Robustness Analysis of Historical Timber Roofs: A Case Study of the Gaggiandre Shipyard at the Arsenale of Venice

Francesca Ferretti; Luca Pozza; Diego Alejandro Talledo

doi:10.3390/buildings12111773

Robustness Analysis of Historical Timber Roofs: A Case Study of the Gaggiandre Shipyard at the Arsenale of Venice

Ferretti, Francesca;Pozza, Luca;Talledo, Diego Alejandro 2022-10-22 00:00:00 buildings Article Robustness Analysis of Historical Timber Roofs: A Case Study of the Gaggiandre Shipyard at the Arsenale of Venice 1 1 , 2 Francesca Ferretti , Luca Pozza * and Diego Alejandro Talledo Department of Civil, Chemical, Environmental and Materials Engineering, University of Bologna, Viale Risorgimento 2, 40136 Bologna, Italy Department of Architecture and Arts, University IUAV of Venice, Dorsoduro 2206, 30123 Venezia, Italy * Correspondence: luca.pozza2@unibo.it Abstract: In this work, a deterministic approach is adopted to analyze the robustness of the timber roof of the Gaggiandre shipyard at the Arsenale of Venice. The capacity of the traditional timber truss to withstand the design loads as a result of the damage in the strut-tie node is evaluated according to the alternative load path method. Two layouts of the trusses are analyzed and compared: before and after the Austrian retroﬁtting intervention, performed in the late 1800s. For both conﬁgurations, robustness analyses are carried out by using linear 2D numerical models that consider the effective rotational capacity of the structural nodes in relation to the construction methods of the timber joints. For the conﬁguration subject to the 19th-century restoration, the 3D response of the roof is also analyzed to verify the additional contribution provided by the longitudinal bracing system to the activation of alternative load paths (bridge effect). The results obtained with the different analyses are thoroughly evaluated, providing an indication of the deterministic robustness index of the rooﬁng system based on different assumptions. The outcomes of this work allow to draw some general considerations on the method that could be used for the robustness assessment of historical wood systems. Citation: Ferretti, F.; Pozza, L.; Keywords: timber truss systems; historical buildings; robustness analysis; numerical modeling Talledo, D.A. Robustness Analysis of Historical Timber Roofs: A Case Study of the Gaggiandre Shipyard at the Arsenale of Venice. Buildings 1. Introduction 2022, 12, 1773. https://doi.org/ Robustness against an accidental action, as reported by the CNR Italian Guidelines [1], 10.3390/buildings12111773 indicates the ability of a structure to avoid damages disproportionate to the entity of the Academic Editor: Wen-Shao Chang action which causes an initial damage. The robustness assessment of large span timber roofs is usually performed on newly built roofs to evaluate the effect of local damage to structural Received: 6 July 2022 joints or elements [2,3]. The methodologies available for the implementation of these Accepted: 20 October 2022 assessments on new structures are well deﬁned and consolidated in design practice [1,4,5]. Published: 22 October 2022 Otherwise, the robustness assessment of historical large span roofs requires speciﬁc in- Publisher’s Note: MDPI stays neutral depth studies and a different methodological approach that has not yet been codiﬁed and with regard to jurisdictional claims in deﬁned in the literature. In fact, it is necessary to acquire an adequate level of knowledge published maps and institutional afﬁl- of the structure [6,7], in particular with reference to reinforcement and consolidation iations. interventions that the structure has undergone during its life as they could signiﬁcantly affect the structural response. In addition, the evaluation of geometry, acting loads, and material properties is more difﬁcult than for new structures, with signiﬁcant implications on the reliability of the analyses, e.g., Ref. [8]. Copyright: © 2022 by the authors. The present paper proposes a simpliﬁed procedure to assess the robustness character- Licensee MDPI, Basel, Switzerland. istics of existing timber roof structures, belonging to cultural heritage, which could provide This article is an open access article a basis for developing an engineer-oriented method to be used in robustness analyses. distributed under the terms and This approach is applied to the very challenging case study represented by the roof conditions of the Creative Commons structure of the Gaggiandre shipyard in Venice. It consists of two very long sheds, called Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ “Tezoni”, built between 1568 and 1573 by Sansovino and belonging to the complex “Ar- 4.0/). senale” in Venice, which was the hub of the naval industry of Venice since the beginning Buildings 2022, 12, 1773. https://doi.org/10.3390/buildings12111773 https://www.mdpi.com/journal/buildings Buildings 2022, 12, x FOR PEER REVIEW 2 of 16 This approach is applied to the very challenging case study represented by the roof structure of the Gaggiandre shipyard in Venice. It consists of two very long sheds, called “Tezoni”, built between 1568 and 1573 by Sansovino and belonging to the complex “Ar- senale” in Venice, which was the hub of the naval industry of Venice since the beginning of the XII century [9,10]. The Arsenale of Venice is a huge complex of docks and sheds, subject to several restoration and strengthening interventions in the past, performed mainly due to changes in the use of the buildings over the centuries or, more recently, due to material degradation phenomena and damages caused by the lack of maintenance of Buildings 2022, 12, 1773 2 of 15 the complex [11]. For the robustness assessments, a deterministic approach is adopted [5,12] aiming to estimate the ability of the roof to withstand the design loads after the damage of some key of the XII century [9,10]. The Arsenale of Venice is a huge complex of docks and sheds, structural nodes, according to the Alternative Load Path (ALP) method. The assessments subject to several restoration and strengthening interventions in the past, performed mainly are performed with numerical models capable of considering the actual rotational capac- due to changes in the use of the buildings over the centuries or, more recently, due to ity of the structural nodes in relation to building procedures of the timber carpentry joints. material degradation phenomena and damages caused by the lack of maintenance of the In this study, the robustness of the roof is evaluated for two layouts of the trusses: complex [11]. the original version and the one subject to Austrian retrofitting works, performed at the For the robustness assessments, a deterministic approach is adopted [5,12] aiming to end of the 1800s. In both configurations, reference is made to the response of the single estimate the ability of the roof to withstand the design loads after the damage of some key truss in its own plane. For the retrofitted case, the 3D system of the entire roof is also structural nodes, according to the Alternative Load Path (ALP) method. The assessments considered. The analysis of the obtained results allows us to understand the effects of the are performed with numerical models capable of considering the actual rotational capacity 19th-century restoration interventions on the robustness of both the truss and the entire of the structural nodes in relation to building procedures of the timber carpentry joints. roof, and to define scenarios and configurations to be analyzed with more refined meth- In this study, the robustness of the roof is evaluated for two layouts of the trusses: the ods to perform probabilistic robustness assessments. original version and the one subject to Austrian retroﬁtting works, performed at the end of the 1800s. In both conﬁgurations, reference is made to the response of the single truss in 2. The Gaggiandre Shipyard its own plane. For the retroﬁtted case, the 3D system of the entire roof is also considered. In the 16th century, the shipbuilding activity in Venice was concentrated in the Ar- The analysis of the obtained results allows us to understand the effects of the 19th-century senale area. The need of the Venetian Senate was to guarantee the regular navigation of restoration interventions on the robustness of both the truss and the entire roof, and to the merchant ships by establishing a shipyard aimed at the construction of Galleys. Dur- deﬁne scenarios and conﬁgurations to be analyzed with more reﬁned methods to perform ing the expansions of the Arsenale Novissimo, Jacopo Sansovino was the builder of the probabilistic robustness assessments. dry dock called “Gaggiandre” (Figure 1). The Gaggiandre (or Gagiandre) are “two aquatic 2. The Gaggiandre Shipyard canopies–only built out of a planned series of three–constituting one of the most signifi- cant achievements of the vast sixteenth-century expansion undergone by the Arsenale of In the 16th century, the shipbuilding activity in Venice was concentrated in the Arse- Venice” [13]. nale area. The need of the Venetian Senate was to guarantee the regular navigation of the The roof of the Gaggiandre shipyard, supported by continuous clay brick masonry merchant ships by establishing a shipyard aimed at the construction of Galleys. During walls, consists of a series of composite type timber trusses, with a length of about 25 m, the expansions of the Arsenale Novissimo, Jacopo Sansovino was the builder of the dry which are among the largest of the 16th century (Figure 2). Figure 3 shows some construc- dock called “Gaggiandre” (Figure 1). The Gaggiandre (or Gagiandre) are “two aquatic tion details of the roof, i.e., the suspension of the tie element (Figure 3a) and detail of the canopies–only built out of a planned series of three–constituting one of the most signiﬁ- cant suppo achievements rt of the truss of othe n th vast e ma sixteenth-ce sonry, realiz ntury ed wiexpansion th a stone ca under ntilev gone er an by d ba the rbArsenale ican (Figure of V 3 enice” b). [13]. Figure 1. The Gaggiandre shipyard, Venice (from Google Earth). Figure 1. The Gaggiandre shipyard, Venice (from Google Earth). The roof of the Gaggiandre shipyard, supported by continuous clay brick masonry walls, consists of a series of composite type timber trusses, with a length of about 25 m, which are among the largest of the 16th century (Figure 2). Figure 3 shows some con- struction details of the roof, i.e., the suspension of the tie element (Figure 3a) and detail of the support of the truss on the masonry, realized with a stone cantilever and barbican (Figure 3b). Buildings 2022, 12, 1773 3 of 15 Buildings 2022, 12, x FOR PEER REVIEW 3 of 16 Buildings 2022, 12, x FOR PEER REVIEW 3 of 16 Buildings 2022, 12, x FOR PEER REVIEW 3 of 16 Figure 2. Bottom view of the roof. Figure 2. Bottom view of the roof. Figure 2. BottomFig view ureof 2. the Botr tom v oof. iew of the roof. (a) (b) (a) (b) (a) (b) Figure 3. Construction details of the roof: (a) suspension of the tie element; (b) support on the ma- Figure 3. Construction details of the roof: (a) suspension of the tie element; (b) support on the ma- Figure 3. Construction details of the roof: (a) suspension of the tie element; (b) support on the ma- Figure 3. Construction details of the roof: (a) suspension of the tie element; (b) support on the sonry by a stone cantilever and barbican. sonry by a stone cantilever and barbican. sonry by a stone cantilever and barbican. masonry by a stone cantilever and barbican. 2.1. Historical Evolution of the Gaggiandre Roof Structure 2.1. Historical Evolution of the Gaggiandre Roof Structure 2.1. Historical Evolution of the Gaggiandre Roof Structure 2.1. Historical Evolution of the Gaggiandre Roof Structure The current co The nfigura curre tio nn t co ofn th figura e tru ti ss on es oo f fth th e e tru Ga ss ges gia o n f d tre he roo Gag f gi isa th nd e re re roo sult f is of th the e result of the The current conﬁguration of the trusses of the Gaggiandre roof is the result of the 19th- The current configuration of the trusses of the Gaggiandre roof is the result of the th th 19 -century sta 19 tic r -ce est ntury sta orationtic r s, cae rr stied ora ti out by ons, ca A rr uied stria on ut by soldier Aus f stria or n st so ruc ldier tura s f l o st r re stn ruc gth tura en-l strengthen- th century static restorations, carried out by Austrian soldiers for structural strengthening 19 -century static restorations, carried out by Austrian soldiers for structural strengthen- ing purposes, as thoroughly described in Ref. [13]. In more detail, the original truss was ing purposes, as thoroughly described in Ref. [13]. In more detail, the original truss was purposes, as thoroughly described in Ref. [13]. In more detail, the original truss was ing purposes, as thoroughly described in Ref. [13]. In more detail, the original truss was reinforced by adding a trapezoid system consisting of lateral King Posts, Struts, and a reinforced by adding a trapezoid system consisting of lateral King Posts, Struts, and a reinforced by adding a trapezoid system consisting of lateral King Posts, Struts, and a reinforced by adding a trapezoid system consisting of lateral King Posts, Struts, and a Horizontal Strut. Figure 4 shows the scheme of the composed truss, highlighting the orig- Horizontal Strut. Figure 4 shows the scheme of the composed truss, highlighting the orig- Horizontal Strut. Figure 4 shows the scheme of the composed truss, highlighting the Horizontal Strut. Figure 4 shows the scheme of the composed truss, highlighting the orig- inal configuration and the structural elements added during the restoration. These inter- inal configuration and the structural elements added during the restoration. These inter- original conﬁguration and the structural elements added during the restoration. These inal configuration and the structural elements added during the restoration. These inter- ventions have significantly modified the static scheme in the plane of the truss, adding a ventions have significantly modified the static scheme in the plane of the truss, adding a interventions have signiﬁcantly modiﬁed the static scheme in the plane of the truss, adding a ventions have significantly modified the static scheme in the plane of the truss, adding a reinforcement substructure and modifying some structural nodes typical of the construc- rre einfor infocement rcement sub substr st uctur ructure e and and modifying modifyinsome g som str e st uctural ructura nodes l nodtypical es typica ofl of the t constr he con uction struc- reinforcement substructure and modifying some structural nodes typical of the construc- tion methods of Venetian timber carpentry. Furthermore, globally, a system of diagonal methods tion metof hoV denet s of ian Ven timber etian ti carpentry mber carp . Furthermor entry. Furte, her globally more, ,gl ao system bally, a of sy diagonal stem of r d ods iago has nal tion methods of Venetian timber carpentry. Furthermore, globally, a system of diagonal rods has been introduced, which stabilizes the trusses out of their plane and connects them been rods intr has oduced, been introduce which stabilizes d, which the stabili trusses zes th out e truss of their es out plane of thand eir pla connects ne and them conne together cts them , rods has been introduced, which stabilizes the trusses out of their plane and connects them together, serving as a transverse bracing system (Figure 5). serving together as , ser a transverse ving as a tra bracing nsverse system bracin (Figur g syst eem ( 5). Figure 5). together, serving as a transverse bracing system (Figure 5). Figure 4. Schematization of the retrofitting intervention. Figure 4. Schematization of the retrofitting intervention. Figure 4. Schematization of the retroﬁtting intervention. Figure 4. Schematization of the retrofitting intervention. Buildings 2022, 12, x FOR PEER REVIEW 4 of 16 Buildings Buildings 2022 202,212 , 12 , 1773 , x FOR PEER REVIEW 4 4 of of 15 16 Figure 5. Detail of the transverse bracing system of the Gaggiandre roof. With regard to the 19th-century interventions, it is noted that the dimensions of the cross section of the elements belonging to the reinforcement system are not consistent with those of the original elements, which respected the unit of measurement of the V enetian foot (equal to 34.77 cm). Figure 5. Detail of the transverse bracing system of the Gaggiandre roof. Figure 5. Detail of the transverse bracing system of the Gaggiandre roof. The most significant change made with the retrofitting interventions is the one that involved W ith the rele egar md ent to s the calle 19th-century d King Posts: interventions, in the originait l sch is noted eme, th that esethe were dimensions connected of to the With regard to the 19th-century interventions, it is noted that the dimensions of the the cr ties, oss section most likely of the usi elements ng wrapping belonging tie or to spec theia reinfor l joints cement . Curresystem ntly, the arK e inot ng Po consistent sts appewith ar cross section of the elements belonging to the reinforcement system are not consistent with those of the original elements, which respected the unit of measurement of the Venetian to be detached from the ties, giving rise to an open King Post-tie connection (Figure 6). those of the original elements, which respected the unit of measurement of the Venetian foot (equal to 34.77 cm). Furthermore, the addition of the lateral struts has halved the span of the lower struts foot (equal to 34.77 cm). The most signiﬁcant change made with the retroﬁtting interventions is the one that by significantly reducing the bending action as well as the effective length with reference The most significant change made with the retrofitting interventions is the one that involved the elements called King Posts: in the original scheme, these were connected to to the buckling phenomenon in the vertical plane of the truss. The tie in the centerline involved the elements called King Posts: in the original scheme, these were connected to the ties, most likely using wrapping tie or special joints. Currently, the King Posts appear turns out to be supported