinge into the adjacent members can be considered to be like a partially loaded area. Under this type of situation, EC 2 27 permits the use of a higher compressive strength of the concrete FRdu = Ac0 ⋅ f cd ⋅ Ac1 / Ac0 ≤ 3.0 ⋅ f cd ⋅ Ac0

(1)

The varying dimensions of the proportional basic area Ac1 are limited to 3 times the size of the partially loaded area Ac0 . This requirement of a proportional basic area should insure the restraint of the lateral strains in both directions. For concrete hinges, this requirement is met by the constriction of the throat ( br ≥ 0.7 ⋅ a ≥ 5cm ) orthogonal to the axis of rotation. Based on Leonhardt’s recommendation for the geometry ( a ≤ 0.3 ⋅ d ) and neglecting the front side constriction, the load capacity for a linear concrete hinge can be determined by: FRdu = Ac0 ⋅ f cd ⋅ 3 11

(2)


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Using the empirical description Leonhardt developed in 25 - that a stronger contraction leads to a higher compressive strength of the concrete in the throat- the minimum area of the throat can be calculated to be: AG,min =

N d,max ⎡ ⎛ ⎞⎤ E c0m 3 ⋅ f cd ⋅ ⎢1 + λ ⋅ ⎜1 − α d ⋅ ⎟⎥ ⋅ ⋅ f 12800 3 ⎢⎣ ⎝ cd ⎠ ⎥ ⎦

(3)

In 5 Leonhardt developed a simple mechanical model to describe the behavior of the hinges under rotation. During his experimental investigations, he measured strains and stresses in the throat of the hinges and transposed these into the model shown in figure 12.

Fig. 12: Mechanical model for the rotation of the hinge5 Leonhardt assumed a linear strain distribution in the throat. Tensile stresses cannot be transmitted due to cracking of the throat. With the assumption of an effective height s=a and a limiting condition of a maximum crack length to the middle of the throat, he determined the maximum allowable rotation. For the actual common unit-system and nomenclature, this maximum value of rotation is defined as: α Rd =

12800 ⋅ N d a ⋅ b ⋅ E c0m

(4)

[‰, MN, m, MN/m²] Only 50% of the value of the long-term rotation must be considered due to the positive influence of concrete creep: α d = 0.5 ⋅ α G + α Q (5) N d = N G,d + N Q,d

(6)

In 1969, Mönnig and Netzel 28 specified an equation for the determination of the maximum area of the throat. This limitation insures the ability of the hinge to rotate and is derived from the direct transposition of (7). It should be noted, that N d and α d belong to the same load situation. 12800 ⋅ N d α d ≤ α Rd = (7) a ⋅ b ⋅ E c0m 12


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12800 ⋅ N d α d ⋅ E c0m

(8)

The characteristic moment-rotation can be expressed separately for condition I (uncracked concrete) and condition II (cracked concrete): 1 ⎧ ⎪⎪ mI 0 ≤ m ≤ 6 m=⎨ ⎪m 1 ≤ m ≤ 1 ⎪⎩ II 6 3

0 ≤ Ψ ⋅ vorh α ≤ 9 ‰ (9) 9 ‰ ≤ Ψ ⋅ vorh α ≤ 36 ‰

mI ( Ψ ⋅ vorh α ) =

Ψ ⋅ vorh α

54

(10)

1 1 mII ( Ψ ⋅ vorh α ) = − Ψ ⋅ vorh α 2

(11)

9 ⋅ Ec0m ⋅ AG 20000 ⋅ N d

(12)

Ψ=

To prove his assumption concerning the behavior of the hinge under rotation, Leonhardt developed a term to express the bending moment that is necessary to produce the hingerotation. This theoretical solution, developed based on data from several experiments, verifies his model (Fig.13).

