Structural vulnerability of two traditional Portuguese timber structural systems

Engineering Failure Analysis 18 (2011) 776–782

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Engineering Failure Analysis journal homepage: www.elsevier.com/locate/engfailanal

Structural vulnerability of two traditional Portuguese timber structural systems António Murta a,1, Jorge Pinto a,1, Humberto Varum b,⇑ a b

Engineering Department, ECT, University of Trás-os-Montes e Alto Douro, Quinta de Prados, 5001-801 Vila Real, Portugal Civil Engineering Department, University of Aveiro, 3810-193 Aveiro, Portugal

a r t i c l e

i n f o

Article history: Available online 31 December 2010 Keywords: Traditional roof timber structures Vulnerability Robustness Failure

a b s t r a c t In general, the traditional Portuguese buildings show an undesirable deterioration level and, consequently, urgent rehabilitation processes are required. These buildings need maintenance and preservation because they are a valuable Portuguese heritage. Knowing and understanding these buildings is the first step for adequate rehabilitation processes. Usually, these buildings show the same pattern of pathologies and failure sequence. This research work is focused on the study of the roof timber structural systems of these buildings and intends to highlight these aspects. An expedite methodology of structural vulnerability assessment of the traditional Portuguese timber roof structures based on the structural vulnerability theory is presented. Real cases of traditional Portuguese timber roof structures are used. It was concluded that the trussed timber roof system seems less robust than the beamed system. Ó 2010 Elsevier Ltd. All rights reserved.

1. Introduction Most of the traditional Portuguese buildings are dwellings. The main vertical structural elements of these buildings are stone or earth based materials masonries. The horizontal ones are timber structural elements such as beams and trusses. Usually, these building materials are local and natural. This aspect indicates that these buildings, besides being a Portuguese heritage, also have an additional value because they are sustainable reference models for the modern building industry. It is a fact that an impressive amount of this heritage shows an advanced stage of deterioration and urgent repair processes are required. Murta et al. [1] has underlined that the main cause for this scenario is the inexistence or deficient maintenance processes of these constructions through their lives. In this work, it is also mentioned that the deterioration process takes on a similar pattern in most of the cases and that it starts from the roof of the building [1]. In order to start a conservation process it is required that one has an understanding and knowledge of the building itself. It is in this context that this research work was developed. It intends to study the structural behaviour of the most relevant traditional Portuguese timber roof systems of dwellings. Real timber roof systems were used as reference. The failure of these structures guided the development of an expedite structural vulnerability assessment approach which is presented and proposed in this paper. This approach was inspired in the structural vulnerability theory [2,3]. Identifying the vulnerable parts of a structure and mitigating that vulnerability contributes to increase the robustness of a structure. In this case, a contribution for increasing the robustness of the traditional Portuguese timber roof systems of dwellings is given. Other authors have developed analysis with similar objectives, but in the context of steel roof structures [4]. ⇑ Corresponding author. Tel.: +351 234 370938; fax: +351 234 370094. 1

E-mail addresses: [email protected] (A. Murta), [email protected] (J. Pinto), [email protected] (H. Varum). Tel.: +351 259 350356; fax: +351 259 350356.

1350-6307/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.engfailanal.2010.12.017

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A6

A7

B2

A2 A3

A5

B1

A1

A4 (a) Trussed (type I)

(b) Beamed (type II)

Fig. 1. The most relevant traditional Portuguese roof timber system types. (a) Trussed (type I). (b) Beamed (type II).

This paper is structured as follows s: Firstly, the most relevant traditional Portuguese timber roof systems of dwellings are identified and described. Secondly, the typical roof failures are presented and the common pattern is highlighted. Thirdly, these traditional roof structures are studied in order to observe if they respect the recommendations of the present codes. Fourthly, an expedite structural vulnerability assessment approach is introduced and its application is exemplified. Finally, the main conclusions are drawn. 2. Traditional Portuguese roof structures The most relevant traditional Portuguese roof structures of dwellings are essentially timber systems. The most common types of these systems are trussed and beamed, designated here as type I and II, respectively. The trussed timber system type has trusses as the main structural elements (elements from A1 to A4, Fig. 1a). These trusses support beams (element A5, Fig. 1a) which support the purlins (element A6, Fig. 1a). Meanwhile, in the beamed timber system type the beams are the main structural elements (element B1, Fig. 1b) which are braced by the beam B2. Usually, they are arranged as a three hinged structure. In this system type, the beams are the purlins. Figs. 3 and 5 will complement schematically the description of these roof timber structural solutions.

