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

Structural analysis of the Caserta Royal Palace timber roof connections

G. Fabbrocino, G. Marcari & C. LaorenzaSchool of Engineering, Structural and Geotechnical Dynamic Laboratory StreGa, University of Molise,Termoli (Cb), Italy

E. CosenzaDepartment of Structural Engineering, University of Naples Federico II, Naples, Italy

ABSTRACT: Preservation of historical structures often includes evaluation of timber roof trusses.According torecent research achievements and European building design codes, connections can play a role in the response oftimber structures, but have paramount relevance for assessment of historical constructions under serviceabilityand ultimate loading conditions. Whenever semi-rigid behaviour of connections is concerned, investigationwithin rotational properties of connections through refined numerical modelling is required. The objective of thepresent paper is to study the response under service loads of typical connections of ancient timber structures, byusing finite element-based modelling. The model is calibrated against experimental and numerical results foundin relevant literature and sensitivity analyses are carried out. An application to different connections of the rooftrusses of the Royal Palace in Caserta is presented.

Finite Element analysis seems to be able to simulate semi-rigid behaviour of joints within the elastic range.Numerical moment-rotation diagrams are calculated for the different connections found on the reference roofstructures as a basic step for the global structural assessment under serviceability loading conditions.

1 INTRODUCTION

Preservation of historical structures often includesevaluation of timber roof trusses. Satisfactory per-formance of existing wood truss system in terms ofboth resistance to applied service loads and long-term response is dependent on wood species, trussproportions and timber connections (Tampone, 2007).Generally, stress concentrations are particularly criti-cal at joints where a component is connected to others,such as those caused by notches (load to angle grain)or other sudden changes in cross section.

This is confirmed by survey and inspections of tim-ber buildings damaged after extreme natural events,which often point out to inadequate connections asthe primary cause of damage (Derinaldis & Tampone,2007). Common connections adopted for modern con-structions can be designed to fit hinge requirements oreven to ensure full stiffness and strength, so that conti-nuity can be assumed at joints. This circumstance doesnot apply to existing and historical wood artefacts areconcerned.

In such cases, connection response can play a rele-vant role both at ultimate and serviceability limit statesof historical timber structures (Branco et al. 2006;Seo et al. 1999) and modern European building codes(prEN 1995).

This means that the level of analysis has tobe enhanced and semi-rigid behaviour of connec-tions properly accounted for. Obviously, this kind ofapproach is by far more complex and requires a thor-ough investigation of the specimens and advancednumerical modelling, being of moderate interest forpractical purposes. The objective of the present paperis to investigate the rotational behaviour under serviceloading conditions of typical joints of historical timbertrusses.

Numerical analyses of the joints have been per-formed using a standard software package used bypractical engineers (http://www.hsh.info). Orthotropicelastic behaviour of wood was accounted, and contactelements friction-based between the timber elementswere considered.

Reference results of the numerical simulations areherein discussed and compared with experimental andnumerical data provided by Parisi et al. (1997) andParisi & Piazza (1995, 1998, 2000).

The model showed the capacity to predict the elasticstiffness of the joints if contact elements are properlysimulated. Calibrated model is used for the numericalinvestigation of the elastic behaviour of the connec-tions of the roof system assemblage of the Royal Palacein Caserta (Italy). It is an interesting case study involv-ing a timber roof truss of the 18th-Century. Some

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Figure 1a. View of the Royal Palace in Caserta, Italy.

Figure 1b. Plan view of the Royal Palace.

critical issues related to modelling of this kind oftimber truss are also discussed.

1.1 The timber roof truss of the Royal Palace inCaserta

The Royal Palace in Caserta is one of the mostfamous historical establishment of the Italian Baroque(Caroselli 1967, Chierici 1984).

