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

Investigating causes of damages to historical timber structures by use of FEM

C. Thelin & K.G. 018son Chalmers University ofTechnology, Goteborg. Sweden

ABSTRACT: Historical timber structures are often complex, their static behaviour being ditTicult to grasp. Such structures are usually statically indeterminate. To determine how a statically indeterminate structure carries the load it supports, the stiffness ofits separate parts needs to be taken into account. Knowledge ofthe static behaviour and of the factors that influence it is important when investigating the causes of damages. The damage analyses suggested involve severa I steps. First, a thorough investigation ofthe structure is needed, aimed at collecting the basic facts required for obtaining sutTicient background information for creating the computational mode!. The next step is to create a computational model based on the Finite Elements Method. Having access to an appropriate computational model allows possible causes of damages to readily be simulated. The roofstructure ofthe medieval Swedish castle of Glimmingehus was selected as an example of how such an analysis can be performed.

INTRODUCTlON

Historical roof trusses of large monumental build­ings such as in cathedrals, large churches, castles and medieval halls are often highly complex structures . Representing the most advanced wooden construc­tions of their time, they are of considerable cultural­historical and technical-historical value. The form and the structure of such buildings are closely integrated. For proper consideration of their form, account needs to be taken oftheir static behaviour as wel!. An under­standing of their static behaviour and the structural principies that apply is necessary in order to adequately preserve and maintain them and to avoid ruination of them and of their value by use of needless or wrongly performed reinforcements, additions or alter­ations. To obtain this knowledge, a structure needs to be investigated thoroughly.

The aim ofthe paper is to propose and demonstrate a way of working involving use of the Finite Element Method (FEM) for investigating causes of damages to historical timber structures. Knowing the causes of damages is essential for restoring and repairing a structure in a satisfactory way. A firm knowledge base concerning the structure's static behaviour facilitates conceptualizing the possible solutions available in a restoration processo The roof truss used as an exam­pie here is that of the Swedish castle Glimmingehus. This has a complex 3-dimensional structure which to a considerable degree is statically indeterminate. Due to its age, size and complexity and to its being so

well preserved, it is a uni que Nordic timber structure of great historical importance.

2 CHARACTERISTICS OF HISTORICAL TlMBER STRUCTURES

The rooftrusses oflarge historical buildings generally show complex static behaviour making them ditTicult to analyze. This complexity is often due to their being highly statically indeterminate, meaning that the load can be carried by several possible load paths. Con­sider the roof truss in Figure I, which shows the main trusses of the Glimmingehus roof construction and

Figure I. The main lrusses and lhe longitudinal slructure of lhe Glimmingehus roof construction.

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a connected longitudinal structure. One such truss, marked in black, is shown in Figure 2. The dead load ofthe longitudinal structure, which applies to the sin­gle truss as indicated by the arrow, can be carried by two main load paths: a lower one provided by the large trestle and an upper one provided by the rafters.

To determine which load path is dominant, the stiff­ness of the separate parts of the structure needs to be taken into account. The load is carried to the sup­ports by the parts that are stiffest. In the truss shown

Figure 2. The lruss marked in figure 1.

in Figure 2, the upper load path is stiffer, due to the parts there carrying the load by pure tension and com­pression, unlike the lower load path, which carries the load thIOUgh bending ofthe trestle, which is a weaker behaviour, despite the beams in the trestles being of great size.

The connections between elements in structures of this type are usually hewn and are nailed together by use of wooden dowels. Such connections nonnally allow small rotations to take place, preventing bending moments from being transferred through the connec­tions. This implies that the global action of the roof structures is truss behaviour, whereas the bending acts locally. Truss behaviour is associated with axial forces (normal forces) that act in tension or in compression along the axis of a structural member. Normal forces and deformations can thus be used to describe the global static behaviour of such historical roof trusses.

An important property of a statically indetermi­nate structure is that a change in it can alter the force distribution considerably and thus strongly affect its structural behaviour.

3 STEPS IN A STRUCTURAL AND DAMAGE ANALYSIS

Gaining an understanding of the static behaviour of timber structures and investigating the causes of dam­ages to them involves severa I steps, as described below and shown in Figure 3.