(a) Trigger failure event

(b) Consequent failure event

(c) Deterioration of the truss

(d) Total roof collapse

Fig. 2. Progressive failure that leads to total roof collapse. (a) Trigger failure event. (b) Consequent failure event. (c) Deterioration of the truss. (d) Total roof collapse.

B2 A6

B1 A1 A2 A3

2.50

A5 A4

4.00

5.00 8.10

4.00

10.88

8.72

5.50

(a) Type I

(b) Type II

Fig. 3. Finite element mesh adopted for each roof timber structural system and identification of the main timber elements of the roof solutions (m): (a) type I and (b) type II.

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In both timber system types the purlins support timber boards (element A7, Fig. 1) which support the roof covering. The traditional Portuguese roof covering material is ceramic tiles. Frequently, the wood species used in the timber structural elements is the maritime pine (Pinus pinaster Ait.), which is the most abundant in Portugal [1,5–7]. 3. Typical roof failures The failures associated to these traditional roof structures are quite often linked to material deterioration manly due to the undesirable presence of water [1]. The roof leaking resulting from a broken tile or the increase of moisture content of the timber boards which are in direct contact with the tiles are the main causes which trigger a progressive failure that, unfortunately, leads to the total roof collapse in most of the cases. Regular maintenance and conservation work are required to prevent the above failure process. Murta et al. [1] has highlighted that this failure process may be very fast if repairing does not take place in time. The stages of this failure process are identified in Fig. 2. Different Portuguese traditional dwellings are used in order to indicate that this failure process has a regular pattern. Dwellings located in the cities of Vila Real (Fig. 2a) and Figueira de Foz (Fig. 2b, c and d) are used in order to exemplify this fact. Fig. 2a shows the roof of a dwelling where some ceramic tiles are missing which represents the trigger failure event [8]. If no repair takes place then consequent failure events [8] occur because the timber elements and also others ceramic tiles located near the damaged roof area collapse, Fig. 2b. This roof failure progresses and the main roof timber structural elements (trusses or beams) start to be affected, Fig. 2c. This failure process ends in the total collapse of the roof, Fig. 2d. 4. Traditional roof structures versus the current codes The traditional Portuguese roof structures were built based on an empirical knowledge in which t experience was fundamental. There were no codes or computer programs that guided the building processes of these heritage structures. This fact inspired us to check if the existing timber structures satisfy the requirements of the present codes, in particular the [9]. For this purpose, the two most common roof timber system solutions identified above, Fig. 1, were studied. For the sake of simplification, two study cases were considered (two dwellings in Figueira da Foz city, Fig. 1) the dimensions of their roof timber systems are delivered in Fig. 3 and Table 1. Furthermore, Fig. 3 represents the geometry of the roof timber structural systems under study. It was assumed that the timber elements are Pinus pinaster Ait. wood (E class –[9,10]). Meanwhile, masonry walls were considered in the model. These walls are made of limestone blocks connected to each other by an earth based mortar, which is a traditional Portuguese building solution for bearing walls. Loads and their combinations were defined taking into account [11]. Dead, imposed, wind and seismic loads were quantified considering that the building is located in the central part of the Portuguese coast. A finite element analysis was done in which the timber structural elements of the roof were simulated by frame elements and the masonry walls were simulated by shell elements, respectively. Fig. 3 shows the adopted finite element mesh for each roof timber system type. Fig. 4 shows schematically the imposed load combination acting on the roof system type I (Fig. 4a). The resulted shear and axial force diagrams (Fig. 4b and c, respectively), the bending moment diagram (Fig. 4d) and deformed shape (Fig. 4e) are also presented. Similar results were obtained for the roof timber structural system type II. The designed solutions of the main structural roof timber elements for each system type are presented in Fig. 5 and Table 2, in which the cross section of each timber element was defined in order to verify the ultimate and the serviceably limit states proposed in [9]. These structures are geometrically and materially symmetric. Comparing these two figures, it may be concluded that for the traditional structural roof systems, the existing timber elements may satisfy the requirements included in current codes and, therefore, the empirical knowledge verified should be reported.

