back   back to menu
ARCHITECTURAL ANALYSIS AND SURVEYS

English english language


5.6 Geometry determination: numerical analysis


Differences among drawings had to be kept under control, documented and analysed, all this could not be easily investigated by printing the results of the described work, this because only the arch voussoirs are 456 and differences of few centimetres have small dimensions compared to the global graphic representation of the bridge which spans almost 29 meters. This has led to a numerical approach which has been directly related to graphics: all the inserted data in CAD have been exported in numeric charts and viceversa.

All this electronic charts can give a synoptic view of all the steps that have been done, of all the corrections that have been made and of all the incoherences and differences found.

These charts have been organised by arch voussoirs: every line represents an ashlar and it is numbered both with current used numbers and with Roman numbers (like the 1955 survey); columns of the chart are generally X and Y co-ordinates of the connections coming from the different surveys; next to these there are "comparing columns" containing differences in centimetres.

Thank to this adopted layout it has been easily possible to locate the most meaningful differences, and this has finally led to the co-ordinates of the final bridge configuration point by point. The charts moreover are so wide that contain also data concerning the whole geometry of the bridge, the logical structure and the main monitored aspects are here next listed:

charts structure
  • ancient survey analysis - (data coming from 1955 and 1982 surveys)
  • survey comparing - (comparing among the ancient survey data)
  • direct survey data - (data directly surveyed on the bridge remaining portions)
  • 2000 survey - (the most likely bridge as it was before destruction)
  • verifies and checks - (checks and verifies of the obtained results)

monitored data

  • differences - (monitoring of differences among data)
  • incoherences - (worked out trough specified methods and parameters)
  • readability - (due to quality level of the ancient documentation)
  • reliability - (due to verifies and checks held on the methodology followed for the survey)
  • corrections - (carried out trough specified procedures and after full data check)
  • lacks - (parts of data not possible to be determined)

The numerical charts are the basis of the whole work, they have been started with all the available input data and with the analysis work; during the developing of the phase A they have been enlarged and right now they represent a full management support for any kind of processing of the design and of the stone cut.

The charts have been divided as follow, and each one contains input data, analysis data, parameter checks, output results, comparing data :

  • general variables
  • intrados (north and south)
  • extrados (north and south)
  • intrados-extrados compare
  • north-south compare
  • archivolt
  • design parameters 2d & 3d co-ordinates
  • design parameters stone cut and stone quarry

The electronic numerical charts are all logically connected and any modification of a value brings all the others to a simultaneous recalculation. In the charts there are special parameters that are monitored to check any anomaly that may lead to constructive difficulties. At the end of the phase A, the numeric data in the charts were thousands.

In order to satisfy the need of full documentation of anything that has been done (restoration principles do foresee this requirement), the numerical approach may be itself a detailed report of the work, and the basis for a correct, exact and scientific final design of the bridge.

In the following paragraphs it will be given a detailed description of the most meaningful portions of the charts, to report the main steps of the work.

 


5.6.1 Numeric intrados chart for the 1955 survey


One of the chart section contains the input data of the 1955 survey, the chart is always structured in the same way: each row represents a voussoir (or the first joint beginning from the origin) and the columns contain data about the co-ordinates of the joints and about the dimensions of the arch stones. Of course the chart is identically repeated both for north and south elevation.

fig.14 - A small portion of the chart related to the 1955 survey north elevation

The above chart is here next detailed explained:

