Structural Analysis of Historical Constructions - Modena, Lourenço & Roca (eds) © 2005 Taylor & Francis Group, London, ISBN 04 15363799

Experimental stress analysis of historical forged tie beams of archaeological museum of Spina in Ferrara, Italy

G. Bruschi & G. Nardoni Studio VM. , Ferrara, ltaly

L. Lanza, F. Laudiero & N. Tullini Department of Engineering - University of Ferrara, ltaly

G. Mezzadri Mezzadri e Associati Sr.L., Ferrara, ltaly

S. Tralli Elletipi SI:!. Laboratorio Prove Materiali, Ferrara, ltaly

ABSTRACT: In historical (ancient) buildings, tie beams may be broken by corrosion anel, in this case, knowl­edge of the axial forces in the remaining tie-beams is very useful to select the tensile force the substitute tie beam is to be given. In the case reported hereafter, a tie-beam of a pavilion vault arcade facing the inner gar­den of Ludovico il Moro Palace (presently Museo di Spina) in Ferrara suddenly broke apart and it was then necessary to substitute the old tie-beam and to verify the resulting homogeneity of the anchoring tensile forces along the arcade. Mechanical and metallurgical analyses ofthe old tie beam were performed to evaluate possible heterogeneities and to yie ld a reliable Young modulus. Vibration tests were adopted to evaluate the tensile forces of the substitute and of the old tie beams as well , and the obtained stress states were confirmed by using the Barkhausen method (magnetostriction technique).

INTRODUCTlON

Nowadays, it is largely acknowledged that restora­tion of historical constructions has to take up two distinct challenges: need for safeness and respect of historical memory. Hence, consolidation of histor­ical buildings calls for both refined analysis tools and the appreciation of traditional construction tech­niques (Grandis et a!. 200 I; Di Francesco et a!. in printing). Masonry arches and vaults of historical buildings usually present iron tie beams that resist thrust actions induced by vertical forces but are also effective in respect horizontal loads beca use they may hamper some mechanisms so as to increase the col­lapse loads. The analysis of the vaulted structure and the estimate of the safety facto r can make profitably use of the experimental evaluation of the anchoring forces exerted by tie beams. The case reported here­after concerns Ludovico il Moro Palace in Ferrara which, since the middle ofthe past century, has housed the national archaeological museum (Museo Archeo­logico di Spina). This museum collects numerous finds

489

ofthe excavations in necropolis ofSpina, once, ancient landing in the proximity ofComacchio, on the Adriatic Sea. In the south, two story, wing ofthe building, there is a pavilion vault arcade, of 5.50 m x 12.00 m, host­ing two lunettes along the short sides and five lunettes along the long sides. The arcade is facing the inner gar­den through three arches resting on two columns and two semi-columns anchoreel, in tum, by four forged 030 iron tie beams (Figs. 1-4).

In the autumn of 2002, a tie beam (n. I in Fig­ure 2) exhibited a complete fracture in the proximity ofthe end (southern) semi-column giving rise to pos­sible overloading of the adjacent reinforcements. The inspection showed that fracture involved about 20% of the cross-section whereas the remaining part appeared to be long since corroded by rus!. Moreover, a sig­nificant distortion consequently developed which, one year later, presented a 28 millimeters drift ofthe abut­ments accompanied by pretty evident cracks at the vault intrados. The old forged rod was subdivided into main five parts and subjected to laboratory chemi­cal, metallographic, and mechanical tests that showed

notable structural and metallurgical non-homogeneity. Inner oxidization, inclusions, cavities and a substan­tia I fragile behavior were put in evidence whereas, the average composition looked like that of a C30 steel.

Moreover, average Young modulus was evaluated so as to enable the vibration tests to yield accurate esti­mates of the tensile forces acti ng in the remaining tie beams. In fact, vibration tests (using impact hammer) on the old three tie beams were able to exclude any possible overloading due to the sudden fracture and to give a reference value of the tensile force the new tie beam was to be given. In fact, the three tie beams, n. 2, 3,4 in Figure 2, showed tensile fo rces of86, 90, 81 kN respectively. Finally, resort was ma de to the magne­tostriction technique (based on Magnetic Barkhausen Etfect) to verify if this relatively new method can be profi tably applied to the evaluation of stress states in historical meta is.

