NL2028808B1 - Method for measuring local rotation of a structural element configured for supporting a load, such as traffic, as well as a method for modelling such a structural element - Google Patents

Method for measuring local rotation of a structural element configured for supporting a load, such as traffic, as well as a method for modelling such a structural element Download PDF

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NL2028808B1
NL2028808B1 NL2028808A NL2028808A NL2028808B1 NL 2028808 B1 NL2028808 B1 NL 2028808B1 NL 2028808 A NL2028808 A NL 2028808A NL 2028808 A NL2028808 A NL 2028808A NL 2028808 B1 NL2028808 B1 NL 2028808B1
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structural element
bridge
supports
load
rotation
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NL2028808A
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Dutch (nl)
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David Reitsema Albert
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Heijmans N V
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M5/00—Investigating the elasticity of structures, e.g. deflection of bridges or air-craft wings
    • G01M5/0008—Investigating the elasticity of structures, e.g. deflection of bridges or air-craft wings of bridges

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  • Aviation & Aerospace Engineering (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Bridges Or Land Bridges (AREA)

Abstract

The invention relates to a method for measuring local rotation of a structural element configured for supporting a load, comprising the steps of: - when the load is positioned on the structural element, measuring a local rotation of the structural element in a vertical plane, aligned with a longitudinal direction of the structural element, with rotation measurement means arranged at one or more supports supporting the structural element, wherein the structural element is rotatably arranged on one or more bearings positioned on the one or more supports, wherein the rotation measurement means are arranged at an upper end of the one or more supports, below the intersection of the structural element and the respective support, such that the local rotation of the structural element relative to the support is measured, characterized in that - the rotation measurement means comprise multiple rotation measurement devices arranged at horizontally spaced-apart positions in a horizontal direction, i.e. direction perpendicular to the vertical plane and the longitudinal direction, along the upper end of the support, such that multiple rotation measurements can be taken in the horizontal direction.

Description

Title: Method for measuring local rotation of a structural element configured for supporting a load, such as traffic, as well as a method for modelling such a structural element
FIELD OF THE INVENTION
The present invention relates to a method for measuring local rotation of a structural element, such as a bridge deck, configured for supporting a load, such as traffic, a method for modelling such a structural element, such as the bridge deck, using the aforementioned measurement method, as well as a structure, such as a bridge, comprising such a structural element, such as the bridge deck.
BACKGROUND OF THE INVENTION
In the Netherlands infrastructure has always been important with regard to its status as transport country with Rotterdam as Europe’s largest port. There has been a large infrastructural expansion in-between the sixties and eighties. Public authorities face a major replacement task given that most of the existing bridges are designed to serve for 50 years. This, combined with a large historical increase in traffic frequency and loads combined with new insights regarding structural behaviour, makes that the performance of some existing bridges can be questionable. Still, there isn’t an indication of structural failing in the near future, so it is clear that the actual capacity of existing bridges is not directly related to a service life of 50 years the bridges were designed for.
Till now, for far most of the existing bridges qualitative and non- continuous methods are used to determine degradation. These methods are not able to give an accurate assessment of the real structural performance of a structure.
Therefore, it can be favourable to apply a “structural health monitoring” (SHM) system on civil structures to conclude whether or not an intervention is mandatory (Cremona 2014). This makes that decisions regarding operating conditions can be made based on quantitative data. In addition to the re-evaluation of older existing bridges, SHM can be used to measure the load response of new bridge techniques and/or materials.
WO 2017/200380 A1 in the name of the present Applicant discloses an advantageous method of employing SHM to evaluate such older bridges and measure the load response of new bridges. This method uses SHM combined with general bending stiffness changes to determine if additional inspection of a bridge is warranted.
US 2015/0198502 A1 furthermore discloses methods and systems for determining bridge load ratings under ambient traffic. One or more strain gauges are installed on one or more bridge girders and a batch of strain readings maybe acquired from the one or more strain gauges. From the batch of strain readings, one or more strain time histories may be randomly sampled based, for example, on a girder peak strain. One or more vehicles may be randomly selected based on the one or more stored vehicle parameters by accessing a database with one or more stored vehicles and stored vehicle parameters. A bridge load rating model may be calibrated based on the one or more randomly sampled strain time histories and the randomly selected one or more vehicles for acquiring, in one embodiment, a bridge load rating distribution. However, the method according to US 2015/0198502 A1 merely measures strain in a length direction of the bridge and therefore results in relatively inaccurate bridge load rating models.
CN 106706239 A discloses a bridge load test method employing a finite element calculation model. Displacement measuring means are arranged at a key part of a test span. Automobiles are slowly driven along the bridge deck, and a displacement influence line of the bridge is acquired. The actually measured curve of the bridge displacement influence line is subsequently drawn. An actually measured displacement value is selected according to the actual result of the displacement influence test data. A loading model is then established according to the actually measured displacement values and the corresponding vehicle load position so as to perform finite element analysis and calculation. A displacement residual error expression is established and a target function is formed to perform finite element model correction. However, the method according to CN 106708232 A also measures strain in girders in a length direction of the bridge and therefore also results in relatively inaccurate and incomplete bridge load rating models.
Thus, there is a need for an improved method for measuring local rotation of a structural element, in particular a horizontally extending structural element, such as a bridge deck, configured for supporting a load, such as traffic, and an improved method for modelling such a structural element, for instance to determine remaining lifespan of the structure, such as a bridge.
SUMMARY OF THE INVENTION
Thereto, according to the invention a method for measuring local rotation of a structural element, such as a bridge deck, configured for supporting a load, such as traffic, is provided, comprising the steps of: - when the load is positioned on the structural element, such as when traffic is passing over the structural element, such as the bridge deck, measuring a local rotation of the structural element, such as the bridge deck, in a vertical plane, aligned with a longitudinal direction of the structural element, with rotation measurement means arranged at one or more supports, such as bridge supports, supporting the structural element, wherein the structural element is rotatably arranged on one or more bearings, such as bridge bearings, positioned on the one or more supports, wherein the rotation measurement means are arranged at an upper end of the one or more supports, below the intersection of the structural element and the respective support, such that the local rotation of the structural element relative to the support is measured, wherein the rotation measurement means comprise multiple rotation measurement devices arranged at horizontally spaced-apart positions in a horizontal direction, i.e. direction perpendicular to the vertical plane and the longitudinal direction, along the upper end of the support, such that multiple rotation measurements can be taken in the horizontal direction. The multiple local rotations can then be summed up in order to obtain a global overview of the (deformation) behaviour of the structure, such as a bridge, and the structural element, such as a bridge deck.
