|back to menu|
|DETAILED ANALYSIS OF THE DESIGN ISSUES||
4.2 Bridge curvature and global geometry determination
One of the main issues that was raised in the Inception Report (see §1.3) was about the performing of the exact curvature and geometry due to different aspects like:
During the 4th session of the ICE it was moreover established that, in the case the arch curvature, as it was just before destruction, had some structural problems due to the thrust line configuration and to any consequent tensile stress, the architectural and structural design should have proposed the less variations as possible to the curvature so that to guarantee the necessary future stability to the structure.
After works studies and calculations have been developed the situation for what concerns the bridge curvature and the general geometry is better than what it could be foreseen, and no modification to the curvature has been required.
4.2.1 The thrust line configuration
For what concern the thrust line of the load bearing arch of the bridge the foreseen structure problem on the basis of a preliminary calculation was reported in the Inception Report §1.3.1 (first part) and here next resumed as: "Since arch shape and arch stability are two parameters strictly linked one to each other, they have to be analysed together to understand and point out whether the performing of the previous arch curvature may lead to any resistance and stability risk for the structure. For this reason, once the final geometry has been defined, it has to be investigated if that shape for the voussoir arch is going to fit the thrust line; in other words it has to be verified that the vault of the bridge is compatible, with secure margins, with dead and live loads so that to transmit the final thrust to the abutments […] the former bridge had a curvature which may have been cracked in different locations and where the thrust line had a configuration different to the original one. The altered configuration was stable and this is why the bridge has been on site for about 500 years with no risk of collapse. But the rehabilitated bridge of Mostar will not work as a cracked bridge, we hope, and for this reason, the previous shape of the bearing vault has to be verified with a different thrust line which may cause local tensile stress resultants; for this reason the finite element calculations and the possible mechanisms of collapse have to be investigated before we can assure to reproduce the identical form […]". (See also the Inception report at chapter 3).
Preliminary calculations for the Inception Report had been worked out on a provisional geometry adopted in the meanwhile the survey 2000 research and data analysis was ongoing. That geometry was mainly a scheme in which there was no difference from north and south elevation and the reference survey was only the one of the year 1955. Moreover in that calculation it wasn’t included the contribute of the whole structure but of the load bearing arch only. (See also the Inception report at chapter 3). That calculation confirmed partially the foreseen tensile stress; but after a more detailed calculation on the 2000 survey (see §2.3.2 of the Inception Report for "2000 survey" definition), and examining the structure as a whole it resulted that there was no risk of tensile local stress. (See also structural report).
For the aforesaid reasons no modification to the arch intrados curve has been required and therefore the geometry (as it was before destruction) will be repeated: this way the 2000 survey is equal and confirmed in the 2000 design.
Prof. Eng. Vignoli, concerning this matter, has also given more structural notes as here next exposed:
The former bridge had on the left side a curvature, where the thrust line had a configuration different to the original one. The altered configuration was stable and this is why the bridge has been on site for about 500 years with no risk of collapse. But the rehabilitated bridge of Mostar will not work as a cracked bridge, because the bridge bearing structure is not limited to the arch alone, but it includes also the spandrels and the upper slab. As a consequence the actual stresses in all the sections of the masonry arch are compressive. There are not local tensile stresses in the arch, as it should appear from a very simplified model, where only the arch is called to bear all the loads.
The actual behaviour of the arch has been investigated through a solid finite element model, where all the elements (arch, spandrels, slab) were considered.
The stability of the bridge is not sensitive to modifications of vault curvatures of some centimetres, differently from what happens in the arch alone, where this variations could take off much more the thrust line from the centreline of the arch (see for more details structural report and calculations).
4.2.2 Geometry determination trough the analysis of the available data
In the Inception Report (see §1.3.1 – third part) about the geometry determination and the elaboration of data it was reported what follows: "[…] But one of the main limit to the exact performing of the former bridge shape is the determination of the exact geometry of the intrados trough the analysis of the available documentation and ancient technical drawings. This, far from being an easy task, has led to interesting findings and with a careful comparing work has brought to encouraging results. Anyhow this should be always considered as a limit since the knowledge of the former bridge can be reached trough probabilistic methods […]"
The above statement is here totally confirmed and it may be added that the works, studies and researches held during the phase A period have been mostly focused on the geometry determination work until the 2000 survey was defined (the "2000 survey" is the conventional name here given for the geometry of "the most likely bridge of Mostar; the 2000 survey is a virtual survey that derives from the analysis and the study of the available data).
It can be said that, even if the available data were scarce, partial, ruined and with many incoherences, it has been possible to obtain good and reliable results proceeding as follow:
It is thank to the different verifies systems that it has been possible to have a fairly good level of reliability on the final obtained results, and some of the checks have given unexpected confirmation of the operative method.
The 1955 survey, the 1982 survey, the photogrammetry elaboration on ancient pictures, and the direct survey of the current condition of the ruined portions have been all integrated and used to gather the best and to make all the necessary compares. The analysis has been brought so deep to allow determinations and corrections of dimensions in the range of ± 2 centimetres on every single stone voussoirs which is even an higher level of what the technology of the stone cutting and assembling may be able to ensure. The 1982 survey has been undoubtedly the base of this work, but it has revealed its incoherences as well in the following data:
The numerical analysis system and the connected cad system has allowed at the same time either a numeric control and compare of all the thousands of data with a predefined tolerance, either a correct digital vectorial representation trough technical drawings that may be printed on any scale and for any future development of the work. Also the numerical electronic sheets are all connected one with the others, and have been used for all the design steps, even including the bill of quantities. For details on all the above mentioned subjects refer to chapter 5 of this report.