3.1 Step 1: Site surveying - investigating the building

The surveying step involves examination ofthe struc­tuIe at hand and conducting a survey of archival material. The aim ofthe investigation is to make mate­rial and information available as a basis for creating computational models.

r ----Understanding of

structural behaviour

~ Results

~ Calcu lations

~ Computational models

~ I nformation base

~ Building investigation

____ j

Figure 3. Steps lo gaining an understanding of the static behaviour of a structure.

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The methods of working include measuring the structure, photographing it, sketching both the whole of it and details and taking notes on the condition of joints and supports.

The geometry of cross-sections of the structure, the location of different building elements, the type of material involved and its quality, along with the form and the state ofthejoints and ofthe support conditions represent important information. An essential part of the investigation is to record the damages, gaps and defonnations that are visible. These are signs of the static behaviour of the structure, their characteristics providing information on the causes of damages, for example of a damaged joint being drawn apart or of its being compressed. In searching for possible causes in the structure itself, it is important to bear in mind the fact that the character of the structure may be such that the cause of some damage that occurs is located in a totally different part of the structure, new force dis­tributions being produced which result in the visible damages that occur. The possible causes of damages should be considered at this stage of the analysis.

lnvestigation of roof structures can be difficult due to limited access to light, or by dirt and dust or their being covered by insulating material. Since the struc­tures can be complex in form , it can be difficult to obtain an adequate overall view ofthem. Carrying out systematic measurements can be the most effective approach. Yet reaching certain parts of a structure can sometimes be troublesome or even impossible, such as in the case of a wooden barrei vault that is unable to support a human being, making it impossible to reach the base of the roof so as to investigate the support conditions.

3.2 Step 2: Creating an information base

The results of investigating a building can be system­atized and assembled to an information base for use in the coming analysis. The information base can consist of architectural and structural drawings, measure­ments, photographs, sketches and notes made during the investigation.

3.3 Step 3: Computational models

The information base provides input to the computa­tio na I model that the structuralmechanical analysis is based on. Such a computational model can be divided up into a load model, a material model, a geometrical model , a structural model and a support model.

- The load model consists of dead load, ofwind- and snow load and ofusefulload (Boverket, 2000). The dead load is calculated by use of the geometrical infonnation available and ofthe density ofthe mate­rial. The useful load is the weight of equipment, furniture or people, for example. The wind and

snow load is usually obtained from statistical data on the weather conditions at the location in ques­tion. In Sweden, such data is given in accordance with Swedish standards (Boverket, 2000).

- The materialmodel describes the materiais that the structure consists of. It includes the characteristics of each material in different directions - isotropic, orthotropic or anisotropic (Saabye Ottosen and Petersson, 1992) - the compressive-tensile strength ofthe various materiais and their moduli of elastic­ity, i.e. their material stiffness. The values of these parameters can be obtained by experimental testing, although the material data can generally be obtained from systematically executed test results collected in compilations.

- The geometrical model describes the spatial dimen­sions of the structure, the relative position of its elements and the cross-sections of the separa te elements.

- The structural model includes the theory used to describe the structural behaviour of the differ­ent elements. Examples of such theories are bar theories, different beam theories (Saabye Ottosen and Petersson, 1992), and first- and second-order theories - the latter based on whether or not account should be taken of the effects of normal forces on the stiffness. The structural model also describes how the separate elements are connected .

- The support model describes the connection of the structure to its surroundings. lt includes a model of how the loading is transferred to the founda­tions and of how the structure is restrained from movement. The restraint provided by the suppor! conditions is often a major facto r in determining the static behaviour (Leftheris and Brebbia, 1995).

Computational models are generally described by use of differential equations. The Finite Element Method, a numerical approach, can be used to solve the equations.

3.4 Step 4: Calculatiol1s

When the choice of a model or models has been made and the specific load, material, geometrical and sup­port parameters have been determined, calculations can be performed. Different commercial compute r codes for Finite Element analysis are available. For the calculations reported in the paper, the program CALFEM was employed (CALFEM: ajinite element toolbox to MATLAB : version 3.3, 1999). This is an open source code that provides closeness both to the mathematics involved and to the computationalmodel.

3.5 Step 5: Results

The calculations produce a set of results. These can consist of deformations and of section forces in different parts ofthe structure.

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3.6 Step 6: Damage analysis and understanding of static behaviour

Analysis of the static behaviour of a structure gener­ally involves carrying out ali of the above steps and employing them in a process that is usually iterative in character. The results obtained can lead to questions being posed regarding the prerequisites that have been assumed and the investigations performed. The rea­sonableness ofthe assumptions made can be tested on the basis of calculations.

