STRUCTURAL ANALYS1S OF H1STORICAL CONSTRUCTlONS P. Roca, J.L. González, A.R. Marí and E. Oilate (Eds.)

© CIMNE, Barcelona 1996

A SUMMARY OF THE OPINIONS PUT FORWARD DURING THE DISCUSSIONS

P. Roca and J.L. González Universitat Politecnica de Catalzmya

08034 Barcelona

Spain

1. . PRESENTATION OF THE SEMIN AR

This chapter aims to present some of t he ideas arosen through the technical discussions held during the celebration of the International Seminar on Structural Analysis of Historical Construcions. The event, which was held in t he Assembly HaU of the School of Civ il Engiueering of Barcelona on November 8 to 10 1995, was a grea t success, with more than two hundred participants come from many countries of Europe and A merica.

The different ledures presented were organized in five monographic sessions. A first series of interventions aimed to establish the methodological and analytical bases for a const ruct.ional study of an ancient building belonging to the historical and architedural heritage. Giorgio Macchi and D. Ant.onio González were t he first speakers, talking ou "General methodology: T he combined use of numerical and experimental techniques" and "A general perspective of the stuclies. The role of the analystsll respectively. Anton ino Giuffre then dealt wi1.h llMethodology for analysis and in1.ervention based on historical knowledge".

The second group of papers aimed to present the state of the art of science and t.echnology concerning the elements available to the technician for approaching

such studies. This sedion induded aspects such as inspectioIl) experimentation, characterization of adions an d numerical modelling . All the papers were illustrated with real cases of great interest. Roberto Meli was thc first speaker, presenting a study of the Metropolitan Cathedral of Mexico as an example of action that. can arrect historical constructions. Giorgio Croci then talked OIl

J' Behavior of dr)' masonry structures present ing the studies 0 11 the tem pies of Angkor Vat in Cambodia and the Pyramid of Kephren in Egypt". Climent

Molins talked on "Constitutive models fo r the mechanical characterization of stone and brick masonryll. Finally, Tim H. Hughes presented an interesting

review of the studies made in the Unit.ed Ki ngdom in connection with the great number of stone or brick arch bridges that exist in this country.

P. ROCA nnd 1. L. GONZÁLEZ I The Discussions 395

The possibilities of experimental techniques in the study of historical constructions - in particular inspection l monitoring and cont rol techniques -were presented by Pier Paolo Rossi ancl by Rafael AstudiUo. Eugenio Oilate gave

an explanation of the possibilities of numerical analysis techniques, presenting as an example the studies carriecl out Oil the domes of the Basilica of San Marco.

Tile last grouf-I of vaf-lcn:i was devutt::J tu ut::.t:riLillg in lidai! the studies) and

if applicable lhe repairs or reinforcements , carried out on emblematic and well~

known historical const ructions. In chronological arder) the speakers considered the cases of the altics of the Casa Milão (Robert Brufau» the Casa de los Botines (José L. González), the Charles Bridge in Prage (Jaroslav Zák)l the Coliseum of Rome (Giorgio Croci), the Basilica of San Marco in Venice (Franco Mola and Renato Vitaliani), the Column of Marcus Aurelio in Rome (Antonino Giuffre), lhe Crypt ofthe Güell Colony (Pere Roca), the spires of the Cathedral of Burgos

(Luís Ortega), the Aqueduct of Segovia (Francisco Jurado) , and the Tower of Pisa (Giorgio Macchi). Finally, José Gómez gave an explanation of the Sagrada FamHia on the si te of the monument, which formed part of one of the technical

visits.

The Seminar induded a technical discussion and a round table, both of which proved to be of great interest due to the quality of the ideas put forward and the opportunity of pointing out some methodological weaknesses which are sti ll today difficult to overcome in order to perform a rigorous study of an ancicllt const ruction. In addition to the already cited lecturers, José María Ballester, Andrea Chiarugi, Javier López~Rey, Antonio R. Marí Bernat l Mircea Mihai lescu, Manuel Melero and O. C. Zienkiewic also took part in the discussion.

The ideas put forward during these discussions are presented in the following

paragraphs.