The inventors have shown the insight that with a structural element, such as a bridge (deck), loading and subsequent deformation are complex and interactive processes. Such processes are hard to measure and analyse by merely having measurement means installed at several locations along the length direction of the structural element, such as the bridge deck. By having multiple rotation measurement devices arranged at horizontally spaced-apart positions in a horizontal direction, i.e. direction perpendicular to the vertical plane and the longitudinal direction, along the upper end of the support, multiple rotation measurements can be taken in the horizontal direction, leading to a far more complete picture of what is happening to the structural element, especially at the supports. The inventors have found out that in “real life” vertical structural element loads are normally more “spread out’, for instance in the horizontal direction, than “expected”. The multiple rotation measurements can be used for improved modelling of the structural element, in particular to determine “real” structural - for instance bridge - behaviour under load compared to the behaviour the structure or structural element was initially designed for. Thus, a “real” load rating and/or an effective remaining lifespan of the structural element and the structure may be determined.
In particular with concrete structural elements, such as bridge decks, rotation of the structural element, such as the bridge deck, near the supports, such as the bridge supports, is a direct measure of the structural element - for instance bridge deck - loading, because concrete linearly elastically deforms under load. Thus, interestingly, when the concrete plastically deforms, one knows that cracks are probably present in the concrete. The above method is thus particularly applicable to concrete structural elements, such as bridge decks. The above method is also particularly applicable to freely rotatable, statically determined structural elements, such as bridge decks. The bearings, such as bridge bearings, may for example comprise neoprene blocks, pads or the like.
Within the context of this patent application, a “load” may mean a non- moving or a moving load and “traffic” may relate to motorized traffic, such as cars or aircraft, or non-motorized traffic, such as humans or animals. The “structural element” may be a bridge deck, but also a floor, a roof, et cetera. Analogously, the “structure” may be a bridge, but also a building or the like.
Furthermore, “rotation measurement means” or “rotation measurement devices” may relate to means or devices indirectly or directly giving a rotation as a result. Thus, as explained with respect to certain embodiments discussed in the present patent application, applying deformation measurement means, wherein the measured deformations indirectly enable the skilled person to derive rotations, also fall under the definitions “rotation measurement means” and “rotation measurement devices”. Moreover, “avioduct” in a broad sense means any viaduct whereto or whereon an “aviation load” is applied.
An embodiment thus relates to an aforementioned method, wherein the supports are bridge supports and wherein the bearings are bridge bearings.
An embodiment relates to an aforementioned method, wherein the rotation measurement means comprise 2 — 50, preferably 10 — 30, more preferably 15 — 25 horizontally spaced-apart rotation measurement devices. In practice, the inventors have found that the abovementioned amounts of rotation measurement devices lead to accurate measurement results, depending on the application and load or traffic type.
An embodiment relates to an aforementioned method, wherein the rotation measurement devices are configured to perform 20 — 80, preferably 40 — 80, 5 preferably 45 — 55 measurements per second, such that accurate measurements can be made of in particular fast traffic - or traffic comprising vehicles having a relatively large contact area with the structural element, such as the bridge deck, such as aircraft (having relatively large tires), such that an accurate analysis can be made of what happens when e.g. an aircraft tire passes the rotation measurement devices.
Furthermore, visualization of measurements can also be improved giving increased insight into the behaviour of the structure, such as the bridge. Such visualizations may e.g. comprise showing a three-dimensional “potential energy” graph, with measurements on the x-axis, the rotation measurement device number on the y-axis and signal intensity on the z-axis.
An embodiment relates to an aforementioned method, wherein the one or more supports have a support width (W), such as a bridge support width, in the horizontal direction, wherein the rotation measurement means cover at least 5%, such as at least 10%, such as at least 25%, preferably at least 40%, more preferably at least 50%, even more preferably at least 70%, most preferably at least 20% of the support width. Thus, a proper analysis can be made of for instance bridge (support) behaviour, in particular when the horizontal position of passing traffic is not consistent.
Another aspect of the invention concerns a method for modelling a structural element, such as a bridge deck, configured for supporting a load, such as traffic, comprising the steps of: - using the aforementioned method for measuring local rotation of the structural element relative to the one or more supports, - calculating reaction forces of the one or more bearings at the one or more supports based on the measured local rotation of the structural element relative to the one or more supports, - obtaining a load configuration of the structural element due to the load being positioned on the structural element, such as traffic passing over the structural element, wherein the load, such as the traffic, has known load characteristics, such as load type and load speed,
- modelling the structural element near the one or more supports, the structural element being modelled as an orthotropic plate, - modelling the load configuration of the structural element near the one or more supports, and iteratively: 1) allocating stiffness parameters to the structural element, 2) modelling reaction forces of the one or more bearings and, preferably, modelling rotations at the one or more supports, and 3) comparing the modelled reaction forces and, preferably, modelled rotations near the one or more supports with the calculated reaction forces and, preferably, calculated rotations until a best fit is achieved.
Thus, by using the above method, i.e. by iteratively varying the stiffness parameters, an accurate model of for instance bridge behaviour can be created, in particular when the structural element, such as the bridge deck, is modelled as an orthotropic plate (on spring supports), instead of e.g. a simply supported one dimensional beam, such as often employed by the prior art. The orthotropic plate on springs supports is essentially the most advanced model available. Normally, such an orthotropic plate is modelled by means of six stiffness parameters, usually denoted by
D141, D22, D12, D33, Das and Dss. The bearings, such as bridge bearings, are modelled by the spring supports. In principle, the use of 3D FEM models with volume elements would also be conceivable (for instance using software like ANSYS, DIANA, et cetera).
An embodiment relates to an aforementioned method, wherein, in addition to allocating stiffness parameters to the structural element, such as the bridge deck, force spread angle parameters are allocated to the structural element. E.g. in case of an aircraft tire, the force applied on the structural element, such as the bridge deck, via the contact surface/patch between the aircraft tire and the structural element, such as the bridge deck, will “spread” through e.g. the bridge deck. The inventors have found that also taking the force spread angle into account considerably improves modelling accuracy.
An embodiment relates to an aforementioned method, wherein in addition to allocating stiffness parameters (D) to the structural element, stiffness parameters are allocated to the one or more bearings to further improve modelling accuracy.
An embodiment relates to an aforementioned method, wherein a plurality of different load configurations, such as related to different aircraft types, are used for modelling the structural element, such as the bridge deck, in order to improve the allocation of stiffness parameters and, when also allocating force spread angle parameters, force spread angle parameters, to the structural element, such as the bridge deck, and, when also allocating stiffness parameters to the one or more bearings, the allocation of bearing stiffness parameters, to achieve the best fit.