by a metal tie rod, connected to the central King Post. the ties, most likely using wrapping tie or special joints. Currently, the King Posts appear to be detached from the ties, giving rise to an open King Post-tie connection (Figure 6). to be detached from the ties, giving rise to an open King Post-tie connection (Figure 6). Furthermore, the addition of the lateral struts has halved the span of the lower struts by significantly reducing the bending action as well as the effective length with reference to the buckling phenomenon in the vertical plane of the truss. The tie in the centerline turns out to be supported by a metal tie rod, connected to the central King Post. (a) (b) Figure 6. King Post–bottom tie joint configuration: (a) original (closed connection type); (b) after Figure 6. King Post–bottom tie joint conﬁguration: (a) original (closed connection type); (b) after retrofitting intervention (open connection type). retroﬁtting intervention (open connection type). Furthermore, the addition of the lateral struts has halved the span of the lower struts 2.2. Geometric Configuration by signiﬁcantly reducing the bending action as well as the effective length with reference to (a) (b) The two roofs belonging to the Gaggiandre shipyard consist of a truss structure, with the buckling phenomenon in the vertical plane of the truss. The tie in the centerline turns a spa Fig nure appr 6. o Kxim ing P ately e ost–bo q tt ua om l to tie 2 joi 5 n m t ,c m ona fid ge ura oft io stn ruts : (a) , or ties ig, in aan l d (c lo Kin sed g Po cons n ts ec . tThe ion td ype); ime n (b si ) o an fts er out to be supported by a metal tie rod, connected to the central King Post. of th ret e rst ofruc ittin tura g intl er ele ven m tents ion (open that c com onnec po tio se nth tye pe) tru . ss are reported in Table 1 and follow the ancient Venetian measure called foot, “piede”, which corresponds to 34.77 cm and repre- 2.2. Geometric Conﬁguration 2.2. Geometric Configuration sents the main reference measure of the time. In fact, the tie, the four struts, and the King The two roofs belonging to the Gaggiandre shipyard consist of a truss structure, with a Posts have a section of about one foot by ¾ foot. The bottom tie is divided into three seg- The two roofs belonging to the Gaggiandre shipyard consist of a truss structure, with span approximately equal to 25 m, made of struts, ties, and King Posts. The dimensions of ments joined by particular double step nodes named “Dardo di Giove”. The angle be- a span approximately equal to 25 m, made of struts, ties, and King Posts. The dimensions the structural elements that compose the truss are reported in Table 1 and follow the ancient tween the strut and the bottom tie is equal to 24° with a truss height of about 5 m. The of the structural elements that compose the truss are reported in Table 1 and follow the Venetian measure called foot, “piede”, which corresponds to 34.77 cm and represents the length of the truss elements is reported in Figure 7 both for the original and the retrofitted ancient Venetian measure called foot, “piede”, which corresponds to 34.77 cm and repre- main reference measure of the time. In fact, the tie, the four struts, and the King Posts configuration. The spacing between the trusses is variable, ranging from 206 to 210 cm, sents the main reference measure of the time. In fact, the tie, the four struts, and the King have a section of about one foot by foot. The bottom tie is divided into three segments equal to about 6 Venetian feet. Posts have a section of about one foot by ¾ foot. The bottom tie is divided into three seg- joined by particular double step nodes named “Dardo di Giove”. The angle between the ments joined by particular double step nodes named “Dardo di Giove”. The angle be- strut and the bottom tie is equal to 24 with a truss height of about 5 m. The length of the tween the strut and the bottom tie is equal to 24° with a truss height of about 5 m. The truss elements is reported in Figure 7 both for the original and the retroﬁtted conﬁguration. length of the truss elements is reported in Figure 7 both for the original and the retrofitted The spacing between the trusses is variable, ranging from 206 to 210 cm, equal to about configuration. The spacing between the trusses is variable, ranging from 206 to 210 cm, 6 Venetian feet. equal to about 6 Venetian feet. Buildings 2022, 12, x FOR PEER REVIEW 5 of 16 Buildings 2022, 12, 1773 5 of 15 Buildings 2022, 12, x FOR PEER REVIEW 5 of 16 Table 1. Size and nomenclature of the main structural elements. Table 1. Size and nomenclature of the main structural elements. Table 1. Size and nomenclature of the main structural elements. Roof Truss-Structural Element Cross Section Dimension ID and Nomenclature B × H [cm] Roof Truss-Structural Element Cross Section Dimension Roof Truss-Structural Element Cross Section Dimension 1 Inclined Strut 26 × 35 ID and Nomenclature B × H [cm] ID and Nomenclature B H [cm] 2 Tie 26 × 35 1 Inclined Strut 26 × 35 1 Inclined Strut 26 35 3 King Post 26 × 35 2 Tie 26 × 35 2 Tie 26 35 4 Horizontal Strut 26 × 35 3 King Post 26 × 35 3 King Post 26 35 5 Shelf 26 × 35 4 Horizontal Strut 26 × 35 4 Horizontal Strut 26 35 6 Additional King Post 26 × 28 5 Shelf 26 × 35 5 Shelf 26 35 7 6 A A dd dd itit io io nn al al KS in trg ut P ost 26 26 × × 20 28 6 Additional King Post 26 28 7 Additional Strut 26 × 20 7 Additional Strut 26 20 (a) (a) (b) (b) Figure 7. Scheme of the roof truss (dimensions reported in cm): (a) original configuration; (b) ret- Figure 7. Scheme of the roof truss (dimensions reported in cm): (a) original configuration; (b) retrofitted Figure 7. Scheme of the roof truss (dimensions reported in cm): (a) original configuration; (b) ret- rofitted configuration. conﬁguration. rofitted configuration. 3. Robustness Analysis of the Individual 2D Timber Roof Truss 3. Robustness Analysis of the Individual 2D Timber Roof Truss 3. Robustness Analysis of the Individual 2D Timber Roof Truss This section reports the analysis of the single roof truss in the two different conﬁg- This section reports the analysis of the single roof truss in the two different configu- This section reports the analysis of the single roof truss in the two different configu- urations, i.e., pre- and post- 19th-century restoration. The 2D linear static analyses are rations, i.e., pre- and post- 19th-century restoration. The 2D linear static analyses are per- rations, i.e., pre- and post- 19th-century restoration. The 2D linear static analyses are per- performed with the software “Strand 7” [14]. formed with the software “Strand 7” [14]. formed with the software “Strand 7” [14]. Preliminarily, the response in the initial conﬁguration of the trusses is analyzed for the Preliminarily, the response in the initial configuration of the trusses is analyzed for Preliminarily, the response in the initial configuration of the trusses is analyzed for vertical loads (self-weight, permanent, and snow loads) and, subsequently, the response of the vertical loads (self-weight, permanent, and snow loads) and, subsequently, the re- the vertical loads (self-weight, permanent, and snow loads) and, subsequently, the re- the trusses subject to a strut-tie node damage is analyzed in order to obtain information on sponse of the trusses subject to a strut-tie node damage is analyzed in order to obtain sponse of the trusses subject to a strut-tie node damage is analyzed in order to obtain the structural robustness. The analyses are performed in a comparative way considering information on the structural robustness. The analyses are performed in a comparative information on the structural robustness. The analyses are performed in a comparative the effect of rotational stiffness of the carpentry structural nodes. way considering the effect of rotational stiffness of the carpentry structural nodes. way considering the effect of rotational stiffness of the carpentry structural nodes. Buildings 2022, 12, x FOR PEER REVIEW 6 of 16 Buildings 2022, 12, 1773 6 of 15 3.1. 2D Model 3.1. 2D Model Two different configurations of the wooden roof trusses, the original (model 1) and Two different conﬁgurations of the wooden roof trusses, the original (model 1) the retrofitted (model 2) one, respectively, are analyzed by using 2D models and adopting and the retroﬁtted (model 2) one, respectively, are analyzed by using 2D models and beam elements (Figure 8). Particular attention is paid to the nodal joints and boundary adopting beam elements (Figure 8). Particular attention is paid to the nodal joints and conditions. boundary conditions. (a) (b) Figure 8. Modeling of the truss accounting for the nodal stiffness: (a) 1—original; (b) 2—post inter- Figure 8. Modeling of the truss accounting for the nodal stiffness: (a) 1—original; (b) 2—post intervention. vention. Each element of the roof trusses was modeled according to the geometry of the section derived from the historical surveys given in Table 1. Due to the uncertainties concerning Each element of the roof trusses was modeled according to the geometry of the sec- the material characterization, which is typical of existing constructions, especially of the tion derived from the historical surveys given in Table 1. Due to the uncertainties con- historical ones, the effect of a variability in the timber mechanical properties was considered cerning the material characterization, which is typical of existing constructions, especially in the analyses with the objective to evaluate its effects on the robustness characteristics. of the historical ones, the effect of a variability in the timber mechanical properties was Therefore, in the following, four different strength classes of the wooden material are considered in the analyses with the objective to evaluate its effects on the robustness char- assumed, corresponding to the categories C22, C24, C27, and C30, in accordance with EN acteristics. Therefore, in the following, four different strength classes of the wooden ma- 14081-2016 [15], and the obtained results are compared in terms of robustness analyses. terial are assumed, corresponding to the categories C22, C24, C27, and C30, in accordance It is worth mentioning that the same material was considered both for the elements in with EN 14081-2016 [15], and the obtained results are compared in terms of robustness the pre-intervention conﬁguration and for the elements added with the 19th century analyses. It is worth mentioning that the same material was considered both for the ele- restoration. This is justiﬁed by the fact that usually, in the retroﬁtting interventions on ments in the pre-intervention configuration and for the elements added with the 19th cen- historical constructions, materials compatible with the existing ones were adopted [16]. tury restoration. This is justified by the fact that usually, in the retrofitting interventions Two comparative modelings of the nodes of the structures were performed: the on historical constructions, materials compatible with the existing ones were adopted [16]. ﬁrst neglects the rotational stiffness of the nodes, therefore all the nodes are treated as Two comparative modelings of the nodes of the structures were performed: the first hinges, while the second (hereinafter referred to as the letter “R”) considers the nodal neglects the rotational stiffness of the nodes, therefore all the nodes are treated as hinges, stiffness (Figure 8), the value of which has been adequately calibrated on consolidated while the second (hereinafter referred to as the letter “R”) considers the nodal stiffness results available in literature. In particular, in the more reﬁned modeling, the interactions (Figure 8), the value of which has been adequately calibrated on consolidated results avail- between the structural elements are deﬁned as follows: (i) the double step-joints of the able in literature. In particular, in the more refined modeling, the interactions between the segments of the bottom tie were modeled as equivalent springs whose axial stiffness is structural elements are defined as follows: (i) the double step-joints of the segments of the deﬁned in accordance with Refs. [17,18]; (ii) the step-joints of the strut-tie and King Post- bottom tie were modeled as equivalent springs whose axial stiffness is defined in accord- strut connections are modeled considering a rotational stiffness deﬁned in accordance with ance with Refs. [17,18]; (ii) the step-joints of the strut-tie and King Post-strut connections Ref. [19]; (iii) the joint between the bottom tie and the King Post in the original conﬁguration are modeled considering a rotational stiffness defined in accordance with Ref. [19]; (iii) of the truss is modeled considering the rotational stiffness deﬁned in accordance with the joint between the bottom tie and the King Post in the original configuration of the truss Ref. [20]; (iv) the interaction between the original struts and the new additional reinforcing is modeled considering the rotational stiffness defined in accordance with Ref. [20]; (iv) struts is modeled with rigid elements (trusses), having an axis perpendicular to the axis of the interaction between the original struts and the new additional reinforcing struts is the strut elements in order to reproduce the ﬂexural coupling but allowing for the reciprocal modeled with rigid elements (trusses), having an axis perpendicular to the axis of the strut sliding. This modeling criterion is also used to reproduce the interaction between all the elements in order to reproduce the flexural coupling but allowing for the reciprocal slid- horizontal strut elements as well as the tie-barbican connection. ing. This modeling criterion is also used to reproduce the interaction between all the hor- The input parameters considered in the models are reported in Table 2, where infor- izontal strut elements as well as the tie-barbican connection. mation about the mechanical properties is included for each strength class in terms of mean Buildings 2022, 12, 1773 7 of 15 elastic modulus parallel (E ) and perpendicular (E ) to grain, and in terms of mean shear 0 90 modulus G. In Table 2, the values considered for the nodal stiffnesses are also reported, considering the nomenclature introduced in Figure 8. Table 2. Input material properties and nodal stiffnesses. Model Symbol Unit Description C22 C24 C27 C30 E MPa Mean elastic modulus parallel to grain 10,000 11,000 11,500 12,000 E Mpa Mean elastic modulus perpendicular to grain 6700 7400 7700 8000 All the models 90 G Mpa Mean shear modulus 630 690 720 750 2 3 3 3 1—Original K N/m Axial stiffness double step joint 9.10 10 1.00 10 1.05 10 1.09 10 DSJ 6 6 6 6 model K Nm/rad Rotational stiffness inclined strut-tie 8.02 10 8.93 10 9.22 10 9.67 10 IS-T 6 6 6 6 with nodal K Nm/rad Rotational stiffness king post-tie 3.05 10 3.41 10 3.50 10 3.67 10 KP-T 6 6 6 6 stiffnesses K Nm/rad Rotational stiffness king post-inclined strut 2.63 10 2.92 10 3.02 10 4.27 10 KP-IS 6 6 6 6 (Figure 8a) K Nm/rad Rotational stiffness king post-horizontal strut 1.80 10 2.00 10 2.07 10 2.17 10 KP-HS 2 3 3 3 K N/m Axial stiffness double step joint 9.10 10 1.00 10 1.05 10 1.09 10 DSJ 6 6 6 6 K Nm/rad Rotational stiffness inclined strut-tie 8.02 10 8.93 10 9.22 10 9.67 10 IS-T 2—Post- K Nm/rad Rotational stiffness king post-tie 0.00 0.00 0.00 0.00 KP-T intervention 6 6 6 6 K Nm/rad Rotational stiffness king post-inclined strut 2.63 10 2.92 10 3.02 10 4.27 10 KP-IS model with 6 6 6 6 K Nm/rad Rotational stiffness king post-horizontal strut 1.80 10 2.00 10 2.07 10 2.17 10 KP-HS nodal 6 6 6 6 K Nm/rad Rotational stiffness additional inclined strut-tie 6.76 10 7.52 10 7.77 10 8.15 10 AIS-T stiffnesses Rotational stiffness additional inclined (Figure 8b) 6 6 6 6 K Nm/rad 2.23 10 2.48 10 2.56 10 2.69 10 AIS-KP strut-king post 5 5 5 5 K Nm/rad Rotational stiffness king post-additional strut 1 4.60 10 5.11 10 5.28 10 5.54 10 KP-AS1 5 5 5 5 K Nm/rad Rotational stiffness king post-additional strut 2 6.59 10 7.32 10 7.57 10 7.94 10 KP-AS2 The models described above are used to obtain the stress state on each structural element for linear static analysis (considering only vertical forces in symmetrical and non- symmetrical conﬁgurations) and robustness analysis (in the hypothesis of failure of the strut- tie node due to degradation phenomena). The two different load conﬁgurations analyzed in the linear static analysis include the snow load, as follows: for the ﬁrst conﬁguration (hereinafter referred to as the letter A), the snow loads are applied symmetrically on the two pitches of the roof, neglecting the accumulation phenomenon, which may occur in the concave portion between the two roofs of the Gaggiandre shipyard (Figure 1), while for the second conﬁguration (hereinafter referred to as the letter B) an asymmetrical load condition due to the phenomenon of snow accumulation is considered. The robustness analyses are instead performed considering the combination of the accidental loads deﬁned by the Italian Building Code [21], i.e., with a symmetrical load pattern. For all the conﬁgurations examined, the permanent and variable loads were deﬁned and applied in compliance with the Italian Building Code [21]. 