2.~ OPENING OF THE DISCUSSIONS

As coordinalor of the first Technical Discussion of the Seminar on 9 November,

P. Roca opened the session by inviting the participants to consider the following

problems:

(1) Many models created in order to study emblematic structures - sueh as those that have been presented in this Seminar - are based OH the acceptance of

the mechanics of a contilluous medium and on the hypothesis of linear elasticity. To what exlent is this approach valid whcn applied to masonry structures?

396 STRUCTURAL ANALYSI$ OF HI$TORICAL CON$TRUCT10NS

(2) Is there any point in working with more sophisticated models? (For example,

mo deis that reproduce the behavior of the mason ry with great realism, including its different forms of failure). In order to function correctly these models require a great amount of data on the mecharucal properties of the materiaIs. As a rule,

it is difficult to obtain these data completely.

(3) Given the unavoidable limitations of the available information, and the

limitations inherent to the methods of analysis that are used, to what extent is it possible to evaluate the strudural safety of an ancient construction ? 1s it really necessary to quantify this safety exactly?

As the coordinator of the Round Table on 10 November, J. L. González wished to consider problems that ranged from very specific aspects to very general anes.

(4) With regard to the specific aspects, he invited the congress members to

continue t he discussion ou the methods for modelling ancient constructions.

(5) With regard to more general aspects, he suggested dealing with the importance of the dialogue between the different professionals, presenting this issue as a key philosophical aspect due to the increasing variety of professionals involved in studies af historical constructions.

However , the discussions raised many more topics related to a greater ar lesser extent to these first problems.

In this article we have decided to order the opinions gathered according to related topics, seeking a greater linearity and coherence of presentatian. Hawever, as a consequence, the final group of the interventians does nat carrespond exactly to the chronalagical order in which they were farmulated.

3.- THE DIALOGUE BETWEEN THE DIFFERENT PROFESSIONALS

Collabaration between different professionals is something obligatary, since th is

type af study mobilizes an increasing amaunt af knowledgc, and it is impossible for a single professianal to cover it ali. Furthermore, it is necessary to avoid the isolation of each expert within his area, anel to seek a maximum dialogue between the different disciplines.

For the praject management, t he main issue lies in the formulation of what questions they must ask each specialist of the team (J. L. González).

P. ROCA and J. L. GONZÁLEZ / The Oiscussions 397

The opinions put forward in this Seminar should serve to aliow those who wish

to work in the study of ancient constructions to understand the need to work in the environment of a multidisciplinary team . In fad, this type of study requires

t he participation of ao increasing number of professionals. \Ve should be capable

of transmitting the complexity of decision-making in this regard and therefore

t he need to have a profound knowledge. Therefore, all the specialists who have presented their projects at this Seminar have sho\\'n ao exemplary humility,

recognizing the need to obtain informatiol1 and to work wit.h collaborators of

ali types (J. L. González).

Though the importance of multidisciplinary collaboration should not be

underestimateel, it is also necessary to assess the individual work of reftection

that each person participating in the study must undertake. The knowledge

phase is more a phase of individual work than teamwork.

It is also important to give fuU consideration to the objective of the study:

:;k nowing" . lf the objective is approached correctly, the methods are secondary

if they are consistent with it. As A. Giuffre has stated, one must "be attentive

to the monument", rather than to the means t.hat we have for knowing it.

As G. Macchi has recalled 1 the criticai and reflexive rclationship with the

monument by the professional is baseei ou knowledge. Those who scorn the

method guided by profound knowledge, and who prefer intuition, should be reminded t hat at the basis of creativit.y there is always a very wide knowledge

base: being intuit.ive is a consequence. One must be attentive lo the monument

on the basis of a profound kuO\ .... ledge of the 1l1eans that. are with in one 1s reach . The aim of t he restoration is to recover the emot.ional relationship of

t he monu1l1ent "vith the community, an asped t,hat the analyst engineer must

bear in mind when he sets about his work (A. González) .

4.- iHE ELEMENTS OF THE STUDY

The study of ancient constructions must include the following aspects (C.