Table 1 Existing cross sections. Element

Width (m)

Height (m)

A1 A2 A3 A4 A5 A6 B1 B2

0.10 0.10 0.10 0.10 0.15 0.10 0.08 0.12

0.20 0.20 0.20 0.20 0.20 0.10 0.12 0.15

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(a) Imposed load combination

(b) Shear force diagram

(d) Bending moment diagram

(c) Axial force diagram

(e) Deformed shape diagram

Fig. 4. Load combination, force and deformed shape diagrams for system type I. (a) Imposed load combination. (b) Shear force diagram. (c) Axial force diagram. (d) Bending moment diagram. (e) Deformed shape diagram.

A1

A3

B1

A2

A4

(a) Trussed-Type I

(b) Beamed-Type II

Fig. 5. Designed solutions – main structural roof timber elements. (a) Trussed – type I. (b) Beamed – type II.

Table 2 Design and existing cross sections. Element

A1 A2 A3 A4 B1

Designed

Existing

Width (m)

Height (m)

Width (m)

Height (m)

0.10 0.10 0.10 0.10 0.05

0.10 0.18 0.18 0.18 0.10

0.10 0.10 0.10 0.10 0.08

0.20 0.20 0.20 0.20 0.12

5. Structural vulnerability assessment The structural vulnerability theory [2,3] and [8] is able to identify the parts of a structure in which small damage results in a disproportionate structural failure consequence. It is a theory focused on the quality of the structural form and the action that causes damage may be any kind including human error or a sabotage act. In short, the application of this theory consists of two main steps. Firstly, a clustering process is applied in order to rearrange the structure in terms of the quality of the structural form resulting in a hierarchical model. Secondly and finally, an unzipping process of that hierarchical model is able to identify different vulnerable failure scenarios. Among those, the total and the maximum failure scenarios have a particular relevance. The total failure scenario is the one in which less effort results in the complete loss of the structure. Meanwhile, the maximum failure scenario is the sequence of damage events in which the relation between effort to cause that damage and the respective overall structural failure consequence is higher. The intrinsic sophistication of the structural vulnerability theory, that requires an iterative and interactive calculation procedure, call for adequate technical skills and computer program for calculation-time saving purposes. Based on these considerations, it is intended to present in this paper an expedite methodology for the assessment of the vulnerability of the traditional Portuguese roof timber structural systems which may be easily applied in the building industry.

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This expedite methodology is based on the main theoretical concepts of the structural vulnerability theory among which we highlight the separateness, the relative damage demand and the vulnerability index. According to [2,3] and [8] these concepts have been defined as: (a) Separateness c is a measure of failure consequence and is the ratio of the loss in structural well formedness of the deteriorated structure to the well formedness of the intact structure. In this analysis c was quantified by Eq. (1).

c ¼ A=AT

ð1Þ

where A is the area of the deteriorated roof structure and AT is the area of the intact roof structure. (b) Relative damage demand Dr is the ratio of the damage demand of the failure scenario to the maximum possible damage demand of a failure scenario in the structural system. Here, it was assumed that Dr may be quantified using Eq. (2), taking into account that the same wood species was used in the whole roof structural system.

Dr ¼ D=Dmax

ð2Þ

where D is the sum of the cross section areas of the timber elements that suffered damage and that define the failure scenario and Dmax is the sum of the cross section area of all timber elements of the roof system. (c) Vulnerability index u is a measure of the vulnerability of a structure and is the ratio of the separateness to the relative damage demand for a given failure scenario, Eq. (3). Thus, the u is a measure of the disproportionateness of the consequences (the separateness) to the damage (the damage demand).

u ¼ c=Dr

ð3Þ

The assessment of the structural vulnerability of the traditional Portuguese timber roof systems was done based on the above measures and simulating different failure scenarios. Thus, for the systems type I and II different structural timber elements were assumed to fail (single or combined) randomly. After each failure, the previously existing roof dead load acting on the failed elements was considered to be redistributed between the surroundings timber elements. In order to check if a progressive failure scenario has occurred in each failure scenario simulated the complete roof timber system was analyzed taking into account the followings aspects: the dead load redistribution; that no majoring factors were used; that only the dead load was acting. The results of this vulnerability study are presented in Figs. 6 and 7 for the systems type I and II, respectively.