3.2. Demand–Capacity Ratio (DCR) Evaluation for Undamaged Conﬁgurations In this section, the main results obtained from the linear static analyses (LSA) of the different conﬁgurations, in terms of the Demand–Capacity Ratio (DCR) of the element or of the carpentry joint, are reported. In particular, the demand is expressed as the stress component obtained by the internal forces (i.e., bending moment, axial, and shear forces) resulting from LSA, while the corresponding capacity is evaluated by the relationships reported in Section 6 of Eurocode 5 [22]. The safety veriﬁcation of each element/joint is satisﬁed if DCR 1. The results of the most relevant veriﬁcations are reported in Figure 9 for the different models and loading conditions considered, i.e., original (1) or retroﬁtted (2) conﬁguration, symmetrical (A) or asymmetrical (B) snow load, accounting for the nodal stiffness (R) or not. Buildings 2022, 12, 1773 8 of 15 Buildings 2022, 12, x FOR PEER REVIEW 8 of 16 1.50 1.50 1.25 1.25 1.00 1.00 0.75 0.75 0.50 0.50 0.25 0.25 0.00 0.00 1-A 1-AR 1-B 1-BR 2-A 2-AR 2-B 2-BR 1-A 1-AR 1-B 1-BR 2-A 2-AR 2-B 2-BR Analyzed Configuration Analyzed Configuration C22 C24 C27 C30 C22 C24 C27 C30 (a) (b) 1.50 1.50 1.25 1.25 1.00 1.00 0.75 0.75 0.50 0.50 0.25 0.25 0.00 0.00 1-A 1-AR 1-B 1-BR 2-A 2-AR 2-B 2-BR 1-A 1-AR 1-B 1-BR 2-A 2-AR 2-B 2-BR Analyzed Configuration Analyzed Configuration C22 C24 C27 C30 C22 C24 C27 C30 (c) (d) 1.50 1.50 1.25 1.25 1.00 1.00 0.75 0.75 0.50 0.50 0.25 0.25 0.00 0.00 1-A 1-AR 1-B 1-BR 2-A 2-AR 2-B 2-BR 1-A 1-AR 1-B 1-BR 2-A 2-AR 2-B 2-BR Analyzed Configuration Analyzed Configuration C22 C24 C27 C30 C22 C24 C27 C30 (e) (f) 1.50 1.50 1.25 1.25 1.00 1.00 0.75 0.75 0.50 0.50 0.25 0.25 0.00 0.00 1-A 1-AR 1-B 1-BR 2-A 2-AR 2-B 2-BR 1-A 1-AR 1-B 1-BR 2-A 2-AR 2-B 2-BR Analyzed Configuration Analyzed Configuration C22 C24 C27 C30 C22 C24 C27 C30 (g) (h) Figure 9. DCR for the most significant structural elements and nodes: (a) Strut-bending/compres- Figure 9. DCR for the most signiﬁcant structural elements and nodes: (a) Strut-bending/compression; sion; (b) King Post-traction; (c) Bottom tie-bending/traction; (d) Strut-bending/compression; (e) (b) King Post-traction; (c) Bottom tie-bending/traction; (d) Strut-bending/compression; (e) “Dardo “Dardo di Giove” joint-shear; (f) “Dardo di Giove” joint-inclined compression; (g) Step joint-shear; di Giove” joint-shear; (f) “Dardo di Giove” joint-inclined compression; (g) Step joint-shear; (h) Step (h) Step joint-inclined compression. joint-inclined compression. DCR DCR DCR DCR DCR DCR DCR DCR Buildings 2022, 12, 1773 9 of 15 It can be observed that in the original conﬁguration some elements and joints of the truss are not veriﬁed (DCR > 1), even considering a high strength class timber. The 19th-century reinforcement intervention has resulted in different stress distri- butions on the elements of the truss, which show a DCR less than 1, even for the lowest timber strength classes. In particular, it can be observed that: (i) the reinforcement system added during the 19th-century retroﬁtting interventions reduces the effective length of the lower strut; (ii) in the original conﬁguration, the King Post has a low level of stress, while in the retroﬁtted conﬁguration it shows a traction state of stress; (iii) the horizontal strut is more stressed after the retroﬁtting intervention due to the redistribution of the stresses that involves the lower struts system; (iv) the DCR of the step joint in the main strut-tie connection exceeds 1 in the original conﬁguration, except for the cases in which high strength timber classes and semi-rigid node are considered, while the addition of an inclined strut and the metal support allow for a better redistribution of stresses reducing the DCR of the joint; (v) the DCR of the “Dardo di Giove” joint is less than 1 in all the considered conﬁgurations; (vi) the asymmetric load condition implies, in general, a greater DCR of the structural elements for both the considered conﬁgurations. 3.3. Demand–Capacity Ratio (DCR) Evaluation for Damaged Conﬁgurations and Robustness Analysis The robustness analysis is conducted using a deterministic approach [5] in order to verify the ability to redistribute the stresses inside the truss as a result of the damage to a structural element or node. The adopted procedure veriﬁes the possibility of activating an alternative load path in the plane of the truss. The damage mechanism taken into consideration in the robustness analyses consists in the shear failure of the step joint between the main strut and the bottom tie, since this is actually the most signiﬁcant mechanism for this type of structure. Indeed, on the one hand, this node is highly stressed as a result of the static analysis, and, on the other hand, experience demonstrates that trusses typically exhibit collapse phenomena due to the damage of this node, which is often caused by degradation phenomena (e.g., inﬁltration of water from the roof covering) or constructional defects. In the numerical model, the shear failure of the step joint between the main strut and the bottom tie is simulated by unlocking the axial translation of the strut so that the transfer of axial forces between the bottom tie and the principal strut is no longer possible. In this damaged conﬁguration, the bottom tie works mainly as a beam over a span of 25 m while all the other elements participate in the bearing mechanism only after they have come into contact with the bottom tie itself. This aspect is particularly signiﬁcant for the 19th-century retroﬁtted conﬁguration, in which the King Post-tie joint was modiﬁed by creating a gap between the elements. To take this aspect into account, the analyses for the 19th-century conﬁguration are carried out assuming the King Post resting in support on the tie but applying a dynamic ampliﬁcation factor of the forces, here assumed equal to 1.5 according to Ref. [5]. Figure 10 shows the schematic deformed shapes of the models used for the robustness analyses in the two conﬁgurations of the roof truss. Figure 11 shows the results of the veriﬁcations of the elements that are found to be the most stressed in the robustness analyses, where an accidental load combination is considered, for both the original and post 19th-century intervention conﬁgurations (the analyses with dynamic ampliﬁcation are identiﬁed with the label “Dyn” in the graphs). It is observed that both conﬁgurations of trusses are not robust in their plane. In particular, for all conﬁgurations, the bottom tie is not veriﬁed due to the excessive bending stress (which particularly exploits the sections weakened by “Dardo di Giove” joints) even if with lower DCR for the original conﬁguration. With regard to the strut, it can be observed that the veriﬁcation against bending/compression is satisﬁed in the original conﬁguration, while it is not satisﬁed in the retroﬁtted conﬁguration due to the bearing mechanism activated by the reinforcing trapezoid substructure. Buildings 2022, 12, x FOR PEER REVIEW 10 of 16 (a) Buildings 2022, 12, x FOR PEER REVIEW 10 of 16 Buildings 2022, 12, 1773 10 of 15 (b) Figure 10. Deformed configuration of the roof truss: (a) 1—original; (b) 2—post intervention. Figure 11 shows the results of the verifications of the elements that are found to be (a) the most stressed in the robustness analyses, where an accidental load combination is con- sidered, for both the original and post 19th-century intervention configurations (the anal- yses with dynamic amplification are identified with the label “Dyn” in the graphs). It is observed that both configurations of trusses are not robust in their plane. In particular, for all configurations, the bottom tie is not verified due to the excessive bending stress (which particularly exploits the sections weakened by “Dardo di Giove” joints) even if with lower DCR for the original configuration. With regard to the strut, it can be observed that the verification against bending/compression is satisfied in the original configuration, while (b) it is not satisfied in the retrofitted configuration due to the bearing mechanism activated by the reinforcing trapezoid substructure. Fig Figure ure 1010. . Defor Deformed med con conﬁguration figuration of of ththe e roof roof truss: truss: (a( )a 1 )— 1—original; original; (b() b2 )— 2—post post inintervention. tervention. Figure 11 shows the results of the verifications of the elements that are found to be the most stressed in the robustness analyses, where an accidental load combination is con- 1.75 1.75 6.00 6.00 sidered, for both the original and post 19th-century intervention configurations (the anal- 1.50 1.50 5.00 5.00 yses with dynamic amplification are identified with the label “Dyn” in the graphs). It is 1.25 1.25 4.00 4.00 observed that both configurations of trusses are not robust in their plane. In particular, for 1.00 1.00 3.00 3.00 0.75 all con 0.7f 5igurations, the bottom tie is not verified due to the excessive bending stress (which 2.00 2.00 0.50 0.50 particularly exploits the sections weakened by “Dardo di Giove” joints) even if with lower 1.00 1.00 0.25 0.25 DCR for the original configuration. With regard to the strut, it can be observed that the 0.00 0.00 0.00 0.00 verification against bending/compression is satisfied in the original configuration, while it is not satisfied in the retrofitted configuration due to the bearing mechanism activated by the reinforcing trapezoid substructure. C22 C24 C22 C24 C22 C24 C22 C24 Analyzed Configuratio A nn alyzed Configuration Analyzed Configuratio An n alyzed Configuration C27 C30 C27 C30 C27 C30 C27 C30 (a) (b) 1.75 1.75 6.00 6.00 Figure 11. Robustness analysis—DCR for the most significant structural elements: (a) Strut-bend- 1.50 Figure 11. Robustness analysis—DCR for the most signiﬁcant structural elements: (a) Strut- 1.50 5.00 5.00 ing/compression; (b) Bottom tie-bending/traction. 1.25 bending/compression; (b) Bottom tie-bending/traction. 1.25 4.00 4.00 1.00 1.00 3.00 3.00 The models that The consider models the tha nodal t consi stif der fness the n pr oovide dal stiff lower ness pr values ovide of lo the wer DCR values for o the f the DCR for the 0.75 0.75 2.00 2.00 structural elements, structura as a l ele demonstration ments, as a dthat emothe nstra degr tion ee th of at interlocking the degree opr f in ovided terlockin byg the provided by the 0.50 0.50 1.00 1.00 0.25 0.25 carpentry joints ca contributes rpentry join positively ts contribute to the s pos overall itivelystr toength the ove of ra the ll st trr uss. ength of the truss. 0.00 0.00 Finally, when considering the 0.00 dynamic effects 0.00 caused by the fact that, in the retroﬁtted Finally, when considering the dynamic effects caused by the fact that, in the retrofit- conﬁguration, the bearing mechanism can only be activated after the contact between ted configuration, the bearing mechanism can only be activated after the contact between the King Post and the bottom tie, it can be, in general, concluded that the 19th-century the King Post and the bottom tie, it can be, in general, concluded that the 19th-century C22 C24 C22 C24 C22 C24 C22 C24 retroﬁtting intervention did not improve the robustness of the truss in its plane. The “closed” Analyzed Configuration Analyzed Configuration Analyzed Configuration Analyzed Configuration C27 C30 C27 C30 C27 C30 C27 C30 type King Post-bottom tie typical of the Venetian carpentry appears to be particularly effective (a) in giving overall robustness to the truss. (b) The results of the analyses are then processed for the purpose of deﬁning the robust- Figure 11. Robustness analysis—DCR for the most significant structural elements: (a) Strut-bend- ness indexes RI reported in Table 3. They are evaluated, for each timber strength class, ing/compression; (b) Bottom tie-bending/traction. as the Robustness Index (RI), deﬁned as the ratio between the maximum DCR for the un- damaged conﬁguration and the maximum DCR for the damaged conﬁguration (RI = max The models that consider the nodal stiffness provide lower values of the DCR for the DCR /max DCR ) [23]. undamaged damaged structural elements, as a demonstration that the degree of interlocking provided by the carpentry joints contributes positively to the overall strength of the truss. Finally, when considering the dynamic effects caused by the fact that, in the retrofit- ted configuration, the bearing mechanism can only be activated after the contact between the King Post and the bottom tie, it can be, in general, concluded that the 19th-century DCR DCR DCR DCR DCR DCR DCR DCR Buildings 2022, 12, 1773 11 of 15 Table 3. Robustness Indexes (RI) for the different analyzed conﬁgurations. Robustness Index (RI) C22 C24 C27 C30 DCR 0.79 0.72 0.65 0.60 undamaged 1-A DCR 3.43 3.14 2.79 2.51 damaged RI 0.23 0.23 0.23 0.24 DCR 0.57 0.52 0.48 0.44 undamaged 1-AR DCR 2.72 2.49 2.22 1.99 damaged RI 0.21 0.21 0.22 0.22 DCR 0.51 0.46 0.41 0.36 undamaged 2-A DCR 3.74 3.43 3.05 2.74 damaged RI 0.14 0.13 0.13 0.13 DCR 0.35 0.32 0.30 0.28 undamaged DCR 3.25 2.98 2.65 2.38 2-AR damaged RI 0.11 0.11 0.11 0.12 DCR 0.51 0.46 0.41 0.36 undamaged 2-A_Dyn DCR 5.61 5.14 4.57 4.11 damaged RI 0.09 0.09 0.09 0.09 DCR 0.35 0.32 0.30 0.28 undamaged 2-AR_Dyn DCR 4.87 4.46 3.97 3.57 damaged RI 0.07 0.07 0.08 0.08 From the results it is possible to observe that the original conﬁguration showed higher RI than the post-intervention conﬁguration. It is worth noting that the contribution of the rotational stiffness of the joints does not signiﬁcantly affect the RI since for both undamaged and damaged cases the DCR reduces, as expected. Nevertheless, the 2D analyses does not account, in the post intervention conﬁguration, for the effects of the transversal bracing system and, therefore, of the possible activation of 3D alternative load path resistant mechanisms. 4. Robustness Analysis of the 3D Timber Roof Truss In this section, the 3D robustness analysis of the Gaggiandre truss timber roof is presented. Only the conﬁguration subject to the 19th-century retroﬁtting intervention is analyzed in order to evaluate the effect of the longitudinal bracing system, inserted during the restoration itself, on the overall structural robustness. In particular, the purpose is to verify whether the longitudinal bracing elements allow, in the event of a local damage to a truss, the activation of a 3D “alternative load path” (ALP) type bearing mechanism or if they introduce a progressive collapse of the entire roof. 4.1. 3D Model The 3D FE model is implemented by reproducing the actual geometry of the rooﬁng system, composed by 18 trusses arranged parallel with a distance of about 210 cm. The end portion of the roof, having a “pavillon” type structure on one side, is not directly modeled as it is not of interest for the purposes of robustness assessments. Even so, the degree of constraint provided by this rooﬁng portion has been considered, in particular with regard to retention in the longitudinal direction provided by the triangular conformation of the pitches. The trusses are modeled with the same criteria adopted for the analyses in the 2D model, also considering the rotational stiffness of the individual structural nodes. The longitudinal bracing system, consisting of a double alignment of diagonals that intercept four trusses each, is modeled by means of truss elements rigidly connected to the structural nodes of the trusses. The system of pitch purlins has been neglected as they are simply supported on the roof trusses and are, therefore, irrelevant for evaluation of the 3D robustness of the system. The input parameters are the same used for the 2D models and reported in Table 2. Figure 12 shows the 3D model of the Gaggiandre truss timber roof, with an indication about the number of trusses. Buildings 2022, 12, x FOR PEER REVIEW 12 of 16 conformation of the pitches. The trusses are modeled with the same criteria adopted for the analyses in the 2D model, also considering the rotational stiffness of the individual structural nodes. The longitudinal bracing system, consisting of a double alignment of diagonals that intercept four trusses each, is modeled by means of truss elements rigidly connected to the structural nodes of the trusses. The system of pitch purlins has been ne- glected as they are simply supported on the roof trusses and are, therefore, irrelevant for evaluation of the 3D robustness of the system. The input parameters are the same used Buildings 2022, 12, 1773 12 of 15 for the 2D models and reported in Table 2. Figure 12 shows the 3D model of the Gaggian- dre truss timber roof, with an indication about the number of trusses. Figure 12. 3D model of the Gaggiandre truss timber roof. Figure 12. 3D model of the Gaggiandre truss timber roof. 4.2. Multi-Failure Analysis 4.2. Multi-Failure Analysis The robustness analysis is performed by considering three different Local Failure The robustness analysis is performed by considering three different Local Failure Scenarios (LFS), typical of historical roof systems, all of them concerning the damaging Scenarios (LFS), typical of historical roof systems, all of them concerning the damaging and subsequent failure of the lateral node of one of the timber trusses, i.e., the step joint and subsequent failure of the lateral node of one of the timber trusses, i.e., the step joint between the main strut and the bottom tie: between the main strut and the bottom tie: 1. LFS1—Shear failure of the strut-tie joint: this is the same failure mode considered in 1. LFS1—Shear failure of the strut-tie joint: this is the same failure mode considered the 2D analyses, in which the support of the truss is guaranteed but the ability to in the 2D analyses, in which the support of the truss is guaranteed but the ability to transfer the axial force between the bottom tie and the strut is lost, and the bottom tie transfer the axial force between the bottom tie and the strut is lost, and the bottom tie results are inflected; results are inﬂected; 2. LFS2—Failure of the support barbican: in this case, the truss remains functional and 2. LFS2—Failure of the support barbican: in this case, the truss remains functional and assembled but it loses its support on the wall; assembled but it loses its support on the wall; 3. LFS3—Failure of the support node and of the strut-tie joint: this situation corresponds 3. LFS3—Failure of the support node and of the strut-tie joint: this situation corre- to the combination of the two previous failure scenarios. sponds to the combination of the two previous failure scenarios. These scenarios are compatible with the main degradation phenomena occurring over These scenarios are compatible with the main degradation phenomena occurring time, i.e., the degradation of the end part (at the support zone) of the roof system due to over time, i.e., the degradation of the end part (at the support zone) of the roof system due water inﬁltration. to water infiltration. In the analyses, the damage is considered to be localized on truss nr. 5 (Figure 12), In the analyses, the damage is considered to be localized on truss nr. 5 (Figure 12), chosen so as not be too close to the extremities of the roof structure and to limit the number chosen so as not be too close to the extremities of the roof structure and to limit the number of trusses involved in the potential redistribution mechanism. Indeed, the longitudinal of trusses involved in the potential redistribution mechanism. Indeed, the longitudinal bracing system is composed of diagonal elements crossing four trusses (i.e., from the bottom bracing system is composed of diagonal elements crossing four trusses (i.e., from the bot- chord of the ﬁrst truss to the top chord of the fourth truss) and anchored on them. The tom chord of the first truss to the top chord of the fourth truss) and anchored on them. three LFS are schematized in Figure 13. The three LFS are schematized in Figure 13. 