Model Study of Structures in Portugal

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Model Study of Structures in Portugal

Rocha, M.

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Structural model study is increasingly recognized not only as a powerful design aid where analytical methods may be inadequate, but also as an aid in developing the

theory of complicated structures. Interest has been

shown, both within the Division and elsewhere, in the

application of model studies to specific research problems, but there was not a great deal of information available in English.

Many of the major engineering works in Portugal are designed experimentally by the use of models at the National Civil Engineering Laboratory, of which Manuel

Rocha is Director. Mr.-Rocha has provided a valuable

discussion of the limits and capabilities of model study techniques in his paper presented at the "Congress of Models in Technology" at Venice in 1955.

The Division of Building Research would like to thank Mr. D.A. Sinclair of the Translations Section, National Research Council Library, for translating this paper, which it is hoped will assist conSiderably in the utilization of model study techniques in research.

Ottawa,

August 1961.

N.B. Hutcheon,

Technical Translation 970

Title: Model study of structures in Portugal

(0 estudo de estruturas sobre mode10 em Portugal)

Author: M. Rocha

Reference: Pub. No.84, Laboratorio Naciona1 de Engenharia Civil,

Lisbon, 1956. 20p.

1. _Introduction

In his continuous struggle to improve living conditions, man is continually confronted with the difficulty of predicting the

behaviour that will be exhibited by the solutions he has conceived

for his problems. This is the result either of ignorance or

insufficient knowledge of the laws which govern this behaviour, or

inadequate acqua'lntiance with the legacy of accumulated experience.

With the rapid technical progress being made at the present time, demanding clarification of problems from the most varied sources, and with the growing preoccupation with economics associated with all executions, the inadequacy of our means of prediction are being felt ever more acutely.

Besides having recourse to the laws which govern the phenomena and to the accumulated empirical results, the behaviour of material systems can also be predicted by another method that shows great promise, namely the use of models.

However, whereas a theory enables us by its very nature to

predict the behaviour of all the phenomena falling within its purview or range of validity, models only permit us to predict the behaviour

of isolated cases. In addition to this, model studies require

material means that are sometimes very considerable.

As far as the prediction of the behaviour of structures is concerned**, our experience in the observation of our own work and in our model studies enables us to state that the theories at our disposal at the present time are very often

ｩｮ｡ｾ･ｱｵ｡ｴ･ＨｬＩＮ

*

**

Paper presented at the request of the Accademia Nazionale dei

Lincei at the Conference on Models in Engineering. Venice,

October 1955.

The term "structure" is defined here as that part of a con-struction having a strength function, regardless of the nature of the materials involved.

This inadequacy is due primarily to the difficulty, encountered, in the fields of strength of materials and soil mechanics, in dealing with the complex forms which structures so often take and with the real properties of the building materials, as a consequence of which these studies are forced to proceed on the basis of oversimplified hypotheses.

This situation, together with the considerable progress realized in recent years in the techniques of studying structures by model, make necessary the wide use of the experimental method of design.

In our country it is accepted that the design of a structure may be made from a model study without requiring an elaborate theoretical

justification in order to confirm its results& Provided the models

can faithfully reproduce the real behaviour of the structures it is obvious that they constitute a fertile research instrument for the

improvement and development of methods of calculation. It should be

noted, however, that the making of models makes us conscious of the great complexity of behaviour of structures and thereby often robs us of the courage to establish working hypotheses with the necessary

simplicity for analytical treatment. As has been found in the

development of various sciences, it is often inconvenient for the

generalization of knowLedge to have excessively detailed information:

Clearly, the essential factor in diminishing the effort to develop methods of calculation is the fact that today we have techniques enabling us to regard experimental design as a routine method of designing structures.

In order to undertake the experimental design of structures it is necessary to have specially equipped laboratories set up so as to produce results that inspire complete confidence within the time

limits generally allowed for the designing of projects. It is only

possible to maintain such laboratories, both for reasons involving the training of personnel and for economic reasons, if a continuous

activity is assured for them. Our own experience and foreign

obser-vations show that if one attempts to develop the techniques and train the personnel just when the necessity of undertaking a model study arises, this study cannot be carried out under satisfactory conditions.