Fig. 13: Theoretical moment-rotation characteristic and test data28 Leonhardt did not carry out any investigations of the shear force bearing capacity of the hinges, however, he was familiar with the results from tests conducted by Base in which 13


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shear-force-to-axial-force-ratios of 1.0 resulted without any sign of failure. Leonhardt, therefore, recommended a limitation of the shear force to be Qy,d ≤ 0,25 ⋅ N d . For ratios higher than Qy,d ≥ 0.125 ⋅ N d , the hinge needs to be doweled. He also provided recommendations for tensile axial forces and bending moments orthogonal to the axis of rotation25. Leonhardt recommended a low allowable design stress for steel reinforcing to provide a transverse tensile force failure. The transverse tensile force should then be calculated with the following equations: Z1,d = 0.3 ⋅ N d,max (13) ⎛ b⎞ Z 2,d = 0.3 ⋅ ⎜1 − ⎟ ⋅ N d,max (14) ⎝ c⎠ a Z 3,d = 0.03 ⋅ ⋅ N d,max (15) b The constructive recommendations and the rules for the design of the transverse tensile forces given by Leonhardt remain the same. Only the design stress for the transverse tensile reinforcement is increased to 250 N/mm² when the additional safety factor of 1.4 is considered which equates to Leonhardt’s proposal ( σ s = 180 N/mm² at service load). Such a rigid confinement secures the tri-axial compressive stress state in the throat of the hinge. Figure 14 summarizes these design rules.

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Fig. 14 Part 1: Summary of design rules for Freyssinet hinges 15


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Fig. 14 Part 2: Summary of design rules for Freyssinet hinges

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BRITISH MODEL In Great-Britain, the design and construction of unreinforced concrete hinges is regulated by the “Technical Memorandum (Bridges) – Rules for the Design and Use of Freyssinet Concrete Hinges in Highway Structures” 23. These design rules are similar to those developed by Leonhardt in25. Both sets of design rules use only 50% of the value of the modulus of elasticity for long-term rotation due to shrinkage, creep, elastic shortening or permanent loads. To ensure the existence of a tri-axial state of stress in the throat of the hinge, both rules require the notching of the front faces. The axial forces are described as linear loads occurring along the hinge length, P=N/b, to determine the minimum width of the throat, a1. The ratio of constriction is not taken into account in contrast to the design rules of Leonhardt; only the absolute width is applicable. The width of the throat is determined by the following four equations. The maximum allowable compressive stress in the throat is, thereby, limited to 2 times the compressive strength, u w, or 105 N/mm², exhibited by the concrete cube-bodies. In order to permit a particular angle of rotation, the width of the throat is restricted by equation (19). a1 ≥ 50mm

(16)

a1 ≥ P / uw (17)

a1 ≥ P /105 N / mm² a1 ≤

380 ⋅ P E ⋅ (φS + φ L / 2 )

(18) (19)

with [mm, N/mm, rad]

Equation (19) limits the stress at the extreme fiber of the throat to zero (no tensile stress is allowed in the throat). The capability of shear forces is restricted to V ≤ 1/ 3 ⋅ N . The confinement of the concrete is secured by an adequately sized reinforcement that must be built-in based on the given arrangements (Fig. 15).

Fig. 15: Possible arrangements for transverse reinforcement23 FRENCH MODEL

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In France, the design and construction of unreinforced concrete hinges is regulated by the French Code BAEL 91 modifiées 99 29. Concrete hinges are, therefore, mainly subjected to axial forces. Shear forces are limited to 1/ 4 ⋅ N . The hinges must be constricted to be no more than 1/3 of the width of the adjacent members. The height of the throat should not exceed 2 cm. The minimum area of the throat can be determined with a limited allowable average stress in the throat for design at the ultimate limit state (ULS). σ m ≤ 3 ⋅ f ck

AG ≤ AG,min =

(20)

N d,max 3 ⋅ f ck

(21)

The maximum rotation at the serviceability limit state is restricted to 1/20 due to the lack of experimental data. (22) α max = 0.05 rad = 5 ‰ The members adjacent to the hinges need to be reinforced with transverse slopereinforcement. The volumetric ratio of confining steel should be at least 1.0% orthogonal and 0.8% parallel to the axis of rotation. The French design rules permit maximum axial loads and rotations for all known calculation models (Fig. 16 and Fig. 18).

