Journal of Wind Engineering and Industrial Aerodynamics, 4 i -44 (1992) 2089-2100 Elsevier

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A 60 year old, 100 m high steel tower: limit states under wind actions

G. Ballio a, F. Maberini b and G. Solari c

aDepartment of Structural Engineering, Polytechnic of Milan, Piazza L. da Vinci 32, 20133 Milan, Italy

blnstitute of Science of Constructions, University of Genoa, Via Montallegro I, 16145 Genoa, Italy

CDepartment of Structures, University of Calabria, 87036 Arcavacata di Rende, Cosenza, Italy

Abstract The present paper deals with the actions and effects of wind on the Park

Tower of Milan , a i00 m high steel tower built in 1933 on the occasion of the Fifth Triennal Exhibition of Decorative Arts. It provides a critical comparative picture of the assumptions and forecasts made by the designers of that epoch, the estimates furnished by present national standards and advanced dynamic analyses, the first results of full-scale experiments.

1. INTRODUCTION

Slnce Prince Albert, husband of Queen Victoria, had in 1850 the idea of transforming National Exhibitions into international ones, these manifestations followed one after the other with increasing frequency in the world's most important cities (London 1851, Paris 1855, London 1862, Paris 1867, Moscow 1872, Wien 1873, Philadelphia 1876, Paris 1878 and 1889, Chicago 1893, Antwerp 1894, Budapest 1896, Brussels 1897, Paris 1900,...). Three great exhibitions were organized in Milan: the National Exhibition of 1881, in the Public Gardens and the Park, the Joined Exhibitions of 1894, the International Exhibition of 1906, which marked the end of the great exhibitions meant as moments in which to celebrate economic and technological progress.

After the First World War there arose the tendency to pass over the ephemeral, siezing the chances for studying and researching new artistic, architectural, technological and engineering solutions, and at Monza, from 1923 to 1930, in Villa Reale and the Park, there was series of Triennal Exhibitions of Decorative Art. The Fifth Triennal Exhibition, held in 1933, was particularly important because, on one hand, it returned to its original site in the Park of Milan, and, on the other, accepted for the first time architecture into the arts exhibited; in this context there was a collection of the works of the best-kuown international architects and of the youngest and most promising of the Italian school. Of all works exhibited, only two were not temporary. One of these was the Tower of the

016%6105/92/$05.00 © 1992 Elsev,er Science Publishers B.V. All rights reserved.

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Lictor, a I00 m high steel tower designed by Gib Ponti and Cesare Chiodi, now called the Park Tower (Fig. I).

Figure I. The Park Tower of Milan.

In spite of the analyses of the designers arriving at the conclusion that the vibratory motion of the tower would have been "perceptible but not disturbing" [I], [2], the reality of the tower was quickly ,evealed to be very different. It several times exhibited vibratory stat~.s well above the threshold of physiological perception, very often complet~? intolerable and as far as the frontiers of panic. Because of these behaviou~s it was more or less unused for about forty years until it was officially declared unsafe in 1972. In 1985 the Municipality of Milan recognized the Park Tower as a ~rk of art and arranged for an investigation into its state of preservation. A series of checks were made in this context which excluded the presence of localized states of plastic deformations and, even less, o~ collapse. At the same time, in order to evaluate the possibility of re-use of the tower, conventional and advanced calculations were developed [3]. The former, based upon present Italian standards and recommendations, gave decisively contradictory results confirming that standards, on average correct if applied to ordinary structures, instead lead to often unreliable results when extrapolated to special constructions. The latter, carried out in the spirit of modern criteria of structural dynamics and wind engineering, confirmed that the structure has a safety coefficient in terms of cQll~pse very near the one estimated, empirically, but with great engineering seniority, by the designers of that epoch; however, it frequently reachs utterly intolerable levels of acceleration. On the basis

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of these results the Municipality of Milan decided to restore the tower, postponing the problem of the destination of use to a future decision. Work started in 1988 and ended in 1990. From 1991 a monitoring system composed of three accelerometers and one anemometer has been operating.

This paper presents a critical comparative picture of the assumptions and forecasts made by the designers 60 years ago, the estimates furnished by present national standards and advanced dynamic analyses, the preliminary results of full-scale experiments. Some considerations about the future developments of the research program of which this study is a part are finally outlined.