Experimental design raises the legal problem of the quality to. be demanded of the person performing it, especially as, unlike the analytical methods, it is generally not economical and in many cases

impossible to carry out a verification of the results obtained. It

is recognized in our country that experimental design must be per-formed or confirmed by an official laboratory wherever the aspects referred to the model are important from the standpoint of structural safety.

2. Similarity Conditions

The conditions necessary for mechanical similarity in the case

of prototypes in elastic deformation are well known. In the majority

of cases it is sufficient to build the models with elastic materials possessing moduli of elasticity to a given scale and to apply to them stresses that are homologous also to a scale that can be chosen

arbitrarily. In certain three-dimensional equilibria, e.g. arched

dams(2), we have however recognized the necessity of respecting the condition of equality of the Poisson ratios of the homologous

materials of the model and of the prototype.

In recent years we have been concerned with the similarity conditions that must be satisfied by the models in cases where the prototypes are subjected to inelastic deformations, regardless of the nature of the materials (steel, concrete, soils, rocks, etc.)(1,3). We shall summarize the results very briefly.

Let Ep be the elongation undergone by a parallelepiped of the prototype material when subjected to a given tensile stress t p• The homologous material of the model must be such that if a

parallele-piped is subjected to homologous tensile stresses t

=

1 t it will

I I I m a p

undergo elongations Em

=

ｾ e_{p '} where

a

and ｾ are constants. This

condition must hold for any state of stress t_p• Obviously, however,

it is sufficient to determine whether it is satlsfied for stress states representative of those that will develop in the equilibrium to be studied.

In many cases, therefore, it will be sufficient to investigate

the eXistence of the scales

ｾ

and

ｾ

for simple tensile or compression

stresses. Then, if the stress-strain diagram of the prototype

material is that indicated in Fig. 1, the model material must have a diagram of the type that may be obtained from the above by

multi-1

1

plying the ordinates thereof by - and the abscissas by 3 •

If the scales

ｾ

and

ｾ

eXistafor the materials of

ｴｾ･

model,

then when the model is subjected to homologous forces of scale value

ｾＬ

the tensile stresses, elongations and deflections developed in

1 1 1 1

the mOdel will be on the scales, respectively,

a'

ｾ and ａｾＧ where A

if the geometric scale of the model ..

When the existence of deformations that are a function of the time must be taken into account the model material must satisfy the condition enunciated below at points on a certain time scale ..

In the case of large deformations the Similarity can only be

maintained if the scale of elong8tions is equal to unity, ｾ = 1.

In the problems of soil equilibrium where it is necessary to take into account the percolation forces resulting from the movement

of the liquid phase thrcugh the solid phase, the relation 1 between

IJ.

the permeabilities at homologous pointG on the model and prototype

1 ｡ｾ 1

must satisfy the condit.ton -

= - - ,

where - is the time scale.

ｾ ａＲｾ ｾ

In the equilibrium of masses the consideration of the speCific

weight is often indispensable. The scale of tensile stresses will

I I I 1

then have to assume the value a

=

ｾＬ p' where

p

is the scale of

specific weights wrence we get a value for the scale of permeability. It is also necessary to satisfy the conditions of equality of

porosity at homologous points.

In the work referred to ｾｮ reference 3 the Similarity conditions

are presented for the special case of equilibrium of masses of more

practical importance. It should be emphasized that we now know the

general laws of similarity which models must satisfy for the study of structures regardless of the nature of the materials or their state of deformation.

Also studied are the conditions of similarity where it is necessary to take into account the distribution of the material

properties (4). These conditions are intended to define the elastic

behaviour of a prototype from a statistical knowledge of the

behaviour of models made of the same material as the prototype. The

conditions corresponding to the various kinds of destruction of a structure are established, i.e. due to fragility, ductility and by deformation.