4.3. Robustness Analysis For the three failure scenarios, the variation of the axial force on the main elements of the roof trusses is evaluated with respect to the undamaged conﬁguration. All the analyses and related structural checks are carried out considering the lowest timber strength class, i.e., C22 in accordance with EN 14081 [15]. As an example, Figure 14 shows the percentage changes, calculated as the ratio between the axial force in the damaged and the undamaged conﬁguration, related to the inclined struts and the bottom tie for all the roof trusses. The results show that the trusses next to the damaged one evidence a signiﬁcant increase in the axial forces. This increase is reduced by moving away from the damaged truss; the furthest trusses are practically not affected by any variation in the axial force; thus, they do not participate in the mechanism of redistribution of the loads. To verify the possibility of activating an ALP-type bearing mechanism, the maximum DCR of the trusses that are the most stressed (i.e., trusses 4 and 6) is evaluated since they are next to the damaged truss. The results are reported in Figure 15 for the different LFS, in terms of DCR of the inclined struts and bottom tie for trusses 4 and 6. For both the elements, the values of DCR are always lower than 1 for all the considered LFS. Buildings 2022, 12, x FOR PEER REVIEW 13 of 16 Buildings 2022, 12, x FOR PEER REVIEW 13 of 16 Buildings 2022, 12, 1773 13 of 15 Figure 13. Scheme of the LFS considered in the robustness analyses and associated schematic de- formed configurations. 4.3. Robustness Analysis For the three failure scenarios, the variation of the axial force on the main elements of the roof trusses is evaluated with respect to the undamaged configuration. All the anal- yses and related structural checks are carried out considering the lowest timber strength class, i.e., C22 in accordance with EN 14081 [15]. As an example, Figure 14 shows the per- centage changes, calculated as the ratio between the axial force in the damaged and the undamaged configuration, related to the inclined struts and the bottom tie for all the roof Figure 13. Scheme of the LFS considered in the robustness analyses and associated schematic de- Figure 13. Scheme of the LFS considered in the robustness analyses and associated schematic truss formed es. c onfigurations. deformed conﬁgurations. 4.3. Robustness Analysis 30% 30% For the three failure scenarios, the variation of the axial force on the main elements 25% 25% of the roof trusses is evaluated with respect to the undamaged configuration. All the anal- 20% 20% yses and related structural checks are carried out considering the lowest timber strength 15% 15% class, i.e., C22 in accordance with EN 14081 [15]. As an example, Figure 14 shows the per- 10% 10% centage changes, calculated as the ratio between the axial force in the damaged and the 5% 5% undamaged configuration, related to the inclined struts and the bottom tie for all the roof 0% trusses. Buildings 2022, 12, x FOR PEER REVIEW 0% 14 of 16 30% 30% 25% 25% To verify the possibility of activating an ALP-type bearing mechanism, the maximum LFS1 LFS2 LFS3 LFS1 LFS2 LFS3 DCR of the trusses that are the most stressed (i.e., trusses 4 and 6) is evaluated since they 20% 20% (a) (b) are next to the damaged truss. The results are reported in Figure 15 for the different LFS, 15% 15% in terms of DCR of the inclined struts and bottom tie for trusses 4 and 6. For both the Figure 14. Variation of the internal actions on the main elements of trusses for the different LFS: 10% Figure 14. Variation of the internal actions 10% on the main elements of trusses for the different LFS: (a) inclined struts; (b) bottom tie. elements, the values of DCR are always lower than 1 for all the considered LFS. (a) inclined struts; (b) bottom tie. 5% 5% 0% 0% The results show that the trusses next to the damaged one evidence a significant in- 0.5 crease in the axial forces. This increase is reduced by moving away from the damaged truss; the furthest trusses are practically not affected by any variation in the axial force; 0.4 thus, they do not participate in the mechanism of redistribution of the loads. LFS1 LFS2 LFS3 LFS1 LFS2 LFS3 0.3 (a) (b) 0.2 Figure 14. Variation of the internal actions on the main elements of trusses for the different LFS: (a) inclined struts; (b) bottom tie. 0.1 The results show that the trusses next to the damaged one evidence a significant in- 0.0 crease in the axial forces. This increase is reduced by moving away from the damaged truss 4 truss 6 truss 4 truss 6 truss; the furthest trusses are practically not affected by any variation in the axial force; LFS1 LFS2 LFS3 thus, they do not participate in the mechanism of redistribution of the loads. Figure 15. DCR of the struts and of the bottom tie of trusses 4 and 6 for the different LFS. Figure 15. DCR of the struts and of the bottom tie of trusses 4 and 6 for the different LFS. The results of the verifications show that, although there is a significant increase in the DCR of the elements of the trusses with respect to the undamaged configuration, the elements are always verified. The bracing system is also suitable to withstand the actions induced by the local damage to a truss, with DCR always lower than 1. The LFS3 turns out to be the most severe scenario for the bracing system as it must compensate for both failure modes, i.e., internal disassembly phenomena and loss of support of the damaged truss. For the worst configuration examined, the corresponding robustness index RI, calcu- lated as reported in Section 3.3, is equal to 0.88. Therefore, a significant robustness increase is registered, due to the beneficial effects of the transversal bracing system, allowing for the activation of a 3D alternative load path resistant mechanism. Indeed, the RIs, which estimated neglecting the 3D behavior, were equal to 0.21 and 0.11 for the original and the retrofitted configurations, respectively (Table 3). The obtained results allow us to state that the roofing system is able to absorb an increase in internal actions due to a localized failure of a truss and that it can therefore be considered robust as it is capable of activating an alternative load path, avoiding a pro- gressive failure of the roof. 5. Conclusions In this work, a simplified method, based on a deterministic approach, for the assess- ment of the robustness of existing timber roof structures is applied to a case study of the Gaggiandre shipyard at the Arsenale in Venice. The analyses are carried out considering two structural configurations of the trusses composing the roof, i.e., the ones before and after the Austrian retrofitting intervention, performed in the late 1800s. Moreover, the ro- bustness assessment is performed both on 2D models, i.e., considering the in-plane be- havior of the single trusses, and on a 3D model of the entire roof, taking into account the presence of the bracing system. In the analyses, the variability of the mechanical proper- ties of the timber elements, which represent a significant uncertainty when dealing with existing buildings, is taken into account by performing the structural analyses considering four different timber classes. In addition, the carpentry joints of the trusses are modeled both as hinges and by considering their proper rotational stiffness. The results obtained show that both the pre- and post-intervention configurations do not guarantee structural internal action increase internal action increase LFS 3 LFS 2 LFS 1 LFS 3 LFS 2 LFS 1 truss 1 truss 1 truss 2 truss 2 truss 3 truss 3 truss 4 truss 4 truss 5 truss 5 truss 6 truss 6 truss 7 truss 7 DCR truss 8 truss 8 truss 9 truss 9 truss 10 truss 10 truss 11 truss 11 truss 12 truss 12 truss 13 truss 13 truss 14 truss 14 truss 15 truss 15 truss 16 truss 16 truss 17 truss 17 truss 18 truss 18 internal action increase internal action increase truss 1 truss 1 truss 2 truss 2 truss 3 truss 3 truss 4 truss 4 truss 5 truss 5 truss 6 truss 6 truss 7 truss 7 truss 8 truss 8 truss 9 truss 9 truss 10 truss 10 truss 11 truss 11 truss 12 truss 12 truss 13 truss 13 truss 14 truss 14 truss 15 truss 15 truss 16 truss 16 truss 17 truss 17 truss 18 truss 18 Buildings 2022, 12, 1773 14 of 15 The results of the veriﬁcations show that, although there is a signiﬁcant increase in the DCR of the elements of the trusses with respect to the undamaged conﬁguration, the elements are always veriﬁed. The bracing system is also suitable to withstand the actions induced by the local damage to a truss, with DCR always lower than 1. The LFS3 turns out to be the most severe scenario for the bracing system as it must compensate for both failure modes, i.e., internal disassembly phenomena and loss of support of the damaged truss. For the worst conﬁguration examined, the corresponding robustness index RI, calcu- lated as reported in Section 3.3, is equal to 0.88. Therefore, a signiﬁcant robustness increase is registered, due to the beneﬁcial effects of the transversal bracing system, allowing for the activation of a 3D alternative load path resistant mechanism. Indeed, the RIs, which estimated neglecting the 3D behavior, were equal to 0.21 and 0.11 for the original and the retroﬁtted conﬁgurations, respectively (Table 3). The obtained results allow us to state that the rooﬁng system is able to absorb an increase in internal actions due to a localized failure of a truss and that it can therefore be considered robust as it is capable of activating an alternative load path, avoiding a progressive failure of the roof. 5. Conclusions In this work, a simpliﬁed method, based on a deterministic approach, for the assess- ment of the robustness of existing timber roof structures is applied to a case study of the Gaggiandre shipyard at the Arsenale in Venice. The analyses are carried out considering two structural conﬁgurations of the trusses composing the roof, i.e., the ones before and after the Austrian retroﬁtting intervention, performed in the late 1800s. Moreover, the robustness assessment is performed both on 2D models, i.e., considering the in-plane behavior of the single trusses, and on a 3D model of the entire roof, taking into account the presence of the bracing system. In the analyses, the variability of the mechanical properties of the timber elements, which represent a signiﬁcant uncertainty when dealing with ex- isting buildings, is taken into account by performing the structural analyses considering four different timber classes. In addition, the carpentry joints of the trusses are modeled both as hinges and by considering their proper rotational stiffness. The results obtained show that both the pre- and post-intervention conﬁgurations do not guarantee structural robustness if reference is made to the behavior in the plane of the single truss. In fact, the 19th-century intervention has not improved the robustness in the truss plane due to the fact that the resistant conﬁgurations can be activated only when the King Post comes into contact with the bottom tie, with consequent dynamic effects. A positive impact on the overall response of the truss, both in operation and in accidental conditions, was observed when considering the appropriate nodal stiffness of the carpentry joints. The 3D analysis of the roof allows us to consider the effect of the transverse bracing system in the evaluation of the structural strength. Different scenarios of local failure of one single truss are considered, and the possibility of activation of an Alternative Load Path type redistribution mechanism is veriﬁed. The results conﬁrm that the bracing system is effective and that the trusses are also able to withstand the increase in stresses due to the redistribution of the actions as a result of a local damage. It can therefore be concluded that the roof system, in its current conﬁguration, is robust, i.e., no progressive failure happens if a local damage to a truss occurs. On the basis of the obtained results, the method applied here and adapted to the case study of the Gaggiandre shipyard could be used as a simpliﬁed engineering-oriented tool to assess the robustness characteristics of historical wooden roof systems. Author Contributions: Conceptualization, L.P. and D.A.T.; methodology, L.P. and D.A.T.; software, L.P. and F.F.; investigation, F.F.; writing—original draft preparation, L.P.; writing—review and editing, F.F. and D.A.T. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Institutional Review Board Statement: Not applicable. Buildings 2022, 12, 1773 15 of 15 Informed Consent Statement: Not applicable. Data Availability Statement: Some or all data presented in this study are available from the corre- sponding author upon reasonable request. Acknowledgments: Special thanks are due to Mario Piana for his valuable contribution in the assessment of geometry, constructive methodologies, and intervention phases of the Gaggiandre shipyard roof. Conﬂicts of Interest: The authors declare no conﬂict of interest. References 1. National Research Council (CNR) (Ed.) CNR-DT 214/2018 Guide to Design of Structures for Robustness; National Research Council (CNR): Rome, Italy, 2018. 2. Sørensen, J.D.; Dietsch, P.; Kirkegaard, P.H.; Köhler, J. (Eds.) Guideline—Design for Robustness of Timber Structures: COST Action E55 “Modelling of the Performance of Timber Structures”; Shaker Verlag: Aachen, Germany, 2011; ISBN 978-3-8322-9949-1. 3. Dietsch, P. Robustness of Large-Span Timber Roof Structures—Structural Aspects. Eng. Struct. 2011, 33, 3106–3112. [CrossRef] 4. Ellingwood, B.; Smilowitz, R.; Dusenberry, D.; Duthinh, D.; Lew, H.; Carino, N. Best Practices for Reducing the Potential for Progressive Collapse in Buildings; NIST Interagency/Internal Report (NISTIR); National Institute of Standards and Technology: Gaithersburg, MD, USA, 2007. 5. Robustness of Structures – COST Action TU0601. Available online: https://www.cost-tu0601.ethz.ch/Documents/Final%20 Report/COST_TU0601_structural_robustness_design_practising_engineers_Version1_2-11Sept11.pdf (accessed on 1 July 2022). 6. Ministry for Cultural Heritage and Activities. Guidelines for Evaluation and Mitigation of Seismic Risk to Cultural Heritage; Moro, L., Neri, A., Eds.; Gangemi: Rome, Italy, 2007; ISBN 8849212690. 7. Berto, L.; Doria, A.; Faccio, P.; Saetta, A.; Talledo, D. Vulnerability Analysis of Built Cultural Heritage: A Multidisciplinary Approach for Studying the Palladio’s Tempietto Barbaro. Int. J. Archit. Herit. 2017, 11, 773–790. [CrossRef] 8. Rodrigues, L.G.; Aranha, C.A.; Sousa, H.S. Robustness Assessment of an Ancient Timber Roof Structure. Lect. Notes Civ. Eng. 2016, 1, 447–457. [CrossRef] 9. Bellavitis, G. L’Arsenale Di Venezia, Storia Di Una Grande Struttura Urbana; Cicero Editore, Ed.: Venice, Italy, 2007. 10. Bettiol, G.; Valluzzi, M.R.; Garbin, E.; Modena, C. Structural Analysis of the Timber Roofs of the “Arsenale” of Venice. In Proceedings of the 10th World Conference on Timber Engineering, Miyazaki, Japan, 2–5 June 2008. 11. Valluzzi, M.R.; Bondì, A.; Da Porto, F.; Franchetti, P.; Modena, C. Structural Investigations and Analyses for the Conservation of the ‘Arsenale’ of Venice. J. Cult. Herit. 2002, 3, 65–71. [CrossRef] 12. Baker, J.W.; Schubert, M.; Faber, M.H. On the Assessment of Robustness. Struct. Saf. 2008, 30, 253–267. [CrossRef] 13. Piana, M. Il Consolidamento Della Carpenteria Lignea Delle Gaggiandre Nell’Arsenale Di Venezia. TEMA. TEMPO Mater. Archit. 1994, 2, 5–13. 14. Strand7 Software Veriﬁcation Manual Release 2.4.6. Available online: https://www.strand7.com/downloads/Strand7%20R246 %20Veriﬁcation%20Manual%20TOC.pdf (accessed on 25 June 2022). 15. EN 14081-1; Timber Structures—Strength Graded Structural Timber with Rectangular Cross Section—Part 1: General Require- ments. European Committee for Standardisations: Brussels, Belgium, 2016. 16. Scotta, R.; Trutalli, D.; Marchi, L.; Pozza, L. Seismic performance of URM buildings with in-plane non-stiffened and stiffened timber ﬂoors. Eng. Struct. 2018, 167, 683–694. [CrossRef] 17. Drdacky, M.F.; Walcf, F.; Mares, J. Modelling of Real Historic Timber Joints. Trans. Built Environ. 1999, 39, 171. [CrossRef] 18. Parisi, M.A.; Piazza, M. Mechanics of Plain and Retroﬁtted Traditional Timber Connections. J. Struct. Eng. 2000, 126, 1395–1403. [CrossRef] 19. Parisi, M.A.; Cordié, C. Mechanical Behavior of Double-Step Timber Joints. Constr. Build. Mater. 2010, 24, 1364–1371. [CrossRef] 20. Branco, J.M.; Descamps, T. Analysis and Strengthening of Carpentry Joints. Constr. Build. Mater. 2015, 97, 34–47. [CrossRef] 21. Ministry of Infrastructures and Transportations NTC. Aggiornamento Delle «Norme Tecniche per Le Costruzioni»; Ministry of Infrastructures and Transportations NTC: Rome, Italy, 2018. (In Italian) 22. EN 1995-1-1; Eurocode 5: Design of Timber Structures—Part 1-1: General—Common Rules and Rules for Buildings. European Committee for Standardisation: Brussels, Belgium, 1995. 23. Sørensen, J.D. Framework for Robustness Assessment of Timber Structures. Eng. Struct. 2011, 33, 3087–3092. [CrossRef] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Buildings Multidisciplinary Digital Publishing Institute http://www.deepdyve.com/lp/multidisciplinary-digital-publishing-institute/robustness-analysis-of-historical-timber-roofs-a-case-study-of-the-P4niBZqlyL

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DOI: 10.3390/buildings12111773
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Abstract