2. DESCRIPTION OF THE TOWER

The Park Tower of Milan was built in record time. The digging of the foundations began on January 15, 1933; the first coh, mn was erected on March 14; the assembly of the carpentry works was completed on June 2; the services and finishing were ready by the end of July; the tower was opened on August 10, 1933 on the occasion of the opening of the Exhibition.

It was Cesare Chiodi, the designer, who described the tower in an extremely clear and synthetic way [1]: "The tower of the lictor is different from its bigger and smaller metallic sisters because of some distinct characteristics: the slender lines, the tubular material of its structures, the connections almost exclusively realized by electric welding. The main steel structure of the tower is a pyramid frustum with hexagonal section with sides of 6 m at the base. The quite slight tapering gives it an almost prismatic appearance. At a height of 100 m the side of the hexagon is still 4.45 m. The summit of the tower is 108.60 m above the floor of the base platform. The six vertical columns, arranged according to the corners of the pyramid, are made of high-resistance steel tubes. The diameters of the tubes vary from 442 mm at the base to 165 mm at the summit with thlcknesq from 15 to 8 mm and are divided into trunks with length decreasing from 15 to 7.998 m with, at the ends, threaded flanges connected by bolts between one and the next, They all have gussets for the attachment of the struts. The struts are developed in the planes of the lateral faces of the pyramid and also consist of tubular elements. They have diameters which vary between 178 and 108 mm and thickness from 9 to 6 mm. The structure of the tower is then braced horizontally by trusses placed at vertical distances from 9.7N to 7,70 m and composed, like the struts, of tubular elements. At the height of 97.00 m a robust platform, supported by six high truss beams in the form of a star within the hexagon of the tower, supports, in its turn, the cabin for the bar containing twelve tables, for four, arranged along the outer wall, as in the dining-car, plus the small room for the kitchen. Above the bar is an open hexagonal belvedere protected by a cantilever roof. Further up, the tower shrinks into the signal light. Inside the structure described, which constitutes the essential bearing organism, there is a second prismatic turret, also exagonal, with sides of 1.35 m, made up of tubular elements with diameters of 60 to 80 mm which form the lift cage. Round this there is a spiral staircase with 520 steps." The foundation consists of a reinforced concrete rigid block resting on good alluvial gravel sand ground.

In its whole, the Park Towt~r has special features with respect to the national and international context of the period in which it was built. Because of i.ts extraordinary slenderness (height/average diameter ~ I0.4), lightness (average mass per unit volume ~ 22 kg/m3), flexibility

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(fundamental period ~ 2 s) and the moderate damping, it was half a century ahead of the generation of structures more susceptible to the dynamic effects of the wind.

3. DESIGN ANALYSES

The papers of the designer [i] and his collaborator [2] show clearly how much the wind problem was recognized at the time of the building of the tower. Reading their account reveals, on one hand, the consciousness of a theme which was not at that period much developed and therefore partly unknown ("experience will show whether these calculation predictions will be confirmed by reality"), and, on the other, the precise desire and the personal effort to frame the problem in a physically correct way, in order to arrive at realistic engineering solutions of ample caution ("the data of wind pressure that have been assumed can therefore be considered as widely prudent"). Calculations were carried out by means of static analyses and dynamic analyses: the former were developed at the quantitative level to design and verify the structure; the latter were made in a qualitative form, aimed at interpreting the vibratory properties.

The static analyses are carried out with all respect for the criteria most relied upon in that period. Pressure P exercised by the wind on orthogonal surfaces is associated with the instantaneous velocity V of the oncoming flow by the relationship P = 0.125 V 2, P and V being quantities expressed respectively in Kg/m 2 and in m/s. This formula, which presupposes a drag coefficient C D = 1.96, is clear evidence of the fact that at the beginning of this century the calculation of wind pressure on constructions was still widely made by the criterion introduced by Rouse and Smeaton in 1759 [4] and perfected by Bixby in 1895 [5]. The wind velocity profile takes into account the friction of ground in an

intuitively but well-reasoned way; the intensity of the design velocity (V = 31 m/s up to 34.18 m; V [] 40 m,'s from 34.18 m to 77.49 m| V • 44 m/s above 77.49 m) is inspired by the knowledge of that period but still seems substantially adequate. The comparison between the kinetic pressure profile used for calculating the tower and the corresponding diagram assigned by the German Reich ordinance of Apr i l 1928 confirms the prudential character of th~ calculations [i].