It represent a masterpiece of the creative geniusof the Italian architect Luigi Vanvitelli (1700–1773)and it was probably the most representative monu-mental building erected in Europe in the 18th-Century(Figure 1a). Due to its magnificence with its surround-ing natural landscape, the site has been included in theWorld Heritage List by the world Heritage Committeein 1997 (http://whc.unesco.org/en/list/549).

Works started in 1752 and were completed in 1847.The building has a rectangular plan and four closecourtyards which are also rectangular, as schemati-cally reported in Figure 1b. It is 36 metres high and hasfive storeys in addition to the underground level. Theoriginal design drawings of the building can be foundin Vanvitelli, (1756). For the construction of the roofsystem, Vanvitelli has been mainly inspired to the tim-ber roof truss of the Basilica of San Paolo Fuori le Muraerected in Rome in the 4th Century a.C. and rebuild in1824 after a serious and wide damage due to fire.

The timber roof of the Royal Palace is made oftrusses of Chestnut species, span of about 23 metersare found. They are typically 3 meters spaced from

Figure 2. Partial view of the Royal Palace roof truss.

Figure 3. Roof truss of the Royal Palace.

the adjacent trusses. The height of the truss, measured,from the top to the bottom of the main chord is 5.75 m.In Figure 2 the partial view of the roof truss of theRoyal Palace in Caserta is showed.

The roof truss of the Royal Palace is a modifiedversion of the queen post truss type (Izenour, 1992).A schematic drawing of such a truss layout is reportedin Figure 3. It consists of a system of two main raftersand two secondary rafters, two horizontal chordsplaced at two different levels, and inner elementsconnected the top and bottom chord.

The inner elements consist of two diagonal strutssupporting the main rafters, two vertical queen postsand a central king post. The bottom chord is connectedto both the king and the queen posts by using ironstirrups.

The bottom chord and the main rafters have across section 270 × 400 mm, while the lower rafters,

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Figure 4. Connection between king post and main rafters.

Figure 5. Connection between the queen post, the lowerrafter and the top tie.

5.80 m long, have a cross section 270 × 340 mm. Thediagonal struts are 1.20 m long, with dimensions of370 × 300 mm. The upper chord is 9.90 m long, witha cross section of 250 × 370 mm. The angle betweenthe rafter and the chord is 24◦.

Connections between timber elements are birdsmouth type, and present single or double mortise andtenon (Figures 4, 5, 6). Timber roof trusses sit onwood bearing supports named ‘gattone’, which arefrequently found in historical buildings (Figure 3). Inaddition, the truss heels were designed without anyoverhang. A binding stirrup was used to improve theresistance of the connection between the main rafter,the lower rafter, the bottom chord, and the ‘gattone’,as showed in Figure 6. The main and the second rafterwere connected by iron stirrups bolted to the elementsand placed at the upper end of the secondary rafter.A system of purlins spaced 1.35 meters and raftersplaced on the top of the purlins, was used as supportof the laths and roofing tiles.

Timber truss structure of the Royal Palace was builtaccording to traditional methods and old construction

Figure 6. Connection between the rafters and the mainchord.

Figure 7. Details of a timber truss from an ancient construc-tion manual (Belidor, 1739).

rules that have been found by an extensive literaturereview (Emy 1842, Mésange 1754; Belidor 1739).Figure 7 reports an example of design and constructiondetails of a timber truss derived from ancient manuals.It is worth noting that truss elements have a cross sec-tion ratio B/H = 0.675 very close to the typical rangeB/H = (5/6 ÷ 3/4) suggested by many authors for tim-ber beam elements (Belidor 1739, Blondel 1771). Inaddition, Blondel (1771) suggested to calculate theheight of the cross section of the elements as H = 4

√L,

where L is the length of the element measured in foot,while B is the base equal to L/2. Conversion can beobtained using the metric conversion chart providedby Rondelet (1802). In this case, an underestima-tion of the cross dimensions is observed, in fact the

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cross section ratios of the elements averaged the valueB/H = 0.50.