3. Model Study Techniques

We shall now recount very briefly the most typical techniques and directions of study practised by us in the experimental

dimen-(1 '1)

sioning of structures ' •

(a) Scales

To ensure rapidity and economy in experimental design the prime importance of keeping the scale of the models as small as possible

is recognized. In order to determine the minimum scale to be adopted

the following factors must be taken into account: (1) The smaller

sections to be reproduced in the model must not be so small that they

are difficult to construct and to observe. It should be noted that

in general it is possible to simplify the shapes of a prototype

either by eliminating details or by SUbstituting others with SUitable

deformability; (2) The determination of the exact means by which the system of applying the loads or other stresses can be realized; (3) The accuracy, the dimensions and the manner of placing the

measuring apparatus, especially gauge lengths of the strain gauges in view of the expected deformation gradients.

(b) Materials

In experimental design the difficulties which arise most fre-quently at the present time relate to the materials to be used in

the construction of the models. Before the appearance of electric

strain gauges the greatest difficulties were experienced in measuring the deformations.

The conditions that must be satisfied by the materials are as follows:

(I) They must have tte mechanical properties required for

mechanical similarity, which must not be appreciably affected by the ambient temperature and humidity variations.

(2) They must be easy to work and jOin.

(3) They must have the necessary deformability so that under the action of stresses of easily attainable intensity the required precision in the measurement of deflections and deformations can be attained.

(4) They must permit easy application of the necessary measur-ing apparatus.

(5) They must be inexpensive.

When the prototype is considered to be in elastic equilibrium the materials normally used in constructing the models are the

Perspex plastics (Fig. 2) and Plexiglas, made of ｾ･ｴｨｹｬ

polymeth-acrylate, or celluloid or plaster of Paris (Fig. 3) and mixtures of

plaster of Paris with diatomite (Fig. 4). When, by virtue of the

small intensity of stresses that can be applied to the models

recourse is made to materials of very low elasticity, the National Civil Engineering Laboratory uses alkathene (Fig. 5) a commercial plastic.

Where three-dimensional elastic equilibria are involved the plastics generally show the disadvantage of having a Poisson's ratio considerably above the current construction materials, especially

that of concrete. In such cases we use plaster of Paris and mixtures

of plaster of Paris and diatomite. These materials have the great

advantage of being very easily moulded and are inexpensive, but they

have poor tensile strength. This latter disadvantage is particularly

serious in cases where cracking of the model may occur without becoming visible, while nevertheless producing a considerable redistribution of the state of stress.

It should be noted that all the materials mentioned have a

marked tendency to flow. However, since they have a modulus of

into consideration the value of the modulus corresponding to the duration of the load applied to the model (Fig. 6).

When it is necessary to make a model study of the behaviour of a prototype in which complex mechanical properties must be taken

into account, e.g. non-linear relationships between stresses and strains, non-reversible strains and flow, we first consider the

possibility of constructing the model with the same materials as the

prototype. In the study of metallic structures (Fig. 7) and certain

soil mechanics problems, we proceed in this manner(5) (Fig. 8).

However, it is not often possible to use the prototype materials

in the construction of the models. In the case of reinforced

con-crete structures, for example, the difficulty often arises from the

necessity of having excessively large dimensions. In metallic

structures and reinforced concretes we have sometimes had difficulty in finding commercial sources of profiles, plates and rods with the right dimensions and the same properties as the steel used in the

construction. For this reason we were obliged to manufacture

pro-files from laminated plates built up to the right ｴｨｩ｣ｙｾ･ｳｳ for the

construction of high tension tower models (Fig. 9).

As is evident from the previous section, however, it is also possible to use models constructed of different materials from those

of the prototype. For concrete structures, for example, it is easy

to obtain cements which satisfy the required conditions (Fig. 10). In order to verify the homogeneity of the models, especially those moulded from plaster of Paris, cement or plastics, it is very useful to measure the propagation velocity of ultrasonic waves in various regions(6).

(c) Application of the load

In applying stresses to the models we follow the usual techniques.

In studying the elastic behaviour of models of dams the

hydro-static pressure is generally applied with mercury. With a view to

reducing the drying times of the plaster of Paris models we have constructed some models with very reduced dimensions which require a

system of jacks for reproducing the hydrostatic pressure. However because of the time and cost necessary for the construction of this system we have preferred to use mercury.

For studying the effect of the specific weight we have used alkathene models in which the state of stress resulting from the

inversion of the model was determined. The accuracy of the results

was not entirely satisfactory.