An embodiment relates to an aforementioned method, wherein, when the stiffness parameters (D) of the structural element (and, optionally, bearings, as well as force spread angle parameters) have been determined in such a way, that a best fit has been achieved between the modelled reaction forces and the calculated reaction forces, the allocated stiffness parameters giving the best fit are used to determine shear forces and/or bending moments acting on the structural element and/or structure comprising the structural element.
An embodiment relates to an aforementioned method, wherein, when the stiffness parameters of the structural element (and, optionally, bearings, as well as force spread angle parameters), such as the bridge deck, have been determined in such a way, that a best fit has been achieved between the modelled reaction forces and the calculated reaction forces, the allocated stiffness parameters giving the best fit are used to determine a load rating and/or effective remaining lifespan of the structural element, such as the bridge deck, and/or the structure, such as the bridge.
In some cases, the inventors have found that the remaining lifespan of some structures, such as bridges, is 10 years, sometimes even 20 years, longer than expected, for instance due to the stiffness being higher than expected and the actual load, such as the traffic load, being more favourable than expected, in particular due to forces spreading though e.g. the bridge deck, instead of these forces being concentrated at a single location on the bridge deck or merely being transmitted vertically through the bridge deck. In particular shear forces are often modelled/examined very “locally”.
An embodiment relates to an aforementioned method, wherein the load comprises traffic. Furthermore, the traffic may comprise aircraft and the bridge may be an avioduct. The inventors have achieved particularly good modelling results with avioducts with aircraft passing over the bridge deck. Aircraft in general have known weights, known tire configurations, known tire pressures, and thus known contact patch areas, and therefore the aforementioned methods are particularly useful for studying the behaviour of avioducts. Furthermore, aircraft pass by at regular, but not too short, intervals and normally only one aircraft passes over the avioduct, instead of multiple aircraft at the same time.
Another aspect of the invention concerns a structure, such as a bridge, comprising a structural element, such as a bridge deck, configured for supporting a load, such as traffic, having: - rotation measurement means arranged at one or more supports, such as bridge supports, supporting the structural element, such as the bridge deck, for measuring a local rotation of the structural element in a vertical plane, aligned with a longitudinal direction of the structural element, when the load is positioned on the structural element, such as when traffic is passing over the structural element, wherein the structural element is rotatably arranged on one or more bearings, such as bridge bearings, positioned on the one or more supports, wherein the rotation measurement means are arranged at an upper end of the one or more supports, below the intersection of the structural element and the respective support, such that the local rotation of the structural element relative to the bridge support is measured, wherein the rotation measurement means comprise multiple rotation measurement devices arranged at horizontally spaced-apart positions in a horizontal direction, i.e. direction perpendicular to the vertical plane and the longitudinal direction, along the upper end of the support, such that multiple rotation measurements can be taken in the horizontal direction.
An embodiment relates to an aforementioned structure, wherein the structural element is a bridge deck, wherein the supports are bridge supports and wherein the bearings are bridge bearings.
An embodiment relates to an aforementioned structure, wherein the rotation measurement means comprise 2 — 50, preferably 10 — 30, more preferably 15 — 25 horizontally spaced-apart rotation measurement devices.
An embodiment relates to an aforementioned structure, wherein the rotation measurement devices are configured to perform 20 — 80, preferably 40 — 60, preferably 45 — 55 measurements per second.
An embodiment relates to an aforementioned structure, wherein the one or more supports have a support width, such as a bridge support width (W), in the horizontal direction, wherein the rotation measurement means cover at least 5%, such as at least 10%, such as at least 25%, preferably at least 40%, more preferably at least 50%, even more preferably at least 70%, most preferably at least 90% of the support width.
An embodiment relates to an aforementioned structure, wherein the load comprises traffic. The traffic may comprise aircraft and the structure may be an avioduct.
BRIEF DESCRIPTION OF THE DRAWINGS
The present invention will be explained hereafter with reference to the drawings. Therein:
Figure 1 schematically shows a side view of a bridge in the form of an avioduct with a bridge deck configured for supporting traffic in the form of aircraft;
Figure 2 schematically shows a perspective, detailed view of a bridge support with several rotation measurement devices installed;
Figures 3 and 4 schematically show a side view of a bridge support, wherein the measurement principles of one of the rotation measurement devices are illustrated;
Figure 5 schematically shows a theoretical response of the rotation measurement devices when an aircraft with a known load configuration passes by;
Figure 6 schematically shows a measured response of the rotation measurement devices when an aircraft with a known load configuration passes by; and
Figure 7 schematically shows the method for modelling the bridge deck in the form of a rudimentary flowchart.
DETAILED DESCRIPTION
The Figures will be discussed in conjunction. Figure 1 shows a structure 1 being a bridge 1 in the form of an avioduct 14, such as the “Handelskade” avioduct 14 at Amsterdam Airport Schiphol (AMS) (also known as the KW2a/b avioduct in the Quebec passage), comprising a structural element 2 in the form of a bridge deck 2 configured for supporting a load 3, in the illustrated case traffic 3 in the form of aircraft 13. Preferably, the bridge deck 2 is made of concrete. Rotation measurement means 5 are arranged at one or more supports 6 in the form of bridge supports 6, preferably made of concrete, such as reinforced concrete, supporting the bridge deck 2 for measuring a local rotation 10 (see Figure 4) of the bridge deck 2 in a vertical plane 4 aligned with a longitudinal direction X of the bridge deck 2, when the load 3 is positioned on the bridge deck 2, i.e. in the illustrated embodiment. when traffic 3 is passing over the bridge deck 2. The bridge deck 2 is rotatably arranged on one or more bearings in the form of bridge bearings 7, such as neoprene pads or blocks, positioned on the one or more bridge supports 6. Figure 1 only shows two end bridge supports 6 to support the bridge deck 2, but intermediate bridge supports (not shown) may also be provided with rotation measurement devices 11.
The aircraft 13 exerts a load L {or in general forces with a load configuration L) on the bridge deck 2 causing the bridge deck 2 to deform. In case of the aircraft 13 as shown, e.g. a civil airliner, a force F1 may be exerted by the main landing gear of the aircraft 13 and a force F2 may be exerted by the nose wheel of the aircraft 13. The forces F4, F2 may not be purely vertically transmitted through the bridge deck 2, i.e. the asphalt and concrete of the bridge deck 2, but in practice are distributed through the bridge deck 2, for instance at an angle, such as the force spread angle 12 as shown, which may be 30 — 60°, such as 40 — 50°, such as around 45°. It should be known that normally only the concrete of the bridge deck 2 is modelled (i.e. without the asphalt).