At present time, timber trusses are characterisedby different types and stages of degradation basicallydue to environmental factors, lack of maintenance,and effects of repeated interventions. Visual inspec-tions revealed confined damaged areas due to frequentexposure to rapid changes in moisture content, orto fungal attack. However, in any case the state ofconservation lead to a loss of serviceability of thewhole roof structure (Ceraldi & Russo Ermolli, 2006).These problems were already detected in the past,and different interventions were performed. In fact,besides the partial replacement of the covering sys-tem (including the purlins), the trusses were subjectedto repeated replacement of members and/or part ofmembers. In particular, the original heels, rafters, kingpost and truss supports were frequently replaced withnew species of timber elements, which exihibited amechanical properties degradation due to the absenceof specific protection from moisture and biologicalattacks.This circumstances lead to a variability of stiff-ness and strength properties of wood truss members,which influence the structural response at global level.

2 MODELING OF CONNECTIONS

2.1 Calibration of the finite element model

In the following, results of finite element (FE) anal-yses performed on a typical birdsmouth connectionof Chestnut wood specie, are presented. In partic-ular, calibration of FE model is performed on thebase of available data which can be found in therelevant literature (Parisi et al. 1997, and Parisi &Piazza 1995, 1998, 2000). In this work, the connec-tion behaviour is simulated with the use of the FEsoftware package STRAUS7 (1999), and results areinvestigated in terms of both force-displacement andmoment-rotation diagrams.

The geometric dimensions of the both main rafterand chord were: length of the elements L = 1.90 m; ele-ment cross section 190 × 225 mm and 200 × 200 mm,skew angle equal to 30◦; rafter cross section notchdepth tv = 35 mm and notch length lv = 200 mm.

Two loading pattern were considered. The first oneconsisted of a vertical pressure uniformly distributedat the free end of the rafter; subsequently a trans-verse force was applied perpendicular to the axis ofthe rafter. The second one consisted of an initial axialpressure uniformly distributed over the cross sectionof the rafter; from this, a linear pressure distributionover the cross section of the element was applied inorder to simulate a bending moment at the end of therafter. With reference to the axial compression stressin the rafter, two values were accounted: fwr equal to1.0 MPa and 1.5 MPa, respectively. These stress werekept constant during the analysis.

Conventionally, transverse force, moment and rota-tions have been assumed positive as the skew anglewas reduced. The main chord of the joint was con-strained in the vertical displacements at the base, andin the horizontal displacements at the vertical right-side border. A structured mesh is used for the rafterand the chord, whereas an irregular transition mesh isused in the vicinity of the connection between rafterand chord.

It is worth noting that wood exhibits anisotropicelastic and inelastic behaviour, and the characteris-tic inner structure which include several defects (e.g.knots, slope grain). The use of refined non linearorthotropic criteria is essential for detailed numericalsimulations of timber joint, since different strengthsand softening/hardening characteristics in orthogonaldirections can be accounted (Lourenço et al. 2007,1997).

For the purposes of the paper, an elastic orthotropicmodel is accounted for wood elements (Parisi & Piazza2000; Bodig & Jayne 1982). Strengths and elasticmaterials properties have been derived from availabletests given in Parisi & Piazza (2000) and representaverage values.

In order to properly fit elastic properties for thewood members, which are characterized by differentgrain directions, a local coordinate system was intro-duced.The 1-axis and 2-axis are related to the directionparallel and perpendicular to the grain, respectively;the 3-axis is orthogonal to the 1–2 plane.

Therefore, the elastic parameters included the elas-tic moduli E1 = 9200 MPa and E2 = 310 MPa par-allel and orthogonal to the grain, respectively; theshear modulus G12 = 580 MPa and the Poisson’s ratiov12 = 0.4. Nonlinearities were concentrated at thecontact interfaces.