(d) Measurement of dislocations and strains

Measurements of the deflection of models were generally carried

out with the aid of 1/100 mm def1ectometers. For smaller

deflec-tions we have sometimes used 1/1000 mm def1ectometers. These

apparatuses require special care in mounting and those requiring

considerable forces for their operation have to be rejected. We

have obtained satisfactory results with Johansson def1ectometers. Although we have used mechanica1(7) and acoustical extensometers, at the present time in the National Civil Engineering Laboratory we use only electric strain gauges(8), which have numerous advantages: small dimensions and weight, easy assembly, remote reading, gauge length occupying only a few mi11imetres, perfectly satisfactory

measuring accuracy. The only difficulties we have encountered were

in measurements over long periods of time. When it is necessary to

make this type of observation we prefer to use vibrating wire strain gauges(S).

Electric strain gauges can also be used for measuring

deforma-tions in the interior of moulded models (Fig. 11). The development

of electric strain gauges greatly enlarges the possibilities of experimental dimensioning of structures.

In reference 4 mechanical extensometers are described together with apparatuses for measuring curvatures and stress angles, which have been used extensively by the author.

(e) Use of brittle varnishes

In order to ､･ｴ･ｲｾｩｮ･ the sta.te of stress in a mOdel we

The test is very simple and has the great virtue of furnishing a general panorama of the state of stress and of helping to reduce the number of observations with strain gauges, which are slow and costly,

by revealing the direction of the main stresses. Fig. 7 shows the

equipment which we employed in applying the stress-coat varnishes. The isostatics that have been developed are visible on the model of the volute.

In studying models of dams where the hydrostatic pressure is exerted by means of mercury the state of stress varies as the level of the mercury rises, making it necessary to evolve a special

teChnique(lO). In order to determine the isostatics of the

down-stream face corresponding to a certain level the model is first

painted With a varnish that does not cracl{ until the mercury attains this level and then a jet of dry ice is directed to it causing the

cracking of the varnish (Fig. 12). In order to obtain another

family of isostatics from the downstream face and one of the families of the upstream face the model is subjected to the load after being painted With the varnish but before evaporation of the solvent;

after drying (under load) the load is removed and the jet of dry ice is applied to both faces.

(f) Photoelastic method

In order to study the two-dimensional states of stress we employ the photoelastic method(ll) (Fig. 13).

Compared With the general method of determining stresses With extensometers, the photoelastic method has the advantage of being quicker and more economical, and at the same time in general gives

greater accuracy. In stuaying the concentration of high stresses

the photoelastic method has been found very convenient, whereas the use of extenscmeters in such a case would require a model of large

dimensions. The photoelastic method has the advantage of enabling

us to make observations over the entire surface, and of directly indicating the regions of higher stress.

Some studies have been made on the possibility of employing photoelasticity in the investigation of three-dimensional

equi1ibria(12). We believe that despite the progress made in recent

years this is of no practical value in the study of structures. In

the very rare cases where it is necessary to determine stresses at points in the interior we have deemed it preferable to use electric strain gauges (Section d).

(g) Models of ｳｾｲｵ｣ｴｵｲ･ｳ composed of rods

For brevity we shall refer to structures consisting of rods (rectilinear or curvilinear) as linear structures.

The remarkable progress that has been made in the theory of hyperstatic linear structures in recent years, especially in

connec-tion with the development of rapid calculaconnec-tion methods, has greatly reduced the importance of model studies of these structures.

Experimental deSign is required only in cases of hyperstatic linear structures of great complexity, and most often when it is necessary

to take into account the three-dimensional action. ｾｾ･ｮ it is

desired to know the behaviour beyond the elastic phase the experi-mental study is generally the only possible way.

Models of linear structure are normally studied by applying the

techniques referred to in the previous sections. In particular, the

bending moments and normal and transverse forces are determined by measuring the strains with electric strain gauges (Fig. 2).

Hyperstatic structures are also studied by direct measurement of the hyperstatic values themselves (forces or moments)(13), according to the techniques described by the author in reference 4.

