Structural Analysis of Historic Construction – D’Ayala & Fodde (eds)© 2008 Taylor & Francis Group, London, ISBN 978-0-415-46872-5

Diagnostic tests and numerical simulations for the preservation oftwo stone stairways in the historic centre of Genoa (Italy)

A. Brignola, A. Del Grosso, S. Podestà, S. Resemini & G. RiottoDICAT, Department of Civil, Environmental and Architectural Engineering, University of Genoa, Italy

ABSTRACT: The study focused on the experimental investigations and numerical analyses regarding thestaircases in the interior of two historical buildings (named Caffa and Metellino) in the refurbished area of thedocks of Genoa harbour (Italy). Those stairways are made up of stone elements (pink granite of Sardinia Island)and show a particular constructive technique that allows the monolithic steps to be linked together, providing anoverall behaviour among steps of a flight and among flights. This technique, suggested by the prescription (orrule of thumb) of various ancient building manuals, allows the stress field to be distributed on each element andit was modelled by means of FEM, in order to verify the effect of this technical measure relative to various loadcases. The numerical simulation, carried out through a detailed non-linear solid model of the flights of steps,was preceded by an exhaustive diagnostic campaign (in situ and laboratory tests), useful in order to define, boththrough direct and indirect tests, the mechanical parameters to be adopted. The obtained results were crucialto preserve the staircases without performing any structural intervention that would have been useless (if notharmful), modifying the architectonical and historical value of the original structure of the stairways.

1 INTRODUCTION

The recent renewal of the dock area of Genoa har-bour (Italy) led to the renovations of various historicalbuildings used as industrial warehouses. The interven-tions determined the need of verifying the existingstructure reliability, with reference to the new enduse and the current technical building rules, aimingto preserve their architectonical features.

In this study, the work focused on the experimen-tal investigations and numerical analyses regardingthe staircases in the interior of two important build-ings (named Caffa and Metellino) in the upgradedarea. Those historical stairways are made up of stonemonolithic steps.

The constructive technique, suggested by the pre-scription of various ancient building manuals (deBelidor 1729, Breymann 1885) and implying a partic-ular moulding on each step edge, leads to the structuralinteraction among the elements. In this way, an overallbehaviour of the flights may be achieved.

Nevertheless, current technical building rules donot take into account this constructive technology(monolithic stone elements) for stairs. So, no clear ref-erence is given to the material behaviour that has to beassumed or safety checks which have to be satisfied.

Moreover, even if the constructive details are rec-ommended by ancient rules of thumb and they areeffective from the static point of view, a detailed

analysis is needed, because no simplified models seemto well reproduce the effect of this technical measure.

The numerical FEM simulation, carried out througha detailed non-linear solid model of the flights of steps,was preceded by an exhaustive diagnostic campaign,useful in order to define, both through direct and indi-rect tests, the mechanical parameters to be adoptedand the presence of crack patterns or defects in eachsingle step.

The obtained results were crucial to preserve thestaircases without performing any structural interven-tion that would have been useless (if not harmful),modifying the architectonical and historical value ofthe original structure of the stairways.

2 THE HISTORICAL DOCK AREA OF GENOAAND ITS RENEWAL

Since the 13th century, the city of Genoa (Italy) wasalready a thriving maritime township in the north-western Mediterranean Sea.

The historical dock area (“Darsena”) of the Old Portwas built from the 11th century and it was subjectedto various modifications and re-organizations duringthe ages, in relation to the evolution of the port and thetown. Since the first of 14th century, the “Darsena”was organized in order to handle the galleys of theGenoese Republic; moreover, there are warehouses for

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Figure 1. The historical dock area in the Old Port of Genoa.

Figure 2. “Quartieri” Caffa and Metellino (Bordoni, 1987).

the galley repair (“Darsena delle galere”) and storageof goods (“Darsena del vino” or “delle barche”).

In the Renaissance age, during the restoration of thenaval dock yard of the Genoese Republic, a tract of thesea water was filled in and the quarters (“Quartieri”)grew up on the new land (Fig. 1).

These are distinct large buildings of a significantarchitectonic value, due to the excellent expertise in thedesign of the architects and the skilfulness in buildingof the craftsmanship.