The rafter and the tie were connected by pointcontact elements which allowed relative tangentialdisplacements of facing surfaces and limited normaldisplacements. In particular, the Normal type contactimplemented in STRAUS7 was used, which providesstiffness in compression and not in tension. In addition,a friction coefficient was introduced in order to con-trol the amount of lateral force that can be transferredthorough the contact surface.

Let α the angle between the horizontal direction andthe normal of the contact, the axial elastic stiffness ofthe contact elements has been estimated as EαA/L,where A is the area of influence of each point con-tact, L is the distance between the rafter and the chord(1 mm) and Eα is the elastic modulus at the angle α.The modulus Eα is calculated for each contact by tak-ing into account the elastic moduli E1 and E2 of thetimber elements as follows (Lekhnitsii 1968):

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Figure 8. Finite element mesh and boundary conditions.

In the following, the contacts are named as con-tact#1 and contact#2. Equation (1) gives: Eα1 =1710 MPa, and Eα2 = 320 MPa, for contact#1 andcontact#2 respectively, and for cross section dimen-sions of 190 × 225 mm. The axial stiffness of theinner point contacts were: Eα1A1/L = 1943 kN/mm;Eα2A2/L = 728 kN/mm; for the contact points atthe end of each contact were Eα1A1/L = 971 kN/mm;Eα2A2/L = 364 kN/mm.

For cross section dimensions of 200 × 200 mm,Eα1 = 2209 MPa, and Eα2 = 416 MPa, for con-tact#1 and contact#2, respectively, are obtained. Theaxial stiffness of the inner point contacts were:Eα1A1/L = 1116 kN/mm; Eα2A2/L = 558 kN/mm; forthe contact points at the end of each contact wereEα1A1/L = 445 kN/mm; Eα2A2/L = 223 kN/mm.

The study included two values of the compressionstress in the rafter, fwr = 1.0 MPa and 1.5 MPa, respec-tively. It is worth noting that self-weight of the woodelements is considered in the analyses.

The Modified Newton-Raphson algorithm was usedin the incremental iterative solution of the nonlin-ear problem. Figure 8 shows the finite element mesh,including loading and boundary conditions of themodel.

2.2 Numerical results

Numerical results are showed in Figures 9–10 in termsof nodal force-displacement diagrams with referenceto the cross section members 190 × 225 mm, and inFigure 11 in terms of moment-rotation diagrams for across section members 200 × 200 mm.

In addition, comparisons against both experimentaland numerical reference curves provided by Parisi &Piazza (2000) are carried out. It is worth noting thatthe nonlinear behaviour of the numerical responseoccurred as the limit conditions of friction resistancewere attained and the rafter started to rotate. However,numerical results have to be considered up to the elasticlimit.

As shown in Figures 9 and 10, major differencesbetween experimental and numerical results are foundin the case of low axial stress. For a compression stress

0

1

2

3

4

5

6

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0 0.6 1.2 1.8 2.4 3

Experimental curve

Parisi & Piazza (2000)

STRAUS7

Force [kN]

Displacement [mm]

Figure 9. Comparisons between numerical andexperimental force-displacement curves for rafter190 × 225 mm under fwr = 1.0 MPa.

0

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2

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9

10

0 0.6 1.2 1.8 2.4 3 3.6 4.2

Experimental curve

Parisi & Piazza (2000)

STRAUS7

Force [kN]

Displacement [mm]

Figure 10. Comparisons between numerical andexperimental force-displacement curves for rafter190 × 225 mm under fwr = 1.5 MPa.

in the rafter of 1.0 MPa, the linear trend was followedup to about a transverse load of 1.6 kN, which is about30% higher than the experimental value (Figure 9). Asthe rafter compression level increases (e.g. 1.5 MPa),the linear trend was followed up to a transverse loadof 1.2 kN, and resulted very close to the experimentalvalue (Figure 10).