The effective pressure on the single elements composing the tower are calculated by multiplying the design kinetic pressure by appropriate shape and exposure coefficients. Quoting Cesare Chiodl [I]: "for cylindrical bodies affected by wind there is the normal reduction coefficient 2/3. Finally for the surfaces struck obliquely by the wind, pressure has been evaluated according to the usual formula P~ = P sen2e, e being the angle between the direction of the wind and that of the wall. No reduction has been made in the intensity of pressure on the leeward surfaces partially sheltered by the windward elements, although the already cited German ordinance allows a reduction of 50% and our 1916 Regulation admits the well-known criterion of reduction of the solidity ratio of the windward wall."

Alongwind forces evaluated by means of the above criteria give rise to a base bending moment M = 46514 kNm [3]. The related stresses are obviously x compatible with the resistence characteristics of materials [2].

Finally, quoting Cesare Chiodi again [1]: "Applying the ordinary determination methods of the elastic deflection f, considering the structure as clamped at the base, one obtains, in the hypothesis of the

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maximum wind pressure considered in the calculations, f = 0.39 m. At the ma height of the bar floor (97.00 m) the elastic deflection is reduced to

about 0.32 m. Apart from the reasons above it is difficult for the pressure shown precedently to be present and that these displacements should really be generated also taking into account that the public will only visit the tower in relatively calm weather and therefore not when the wind is force 7 of the Beaufort scale (moderate gale). The maximumdeflection of the tower with the public present is therefore below 2 cm. With a fresh wind of 10 m/sec (grade 5 of the scale) there should be a displacement of 0.019 m at the summit and of 0.015 m at the bar floor."

The dynamic analyses concern three different aspects: the natural periods and modes of vibration, the dynamic effects of gusty wind, the structural acceleration with respect to physiological tolerability.

The free vibration analysis reveals, on one hand, the already perfect knowledge of structural dynamics and, on the other, the lack of adequate tools for the resolution of complex problems. The evaluation of the natural flexural periods T k is made by schematizing the tower as an elastic, homogeneous, prlsmatlc, cantilever beam. The comparison between the results obtained in this way (T I = 1.5 s, T 2 = 0.25 s, T s = 0.083 s) and those furnished by successive rigorous dynamic analyses and even more by full- scale experiments demonstrates the inadequacy of the approximation adopted.

The study of the dynamic effects of gusty wind is based on concepts which are still too distant from being acceptable. Following the studies carried out by Rausch of the Berlin Polytechnic, very recent in that period, the wind is schematized by a periodic succession of pulses. Returning to Cesare Chiodl [I]: "The static load P , to replace the dynamic load P to obtain

S equal results, would depend on a coefficient v, function of the rapidity of application of the wind pulses and of the natural period of the structure,

P ffi vP and would be precisely _ . According to the experiments of the de Belt Observatory in Holland~ quoted by Rausch, the rapidity of application of the wind pulses varies from 2 to 3 s and can be prudently considered as 2 s." In this case, being T~ = 1.5 s, v ~ 1.2, well below the safety factor adopted for calculations. It is apparent that the concepts of the power spectrum of the wind velocity and of the dynamic response to random forces are still a long way off. Thus there is no reference to the problem of the reduction of the loads due to the non-contemporanelty of the peak pressures and, above all, of the resonant amplification; this is testified by the complete lack in [I] and [2] of explicit references to the structural damping.

The most important aspect of the dynamic analyses is however represented by the splendid intuition of Cesare Chiodi concerning an almost unknown problem in that period, the physiological tolerability to the structural motion [I]: "... it could be interesting to know the maximum acceleration of the to-and-from motion, in that more than the displacement itself, it is the acceleratlon with which the displacement takes place that gives the perpeptibility of the phenomenon to people at the top of the tower". The calculation of the acceleration at the summit of the tower is carried out on the basis of the formula a. = f~; attributing to the displacement the

1 value already quoted of f = 0.019 m (no separation is made between the fluctuating and the constant part of deflection), and being ~I = 2~/TI = 4.19 tad/s, one obtains a I = 0.335 m/sec2; according to Cesare Chiodi this value is "perfectly perceptible but not such as to cause trouble" [I]. Studies carried out after the 70's all define, however, similar acceleratlon as well above the disturbance threshold" [6]. In other words, in the light of today's knownledge, Cesare Chiodi's affirmations are an

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explicit prediction, absolutely confirmed by the facts, of the unpracticability of the tower.