In the very inside of the docks, the Quartieri Caffaand Metellino were built (Fig. 2). These two twinpalaces are connected to each other through a hugeglass gallery (Fig. 3), which the main part of theirappeal is ascribed to.The morphology of the two build-ings is similar, but significant differences, which thepeculiarity of each palace is due to, may be noted. Inparticular, the stairs compartments, being key-pointsfor the ancient end use of the buildings (storehouses)and are object of this study, show the same struc-tural typology, typical of Genoese architecture (Franco1995), but they are differently located in plan (Fig. 4).

In the last decades, thanks to various fundsobtained by Genoa city in relation to important events(Columbus celebrations in 1992, G8 meeting in 2001,European Capital of Culture in 2004), the area of

Figure 3. The glass gallery between Caffa and Metellinopalaces (Bordoni, 1987).

Figure 4. Plan view of Caffa and Metellino palaces.

the historical docks was deeply modified. Nowadays,the Faculty of Economics and the “Galata MaritimeMuseum” are based in the old quarters; from 2004,Caffa, Metellino and Tabarca buildings were restoredand they currently house a contemporary music centre(studios, auditorium, etc.) and contemporary-art com-plex (devoted to permanent exhibitions, artist atelier,bookshop and other shops), as well as a civic cen-tre, having a multifunctional room for exhibitions andmeetings, to be used by local associations.

The modification of their end use led to a com-plete verification of the static behaviour of the pre-viously mentioned palaces. In particular, this workmay be included into this ambit, among which themain staircases of Caffa e Metellino palaces are underinvestigation.

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3 THE STAIRCASES OF CAFFA ANDMETELLINO PALACES

The staircases of Caffa e Metellino palaces are made upof stone elements (pink granite of Sardinia Island) andshow a particular constructive technique that allowsthe monolithic steps to be linked together, providingan overall behaviour among steps of a flight and amongflights.

The lack of indications, in current technical build-ing rules, about how to model and verify the staticbehaviour of stairs made up of monolithic stoneelements rules led to perform in depth analyses.

Numerical FEM simulations through a detailednon-linear solid model of the flights of steps andan exhaustive diagnostic campaign, aimed to char-acterize the material mechanical parameters and toidentify the presence of defects in the stone elements,were carried out. Besides that, an accurate historicalinvestigation about the ancient building technology incase of monolithic stone stairways seemed to be veryimportant.

3.1 Historical and technological aspects

In many ancient building manuals, technical char-acteristics and constructive details of the monolithicstone stairways are described. Generally, they aremade up of large freestone elements. In his treatise“Wooden, stone and brick stairs” (1885), Breymannwrote “Using freestones, one may obtain very strong,durable and nice stairs and also very easy to build”. Ina few words, he highlighted the main features of thistypology. In Figure 5, the original drawings are shown.

The section shapes of the step are various: start-ing from the simplier rectangular profile, up to moreelegant ones, characterised by moulding, carving orspecial intrados outline, aiming to give a more aesthet-ical sight from below, but also to facilitate the flightconstruction.

The way through which the steps are laid one uponthe other depends on the support typology of the stepedges: they can be fixed in the masonry walls on eachside or they can be simply supported by beams, wallsor arches.

According to Breymann, in case of fixed supportsof the edge, having at least an insertion depth equal to10–12 cm, the step overlapping could be only nec-essary to hide the back of the element and ensurethe laying clearance; the overlapping distance maybe minimal (4–6 cm, as in Figure 5, image 466). If,on the contrary, one or both the edges of the stepare free-standing, the element superposition is neededto avoid relative displacements among them. In thiscase, an almost 2 cm moulding has to be trimmed. Theshape can be various: the profiles in Figure 5, images464 ans 465, aim to avoid the movement of the step,by means of a of 2–3 cm backing. The same scope

Figure 5. Monolithic stone stairs: examples of step profile –reprinted from Breymann (1885).

Figure 6. Lateral view of the stairs: moulding.

may be identified in the 6 cm trim shown in Figure 5,image 467.

The geometry of the staircases in the interior ofCaffa and Metellino palaces is ascribable to this lasttypology. However, in the examined stairs, the super-position of the shaped steps, regards elements havingtheir edge fixed in the walls for about 20 cm (Fig. 6).