In studying linear, two-dimensional and elastic structures it is advisable to proceed with the experimental determination of the influence lines on the basis of Maxwell-Betti's theorem of

reciProcity(14,15). Obtaining the influence lines by this means has

the advantage of aVOiding the application of forces to the model, which is particularly important in the case of structures having many parts.

Our experience shows that in complex studies, which are those that require experimental investigation, the determination of the

influence lines corresponding to internal hyperstatics is often

difficult. Often, in fact, the rigidity of the model will not

per-mit imposition of a sufficiently large strain on the edges of a section to be studied, and moreover the strain cannot be imposed at the edges themselves, but only at a certain distance from them,

which may be excessive. Sometimes there is insufficient space for

mounting the strain apparatus unless the dimensions of the model are large.

In determining the influence lines we impose the deflections on the models by means of Beggs deformeter, and the strains at the

various points on the model are measured by the photographic

method(16). In this method the model is photographed on the same

plate before and after straining. The strains can be measured with

the microscope or on the screen on which the plate is projected.

The photographic method gives us a record of the test results and

the conditions under which they are realized.

For direct determination of the bending moments we use the so-called "moment lndicator,,(lS), which is of little interesto

4. Typical Results

In order to give some idea of the variety of problems which have been attacked and the sort of results obtained we shall give a brief account of some of the studies that have been undertaken.

(a) ｾ

In designing concrete arched dams it has been found that the results obtained are rather interesting both for the information provided on the conditions of furnishing their structures and for

the very considerably economies realized(Z). In Portugal the final

deSign of arched dams has been carried out experimentally, submit-ting to verification the form or forms chosen in the predesign stage by applying the known method of calculation by the method of

independent arches, and often also the trial-load method.

The experience acqUired in the numerous investigations under-taken, and comparison of the results obtained with those furnished

by the calculation method enable us to state that only where an

arched dam is very simple can experimental dimensioning be dispensed

with. Actually, if the dam is decidedly asymmetrical, or has an

irregular foundation profile, or possesses special features such as clefts, gravity abutments, large discharge openings or if the

foundations show marked heterogeneity, etc., even the most

sophisti-cated analytical dimensioning methods are unsatisfactory. Even when

conditions are simple, analytical calculation by a reliable method such as the trial load is only qUicker and more economical if one has a design office already experienced in its application.

Furthermore, it is often possible to investigate the shapes resulting from successive modifications on one and the same model, thus

incurring only a small amount of extra work. In Fig. 15, by way of

example, we show the stresses determined by an experimental study of the Castelo do Bode dam, which was carried out on models of very

small scale (1 : 500)(2). In view of the gravity abutment with its

relevant role in the safety of the structure, and because of the wide discharge openings and the heterogeneity of the foundations,

only experimental design could be considered reliable. In Fig. 16

are shown the values of the modulus of elasticity for the prototype, and the corresponding ones adopted in the models; note the low value of the modulus of elasticity of the foundation of the gravity

abutment. Despite the small dimensions of the models a complete

determination of the state of stress in the interior and in the vicinity of the discharge openings was carried out by the use of

electrical extensometers of 3 mm base. The effect of the intrinsic

weight and the hydrostatic pressure was considered and the results obtained were compared with those furnished by a photoelastic

investigation carried out on a model of variable thickness(12). At

the Castelo do Bode dam the flood crest is discharged through two openings blocked by two floodgates each of which has to withstand a maximum stress of about 4,000 tons, which must be supported by the

gUide walls of the discharge opening. The reinforcements for the

In ｾｨ･ experimental dimensioning of the Venda Nova dam a special study was made of the unusual foundation surface and also of the

functioning of a joint at the base of the dam on the upstream side, which is intende1 to prevent the development of tensile stresses

which were revealed in the first test. The concentration of the

stresses in the vicinity of the joint was investigated in

two-dimensional models by the photcelastic method. As in the case of the

Castelo do Bode dam, the dimensioning of the reinforcements in the vicinity of the discharge opening was carried out from an experi-mental determination of the stresses.

Similar investigations have been made in relation to the

following dams: Santa LUZia(9), do Cabril, de Salamonde, do Covao

do Meio, da Caniyada, da Bou9a and for the cofferdam at Castelo do

BOde(17). We may also mention the study of a buttress dam of great

height(2) (Fig. 5).