  • stone number: is a progressive number which represents the arch stones but could be better referred to the first joint of each stone (as it is represented in the drawings)
  • roman number: is the same numbering system adopted in the 1955 survey, and it has been maintained to allow easier checks; it is referred to arch stones
  • X global survey: it is the numeric value that could be read on the ancient drawings about the X co-ordinates of all the joints of the arch stones. The system had its origin on the east arch springer (both for north and south side). It is a "global" value since it gives information on global measures of the arch shape point by point.
  • readability: is a column which is related to the previous data and may contain the following conventional items: "?", "c", "x". The first one ("?") means that the value could be hardly readable from the ancient drawings and for this reason it is not sure; the second one ("c") means that the value has been changed or corrected due to obvious mistakes (better explained in the followings pages); the last one ("x") means that the value was missing and it has been replaced with a presumable dimension (see next).
  • Y global survey: as the above X global survey but related to the Y dimensions.
  • readability: as the above
  • length global survey: is the value of the length of each voussoir deduced by calculations from the X,Y global survey co-ordinates; the simple calculation is the one reported in 5.4.3 of this report.
  • length local survey: is the dimension that could be read on the 1955 survey next to each voussoir: it is a local dimension since it is presumable that it was taken directly stone by stone.
  • readability: as the above
  • differences: are the absolute values of the difference among length global survey and length local survey. In other words, if the values are equal, there would be a zero, if the values are different there would be the difference of them without sign.
  • incoherences: it is an arbitrary parameter of a practical and simple use: if differences are higher (or equal) than cm 2.5 it gives "1", if they are lower it gives "0". This is aimed to an easy and synoptic localisation of the highest differences. The value of cm 2.5 has been chosen arbitrary, and also because a wide percentage of the dimensions were affected by small differences, (due to the survey method), that in this type of analysis should not be considered.

The exposed chart is precious for any type of analysis on the data and for their recording, but for a complete check of the dimensions it has been necessary to insert the above data in a CAD (Computer Aided Drawing) file, this way the co-ordinates could be represented by a curve with no graphic error (which is common in hand drawings). To avoid any mistakes the numbers have been checked many times comparing the ancient surveys and the digital chart, and for importing data in the CAD file it has been written a small LISP routine (internal CAD language) that has allowed an automatic insertion of data with no possibility of differences among the two digital systems.

The graphical representation of the chart has allowed the location of incoherences due to the inaccuracies of the original 1955 survey: some of the data were clearly outside from the range of the bridge curve for this reason the 1955 survey has been in some cases corrected. Corrections have been made following different methods depending on different elements and with an interconnected system of verify: like interpolations with previous and following data, verify with the results coming from the local length dimensions, check with possible combination of similar numbers that may have been misunderstood during the dimension transcription from the original on site sketches. These corrections, (about 15 cases out of 448 dimensions) are not many, and have been documented in the readability column.

Instead, some more were the situation of hardly readability due the very bad condition of the drawings of the survey, those data have been sometimes interpreted with the help of the graphic checks and thanks to a comparing job with the local length data.

Lacks were really a few, and were all located close to the origin; this has helped very much in solving the problem, since direct measure on the small portion of drawing, which was belonging to the same piece of copy, has given good results either with the graphic check either with the position of the springer.

All these cases have been documented in the digital chart, so that nothing has been done without a written indication, this is a methodology system that will allow any future revision or check of the work.

 


5.6.2 Numeric intrados chart for the 1982 survey


While the 1955 survey, being reliable for numeric dimensions only, was first mounted in a numerical chart and then exported in a CAD file, the 1982 survey, being graphically reliable and with no dimensions, has been first scanned, then put in CAD as raster image, then vectorialised and finally exported in a numeric chart for other checks. So the mentioned, (see 5.5.5 of this report), numerical output has been automatically inserted in the numerical chart, avoiding any possibility of error due to operator's wrong inputs.

fig.15 - A small portion of the chart related to the 1982 survey north elevation

The chart is structured identically to the one of the 1955 survey (global dimensions) and it is repeated for north and south side of the bridge: each row represents a voussoir (or the first joint beginning from the origin) and the columns contain data about the co-ordinates of the joints and about the dimensions of the arch stones.

The above chart is here next detailed explained:

  • stone number: as the 1955 survey chart
  • roman number: as the 1955 survey chart
  • X survey 82: it is the numeric value that has been imported from the CAD vectorial drawing of the 1982 survey and represents the X co-ordinates of all the joints of the arch stones. The system has its origin on the east arch springers (both for north and south side) like the 1955 survey. It gives information on global measures of the arch shape point by point.
  • Y survey 82: as the above X global survey but related to the Y dimensions.
  • length: is the value of the length of each voussoir deduced by calculations from the X,Y co-ordinates; the simple calculation is the one reported for the 1955 survey (see 5.4.3)

In this chart the parameter of readability doesn't exist, since data were absolutely complete and with no possibility of misunderstanding, due to the graphical origin of the information. Although some dimensions, even here, have been corrected but only next to the springers, where there were some graphic representation problems (on the west side, north elevation there was a small ruined portion of the arch and the last joints were not represented).