Again, differences between numerical and exper-imental diagrams in terms of initial stiffness arefound for low axial compressive stress (e.g. 1.0 MPa),because of the regularity in the numerical representa-tion of the facing surfaces, which contrasts the realityof hand-sawn indentations. This may explain also thebetter agreement of results for higher compression val-ues (e.g. 1.5 MPa), that partially mitigate effects oflocal irregularities before that rotation of the rafter wasexperienced.

Results in terms of moment vs rotation curvesfor joint members are illustrated in Figure 11 foraxial stress levels in the rafter equal to fwr = 1.0 MPaand 1.5 MPa. It can be observed that the numericalresponse is in good agreement with those provided byParisi & Piazza (2000). Besides, the rotational elasticstiffness is not affected by the rafter axial compres-sion level, in accordance with the reference FE model.

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0

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0.0015

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0 0.5 1 1.5 2 2.5 3 3.5

STRAUS7 (1.0 MPa)Parisi & Piazza (2000) - 1.0 MPaSTRAUS7 (1.5 MPa)Parisi & Piazza (2000) - 1.5 Mpa

Moment [kNm]

Rotation [rad]

Figure 11. Comparisons of moment vs rotation curvesfor joint members 200 × 200 mm for fwr = 1.0 MPa andfwr = 1.5 MPa.

Figure 12. Contour of the compressive stress along the grain(values in N/mm2). Rafter 200 × 200 mm – fwr = 1.5 MPa.

A sketch of the principal compressive stresses is plot-ted in Figure 12, where the compressed zone are dueto the rotation mechanism of the joint.

2.3 Sensitivity analysis

A key point related to the reliability of numerical anal-ysis is to know the influence of material data on thestructural response.A sensitivity analysis of the resultsdepending on the friction coefficient and the compres-sive level fwr in the rafter is herein presented. Themodel sensitivity with respect to the material parame-ters and the skew angle have been also assessed, but notreported herein for sake of brevity. The sensitivity ofthe analysis with respect of the compressive strengthin the rafter has been illustrated in Figure 11.

A comparisons in terms of friction coefficient isgiven in Figure 13 with reference to a rafter crosssection 200 × 200 mm. In particular, two values ofthe friction coefficient were accounted: µ = 0.3 andµ = 0.4.

Figure 13 illustrates results in terms of moment-rotation plots. From Figure 11 it can be observed thatvariation of fwr did not alter the response of the plainjoint in the elastic part (rotational stiffness remainsalmost identical). Increase of friction factorµ results in

0

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0.0025

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0 0.8 1.6 2.4 3.2 4 4.8 5.6

µ=0.3

µ=0.4

Moment [kNm]

Rotation [rad]

Figure 13. Results of sensitivity analysis for µ= 0.3 andµ= 0.4 for joint members 200 × 200 mm – fwr = 1.5 MPa.

an increase of the slope of the first part of the responseof about +10% (Figure 13).

2.4 Connections of the Royal Palace in Caserta

In the present section, numerical analyses of the jointsof the timber truss of the Royal Palace in Caserta arepresented. In particular, the behaviour of connectionswas investigated by using the calibrate model abovediscussed. The analyses accounted the joints between:the rafters and the main chord, the king post and therafter, the diagonal strut and the rafter, the diagonalstrut and the king post. Due to the lack of experimentaldata, the Chestnut wood class C30 is used for jointelements in compliance to prEN 338 standard (1985).

The constitutive law of the wood elements wasreproduced according to an orthotropic elasticityapproximation. Mean values of the elastic Young’s moduli parallel and orthogonal to the grain wereE1 = 10000 MPa and E2 = 640 MPa, respectively. Inaddition the shear modulus G12 = 600 MPa and thePoisson’s coefficient υ12 = 0.4 have been assumed.Proper boundary conditions were considered and con-tact points type Normal are used to model the interfacebetween the truss elements. The elastic stiffness ofeach contact element was estimated as EA/L, in accor-dance with Equation (1). In addition, a value of µ = 0.4is assumed.