It mus~ finally be observed that the designer already knew, from Padre Alfani's studies of the tower of the Palazzo Vecchio [7] and Eiffel's for the tower that took his name [8], of the existence of crosswind vibrations. However, he did not consider this problem important.

4. NORMAI'IVE CHECKS

The restoring of the tower requires its behaviour, evaluated with respect to the present regulations, or adopting higher level criteria, to be appropriate to the resistance of its materials and its use.

The application of the Italian Standards [9] gives static alongwind forces producing a base bending moment M = 39362 kNm and related internal stresses lower than those estimated by t~e designer [3]. One sees also that [9] excludes the presence of significant crosswind forces. The application of the recent recommendations issued by the National

Research Council [i0], following on the present standards [9] and as such, in principle, at a higher level, puts anyone who concerns himself with the Park Tower in front of two questions: is a point-like model or a vertical model [II] closer to the actual scheme of the tower? and, between the limit values of the damping coefficient ~ = 0.002 (unlined welded steel stacks) and ~ = 0.01 (steel buildings) which is more representative of the structural dissipation? Being almost impossible to give an answer without going deeply into the merits of both problems, it seems reasonable to develop the analyses in parametic form. This kind of approach leads to a band of actions and effects which ranges from a minimum stress situation (6 m 0.01, vertical model, H x ~ 48410 kNm) close enough to designer's estimate to a maximum stress situation (~ ffi 0.002, point-like model, 100680 kNm) so high as to cause, whenever present, the collapse of the structure [3]. The situation of the tower is even more delicate as far as wake excitation is concerned according to [I0]. The critical wind velocity of the upper part of the tower determines equivalent static crosswind forces which, for ~ =

0.01, cause stresses comparable with the stresses corresponding to the worst condition of alongwind forces (H. m 98329 kNm). Reducing the damping coefficient one finds that the equivalent damping (i.e. the difference between the structural dampin s and the aerodynamic damping) becames negative| this takes the structure into the self-excitation regime.

The real situation is absolutely different. Standards gives, on average, correct and in general reliable results if applied to normal structures, in relation to which they have been conceived, calibrated and tested. They often lead, instead, to unreliable results, at times prudential, but frequently unsafe, if extrapolated to particular constructions. The Park Tower exemplifies this concepts showing that documents [9], [I0] are not able to interpret its behavlour.

5. DYNAMIC ANALYSES

Given the proclaimed inadequacy of standards to interpret the effective behaviour of the Park Tower, the analysis of the dynamic response to wind action was carried out in integrally mathematical form using the most qualified and modern calculation criteria according to an articulated procedure in 5 sequential phases: (I) wind climate analysis; (2) analysis

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of the dynamic properties of the structure; (3) analysis of wind induced forces on the construction; (4) analysis of the dynamic response of the tower; (5) risk analysis. The theoretical and operative details of the procedure adopted and the results obtained are given in [3]. This section summarizes the salient steps of this study.

The wind climate analysis is carried out by processing the directions and the intensities of the wind velocity (averaged over 10 minutes, at I0 m above ground) measured by the Air Force Meteorological Station at the Forlanini Airport of Milan Linate. The data acquired are carefully checked and corrected according to the criteria illustrated in [12]. The corrected data base are homogeneized, by transforming the anemometric measures into refereuce speed V ~ (average velocity over 10 minutes, at 10 m above ground, which the a~ometer would register whenever placed on indefinitely flat and homogeneous terrain with roughness coefficient z = 0.07 m) [13]. The values thus obtained are subjected to statistica~ analysis by the methods described in [14]. Finally, they are again transformed to model the configuration and the recurrence of the wind on the tower site [13]; it is fundamental the law expressing the mean wind velocity V at height z = 108 a m at which the anemometer is placed in terms of the mean return period R (see Fig. 4). The schematization of the dynamic behaviour of the Park Tower is based