 


5.6.3 Survey comparing: intrados of 1955 and 1982


Anything that has been done in the numeric chart was aimed mostly at the comparing phase, where all the data coming from different sources may be related to understand what kind of data we are using and how much reliable they are. Of course all the compares have been made both on north and south side.

The first comparing chart is the one that simply quantifies the differences among the X and Y co-ordinates coming from the 1955 survey and from 1982 survey.

fig.16 - A small portion of the chart related to the X,Y comparing of north elevation

The above chart is here next detailed explained:

  • X survey 55: is the X co-ordinates coming from the 1955 chart
  • X survey 82: is the Y co-ordinates coming from the 1982 chart
  • differences: are the values (with sign) of the difference among the previous columns.
  • incoherences: gives 1 if the absolute value of the difference is bigger or equal to 2.5 otherwise it gives 0
  • Y survey 55: is the Y co-ordinates coming from the 1955 chart
  • Y survey 82: is the Y co-ordinates coming from the 1982 chart
  • differences: are the values (with sign) of the difference among the previous columns.
  • incoherences: gives 1 if the absolute value of the difference is bigger or equal to 2.5 otherwise it gives 0

Another interesting compare is among the length calculated of the 1955 survey and the one calculated of the 1982 survey. But maybe the most interesting, (next by to the previous), is the comparing among the local length of the 1955 survey and the length calculated using the 1982 survey.

In fact, in this last chart, the measures that are compared are the most reliable ones that may be gathered from the available sources.

fig.17 - A small portion of the two charts of length comparing of north elevation

The above charts are here next detailed explained:

  • length survey 55: is the calculated length coming from the 1955 chart
  • length survey 82: is the calculated length coming from the 1982 chart
  • differences: are the values (with sign) of the difference among the previous columns.
  • incoherences: gives 1 if the absolute value of the difference is bigger or equal to 2.5 otherwise it gives 0
  • length local survey 55: is the local length coming from the 1955 chart
  • length survey 82: is the calculated length coming from the 1982 chart
  • differences: are the values (with sign) of the difference among the previous columns.
  • incoherences: gives 1 if the absolute value of the difference is bigger or equal to 2.5 otherwise it gives 0

 


5.6.4 Comparing results: intrados of 1955 and 1982 surveys


The above described comparing systems and the global examination of the numeric chart have been really precious to understand many useful things on the source data. But to gather the meaning of the results of these charts it is important to point out two main findings coming from the survey analysis:

  • the most reliable data seems to be the local ones for the 1955 survey and the global ones for the 1982 survey
  • the 1982 survey is likely to be more reliable than the 1955 survey

For the above reasons, the X,Y compare among 1955 and 1982 has given bad results specially on the north side on the Y dimension, and this was foreseeable since, as it has been said in the survey analysis, the global co-ordinates coming from the 1955 survey may be affected by errors due to the way the survey was held. Moreover it seems that during the on site survey of the 1955 there have been on the north elevation a sort of origin shift: data in fact may be compared successfully group by group. And it seems that this discontinuity is approximately located every 10 meters.

One more confirmation of the above is given by the 1955 survey itself: on an additional chart there is reported a different dimensioning system of the arch profile which has been mounted numerically in the CAD file and this is a lot better in the area where the Y co-ordinates are in contrast with the 1982 survey.

Another observation that we can make about the 1955 survey is that, after all the checks, corrections, and verifies, the interior incoherences (among stone lengths measured locally and lengths coming from the global calculation) are not so many and not so high, this means that the most remarkable inaccuracies are related to the co-ordinate system where a mistake may lead to invalidate all the following metric data.

This is also confirmed by an exceptional result: the sum of all the local lengths of each voussoir gives good results in all the data systems and in both surveys: for the north elevation varies from cm 4053 to cm 4058 while for the south elevation it varies from cm 4034 to cm 4044.