So it can be presumed that those structures, rely-ing on both the housing in the masonry walls and theoverlapping of the steps through the moulding, showa good behaviour in relation to loads applied on them.

According to what specified in the “Traité théoriqueet pratique de l’art de bâtir” (Rondelet, 1802), thebehaviour of the open staircases, that are stairs onlysupported by the moulded shape of the steps, is inde-pendent from the presence of a beam propping up

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Table 1. Geometry of the stone step.

Dimensions

Total height H (m) 0.19Total depth B (m) 0.39Moulding height h (m) 0.05Moulding depth b (m) 0.05Total length (m) 3.4Free span L (m) 3.0

the parapet: “The step chase along the walls andthe landing constraint [at turn of stairs] provide,together with the moulding and the superposition, aningenious system that stands up well without beams. . . [omissis] . . . It is essential observing that in stairswithout beams, when the mouldings are not sufficient,the minimal movement can lead the step to rotate andslide out of the mouldings if: 1st their chase in the wallis not sound, 2nd it does not have a sufficient depth,3rd as a consequence of the movement, the steps failalong their span. The beams added to the stairs, inany way they are built, have the advantage of fixingthe steps at each end, preventing them to slide out ofthe mouldings, being constrained by the wall, on oneside, and by the beam on the other”.

Therefore, from what Rondelet suggested, the gran-ite staircases of Caffa e Metellino palaces are inagreement to the rules of thumb. Moreover, stand-ing that the elements are fixed in the walls on bothsides, the troubles described by Rondelet should bepresumably warded off.

Nevertheless, even if the constructive details arerecommended by ancient rules of thumb, more detailedstudies are needed to enforce that they are effectivefrom the static point of view.

3.2 Geometry of the staircase

The analyses focus on the staircases in the interiorof Caffa and Metellino palaces. Those stairways aremade up of stone monolithic steps and the previ-ously described constructive technique allows theseelements to be linked together. In Figure 7a-b, anoverall view of the staircase is proposed.

The geometry considered for each single step is rep-resentative of the most part of the stone elements. Infact, each flight is sensibly similar in terms of dimen-sions and very low scatter was found by the surveyanalysis of the complete staircases in the two palaces.

On the safe side, the most conservative hypotheseson the geometry were assumed. In Table 1, data of thegeometric model are reported, focusing on the dimen-sions significant for the FEM model; the nomenclatureis in Figure 7c.

The free span of the step results from the detailed in-situ geometric survey, while its total length derives by

Figure 7. Overall view of the staircase (a) top; (b) bottom;(c) Geometric model: lateral view – YZ plane.

a realistic hypothesis (enforced by examples of similarconstructive typology in other case studies) of a 0.2 mdeep insertion in the masonry walls on each side.

This aspect was however a posteriori partially con-firmed by the information obtained by techniciansworking on the building restoration, who directlychecked the considerable chase depth of the stone stepin the walls.

4 EXPERIMENTAL CAMPAIGN

The lack of indications, in current Technical BuildingRules, about the mechanical parameter of monolithicstone elements led to perform detailed experimentaltests.

During renewal works, some slabs, with the sizeof half a step, were found. Some of them were useddirectly for bending destructive test.

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Table 2. Results of compression tests.

Sample Diameter (cm) Length (cm) fc (MPa)

Slab 1/2 7.3 14.6 143.36Slab 2/1 7.3 14.6 109.43Slab 3/1 7.3 14.4 129.98Slab 3/2 7.3 14.7 133.80Slab 3/3 7.3 14.6 138.58C 1 7.3 14.5 96.05C 3 7.3 14.6 99.39M 1 7.3 14.5 100.35M 2 7.3 14.5 110.38

Mean 117.92Standard Deviation 18.485% Percentile 97.39

From the others, we obtained cylindrical samplesthat were used to determine uniaxial compressionstrength, uniaxial tensile strength and density (it turnsout to be 2618 kg/m3).

As well as these partially destructive tests, sclero-metric, direct and indirect ultrasonic tests were carriedout (non-destructive tests).

The extensive experimental campaign aims toobtain a statistical characterization of mechanicalparameters and, possibly, to identify local defects inthe steps.

Considering the age of the structure and the mate-rial, which the stairs are made up of (not commonlyused in modern constructions), this kind of analysiswas considered essential to preserve these attractivebuildings in their original form and, at the same time,to ensure a suitable safety level.