As a matter of fact , the method needs to be calibrated by working on an unstressed simi lar material anel, this was the case fo r the old (broken) tie beam.

Figure I. Plan of Museum of Spina showing the pavilion vault arcade under investigati on.

Figure 2. Plan ofthe pavilion vault arcade showing the four tie beams.

Finally, at the end of the year 2003, it was decided to insert, in the place o(the old tie-beam, a drawn steel rod with threaded ends, to be anchored by means of ribbed plates. In turn, the plates were bui lt into the masonry (subjected to a proper consolidation) anel, working at the two extremities, a tensile force of 90 kN was imposed by means of a dynamometric wrench.

The vibration tests, as well as the magnetostriction technique confirmed the value of the force imposed to the new tie beam; yet, the analogous vibration test, repeated thirty days later at a simi lar temperature levei, revealed a reduction ofthe tensile force more than 50% whereas the adjacent tie beam showed a reduction of 5 kN. Apparently, the masonry had recovered part of the suffered distortions causing a notable reduction of the anchoring force in the new tie beam. Hence, supplementary vibration tests were planned to monitor the future behavior.

Figure 3. Image of the pavilion vault arcade under investigation.

Figure 4. Image ofthe tie beams n. 2, 3, 4.

490

2 METALLURGICAL TESTS

The old tie beam was subdivided into 5 main segments from which specimens were obtained (Figure 5) to perform metallurgical and mechanical tests .

For tensi le tests, two distinct zones were chosen, i.e .: segment 4 (with fewer internai defects) and segment 2, which presented the highest number of defects and was close to the fracture point. Moreover, segment 2A was used for chemical and metallographic analyses, segment 3A was used for hardness tests and segment 5A was used for hardness and metallographic tests. Finally, segments I and 5 were used for the evaluation ofYoung elastic modulus.

2.1 X-rays and microscopic fesls

X-rays showed the main defects due to forging process, i.e.: extensive longitudinal cracks with more or less accentuated transversal ramifications with openings growing from the core to the surface (Figure 6).

The heads of the fracture (Figure 7) showed that there had been no significant reduction of area, and no development of plastic deformation.

Observation through electronic microscope showed that the surfaces were diffusely corroded. There was a significant externai area showing the morphology of a cleavage fracture, a type of low energy fracture quite different from discontinuous yielding that shows evi­dent plastic deformation spreading along well defined crystallographic planes. The cleavage fracture had the particular form of the "ri ver" pattern, (Figure 8) slightly 'polluted' by the products of corrosion. The

6m

5 5A 4 3

fracture had a crystalline appearance with a character­istic shine that covers areas over one half ofthe circular sector.

2.2 Chemical analysis

First of ali, sample 2A was analysed by optical emis­sion spectrometer. In Table I, the resulting chemical composition is shown. As is known, the method may find it difficult to yield reliable results in terms of carbon and sulphur; hence, the same sample was sub­jected to chemical analysis for combustion using a

Figure 7. Details of heads of fracture: sample 3A on the left, and sample 2A on the right.

3A 2A 2 ,-----.. ,-----..

Clc ... ------------u---------CO~ )

12) 25 mm 12) 35 mm

Figure 5. Segmentation of the old tie beam for the experimental analyses.

Figure 6. Detail of positive x-ray with transversal cracks on segment 5.

491

high frequency induction oven and IR sensors (Table 2). The chemical composition suggested to assimilate the material under investigation to a C30 type steel.

2.3 Metallographic tests

Optical microscope analysis was also necessary to observe inclusions and microstructure subject to chemical attacks: useful information for an explana­tion of the "thermal history" of the sample. A lot of inclusions was found in the centre of the samples, with gray stripes of two different tones, which, in morphological terms, suggest aluminates or silicates (confirmation was obtained using electronic micro­probe (EDS». Following metallographic attack with NitaI2%, several different microstructures were found confirming a high heterogeneity leveI: a ferritic type structure with limited perlitic areas in the joints of the ferritic granules; a very compact perlitic struc­ture, a ferritic, bainitic and perlitic structures occurring without any evident explanation and some intergran­ular cracks, corresponding to austenitic grains. These cracks have rendered the material response even more fragile.