Having access to an appropriate computational model allows changes and variations in the structure to readily be simulated. Damages can be simulated in terms of possible causes detected during the processo The force distribution obtained from the simulations can then be compared with the damage patterns found in the structure. Causes can, for example, be wood rot or settlement of the walls. The weakening of a mem­ber by rot can be simulated by reducing the modulus of elasticity. Settlement or other changes in the support conditions can be simulated by removing or replacing support conditions locally.

3.7 Visualisation

Visualisation is a useful aid to structural and damage analysis. By methodical use of representative images for the different steps in the analysis, connections between what one can see in a building, what is being modelled and the response of the structure to various possible causes of damage can be made visually acces­sible. Visualisation of the computational model itself and of the results it provides is intimately connected. The images connected with a model show the prereq­uisites for use ofthe model, whereas the images ofthe results show the response of the structure.

4 EXAMPLE - THE ROOF TRUSS OF GLTMMINGEHUS

4.1 Glimmingehus

Glimmingehus is located on the plains of the south­eastermost part of the county of Skania in southern Sweden. Work on building it was begun in 1499 and continued for severa I years on into the Sixteenth Century. It stands today as an extraordinarily well­preserved medieval castle with a roof construction, the parts of which can largely be dated back to the time the building was erecled.

Glimmingehus is built of stone. lt stands three sto­ries high and, in addition, has a basement and an attic. It is 30 meters long, 12 meters wide and has a total height of26 meters as measured from the ground leveI to the ridge of the roof. The roof truss consists of a longitudinal structure and 28 transverse trusses (see

Figure 4. The Castle of Glimmingehus. Photographed by Bengt A. Lundberg, RAÀ, 1998.

Figure 5. The rooftruss.

Figures 5 and 6). The longitudinal structure has five king posts connected with three leveIs ofbeams that are provided with braces. The king posts are parts of five of lhe transverse trusses that together constitute the main trusses of the structure. Four of the five king posts stand on trestles, whereas the fifth, the one furthest to the west, lacks such a support. The connection between the longitudinal structure to which the main trusses belong and the rema in der of the transverse trusses is provided by two longitudinal beams, at the leveI of the lowest collar beams on the inside of the wall, and by the outer roofing. Each of the transverse trusses has three different leveIs of collar beams. Six ofthem, three on the eastern and three on the western side, have tie beams. From the upper side ofthe walls to the ridge it measures roughly 10 meters.

During the 1990s, damages to the roof truss were discovered. This led to a number of different inquiries

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19 27

A. KING POST F. COLLAR BEAM B. LONGITUDINAL BEAM G. TIE BEAM C. BRACE H. STRUT BEAM D. TRESTLE J . RAFTER E. OUTER LONGITUDINAL BEAM K. SOLE PIECE

Figure 6. The main trusses, their numbering, and the naming Df the various elements Df the roof truss.

and reports concerning the structure's condition, its physical behaviour, how it was built, and various restoration measures suggested. Some of those which concerned the building's static behaviour were the following: a report by Karl-Gunnar Olsson on the static behaviour of the roof truss (Olsson, 1995), a masters dissertation by Jesper Ahlquist and Tngrid Lassen that represents a historical and a structural analysis of it (Ahlquist and Lassen, 1996), various reports that constitutes a preliminary study of repair of the roof structure (Edstrõm, et aI., 1997), a report by Ove Hidemark and Krister Berggren concerning the roof truss and possible measures for restoring it (Hidemark and Berggren, 1997), and a masters dis­sertation by Carl Thelin using FEM and three dimen­sionaI models to provi de a virtual tour of the truss (Thelin, 2000) (ali in Swedish).

Since the truss is of 3-dimensional character, hav­ing a load-carrying function in two directions, and is statically indeterminate in the sense of having several different load paths, obtaining an overall view of its static behaviour without a thorough analysis ofit is dif­ficult. Although the trestles are large in size and give the appearance ofplaying a major role as load carriers within the structure, ana1ysing the structure indicates this to not be the case. The preliminary studies con­ducted prior to the structure being repaired concerned to a considerable extent facts and speculations con­cerning what caused the damages that were visible. Tt beca me c1ear that the causes of the damages to some parts of the structure were to be found in completely different parts of the truss.