4.1 Test set-up and data processing

For the sake of brevity, in the following, only the teststhat were used to define numerical analysis parame-ters are reported. Setup, data processing and results ofthese tests are described.

4.1.1 Compression testsThe cylindrical samples were subjected to compres-sion test to identify the uniaxial strength. The failurepoint is the loss of proportionality between the constantload increment and the deformation.

In Table 2, uniaxial compression strength, diameterand length for each sample are reported.

4.1.2 Indirect tensile tests (“Brazilian” tests)In order to estimate the ultimate tensile strength, theso-called “Brazilian tests” were performed, accordingto UNI EN 12390-6/2000. These tests are based onthe fact that a cylinder subjected to a line load on twoopposite diameters will break due to the orthogonaltensile strength (Fig. 8).

Figure 8. Test setup according to UNI EN 12390-6/2000.

Table 3. Results of indirect tensile tests.

Sample Diameter (cm) Length (cm) fc (MPa)

Slab 1/1A 7.3 9.2 8.66Slab 1/1B 7.3 8.6 9.36Slab 2/2A 7.3 8.5 8.31Slab 2/2B 7.3 8.0 9.48C 2A 7.3 10.5 7.27C 2B 7.3 8.3 7.99M 3A 7.3 8.6 9.04M 3B 7.3 7.8 8.73

Mean 8.60Standard Deviation 0.745% Percentile 7.52

In Table 3, uniaxial tensile strength, diameter andlength for each sample are shown.

4.1.3 Ultrasonic testsUltrasonic tests provide a measurement for the “timeof flights” of ultrasonic waves in the material. Hypoth-esizing the wave paths, the velocities may be obtained.They were used to verify the structural element homo-geneity, localize possible reduction of material prop-erties (e.g. cracks or cavity) and to estimate the valueof Young’s modulus.

During experimental campaign, two different typeof ultrasonic test were performed: direct test (i.e.receiver and emitter are placed on two opposite sideof the step) and indirect test (i.e. emitter and receiverare placed on the same side of the step).

4.1.3.1 Direct ultrasonic testsDirect tests were carried out near the landing at turnof stairs, where the sensor can be placed on thetwo opposite side of the steps. The resulting velocitywas processed to obtain the p.d.f. (probability den-sity function), as in Figure 9, and to estimate the

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0.0000

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ultrasonic velocity (m/s)

1907 2907 3907 4907 5907

experimental data

lognormal distribution

normal distribution

Figure 9. Probability density function of direct ultrasonicvelocity of Metellino palace.

Figure 10. Indirect ultrasonic test setup.

dynamic Young’s modulus that turns out to be around30,000 MPa (mean value) with modest variability.

4.1.3.2 Indirect ultrasonic testsIndirect ultrasonic tests were performed on every sin-gle step of the two stairways, in order to obtain a wideset of values that may represent a significant statisticalsample.

The “time of flight” was obtained placing thereceiver on the “first column” (the black one in Fig-ure 10) and moving the emitter in the other threedifferent positions on each step.

The processing phase of these tests is a little morecomplex then the direct ultrasonic ones, due to diffi-culty in the estimation of the wave path. For this reason,it was decided to divide the data in three different sets,one for each horizontal distance between the sensor(i.e. 70 cm, 140 cm, 210 cm). In this way, the possibleerror in the path estimation was minimized.

0.0000

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ultrasonic velocity (m/s)

1586 2086 2586 3086 3586 4086 4586

experimental data

lognormal distribution

normal distribution

d = 140 cm

Figure 11. Probability density function of indirect ultra-sonic velocity, sensor distance 140 cm, of Caffa palace.

For each distance, the p.d.f. of the velocity wasobtained (Fig. 11) and the extreme values were ana-lyzed in detail. It results that the state of preservationof the stair is essentially homogeneous.

Thanks to this wide experimental campaign, theresults of the following numerical analyses can be rea-sonably extended to the whole stairways of both thepalaces.

5 NUMERICAL ANALYSES

In order to assess the structural safety of the ancientstone stairways of Caffa and Metellino palaces, a setof numerical simulations, using the code ANSYS rel.8.0, were performed.