Croci):

1. The role of history: history is the greatest laborat.ory on a real scale: its

interpretation can produce valuable elements for the diagnosis.

2. Direct observation: This obviously depends ou the experience of the <lllalyst. 1t illdudes an inductive process based on the capacity to accumulate t'xperien('('

and to lnake judge1l1ents. lt adds and compares the case being si lldif'rI \Vil h

398 STRUCTURAL ANALYS IS OF HISTORICAL CONSTRUCTIONS

otlter previous cases that are already known (which explains its inductive

nature).

3. Mathcmatical modcl: This can be a very powcrful, vcry useful and CVCIl

indispcllsable tool. The controversy concerning its use stems exclusively from

tbe wrong use by persons who do not have sufficient knowledge of the problem

that t,hey wish to solve. The 1I10del does not represent absolute reality, but

only all app roximation. However, the knowledge that can be gathered from

this approximation can be of very great utility. In any case, the model should

not be confused with reaüty; one should be aware of the hypotheses adopted

and be criticai with them, appraising their suitability.

4. Experimentation and inst rumentat ion. It shoulel be clearly stated that, in the

worst case, such activities can turn out to be useless as a consequence of

improper planning. This can occur, particularly, if a preliminary project of

experimental research has not been drawn up . However, if these activities are

accomplished with wisdom anel proper planning, they caIl proeluce very useful

results that provide a greater knowledge of the structure and its safety. Another problem stems from their cost, which in certain cases can be unjustifiably high

taking into account the real needs.

The study of au ancient construction should be based on the following premises:

(1) start from a constructional knowledge that is as complete anel perfect

as possible; (2) use sim pie analysis methods before using more sophisticated

methods; (3) do not neglect the importance of thc "clinical eye" - the

experience of the researcher (F. Jurado).

5.- ON THE USE OF NUMERICAL AN A LYSI S METHODS

5 .1 T h e p urp ose o f numerical modelling

Numerical methods are one more of the different elements that are used in

studies of historical constructions. Their great value, however, lies in their

capacity to quantify, which is an as pect of great importance. In fact, rather

than knowing what occurs to the structures, what we wish to do is to define

suitable interventions, and knowledge is a condition for this. From this point

of view, numerical models can be seen as a "numericallaboratory" in which it

is possible to simulate the interventions (E. Dilate).

In my own experience in the field of monumental restoration, I have never

decided a solution based only on the results of a structural analysis . There are

P. ROCA :md J. L. GONZÁLEZ I Thc Discussiolls 399

filany other factors (historical, construction , functional...) which most of the

t imes have a larger influence on the decision (F. Jurado).

The use of numerical models is unavoidable due to the high cost of making physical scale models. However, in order to use them it is necessary to establish

many hypotheses , towards which the analyst must maintain a criticai attitude (M. Mihailescu).

In fact, these sludies are based on lhe scientific method, which involves: (1) a preLiminary campaign of gat hering of datai (2) proposing all abstractioll, in the form of a model; and (3) testing the representativeness of the model with respect to reality through a new experiment. However, such a great number of variables

are involved , 50 many faclors bear an influence, there are so many unknowns, that in no case wiU the model be able to gather the whole complexity of the problem. Nevertheless, without disregarding the imporlance of the historical analysis, there is no doubt that numerical mo deIs are an imporlanl elemenl in the studies (M. Melero).

\Ve wish to define light inlerventions that are as respectful as possible to the

monument. Bul this must be dane on the basis of a fuU knowledge of lhe current state and lhe real needs of reinforcemenl, which normaUy requires quant ifying the phenomcna. However, il must be borne in mind thal lhe choice of an analysis method anel lhe process of preparation of a mode! involve from

lhe begin nillg a profound interpretation of the conslruction and its resistant mechanisms (P. Roca).

5.2 The interest and applicability of classical t heories

\Vhene\'er lhe characleristics and simplicily of the problem permit classical mcthods based on the equilibrium of thrusls to be used, these are preferable to

more sophisticated techniques of analysis (J. L. González).