Figure 8. "Ri ver Pattern" of a cleavage fracture present in the fracture head 2A.

3 MECHANICAL TESTS

3.1 Hardness tests

Hardness tests showed surface values approximately twice as those evaluated in the central area. In section 3A (next to the fracture, Figure 9) values were found higherthan in 5A. The average Vickers hardness values for two test point !ines were almost identical (135 and 137 HV 10). A peak ofhardness of213 HV 10 in section 3A could indicate a greater fragil ity induced by the forging processo It should emphasized that the average diameter in section 5 is smaller than those of sections 2 and 3.

3.2 Tensile tests

Two cy!indrical specimens, obtained from segment 4 (far from the head of the rracture, with few inner defects) and from segment 2 ( close to the fracture, wi th high defect density), were subjected to a tensile test. The results confirmed the fragile behavior suggested by metallurgical tests. Figure 10 shows the stress­strain curve for the specimen obtained from segment 4.

3.3 Young modulus test

The Young modulus test was carried out on two differ­ent specimens obtained by segments marked I and 5. It was performed using two different systems for strain acquisition: one mechanical strain gauge (M in Fig­ure 11 a) and three electrical strain gauges (E 1, E2, E3 in Figure lIa). The electrical gauge gives a localized value ofthe strain whereas the mechanical gauge refers the extension to a fifty millimeters base. Actually, two

Table 2. Carbon/Sulphur analysis using combustion method (LECO instruments).

Average Elements Analysis I Analysis 2 Analysis 3 value

c S

0.284 0.0066

0.324 0.0062

0.307 0.0063

0.305 0.0064

Table I. Chemical composition of sample "2A;' obtained using spectrometer with optical emission.

Test C Si Mn P S Cu Cr Ni AI Mo V Ti W Pb Zn

I 15.56 8.03 0.815 0.001 O.R* 0.568 0.289 0.167 1.546 0.807 0.316 0.313 1.498 2.235 2.456 2 0.692 0.278 0.148 0.001 O.R. 0.017 0.005 0.006 0.043 0.142 0.005 0.007 0.029 0.048 0.048 3 8.950 1.995 0.458 0.002 O.R. 0.275 0.150 0.085 0.606 0.395 0.159 0.146 0.760 1.202 1.260 4 25.41 6.677 1.21 1 0.001 O.R. 0.656 0.324 0.178 1.399 0.970 0.367 0.380 1.574 2.495 2.542 5 10.86 13 .84 1.988 0.003 O.R. 0.122 0.069 0.034 0.52 1 0.179 0.088 0.078 0.289 0.859 0.641 6 0.177 0.507 0.1 44 0.001 O.R. 0.146 0.079 0.007 0.082 0.008 0.008 0.010 0.038 0.100 0.081

* O.R.: out ofrange.

492

250

200

; 150

:x: 100

50

O+--'--~--.-~~-.--~--r-~--~--~~

3 6 9 12 15 18 21 24 27 30 33

mm

Figure 9. HV 1 O hardness test point lines along the diameter of sample 3A (near the fracture head).

20

[kN] 16

12

10 12 [mm] "

Figure 1 O. Stress- strain curve (Diameter = 6.35 mm, Area = 31.67 mrn2 ; Maximum load = 14.49 kN; Yie]d stress = 322.39 N/mm2, Tensile strength Rm = 457 N/nun2).

displacement transducers, working on a 340 mm base, were also adopted to verify that local and average val­ues were not in conflict. The stress- strain diagrams were plotted up to 150 kN of the axial force value. The four records for specimen I are reported in figure I I b whereas Table 3 summarizes the main results for both the specimens.

4 VIBRATION ANALYSIS

Static and dynamical methods have been proposed aimed at determining tensile forces acting in tie­beams of masonry arches or vaults and, in general, dynamic methods require lesser experimental effort. In fact they need the response of few accelerome­ters rigidly connected to the beam under investigation when it vibrates due to a given perturbation. Some formulations (Livingston et aI. 1995, Calderini & Lagomarsino 2003) work on vibration frequencies only and the evaluation of the tensile force has resort to a proper error function, whereas other formula­tions make use ofboth static deflections and vibration frequencies (Biasi & Sorace 1994).