The numerical analyses have a double role. On theone hand, they are useful in evaluating stress and strainfields in case of the loads prescribed by the ItalianTechnical Building Rules (2005). On the other hand,these simulations were carried out aiming to assessthe safety coefficient (in terms of load multiplier) withreference to live loads.Those may be due, for example,to crowding.

In order to come through the computational effortrequired, the FEM model simulates an assemblage ofsix steps. Nevertheless, this is representative of theoverall behaviour of one stairway.

In particular, aiming to study the static behaviourof the steps in the middle and at the end of the stair-case, it was checked that adding other elements doesnot influence (conceptually and quantitatively) thebehaviour.

5.1 General description of the FEM model

The numerical simulation, preceded by an exhaus-tive diagnostic campaign and geometrical survey, isparticularly useful when dealing with the historicalheritage.

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Table 4. Element types in the FEM model.

Constitutive element FEM element No.

Stone step SOLID65 33480Interface CONTACT52 1150

In this framework, the development of very accuratemodels is generally required, both in case of serviceloads (for which cracks formation may represent acondition to avoid) and ultimate limit state. In fact,non-linear analyses may give information, by meansof incremental analysis, about the collapse, but themodels should be able to reproduce the limited ten-sile strength and possible crushing of stone material,the frictional behaviour on the contact surface of themoulding.

To this aim, the modelling was carried out througha detailed non-linear solid model of the flights ofsteps, focusing on effectively describe the interfacebehaviour.

Brick elements (SOLID65) are used to model thestone material of the monolithic steps. The frictionalbehavior on the contact-planes (horizontal and verti-cal) of the moulding is simulated by CONTACT52elements.

In Table 4, the basic information about the FEMmodel, made up of 34630 elements and 41124 nodes,are provided.

The boundary conditions of FEM model areintended to simulate two situations, related to differ-ent hyphotesis of interaction between the step and themasonry walls:

– Model A: displacements along Y and Z axes areavoided on the bottom surface of the steps, in corre-spondence of the insertion surface of the step (0.2 min depth) in the wall.This condition aims to simulatestructural fixed ends (Fig. 12).

– Model B: displacements along Y and Z axes areavoided on the bottom of the steps, in correspon-dence of the chase of the step in the wall. A line ofnodes only (0.2 m in distance from each ends of thestep) is constrained, in order to enable the rotation,aiming to simulate structural hinges.

The actual condition is intermediate between theanalysed ones; due to the chase depth in the walls, itis probably better described by Model A.

Moreover, the steps at both ends of the flight needto be realistically constrained. On the bottom one, thevertical support of the masonry arch below (Fig. 7b)and the horizontal constraint of the floor have to besimulated. On the top step, instead, horizontal con-straints are needed to model the interaction of the stepand the landing at turn of stairs, made up of stone slabshaving the same thickness.All this kinds of constraintsbehave obviously as compression-only elements.

Figure 12. FEM model: fixed ends boundary condition.

5.1.1 Mechanical parametersThe pink granite stone mechanical characteristics arederived by the experimental test campaign previouslydescribed.

In the FEM simulations, in the elastic range, a lin-ear isotropic constitutive law was assumed. This kindof behaviour can be appropriate to satisfy the require-ments of the safety check, serviceability and ultimatelimit state, of the Technical Rules (2005).

The values of the mechanical characteristicsassumed correspond to the average of the statisti-cal distribution of each quantity (in case of Young’smodulus E = 30,000 MPa, the value is derived by theexperimental tests on the stone of the Caffa palace).

Moreover, the non-linear behaviour is modelledthrough the CONCRETE model (enclosed in theANSYS 8.0 library), whose constitutive law simulatesthe limited tensile and compressive strength of stonematerial. The failure surface in the stress domain isrepresented by a law that depends on the hydrostaticstress, as Mohr-Coulomb or Drucker-Prager ones.Cracking along three orthogonal axes and crushingare allowed and five failure-surface parameters haveto be assigned. If only two (ft and fc) are set, the failuresurface is defined as in Willam and Warnke (1975).

The non-linear parameters in terms of strengthvalues are obtained as the 5% percentile of the stochas-tic distribution of the experimental results. In themodel, the uniaxial tensile strength is set ft equal to7.52 Mpa for and the uniaxial compressive strength fcto 97.39 Mpa.