The rotation measurement means 5 are arranged at an upper end 8 of the one or more bridge supports 6, below the intersection 9 of the bridge deck 2 and the respective bridge support 6, such that the local rotation 10 of the bridge deck 2 relative to the bridge support 6 is measured, as more clearly shown in Figure 3 and, in particular, Figure 4. The rotation measurement means 5 comprise multiple rotation measurement devices 11 arranged at horizontally spaced-apart positions in a horizontal direction Y, i.e. direction perpendicular to the vertical plane 4 and the longitudinal direction X. The rotation measurement devices 11 are arranged along the upper end 8 of the bridge support 6, such that multiple rotation measurements can be taken in the horizontal direction Y. Because the bridge deck 2, in particular a concrete bridge deck 2, deforms linearly elastically, it is possible to relate rotations/rotational deformations to the loads or forces exerted on the bridge deck 2.
The rotation measurement means 5 may comprise 2 — 50, preferably 10 — 30, more preferably 15 — 25 horizontally spaced-apart rotation measurement devices 11. The rotation measurement devices 11 may be configured to perform 20 — 80, preferably 40 — 60, preferably 45 — 55 measurements per second. Figure 2, for instance, shows a total of 19 installed rotation measurement devices 11. Preferably,
the rotation measurement devices 11 each have two sensors, spaced-apart in the longitudinal direction X, for sensing vertical deformations (as will be explained hereafter), each sensor having a precision of 1/1000 mm or better.
Figures 3 and 4 show the measurement principles behind/underlying the used rotation measurement devices 11. In essence, the rotation measurement devices 11 measure two vertical deformations in the two sensor directions Sz, S3, as well as a horizontal deformation in sensor direction S4. Figure 3 shows the condition wherein the bridge deck 2 is not loaded. The rotation measurement devices 11 then do not measure any deformations or rotations. Figures 4 shows a condition wherein the bridge deck 2 is loaded with a load (configuration) L. A local rotation 10 of the bridge deck 2 with respect to the bridge bearing 7 and the bridge support 6 then occurs.
The rotation measurement devices 11 now measure two vertical deformations in the two sensor directions Sz, Si, as well as a horizontal deformation in sensor direction
Ss. From the measured deformations in the three sensor directions S+, S; and S;, the local rotation 10 can then be determined/derived. In a typical embodiment, the sensors for measuring the two vertical deformations in the two sensor directions Sy, Ss, are spaced apart at a distance of 200 mm (in the longitudinal direction X). Combined with the measurement precision of 1/1000 mm or better, the measurable rotation is 90 - 89.99971 degrees = 0.00029 degrees. In practice, the inventors have found that by highly accurately measuring the two vertical deformations, the rotation 10 can also be accurately calculated. Of course, other types of deformation/rotation measurement devices may also be used to determine the local rotation 10. The reaction force exerted by the bridge bearing 7 in response to the load L is indicated by R. As a general remark, in the context of the present application Rm is used to indicate a modelled reaction force, whereas Rs is used to indicate a calculated (i.e. measured/derived) reaction force at the bridge bearing 7.
The one or more bridge supports 6 may have a bridge support width
W in the horizontal direction Y, e.g. of 5 -50 m, such as 5 — 25m, such as 10 — 25m.
The rotation measurement means 5 may cover at least 5%, such as at least 10%, such as at least 25%, preferably at least 40%, more preferably at least 50%, even more preferably at least 70%, most preferably at least 90% of the bridge support width W.
Preferably, one or more end bridge supports 6 are provided with the rotation measurement devices 11. However, providing intermediate bridge supports (not shown) with rotation measurement devices 11 is also conceivable. Preferably, such the rotation measurement devices 11 at the intermediate bridge supports 6 are aligned with the rotation measurement devices 11 at the end bridge supports 6 in the longitudinal direction X, e.g. to be able to determine the actual traffic direction (which may deviate a bit from the longitudinal direction X of the bridge deck 2).
The rotation measurement devices 11 may be arranged at a horizontal spacing of for instance 10 — 50 cm, such as 20 — 30 cm (i.e. a horizontal distance between adjacent sides of the rotation measurement devices 11).
According to an aspect of the invention, a method for measuring the local rotation 10 of the bridge deck 2 configured for supporting the load 3, such as the traffic 3, is provided, comprising the steps of: when the load 3 is positioned on the structural element 2, in the illustrated embodiment: when the traffic 3 is passing over the bridge deck 2, measuring the local rotation 10 of the bridge deck 2 in the vertical plane 4, aligned with the longitudinal direction X with the rotation measurement devices 11 arranged at the one or more bridge supports 6 supporting the bridge deck 2.
According to another aspect of the invention, a method for modelling the bridge deck 2 configured for supporting the load 3, such as the traffic 3 (as shown), is provided, comprising: - using the aforementioned (measurement) method for measuring the local rotation 10 of the bridge deck 2 relative to the one or more bridge supports 6, - calculating reaction forces R (Rs) of the one or more bridge bearings 7 at the one or more bridge supports 6 based on the measured local rotation 10 of the bridge deck 2 relative to the one or more bridge supports 6, - obtaining a load configuration (L; F4, Fz) of the bridge deck 2 due to the traffic 3 passing over the bridge deck 2, wherein the traffic 3 has known load characteristics, such as load type and load speed, - modelling the bridge deck 2 near the one or more bridge supports 6, the bridge deck 2 being modelled as an orthotropic plate, - modelling the load configuration (L; F4, Fz) of the bridge deck 2 near the one or more bridge supports 6, and iteratively: 1) allocating stiffness parameters (D) to the bridge deck 2, 2) modelling reaction forces R (Rm) of the one or more bridge bearings 7 and, preferably, modelling rotations at the one or more bridge supports 6, and
3) comparing the modelled reaction forces Rm and, preferably, the modelled rotations near the one or more bridge supports 6 with the calculated reaction forces R. and, preferably, calculated rotations until a best fit is achieved.
E.g. in case of the traffic 3 being formed by aircraft 13, the aircraft 13 type may be obtained by means of the aircraft’s identification number. The aircraft's weight may then e.g. be obtained by requesting the airport or like authority to provide the minimum and maximum weights adopted for the aircraft 13 type and/or identification number. A wheel configuration for the aircraft type may be obtained from, for instance, the aircraft's manual.
Modelling the bridge deck 2 near the one or more bridge supports 6 is also referred to as modelling the “end field” of the bridge 1 or bridge deck 2.