4.2 Computational model and analysis

The computational model involves use of a 3-dimensional coordinate system based on drawings

(Iacobi, et aI., 1995) of the roof truss. The measure­ments utilized were obtained in situ or were taken from the masters dissertation of Ahlquist and Lassen (Ahlquist and Lassen, 1996). The cross sections ofthe different members vary somewhat. Thus the rafters, the collar beams and the longitudinal beams are approxi­mately 175 x 175 mm in cross-section, the king posts and the trestles about 250 x 250 mm, the upper beam of the trestles 275 x 250 mm and the tie beams, with certain variation, about 220 x 220 mm. The strut beams have a g reater variation in cross-sectional height and width than this, with dimensions that range from about 100mm to 150mm.

The rooftruss material is usually pine, but in a few members it is oak. The material is modeled as being linear elastic and orthotropic. The modulus of elastic­ity is set to 12 GPa, a value taken from Ahlquist and Lassen and assumed to be applicable here.

Ali of the structural elements are modelled as 3-dimensional beams of the Bernoulli type. They are connected by wooden dowels, the connections being assumed to permit small rotations to occur. Ali the con­nections between elements are modelled as allowing them to rotate freely in ali directions. Since torsion is not involved in the static behaviour here, at least one of the torsional degrees of freedom of each of the structural beam elements needs to be locked so as to prevent rigid-body motion from occurring. Spring ele­ments are used to simulate the connections between the rafters, the lower collar beams and the strut beams. The forces that develop in these springs when the structure is subjected to load are monitored, the springs being decoupled if subjected to a pulling force.

In the study it is the effects on the structure of dead load that are considered. The dead load consists ofthe load from the wood and from the outer roofing. The density ofthe wood is set to 500 kg!m3 . The outer roof­ing consists oflath and brick and the roofing's overall weight being approximately 45 kg per m2. The load that the outer roofing produces is distributed over the rafters of the trusses.

Since the structure is not tied down to its support, the supportconditions need to allow it to be Iifted ifit is subjected to a Iifting force. The wall provides the ver­tical support. When the structure is subjected to only a dead load, it is supported on both the inner and the outer side ofthe wall. Horizontal support ofthe structure is provided either by friction between it and the upper part of the wall , by direct support of the elements of which it is composed, or internally within the structure itselfthrough the presence ofthe tie beams. In terms of the model, horizontal support of the trusses that have no tie beams is placed at the inner side of the wall. The main trusses are supported longitudinally at the top ofthe first main truss. That support is considered in the model as being provided by the gable-wall. The longitudinal support ofthe remainder ofthe trusses is

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represented in the model by support at the top of each truss. Although in reality the support is provided by the lath and the brick, the support the model assumes to be provided is sufficient for the analysis conducted in the present study, which concerns only loading perpendic­ular to the longitudinal direction. A realistic alternative could be to introduce various elements, consisting of the lath and the bricks of the outer roofing, between these remaining trusses for connecting them to the main trusses. Each ofthe trusses also has a longitudi­nal support at its base, provided either by friction or by direct contact with the upper part ofthe wall. Each of the outer longitudinal beams is supported in ali direc­tions at the one end by its connections with the walls there. The trestles are restrained from rotation at the joint by the king posls. This restraint, which has been found to be necessary from a numerical point ofview, also represents one of lhe weaknesses of the trusses, since the trestles are sensitive to rotational movement.

The results of the analysis pertain to normal forces and deformations. Since the joints of the roof truss were modelled as rotating freely, the global action is truss behaviour whereas bending is local. Truss behaviour is associated with axial forces, analysis of them being sufficient to describe the globalload paths ofthe rooftruss. To examine the stress within the struc­ture, the normal forces involved needed to be investi­gated in combination with the bending moments. Since no analysis of strength was performed, the magnitude of the bending moments was not taken into account.

4.3 Undamaged state

Understanding the reasons for damage occurring requires that the static behaviour of the undamaged structure be determined. The most significant result obtained for the undamaged state was to find that it is not the trestles but lhe rafters that provi de the ma in support for the king posts. Since the rafters are sub­jected to tension, they are suspended from the ridge. This illustrates the difference between carrying that involves pure compression or tension and that which involves bending. The action ofthe trestles in carrying the king posts in a direction perpendicular to their axis is much weaker than that ofthe rafters, which support the king posts in an axial direction through compres­sion ali the way from the ridge to the top of the wall; see Figure 2.