upon three finite element models respectively referred to as "global model", "simplified equivalent model" and "complete equivalent model". The global model (Fig.2a) schematizes the principal parts of the structure by means of a space truss with 1170 elements and 360 nodes. The simplified equivalent model (Fig. 2b) is a lumped mass system (Fig. 2c) with 6 degrees of freedom per node; the whole model has 19 elements and 20 nodes; the node at the base is assumed to be perfectly clamped; the mechanical parameters and the geometric characteristics of the beam elements are adapted so that its natural frequencies and modes approximate, as well as possible, the natural frequencies and modes of the global model. The complete equivalent model integrates the two preceding schematizatlons taking into account the soil-foundatlon-structure dynamic interaction [15] and the P-A effect; Fig. 2d shows the resultant flexural modes ~b indicating, beside them, the related frequencies n k and the periods Tb, The dissipative properties are assigned giving each mode a damping coefYicielJt ~. = ~ . + ~ ~, ~ . being

K SK aK SK the k-th modal damping of the soil-foundatlon-structure system, ~_~ being the k-th modal aerodynamic damping. Applying the criteria illust~ted in [16] it is assumed {s = 0.0046 invarlant with the deformatlve level of the tower. {~ instead ~Is calculated on the basis of [17] obtaining values ranging ~om ~ = 0 (for V = 0) to ~. = 0.0144 (for Vo = 43 m/s). The value of &~ a{s prudentl~ cut by "half in concurrenc~ with crosswind vibrations. ~inally, {b = 0.0! for k>1.

The analysis of t~e forces induced by the wind on the Park Tower is developed by applying the method [18]. The aerodynamic actions are schematized by two independent arrays of alongwind and crosswind nodal forces; the twisting actions are neglected. The alongwind forces are expressed as the sum of a mean constant value plus a zero-mean fluctuating function associated with the longitudinal component of turbulence. The crosswind forces, assumed as zero-mean fluctuating functions, are expressed in terms of the lateral component of turbulence and of the vortex shedding. All the fluctuating actions are assigned by means of cross-power spectral density matrices. The alongwind force coefficients C are evaluated on the basis of the criteria [19,20]. The evaluation of the ~ake parameters of the turret is developed by interpreting some results published in [21,22].

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& H

NODE Z(m) M(kg) 1 o.oo 2390000. 2 5.13 17676. 3 1 5 . 1 3 18000. 4 2 4 . 8 1 16002. 5 34.19 14460. 6 4 3 . 3 1 11682. 7 52.19 9588. 8 60.81 8564. 9 69.25 7184.

10 77.49 5745. 11 85.49 4716. 12 93.2.~ 4149. 13 97.00 36865. 14 99.09 2650. 15 99.85 13453. 16 101.97 2700. 17 102.75 20060. 18 104.23 1700. 19 105.72 850. 20 107.66 1000.

20 19

15 13

12

11

10

9

8

7

6

5

4

3

2 1

(0) ~ (b) (c)

Figure 2. Structural models and modes of vibration.

......./"

/ ~ 2.22 s

\ H=~ n3= 5.42 Hz

T3 = 0.18 s

n2= 2.63 / T2= 0.38 s

<d)

The analysis of the dynamic response of the Park Tower to wind action is carried out on the basis of the WL3D computer program [23]. The program receives, as input data, the configuration and the intensity of the oncoming wind, the aerodynamic parameters of the construction, the dynamic properties of the structure. It furnishes, among other output quantities, the mean value, the standard deviation, the maximum and the minimum of required structural effects (displacements, accelerations, internal forces). The diagrams in Fig. 3 illustrate the relationship between the standard deviation of the alongwind and crosswlnd components of the acceleration, ~ and o , at z = 97 m (whore the accelerometers are placed) and the moan wind v~locity V at z = I08 m (where the anemometer is placed). Th,, e×porimontal points wil~ be commented in the next paragraph.

The conclusive risk analysis involves the combination of the results glven by the analysis of the wind climate and of the dyn@mic response. The comparison of the resultant base bending moment for R = 50 years (M = 30000 kNm, M = 19500 kNm) with the original estimate of the designer ~nd with the results furnished by the national standards confirms, on the one side, the non applicability of standards to the structure in question and, on the other, that the Park Tower has a degree of safety in relation to the ultimate limit states higher than that estimated empirically, but with great engineering sense, by the designer of that epoch. Fig. 4 illustrates the relationship between the standard deviation o of the resultant acceleration at z = 97 m, Va and R; the same ~igure indicates the perception, annoyance, great annoyance and intolerability thresholds given in [6] and the allowable limits prescribed by [6,24-26]. Although these limits refer, in fact, to office buildings, and as such are not d~re~:ly extrapolable to the structure in question, their extreme distance from the calculation diagram confirms the presence of vib~-~tory states weil above those considered as usually acceptable. Also In this case the experimental points will be commented in the next paragraph.