In this work, any interaction mechanism betweenthe main and secondary rafters has been accountedfor. It is worth noting that for accurate evaluation ofdeformation behaviour of the joint, the partial com-posite action between the rafters should be properlymodeled. Conversely, the effect of the metal stirrupat the truss heel has been included in the finite ele-ment model by using a set of linear spring elements.The spring elements were placed diagonally with thechord grain direction (1-axis) within the joint, and theirstiffness was derived based on formulation availablein literature (Gelfi et al. 1998). The analyses were car-ried out under plane stress conditions and the Modified

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0 0.5 1 1.5 2 2.5 3 3.5

Diagonal strut and king post

Diagonal strut and rafter

Rafters and main chord

Main rafter and king post

Moment [kNm]

Rotation [rad]

Figure 14. Rotational response of the connection betweenthe rafters and the chord.

Newton-Raphson iteration method was used iterativealgorithm.

Long-term behaviour and moisture content of woodelements were taken into account in a simplifiedmanner. In fact, modification factors were used toreduce the mean elastic moduli to account for long-term behaviour and the effects of moisture contentof wood elements, in accordance with technical lit-erature (Giordano, 1999) and relevant building codes(EC5, 1995). Joint between the main chord and therafters are characterized by a double tenon and mor-tise, see Figure 6; the other joints have a single tenonand mortise (Figure 4 and 5). Values of elastic stiffnessof the interface elements were calculated according toEquation (1).

The loading scheme consisted of an initial axialcompressive force applied at the upper edge of themain rafter, which was derived from the elastic anal-ysis of the whole truss structure. In addition, a lineardistribution of pressure load was applied over the upperedge of both rafters which generated a positive bendingmoment in the joint. The behaviour of the connectionsis reported in Figure 14 in terms of moment vs rotationscurves.

As the rafters-chord connection is considered, theglobal stiffness of the joint increased after a first partof the response. This circumstance can be related tothe loading sequence, that basically reflects the instal-lation process. In fact, during the application of theaxial force in the rafter, the contact elements at thejoint are firstly engaged and give an initial stress andstrain distribution. The subsequent bending momentapplied at the edge of the rafter, forcing the skewangle to decrease, interacts with contact elements andgenerates the observed non linear behaviour.

This trend was also detected for the joints betweenthe diagonal strut and the king post, and between themain rafter and the king post. With reference tothe initial linear branch, an estimation of the initialstiffness can be carried out: 1700 kNm/rad for rafters-chord joint; 5000 kNm/rad for main rafter-king post

Figure 15. Contour of the compressive stress along the grain(values in N/mm2).

joint; 2900 kNm/rad for diagonal strut-rafter joint;2800 kNm/rad for diagonal strut-king post joint.

Therefore the elastic behaviour of the joint betweenthe rafters and the chord was influenced significantlyby the stiffness of the metal stirrup. In fact, the mod-elling of the metal stirrup ensured the engagement ofthe contact elements between the joint elements in the

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elastic phase, as demonstrated by deformed mesh inFigure 15 (a).

Contours of compressive stress in the 1-axis direc-tion are also plotted up to the elastic limit value ofrotation for each connection. It is easy to recognise aconcentration of stresses at the right end of the carvingin the chord.

3 CONCLUSIONS

The present paper dealt with the structural responseof historical wooden trusses present in historical con-structions. In particular, stiffness and moment-rotationperformances of connections surveyed on the roof ofthe Royal Palace in Caserta, Italy have been studied byFEM numerical analyses. An advanced, but common,numerical tool has been used to explore the capabil-ities of general purposes program for assessment ofhistorical trusses under serviceability loads.

Model has been preliminarily calibrated againstnumerical and experimental data available in techni-cal literature. Satisfactory results have been found, sothat relevant information for real application have beenderived for a variety of connections found in CasertaRoyal Palace.

Obviously, results are not comprehensive, but repre-sent an initial and crucial step for the global structuralassessment of roof trusses using advanced non linearnumerical tools.

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