The bridge deck 2 is modelled as an orthotropic plate on spring supports. Therein, the stiffness of the bridge deck 2 is controlled by a stiffness matrix
K, having the following form:
Dit Do, oi Bs,
K = | Dag
Dis | Dsl
Table 1 — Stiffness matrix K of orthotropic plate
Therein:
D4 is the bending stiffness in the X direction,
Dz2 is the bending stiffness in the Y direction,
D:2 is the mixed/combined bending stiffness of Diy and Da (transversal contraction), i.e. v. V(D11 . Das),
Dis is the torsion stiffness,
Daa4 is the shear bending stiffness in the X direction, and
Dss is the shear bending stiffness in the X direction.
In addition to allocating stiffness parameters (D) to the bridge deck 2, force spread angle 12 parameters may be allocated to the bridge deck 2. Stiffness parameters may also be allocated to the bridge bearings 7.
By way of example, consider two load configurations: a first load configuration Li and a second load configuration Ls. The first load configuration L:
involves a Boeing 777-200. The second load configuration Lz involves an Airbus A319- 314. From the measurement data obtained by the rotation measurement devices 11, for the first load configuration L; it is determined that the nose wheel(s) support 25.380 kg of aircraft 13 weight on the bridge deck 2 and the main landing gear wheel(s) support 197.560 kg of the aircraft 13 weight. From the measurement data obtained by the rotation measurement devices 11, for the second load configuration Ls it is determined that the nose wheel(s) support 6.243 kg of aircraft 13 weight on the bridge deck 2 and the main landing gear(s) support 42.154 kg of the aircraft 13 weight. From the aircraft 13 manuals, parameters like wheel dimensions, tire pressures, relative spatial configuration of the nose wheel(s) with respect to the main landing gear wheel(s), and the like, can be determined.
The bridge 1 may be the “Handelskade” avioduct 14 at Amsterdam
Schiphol Airport (AMS), as schematically indicated in Figures 1 and 2. The “end field” of the avioduct 14 may be modelled as a plate element with a thickness of 750 mm.
Modelling may take place using FEM software such as “SCIA Engineer”. Further geometric details may be derived for instance from original engineering drawings. The plate element, with a length of 13.980 m and a span of 13.165 m, has orthotropic properties. The stiffness parameters (D) describing the orthotropic of the bridge deck 2 will be discussed later. The plate element is supported on vertical point springs which correspond to the position of the bridge bearings 7, comprising rubber bearing blocks.
The rubber bearing blocks (with dimensions 200 x 300 x 20mm) are modelled as a vertical point spring with a stiffness of:
K, = EA/L > zoover = 6000 MN/m
For the above-illustrated example, the Handelskade avioduct 14 is modelled as a bridge deck 2 with pretensioned full girders. The total thickness of the bridge deck 2 is 750 mm. The thickness of the lower girder flange is 250 mm. The girders have a width of approximately 1000 mm. Therein: ltransverse = (1/12) * Niansverse™3 = 8.33 x 1076
D22 = Etransverse * 8.33 x 1046
Longitudinal ~ (1/12) *X Niongituainai®3 = 3.45 x 1057 mm4
Dis = Eiongitudinat X 3.45 x 1047 Nmm2
Interaction term
Torsion stiffness lk = (1/6) x (b x* hiongitudina™3 + b x
Ntranserverse\3)
EE om
D33=04x %xG12x k/b
The above parameters have been calculated below with Erongtudina ~ 37250 N/mm? (uncracked concrete C45/55) and Etransverse ~ 15000 N/mm? (cracked concrete C20/25):
D= 1341 MNm
D22 = 124 MNm
D33 = 104 MNm
Stiffness parameters D4s and Dss have been taken from an earlier recalculation. These parameters have not been varied.
As explained in the foregoing, the weight of the aircraft 13 is obtained from the measurement data. It is then determined how much load is applied to the bridge deck 2 per (landing gear) wheel. The aircraft information (manual) contains wheel dimensions and tire pressure information. This information determines the contact patch created by the wheels on the bridge deck 2:
Acontact patch = Fwheel/Pire and
Lcontact patch = Acontact patch! Wheel
Contact patch Boeing 777-200: - Nose wheel(s) Wx L — 432 x 220 mm - Main landing gear wheel{s) W x L — 508 x 263 mm
Contact patch Airbus A319-314: - Nose wheel(s) W x L — 225 x 120 mm - Main landing gear wheel(s) W x L — 432 x 200 mm
As mentioned before, the resulting surface load will spread in the concrete structure of the bridge deck 2. The force spread angle 12 involved preferably forms part of the analysis. Starting point for varying the force spread angle 12 may be 45°, other spreading angles that may be considered are 0° and 30°.
The adopted step size with which the aircraft 13 moves over the bridge deck model 2 may e.g. be 0.25 m.
For each aircraft 13 and (thus) load configuration L4 and Ls, the following orthotropy parameters and force spread angles are chosen, for a total number of 8 variants, to. determine which variant offers the best fit (with a Poisson ratio of 0, leading to D12 = 0). Although several predefined variants are shown below, preferably, this is an iterative process:
LL
04 oP [aal [zen | ao [aa Lae
Table 2 — Orthotropy parameters and force spread angles for 8 variants
For the Boeing 777-200 (L,), variant 7 appeared to offer the best fit.
For the Airbus A319-314 (Lz), variant 7 also led to the best fit.
Subsequently, the measured responses and theoretical responses for the best fits may be visualized in graphs such as shown in Figures 5 and 6.
Preferably, a plurality of different load configurations (L, Ls, Ls) are (thus) used for modelling the bridge deck 2, such as explained above in relation to two different aircraft types, in order to improve the allocation of stiffness parameters (D) and, when applicable, force spread angle 12 parameters, to the bridge deck 2 to achieve the best fit. The force spread angle 12, e.g. as shown in Figure 1, may be 30 — 60°, such as 40 — 50°, such as around 45°.
As mentioned before, Figure 5 schematically shows a theoretical response of the rotation measurement devices when an aircraft with a known load configuration passes by. Figure 6 schematically shows a measured response of the rotation measurement devices when an aircraft with a known load configuration passes by. On the horizontal axes, the rotation measurement devices 11 (numbers) are shown, in this case 19 rotation measurement devices 11 were used. The vertical axes show the consecutive datapoints, i.e. the (chronological) rotation measurements over a certain period of time.