But the most interesting and useful result of all this work is contained in the last comparing work chart, where there are only the most reliable measures of the 1955 survey (local lengths) that have been related to the co-ordinates and calculated lengths of the 1982 survey. The result is really extraordinary since incoherences are really a few (7-8 per side) and most of them are couples of adjacent cases of opposite sign. The meaning of this is clear: if a joint is in the wrong position it generates two mistakes at the same time (the first stone gets shorter and the second gets longer or viceversa). So for each case found we had four measures (two local and two global) of the 1955 survey that could demonstrate that the 1982 survey in that point had a small inaccuracy in the location of the joint. So we have a confirmation of what it has been hypothesised during the 1982 survey analysis about the surface details.

Followed methodology and worked out hypothesis have been, at the end of the documented procedure, partially verified, and have brought to the final intrados geometry of the bridge: "the most likely bridge of Mostar" defined by the "2000 survey" as it has been called in this work.

 


5.6.5 The 2000 survey and verifies - intrados


The "2000 survey" is the conventional name here given for the geometry of "the most likely bridge of Mostar" worked out trough the described procedures. The 2000 survey is a virtual survey that derives from the analysis and the study of the available data.

Corrections, (performed following the method specified in the above paragraph), have been:

  • only the ones where the 1955 survey had no incoherences
  • only where there were couples of equal and opposite data
  • all documented putting "c" tags next to the values
  • performed trough a geometric construction to maintain unchanged the original curve profile coming from the 1982 survey
  • on the still existing portions measured either with direct survey either with photogrammetry

After that a new chart has been fixed with the results coming from this inquiry:

fig.18 - A small portion of the 2000 survey chart and the measures coming from the direct survey of north elevation

Another compare has been made to check how the final situation was related to the ancient survey best data, and this has been done either for the stones lengths, either for the X,Y co-ordinates of the 1982 surveys, as showed in the following samples of the charts.

fig.19 - A small portion of the comparing among 2000 survey and ancient data - north elevation

fig.20 - A small portion of the comparing among 2000 and 1982 survey co-ordinates - north elevation

The 2000 survey is therefore numerically defined for what concern the intrados lines of the north and south side. But bridge geometry is not only that curve: many other elements have to be considered.

 


5.6.6 Numeric extrados chart for the 1955 and 1982 survey


A similar analysis, to the one of the intrados, has been performed for the extrados curves of the bridge archivolt, north and south side.

fig.21 - A small portion of the chart related to the 1955 & 1982 survey north elevation extrados curve

In this case the input data were not so many, and the 1955 survey contained only a local measure specification, while from the 1982 survey could be gathered the same type of data available for the intrados curves.

Data of the extrados analysis start from the 8th row about, and end at the 103rd row; this because the ancient surveys contain no information related to the interior portions, and the extrados curves ends are inside the abutments, probably until the springers level.

The above chart is here next explained:

  • stone number: is a progressive number which represents the arch stones but could be better referred to the first joint of each stone (as it is represented in the drawings)
  • roman number: is the same numbering system adopted in the 1955 survey, and it has been maintained to allow easier checks; it is referred to arch stones (rows)
  • length: is the local dimension reported on the 1955 survey
  • readability: is a column which is related to the previous data and may contain the following conventional items: "?", "c", "x". The first one ("?") means that the value could be hardly readable from the ancient drawings and for this reason it is not sure; the second one ("c") means that the value has been changed or corrected due to obvious; the last one ("x") means that the value was missing and it has been replaced with a presumable dimension.
  • X survey 82: it is the numeric value that has been imported from the CAD vectorial drawing of the 1982 survey and represents the X co-ordinates of all the joints of the arch stones. The system has its origin on the east arch springers (both for north and south side) like the 1955 survey. It gives information on global measures of the arch shape point by point.
  • Y survey 82: as the above X global survey but related to the Y dimensions.
  • length: is the value of the length of each voussoir deduced by calculations from the X,Y co-ordinates; the simple calculation is the one reported for the 1955 survey (see 5.4.3)

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 -

SOURCE:

Final Design Report

back   back to menu
ani.gif (16635 bytes)
GENERAL ENGINEERING - P.zzale Donatello 4 - 50132 Firenze - Italy - ph. +39 055 2345256 - fax. +39 055 2476074