Two cases of damage to the structure that occurred have been considered. The f irst was that of the damage to truss no. 9, one ofthe main trusses, the lowest collar beam there having been pulled out of its joint to the king post. The damage indicated that the collar beam had been subjected to tension and that it had acted as a tie beam that held the structure together. The second case of damage considered was that of dislocations that occurred at several ofthe joints in the longitudinal

structure on both sides of truss no. 15, the main truss in the middle ofthe structure.

4.4 Damage 1

Figure 7 displays the visibly damaged members, nos. N 185 and N 186, where the lowest collar beam had been pulled out of its joint to the king post on truss no. 9. The following are possible causes of damages that were suggested:

I. The truss lacked sufficient horizontal support at the wall.

2. The lower part ofthe rafter was weakened due either to wood rot, to earlier repairs having been poorly performed or to the connections having been poorly constructed.

3. The sole piece was weakened by wood rot.

The first cause was simulated by removing the hor­izontal support condition for truss no. 9. The second and th ird causes were simulated by giving the members affected a lower E-module, one which implied that ali bearing capacity ofthe members was lost.

Table I shows the behaviour the collar beam would have on the basis of each of the three suggested causes of damage, Figure 8 providing a visualization of the second cause suggested . Since the joints between the king posts and the lowest collar beams are simple tenon joints involving single dowels, their strength under tension is limited. A simple calculation of the shear

Figure 7. Members having damaged joints.

Table I. Damage to truss no . 9.

Forces in members (kN)

NI85 NI86

Undamaged 1,33 1,33 I. Insufficient 4,20 4,07

horizontal support 2. Rot in rafter 5,59 5,63 3. Rol in sole piece 3,61 3,62

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strength of the dowel showed it to have a strength of 3 kN, F = f I' * A * 2/3, F: force, f I' : shear strength, A: shear area. The dowel has two shear areas in a tenonjoint. Test results that have been reported shows tenon joints to have a measured strength of up till 10 kN (Ehlbeck and Hãttich, 1988). All simulations of damages to truss no. 9 indicated the tension forces to exceed 3 kN, see Table I. Although in simulation of rot in the rafter the highest value was obtained for the normal force that was computed, it is possible that the strong tension found in the collar beam is caused by a combination of the various of the causes that were simulated.

4.5 Damage 2

Figure 9 displays the location of the members, ele­ments no. N48, N41 , N67 and N79, in which disloca­tions of the joints in the longitudinal structure appear. Two examples of damages of this sort are shown in Figures 10 and 11. Figure 10 shows element no. N67 being pulled out of the king post. Figure 11, in tum, shows the damaged joint between element no. 48 and

Figure 8. Damage lo truss no. 9: rOI in the rafter.

Figure 9. Members having damagedjoints.

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the horizontal beam. The following are possible causes of damages that were suggested:

I. The connection between the rafters and the king post was weakened by wood rot.

2. Settlement ofthe wall due to a window frame being broken resulting in a lack of vertical support for truss no. 15.

Figure 10. Damage to the longitudinal structure: elemenl N67 being pulled out ofthe king post. Photographed by Johan lacobi and Martin Seitzberg.

Figure lI. Damage to the longitudinal structure: element N48 having a damaged joint. Photographed by Johan lacobi and Martin Seitzberg.

Table 2. Damage to the longitudinal structure.

Forces in members (kN)

N48 N41 N67 N79

Undamaged 0,94 - 0, 11 -0,18 0,40 1. Rol in the king post 3,04 3,17 2,90 3,48 2. Settlemenl ofthe wall 1,92 1,46 1,10 1,70 3. Greater settlement 5,70 7,28 6,9 1 7,48

of the wall

compression

Figure 12. Damage lo the longitudinal structure, the defor­mations shown in the figure being magnified 30 times.

3. Extensive settlement ofthe wall, resulting in a lack of vertical support for the ma in truss and for the two adjacent trusses.

The first cause was simulated by ass igning the upper part of the king post a lower E-module, such that all bearing capacity of the member was lost. The second and the th ird causes were simulated by removing the vertical support conditions fo r the trusses affected by settlement of the wall.