For the particular situation shown in Figures 5 and 6, e.g. when an aircraft 13 having a main landing gear and a nose wheel, such as shown in Figure 1 passes over the bridge deck 2 (such as explained with reference to the abovementioned example case with two different aircraft), the inventors have found that the measured response 16 as shown in Figure 6 actually proved to be much more favourable than anticipated, i.e. compared to the theoretical response 15 shown in
Figure 5. The two response “areas” in the upper halves of Figures 5 and 6, by the way, relate to the forces F; exerted by the main landing gear of the aircraft 13 (1/2F; for the left main landing gear portion and 1/2F, for the right main landing gear portion), whereas the (smaller) response area in the lower halves of Figures 5 and 6 relates to the force F2 exerted by the nose wheel. As shown in Figure 6, in “real life” the forces occurring due to the load L appeared to be much more evenly distributed on/in the bridge deck 2 (having a lower intensity) leading to lower stress concentrations, i.e. about 13% lower than anticipated. Furthermore, the longitudinal bending moments also appeared to be much lower in real life, i.e. about 37% lower than anticipated (i.e. compared to the theoretical response 15 shown in Figure 5).
When the stiffness parameters (D) of the bridge deck 2 have been determined in such a way, that a best fit has been achieved between the modelled reaction forces R (Rm) and the calculated reaction forces R (Rs), the allocated stiffness parameters (D) (and, optionally, force spread angle parameters and bearing stiffness parameters) giving the best fit are used to determine shear forces and bending moments, and, ultimately, a load rating and/or effective remaining lifespan of the bridge deck 2 and/or the bridge 1. For instance, the remaining lifespan may be much longer than theoretically anticipated, in some cases even 10 or even 20 years longer.
In such cases, it is conceivable that maintenance requirements may be lower, due to the bridge 1 and bridge deck 2 having better “health” than expected, leading to lower downtime, lower maintenance costs, lower replacement costs and lower CO: emissions and increased durability.
Figure 7 schematically shows the method for modelling the structural element embodied by the bridge deck in the form of a rudimentary flowchart. In essence, with the present method, geometric input 17 (such as dimensions, constructional details, materials used, et cetera), stiffness parameters (D), a measured response 16 and a known load configuration L (all shown on the left side) are used to model actual bridge behaviour 18 (shown on the right side). Previously, only the geometric input 17, (assumed) stiffness parameters (D) and the known load configuration L were used to model bridge behaviour 18, leading to far less accurate modelling of the bridge 1 and bridge deck 2. As a general remark, the measured response 16 can be advantageously visualized by means of a “potential energy” response graph, as shown in Figure 7.
It should be clear that the description above is intended to illustrate the operation of embodiments of the invention, and not to reduce the scope of protection of the invention. Starting from the above description, many embodiments will be conceivable to the skilled person within the inventive concept and scope of protection of the present invention.
LIST OF REFERENCE NUMERALS
1. Bridge 2. Bridge deck 3. Traffic (load) 4. Vertical plane 5. Rotation measurement means 6. Bridge support 7. Bridge bearing 8. Upper end of bridge support 9. Intersection of bridge deck and bridge support 10. Local rotation 11. Rotation measurement device 12. Force spread angle 13. Aircraft 14. Avioduct 15. Theoretical (FEM) response 16. Measured response 17. Geometric input 18. Bridge behaviour xX = Longitudinal direction
Y = Horizontal direction
Zz = Vertical direction
W = Bridge support width
Re = Calculated reaction force
Rm = Modelled reaction force
L = Load (configuration)
Fi, F2 = Traffic load
Si, Sz, Ss = Sensor (direction)
D = Orthotropic plate stiffness(es)

Claims (20)

CONCLUSIESCONCLUSIONS 1. Werkwijze voor het meten van lokale rotatie (10) van een constructief element (2), zoals een brugdek (2), geconfigureerd voor het ondersteunen van een last (3), zoals verkeer (3), omvattende de stappen van: - wanneer de last is gepositioneerd op het constructieve element, zoals wanneer verkeer over het constructieve element (2), zoals het brugdek, passeert, het meten van een lokale rotatie (10) van het constructieve element, zoals het brugdek, in een verticaal vlak (4), uitgelijnd met een langsrichting {X) van het constructieve element, met rotatiemeetmiddelen (5) aangebracht aan een of meer steunen (6), zoals brugsteunen (6), die het constructieve element ondersteunen, waarbij het constructieve element roteerbaar is aangebracht op een of meer lagers (7), zoals bruglagers (7), gepositioneerd op de een of meer steunen, waarbij de rotatiemeetmiddelen zijn aangebracht aan een boveneinde (8) van de een of meer steunen, onder de kruising (9) van het constructieve element en de respectieve steun, zodanig dat de lokale rotatie (10) van het constructieve element ten opzichte van de steun wordt gemeten, waarbij de rotatiemeetmiddelen meerdere rotatiemeetinrichtingen (11) omvatten, aangebracht op horizontaal op afstand van elkaar gelegen posities, in een horizontale richting (Y), ie. een richting loodrecht op het verticale vlak en de langsrichting, langs het boveneinde van de steun, zodanig dat meerdere rotatiemetingen kunnen worden uitgevoerd in de horizontale richting.A method of measuring local rotation (10) of a structural element (2), such as a bridge deck (2), configured to support a load (3), such as traffic (3), comprising the steps of: - when the load is positioned on the structural element, such as when traffic passes over the structural element (2), such as the bridge deck, measuring a local rotation (10) of the structural element, such as the bridge deck, in a vertical plane ( 4), aligned with a longitudinal direction {X) of the structural element, with rotation measuring means (5) mounted on one or more supports (6), such as bridge supports (6), supporting the structural element, the structural element being rotatably mounted on one or more bearings (7), such as bridge bearings (7), positioned on the one or more supports, the rotation measuring means being arranged at an upper end (8) of the one or more supports, below the intersection (9) of the structural element and the respective e support, such that the local rotation (10) of the structural element relative to the support is measured, the rotation measuring means comprising a plurality of rotation measuring devices (11) arranged at horizontally spaced positions, in a horizontal direction (Y) , ie. a direction perpendicular to the vertical plane and the longitudinal direction, along the top end of the support, such that multiple rotation measurements can be made in the horizontal direction. 2. Werkwijze volgens conclusie 1, waarbij het constructieve element (2) een brugdek (2) is, waarbij de steunen (6) brugsteunen (6) zijn en waarbij de lagers (7) bruglagers (7) zijn.A method according to claim 1, wherein the structural element (2) is a bridge deck (2), wherein the struts (6) are bridge struts (6) and wherein the bearings (7) are bridge bearings (7). 