Fig. 16: Constructive requirements of the French code29 DUTCH MODEL The design of unreinforced concrete hinges in the Netherlands is carried out according to NEN 6723: 1995 Chapter “9.2 Betonscharnieren” 30 in the serviceability limit state. The rules given are related to and comprised from the design rules from Great-Britain and Leonhardt. The largest, positive defined compressive stress can, thus, be calculated as: ' σ Rand

N d' 3 ⋅ α − 2 0.6 ⋅ Eb' ⋅ Θ ⋅ a1 = ⋅ + a1 ⋅ b1 α 2 ⋅ he

(23)

The stress at the extreme fiber of the other side of the throat (at maximum tension) is then: ' σ Rand

N d' 3 ⋅ α − 2 0.6 ⋅ Eb' ⋅ Θ⋅ a1 = ⋅ − α 2 ⋅ he a1 ⋅ b1 18

(24)


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with ' σ Rand ' d

N α

E ' Θ

concrete stress at the extreme fiber of the throat in N/mm² axial force at the SLS (serviceability limit state) ratio of a/a1 modulus of elasticity of the concrete angle of rotation in radiant

The size of the maximum stress of the extreme fiber of the throat is limited by equations (25) and (26) ' σ Rand (25) ≤ 2.0 ⋅ f b ' σ Rand ≥ − f b

(26)

For further information, please refer to the design rules of 23 and 25. CALCULATION MODEL ACCORDING TO MAX HERZOG For the construction of the Ruppoldingen Aare-Bridge, Herzog intensively researched known experimental investigations of concrete hinges and developed his own empirical design rules31. As his own understanding of load-bearing behavior evolved, he defined a lower and upper limit of bearing capacity dependent on the volumetric ratio of confining steel in the adjacent members. The associated analysis showed a good correlation between his empirical formulations and experimental results. SWEDISH MODEL The design of Freyssinet hinges in Scandinavia is primarily done under the rules provided for by Fritz Leonhardt25. In Sweden, concrete hinges are regulated in the Swedish code BBK Boverket Handbok Chapter 3.11 32. Three variations of hinges can be distinguished. One of these 3 designs provided must be chosen based upon bearing loads and environmental conditions present (Fig. 17).

Fig. 17: Different variants of concrete hinges32 The compressive stress should not exceed 2 ⋅ f cc for the ULS (ultimate limit state) at the bottom and f cc at the sides. Rotations of 15‰ are permitted. 19


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The load of frequent load combinations should not exceed 0.2 MN/m, and rotations are restricted to 10‰ for the serviceability limit state (SLS) CONCLUSIONS

Existing models in GB, France, Germany or other countries need empirical terms to describe the compressive strength of concrete in the throat under tri-axial stress states. There are currently numerous accepted mechanical models, grounded in extensive research, to describe the tri-axial stress states in the hinge throat. Plans are in place to develop a proper model to describe the load-bearing behavior of hinges and to use FE calculations to verify and support relevant design rules. For this new model the confinement of the concrete can be taken into account by applying the model developed by Sigrist 33 which has also been incorporated into the new CEB-FIB Model Code 2010. Figure 18 shows a comparison of the various international design rules for one specific concrete hinge.

Fig. 18: Comparison of various design rules REFERENCES

1. Köpcke, „Über die Verwendung von drei Gelenken in Steingewölben“, Zeitschrift des Architekten- und Ingenieur Vereins zu Hannover , 1888, S. 374-380. 2. von Leibbrand, „Gewölbte Brücken“, Fortschritte der Ingenieurwissenschaften, 2.Gruppe, 7. Heft, Leipzig, 1897. 3. Mesnager, „Experiences sur une semi-articulation pour routes en Béton armé“, Annales de Ponts de Chaussees , 1907. 4. Eugène Freyssinet, „Un amour sans limite“, Èditions du Linteau, Paris, 1993. 5. Leonhardt/Reimann, „Betongelenke“, Heft 175 DAfStb, Berlin, 1965. 20