It is already possible to compare the predictions of some of our experimental investigations with the results of observations of

actual structures(9,17). These comparisons confirm Our preference

for experimental design. The systematic observation of all the

arched dams studied by models is now under way and we hope in the near future to have some very interesting conclusions to report(18).

(b) ｾｧ･ｳ and ｢ｵｩｬ､ｬｮｾｳ

Many of the bridges constructed in the country in recent years

have been the object of model studies(4). These studies have

enables us to clarify many problems, particularly those which arose when it is necessary to consider three-dimensional functioning.

Among the problems studied we may cite the following:

Effective forces acting outside the plane of the structure, such as the wind and the effect of curvature, the contribution of the bridge floor to the strength of arched bridges, and the effect of loads concentrated en the floors (Fig. 17).

As far as bUildings are concerned only a very few experimental

studies have been made. This is due to the fact that considerable

also because no large bUildings have been built. We may mention the

study of a theatre bUilding (Fig. 14). Because of the great

complexity of the structure, a satisfactory calculation was

impossible. We may also mention briefly an investigation of a

20-storey bUilding for Brazil (Fig.

2).

The wind action and the

settle-ment of the foundations were studied.

(c) Miscellaneous

A number of different types of metal towers for high tension

lines were investigated with models (Fig.

9).

Their behaviour was

determined in relation to wind action and intrinsic weight, assuming

both intact conductor cables and broken ones. The study, which led

to considerable economies, revealed in particular the defects of the calculation when the stresses determine the torsion of towers.

Among the metallic constructions studied we may refer to the complete determination of the state of stress at the branchings of forked conduits (Fig. 18) and in the spiral of a Francis turbine (Fig. 7).

Fig. 20 shows the model of the monument at Cristo-Rei, 110 m

in height now under construction near Lisbon. The wind effect was

studied in a wind tunnel; the effects of earth tremors and founda-tion settlement were investigated and much important informafounda-tion was obtained.

Fig. 21 shows a model of a cupola of 90 m span. The model was

studied for the effect of intrinsic wei ght , concentrated loads and

also of settlements of the supports.

We may also refer to the investigation of the effects of foundation soil deformability on the behaviour of an underground

conduit (Fig. 13). This effect was found to be very important.

Finally we may mention model studies of soil mechanics problems. We have studied the foundations of large metal fuel tanks (Fig. 8). The conditions of foundation rupture have been observed and the effect of a ring encircling the foundation has been investigated.

Models have also been used to determine the settlements of wall footings resting on beds of varying deformability.

5. Conclusions

We have briefly considered the activity that has developed in our country in the field of experimental dimensioning of structures.

The experience acquired clearly shows that the choice of shapes and determination of dimensions of any structure can as a rule be carried out on the basis of observation on models, even when it is necessary to consider inelastic behaviour.

It may indeed be stated that even a very small-scale model is a more faithful representation of the prototype than the plans currently adopted in analytical calculations, whether from the

standpoint of shapes, materials or stresses. This however, does not

detract from the analytical methods, which have the great advantage, except in very special cases, of being qUicker and more economical and not requiring large amounts of material.

Concerning the respective scopes of application of the experi-mental and analytical methods, it may be stated that the former must be employed in designing large structures unless entirely reliable

analytical methods are available, which is rarely the case. In the

case of structures of medium and small size the analytical methods are generally more appropriate in view of their economy and rapidity_ However, where large structures are concerned the analytical methOds, even the cruder ones, can render valuable service in the predesign stage, where a summary decision must be made between various possible solutions.

The analytical and experimental methods should not be considered mutually exclusive, as is the tendency from time to time, but should be rather thought of as tools to be employed judiciously for the the safe and economical designing of structures.

The cost of the experimental designing of a structure varies greatly depending on the problems that have to be solved and the

laboratory preparation required. To give some idea of cost it may

be mentioned that in the National Civil Engineering Laboratory the real costs vary, for most of the studies involved, between 20,000

of large structures. 1 and 4 months.