3. Werkwijze volgens conclusie 1 of 2, waarbij de rotatiemeetmiddelen (5) 2 — 50, bij voorkeur 10 — 30, bij grotere voorkeur 15 — 25 horizontaal op afstand van elkaar gelegen rotatiemeetinrichtingen (11) omvatten.Method according to claim 1 or 2, wherein the rotation measuring means (5) comprise 2 - 50, preferably 10 - 30, more preferably 15 - 25 horizontally spaced rotation measuring devices (11). 4. Werkwijze volgens een van de voorgaande conclusies, waarbij de rotatiemeetinrichtingen (11) zijn geconfigureerd om 20 — 80, bij voorkeur 40 — 60, bij grotere voorkeur 45 — 55 metingen per seconde uit te voeren.A method according to any one of the preceding claims, wherein the rotation measuring devices (11) are configured to perform 20 - 80, preferably 40 - 60, more preferably 45 - 55 measurements per second. 5. Werkwijze volgens een van de voorgaande conclusies, waarbij de een of meer steunen (6) een steunbreedte (W) hebben, zoals een brugsteunbreedte (W), in de horizontale richting (Y), waarbij de rotatiemeetmiddelen (5) ten minste 5%, zoals ten minste 10%, zoals ten minste 25%, bij voorkeur ten minste 40%, bij grotere voorkeur ten minste 50%, bij nog grotere voorkeur ten minste 70%, bij grootste voorkeur ten minste 90% van de steunbreedte bestrijken.A method according to any one of the preceding claims, wherein the one or more supports (6) have a support width (W), such as a bridge support width (W), in the horizontal direction (Y), the rotation measuring means (5) being at least 5 %, such as at least 10%, such as at least 25%, preferably at least 40%, more preferably at least 50%, even more preferably at least 70%, most preferably at least 90% of the support width. 6. Werkwijze voor het modelleren van een constructief element (2), zoals een brugdek (2), geconfigureerd voor het ondersteunen van een last (3), zoals verkeer (3), omvattende de stappen van: - het gebruiken van de werkwijze volgens een van de voorgaande conclusies voor het meten van lokale rotatie (10) van het constructieve element ten opzichte van de een of meer steunen (6), - het berekenen van reactiekrachten (Rc) van de een of meer lagers (7) aan de een of meer steunen (6) gebaseerd op de gemeten lokale rotatie (10) van het constructieve element ten opzichte van de een of meer steunen, - het verkrijgen van een lastconfiguratie (L; F+, Fz) van het constructieve element als gevolg van het gepositioneerd zijn van de last, zoals verkeer dat over het constructieve element passeert, op het constructieve element, waarbij de last, zoals het verkeer, bekende lasteigenschappen heeft, zoals lasttype en lastsnelheid, - het modelleren van het constructieve element nabij de een of meer steunen, waarbij het constructieve element wordt gemodelleerd als een orthotrope plaat, - het modelleren van de lastconfiguratie (L; F1, Fz) van het constructieve element nabij de een of meer steunen, en het iteratief: 1) toewijzen van stijfheidsparameters (D) aan het constructieve element, 2) modelleren van reactiekrachten (Rm) van de een of meer lagers en, bij voorkeur, het modelleren van rotaties aan de een of meer steunen, en 3) vergelijken van de gemodelleerde reactiekrachten (Rm) en, bij voorkeur, de gemodelleerde rotaties nabij de een of meer steunen met de berekende reactiekrachten (Rc) en, bij voorkeur, berekende rotaties, totdat een beste fit wordt bereikt.A method for modeling a structural element (2), such as a bridge deck (2), configured to support a load (3), such as traffic (3), comprising the steps of: - using the method according to one of the preceding claims for measuring local rotation (10) of the structural element relative to the one or more supports (6), - calculating reaction forces (Rc) of the one or more bearings (7) on the one or more supports (6) based on the measured local rotation (10) of the structural element relative to the one or more supports, - obtaining a load configuration (L; F+, Fz) of the structural element as a result of being positioned of the load, such as traffic passing over the structural element, on the structural element, where the load, such as traffic, has known load properties, such as load type and load speed, - modeling the structural element near the one or more supports, w where the structural element is modeled as an orthotropic plate, - modeling the load configuration (L; F1, Fz) of the structural element near the one or more supports, and iteratively: 1) assign stiffness parameters (D) to the structural element, 2) model reaction forces (Rm) of the one or more bearings and, preferably , modeling rotations at the one or more supports, and 3) comparing the modeled reaction forces (Rm) and, preferably, the modeled rotations near the one or more supports with the calculated reaction forces (Rc) and, preferably, calculated rotations, until a best fit is achieved. 7. Werkwijze volgens conclusie 8, waarbij, naast het toewijzen van stijfheidsparameters (D) aan het constructieve element (2), krachtspreidingshoek (12) parameters worden toegewezen aan het constructieve element.A method according to claim 8, wherein, in addition to assigning stiffness parameters (D) to the structural member (2), force spread angle (12) parameters are assigned to the structural member. 8. Werkwijze volgens conclusie 6 of 7, waarbij, naast het toewijzen van stijfheidsparameters (D) aan het constructieve element (2), stijfheidsparameters worden toegewezen aan de een of meer lagers (7).A method according to claim 6 or 7, wherein, in addition to assigning stiffness parameters (D) to the structural element (2), stiffness parameters are assigned to the one or more bearings (7). 9. Werkwijze volgens een van de conclusies 6 - 8, waarbij een veelheid van verschillende lastconfiguraties (L) wordt gebruikt voor het modelleren van het constructieve element (2) om de toewijzing van stijfheidsparameters (D) en, wanneer afhankelijk van conclusie 7, krachtspreidingshoek (12) parameters aan het constructieve element en, wanneer afhankelijk van conclusie 8, de toewijzing van stijfheidsparameters aan de een of meer lagers (7) te verbeteren, om de beste fit te bereiken.A method according to any one of claims 6 - 8, wherein a plurality of different load configurations (L) are used to model the structural element (2) to determine the assignment of stiffness parameters (D) and, when dependent on claim 7, force spread angle (12) parameters to the structural element and, when dependent on claim 8, to improve the assignment of stiffness parameters to the one or more bearings (7), to achieve the best fit. 10. Werkwijze volgens een van de conclusies 6 - 9, waarbij, wanneer de stijfheidsparameters (D) van het constructieve element (2) op zodanige wijze zijn bepaald, dat een beste fit is bereikt tussen de gemodelleerde reactiekrachten (Rm) en de berekende reactiekrachten (R.), de toegewezen stijfheidsparameters die de beste fit geven, worden gebruikt om dwarskrachten en/of buigmomenten die uitgeoefend worden op het constructieve element (2), en/of de constructie (1) omvattend het constructieve element, te bepalen.A method according to any one of claims 6 - 9, wherein, when the stiffness parameters (D) of the structural element (2) are determined in such a way that a best fit is achieved between the modeled reaction forces (Rm) and the calculated reaction forces (R.), the assigned stiffness parameters giving the best fit, are used to determine transverse forces and/or bending moments applied to the structural element (2), and/or the structure (1) comprising the structural element. 