The stiffness parameters of the contact elementon the interface of the step moulding are assumedto simulate the interaction effect (equivalent Young’smodulus equal to 30,000 MPa). Being difficult to havean estimation of these quantities, it was verified thattheir variation among a pre-defined range does notsignificatively affect the results.

The frictional coefficient on the contact surface isset equal to 0.5.

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5.2 Scheme of the numerical simulations

Two analysis phases were carried out: in the first one,the load cases prescribed by the technical rules (ulti-mate and serviceability limit state) were imposed and,in the second one, the behaviour related to incrementalloads was studied.

Phase 1: on the two models (A and B), the followinganalyses were performed:

LC1 (ULS): 1.4 Gk + 1.5 Wk1LC2 (SLS): Gk +Wk1

where Gk is the dead load and Wk1 is the live load(equal to 4 kN/m2 in case of common stairs);

– Phase 2: on the two models (A and B), the analysescarried out concerned the monotonic increase oftwo load typologies (uniform pressure on every stepand transversal line load on the central step), afterthe dead load assignment.

It has to be noted that, in case of Phase 1, thebehaviour is very far from the inelastic range; so, itwas verified that the action assignment in two subse-quent stages or the concurrent loading did not lead todifferent results (i.e., the effect superposition is stillcorrect).

In both cases, live loads were assigned to thewalking surface of the steps.

5.3 Analysis results

In the following, the main results obtained from thenumerical simulations are discussed. Special emphasisis put on the evaluation of interaction effects amongthe steps.

5.3.1 Phase 1: technical rule requirementsAs previously noticed, the analyses results may beuseful in order to obtain some information about theserviceability and structural safety of the stairways,according to Italian Technical Building Rules.

In case of SLS, the mid-span vertical displacementis maximum in the central steps of the flight: withreference to Models A and B, it is equal to 0.06 mmand 0.07 mm respectively. Those values are both muchlower than the limit displacement L/400 (7.5 mm).

In case of ULS, the stress field in Model B is higher.The extreme values (in terms of average nodal stresses)are reported in Table 5.

From these results, it can be highlighted that thestress state is much lower than the material strength.This is much more significant if one considers thatthose values are concentrated in very narrow areas,near the constraints: the safety evaluation is amplyconservative.

Focusing the attention on longitudinal sections ofsteps, corrisponding to the portion near the supportsand the mid-span one, interesting remarks about the

Table 5. Values of maximum (σI) and minimum (σIII)principal stresses in Models A and B.

MODEL A MODEL B

σI 1.03 MPa 1.76 MPaσIII 1.88 MPa 2.67 MPa

Figure 13. Model B – USL stress state. Direction ofmaximum (a–b) and minimum (c–d) principal stresses.

structural performance may be obtained (Fig. 13).Checking the direction of minimum principal stressσIII, in the the mid-span section, some sort of strut,due to the transfer of compressive forces through thesteps, may be identified. This phenomenom appears,thanks to the moulding, in both the models. Along the

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Figure 14. Cracking pattern in case of Wk1 = 2 kN/m2:axonometric view from above (a) Model A; (b) Model B.

lateral section near the supports, the behaviour seemsinstead to be more affected by torsional effects.

The strong interaction among the steps of one flight,revelead by the formation of the strut in the numericalsimulations, confirms once more the static intuitionsof the ancient builders and engineers.

5.3.2 Phase 2: incremental analysisAfter the dead load assignment, two load typologies(uniform pressure on every step and transversal lineload on the central step) were monotonically increased.

5.3.2.1 Uniform pressureWith reference to uniform live load, even the nominalaction amplified more than 15 times does not causesignificant damage pattern in the steps. In case of Wk1equal to 72 kN/m2, only slight cracking phenomenadevelop near the supports (Fig. 14).

In both the models, crushing states are not evidentand, in fact, during the loading phase, the principalstress σIII has not reached the surface of the fail-ure domain. The higher obtained values for σIII are12.6 MPa (Model A) and 22.9 MPa (Model B). Even

Figure 15. ModelA, stress state in case of Wk1 = 72 kN/m2:(a) maximum principal stress σI[N/m2]; (b) minimum prin-cipal stress σIII[N/m2].

in this case, the stress peaks are located near theconstraints (Fig. 15).