493

4.1 Theoretical background

In the present case, for the vibration analysis, a method recently proposed (Tullini & Laudiero 2003 , Tullini & Laudiero 2004) was adopted which gives both the tensile force acting in the tie-beam and the rotational stiffness of the constraints offered by the side walls. To this purpose, three accelerometers are required to know a vibration frequency w and three amplitudes VI , V2, V} of the corresponding modal shape. As is known, the equation governing the vibrations ofEuler­Bernoulli beam of length L and uniform cross section, subjected to end rotational constraints of stiffness ko e k l , and to an axial force N can be written as (Graff 1975):

V""(x) - n v"(x) - À 4 v(x) = O O<x<l, (1)

subjected to the boundary conditions, where

x .X=-,

L (2)

E, /-i and J represent Young modulus, linear density and cross section inertia moment respectively and, finally, the positive sign of N corresponds to traction. The solution to equation (l ) is:

with:

(4)

where qj is determined by the frequency characteristic equation and the boundary conditions yield constants C j - C4 . When the accelerometers are placed at L/4,

FORCE

250 Tr---------------,,-,------,-----,------,-----, --- eleclrical gauge n01

-e- eleclrical gauge n02

200 ........ e leclrical gauge n03 I-_+_----I---.,~-Y'----------=-...s-I"'----I

- mechanical gauge

~ 150 +_----~------~------+_--?S~~~--~------+_----~

(a)

! 1/1 1/1

~ 100 +_---~--~-76L-~'-------_+---_+_----I---~ ~

50 +------+~~--+------+------+------+------+-----~

O~~--~~--~--~~+-----~~--~--~~+-----~

O.OE+OO 2.0E-04 4.0E-04 6.0E-04 8.0E-04 1.0E-03 1.2E-03 1.4E-03 strain [mIm]

(b)

Figure 11. Young modulus text: (a) equipment forYoung modulus test and (b) stress- strain curve for specimen l.

Table 3. Main data for the two traction tests.

Specimen I Measurement method

Mechanical gauge Electrical gauge EI Electrical gauge E2 Electrical gauge E3 Mean value

Specimen 5 Measurement method

Mechanical gauge Electrical gauge E 1 Electrical gauge E2 Electrical gauge E3 Mean value

Young modulus [GPa]

193.24 181.47 190.26 163.75 182.18

Young modulus [GPa]

207.44 172.89 197.10 168.36 186.44

L/2 and 3L/4, if the middle section does not coin­cide with a node, the boundary conditions yield the equations:

I + 2cos~ cosh q2 4 4 (5)

(6)

(7)

where constants a, b, c, d take lhe fo llowing expressions:

a = sin q l sinh q2 - sin iLsinh q2' 2 2

(8)

b · . h q2 . q l . h =smql sm -- -sm-sm q2' 4 4

(9)

c = 2 ( cos i -cosh ~ ) x

d = q, ( cos q, sinh qz + sinh ~ - cos1c. sinh qz) + 4 4 4

+qz (COShqZ sin1c. + sin2iL-coshil.sinq,). (11) 4 4 4

Equation (5) represents a transcendental equation which yields the value of n for any given value of À (that is to say of w) whereas equations (6, 7) gives the nondimensional stiffness of the rotational end constraints. With reference to the fi rst vibration

494

0.75

0.70 N >

~ 0.65

'" +

-=-0.60

0.55 /

,,,,,,/ ko=kJ =00 0.50

O 2 3 4 5 6 7 8 9 10 II 12 I 3 14 15 16 17 18 19 20

Figure 12. Ratio (VI + v3)/2v2 versus first nondimensional frequency À for some values of the nondimensional tensile force n. Dots indicate experimental values.

Table 4. Main data oftie beams.