The theory of thrusts, as it was formnJatprl hy C;o1l1omb, is applicable in lhe case of a sim pie or isolaled arch , but is difficult to use in the case of more complex

structures. In the case of a bultress (or a system of buttresses and f1ying

buttresses) there is a priori an infinity of solulions for lhe line of thrusts, and il is extremely difficult to determine the real solulioll. Because of this , attempting

to apply this theory to the case of complex structures is nol ver)' ralionaI. From this point of view, it is belter to apply the mechanics of the cont inuous soLid

since it simultaneously envisages equili brium and compatibility conditions (G.

~ I acchi ).

400 STRUCTURAL ANA LYSIS OF HISTORICAL CONSTRUCTIONS

It is not corred to attempt to solve with sim pie methods problems that actually

cannot be solved by them. Nor is it correct to ignore the poss ibilities of the new techniques of analysis and experiment ation. Let us consider , for example, the case of the Cathedral of Mexico presented by R. Meu: t he problem s dealt with

t here and simulated in the analysis are fundamentally ones of cornpatibility,

which demands the use of sophistica ted analysis (J. M. Izquierdo).

It is possible to distinguish between three possible objects of study, to which

differeot analysis methods correspond (J. M. lzquierdo):

(1) For a sim pIe safety study, t he use of methods based on the decomposition of stresses may be suffi cient.

(2) If t he study is of stability, these methods are insufficient, even if equiubrium is imposed secondarily,

(3) lf the study is of behavior , even simplc mode!s thí\t consider the equilibrium secondarily are insuffi cient since it is necessary to include the condition concerning compatibility of deformations.

In 90% of cases the problems to be studiccl involve cOllstructions under the effect of gravitational loads, and t herefore m ethods based ou direct equilibrium are sufficient (F. Jurado),

Any calculation method that i5 useful and proves to providc information 00 the authentic st ru ctural behavior of t he construction can be cOllsidered sa tisfactory. On the basis of t he available experience, it should be said that eJast ic calculation is reaUy a possible form of approxim ating the solut ion. However , experience

al so shows t hat , though useful in given sit uations, methods based on dired equilibriu m are in general insufficient ( A. Chiarugi ) .

In many cases, reality imposes an isostatic model based purely on the

equilibriulU (A. Giuffre ).

5.3 The validity of the mechanics of the continuous medium

Masonry is a very difficult material to mode!. In any case, a mode! that

does not have adcquate references wiU !lot be useful. The numerical model must bc drawn up taking as a reference the behavioral reaüty af the masonry.

It wiU have to be weU calibrated by expcrimentation. At t hc University of

Rome) 50phisticated models based on cri tc ria of homogenizat ion are being used ;

P. ROCA 3nd J. L. GONZÁLEZ I Thc Discussions 401

however I such models are still not applicable to the general analysis of large masonry structures ( A. Giuffre).

In any case, the numerical model must be chosen 50 as to produce good

results t hat are e10se to reality. For thi s, it is useful to observe masonry as an assembly of a wid e sample of individual blocks . Ali modelling must en .... isage the kinematics c f these bloch. It is thus necessary to takt illtu accuunt t hat the collapse of a masonry structure (for example, under t he achon of an earthquake)

cao be aceompanied or followed by large m ovements of it s bloeks (A. Giuffre).

On eonsidering this quest ion , it is necessary to consider the existenee of different types of masonry, t he differentiation of which is essent ial for analysis methods. These are:

1. Brick masonry, essentially not homogeneous and not isotropic.

2. Irregular masonry (conglomerate), whieh is present in Roman eonst ruct ions, medieval bridges and other const ructions such as the Tower of P isa. The models speci fi calIy formulated for briekwork masonry are fiot valid for rubble work. The models formulated for eouerete can produce good approximations in this case.

3. Dry joint works, in which the mechanies of the continllllm is certainly not applicable (G. Macchi).

When considcring existing constructions and monuments, the structural engineer should approach his projects on t he basis of two poss ible ob jectives:

1. The knowledge of their current situation. This is a typ ical " in verse" problem, or a problem of identifi cation: knowing t he answer, we wish to find the question. To solve it , we act through the procedure of diagnosis. It is neeessary fi rst

of a lI to have a virtual mode!. ThllS, the models should not only account for the equilibrium , but also for the compatibili ty of movements and for the

behavioral mechanics of the st ructure. It is a lso necessary to have a whole range of informat ion on the construction and , using this information , to improve the model by obtaining a progressive approximation to reality.