The times required for testing vary between

References

(I) Rocha M. - «Dime nsionnc rne nt experimental des constructionss , Paris, Ann. Inst. Techn. Batim. Trav. Puh., N." 2::15, Fev. 1952.

(2) Rocha, M.; Serafim,J.L.-<Analysis of Concrete Dams by Model Tcsts », Comun. N." 36, 5.". Con g., Com. Int. Grandes Barragens, Paris, 1955.

(3) Rocha, M. - «Conditions de similitude dans I'etude sur modcles de problerncs de rnecanique du sol>, Paris, Ann. Inst. Tcchn, Batim. Trav. Publ., N,? 86, Fev. 1955.

(4) Borges,J.1".-«0 dimensionamento de estruturas», Pub. N.· 54, Lab. Nac. Eng. Civil, Lisboa, 1954. (5) Cardoso, E. - <Alguns rnetodos de calculo

expe-rimental e sua aplicacao ao estudo de pontes», Lisboa, Oficinas Graficas A fonso Ramps & Moita, 1950 .

(6) Rocha, M.; Folque, j. - < Quelques resultats

d'observations de tassements sur les constructions

et sur modeles», Paris, Ann. Inst. Te chn, Batim.

Trav.,Pub., N.·86, Fev. 1955.

(7) Borges,J.F. - <A utilizacao dos ultrasons para para 0 estudo das propriedades dos mate riais»

Lisbaa,Tecnica N."239, Fev. 1954.

(8) Lima, J.A.-<Medic;ao de deforrnacfies com exten-s6metros mecanicos. A pl icacoes no laborat6rio e nas obras», Pub. N.· 19, Lab. Na e. Eng. Civil, Lisboa, 1951•

(9) Fialho, J.F. L. - <Extens6metros electricos de resistencia», Lisboa, Tecnica N." 239, Fev. 1954. (10) Rocha, M.; Serafim,J.L. - «Model tests of Santa

Luzia Dam», Com un. N.· 5, 3." Congr.,Com. Int. Grandes Barragens, Stockho 1m 1948.

(II) Serafim,J.L. - «Deterrninacao de t ensoes com vernizes frageis», Lisboa, Tecnica N." 231, Abril, 1953·

(12) Rocha, M.; Borges.J.F. - cPhotoelasticity Applied to Structural Design», Pub\. Prelim. 3: Co ngr., Ass. Int. Pontes Estruturas, Cambridge, 1952. (13) Rocha, M. - cA fotoelasticidade nos equillbrios

elastico s de revolucao s , Lisboa, Te cnica N." II5, Dez. 1940.

(14) Cardoso, E. - .Um metodo para 0 estudo experi-mental dos sistemas hipe restaticos», Porto, Rev.

Fac, Eng., Univ. Porto, Vol. VI, N: 4, Ag. 1940. (IS) Araujo, F. C. - «0 estudo e xp er im enta l das linhas

de influencia das construcoes hipcrestaticas pla-nas», Porto, Rev. Fa c. Eng., Univ. Porto, Vol. VI,

N."I, Fev, 1940.

(16) Rocha, M. - «Estudo de estruturas hiperestaticas pelos teoremas de Castiglia no e pe lo meto do de

Beggs", Lisboa, Tecnica N: 142, Vez. 1943. (17) Rocha, M.; Borges,J.F. - .Photografic Method

for Model Analysis of Structures», Cambridge, Mass., Proc. Exp. Stress Anal., Vol. 8, N.· 2,1951. (18) Reis, E. A. H. - .0 medidor de momentos e a sua aplicacao a modelos de estruturas a duas dimcn-soes., Pub. N." 2, Lab. Nac. Eng. Civil, Lisboa, 1944. (19) Rocha, M.; Serafim, J.L.; Silveira, A. F.; Neto, J.M. R. - «Model Tests, Analytical Computation and Observation of an Arch Dam», New York, N. Y., Proc. Amer. Soc. Civ. Eng., Sep. 696, Vol. 81, Maio 1955.