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R(years) .01 . I ! 10 100 !000

100 _.--..J--. -..~__ i,, I

.. C-jc % 1 0 -- ' j O0 ~ " I " " " ~ . ,

~ ,

' " / e oo

0 CROSSWIND i, ! / '

• 1 bo ?'

1 O-- "~ 'L 1 I l i ! "1 0. 5. 10. 15. 20. 25. 30. 3~5. 40.

Vo(m/s) Figure 3. Standard deviation of alongwind and crosswind acceleration.

.

C" ~o-!

E b o lO -2_

R(years) .01 ,1 1 10 100 1000

I I t I I I.

• . . /~< _ =N_XOLE~B~

" I - + VERY ANNOYINO.j

- - _ / ~ PERCEPTIBLE

~RWIN [24] • e , ~ CODES [25] n ,so [2s]

! i ~ I' ' I | "1"-* O, 5. 10. 15, 20. 25, 30. 35, 40,

Vo(m/ )

Figure 4. Standard deviation of resultant acceleration.

6. FULL-SCALE MEASUREMENTS

The monitoring system of the Park Tower consists of a cup anemometer and a wind vane, three accelerometers and a data acquisition system. The cup anemometer and the wind vane are installed at the summit of the tower at height z = 108 m; it is recognized that wind flow past the anemometer is partially affected by the flow around and over the turret and, for some wlnd directions, the anemometer is shielded by the spire. The three accelerometers are placed at the height z = 97 m of the bar. While this report was In preparation, the systematic data acquisition has been operative only quite recently; the results given below are therefore to be interpreted as preliminary and partial indications.

Figs. 5 show two records of the alongwlnd and crosswlnd acceleration, a (t) and a.(t), corresponding to a mean wlnd velocity V = 12.5 m/s. Figs~ 6 and 7 ~how, In order, the power spectra, S x(n) ~nd S .(n), and the autocorrelatlon function, Rex(T) and Ray(T), of t~e tlme hls~6ry ax(t) and a_(t) shown In Figs. 5. YExamlnlng Figs. 6 and 7 a fundamental frequency value comes to light vlz

nt = 0.5 Hz (Tt = 2 s), greater than the calculated value n t = 0.45 Hz (T I = 2.22 s) and even more different from the value n I = 0.67 Hz (T I = 1.5 s) estimated by the designer of the epoch; one arrives at thls same result by elaborating other different records. It is maintained that this difference is attributable to three main concomitant causes: (I) the dynamic model of the tower envisages iwposed loads on the turret which were not present when the measures were made; (2) the structural idealization according to a space truss ignores the stiffness, even though modest, of the nodes; (3) the static scheme by which the Park Tower is represented reproduces onl~, the principal frameworks, omittins the stiffening contribution of the stair and llft cage.

The alongwind and crosswind damping coefficients of the first flexural mode of the tower, ~ and ~ , are evaluated by elaborating the diagrams in Figs. 6 and 7 according to ~hree different criteria: (a) the method of the decrement of correlation [27 28] (~_ = 0.0041, ~. = 0.0030); (b) the method of the spectral moments [29] (~x =x0"0041"0"904~' ~y = 0.0040-C.0043); (c)

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the method of the spectral band-width (~ = 0.0038, 6 = 0.0042). The examination of the results indicates: (1)x a notable ~tability of the estimates independently of the evaluation criterion; (b) dissipative properties clearly less than that envisaged d~ring dynamic analyses (for V a = 12.5 m/s, gx = 0.0090, g. = 0.0068). The application of the same criteria to different records sub~tantially confirms the comments (i) and (2) also revealing a modest dependence of 6_ and 6_ on V ; were this to be confirmed by future experiments, it would mean thatY[18] @ends to overesti- mate the aerodynamic damping of the structural typology here examined.

.10 -.

.05 -

.00

O -.05

- .10

O. I 1

6 0 . 1 2 0 .