Tie beam 2 3 4

o [mm] 30 30 33 33 L [mm] 5036 5100 5160 5060 E [GPa] 200 185 185 185

fi [Hz] 10045 13 .35 12.28 12.59 VI 0.6246 0.6657 0.6879 0.6291 V2 1.0000 1.0000 1.0000 1.0000 VJ 0.6053 0.6650 0.6531 0.6530

À 6.6323 7. 7414 7.1630 7.1109 ( VI + V3)/ 2v2 0.6150 0.6654 0.6705 0.6411 n 127.6 303.2 222.5 193.2 f30 93.5 3004 9.8 9304 f31 38404 31.0 24.2 40.0 N [kN] 40.0 85.7 90.0 81.3

frequency, in Figure 12 curves reporting different val­ues of the non dimensional tensile force NL2/EJ are plotted with respect to axes reporting the non dimen­sionai circular frequency À, and the ratio belween the modal amplitudes corresponding to equation (5). Once lhe two coordinates have experimentally been deter­mineel, the curve NL2/EJ passing through that point gives the requested tensile force . These curves are enclosed by upper and lower bounds (dotted lines) corresponding to simply supported and fully clamped beams respectively.

4.2 Experimentallests

Average geometrical and mechanical properties oftie beams are reported in Table 4; in particular, a density p = 7.85 kg/dm3 was systematically adopted.

Dynamic tests were performeel, hitting each tie beam with an impact hammer PCB/086C04, able to measure a pulse up to 4.4 kN with sensitivity of 1.2 mV!N; the dynamic response was acquired by

495

three piezoelectric accelerometers PCB/353B 18 hav­ing sensitivity of 10 mV/g and weightof 1.8 grams. The three accelerometers were fastened at each tie beam, at equal distances, by means of metallic wrappers. Ali the instruments were connected to a signal condi­tioner anel, eventually, to a PC data acquisition system. Hence, the ratio between the Fast Fourier Transform (FFT) of the acceleration record a(t) and the FFT of the pulse F(I) yields the inertance at the instrumented points ofthe tie beam (Ewins 1984). To set an example, Figure 13 shows the diagrams ofthe inertance moduli for the three accelerometers fastened at tie beam no. 2. Tests were performed hitting, three times, each of the three, instrumented points ofthe tie beam. Table 4 shows average frequency values together with the cor­responding amplitudes ofthe modal shapes; moreover, values of À and of(v, + v3)/2v2 were computed so as to evaluate the non dimensional tensile force n by means of equation (5). In fact, the two coordinates locate points marked with a dot in Figure 12. Hence, by sim­pie inspection, the same figure yields a Irial value of 11

that can be adopted for the numerical solution of equa­tion (5). Data oftie beam no. I refer to tests performed one month after it had been tighten up to allow mortar ofthe sealing masonry to reach proper maturity.

5 MAGNETOSTRICTION ANALYSIS

Magnetostriction analysis is a non destructive tech­nique, based on Barkhausen Effect (MBE), for the evaluation of stress states in ferromagnetic materiais (Jiles 1991). "Barkhausen Effect" is based on electro­magnetic impulses (Jumps), that are generated during the magnetization of a metallic material , due the effect of union/orientation of the "magnetic domain" when they overcome the separation barriers (Block walls). Local stresses are able to influence the intensity of the electromagnetic impulses (Jumps); In fact , tensile

IxlO2

~ l xlO l :[ <i IxlOo

~ l x10-1 çG

~

Ix 10-2

O 20 40 60 80 100 120 l40 l60

lxl02

~ Ix l0 1

'ê "-;:', IxlOo « ~ Ix10-1 çG ~ J[Hz]

Ix 10-2

O 20 40 60 80 100 120 140 160

Ixl02

~ Ix l OI

'" E '-;:, Ix lOO

« ~ IxlO-1

~

I x 10-2

O 20 40 60 80 100 120 140 160

Figure 13 . Frequency Response Functions (FRF) for the three instrumented sections of tie beam no. 2 with a pu lse at L/4.

stresses favour the unionJorientation of the "mag­netic domain" whereas compressive stresses hamper such orientation. Hence, through the measure of the delay time, compared with the analogous time of an unstressed calibration specimen, it becomes possible to evaluate the (tensile or compressive) stress state of the manufact under investigation. Moreover, when dealing with historical materiais, a metallurgic and microstructural characterization ofthe material inves­tigated is necessary to develop a proper calibration of the experimental results. To this purpose, the results of chemical and metallographic analyses were profitably made use of. In the present case, both the new and the old tie beam were available in stressed and unstressed conditions as well. The equipment used was Intromat 2000 by R&D Diagnostic - Minsk.