buildings Article Robustness Analysis of Historical Timber Roofs: A Case Study of the Gaggiandre Shipyard at the Arsenale of Venice 1 1 , 2 Francesca Ferretti , Luca Pozza * and Diego Alejandro Talledo Department of Civil, Chemical, Environmental and Materials Engineering, University of Bologna, Viale Risorgimento 2, 40136 Bologna, Italy Department of Architecture and Arts, University IUAV of Venice, Dorsoduro 2206, 30123 Venezia, Italy * Correspondence: luca.pozza2@unibo.it Abstract: In this work, a deterministic approach is adopted to analyze the robustness of the timber roof of the Gaggiandre shipyard at the Arsenale of Venice. The capacity of the traditional timber truss to withstand the design loads as a result of the damage in the strut-tie node is evaluated according to the alternative load path method. Two layouts of the trusses are analyzed and compared: before and after the Austrian retroﬁtting intervention, performed in the late 1800s. For both conﬁgurations, robustness analyses are carried out by using linear 2D numerical models that consider the effective rotational capacity of the structural nodes in relation to the construction methods of the timber joints. For the conﬁguration subject to the 19th-century restoration, the 3D response of the roof is also analyzed to verify the additional contribution provided by the longitudinal bracing system to the activation of alternative load paths (bridge effect). The results obtained with the different analyses are thoroughly evaluated, providing an indication of the deterministic robustness index of the rooﬁng system based on different assumptions. The outcomes of this work allow to draw some general considerations on the method that could be used for the robustness assessment of historical wood systems. Citation: Ferretti, F.; Pozza, L.; Keywords: timber truss systems; historical buildings; robustness analysis; numerical modeling Talledo, D.A. Robustness Analysis of Historical Timber Roofs: A Case Study of the Gaggiandre Shipyard at the Arsenale of Venice. Buildings 1. Introduction 2022, 12, 1773. https://doi.org/ Robustness against an accidental action, as reported by the CNR Italian Guidelines [1], 10.3390/buildings12111773 indicates the ability of a structure to avoid damages disproportionate to the entity of the Academic Editor: Wen-Shao Chang action which causes an initial damage. The robustness assessment of large span timber roofs is usually performed on newly built roofs to evaluate the effect of local damage to structural Received: 6 July 2022 joints or elements [2,3]. The methodologies available for the implementation of these Accepted: 20 October 2022 assessments on new structures are well deﬁned and consolidated in design practice [1,4,5]. Published: 22 October 2022 Otherwise, the robustness assessment of historical large span roofs requires speciﬁc in- Publisher’s Note: MDPI stays neutral depth studies and a different methodological approach that has not yet been codiﬁed and with regard to jurisdictional claims in deﬁned in the literature. In fact, it is necessary to acquire an adequate level of knowledge published maps and institutional afﬁl- of the structure [6,7], in particular with reference to reinforcement and consolidation iations. interventions that the structure has undergone during its life as they could signiﬁcantly affect the structural response. In addition, the evaluation of geometry, acting loads, and material properties is more difﬁcult than for new structures, with signiﬁcant implications on the reliability of the analyses, e.g., Ref. [8]. Copyright: © 2022 by the authors. The present paper proposes a simpliﬁed procedure to assess the robustness character- Licensee MDPI, Basel, Switzerland. istics of existing timber roof structures, belonging to cultural heritage, which could provide This article is an open access article a basis for developing an engineer-oriented method to be used in robustness analyses. distributed under the terms and This approach is applied to the very challenging case study represented by the roof conditions of the Creative Commons structure of the Gaggiandre shipyard in Venice. It consists of two very long sheds, called Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ “Tezoni”, built between 1568 and 1573 by Sansovino and belonging to the complex “Ar- 4.0/). senale” in Venice, which was the hub of the naval industry of Venice since the beginning Buildings 2022, 12, 1773. https://doi.org/10.3390/buildings12111773 https://www.mdpi.com/journal/buildings Buildings 2022, 12, x FOR PEER REVIEW 2 of 16 This approach is applied to the very challenging case study represented by the roof structure of the Gaggiandre shipyard in Venice. It consists of two very long sheds, called “Tezoni”, built between 1568 and 1573 by Sansovino and belonging to the complex “Ar- senale” in Venice, which was the hub of the naval industry of Venice since the beginning of the XII century [9,10]. The Arsenale of Venice is a huge complex of docks and sheds, subject to several restoration and strengthening interventions in the past, performed mainly due to changes in the use of the buildings over the centuries or, more recently, due to material degradation phenomena and damages caused by the lack of maintenance of Buildings 2022, 12, 1773 2 of 15 the complex [11]. For the robustness assessments, a deterministic approach is adopted [5,12] aiming to estimate the ability of the roof to withstand the design loads after the damage of some key of the XII century [9,10]. The Arsenale of Venice is a huge complex of docks and sheds, structural nodes, according to the Alternative Load Path (ALP) method. The assessments subject to several restoration and strengthening interventions in the past, performed mainly are performed with numerical models capable of considering the actual rotational capac- due to changes in the use of the buildings over the centuries or, more recently, due to ity of the structural nodes in relation to building procedures of the timber carpentry joints. material degradation phenomena and damages caused by the lack of maintenance of the In this study, the robustness of the roof is evaluated for two layouts of the trusses: complex [11]. the original version and the one subject to Austrian retrofitting works, performed at the For the robustness assessments, a deterministic approach is adopted [5,12] aiming to end of the 1800s. In both configurations, reference is made to the response of the single estimate the ability of the roof to withstand the design loads after the damage of some key truss in its own plane. For the retrofitted case, the 3D system of the entire roof is also structural nodes, according to the Alternative Load Path (ALP) method. The assessments considered. The analysis of the obtained results allows us to understand the effects of the are performed with numerical models capable of considering the actual rotational capacity 19th-century restoration interventions on the robustness of both the truss and the entire of the structural nodes in relation to building procedures of the timber carpentry joints. roof, and to define scenarios and configurations to be analyzed with more refined meth- In this study, the robustness of the roof is evaluated for two layouts of the trusses: the ods to perform probabilistic robustness assessments. original version and the one subject to Austrian retroﬁtting works, performed at the end of the 1800s. In both conﬁgurations, reference is made to the response of the single truss in 2. The Gaggiandre Shipyard its own plane. For the retroﬁtted case, the 3D system of the entire roof is also considered. In the 16th century, the shipbuilding activity in Venice was concentrated in the Ar- The analysis of the obtained results allows us to understand the effects of the 19th-century senale area. The need of the Venetian Senate was to guarantee the regular navigation of restoration interventions on the robustness of both the truss and the entire roof, and to the merchant ships by establishing a shipyard aimed at the construction of Galleys. Dur- deﬁne scenarios and conﬁgurations to be analyzed with more reﬁned methods to perform ing the expansions of the Arsenale Novissimo, Jacopo Sansovino was the builder of the probabilistic robustness assessments. dry dock called “Gaggiandre” (Figure 1). The Gaggiandre (or Gagiandre) are “two aquatic 2. The Gaggiandre Shipyard canopies–only built out of a planned series of three–constituting one of the most signifi- cant achievements of the vast sixteenth-century expansion undergone by the Arsenale of In the 16th century, the shipbuilding activity in Venice was concentrated in the Arse- Venice” [13]. nale area. The need of the Venetian Senate was to guarantee the regular navigation of the The roof of the Gaggiandre shipyard, supported by continuous clay brick masonry merchant ships by establishing a shipyard aimed at the construction of Galleys. During walls, consists of a series of composite type timber trusses, with a length of about 25 m, the expansions of the Arsenale Novissimo, Jacopo Sansovino was the builder of the dry which are among the largest of the 16th century (Figure 2). Figure 3 shows some construc- dock called “Gaggiandre” (Figure 1). The Gaggiandre (or Gagiandre) are “two aquatic tion details of the roof, i.e., the suspension of the tie element (Figure 3a) and detail of the canopies–only built out of a planned series of three–constituting one of the most signiﬁ- cant suppo achievements rt of the truss of othe n th vast e ma sixteenth-ce sonry, realiz ntury ed wiexpansion th a stone ca under ntilev gone er an by d ba the rbArsenale ican (Figure of V 3 enice” b). [13]. Figure 1. The Gaggiandre shipyard, Venice (from Google Earth). Figure 1. The Gaggiandre shipyard, Venice (from Google Earth). The roof of the Gaggiandre shipyard, supported by continuous clay brick masonry walls, consists of a series of composite type timber trusses, with a length of about 25 m, which are among the largest of the 16th century (Figure 2). Figure 3 shows some con- struction details of the roof, i.e., the suspension of the tie element (Figure 3a) and detail of the support of the truss on the masonry, realized with a stone cantilever and barbican (Figure 3b). Buildings 2022, 12, 1773 3 of 15 Buildings 2022, 12, x FOR PEER REVIEW 3 of 16 Buildings 2022, 12, x FOR PEER REVIEW 3 of 16 Buildings 2022, 12, x FOR PEER REVIEW 3 of 16 Figure 2. Bottom view of the roof. Figure 2. Bottom view of the roof. Figure 2. BottomFig view ureof 2. the Botr tom v oof. iew of the roof. (a) (b) (a) (b) (a) (b) Figure 3. Construction details of the roof: (a) suspension of the tie element; (b) support on the ma- Figure 3. Construction details of the roof: (a) suspension of the tie element; (b) support on the ma- Figure 3. Construction details of the roof: (a) suspension of the tie element; (b) support on the ma- Figure 3. Construction details of the roof: (a) suspension of the tie element; (b) support on the sonry by a stone cantilever and barbican. sonry by a stone cantilever and barbican. sonry by a stone cantilever and barbican. masonry by a stone cantilever and barbican. 2.1. Historical Evolution of the Gaggiandre Roof Structure 2.1. Historical Evolution of the Gaggiandre Roof Structure 2.1. Historical Evolution of the Gaggiandre Roof Structure 2.1. Historical Evolution of the Gaggiandre Roof Structure The current co The nfigura curre tio nn t co ofn th figura e tru ti ss on es oo f fth th e e tru Ga ss ges gia o n f d tre he roo Gag f gi isa th nd e re re roo sult f is of th the e result of the The current conﬁguration of the trusses of the Gaggiandre roof is the result of the 19th- The current configuration of the trusses of the Gaggiandre roof is the result of the th th 19 -century sta 19 tic r -ce est ntury sta orationtic r s, cae rr stied ora ti out by ons, ca A rr uied stria on ut by soldier Aus f stria or n st so ruc ldier tura s f l o st r re stn ruc gth tura en-l strengthen- th century static restorations, carried out by Austrian soldiers for structural strengthening 19 -century static restorations, carried out by Austrian soldiers for structural strengthen- ing purposes, as thoroughly described in Ref. [13]. In more detail, the original truss was ing purposes, as thoroughly described in Ref. [13]. In more detail, the original truss was purposes, as thoroughly described in Ref. [13]. In more detail, the original truss was ing purposes, as thoroughly described in Ref. [13]. In more detail, the original truss was reinforced by adding a trapezoid system consisting of lateral King Posts, Struts, and a reinforced by adding a trapezoid system consisting of lateral King Posts, Struts, and a reinforced by adding a trapezoid system consisting of lateral King Posts, Struts, and a reinforced by adding a trapezoid system consisting of lateral King Posts, Struts, and a Horizontal Strut. Figure 4 shows the scheme of the composed truss, highlighting the orig- Horizontal Strut. Figure 4 shows the scheme of the composed truss, highlighting the orig- Horizontal Strut. Figure 4 shows the scheme of the composed truss, highlighting the Horizontal Strut. Figure 4 shows the scheme of the composed truss, highlighting the orig- inal configuration and the structural elements added during the restoration. These inter- inal configuration and the structural elements added during the restoration. These inter- original conﬁguration and the structural elements added during the restoration. These inal configuration and the structural elements added during the restoration. These inter- ventions have significantly modified the static scheme in the plane of the truss, adding a ventions have significantly modified the static scheme in the plane of the truss, adding a interventions have signiﬁcantly modiﬁed the static scheme in the plane of the truss, adding a ventions have significantly modified the static scheme in the plane of the truss, adding a reinforcement substructure and modifying some structural nodes typical of the construc- rre einfor infocement rcement sub substr st uctur ructure e and and modifying modifyinsome g som str e st uctural ructura nodes l nodtypical es typica ofl of the t constr he con uction struc- reinforcement substructure and modifying some structural nodes typical of the construc- tion methods of Venetian timber carpentry. Furthermore, globally, a system of diagonal methods tion metof hoV denet s of ian Ven timber etian ti carpentry mber carp . Furthermor entry. Furte, her globally more, ,gl ao system bally, a of sy diagonal stem of r d ods iago has nal tion methods of Venetian timber carpentry. Furthermore, globally, a system of diagonal rods has been introduced, which stabilizes the trusses out of their plane and connects them been rods intr has oduced, been introduce which stabilizes d, which the stabili trusses zes th out e truss of their es out plane of thand eir pla connects ne and them conne together cts them , rods has been introduced, which stabilizes the trusses out of their plane and connects them together, serving as a transverse bracing system (Figure 5). serving together as , ser a transverse ving as a tra bracing nsverse system bracin (Figur g syst eem ( 5). Figure 5). together, serving as a transverse bracing system (Figure 5). Figure 4. Schematization of the retrofitting intervention. Figure 4. Schematization of the retrofitting intervention. Figure 4. Schematization of the retroﬁtting intervention. Figure 4. Schematization of the retrofitting intervention. Buildings 2022, 12, x FOR PEER REVIEW 4 of 16 Buildings Buildings 2022 202,212 , 12 , 1773 , x FOR PEER REVIEW 4 4 of of 15 16 Figure 5. Detail of the transverse bracing system of the Gaggiandre roof. With regard to the 19th-century interventions, it is noted that the dimensions of the cross section of the elements belonging to the reinforcement system are not consistent with those of the original elements, which respected the unit of measurement of the V enetian foot (equal to 34.77 cm). Figure 5. Detail of the transverse bracing system of the Gaggiandre roof. Figure 5. Detail of the transverse bracing system of the Gaggiandre roof. The most significant change made with the retrofitting interventions is the one that involved W ith the rele egar md ent to s the calle 19th-century d King Posts: interventions, in the originait l sch is noted eme, th that esethe were dimensions connected of to the With regard to the 19th-century interventions, it is noted that the dimensions of the the cr ties, oss section most likely of the usi elements ng wrapping belonging tie or to spec theia reinfor l joints cement . Curresystem ntly, the arK e inot ng Po consistent sts appewith ar cross section of the elements belonging to the reinforcement system are not consistent with those of the original elements, which respected the unit of measurement of the Venetian to be detached from the ties, giving rise to an open King Post-tie connection (Figure 6). those of the original elements, which respected the unit of measurement of the Venetian foot (equal to 34.77 cm). Furthermore, the addition of the lateral struts has halved the span of the lower struts foot (equal to 34.77 cm). The most signiﬁcant change made with the retroﬁtting interventions is the one that by significantly reducing the bending action as well as the effective length with reference The most significant change made with the retrofitting interventions is the one that involved the elements called King Posts: in the original scheme, these were connected to to the buckling phenomenon in the vertical plane of the truss. The tie in the centerline involved the elements called King Posts: in the original scheme, these were connected to the ties, most likely using wrapping tie or special joints. Currently, the King Posts appear turns out to be supported by a metal tie rod, connected to the central King Post. the ties, most likely using wrapping tie or special joints. Currently, the King Posts appear to be detached from the ties, giving rise to an open King Post-tie connection (Figure 6). to be detached from the ties, giving rise to an open King Post-tie connection (Figure 6). Furthermore, the addition of the lateral struts has halved the span of the lower struts