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6. Marx, S.; Schacht, G., „Betongelenke im Brückenbau“, Zwischenbericht, Forschungsvorhaben DBV 279, Dresden, 2009. 7. Köpcke, „Über die Kompression von Körpern mit gekrümmten Oberflächen“, Deutsche Bauzeitung, 1869, S. 120-121. 8. Colberg, „Die Illerbrücken bei Kempten im Allgäu“, Deutsche Bauzeitung, 1906, S. 218222, S. 232-237, S. 261-264, S. 318. 9. Emperger, „Handbuch für Eisenbeton: Band 6 – Brückenbau“, Berlin, 1911, S. 394. 10. Mörsch, „Über die Berechnung der Gelenkquader“, Beton und Eisen , 1924, Heft 12, S. 156-161. 11. Bortsch, „Die Spannungen in Wälzgelenkquadern“, Beton und Eisen , 1935, Heft 4, S. 61-66. 12. Misch, „Technische Gesichtspunkte beim Bau von Hochstraßen“, Beton- und Stahlbetonbau, 56 (1961), Heft 7, S. 163-173. 13. Burkhardt, „Betongelenke mit gepanzerter Wälzfläche“, Die Bautechnik , 11. Jg., 10. Nov. 1933, Heft 48, S. 651-658. 14. Mörsch, „Der Eisenbeton – Seine Theorie und Anwendung“, 6. Auflage, 2 Bände, Konrad Wittwer Verlag, Stuttgart, 1929. 15. Jesinghaus; Bieligk, „Ausbildung unvollkommener Betongelenke“, Zement , 19 (1930), Heft 36 S. 850/855 und Heft 37 S. 873/879. 16. Moreell, B., “Articulations for concrete structures – the Mesnager hinge”, Journal Proceedings, March 1935, S. 368-381. 17. Kammüller, K., Jeske,O., „Federgelenke“, Heft 125 DAfStb, Berlin, 1957. 18. Sallenbach, H. H., „Betongelenke beim Hardturm-Viadukt“, Schw. BZ , Vol. 85, 1967. 19. McCollough, “Modern design and construction practise for wide-span arches in U.S.A”, IABSE Abhandlungen , Vol. 6, 1940-1941. 20. Riessauw,Passelecq, “Essais sur les articulations en béton armé”, Annales des Travaux public de Belgique, Bruxelles, 1948. 21. S. Chaudesaigues, “La reconstruction en béton précontraint des ponts sur la Marne a Annet; Trilbardou, Esbly, Ussy et Changis-Saint-Jean”, Annales de l’institut technique du bâtiment et des travaux publics , No. 228, Paris, 1952. 22. Base, G.D., “Tests on Reinforced Concrete hinge with a large design rotation”, Cement and Concrete Association , Techn. Report TRA/359, 1962. 23. BE 5/75 Technical Memorandum (Bridges) – Rules for the Design and Use of Freyssinet Concrete Hinges in Highway Structures, 1975. 24. Dix, „Betongelenke“; Heft 150 DAfStb, Berlin, 1962. 25. Leonhardt, Mönnig, „Sonderfälle der Bemessung im Stahlbetonbau“, Vorlesungen über Massivbau Teil 2 , 3. Auflage, Springer-Verlag, 1986 26. Franz,G., Fein, H.-D., „Betongelenke unter wiederholten Gelenkverdrehungen“, Heft 200 DAfStb, Berlin, 1968. 27. EN 1992-1-1: 2004 – Bemessung und Konstruktion von Stahlbeton- und Spannbetontragwerken. 28. Mönnig,Netzel, „Zur Bemessung von Betongelenken“, Der Bauingenieur , 44 (1969), Heft 12. 29. Règles BAEL 91 modifiées 99; Règles techniques de conception et de calcul des ouvrages et constructions en béton armé suivant la méthode des états-limites; Editions Eyrolles, 1999. 30. NEN 6723: Vorschriften beton. Bruggen (VBB 1995) - Constructieve eisen en rekenmethoden, 1995. 31.Herzog, M, „Wirtschaftliche Stahlbeton- und Spannbetonbemessung“, Band 5 Spezialprobleme, Bauwerk-Verlag, Berlin, 2005, Kapitel 31, S. 1-25. 32. BVVVTK Bro 08, VV Publ 2008, http://documents.vsect.chalmers.se/structuralengineering/SorenLindgren/bro/Bro08.pdf. 21


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33. Sigrist, V., „Zum Verformungsvermögen von Stahlbetonträgern“, Institut für Baustatik und Konstruktion, ETH Zürich, IBK Bericht 210 , Birkhäuser Verlag, Basel, Juli 1995.

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