On site magnetization process gave the following values: New tie beam: calibration block 35 mA; installed element 55 mA. Old tie beam: calibration block 55 mA; installed elements 55 mA.

New tie beam (Table 5)

reference Hysteresis curve: Fe 360 B; - difference between digit calibration data and control

data: 61; - estimated tensile stress value: 132 MPa.

Table 5. Magnetostriction analys is data.

New tie beam Digits Average

Calibration block 173 175 166 170 171 171 Tie beam 23523 1 232229227236 232

Old tie beam Digits Average

Calibration block 206 199 210 208 203 205 Tie beam 225 230 232 229 227 229

Assuming 0 = 30 mm, the total tensile force turns out to be 93.30 kN_

Comparison old tie beam (Table 5):

- reference Hysteresis curve: C30; - difference between digit calibration data and control

data: 24; - estimated tensile stress value: 123 .3 MPa.

Assuming 0 = 30 mm, the total tensi le force turns out to be 87.15 kN.

CONCLUSIONS

Few remarks to close this multidi sciplinary expe­rience. First of ali, chemical and metallurgical

496

composition, high heterogeneity and relatively frag­ile behaviour of ancient forged tie beams were quite surprising and seem to require a very cautious approach. Laboratory metallurgical tests highlighted these unusual properties and gave basic information necessary to develop strengthening designo Vibra­tion tests had previously been developed in labora­tory conditions but (laboratory) mechanical tests gave reference values that enabled the authors to rely on in situ tests as well. Metallurgical tests made possible magnetostriction analysis that requires specific cali­bration curves for a given material. In spite of more or less refined analyses, masonry has extraordinary resources; in fact, it can undergo a drift of 28 mm between the vault abutments without giving rise to appreciable overloading of adjacent tie beams and without showing significant sufferings. At the same time, it can recover part ofthe suffered distortions and change the value tensile forces acting in tie beams, perhaps cyclically, according to season conditions.

ACKNOWLEDGEMENTS

The authors would like to acknowledge the respec­tive contributions. G. Mezzadri was in charge for the strengthening designo Elletipi (Laboratory) S.r.l. in Ferrara developed chemical , metallurgical and mechanical tests. Department of lngegneria of University ofFerrara was responsible for the vibration analyses. Studio VM. in Ferrara developed magne­tostriction tests.

REFERENCES

BIasi, C. & Sorace, S. 1994. Determining the axial force in metallic rods. Struetllral Engineering Interna­tional, Vol. 4(4), 24 1-246.

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Calderoni , C. & Lagomarsino, S. 2003. Una metodolo­gia diagnostica per l'identificazione dinamica deI tiro nelle catene metalliche antiche. Atti deI XVI Congresso AIMETA di Meceanica Teorica eApplicata. Ferrara, 9- 12 September 2003, C D-ROM.

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Jiles, D. 1991. Introduction to magnetislll and lIIagnetic materiais. Chapman & Hall, New York.

Lagomarsino, S. 200 I. Sicurezza e cOllservazione del/e ehiese in zona sismiea in Model/i Ch iese. DISEG , HTML Doc­ument: http: //adic.diseg.unige.itlMarche/Marche.htm.

Li vingston , T. , Béliveau, J.G. & Huston, D.R. 1995. Estima­tion ofaxial load in prismatic members using tlexural vibrations. JOllrnal 01 SOllnd and Vibratiol1 , Vol. 179 (5), 899- 908.

Tullini , N. & Laudiero, F. 2003. Valutazione dello sforzo normale in travi prismatiche tramite parametri modali tless ionali . Atti deI XVI Congresso AIMETA di Mecca­nica Teorica e Applicata. Ferrara, 9- 12 September 2003 , CD-ROM.

Tullini , N. & Laudiero, F. 2004. Valutazione sperimentale deI tiro nelle catene mediante prove dinamiche. Atti deI XI Congresso Nazionale "L'lngegneria Sismica in Italia". Genova 25- 29 January 2004, C D-ROM .