I . L I I i i

C~ = 12.5 m/s CTcx = .0204 m/s 2

9 = l Z S m/s

I I ....... I I '1 1 8 0 . 2 4 0 . 3 0 0 . 3 6 0 , 4 ' 2 0 . 4 8 0 .

t(s)

.10 ! . . . . . .

,,'=',, .05 .,=

"~" .00

0"" '°.05 w

= , 1 0 . . . . . . . . . i ' - I . . . . . . . T I O, 60. 120, 180, 240,

is)

t Coy : . o 2 3 4 m/s 2

m

, r

I I I 300. 3 6 0 . 4 2 0 . 4 8 0 .

Figure 5. Time histories of acceleration.

Figs 3 and 4 previously described are finally completed by means of the measured quantities o , o and o relative to the diagrams in Figs. 5 and

ax ay al~ other records not glven here. is evinced that in spite of the differeuces, already quoted, between the calculated and measured fundamental period and damping (other differences, not as yet investigated, are certainly present in relation to the wind configuration and the ~erodynamic properties of the construction) the theoretical analyses had given reasonable approximations on the safe side. Notwithstanding this structural vibrations are really much higher than those usually accepted.

2099

,,o

% 'o "a

O0 ~ 0

,o! ~.o

.31 ,I 1. 10.

~ 0 .~ , _

-2 10- 2

I0

U) ;O -8

I0-~°~

,01 , ~,i,,, I , , ,,,,,,[ ~ I ~,,

.I I.

(Hz) Figure 6. Power spectra of acceleration.

F

O.

6 . . i I , I I l I I I

~ O, o o_..._ !ilVVVVVVVVVVVVVVVVVVV I I ! |

~. ~. lo. ~5. 20. 2%. 30. ~5. ~o. 45.

. . - . & / , , , , , i . , , iF

o. s. ,o. ,5 . 2o. 2 5 . - , o . ~5. ~o. ~ .

r ( s )

Figure 7. Autocorre!ation functions of acceleration.

7. CONCLUSIONS AND PROSPECTS

The p r e s e n t r e sea rch can be cons idered as the nodal po in t of two study programs r e s p e c t i v e l y aimed a t a spec i f iL o b j e c t and a genera l o b j e c t .

The s p e c i f i c ob jec t i s to r e t u r n the ~'ark Tower to i t s o r i g i n a l purpose as a vantage po in t over Milan. At the base of t h i s theme t h e r e are th ree ext remely complex, a r t i c u l a t e d and mutua l ly i n t e r a c t i n g problems: (a) the d e s t i n a t i o n and the use l i m i t s of the tower; (b) the fo rmula t ion of a physiological tolerability criterion compatible with the problem of retrieval and the choices set out in (a); (c) the selection of the most appropriate intervention criteria to mitigate the structural oscillations to the extent desired for the achieving of the objectives (a) and (b), accepting the limits imposed by the Fine Arts Superintendent for the non alteration of the external appearance of the tower. Since the problem of the physiological tolerability to structural motion almost exclusively concerns new constructions, it is maintained that this research is one of the first examples, perhaps the very first, in which this problem is treated from the viewpoint of the reclaiming of a historic building with artistic value.

The general objective concerns the attempt at giving full-scale experi- ments a wider value. In an experimental sector too often aimed at a mere

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comparison between calculated and measured values, the Authors are develop- ing a theoretical-experimental method for the dynamic and aerodynamic identification of structures. The method aims at validating the analytic forecasting models, identifying their parameters, allowing their applica- tion outside the domain, generally much limited, of the directly measured values. The Authors believe that only a perfect integration of mathematical methods with experimental techniques can guarantee a real advance in the inherent knowledge of the real behaviour of structures.

8 . REFERENCES

i C. Chiodi, Ii Politecnico, Anno LXXXl, No. 8 (1933) 455. 2 L. Pinciroli, Ii Politecnico, Anno LXXXI, No. I (1934) 3. 3 G. Ballio, F. Maberini, L. Romano and G. Solari, Costruzioni

Metalliche, in press. 4 J. Smeaton, Proc. Roy. Soc., II (1759) 366. 5 W.H. Bixby, Eng. News Rec., 33 (1895) 175. 6 R.J. Hansen, J.W. Reed and E.H. Vanmarcke, J. Struct. Div., ASCE, 98

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