γ = 0.02 Dr = 0.01 φ = 1.44 (a) Failing 1 purlin. No progressive failure γ = 0.25 Dr = 0.03 φ = 7.67 (c) Failing 1 beam. 25% roof failure γ = 1.00 Dr = 0.02 φ = 46.00 (e) Failing A2. Total roof failure γ = 1.00 Dr = 0.02 φ = 46.00 (g) Failing A3. Total roof failure

γ = 0.25 Dr = 0.02 φ = 11.50 (b) Failing 2 purlins. 25% roof failure γ = 1.00 Dr = 0.02 φ = 46.00 (d) Failing A1. Total roof failure γ = 1.00 Dr = 0.02 φ = 46.00 (f) Failing A3. Total roof failure γ = 0.001 Dr = 0.03 φ = 0.04 (h) Failing the top beam. No progressive failure

Fig. 6. Structural vulnerability assessment of the timber roof system type I. (a) Failing 1 purlin. No progressive failure. (b) Failing 2 purlins. 25% roof failure. (c) Failing 1 beam. 25% roof failure. (d) Failing A1. Total roof failure. (e) Failing A2. Total roof failure. (f) Failing A3. Total roof failure. (g) Failing A3. Total roof failure. (h) Failing the top beam. No progressive failure.

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γ = 0.02 Dr = 0.02 φ = 1.39 (a) Failing 1 purlin. No progressive failure

γ = 0.05 Dr = 0.03 φ = 1.39 (b) Failing 2 purlins. No progressive failure γ = 0.001 Dr = 0.03 φ = 0.06

γ = 0.07 Dr = 0.05 φ = 1.39 (c) Failing 3 purlins. No progressive failure

(d) Failing the top beam. No progressive failure

Fig. 7. Structural vulnerability assessment of the timber roof system type II. (a) Failing 1 purlin. No progressive failure. (b) Failing 2 purlins. No progressive failure. (c) Failing 3 purlins. No progressive failure. (d) Failing the top beam. No progressive failure.

(a) Trigger failure events

(b) Predicted failure consequence

(c) Real failure consequence

Fig. 8. Validating the approach. (a) Trigger failure events. (b) Predicted failure consequence. (c) Real failure consequence.

In the system type I the failure of one element of the truss leads to total failure (i.e. the roof collapses). The increasing forces resulting from the forces redistribution caused by that failure resulted in a progressive failure of the system. Taking into account that the damage demand has been considered to be related to the cross section area (Eq. (2)), and, on the other hand, that all truss elements have the same cross section area, the total failure scenario consists basically in damaging one of the elements of the truss, because it was obtained c = 1 and umax = 46.00 (Fig. 6d–g). In this case, the total and the maximum failure scenarios are coincident. This is a coincidence rather than a rule. On the other hand, the system type II seems to be much more robust than the system I since its vulnerability is undoubtedly smaller. No progressive failure collapse occurred after a trigger failure event took place, Fig. 7. Fig. 8 intends to validate the structural vulnerability assessment approach proposed in this paper in which a predicted feature matches the real one. 6. Conclusions and final comments In general the traditional Portuguese roof structure solutions are a timber system formed by purlins, beams and trusses or formed by purlins and beams. The most common pathologies are broken ceramic tiles and deteriorated timber structure elements. They are associated to the lack of maintenance. The traditional Portuguese roof timber structures were built based on a valuable empirical knowledge. They may verify most of the recommendations of the current standards, in particular [9]. An expedite structural vulnerability assessment approach for traditional roof timber systems was proposed. Based in two study cases, the beamed solution seems to be less structurally vulnerable than the trussed solution. It is important to highlight that the trussed solution studied only included the existence of one truss which is a very common building solution in the Portuguese traditional dwellings. In case of several trusses the above conclusion remains. The assessment of the vulnerability of these types of structures may allow the identification of their parts where small damage demand may lead to disproportionate structural failure consequences. This information may give an important contribution for future rehabilitation processes of the remarkable traditional Portuguese building heritage [12]. Reducing the vulnerability of these structural systems contributes to increase their robustness. References [1] Murta A, Pinto J, Varum H, Guedes J, Lousada J, Tavares P. Survey on the main defects in ancient buildings constructed mainly with natural raw materials – Portugal SB10. In: Bragança L, Pinheiro M, Mateus R, Amoêda R, Almeida M, Mendonça P, et al. editors. Sustainable building, affordable to all, low cost sustainable solutions. 1st ed. Monitoring and evaluation, March; 2010. p. 589–96. ISBN 978-989-96543-1-0 [Chapter 5]. [2] Agarwal J, Blockley DI, Woodman NJ. Vulnerability of 3-dimensional trusses. Struct Saf 2001;23(3). [3] Pinto JT, Blockley DI, Woodman NJ. The risk of vulnerable failure. J Struct Saf 2002;24:107–22.

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