11. Werkwijze volgens een van de conclusies 6 - 10, waarbij, wanneer de stijfheidsparameters (D) van het constructieve element (2) zijn bepaald op zodanige wijze, dat een beste fit is bereikt tussen de gemodelleerde reactiekrachten (Rm) en de berekende reactiekrachten (Rs), de toegewezen stijfheidsparameters die de beste fit geven, worden gebruikt om een draagvermogen en/of effectief resterende levensduur van het constructieve element (2), en/of de constructie (1) omvattend het constructieve element, te bepalen.A method according to any one of claims 6 - 10, wherein, when the stiffness parameters (D) of the structural member (2) are determined in such a way that a best fit is achieved between the modeled reaction forces (Rm) and the calculated reaction forces (Rs), the assigned stiffness parameters giving the best fit, are used to determine a bearing capacity and/or effective remaining life of the structural member (2), and/or the structure (1) comprising the structural member. 12. Werkwijze volgens een van de voorgaande conclusies, waarbij de last verkeer (3) omvat.A method according to any one of the preceding claims, wherein the load comprises traffic (3). 13. Werkwijze volgens conclusie 12, waarbij het verkeer (3) vliegtuigen (13) omvat en de constructie een avioduct (14) is.A method according to claim 12, wherein the traffic (3) includes aircraft (13) and the structure is an avioduct (14). 14. Constructie (1), zoals een brug (1), omvattend een constructief element (2), zoals een brugdek (2), geconfigureerd voor het ondersteunen van een last (3), zoals verkeer (3), omvattend: - rotatiemeetmiddelen (5) aangebracht aan een of meer steunen (6), zoals brugsteunen (6), die het constructieve element, zoals het brugdek, ondersteunen, voor het meten van een lokale rotatie (10) van het constructieve element in een verticaal vlak (4), uitgelijnd met een langsrichting (X} van het constructieve element, wanneer de last is gepositioneerd op het constructieve element, zoals wanneer verkeer over het constructieve element passeert, waarbij het constructieve element roteerbaar is aangebracht op een of meer lagers (7), zoals bruglagers (7), gepositioneerd op de een of meer steunen, waarbij de rotatiemeetmiddelen zijn aangebracht aan een boveneinde (8) van de een of meer steunen, onder de kruising (9) van het constructieve element en de respectieve steun, zodanig dat de lokale rotatie (10) van het constructieve element ten opzichte van de steun wordt gemeten, waarbij de rotatiemeetmiddelen meerdere rotatiemeetinrichtingen (11) omvatten, aangebracht op horizontaal op afstand van elkaar gelegen posities, in een horizontale richting (Y), i.e. een richting loodrecht op het verticale vlak en de langsrichting, langs het boveneinde van de steun, zodanig dat meerdere rotatiemetingen kunnen worden uitgevoerd in de horizontale richting.14. Construction (1), such as a bridge (1), comprising a structural element (2), such as a bridge deck (2), configured to support a load (3), such as traffic (3), comprising: - rotation measuring means (5) mounted on one or more supports (6), such as bridge supports (6), supporting the structural element, such as the bridge deck, for measuring a local rotation (10) of the structural element in a vertical plane (4 ), aligned with a longitudinal direction (X} of the structural element, when the load is positioned on the structural element, such as when traffic passes over the structural element, the structural element being rotatably mounted on one or more bearings (7), such as bridge bearings (7), positioned on the one or more supports, the rotation measuring means being arranged at an upper end (8) of the one or more supports, below the intersection (9) of the structural element and the respective support, such that the local rotation (10) of the structural element relative to the support is measured, the rotation measuring means comprising a plurality of rotation measuring devices (11) arranged at horizontally spaced positions, in a horizontal direction (Y), i.e. a direction perpendicular to the vertical plane and the longitudinally, along the top end of the support, such that multiple rotational measurements can be made in the horizontal direction. 15. Constructie (1) volgens conclusie 14, waarbij het constructieve element (2) een brugdek (2) is, waarbij de steunen (8) brugsteunen (6) zijn en waarbij de lagers (7) bruglagers (7) zijn.A construction (1) according to claim 14, wherein the structural element (2) is a bridge deck (2), wherein the supports (8) are bridge supports (6) and wherein the bearings (7) are bridge bearings (7). 16. Constructie (1) volgens conclusie 14 of 15, waarbij de rotatiemeetmiddelen (5) 2 — 50, bij voorkeur 10 — 30, bij grotere voorkeur 15 — 25 horizontaal op afstand van elkaar gelegen rotatiemeetinrichtingen (11) omvatten.A construction (1) according to claim 14 or 15, wherein the rotation measuring means (5) comprise 2 - 50, preferably 10 - 30, more preferably 15 - 25 horizontally spaced rotation measuring devices (11). 17. Constructie (1) volgens een van de conclusies 14 - 16, waarbij de rotatiemeetinrichtingen (11) zijn geconfigureerd om 20 — 80, bij voorkeur 40 — 60, bij grotere voorkeur 45 — 55 metingen per seconde uit te voeren.A construction (1) according to any one of claims 14 - 16, wherein the rotation measuring devices (11) are configured to perform 20 - 80, preferably 40 - 60, more preferably 45 - 55 measurements per second. 18. Constructie (1) volgens een van de conclusies 14 — 17, waarbij de een of meer steunen (6) een steunbreedte (W) hebben, zoals een brugsteunbreedte (W), in de horizontale richting (Y), waarbij de rotatiemeetmiddelen (5) ten minste 5%, zoals ten minste 10%, zoals ten minste 25%, bij voorkeur ten minste 40%, bij grotere voorkeur ten minste 50%, bij nog grotere voorkeur ten minste 70%, bij grootste voorkeur ten minste 90% van de steunbreedte bestrijken.A structure (1) according to any one of claims 14 - 17, wherein the one or more supports (6) have a support width (W), such as a bridge support width (W), in the horizontal direction (Y), the rotation measuring means ( 5) at least 5%, such as at least 10%, such as at least 25%, preferably at least 40%, more preferably at least 50%, even more preferably at least 70%, most preferably at least 90% of the support width. 19. Constructie (1) volgens een van de conclusies 14 — 18, waarbij de last verkeer (3) omvat.A construction (1) according to any one of claims 14 - 18, wherein the load comprises traffic (3). 20. Constructie (1) volgens conclusie 19, waarbij het verkeer (3) vliegtuigen (13) omvat en de constructie een avioduct (14) is.A structure (1) according to claim 19, wherein the traffic (3) includes aircraft (13) and the structure is an avioduct (14).
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