Observing the failure pattern, it can be noted that,in Model A (as Rondelet wrote), the described con-structive technique leads these elements to be moreeffectively linked together.

The force transfer through the moulding is more evi-dent in respect to the other model, in which the rotationof the ends of the step is allowed. In fact, the lowersteps are more loaded in compression in correspon-dence of the mid-span point than the upper ones; thisforce transfer lead the vertical planes in correspon-dence of the fixed ends to be subjected to high tensilestresses and cracking develops in the lower part of theflight.

Further increase of the uniform pressure is notinvestigated, because the hypothesis of fixed con-straints at the ends of the step (modelling the effectof the masonry walls) would have been not totallycorrect. In fact, higher loads in the masonry could

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Figure 16. Model A – line load. Direction of minimumprincipal stress.

have led to local crushing and stiffness degradationof the supports. This condition has not permitted theinvestigation of the stair behaviour for the highly non-linear range. Nevertheless, this kind of load seems notto affect significantly the safety of the structure.

5.3.2.2 Line loadAssigning the transversal line load on the central step(along X-axis), some information about the non-linearbehaviour modification is achieved.

A final value of 7.5 kN/m is reached, pointing outslight cracking located on the central step itself, nearthe supports.

Also in this case, the highly non-linear range can notbe studied, due to the unrealistic boundary conditionswhich further load increase would have led to.

In ModelA, the force transfer through the mouldingis less evident in respect to the uniform load (Fig. 16).

In the mid-span section, the strut, due to the transferof compressive forces through the steps, is not identi-fiable anymore. Moreover, even the torsion effect nearthe supports cannot be highlighted.

From the result review, one can put forward that thedirection of the minimum principal stress is almostorthogonal to these longitudinal sections. This may beexplained through the creation of a transversal line ofthrust along each single step (especially the loadedone). In this way, the load is directly transferred to thesupports of the step, achieving only partially the overallbehaviour of the stairway. Nevertheless, the lower stepsseem to interact with the loaded one.

6 CONCLUSIONS

The significance of synthesis and comparison of datafrom different ambits, in order to obtain a moredetailed and more realistic overview of the problemof safety and conservation of historical structures isevident.

This study provided an exhaustive investigation ofthe two stone stairways of Caffa and Metellino palaces,having the aim of preserving them without performingany structural intervention.

Combining the elements from the in situ and labo-ratory testing, from the historical studies and from thenumerical simulations, it was demonstrated that theoriginal conception of the granite monolithic stairwaysis amply safe, even in relation the modification of theirend use. So, it is clear that no retrofitting interventionis needed.

On the other hand, the contribution of FEM investi-gations played a fundamental role in achieving anothergoal: by means of non-linear incremental analyses, thestructural effect of an ancient constructive technique(moulding and superposition of the steps of a flight)was examined and understood.

The research confirms that, in this case, the staticperception of ancient builders and engineers is essen-tially validated and it states once more that if a largerpart of the past knowledge would have been trans-ferred, useless (and sometimes harmful) structuralmodifications could be avoided.

REFERENCES

Breymann G.A. 1885. Wooden, stone and brick stairs.Librerie Dedalo (eds.), Rome, 2003 (in Italian).

Bordoni S., Ighina A.G., Tuscano C. 1987. Steel and buildingreuse: The “Darsena” of Genoa, a development design.Busalla, Italsider Publication (in Italian).

de Belidor B.F. 1729. The engineers’ science by de Beli-dor with notes by Mr Navier, Italian translation by LuigiMasieri, Milan, Truffi, 1832 (in Italian).

Franco G. 1995. Halls and staircases in the Genoese Archi-tecture, Book of Architectural technology – Collection byGianni V. Galliani, Grafica KC, Genoa, 1995, p. 126 (inItalian).

Ministry of Infrastructures and Transportation, D.M.14/09/05 – Building Technical Rules. Official Bulletin no.222, 23 September 2005.

Rondelet J. 1802.Traité théorique et pratique de l’art de bâtir.Italian translation by Soresina B., Vol. II, Librerie Dedalo(eds.), Rome, 2004.

Willam K.J., Warnke K.D. 1975. Constitutive model forthe triaxial behaviour of concrete. Proc. of InternationalAssociation for Bridge and Structural Engineering, 19,ISMES, Bergamo, Italy, p. 174.

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