2. The knowledge of it s safety. This problem , which is essentially different to the previous one, is of t he "direct" type, that is to say, it is similar to the study of

a new cons truction. It is necessary to analyze the future behavior, that is to say, the evolution of the structure. This requires the use of very sophisticated

and accurate methods. But is it really necessary to es tablish the safety margin of the structure of a monument? ( A: Chiarugi).

402 STRUCTURAL ANALYSIS OF HISTORICAL CONSTRUCTIONS

The model used wiU have to be adapted to the resistaot mechanism of the

structure that we wish to analyze. \ I\fhen wc formulate a mechaoism we merely

1110del rea.lity. \iVhen t his reality is oot knowll, lleither do we koow how it should

be modelled . An analysis that is not baseei OIl a mode! adjusted to reality can

lead to inappropriatc interventions (for example, seeking lateral binding in the

example of the Antonine ColuIIln) (A. Giufre).

An elastic analysis cannot be acceptcd when the structure is not elastic. If the

problem is of a non-elastic type, the analysis method should also be non-e!astic.

For complex problems, complex rncthods are required, but l10t fictitious and

inappropriate methods (A. Giuffn!).

5.4 T h e value o f sop hist icated ll10 dels

For the moment, it is advisable to use models of linear elastic analysis to mode!

large masonry structures. As they deal with very large structures, non-linear

analysis models could produce impodant problems of convergence. In any case,

whatevcr the type of 1l10del used, it is fundamental to validate it by using it in

combination with experimentation (P. P . Rossi).

As more complex tools become available, there is a tendency to use them for all

types of projects, induding those t hat in fact cao be solved maouaUy. As a rulc,

it is necessary to adjust the scope of the t.ools that a re used to the needs of the

problem and to the means available. Particularly, I have seen very sophisticated

non-linear methods used in situations in which hardly any data \Vere available

(R. Astudillo).

Oue must not feel persuaded to introduze more variables than actually needed,

just because more and more powerful computers and numerical methods become

available. lf our model has 110t been calibratcd with respect to reality, we

should not be confident with the results obtained using it. Calibrating means

to reproduce strengthes, dcformatioIls and failures (F. J urado).

A further sophistication in the method of aoalysis must carry together a greater

refillcment 011 the solution. A larger study must have as a cOllscqllence a

minimun interventioIl, which mcans t hat t he usage of more sohisticated method s

should be dircctcd to elllarge our safcty, but not to cause a more heavy

intervention (F. Jurado).

The p roblems of strllctu ral analysis have reccntly undergolle a great evollltioll,

cspccially 011 account of the availability of the Method of Finite Elelllcnt.s.

P. ROCA and J. L. GONZÁLEZ I Thc Discussions 403

The great use that is eu rrently made of this mcthod was show n during the

Seminar. Howcver 1 this ap plieation must be observed critically. especially if il leads lo lhe pereeplion th80l its applic8otion is rclated to lhe possibi!ity of

applyi ng a strict scientific method. Thus: upon analyzing an aqueeluet under

lhe effect of l he gra.vilational ioads, the most suitable melhod seeOlS lo be thal of direcl equilibri um under lhe impased loads; on lhe other hallel, if we wish to study this aqueduet under the effect af the tempera.ture) sinee there appears to be a eompatibility problem, it is Ileccssary to work with the

method of finile e1ements. Apparently (fram a scientific paint of view) we should not use two differenl 1l10dels to study lhe same structure. However,

the result may be correet from the engineerillg point of vicw. In the analysis that. was presented , the elastic approach was the most important. Another approximation tha1 is adopted, but was not evaluated in the diseussion, is that

of small movements. This seeond hypothesis leads to mistakes of the arder of the 5%, which a mathematieian \ ... ·ould eonsider incompatible with seience. "Engineering science" is sOInething different to strict "science". Simple, weU­calibrated formulations mal' be suitable for reaching satisfactory enginccring solutions, thus making it unneeessary to use very sophist icated models. The use of models of a nou-linear type was also proposed. Will ihe engineer that uses them be able to lake "engineering" decisions with them? These methods are necessary, but it is also necessary to maintain a criticai attitude toward their use. The technique of finitc clcments is without doubt a powerful too1. But

science is somethillg clse. 1t is Ilecessary to redefine w1lat we understand by a "solution", since its goodness depends on the context: an unsatisfactory solution for structuralm echanics may be a good solution for engineering Illcehanics (F. Mola).