by significantly reducing the bending action as well as the effective length with reference to the buckling phenomenon in the vertical plane of the truss. The tie in the centerline turns out to be supported by a metal tie rod, connected to the central King Post. (a) (b) Figure 6. King Post–bottom tie joint configuration: (a) original (closed connection type); (b) after Figure 6. King Post–bottom tie joint conﬁguration: (a) original (closed connection type); (b) after retrofitting intervention (open connection type). retroﬁtting intervention (open connection type). Furthermore, the addition of the lateral struts has halved the span of the lower struts 2.2. Geometric Configuration by signiﬁcantly reducing the bending action as well as the effective length with reference to (a) (b) The two roofs belonging to the Gaggiandre shipyard consist of a truss structure, with the buckling phenomenon in the vertical plane of the truss. The tie in the centerline turns a spa Fig nure appr 6. o Kxim ing P ately e ost–bo q tt ua om l to tie 2 joi 5 n m t ,c m ona fid ge ura oft io stn ruts : (a) , or ties ig, in aan l d (c lo Kin sed g Po cons n ts ec . tThe ion td ype); ime n (b si ) o an fts er out to be supported by a metal tie rod, connected to the central King Post. of th ret e rst ofruc ittin tura g intl er ele ven m tents ion (open that c com onnec po tio se nth tye pe) tru . ss are reported in Table 1 and follow the ancient Venetian measure called foot, “piede”, which corresponds to 34.77 cm and repre- 2.2. Geometric Conﬁguration 2.2. Geometric Configuration sents the main reference measure of the time. In fact, the tie, the four struts, and the King The two roofs belonging to the Gaggiandre shipyard consist of a truss structure, with a Posts have a section of about one foot by ¾ foot. The bottom tie is divided into three seg- The two roofs belonging to the Gaggiandre shipyard consist of a truss structure, with span approximately equal to 25 m, made of struts, ties, and King Posts. The dimensions of ments joined by particular double step nodes named “Dardo di Giove”. The angle be- a span approximately equal to 25 m, made of struts, ties, and King Posts. The dimensions the structural elements that compose the truss are reported in Table 1 and follow the ancient tween the strut and the bottom tie is equal to 24° with a truss height of about 5 m. The of the structural elements that compose the truss are reported in Table 1 and follow the Venetian measure called foot, “piede”, which corresponds to 34.77 cm and represents the length of the truss elements is reported in Figure 7 both for the original and the retrofitted ancient Venetian measure called foot, “piede”, which corresponds to 34.77 cm and repre- main reference measure of the time. In fact, the tie, the four struts, and the King Posts configuration. The spacing between the trusses is variable, ranging from 206 to 210 cm, sents the main reference measure of the time. In fact, the tie, the four struts, and the King have a section of about one foot by foot. The bottom tie is divided into three segments equal to about 6 Venetian feet. Posts have a section of about one foot by ¾ foot. The bottom tie is divided into three seg- joined by particular double step nodes named “Dardo di Giove”. The angle between the ments joined by particular double step nodes named “Dardo di Giove”. The angle be- strut and the bottom tie is equal to 24 with a truss height of about 5 m. The length of the tween the strut and the bottom tie is equal to 24° with a truss height of about 5 m. The truss elements is reported in Figure 7 both for the original and the retroﬁtted conﬁguration. length of the truss elements is reported in Figure 7 both for the original and the retrofitted The spacing between the trusses is variable, ranging from 206 to 210 cm, equal to about configuration. The spacing between the trusses is variable, ranging from 206 to 210 cm, 6 Venetian feet. equal to about 6 Venetian feet. Buildings 2022, 12, x FOR PEER REVIEW 5 of 16 Buildings 2022, 12, 1773 5 of 15 Buildings 2022, 12, x FOR PEER REVIEW 5 of 16 Table 1. Size and nomenclature of the main structural elements. Table 1. Size and nomenclature of the main structural elements. Table 1. Size and nomenclature of the main structural elements. Roof Truss-Structural Element Cross Section Dimension ID and Nomenclature B × H [cm] Roof Truss-Structural Element Cross Section Dimension Roof Truss-Structural Element Cross Section Dimension 1 Inclined Strut 26 × 35 ID and Nomenclature B × H [cm] ID and Nomenclature B H [cm] 2 Tie 26 × 35 1 Inclined Strut 26 × 35 1 Inclined Strut 26 35 3 King Post 26 × 35 2 Tie 26 × 35 2 Tie 26 35 4 Horizontal Strut 26 × 35 3 King Post 26 × 35 3 King Post 26 35 5 Shelf 26 × 35 4 Horizontal Strut 26 × 35 4 Horizontal Strut 26 35 6 Additional King Post 26 × 28 5 Shelf 26 × 35 5 Shelf 26 35 7 6 A A dd dd itit io io nn al al KS in trg ut P ost 26 26 × × 20 28 6 Additional King Post 26 28 7 Additional Strut 26 × 20 7 Additional Strut 26 20 (a) (a) (b) (b) Figure 7. Scheme of the roof truss (dimensions reported in cm): (a) original configuration; (b) ret- Figure 7. Scheme of the roof truss (dimensions reported in cm): (a) original configuration; (b) retrofitted Figure 7. Scheme of the roof truss (dimensions reported in cm): (a) original configuration; (b) ret- rofitted configuration. conﬁguration. rofitted configuration. 3. Robustness Analysis of the Individual 2D Timber Roof Truss 3. Robustness Analysis of the Individual 2D Timber Roof Truss 3. Robustness Analysis of the Individual 2D Timber Roof Truss This section reports the analysis of the single roof truss in the two different conﬁg- This section reports the analysis of the single roof truss in the two different configu- This section reports the analysis of the single roof truss in the two different configu- urations, i.e., pre- and post- 19th-century restoration. The 2D linear static analyses are rations, i.e., pre- and post- 19th-century restoration. The 2D linear static analyses are per- rations, i.e., pre- and post- 19th-century restoration. The 2D linear static analyses are per- performed with the software “Strand 7” [14]. formed with the software “Strand 7” [14]. formed with the software “Strand 7” [14]. Preliminarily, the response in the initial conﬁguration of the trusses is analyzed for the Preliminarily, the response in the initial configuration of the trusses is analyzed for Preliminarily, the response in the initial configuration of the trusses is analyzed for vertical loads (self-weight, permanent, and snow loads) and, subsequently, the response of the vertical loads (self-weight, permanent, and snow loads) and, subsequently, the re- the vertical loads (self-weight, permanent, and snow loads) and, subsequently, the re- the trusses subject to a strut-tie node damage is analyzed in order to obtain information on sponse of the trusses subject to a strut-tie node damage is analyzed in order to obtain sponse of the trusses subject to a strut-tie node damage is analyzed in order to obtain the structural robustness. The analyses are performed in a comparative way considering information on the structural robustness. The analyses are performed in a comparative information on the structural robustness. The analyses are performed in a comparative the effect of rotational stiffness of the carpentry structural nodes. way considering the effect of rotational stiffness of the carpentry structural nodes. way considering the effect of rotational stiffness of the carpentry structural nodes. Buildings 2022, 12, x FOR PEER REVIEW 6 of 16 Buildings 2022, 12, 1773 6 of 15 3.1. 2D Model 3.1. 2D Model Two different configurations of the wooden roof trusses, the original (model 1) and Two different conﬁgurations of the wooden roof trusses, the original (model 1) the retrofitted (model 2) one, respectively, are analyzed by using 2D models and adopting and the retroﬁtted (model 2) one, respectively, are analyzed by using 2D models and beam elements (Figure 8). Particular attention is paid to the nodal joints and boundary adopting beam elements (Figure 8). Particular attention is paid to the nodal joints and conditions. boundary conditions. (a) (b) Figure 8. Modeling of the truss accounting for the nodal stiffness: (a) 1—original; (b) 2—post inter- Figure 8. Modeling of the truss accounting for the nodal stiffness: (a) 1—original; (b) 2—post intervention. vention. Each element of the roof trusses was modeled according to the geometry of the section derived from the historical surveys given in Table 1. Due to the uncertainties concerning Each element of the roof trusses was modeled according to the geometry of the sec- the material characterization, which is typical of existing constructions, especially of the tion derived from the historical surveys given in Table 1. Due to the uncertainties con- historical ones, the effect of a variability in the timber mechanical properties was considered cerning the material characterization, which is typical of existing constructions, especially in the analyses with the objective to evaluate its effects on the robustness characteristics. of the historical ones, the effect of a variability in the timber mechanical properties was Therefore, in the following, four different strength classes of the wooden material are considered in the analyses with the objective to evaluate its effects on the robustness char- assumed, corresponding to the categories C22, C24, C27, and C30, in accordance with EN acteristics. Therefore, in the following, four different strength classes of the wooden ma- 14081-2016 [15], and the obtained results are compared in terms of robustness analyses. terial are assumed, corresponding to the categories C22, C24, C27, and C30, in accordance It is worth mentioning that the same material was considered both for the elements in with EN 14081-2016 [15], and the obtained results are compared in terms of robustness the pre-intervention conﬁguration and for the elements added with the 19th century analyses. It is worth mentioning that the same material was considered both for the ele- restoration. This is justiﬁed by the fact that usually, in the retroﬁtting interventions on ments in the pre-intervention configuration and for the elements added with the 19th cen- historical constructions, materials compatible with the existing ones were adopted [16]. tury restoration. This is justified by the fact that usually, in the retrofitting interventions Two comparative modelings of the nodes of the structures were performed: the on historical constructions, materials compatible with the existing ones were adopted [16]. ﬁrst neglects the rotational stiffness of the nodes, therefore all the nodes are treated as Two comparative modelings of the nodes of the structures were performed: the first hinges, while the second (hereinafter referred to as the letter “R”) considers the nodal neglects the rotational stiffness of the nodes, therefore all the nodes are treated as hinges, stiffness (Figure 8), the value of which has been adequately calibrated on consolidated while the second (hereinafter referred to as the letter “R”) considers the nodal stiffness results available in literature. In particular, in the more reﬁned modeling, the interactions (Figure 8), the value of which has been adequately calibrated on consolidated results avail- between the structural elements are deﬁned as follows: (i) the double step-joints of the able in literature. In particular, in the more refined modeling, the interactions between the segments of the bottom tie were modeled as equivalent springs whose axial stiffness is structural elements are defined as follows: (i) the double step-joints of the segments of the deﬁned in accordance with Refs. [17,18]; (ii) the step-joints of the strut-tie and King Post- bottom tie were modeled as equivalent springs whose axial stiffness is defined in accord- strut connections are modeled considering a rotational stiffness deﬁned in accordance with ance with Refs. [17,18]; (ii) the step-joints of the strut-tie and King Post-strut connections Ref. [19]; (iii) the joint between the bottom tie and the King Post in the original conﬁguration are modeled considering a rotational stiffness defined in accordance with Ref. [19]; (iii) of the truss is modeled considering the rotational stiffness deﬁned in accordance with the joint between the bottom tie and the King Post in the original configuration of the truss Ref. [20]; (iv) the interaction between the original struts and the new additional reinforcing is modeled considering the rotational stiffness defined in accordance with Ref. [20]; (iv) struts is modeled with rigid elements (trusses), having an axis perpendicular to the axis of the interaction between the original struts and the new additional reinforcing struts is the strut elements in order to reproduce the ﬂexural coupling but allowing for the reciprocal modeled with rigid elements (trusses), having an axis perpendicular to the axis of the strut sliding. This modeling criterion is also used to reproduce the interaction between all the elements in order to reproduce the flexural coupling but allowing for the reciprocal slid- horizontal strut elements as well as the tie-barbican connection. ing. This modeling criterion is also used to reproduce the interaction between all the hor- The input parameters considered in the models are reported in Table 2, where infor- izontal strut elements as well as the tie-barbican connection. mation about the mechanical properties is included for each strength class in terms of mean Buildings 2022, 12, 1773 7 of 15 elastic modulus parallel (E ) and perpendicular (E ) to grain, and in terms of mean shear 0 90 modulus G. In Table 2, the values considered for the nodal stiffnesses are also reported, considering the nomenclature introduced in Figure 8. Table 2. Input material properties and nodal stiffnesses. Model Symbol Unit Description C22 C24 C27 C30 E MPa Mean elastic modulus parallel to grain 10,000 11,000 11,500 12,000 E Mpa Mean elastic modulus perpendicular to grain 6700 7400 7700 8000 All the models 90 G Mpa Mean shear modulus 630 690 720 750 2 3 3 3 1—Original K N/m Axial stiffness double step joint 9.10 10 1.00 10 1.05 10 1.09 10 DSJ 6 6 6 6 model K Nm/rad Rotational stiffness inclined strut-tie 8.02 10 8.93 10 9.22 10 9.67 10 IS-T 6 6 6 6 with nodal K Nm/rad Rotational stiffness king post-tie 3.05 10 3.41 10 3.50 10 3.67 10 KP-T 6 6 6 6 stiffnesses K Nm/rad Rotational stiffness king post-inclined strut 2.63 10 2.92 10 3.02 10 4.27 10 KP-IS 6 6 6 6 (Figure 8a) K Nm/rad Rotational stiffness king post-horizontal strut 1.80 10 2.00 10 2.07 10 2.17 10 KP-HS 2 3 3 3 K N/m Axial stiffness double step joint 9.10 10 1.00 10 1.05 10 1.09 10 DSJ 6 6 6 6 K Nm/rad Rotational stiffness inclined strut-tie 8.02 10 8.93 10 9.22 10 9.67 10 IS-T 2—Post- K Nm/rad Rotational stiffness king post-tie 0.00 0.00 0.00 0.00 KP-T intervention 6 6 6 6 K Nm/rad Rotational stiffness king post-inclined strut 2.63 10 2.92 10 3.02 10 4.27 10 KP-IS model with 6 6 6 6 K Nm/rad Rotational stiffness king post-horizontal strut 1.80 10 2.00 10 2.07 10 2.17 10 KP-HS nodal 6 6 6 6 K Nm/rad Rotational stiffness additional inclined strut-tie 6.76 10 7.52 10 7.77 10 8.15 10 AIS-T stiffnesses Rotational stiffness additional inclined (Figure 8b) 6 6 6 6 K Nm/rad 2.23 10 2.48 10 2.56 10 2.69 10 AIS-KP strut-king post 5 5 5 5 K Nm/rad Rotational stiffness king post-additional strut 1 4.60 10 5.11 10 5.28 10 5.54 10 KP-AS1 5 5 5 5 K Nm/rad Rotational stiffness king post-additional strut 2 6.59 10 7.32 10 7.57 10 7.94 10 KP-AS2 The models described above are used to obtain the stress state on each structural element for linear static analysis (considering only vertical forces in symmetrical and non- symmetrical conﬁgurations) and robustness analysis (in the hypothesis of failure of the strut- tie node due to degradation phenomena). The two different load conﬁgurations analyzed in the linear static analysis include the snow load, as follows: for the ﬁrst conﬁguration (hereinafter referred to as the letter A), the snow loads are applied symmetrically on the two pitches of the roof, neglecting the accumulation phenomenon, which may occur in the concave portion between the two roofs of the Gaggiandre shipyard (Figure 1), while for the second conﬁguration (hereinafter referred to as the letter B) an asymmetrical load condition due to the phenomenon of snow accumulation is considered. The robustness analyses are instead performed considering the combination of the accidental loads deﬁned by the Italian Building Code [21], i.e., with a symmetrical load pattern. For all the conﬁgurations examined, the permanent and variable loads were deﬁned and applied in compliance with the Italian Building Code [21]. 