Table 2 displays the values of the normal forces in the damaged members of the rooftruss that the causes of damage that were suggested would have brought about. In the undamaged state, the normal force in ele­ments N48, N4l, N67 and N79 is relatively small, the horizontal beams also being compressed. Each of the three causes that were suggested results in an increase in the normal force in each of the members consid­ered. Since the king post can no longer be suspended from the ridge, either because of a lack of support or because of rot, it needs to be supported in some other way. The longitudinal structure at the centre ofthe roof truss distributes some of the load to the main trusses closest to it, creating a damage pattem in which the members in question are subjected to tension.

A comparison of causes 2 and 3 is presented in Fig­ures 12- 14. In Figure 12 it is only truss no. 15, the main truss that lacks vertical support. Compression 'of the rafter to the si de ofthe settled area is then transmitted by the outer longitudinal beam to the strut beams of the adjacent trusses. The forces present in the damaged members are fairly modest, due to this reallocation of

compression " GREATER SETTLE­MENT OF THE WALL

Figure 13. Damage lO the longitudinal structure, the de for­mations shown in lhe figure being magnified 30 times.

Figure 14. Damage to the longitudinal structure, the defor­mations shown in the figure being magnified 30 times.

forces within the structure. Since the aim here was to simulate settlement ofthe wall , it is likely that what was affected was more than simply the support conditions of one of the trusses. Accordingly, a simulation was made in which the trusses closest to truss no. 15 also lost their vertical support. This resulted in a dramatic change in the forces present in the damaged members. The same reallocation offorces in the structure as when settlement was limited to truss no. 15 is evident here, yet since a longer span of the outer longitudinal beam is bent, due to its carrying the load, support of the king post is much weaker here.

5 CONCLUSIONS

The causes of damage to a historical timber struc­ture are frequently located in a different part of the structure than where the visible damage is found. An understanding of the static behaviour of the structure and of the causes of damages occurring is necessary if adequate restoration or repairs are to be carried out. The paper suggests and exemplifies a way of working in wh ich FEM is used as a tool for under­standing the static behaviour involved and for enabling adequate damage analysis to be carried out. By exam­ining changes in the normal force distribution as these

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relates to the stiffness of the separate elements of the structure, allows one to study both observed and assumed changes in the structure.

In creating the FEM-models employed in the study, it became evident that visualization not only provides a basis for discussing the static behavior of a structure but is also of advantage to the engineer in constructing complex FEM-models providing as it does a means of testing solutions, of verifying the reasonableness of results, of troubleshooting computational models and ofproviding an overall view ofthe structure being analyzed.

The advantages of using FEM for studying static behaviour and the effects of changes in a structure were obvious. Having access to an appropriate computa­tional model allowed changes to readily be simulated, providing the opportunity oftesting different solutions with little additional effort.

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Boverket 2000. Boverkets konstruktionsreg/er: foreskrifter och a/lmanna rtid. Karlskrona, Stockholm: Boverket; Fritze: Fritzes kundtjãnst.

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N. Saabye Ottosen and H. Petersson 1992. lntroduction to the finite element method. New York: Prentice Hall.

B. Leftheris and C. A. Brebbia 1995. Struc/ura/ studies of hislorical buildings Iv. Southampton: Computational Mechanics.

CALFEM: afinite e/ement too/box to MATLAB: version 3.3 . 1999. Lund: Structural Mechanics LTH.

l-deas. 2003. Plano, Texas, USA: EDS. K.-G. Olsson 1995. Kraftspe/et i takkonstruktionen i Glim­

mingehus. Lund: 1. Ahlquist and 1. Lassen 1996. Takkons/ruk/ionen pti Glim­

mingehus: en historisk och srrukturmekanisk ana/ys. Lund:

M. Edstrõm, S. Jacobsen and T. Alsmarker 1997. Glim­mingehus - forsludier /i11 delfasta husets /akkonstruktion. Lund:

O. Hidemark and K. Berggren 1997. Glimmingehus tak/ag. Stockholm:

C. Thelin 2000. Takkonslrllktionen pti Glimmingehus, en virlueU bildberatlelse. Lund: Lund University.

1. Iacobi , M. Seitzberg and E. Haedersdahl 1995. Drawings oflhe RoofTrllss ofGlimmingehus. Lund: LTH.

1. Ehlbeck and R. Hãttich 1988. Tragfàhigkeit und Verfor­mungsverhalten von ein- und zweischnittig beanspruchten Holznãgeln. Erha/ten his/orisch bedell/samer Ballwerke: Ballgefiige, Konslrllktionen, Werks/oJJe . Jahrbuch 1988 vii , 167 s. 6.