For the aforesaid reasons the geometry determination of the Old Bridge could be considered an issue that has found its best solution compared to the available data; what is still left and is affected by serious lacks is here listed:
The PCU has been informed of the above matters but has declared that General Engineering didn't need any other data to perform the assignment. This way all the above matters have not been further discussed.
4.2.3 Geometry determination of the detailed dimensions: theoretical approach
As it has been already introduced in the previous paragraph, there was no documentation at all of the irregularities and of the ordinary imperfections of the structure that are lower than a centimetre. These small variations are precious and are part of the beauty of the monument and may be not neglected to guarantee the final global aspect of the bridge and have been considered and analysed to fulfil to the required aim of reproducing the ancient bridge as it was, and to avoid the construction of a polished arch quite different from the original. The prove that these slightly anomalies were present comes from the observation of the recovered assembled stones, and may be confirmed by the ancient masonry constructive method itself, that leads to ordinary irregularities.
The above mentioned issue is a general one and characterises almost all bridge elements and mostly all the cornices and finishes. A list of the most remarkable cases is the following:
These anomalies and imperfections could not be exactly planned in the future bridge of Mostar, not even if they were known one by one, for obvious practical reasons. And as Eng. Gilles Pequeux has first underlined, this would be far from the conceptual and theoretical approach that should be followed during the designing stage.
The correct approach has been reached trough the analysis of those peculiarities and will be performed, during the construction stage, simply by following similar assembling methods that will ensure the presence of new imperfections with a random location.
Nevertheless one of the most delicate matter, (evaluating only the geometrical issue: refer to structural report for more notes), is the one concerning the joints: the joint thickness may be not left to a complete randomly criteria and have been carefully analysed to avoid huge constructive unexpected problems. In fact even a small thickness of some millimetres due to the joint among stones may, if repeated one hundred times, lead to unforeseen differences of many centimetres. This issue was raised and analysed even in the Inception Report see §1.4.3.
The work and studies that have been carried out, either concerning the 2000 survey, either concerning the design stage, (and mostly the final stone cut drawings and charts of every single load bearing arch voussoir), has been performed with the "zero tolerance": considering the joints equal to zero.
This delicate choice has been agreed with PCU TA and is here next explained. First of all it has to be underlined what follows:
Moreover we should refer to the above explained methodology to gather the spirit of the work in its main aims and methodology. What is important to point out is that: leaving this parameter free to be slightly managed during the on site stone assembling, by practical and manual adjustments, similar to the ancient adopted techniques, of course we will guarantee the reproducing of the same level of imperfections of the former bridge having an additional stone cut tolerance, (see chapter 7 of this report). A special system of progressive control has been worked out to make sure, step by step, that we are not going far from the final design and far from the former bridge. Nevertheless additional warnings are provided about this issue for what concern the structural behaviour: refer to structural design report and to LGA final report.
4.2.4 Arch centering different settlings
Since the beginning of the works, in the Inception Report, (see §1.3.1 – second part), about the arch curvature and the reproducing of it trough the use of a centering and scaffolding system it was reported what follows: "Another limit to the exact performing of the former bridge shape is related to the scaffolding and to the arch falsework: a wide number of variables are involved in the final configuration of the vault, and by now it seems to be a delicate task to foresee the exact behaviour of every single one.
The arch falsework will determine the geometry of the intrados of the bridge, but this special scaffolding structure undergoes to different settlements and load variations during the on site works that may change its original configuration.".
What above is confirmed and this theme has been developed by Prof. Eng. Vignoli, analysing the structural issue, and finally the foreseen settlements have been updated (from what was listed in the Inception report §1.3.1):
However, using a very stiff centering, it is possible to limit drastically the centering deformations and to get a shape of the arch intrados very near to the initial shape of the centering, also after the centering deformations. Therefore, the centering shape can be chosen equal to the shape of the former bridge: the stiffness of the centering will assure the maintenance of this shape, with only insignificant deformations.
Each centering foot should be placed over oleodynamic jack to recover the initial position after eventual settlements at the foots during the works preceding the completion of the arch.
Among the most important variables to be taken into consideration there are:
4.2.5 Conclusion about the geometry determination issue
The importance of rebuilding the new structure as much close as possible to the original one, (since a structure just alike to the ancient bridge would be meaningless) has been exposed in the §4.1.1 of this report. And many more are the reasons that may be added to this issue (see also §1.3 of the Inception report):
During the whole assignment, the exact geometry determination is one of the theme on which it has been spent a considerable effort, and the results of which are here next widely exposed, (see chapter 5 of this report); of course other issues will raise about this subject, during on-site works, but trying to overcome these kind of difficulties is undoubtedly worthy, either for the value of an unique historical documentation of a monument that doesn’t exist anymore, either for the maintenance of one of the basic objective of the project without which it would loose the widest part of its aims and of its meanings.
CREDITS:Intellectual property of this report and of the design drawings is owned by General Engineering s.r.l.
author of the text: arch. Manfredo Romeo – other contributes have been mentioned in related paragraphs
© - General Engineering Workgroup -
Final Design Report
|back to menu|
|GENERAL ENGINEERING - P.zzale Donatello 4 - 50132 Firenze - Italy - ph. +39 055 2345256 - fax. +39 055 2476074|