3.2. Demand–Capacity Ratio (DCR) Evaluation for Undamaged Conﬁgurations In this section, the main results obtained from the linear static analyses (LSA) of the different conﬁgurations, in terms of the Demand–Capacity Ratio (DCR) of the element or of the carpentry joint, are reported. In particular, the demand is expressed as the stress component obtained by the internal forces (i.e., bending moment, axial, and shear forces) resulting from LSA, while the corresponding capacity is evaluated by the relationships reported in Section 6 of Eurocode 5 [22]. The safety veriﬁcation of each element/joint is satisﬁed if DCR 1. The results of the most relevant veriﬁcations are reported in Figure 9 for the different models and loading conditions considered, i.e., original (1) or retroﬁtted (2) conﬁguration, symmetrical (A) or asymmetrical (B) snow load, accounting for the nodal stiffness (R) or not. Buildings 2022, 12, 1773 8 of 15 Buildings 2022, 12, x FOR PEER REVIEW 8 of 16 1.50 1.50 1.25 1.25 1.00 1.00 0.75 0.75 0.50 0.50 0.25 0.25 0.00 0.00 1-A 1-AR 1-B 1-BR 2-A 2-AR 2-B 2-BR 1-A 1-AR 1-B 1-BR 2-A 2-AR 2-B 2-BR Analyzed Configuration Analyzed Configuration C22 C24 C27 C30 C22 C24 C27 C30 (a) (b) 1.50 1.50 1.25 1.25 1.00 1.00 0.75 0.75 0.50 0.50 0.25 0.25 0.00 0.00 1-A 1-AR 1-B 1-BR 2-A 2-AR 2-B 2-BR 1-A 1-AR 1-B 1-BR 2-A 2-AR 2-B 2-BR Analyzed Configuration Analyzed Configuration C22 C24 C27 C30 C22 C24 C27 C30 (c) (d) 1.50 1.50 1.25 1.25 1.00 1.00 0.75 0.75 0.50 0.50 0.25 0.25 0.00 0.00 1-A 1-AR 1-B 1-BR 2-A 2-AR 2-B 2-BR 1-A 1-AR 1-B 1-BR 2-A 2-AR 2-B 2-BR Analyzed Configuration Analyzed Configuration C22 C24 C27 C30 C22 C24 C27 C30 (e) (f) 1.50 1.50 1.25 1.25 1.00 1.00 0.75 0.75 0.50 0.50 0.25 0.25 0.00 0.00 1-A 1-AR 1-B 1-BR 2-A 2-AR 2-B 2-BR 1-A 1-AR 1-B 1-BR 2-A 2-AR 2-B 2-BR Analyzed Configuration Analyzed Configuration C22 C24 C27 C30 C22 C24 C27 C30 (g) (h) Figure 9. DCR for the most significant structural elements and nodes: (a) Strut-bending/compres- Figure 9. DCR for the most signiﬁcant structural elements and nodes: (a) Strut-bending/compression; sion; (b) King Post-traction; (c) Bottom tie-bending/traction; (d) Strut-bending/compression; (e) (b) King Post-traction; (c) Bottom tie-bending/traction; (d) Strut-bending/compression; (e) “Dardo “Dardo di Giove” joint-shear; (f) “Dardo di Giove” joint-inclined compression; (g) Step joint-shear; di Giove” joint-shear; (f) “Dardo di Giove” joint-inclined compression; (g) Step joint-shear; (h) Step (h) Step joint-inclined compression. joint-inclined compression. DCR DCR DCR DCR DCR DCR DCR DCR Buildings 2022, 12, 1773 9 of 15 It can be observed that in the original conﬁguration some elements and joints of the truss are not veriﬁed (DCR > 1), even considering a high strength class timber. The 19th-century reinforcement intervention has resulted in different stress distri- butions on the elements of the truss, which show a DCR less than 1, even for the lowest timber strength classes. In particular, it can be observed that: (i) the reinforcement system added during the 19th-century retroﬁtting interventions reduces the effective length of the lower strut; (ii) in the original conﬁguration, the King Post has a low level of stress, while in the retroﬁtted conﬁguration it shows a traction state of stress; (iii) the horizontal strut is more stressed after the retroﬁtting intervention due to the redistribution of the stresses that involves the lower struts system; (iv) the DCR of the step joint in the main strut-tie connection exceeds 1 in the original conﬁguration, except for the cases in which high strength timber classes and semi-rigid node are considered, while the addition of an inclined strut and the metal support allow for a better redistribution of stresses reducing the DCR of the joint; (v) the DCR of the “Dardo di Giove” joint is less than 1 in all the considered conﬁgurations; (vi) the asymmetric load condition implies, in general, a greater DCR of the structural elements for both the considered conﬁgurations. 3.3. Demand–Capacity Ratio (DCR) Evaluation for Damaged Conﬁgurations and Robustness Analysis The robustness analysis is conducted using a deterministic approach [5] in order to verify the ability to redistribute the stresses inside the truss as a result of the damage to a structural element or node. The adopted procedure veriﬁes the possibility of activating an alternative load path in the plane of the truss. The damage mechanism taken into consideration in the robustness analyses consists in the shear failure of the step joint between the main strut and the bottom tie, since this is actually the most signiﬁcant mechanism for this type of structure. Indeed, on the one hand, this node is highly stressed as a result of the static analysis, and, on the other hand, experience demonstrates that trusses typically exhibit collapse phenomena due to the damage of this node, which is often caused by degradation phenomena (e.g., inﬁltration of water from the roof covering) or constructional defects. In the numerical model, the shear failure of the step joint between the main strut and the bottom tie is simulated by unlocking the axial translation of the strut so that the transfer of axial forces between the bottom tie and the principal strut is no longer possible. In this damaged conﬁguration, the bottom tie works mainly as a beam over a span of 25 m while all the other elements participate in the bearing mechanism only after they have come into contact with the bottom tie itself. This aspect is particularly signiﬁcant for the 19th-century retroﬁtted conﬁguration, in which the King Post-tie joint was modiﬁed by creating a gap between the elements. To take this aspect into account, the analyses for the 19th-century conﬁguration are carried out assuming the King Post resting in support on the tie but applying a dynamic ampliﬁcation factor of the forces, here assumed equal to 1.5 according to Ref. [5]. Figure 10 shows the schematic deformed shapes of the models used for the robustness analyses in the two conﬁgurations of the roof truss. Figure 11 shows the results of the veriﬁcations of the elements that are found to be the most stressed in the robustness analyses, where an accidental load combination is considered, for both the original and post 19th-century intervention conﬁgurations (the analyses with dynamic ampliﬁcation are identiﬁed with the label “Dyn” in the graphs). It is observed that both conﬁgurations of trusses are not robust in their plane. In particular, for all conﬁgurations, the bottom tie is not veriﬁed due to the excessive bending stress (which particularly exploits the sections weakened by “Dardo di Giove” joints) even if with lower DCR for the original conﬁguration. With regard to the strut, it can be observed that the veriﬁcation against bending/compression is satisﬁed in the original conﬁguration, while it is not satisﬁed in the retroﬁtted conﬁguration due to the bearing mechanism activated by the reinforcing trapezoid substructure. Buildings 2022, 12, x FOR PEER REVIEW 10 of 16 (a) Buildings 2022, 12, x FOR PEER REVIEW 10 of 16 Buildings 2022, 12, 1773 10 of 15 (b) Figure 10. Deformed configuration of the roof truss: (a) 1—original; (b) 2—post intervention. Figure 11 shows the results of the verifications of the elements that are found to be (a) the most stressed in the robustness analyses, where an accidental load combination is con- sidered, for both the original and post 19th-century intervention configurations (the anal- yses with dynamic amplification are identified with the label “Dyn” in the graphs). It is observed that both configurations of trusses are not robust in their plane. In particular, for all configurations, the bottom tie is not verified due to the excessive bending stress (which particularly exploits the sections weakened by “Dardo di Giove” joints) even if with lower DCR for the original configuration. With regard to the strut, it can be observed that the verification against bending/compression is satisfied in the original configuration, while (b) it is not satisfied in the retrofitted configuration due to the bearing mechanism activated by the reinforcing trapezoid substructure. Fig Figure ure 1010. . Defor Deformed med con conﬁguration figuration of of ththe e roof roof truss: truss: (a( )a 1 )— 1—original; original; (b() b2 )— 2—post post inintervention. tervention. Figure 11 shows the results of the verifications of the elements that are found to be the most stressed in the robustness analyses, where an accidental load combination is con- 1.75 1.75 6.00 6.00 sidered, for both the original and post 19th-century intervention configurations (the anal- 1.50 1.50 5.00 5.00 yses with dynamic amplification are identified with the label “Dyn” in the graphs). It is 1.25 1.25 4.00 4.00 observed that both configurations of trusses are not robust in their plane. In particular, for 1.00 1.00 3.00 3.00 0.75 all con 0.7f 5igurations, the bottom tie is not verified due to the excessive bending stress (which 2.00 2.00 0.50 0.50 particularly exploits the sections weakened by “Dardo di Giove” joints) even if with lower 1.00 1.00 0.25 0.25 DCR for the original configuration. With regard to the strut, it can be observed that the 0.00 0.00 0.00 0.00 verification against bending/compression is satisfied in the original configuration, while it is not satisfied in the retrofitted configuration due to the bearing mechanism activated by the reinforcing trapezoid substructure. C22 C24 C22 C24 C22 C24 C22 C24 Analyzed Configuratio A nn alyzed Configuration Analyzed Configuratio An n alyzed Configuration C27 C30 C27 C30 C27 C30 C27 C30 (a) (b) 1.75 1.75 6.00 6.00 Figure 11. Robustness analysis—DCR for the most significant structural elements: (a) Strut-bend- 1.50 Figure 11. Robustness analysis—DCR for the most signiﬁcant structural elements: (a) Strut- 1.50 5.00 5.00 ing/compression; (b) Bottom tie-bending/traction. 1.25 bending/compression; (b) Bottom tie-bending/traction. 1.25 4.00 4.00 1.00 1.00 3.00 3.00 The models that The consider models the tha nodal t consi stif der fness the n pr oovide dal stiff lower ness pr values ovide of lo the wer DCR values for o the f the DCR for the 0.75 0.75 2.00 2.00 structural elements, structura as a l ele demonstration ments, as a dthat emothe nstra degr tion ee th of at interlocking the degree opr f in ovided terlockin byg the provided by the 0.50 0.50 1.00 1.00 0.25 0.25 carpentry joints ca contributes rpentry join positively ts contribute to the s pos overall itivelystr toength the ove of ra the ll st trr uss. ength of the truss. 0.00 0.00 Finally, when considering the 0.00 dynamic effects 0.00 caused by the fact that, in the retroﬁtted Finally, when considering the dynamic effects caused by the fact that, in the retrofit- conﬁguration, the bearing mechanism can only be activated after the contact between ted configuration, the bearing mechanism can only be activated after the contact between the King Post and the bottom tie, it can be, in general, concluded that the 19th-century the King Post and the bottom tie, it can be, in general, concluded that the 19th-century C22 C24 C22 C24 C22 C24 C22 C24 retroﬁtting intervention did not improve the robustness of the truss in its plane. The “closed” Analyzed Configuration Analyzed Configuration Analyzed Configuration Analyzed Configuration C27 C30 C27 C30 C27 C30 C27 C30 type King Post-bottom tie typical of the Venetian carpentry appears to be particularly effective (a) in giving overall robustness to the truss. (b) The results of the analyses are then processed for the purpose of deﬁning the robust- Figure 11. Robustness analysis—DCR for the most significant structural elements: (a) Strut-bend- ness indexes RI reported in Table 3. They are evaluated, for each timber strength class, ing/compression; (b) Bottom tie-bending/traction. as the Robustness Index (RI), deﬁned as the ratio between the maximum DCR for the un- damaged conﬁguration and the maximum DCR for the damaged conﬁguration (RI = max The models that consider the nodal stiffness provide lower values of the DCR for the DCR /max DCR ) [23]. undamaged damaged structural elements, as a demonstration that the degree of interlocking provided by the carpentry joints contributes positively to the overall strength of the truss. Finally, when considering the dynamic effects caused by the fact that, in the retrofit- ted configuration, the bearing mechanism can only be activated after the contact between the King Post and the bottom tie, it can be, in general, concluded that the 19th-century DCR DCR DCR DCR DCR DCR DCR DCR Buildings 2022, 12, 1773 11 of 15 Table 3. Robustness Indexes (RI) for the different analyzed conﬁgurations. Robustness Index (RI) C22 C24 C27 C30 DCR 0.79 0.72 0.65 0.60 undamaged 1-A DCR 3.43 3.14 2.79 2.51 damaged RI 0.23 0.23 0.23 0.24 DCR 0.57 0.52 0.48 0.44 undamaged 1-AR DCR 2.72 2.49 2.22 1.99 damaged RI 0.21 0.21 0.22 0.22 DCR 0.51 0.46 0.41 0.36 undamaged 2-A DCR 3.74 3.43 3.05 2.74 damaged RI 0.14 0.13 0.13 0.13 DCR 0.35 0.32 0.30 0.28 undamaged DCR 3.25 2.98 2.65 2.38 2-AR damaged RI 0.11 0.11 0.11 0.12 DCR 0.51 0.46 0.41 0.36 undamaged 2-A_Dyn DCR 5.61 5.14 4.57 4.11 damaged RI 0.09 0.09 0.09 0.09 DCR 0.35 0.32 0.30 0.28 undamaged 2-AR_Dyn DCR 4.87 4.46 3.97 3.57 damaged RI 0.07 0.07 0.08 0.08 From the results it is possible to observe that the original conﬁguration showed higher RI than the post-intervention conﬁguration. It is worth noting that the contribution of the rotational stiffness of the joints does not signiﬁcantly affect the RI since for both undamaged and damaged cases the DCR reduces, as expected. Nevertheless, the 2D analyses does not account, in the post intervention conﬁguration, for the effects of the transversal bracing system and, therefore, of the possible activation of 3D alternative load path resistant mechanisms. 4. Robustness Analysis of the 3D Timber Roof Truss In this section, the 3D robustness analysis of the Gaggiandre truss timber roof is presented. Only the conﬁguration subject to the 19th-century retroﬁtting intervention is analyzed in order to evaluate the effect of the longitudinal bracing system, inserted during the restoration itself, on the overall structural robustness. In particular, the purpose is to verify whether the longitudinal bracing elements allow, in the event of a local damage to a truss, the activation of a 3D “alternative load path” (ALP) type bearing mechanism or if they introduce a progressive collapse of the entire roof. 4.1. 3D Model The 3D FE model is implemented by reproducing the actual geometry of the rooﬁng system, composed by 18 trusses arranged parallel with a distance of about 210 cm. The end portion of the roof, having a “pavillon” type structure on one side, is not directly modeled as it is not of interest for the purposes of robustness assessments. Even so, the degree of constraint provided by this rooﬁng portion has been considered, in particular with regard to retention in the longitudinal direction provided by the triangular conformation of the pitches. The trusses are modeled with the same criteria adopted for the analyses in the 2D model, also considering the rotational stiffness of the individual structural nodes. The longitudinal bracing system, consisting of a double alignment of diagonals that intercept four trusses each, is modeled by means of truss elements rigidly connected to the structural nodes of the trusses. The system of pitch purlins has been neglected as they are simply supported on the roof trusses and are, therefore, irrelevant for evaluation of the 3D robustness of the system. The input parameters are the same used for the 2D models and reported in Table 2. Figure 12 shows the 3D model of the Gaggiandre truss timber roof, with an indication about the number of trusses. Buildings 2022, 12, x FOR PEER REVIEW 12 of 16 conformation of the pitches. The trusses are modeled with the same criteria adopted for the analyses in the 2D model, also considering the rotational stiffness of the individual structural nodes. The longitudinal bracing system, consisting of a double alignment of diagonals that intercept four trusses each, is modeled by means of truss elements rigidly connected to the structural nodes of the trusses. The system of pitch purlins has been ne- glected as they are simply supported on the roof trusses and are, therefore, irrelevant for evaluation of the 3D robustness of the system. The input parameters are the same used Buildings 2022, 12, 1773 12 of 15 for the 2D models and reported in Table 2. Figure 12 shows the 3D model of the Gaggian- dre truss timber roof, with an indication about the number of trusses. Figure 12. 3D model of the Gaggiandre truss timber roof. Figure 12. 3D model of the Gaggiandre truss timber roof. 4.2. Multi-Failure Analysis 4.2. Multi-Failure Analysis The robustness analysis is performed by considering three different Local Failure The robustness analysis is performed by considering three different Local Failure Scenarios (LFS), typical of historical roof systems, all of them concerning the damaging Scenarios (LFS), typical of historical roof systems, all of them concerning the damaging and subsequent failure of the lateral node of one of the timber trusses, i.e., the step joint and subsequent failure of the lateral node of one of the timber trusses, i.e., the step joint between the main strut and the bottom tie: between the main strut and the bottom tie: 1. LFS1—Shear failure of the strut-tie joint: this is the same failure mode considered in 1. LFS1—Shear failure of the strut-tie joint: this is the same failure mode considered the 2D analyses, in which the support of the truss is guaranteed but the ability to in the 2D analyses, in which the support of the truss is guaranteed but the ability to transfer the axial force between the bottom tie and the strut is lost, and the bottom tie transfer the axial force between the bottom tie and the strut is lost, and the bottom tie results are inflected; results are inﬂected; 2. LFS2—Failure of the support barbican: in this case, the truss remains functional and 2. LFS2—Failure of the support barbican: in this case, the truss remains functional and assembled but it loses its support on the wall; assembled but it loses its support on the wall; 3. LFS3—Failure of the support node and of the strut-tie joint: this situation corresponds 3. LFS3—Failure of the support node and of the strut-tie joint: this situation corre- to the combination of the two previous failure scenarios. sponds to the combination of the two previous failure scenarios. These scenarios are compatible with the main degradation phenomena occurring over These scenarios are compatible with the main degradation phenomena occurring time, i.e., the degradation of the end part (at the support zone) of the roof system due to over time, i.e., the degradation of the end part (at the support zone) of the roof system due water inﬁltration. to water infiltration. In the analyses, the damage is considered to be localized on truss nr. 5 (Figure 12), In the analyses, the damage is considered to be localized on truss nr. 5 (Figure 12), chosen so as not be too close to the extremities of the roof structure and to limit the number chosen so as not be too close to the extremities of the roof structure and to limit the number of trusses involved in the potential redistribution mechanism. Indeed, the longitudinal of trusses involved in the potential redistribution mechanism. Indeed, the longitudinal bracing system is composed of diagonal elements crossing four trusses (i.e., from the bottom bracing system is composed of diagonal elements crossing four trusses (i.e., from the bot- chord of the ﬁrst truss to the top chord of the fourth truss) and anchored on them. The tom chord of the first truss to the top chord of the fourth truss) and anchored on them. three LFS are schematized in Figure 13. The three LFS are schematized in Figure 13. 