(20) Rocha, M.; Serafim, J.L.; Silveira, A. F.; Rodri-gues, O. V. - «The observation or the Behaviour of the Portuguese ConcreteDarns»,CoIIIlin. N." 33, 5.· Congr., Com. lnt. Grandes Barragens, Paris 1955.

t 1 If Ｍ ｾ , -I I I I I I :f l-1 0 ( I I I I I I Fig. 1 I I I Iｾ --1 0 ( I

Fig. 2

Perspex model in a scale of 1 : 50 of the reinforced

concrete skeleton of a 20-storey bUilding of circular

plan. The model is rotated through 90° in order

to

determine the effect of the wind, which is reproduced by means of weights

Fig. 3

Plaster of Paris model of a multiple-arch bridge (reproduced from Publication NO.5)

Fig. 4

Plaster of Paris and diatomite model in the scale of I : 200 of the Bouce dam, an arched dam 65 m in height

Fig. 5

An "a1kathene" model of a dam buttress 123 m in height. Mounted so that the effect of intrinsic weight can be

3

700 aoo Lei">

Fig. 6

Flow area of "alakthene" at room temperature. The straight lines

from the pOints of intersection of the surface with the normals to the time axis show the existence of a modulus of

elasticity which is a function of the time

Fig. 7

Determination of the isostatics in the model of a Francis turbine spiral by the brittle varnish method

Deflectometers .Rubbe r gasket Annular rubber cushion

Compressed air connection

Prototype sand

ＱＱｾｩｩ［ｩｩｾｩｬ［ｦｩｾｩｬｴ

Concrete caisson

Prototype clay

Y.a..I'"

ｾ __ｾｾ __ｾｄｲ｡ｩｮ pipes

Fig. 8

Transverse section of a model for studying the foundations of fuel storage tanks

Fig. 9

Steel model in the scale of 1 : 6, of a tower 33 m high for high-tension electric lines

Fig. 10

Reinforced plaster model in the scale of 1 : 50 of a dam discharge gate

guide wall. Tested up to rupture

under the action of the floodgate support reactions

Fig. 11

Electric strain gauge in the interior

of a plastic prism. In the

com-ression test the readings of the strain gauge were in agreement

with those relating to the strain gauge on the surface

Fig. 12

Isostatics of the downstream face of a plastic model in the scale of 1 : 200 of the Salamonde dam, 70 m high

Fig. 13

Photoelastic test of a model of the transverse section of an aquaduct

Fig. 14

Photograph obtained in the study of a linear structure by the photographic method

Downstream wall -16 :;'-1ｾｂＧＢ -37 100 • - "'-8 Ｌｾ 80 " ":' CD C)I: ＱｾＷ :.. 60 ｾＹ -B 40 20 -16

..

-

-10 -13 -29 • ｾ ... ·5 ., ｾ ! ｾ 5 • Ｍｾｓ ｾ <, ｾ -15 ｾ »s Upstream wall Q) n ｾ (Q s:: ｑＩｾ ｾｳｯ Compression 120-100 BO 60 40 20 '< Stresses due to ｾＮｳ ＼ｾ .,,,> ｾｴｾｨｹ､ｲｯｳｴ｡ｴｩ｣ pressure ｾｨｹ､ｲｯｳｴ｡ｴｩ｣ pressure Fig. 15 ｾＧＲ + weight

...

'""-8

...

...

_-8

］ｦ［ﾷＵｾＰＰＰｫＹ｣ｩｊ ___

=-e'"

a 5,000 kg,cift2

:::

" /

ｾ

ｅｾ =110.000 kg｣ｾＲ :,// fill" 10,000kgcrn2 . / / // / / / / / / / / Fig. 16

Moduli of elasticity of the Castelo do Bode dam and its foundation and the corresponding ones

adopted in the model

Fig. 17

Plaster of Paris model of a pavestone bridge supported so as to receive oblique reactions

Fig. 18

Plaster of Paris model of a reinforced concrete bridge. The

effect of concentrated loads on the bridge floor was determined

Fig. 19

Investigation of a metallic branch conduit. Note the

Fig. 20

Determination of the vibration char-acteristics of the model of a rein-forced concrete monument 110 m high

Fig. 21

Study of the effect of intrinsic weights of the cupola of the

·Palacio dos Desportos" of Porto