The use of sophisticated and precise methods would have a ver)' significant effect on lhe eost of the intervention, that is to say, the cost of an incorrect intervention would be avoided (A. R. Marí).

Ali interesting way of overcoming the limitations of a linear e1astic analysis can bc given by the use of a "non-tcnsion" model. The non-linear analysis based 011

a model of this type is not difficult but it could provi de a very precise resulto He would have liked to see examples of this type of analysis during the Seminar

(A. R. Mari).

5.5 The evaluation of the safety of ancient constl'uctions

lt is possible to obtain an idea about the safety of these structures using

experimentation anel numerical analysis in eombination. Beeause they make

•

404 STRUCTURAL ANALYSIS OF HISTORICAL CONSTRUCTIONS

it possible to control stress distributions and movements, experimentation and

monitoring are a fundamental tooI for controlling working conditions and the

maintenance a f the safcty of these structures (P. P. Rossi).

One must be extremely cautious about using the results of the analysis to

value the safety of an ancient construction. lt is advisable to combine various methods, calibrat ing tbem through comparison with other known cases, and to

control the behavior of the structure by monitoring it. In particular, in order

to assess the safety, it is preferable to use sim pie modcls directly based on the

equilibrium (R. Meli).

As is statcd in Section 6.2, the safety study would require an analysis of the

future behavior of the structure, that is to say, its evolution in time. It also

requires very sophisticated and accurate methods that would in particular be

capable of reproducing the collapse of the structure (A. Chiarugi) .

5.6 The training and experience of the analysts

The person directing the studies wiU require a great deal of experience. AIso ,

we must insist that the teehnieal staff must not be the victim of their "faith

in numbers" ar their faith in computers. The studies should be based on the

knowledge and experienee of the analysts (L. Ortega).

Seienee (ba.sed on rationality) should not be confused with mathematies a nd

numerical models. In fact, the objective is to use with the best benefit aU the

numerieal information, and this benefit depends on the reliability of the models

anel of the results produced. HO\\rever, evcn whcn the models do not represent

suitably the reali ty, usefu ll information can be adquired if the designer is able

to interpret them (G. Crocci) .

are far removed from qualitative reasoning and írom expenenee, therefore

offering little reliability (G . Croei).

The su bject Mechanical Surveying should be included in the training of

st ructural engineers (A. Chiarugi).

Until ten years ago the main tool for understanding monuments was experience

and qllalitative reasoning. Numerical methods are often of little use, but at

times they are ext remely IlsefuL It would have to be determined in each case

whether the results are better or \Vorse than the result s that can be obtained

through experience and qualitative reasoning (M. Mihailescu).

P. ROCA and J. L. GONZÁLEZ I Thc Discussiolls 405

The technician must use familiar techniques that he really knows how to use.

He should fiOt use the computer to petform calculations of a st ructure that he does fiOt know how to calculate by hand. He can thus make a. subsequent criticai analysis of the general results and of the hypothesis employed (J. M.

Izquierdo).

5.7 Relations hip between history and structural analysis

The studies must not be based purely 011 considerations of a historical type. Indeed , t he fad that the st ructure has remained stallding for hundred or

thousands of years does 110t meal1 that it wiU be safe in the present. We should recaU the cases of the Campanile of Venice, which coUapsed in 1902, 800 years after its cOl1struction, or of the Civic Tower of Pavia, whose recent coUapse - in 20 seconds after more than 800 years of life- occurred without any fissures having been previously detected. In this last case, nurnerical analysis rnade it possible to understand very clearly the reasons for its collapse.