4.3. Robustness Analysis For the three failure scenarios, the variation of the axial force on the main elements of the roof trusses is evaluated with respect to the undamaged conﬁguration. All the analyses and related structural checks are carried out considering the lowest timber strength class, i.e., C22 in accordance with EN 14081 [15]. As an example, Figure 14 shows the percentage changes, calculated as the ratio between the axial force in the damaged and the undamaged conﬁguration, related to the inclined struts and the bottom tie for all the roof trusses. The results show that the trusses next to the damaged one evidence a signiﬁcant increase in the axial forces. This increase is reduced by moving away from the damaged truss; the furthest trusses are practically not affected by any variation in the axial force; thus, they do not participate in the mechanism of redistribution of the loads. To verify the possibility of activating an ALP-type bearing mechanism, the maximum DCR of the trusses that are the most stressed (i.e., trusses 4 and 6) is evaluated since they are next to the damaged truss. The results are reported in Figure 15 for the different LFS, in terms of DCR of the inclined struts and bottom tie for trusses 4 and 6. For both the elements, the values of DCR are always lower than 1 for all the considered LFS. Buildings 2022, 12, x FOR PEER REVIEW 13 of 16 Buildings 2022, 12, x FOR PEER REVIEW 13 of 16 Buildings 2022, 12, 1773 13 of 15 Figure 13. Scheme of the LFS considered in the robustness analyses and associated schematic de- formed configurations. 4.3. Robustness Analysis For the three failure scenarios, the variation of the axial force on the main elements of the roof trusses is evaluated with respect to the undamaged configuration. All the anal- yses and related structural checks are carried out considering the lowest timber strength class, i.e., C22 in accordance with EN 14081 [15]. As an example, Figure 14 shows the per- centage changes, calculated as the ratio between the axial force in the damaged and the undamaged configuration, related to the inclined struts and the bottom tie for all the roof Figure 13. Scheme of the LFS considered in the robustness analyses and associated schematic de- Figure 13. Scheme of the LFS considered in the robustness analyses and associated schematic truss formed es. c onfigurations. deformed conﬁgurations. 4.3. Robustness Analysis 30% 30% For the three failure scenarios, the variation of the axial force on the main elements 25% 25% of the roof trusses is evaluated with respect to the undamaged configuration. All the anal- 20% 20% yses and related structural checks are carried out considering the lowest timber strength 15% 15% class, i.e., C22 in accordance with EN 14081 [15]. As an example, Figure 14 shows the per- 10% 10% centage changes, calculated as the ratio between the axial force in the damaged and the 5% 5% undamaged configuration, related to the inclined struts and the bottom tie for all the roof 0% trusses. Buildings 2022, 12, x FOR PEER REVIEW 0% 14 of 16 30% 30% 25% 25% To verify the possibility of activating an ALP-type bearing mechanism, the maximum LFS1 LFS2 LFS3 LFS1 LFS2 LFS3 DCR of the trusses that are the most stressed (i.e., trusses 4 and 6) is evaluated since they 20% 20% (a) (b) are next to the damaged truss. The results are reported in Figure 15 for the different LFS, 15% 15% in terms of DCR of the inclined struts and bottom tie for trusses 4 and 6. For both the Figure 14. Variation of the internal actions on the main elements of trusses for the different LFS: 10% Figure 14. Variation of the internal actions 10% on the main elements of trusses for the different LFS: (a) inclined struts; (b) bottom tie. elements, the values of DCR are always lower than 1 for all the considered LFS. (a) inclined struts; (b) bottom tie. 5% 5% 0% 0% The results show that the trusses next to the damaged one evidence a significant in- 0.5 crease in the axial forces. This increase is reduced by moving away from the damaged truss; the furthest trusses are practically not affected by any variation in the axial force; 0.4 thus, they do not participate in the mechanism of redistribution of the loads. LFS1 LFS2 LFS3 LFS1 LFS2 LFS3 0.3 (a) (b) 0.2 Figure 14. Variation of the internal actions on the main elements of trusses for the different LFS: (a) inclined struts; (b) bottom tie. 0.1 The results show that the trusses next to the damaged one evidence a significant in- 0.0 crease in the axial forces. This increase is reduced by moving away from the damaged truss 4 truss 6 truss 4 truss 6 truss; the furthest trusses are practically not affected by any variation in the axial force; LFS1 LFS2 LFS3 thus, they do not participate in the mechanism of redistribution of the loads. Figure 15. DCR of the struts and of the bottom tie of trusses 4 and 6 for the different LFS. Figure 15. DCR of the struts and of the bottom tie of trusses 4 and 6 for the different LFS. The results of the verifications show that, although there is a significant increase in the DCR of the elements of the trusses with respect to the undamaged configuration, the elements are always verified. The bracing system is also suitable to withstand the actions induced by the local damage to a truss, with DCR always lower than 1. The LFS3 turns out to be the most severe scenario for the bracing system as it must compensate for both failure modes, i.e., internal disassembly phenomena and loss of support of the damaged truss. For the worst configuration examined, the corresponding robustness index RI, calcu- lated as reported in Section 3.3, is equal to 0.88. Therefore, a significant robustness increase is registered, due to the beneficial effects of the transversal bracing system, allowing for the activation of a 3D alternative load path resistant mechanism. Indeed, the RIs, which estimated neglecting the 3D behavior, were equal to 0.21 and 0.11 for the original and the retrofitted configurations, respectively (Table 3). The obtained results allow us to state that the roofing system is able to absorb an increase in internal actions due to a localized failure of a truss and that it can therefore be considered robust as it is capable of activating an alternative load path, avoiding a pro- gressive failure of the roof. 5. Conclusions In this work, a simplified method, based on a deterministic approach, for the assess- ment of the robustness of existing timber roof structures is applied to a case study of the Gaggiandre shipyard at the Arsenale in Venice. The analyses are carried out considering two structural configurations of the trusses composing the roof, i.e., the ones before and after the Austrian retrofitting intervention, performed in the late 1800s. Moreover, the ro- bustness assessment is performed both on 2D models, i.e., considering the in-plane be- havior of the single trusses, and on a 3D model of the entire roof, taking into account the presence of the bracing system. In the analyses, the variability of the mechanical proper- ties of the timber elements, which represent a significant uncertainty when dealing with existing buildings, is taken into account by performing the structural analyses considering four different timber classes. In addition, the carpentry joints of the trusses are modeled both as hinges and by considering their proper rotational stiffness. The results obtained show that both the pre- and post-intervention configurations do not guarantee structural internal action increase internal action increase LFS 3 LFS 2 LFS 1 LFS 3 LFS 2 LFS 1 truss 1 truss 1 truss 2 truss 2 truss 3 truss 3 truss 4 truss 4 truss 5 truss 5 truss 6 truss 6 truss 7 truss 7 DCR truss 8 truss 8 truss 9 truss 9 truss 10 truss 10 truss 11 truss 11 truss 12 truss 12 truss 13 truss 13 truss 14 truss 14 truss 15 truss 15 truss 16 truss 16 truss 17 truss 17 truss 18 truss 18 internal action increase internal action increase truss 1 truss 1 truss 2 truss 2 truss 3 truss 3 truss 4 truss 4 truss 5 truss 5 truss 6 truss 6 truss 7 truss 7 truss 8 truss 8 truss 9 truss 9 truss 10 truss 10 truss 11 truss 11 truss 12 truss 12 truss 13 truss 13 truss 14 truss 14 truss 15 truss 15 truss 16 truss 16 truss 17 truss 17 truss 18 truss 18 Buildings 2022, 12, 1773 14 of 15 The results of the veriﬁcations show that, although there is a signiﬁcant increase in the DCR of the elements of the trusses with respect to the undamaged conﬁguration, the elements are always veriﬁed. The bracing system is also suitable to withstand the actions induced by the local damage to a truss, with DCR always lower than 1. The LFS3 turns out to be the most severe scenario for the bracing system as it must compensate for both failure modes, i.e., internal disassembly phenomena and loss of support of the damaged truss. For the worst conﬁguration examined, the corresponding robustness index RI, calcu- lated as reported in Section 3.3, is equal to 0.88. Therefore, a signiﬁcant robustness increase is registered, due to the beneﬁcial effects of the transversal bracing system, allowing for the activation of a 3D alternative load path resistant mechanism. Indeed, the RIs, which estimated neglecting the 3D behavior, were equal to 0.21 and 0.11 for the original and the retroﬁtted conﬁgurations, respectively (Table 3). The obtained results allow us to state that the rooﬁng system is able to absorb an increase in internal actions due to a localized failure of a truss and that it can therefore be considered robust as it is capable of activating an alternative load path, avoiding a progressive failure of the roof. 5. Conclusions In this work, a simpliﬁed method, based on a deterministic approach, for the assess- ment of the robustness of existing timber roof structures is applied to a case study of the Gaggiandre shipyard at the Arsenale in Venice. The analyses are carried out considering two structural conﬁgurations of the trusses composing the roof, i.e., the ones before and after the Austrian retroﬁtting intervention, performed in the late 1800s. Moreover, the robustness assessment is performed both on 2D models, i.e., considering the in-plane behavior of the single trusses, and on a 3D model of the entire roof, taking into account the presence of the bracing system. In the analyses, the variability of the mechanical properties of the timber elements, which represent a signiﬁcant uncertainty when dealing with ex- isting buildings, is taken into account by performing the structural analyses considering four different timber classes. In addition, the carpentry joints of the trusses are modeled both as hinges and by considering their proper rotational stiffness. The results obtained show that both the pre- and post-intervention conﬁgurations do not guarantee structural robustness if reference is made to the behavior in the plane of the single truss. In fact, the 19th-century intervention has not improved the robustness in the truss plane due to the fact that the resistant conﬁgurations can be activated only when the King Post comes into contact with the bottom tie, with consequent dynamic effects. A positive impact on the overall response of the truss, both in operation and in accidental conditions, was observed when considering the appropriate nodal stiffness of the carpentry joints. The 3D analysis of the roof allows us to consider the effect of the transverse bracing system in the evaluation of the structural strength. Different scenarios of local failure of one single truss are considered, and the possibility of activation of an Alternative Load Path type redistribution mechanism is veriﬁed. The results conﬁrm that the bracing system is effective and that the trusses are also able to withstand the increase in stresses due to the redistribution of the actions as a result of a local damage. It can therefore be concluded that the roof system, in its current conﬁguration, is robust, i.e., no progressive failure happens if a local damage to a truss occurs. On the basis of the obtained results, the method applied here and adapted to the case study of the Gaggiandre shipyard could be used as a simpliﬁed engineering-oriented tool to assess the robustness characteristics of historical wooden roof systems. Author Contributions: Conceptualization, L.P. and D.A.T.; methodology, L.P. and D.A.T.; software, L.P. and F.F.; investigation, F.F.; writing—original draft preparation, L.P.; writing—review and editing, F.F. and D.A.T. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Institutional Review Board Statement: Not applicable. Buildings 2022, 12, 1773 15 of 15 Informed Consent Statement: Not applicable. Data Availability Statement: Some or all data presented in this study are available from the corre- sponding author upon reasonable request. Acknowledgments: Special thanks are due to Mario Piana for his valuable contribution in the assessment of geometry, constructive methodologies, and intervention phases of the Gaggiandre shipyard roof. Conﬂicts of Interest: The authors declare no conﬂict of interest. References 1. National Research Council (CNR) (Ed.) CNR-DT 214/2018 Guide to Design of Structures for Robustness; National Research Council (CNR): Rome, Italy, 2018. 2. Sørensen, J.D.; Dietsch, P.; Kirkegaard, P.H.; Köhler, J. (Eds.) Guideline—Design for Robustness of Timber Structures: COST Action E55 “Modelling of the Performance of Timber Structures”; Shaker Verlag: Aachen, Germany, 2011; ISBN 978-3-8322-9949-1. 3. Dietsch, P. Robustness of Large-Span Timber Roof Structures—Structural Aspects. Eng. Struct. 2011, 33, 3106–3112. [CrossRef] 4. Ellingwood, B.; Smilowitz, R.; Dusenberry, D.; Duthinh, D.; Lew, H.; Carino, N. Best Practices for Reducing the Potential for Progressive Collapse in Buildings; NIST Interagency/Internal Report (NISTIR); National Institute of Standards and Technology: Gaithersburg, MD, USA, 2007. 5. Robustness of Structures – COST Action TU0601. Available online: https://www.cost-tu0601.ethz.ch/Documents/Final%20 Report/COST_TU0601_structural_robustness_design_practising_engineers_Version1_2-11Sept11.pdf (accessed on 1 July 2022). 6. Ministry for Cultural Heritage and Activities. Guidelines for Evaluation and Mitigation of Seismic Risk to Cultural Heritage; Moro, L., Neri, A., Eds.; Gangemi: Rome, Italy, 2007; ISBN 8849212690. 7. Berto, L.; Doria, A.; Faccio, P.; Saetta, A.; Talledo, D. Vulnerability Analysis of Built Cultural Heritage: A Multidisciplinary Approach for Studying the Palladio’s Tempietto Barbaro. Int. J. Archit. Herit. 2017, 11, 773–790. [CrossRef] 8. Rodrigues, L.G.; Aranha, C.A.; Sousa, H.S. Robustness Assessment of an Ancient Timber Roof Structure. Lect. Notes Civ. Eng. 2016, 1, 447–457. [CrossRef] 9. Bellavitis, G. L’Arsenale Di Venezia, Storia Di Una Grande Struttura Urbana; Cicero Editore, Ed.: Venice, Italy, 2007. 10. Bettiol, G.; Valluzzi, M.R.; Garbin, E.; Modena, C. Structural Analysis of the Timber Roofs of the “Arsenale” of Venice. In Proceedings of the 10th World Conference on Timber Engineering, Miyazaki, Japan, 2–5 June 2008. 11. Valluzzi, M.R.; Bondì, A.; Da Porto, F.; Franchetti, P.; Modena, C. Structural Investigations and Analyses for the Conservation of the ‘Arsenale’ of Venice. J. Cult. Herit. 2002, 3, 65–71. [CrossRef] 12. Baker, J.W.; Schubert, M.; Faber, M.H. On the Assessment of Robustness. Struct. Saf. 2008, 30, 253–267. [CrossRef] 13. Piana, M. Il Consolidamento Della Carpenteria Lignea Delle Gaggiandre Nell’Arsenale Di Venezia. TEMA. TEMPO Mater. Archit. 1994, 2, 5–13. 14. Strand7 Software Veriﬁcation Manual Release 2.4.6. Available online: https://www.strand7.com/downloads/Strand7%20R246 %20Veriﬁcation%20Manual%20TOC.pdf (accessed on 25 June 2022). 15. EN 14081-1; Timber Structures—Strength Graded Structural Timber with Rectangular Cross Section—Part 1: General Require- ments. European Committee for Standardisations: Brussels, Belgium, 2016. 16. Scotta, R.; Trutalli, D.; Marchi, L.; Pozza, L. Seismic performance of URM buildings with in-plane non-stiffened and stiffened timber ﬂoors. Eng. Struct. 2018, 167, 683–694. [CrossRef] 17. Drdacky, M.F.; Walcf, F.; Mares, J. Modelling of Real Historic Timber Joints. Trans. Built Environ. 1999, 39, 171. [CrossRef] 18. Parisi, M.A.; Piazza, M. Mechanics of Plain and Retroﬁtted Traditional Timber Connections. J. Struct. Eng. 2000, 126, 1395–1403. [CrossRef] 19. Parisi, M.A.; Cordié, C. Mechanical Behavior of Double-Step Timber Joints. Constr. Build. Mater. 2010, 24, 1364–1371. [CrossRef] 20. Branco, J.M.; Descamps, T. Analysis and Strengthening of Carpentry Joints. Constr. Build. Mater. 2015, 97, 34–47. [CrossRef] 21. Ministry of Infrastructures and Transportations NTC. Aggiornamento Delle «Norme Tecniche per Le Costruzioni»; Ministry of Infrastructures and Transportations NTC: Rome, Italy, 2018. (In Italian) 22. EN 1995-1-1; Eurocode 5: Design of Timber Structures—Part 1-1: General—Common Rules and Rules for Buildings. European Committee for Standardisation: Brussels, Belgium, 1995. 23. Sørensen, J.D. Framework for Robustness Assessment of Timber Structures. Eng. Struct. 2011, 33, 3087–3092. [CrossRef]

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Buildings – Multidisciplinary Digital Publishing Institute

Published: Oct 22, 2022

Keywords: timber truss systems; historical buildings; robustness analysis; numerical modeling

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Robustness Analysis of Historical Timber Roofs: A Case Study of the Gaggiandre Shipyard at the Arsenale of Venice

Robustness Analysis of Historical Timber Roofs: A Case Study of the Gaggiandre Shipyard at the Arsenale of Venice

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Robustness Analysis of Historical Timber Roofs: A Case Study of the Gaggiandre Shipyard at the Arsenale of Venice

Robustness Analysis of Historical Timber Roofs: A Case Study of the Gaggiandre Shipyard at the Arsenale of Venice

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