Thus, it must be stated that historical permanency is no guarallt ce of safety on its OWI1. Though this of course depends on the type of construction (mauy existing const ruction s may be elose to coUapse), as a rule, allalysis can be collsidered as Ilecessary (G. Macchi ).

Thc historical ev idence must be used to calibrate the Illodel , and the model must be capable of rcproducing the historical evidence. The diagnosis consists in understanding what has occurred. If fi ssures are detected (as in Bruneleschi 's dome) it is necessary nrst of all to study their cause - to make a diagnosis­

using the best analytical procedures. It is necessary to individualize the mechanical history, which means modifying the model iteratively during its preparation) reproduci llg in some form the history of the construction) until the model corresponds to reality and predicts the observed damage. The mode!

wil! have to predict what ex.ists in reality. Thus, for exam ple, it was possiblc to ullderstand the principal fissure system of Brulleleschi 's dome by employing the

conditions of equilibrium and compatibility from a continuous medium mode!; when these nssures were introduced in the model, it predided the second family of nssures that e.x.isted. Thanks to aU this , a [ar better knowledge of this construction has been obtained (A. Chiarugi).

IdeaUy, analyses of an evolutionary type should be accomplished) that is to say, working with mcthods capable of reprodu cing the cons tructional history and

the history of repairs and restorations (A. R. . Marí).

406 STRUCTURAL ANALYSIS OF HISTORICAL CONSTRUCTIONS

5.8 Final comments ou numerical modelling

In relation to the preparation of large numerical models, we must separate

different situations Of differentiate betwecn different leveis of detail:

(3) General models: as a rule these are very useful for this type of study. There importance lies Hot 50 much in that they are bettcr than the hypothesis of linear

c1asticity, bui Lha! they provide a good understanding, and suitably account for ,

the state of continuity of the structure.

(b ) Local models: used in order to study a criticaI part of the structure with great refinement and detail, once the parts have been identified through t~e

previous general analysis. In these mo deis it makes sense to use more refined

and sophisticated modelling tcchniqucs.

(c) Models for dynamic studies: their use requires knowing a great number

of propertics that are not always availablc, or must be obtained by direct

measurement (R. Meti).

As a rule, it is advisable to eitber combine different types of methods that

consider leveis of different detail (the local or general levei [R. Melli]), or

correspond to differcnt theories or leveIs of sophistication in the analysis

(cla5sical methocls based on the equilibrium of thru5ts , calculation as a

continuous medium ... [J. L. González]).

Much is said about the cost of numerical models. Obviously, it is necessary

to aclapt the means to the magnitude of the prob!em and to the available

resources. However , it should be remembered t hat the cost of the preparation

and utilization of a numerical model is as a rule low wi thin the general process

of study in comparison with the cost of an experimcntation and monitoring

campaign (P. Roca).

First of ali, it is necessary to decide what one wishes to achieve through the numericaI study. In fact, tbe purpose of studying an al1cient structure is to

understand an existing reality, anel it therefore requires the use of methods

baseei on what are called second-order systems in information theory. It is not

a question of unclerstanding how one must design the structure so tha t it will be

stable, but of understanding what happens to the existing structure. The most

customary calculation methods (based OIl first order systems within infonnation

theory) may t herefore be totally unsuitable.

Furthermore, since second-order systems are oftcn very unstable , which can

P. ROCA :md J. L. GONZALEZ I Thc lJi ~(" lI ~sions .07

lead to very largc variations in the results, it is necessary to emphasize the !leed to work with methods that are highly controllable and wel! adapted to the questions considered; it is necessary to establish a strong contrai over each calculation phase. (J. M. lzquierdo).

A sensitivity analysis would in many cases compcnsate for a lack of knowledgc cf thc lIlechau..i cal jJl"UjJcrtic:. <l.IIJ strength uf the llHl.terials (A. R. r-.'Iarí).

6. F I N AL C ONSID ERAT I ON

There is obviously a consensus on the main problcms. The conclusions of these discussions should serve as a guide to those who wish to cnter the world af studies of ancient cons1ructions_ The conclusions lI1ust convey the complexity af the tapics discussed (J. M. Ballester).